1 

February, 2005 

FASOMGHG Conceptual Structure, and 

Specification: Documentation

Principal Authors 

Darius Adams 

Ralph Alig 

Bruce A. McCarl 

Brian C. Murray 

With the assistance of 

Lucas Bair 

Brooks Depro 

Greg Latta 

Heng-Chi Lee 

Uwe Schneider 

And earlier contributions from 

Mac Callaway 

Chi Chung Chen 

Dhazn Gillig 

William Nayda 
2 

CONTENTS 

Section Page

Section 1 : Background............................................................................................................19 

1 Chapter 1: Introduction...................................................................................................19 

2 Chapter 2: Origins of and new features in FASOMGHG...............................................21 

2.1 Brief review of predecessor projects .....................................................................21 

2.1.1 ASM Modeling, Environmental and Farm Policy Analysis ......................22 

2.1.2 Forest Service RPA Models.......................................................................23 

2.1.3 Forest Service FORCARB Modeling System............................................24 

2.1.4 First Generation of FASOM ......................................................................25 

2.1.5 Agricultural Greenhouse Gas Mitigation Modeling—ASMGHG.............26 

2.1.6 Original FASOMGHG by Lee...................................................................26 

2.1.7 Project-Level GHG Mitigation Issues .......................................................26 

2.2 New developments in this FASOMGHG version .................................................27 

Section 2 Foundations..............................................................................................................28 

3 Chapter 3 Conceptual Scope of FASOMGHG ...............................................................29 

3.1 Resources, Production, Processing, and Commodity Flows .................................30 

3.2 Commodity Scope .................................................................................................30 

3.3 Geographic Coverage ............................................................................................35 
3 

3.4 Land base coverage................................................................................................39 

3.4.1 Agricultural land ........................................................................................39 

3.4.2 Forestland 40 

3.5 Production Modeling .............................................................................................41 

3.5.1 Agricultural and Biofuel feedstock Production .........................................42 

3.5.2 Forest Production.......................................................................................43 

3.6 Land Allocation .....................................................................................................44 

3.6.1 Scope for Land exchanges between sectors...............................................44 

3.6.2 Nature of Land Supply...............................................................................45 

3.7 Non-Land Factor Modeling ...................................................................................45 

3.8 Product Processing Modeling................................................................................46 

3.9 Market Modeling ...................................................................................................48 

3.10 GHG Treatment .....................................................................................................49 

3.10.1 Forest GHG Accounts................................................................................50 

3.10.2 Agricultural GHG Accounts ......................................................................51 

3.10.3 Biofuels 52 

3.10.4 Land to Development.................................................................................53 

3.10.5 Non-GHG Environmental Indicators.........................................................53 

3.11 Temporal Scope and Dynamics.............................................................................53 

3.12 Dynamic Yield, Cost, and Demand Updating .......................................................54 

4 Chapter 4 Economics underlying FASOMGHG ............................................................55 

4.1 Simulation of perfectly competitive behavior .......................................................55 

4.1.1 Adding production .....................................................................................58 

4.2 Behavior over time using discounted NPV ...........................................................60 

4.2.1 Discounting................................................................................................61 
4 

4.2.2 Need for terminal conditions .....................................................................61 

4.3 Dynamics of harvest ..............................................................................................61 

4.4 Land exchanges .....................................................................................................62 

4.5 Commodity exchanges between sectors ................................................................62 

4.6 Aggregation, Calibration profits, and mixes .........................................................63 

4.6.1 A discussion of calibration, aggregation and sectoral models...................63 

4.6.1.1 Sector models typically depict groups of farms.......................64 

4.6.1.2 Resource availability details ....................................................64 

4.6.1.3 Sector models typically ignore certain market factors.............65 

4.6.1.4 Data availability forces aggregation on the modeler ...............65 

4.6.1.5 Differences exist between the producer problem and the model65 

4.6.1.6 Insufficient depiction of production possibilities in budgets...65 

4.6.1.7 Specialization and mathematical programming solutions .......66 

4.6.1.8 Transaction costs are often omitted .........................................66 

4.6.2 Addressing the aggregation problem .........................................................66 

4.6.2.1 Justification 1: Observed practices reflect constrained choices68 

4.6.2.2 Justification 2: Theory indicates use of approach solves 

problem ....................................................................................68 

4.6.2.3 Omitted costs -- profit calculation ...........................................70 

Section 3: The FASOMGHG programming Model.................................................................72 

5 Chapter 5: Overall FASOMGHG Programming model structure ..................................73 

5.1 Static, single region portrayal................................................................................73 

5.1.1 Forestry sector submodel ...........................................................................76 

5.1.2 Agricultural sector submodel.....................Error! Bookmark not defined.

5.1.3 Intersectoral transfer submodel..................Error! Bookmark not defined.
5 

5.1.3.1 Land definition synchronizationError! Bookmark not defined.

5.1.3.2 Tableau components ................Error! Bookmark not defined.

5.1.4 GHG submodel ..........................................Error! Bookmark not defined.

5.1.4.1 GHG payment variable ............Error! Bookmark not defined.

5.1.4.2 GHG balance equation.............Error! Bookmark not defined.

5.1.4.3 GHG mitigation alternatives portrayedError! Bookmark not defined.

5.1.4.4 Other GHG related features .....Error! Bookmark not defined.

5.1.5 Integrating objective function....................Error! Bookmark not defined.

5.2 Aggregate spatial portrayal....................................Error! Bookmark not defined.

5.3 Aggregate intertemporal portrayal.........................Error! Bookmark not defined.

6 Chapter 6 Description of Greenhouse Gas Modeling...................................................112 

6.1 GHG accounting in FASOMGHG ......................................................................112 

6.2 Types of net GHG gains ......................................................................................112 

6.2.1 Carbon sequestration................................................................................112 

6.2.2 Direct GHG emissions .............................................................................113 

6.2.3 Biofuel offsets..........................................................................................113 

6.3 Multi Gases and climatic forcing equivalency ....................................................114 

6.4 Including GHGs in Economic Incentive Scenarios.............................................115 

6.4.1 Pricing GHG Increments..........................................................................115 

6.4.2 Use of a GHG Baseline............................................................................115 

6.4.3 Possible Inclusion of GHG Discounts .....................................................116 

6.4.3.1 Permanence............................................................................116 

6.4.3.2 Leakage..................................................................................117 

6.4.3.3 Additionality ..........................................................................117 

6.4.3.4 Uncertainty.............................................................................117 
6 

6.4.3.5 Avoid double-counting of discounts......................................118 

6.5 Which GHG categories count..............................................................................118 

6.6 GHG mitigation alternatives in FASOMGHG ....................................................118 

6.6.1 Forest mitigation ......................................................................................118 

6.6.2 Agricultural mitigation.............................................................................119 

6.6.2.1 Agricultural carbon sequestration enhancement....................119 

6.6.2.2 Agricultural emissions reduction ...........................................120 

6.6.3 Biofuel production ...................................................................................122 

6.7 Dynamics of GHG modeling...............................................................................122 

6.7.1 Sequestration............................................................................................123 

6.7.2 Emissions/Biofuel offsets ........................................................................123 

6.8 Programming model GHG implementation.........................................................123 

6.8.1 Tableau 123 

6.8.2 GAMS implementation............................................................................127 

6.8.2.1 GHG part of objective function .............................................127 

6.8.2.2 GHG equations.......................................................................129 

7 Chapter 7 Forest sector submodel.................................................................................130 

7.1 Whole forest model overview..............................................................................130 

7.2 Model elements....................................................................................................139 

7.2.1 Stand representation.................................................................................139 

7.2.1.1 Regions ..................................................................................140 

7.2.1.2 Land owner ............................................................................140 

7.2.1.3 Land use suitability................................................................140 

7.2.1.4 Forest type..............................................................................141 

7.2.1.5 Site productivity.....................................................................141 
7 

7.2.1.6 Management intensity classes................................................142 

7.2.1.7 Cohorts...................................................................................143 

7.2.2 Initial inventory........................................................................................143 

7.2.3 The new and existing stands distinction plus isnew/isnewexist ..............144 

7.2.3.1 New versus existing stands ....................................................144 

7.2.3.2 Isnew and isexist....................................................................145 

7.2.4 Forest management representation ..........................................................146 

7.2.5 Forest Establishment and Growing Costs................................................148 

7.2.6 Stand Growth ...........................................................................................149 

7.2.7 Harvest representation .............................................................................150 

7.2.7.1 Even-aged Timber Management............................................152 

7.2.7.2 Partial cutting timber management ........................................153 

7.2.7.3 Minimum harvest age ............................................................153 

7.2.8 Reforestation, Afforestation and Deforestation .......................................153 

7.2.8.1 Species succession .................................................................156 

7.2.8.2 Developed use........................................................................157 

7.2.9 Wood products.........................................................................................157 

7.2.9.1 Log and solid wood products.................................................158 

7.2.9.2 Pulp and fiber products ..........................................................159 

7.2.10 Log and intermediate processing .............................................................160 

7.2.11 Harvest, hauling and processing costs .....................................................166 

7.2.12 Other sources of log supply .....................................................................167 

7.2.12.1 US Public log supplies......................................................167 

7.2.12.2 Canadian log supplies .......................................................167 

7.2.12.3 Other log supply................................................................168 

7.2.13 Wood product movement and markets ....................................................168 

7.2.13.1 Logs and residues..............................................................168 
8 

7.2.14 International trade ....................................................................................169 

7.2.14.1 Canada...............................................................................169 

7.2.14.2 Other regions.....................................................................169 

7.2.15 Wood product prices................................................................................169 

7.2.16 Price expectations ....................................................................................170 

7.2.17 Timing issues ...........................................................................................170 

7.2.17.1 Annuities and time periods ...............................................171 

7.2.17.2 Discounting forestry returns after the projection period .172 

7.2.18 Markets over time ....................................................................................172 

7.2.19 Valuing terminal standing inventory .......................................................173 

7.2.20 GHG involvement....................................................................................173 

7.2.21 Non-market management considerations.................................................178 

7.3 Algebraic model...................................................................................................178 

7.3.1 Objective Function...................................................................................178 

7.3.2 Constraints ...............................................................................................180 

7.3.2.1 Manufacturing capacity limitations. ......................................180 

7.3.2.2 Residue generation at processing facilities............................180 

7.3.2.3 Supply of recycled paper products.........................................180 

7.3.2.4 Materials balance ...................................................................180 

7.3.2.5 Harvest balances ....................................................................181 

7.3.2.6 Management allocation of initial areas..................................182 

7.3.2.7 Reforestation of clearcut areas...............................................182 

7.3.2.8 Afforestation. .........................................................................182 

7.3.3 Symbol definition.....................................................................................182 

8 Chapter 8 Ag sector Modeling details ..........................................................................185 

8.1 Scope of agricultural sector representation..........................................................186 
9 

8.1.1 Regional Disaggregation..........................................................................186 

8.1.2 Characterizing the landscape and the sector ............................................187 

8.1.2.1 Land .......................................................................................187 

8.1.2.2 Crops......................................................................................187 

8.1.2.3 Animals..................................................................................188 

8.1.3 Commodities............................................................................................188 

8.1.3.1 Primary Commodities ............................................................188 

8.1.3.2 Secondary commodities.........................................................189 

8.1.3.3 Blended feeds.........................................................................190 

8.1.4 Non land inputs........................................................................................190 

8.1.4.1 Water......................................................................................190 

8.1.4.2 Labor......................................................................................191 

8.1.4.3 Grazing in AUMS..................................................................191 

8.1.4.4 National Inputs.......................................................................191 

8.1.4.5 Blended and other feed ..........................................................191 

8.1.5 Agricultural Production ...........................................................................191 

8.1.5.1 Crops......................................................................................192 

8.1.5.2 Livestock................................................................................192 

8.1.6 Agricultural Processing............................................................................192 

8.1.7 Feed blending...........................................................................................194 

8.1.8 Commodity Markets ................................................................................195 

8.1.9 International Trade...................................................................................197 

8.1.9.1 Spatially traded commodities.................................................198 

8.1.9.2 Excess supply/demand commodities .....................................199 

8.1.9.3 Commodities without trade....................................................200 

8.2 Tableau overview.................................................................................................201 

8.2.1 Equations defined.....................................................................................202 
10 

8.2.2 Variables defined .....................................................................................205 

8.2.3 Coefficient definitions .............................................................................212 

8.3 Details on features of the agricultural model.......................................................213 

8.3.1 Crop production modeling .......................................................................213 

8.3.1.1 Tillage choice.........................................................................220 

8.3.1.2 Land transfer dynamics..........................................................225 

8.3.1.3 Crop mixes.............................................................................225 

8.3.2 Livestock production/Feed blending........................................................228 

8.3.2.1 Livestock mixes .....................................................................236 

8.3.2.2 Dynamics ...............................................................................237 

8.3.3 Processing and feed blending...................................................................238 

8.3.4 Factor markets..........................................................................................245 

8.3.4.1 Land modeling of crop and pasture land................................245 

8.3.4.2 Water, AUM grazing and labor which have explicit factor 

supply curves .........................................................................245 

8.3.4.2.1 Irrigation water supply...............................................252 

8.3.4.2.2 AUM grazing supply..................................................252 

8.3.5 Labor supply ............................................................................................252 

8.3.5.1 Purchased input supply ..........................................................253 

8.3.6 Commodity consumption and markets ....................................................253 

8.3.7 Spatial international trade and interaction with domestic regions...........260 

8.3.8 Biofuels 264 

8.3.9 Time 270 

8.3.9.1 Coordinating the agriculture and forestry submodels............270 

8.3.9.2 Discounting and annuities......................................................271 

8.3.9.3 Terminal period agricultural land use valuation................272 

8.3.9.4 Updating yields, demand levels and other factors over time .272 
11 

8.3.10 Varying regional granularity over time....................................................274 

8.3.11 Environmental accounts...........................................................................278 

9 Chapter 9 Forest and agriculture linkages ...................................................................279 

9.1 Intersectoral land transfers...................................................................................279 

9.2 Intersectoral commodity transfers .......................................................................285 

9.3 Synchronizing different geographies...................................................................285 

9.4 Synchronizing different geographies...................................................................286 

9.5 Synchronizing time -- discounting and annuities ................................................287 

9.6 Intersectoral tradeoffs under policies...................................................................288 

10 Chapter 10 Approaches used to insure tractability .......................................................289 

10.1 Handling the demand and supply curves.............................................................289 

10.1.1 Demand and supply curve form...............................................................289 

10.1.2 Passing the curve through a known point ................................................290 

10.1.3 Integrating the functions ..........................................................................290 

10.1.4 Truncating the demand evaluation...........................................................291 

10.2 Adopting separable programming .......................................................................292 

10.3 Selecting grid points ............................................................................................296 

10.4 Crop and livestock mixes – concept and relaxation ............................................298 

10.4.1 Upper and lower limits.............................................................................299 

10.4.2 Temporal relaxation.................................................................................299 

10.5 Geographic expansion/collapse ...........................................................................299 

10.6 Time horizon and terminal conditions.................................................................300 

10.7 Substituting Memory for Time ............................................................................301 
12 

10.8 Artificial variable addition to insure feasibility...................................................301 

10.9 Right hand side perturbation to avoid degenerate cycling...................................302 

11 Chapter 10 Modeling of effects of climatic change......................................................303 

12 Chapter 11 Modeling lagged production restrictions....................................................304 

Section 4: Data Specificaton..................................................................................................306 

13 Chapter 12 GHG data specification ..............................................................................307 

13.1 Forest Carbon Detail............................................................................................307 

13.2 Carbon Accumulation Before Harvest.................................................................308 

13.2.1 Trees 309 

13.2.1.1 Total Growing Stock Volume in Standing Trees..............310 

13.2.1.2 Live and Standing Dead Trees..........................................311 

13.2.2 Understory314 

13.2.3 Forest Floor and Coarse Woody Debris...................................................315 

13.2.4 Soil 319 

13.3 Carbon disposition after harvest ..........................................................................321 

13.3.1 Wood and Paper Products........................................................................323 

13.3.1.1 Fraction Remaining in Product .........................................326 

13.3.1.2 Fate of Carbon Leaving Wood and Paper Products..........329 

13.3.2 Disposition of Mill Residue.....................................................................329 

13.3.3 Disposition of Fuelwood..........................................................................331 

13.4 Disposition of Site Carbon after Deforestation ...................................................332 

14 Chapter 14 Forest Sector Data Detail (Adams and Alig) .............................................334 
13 

14.1 Changes in Timberland Area...............................................................................334 

14.1.1 Timberland Inventory Representation .....................................................334 

14.1.2 Land Base Adjustments ...........................................................................340 

14.2 Forest Inventory...................................................................................................341 

14.2.1 Even-aged Forest Inventory.....................................................................342 

14.2.2 Partial cutting Intensity Classes...............................................................345 

14.3 Timber growth and yield .....................................................................................347 

14.3.1 Existing Aggregates of Private Timberland.............................................347 

14.3.2 New or regenerated aggregates of private timberland .............................349 

14.3.3 Afforested aggregates ..............................................................................350 

14.4 Harvest.................................................................................................................351 

14.5 Costs 352 

14.5.1 Land Conversion......................................................................................352 

14.5.2 Forest establishment costs........................................................................353 

14.5.3 Timber growing costs ..............................................................................354 

14.6 Forest processed Commodities............................................................................362 

14.7 Forest Processing.................................................................................................367 

14.7.1 Forest non-wood input (solid wood products only).................................368 

14.8 Wood products Demand ......................................................................................369 

14.8.1 Solid Wood Products ...............................................................................369 

14.9 International Trade in Wood products.................................................................371 

14.9.1 Canada 372 

14.9.1.1 Exchange rates and tariffs.................................................372 

14.9.1.2 Canadian timber supply ....................................................373 

14.9.1.3 Other world regions ..........................................................375 

14.10 Public land harvests .............................................................................................375 
14 

15 Chapter 14 Agriculture Sector Economic Detail (McCarl) ..........................................377 

15.1.1 Commodities disappearance ....................................................................377 

15.1.2 Production budgets...................................................................................377 

15.1.2.1 Crops.................................................................................377 

15.1.2.2 Livestock...........................................................................377 

15.1.3 Factor supply............................................................................................377 

15.1.3.1 land....................................................................................377 

15.1.4 types 377 

15.1.4.1 AUMs................................................................................379 

15.1.4.2 labor ..................................................................................379 

15.1.4.3 water..................................................................................379 

15.1.4.4 Other inputs.......................................................................379 

15.1.5 Crop mixes...............................................................................................379 

15.1.6 Livestock mixes .......................................................................................379 

15.1.7 Agricultural Product Demand ..................................................................379 

15.1.8 International Trade in Agricultural Products ...........................................379 

15.1.9 Biofuels: additional detail........................................................................379 

15.1.10 Non-CO2 Environmental Indicators (McCarl).......................380 

15.1.10.1 Natural resource use (land, water,...) .............................380 

15.1.10.2 Nutrient loadings (N,P,K, erosion,...) ............................380 

15.1.10.3 Pesticide loadings............................................................380 

Section 5: FASOMGHG Output and validation ....................................................................382 

16 Chapter 15 Broad Categorizations of Output................................................................383 

17 Chapter 16 GAMS Implementation..............................................................................387 
15 

17.1 File Structure .......................................................................................................387 

17.2 Run File Sequence and Control Switches............................................................393 

17.3 File Functions and Sequence ...............................................................................394 

17.4 Flow Chart of Model Segments...........................................................................399 

Section 6: FASOMGHG Applications and future plans........................................................403 

18 Chapter 17 Validation...................................................................................................404 

19 Chapter 18 policy applications......................................................................................405 

19.1 Types of policies and problems that can be evaluated using FASOMGHG .......405 

19.2 Climate Analysis..................................................................................................408 

19.2.1 GHG Mitigation.......................................................................................408 

19.2.1.1 Land Use Projection..........................................................410 

19.2.1.2 GHG Mitigation Supply Function ....................................411 

19.2.1.3 Cumulative Mitigation over Time ....................................412 

19.2.1.4 Targeting Activities and Regions......................................413 

19.2.2 Climate Change Impacts and Adaptation ................................................414 

19.3 General Land Use, Forest, and Agricultural Policies and Trends .......................415 

19.3.1 Land Use 415 

19.3.2 Forest sector.............................................................................................416 

19.3.3 Agricultural sector ...................................................................................416 

19.3.4 Bio-Energy Analysis................................................................................417 

20 Chapter 18 Uncertainties, Caveats, and future plans ....................................................418 

Section 7: Bibliography .........................................................................................................419 
16 

Section 8: Appendices............................................................................................................439 

21 Appendix: Glossary of Forestry Terms........................................................................439 

22 Appendix National Forest yields ..................................................................................447 
17 

LIST OF FIGURES 

Number Page

1-1 Figure Title ......................................................................... 1-5 

1-2 Figure Title ......................................................................... 1-6 

2-1 Figure Title ......................................................................... 2-3 
18 

LIST OF TABLES 

Number Page

1-1 Table Title........................................................................... 1-5 

1-2 Table Title........................................................................... 1-6 

2-1 Table Title........................................................................... 2-3 
19 

SECTION 1 : BACKGROUND 

1 CHAPTER 1: INTRODUCTION 

This report describes the structure of the Forest and Agricultural Sector Optimization 

Model—Green House Gas version (FASOMGHG), a dynamic, nonlinear programming model 

of the forest and agricultural sectors in the United States (US). The model simulates the 

allocation of land over time to competing activities in both the forest and agricultural sectors and 

the resultant consequences for the commodity markets supplied by these lands and, importantly 

for policy purposes underlying the development of this model, the net greenhouse gas (GHG) 

emissions. The model was developed to evaluate the welfare and market impacts of public 

policies that cause land transfers between the sectors and alterations of activities within the 

sectors. To date, FASOMGHG and its predecessor model FASOM have been used to examine 

the effects of GHG mitigation policy, climate change impacts, public timber harvest policy, 

federal farm program policy, biofuel prospects, and pulpwood production by agriculture. It can 

also aid in the appraisal of a wider range of forest and agricultural sector policies. 

This report describes the structure of the FASOMGHG model in several levels of detail. 

Primary attention is devoted to the description of the model structure with alternative levels of 

detail: 

McCarl note this needs to be updated to reflect full document when it is done it should 

correspond to the structure of the document 

• Conceptual description of FASOMGHG model scope 

• Economic description of FASOMGHG sectoral function 

• Description of GHG modeling 

• Detailed sectoral-specific description of modeling approach 

• Operational description of approaches used to ensure tractability 

• Description of model implementation in precise GAMS terms (see Appendix A) 

• In addition we present material on the following subjects 

• Origins and evolution of FASOMGHG 

• Data specification approaches 

• Broad categorizations of model output 

• Policy applications to date and a review of findings 

• Future plans 

The report is divided into xxx text sections and four appendices. Following this 

Background section, the next section provides an overview of the major features of the model, 
20 

such as the regional delineation and the basic structure of the forest, agricultural, and carbon 

accounting sectors in the model. The third text section describes the outputs of the FASOMGHG 

model, discusses how the model can be used to evaluate alternative policies for mitigating 

GHGs, and outlines potential future directions for the model. Appendix A contains additional 

detail on the scope of the agricultural model and Appendix B contains additional detail on the 

scope of the forest model. Appendix C provides a description of the computer program and data 

file structure for the FASOMGHG modeling system as a whole. Appendix D contains a detailed 

listing of the outputs of the model. 
21 

2 CHAPTER 2: ORIGINS OF AND NEW FEATURES IN FASOMGHG 

FASOMGHG is an outgrowth of a number of previous lines of work: 

• Agricultural Sector Modeling for environmental appraisal involving the Agricultural 

Sector Model (ASM) in its US Environmental Protection Agency (EPA), USDA Natural 

Resource Conservation Service (NRCS) and USDA Economic Research Service (ERS) 

supported applications to environmental and farm policy issues. 

• Models of the US and Canadian forest sectors developed for the US Department of 

Agriculture (USDA) Forest Service’s Resource Planning Act (RPA) Assessment process. 

• USDA Forest Service efforts to examine the carbon sequestration consequences of 

changes in forest management using the FORCARB modeling system. 

• Earlier EPA-supported efforts on the precursor to FASOMGHG - FASOM -that were 

motivated by the insight that the existing Forest Service Timber Assessment Market 

Model (TAMM) and ASM could neither simultaneously function together, nor 

adequately accommodate the dynamic and producer expectation issues raised by 

intersectoral land movement. 

• Earlier EPA, USDA-Consortium for Agricultural Soils Mitigation of GHGs program 

(CASMGS), US Department of Energy (DOE)-- Carbon sequestration in terrestrial 

ecosystems program(CSiTE), and DOE--Office of Science- supported efforts to model 

agricultural GHG mitigation possibilities via a variety of sequestration, emission 

reduction, and biofuels-related possibilities. 

• EPA-sponsored work to examine GHG mitigation “project-level” issues such as 

permanence, leakage, additionality, uncertainty, transactions costs, reversal and 

saturation. 

Collectively all of these efforts came together in the form of a project to create 

FASOMGHG that involved participants from Texas A&M University, EPA, RTI International 

(RTI), Oregon State University, and USDA--Forest Service, along with important advice from 

numerous others. This project yielded a number of new features, an improved computer 

implementation and this document. Previously the only document that drew these components 

together was the PhD dissertation at Texas A&M by Lee (2002). 

2.1 Brief review of predecessor projects 

Below, we briefly review the main efforts and contributions of each of these lines of 

work to the overall FASOMGHG model. 
22 

2.1.1 ASM Modeling, Environmental and Farm Policy Analysis 

One of the primary roots of FASOMGHG involves efforts by McCarl and colleagues to 

use sector modeling to appraise the economic and environmental implications of environmental 

and agricultural policy-related developments within the agricultural sector. This work began 

initially at Purdue University, was carried on later at Oregon State University, and eventually at 

Texas A&M University. The project originally began in the context of a cooperative agreement 

with USDA supporting a thesis by Baumes (1978). The model, hereafter called ASM, was 

subsequently improved for pesticide analysis by Burton (1982), as reported in Burton and Martin 

(1987). It was documented by Chattin et al. (1978), Adams et al. (1984), and Chang et al. (1992). 

Component documentation has appeared in McCarl and Spreen (1980), McCarl (1982), and 

Hamilton et al. (1985). In the late 1970s, ASM began to be used for environmental and resource 

analysis, first on biofuels (Tyner et al., 1979; Chattin, 1982; Hickenbotham, 1987), then on 

ozone (Hamilton, 1985; Adams et al., 1984), acid rain (Adams et al., 1993), soil conservation 

policy (Chang et al., 1994), global climate change (Adams et al., 1988, 1990, 1999, 2001; 

McCarl, 1999; Reilly et al., 2000, 2002), and climate change mitigation (Adams et al., 1993; 

McCarl and Schneider, 2001). It has also been used extensively for research evaluation (TanyeriAbur, 1990; Coble et al., 1992; Chang et al., 1991). A variant of the model has been adapted and 

used for about 20 years by the USDA Economic Research Service (House, 1987; Heimlich et al., 

1998). ASM is incorporated into FASOMGHG, as will be discussed below. 

The ASM model is a spatially disaggregated agricultural sector model representing the 

US in terms of 63 production regions and 10 market regions depicting trade with a number of 

foreign countries. ASM depicts production in an equilibrium year and is thus an intermediate run 

model giving implications for policy after it has been fully worked into the sector. 

The FASOMGHG concept in part came out of the recognized limitations of an ASM 

study that was designed to examine issues regarding joint forestry and agricultural climate 

change mitigation (Adams et al., 1993). That study provided estimates of: (a) costs of 

sequestering carbon that took into account the increases in agricultural prices when agricultural 

crops were displaced by trees, and (b) impacts of different size programs on both the total and 

the distribution of the consumers' and producers’ welfare in the agricultural sector. The study 

showed that harvesting the trees used to sequester carbon had the potential to greatly depress 

regional stumpage prices in the US. 

That analysis incorporated forestry in terms of annualized equilibrium production 

budgets, containing a forestry representation with average (over time) wood product yields and 
23 

also average costs. Such assumptions were required to reflect forestry production possibilities 

within the ASM static single-year equilibrium representation. An important limitation thereof is 

that there is no modeling of the dynamics of tree growth and timber harvesting decision making 

(i.e., trees were assumed to be harvested in a uniform, steady state fashion, and harvest age was 

not endogenous). Such assumptions do not adequately reflect a number of dynamic issues 

involved with land allocations to forestry versus agriculture. In turn, it was decided to develop a 

model that could depict such dynamics and FASOMGHG eventually arose. 

2.1.2 Forest Service RPA Models 

The basic structure of the forest sector was drawn from the family of models developed 

to support the US Forest Service's decennial RPA Timber Assessment process: TAMM (Timber 

Assessment Market Model; Adams and Haynes, 1980, 1996; Haynes, 2003), NAPAP (North 

American Pulp and Paper model; Ince 1994; Zhang et al 1993, 1996), ATLAS (Aggregate 

Timberland Assessment System; Mills and Kincaid, 1992), and AREACHANGE (Alig et al. 

2003, 2004). Timber inventory data and estimates of current and future timber yields were taken 

in large part from the ATLAS input used for the 2000 RPA Timber Assessment (Haynes, 2003). 

The AREACHANGE models provide timberland area and forest type allocations to the ATLAS 

model. TAMM and NAPAP are “myopic” market projection models (they project ahead one 

period at a time) of the solid wood and fiber products sectors in the US and Canada. They treat 

markets at the wholesale product level (e.g., softwood lumber, softwood plywood, newsprint, 

linerboard, etc.) using econometric demand relations and a mix of econometric and activity 

analysis representations of supply. Log and timber demand relations are derived using fixed 

coefficients production representations. Timber supply functions (for sawtimber and pulpwood) 

are based on econometric analysis of historical harvest behavior by region and private owner 

class. Between annual market projections (supply-demand balance), both models update 

estimates of quasi-fixed capital stock (processing capacity) using either accelerator or Tobin's q 

approaches. Total harvest for all products is sent to ATLAS, which updates the timber inventory 

for removals and growth. ATLAS employs Johnson and Scheurman's (1977) "type II" format to 

represent the intertemporal development of timberland managed on an even-aged basis (using 

clearcuts) and their "type I" form for partially cut or selectively managed lands. In ATLAS, 

harvested lands are regenerated (grown) according to exogenous assumptions regarding the 

intensity of management and associated yield volume changes. The timberland base is adjusted 

for gains and losses projected over time by the AREACHANGE models, including afforestation 

of the area moving from agriculture into forestry. 
24 

The earliest version of the FASOM model considered only the log market. Secondary 

products (such as lumber or newsprint) were not explicitly represented, although the impacts of 

changes in the markets for those products were implicit in the shifts in log demand. Log demand 

relations were based on projections of the TAMM and NAPAP models. ATLAS provided the 

inventory and management input data but with a compressed set of management intensity 

options. The current FASOMGHG, in contrast, includes the full set of TAMM and NAPAP 

product, log, and stumpage markets. Product demand relations were extracted directly from the 

latest versions of TAMM and NAPAP, as were product supply relations for the solid wood 

products (such as lumber) and all product conversion coefficients for both solid wood and fiber 

commodities. Trade between the US and Canada in all major classes of wood products is 

endogenous and subject to the full array of potential trade barriers and exchange rates. Timber 

supply also uses nearly the full set of management intensity options available in ATLAS (e.g., 

for the South, seven planted pine management intensity classes directly from ATLAS), and the 

selection of management intensity is endogenous. 

2.1.3 Forest Service FORCARB Modeling System 

The forest carbon accounting component of FASOMGHG is largely derived from the 

Forestry Carbon (FORCARB) modeling system. FORCARB is an empirical model of forest 

carbon budgets simulated across regions, forest types, land classes, forest age classes, ownership 

groups, and carbon pools. The USDA Forest Service uses FORCARB, in conjunction with 

economic forest sector models (e.g., TAMM, NAPAP, ATLAS, and AREACHANGE) to 

estimate the total amount of carbon stored in US forests over time as part of the Forest Service’s 

ongoing assessment of forest resources in general (i.e., pursuant to the RPA) and forest carbon 

sequestration potential in particular (Joyce 1995, Joyce and Birdsey 2000). Deriving 

FASOMGHG’s forest carbon accounting structure from FORCARB ensures that forest carbon 

estimates from FASOMGHG can be analyzed and compared with ongoing efforts by the USDA 

Forest Service to estimate and project forest carbon estimates at the national level. It also enables 

FASOMGHG to be updated over time as the FORCARB system evolves to incorporate 

improved science. 

FORCARB’s in-forest carbon pool (trees, understory, litter, and soil) allocations were 

initially developed by researchers from the USDA Forest Service and colleagues in the mid1990s (Plantinga and Birdsey, 1993; Birdsey and Heath, 1995; Birdsey, 1996). These model 

components have been modified in recent years via ongoing work by Smith et al. (2003) and 

Smith and Heath (2002). In addition, FORCARB tracks carbon stored in harvested wood 

products at and after the time of harvest. The wood product accounting component of 
25 

FORCARB was originally based on the work of Row and Phelps (1991) but has been modified 

based on the work of Skog and Nicholson (2000). 

2.1.4 First Generation of FASOM 

Development of the initial version of the FASOM model was motivated in part by the 

desire to project the carbon flux impacts of large areas of forest plantations resulting from 

hypothetical programs of afforestation on marginal agricultural lands. If trees on these afforested 

lands could be harvested for timber products, expected future prices in the forest sector would be 

affected, together with private owners' desires to hold timber stock and invest in the management 

of future timber stands. Future timber market changes would likely feed back to current 

decisions via price expectations. Similarly, the removal of large areas of agricultural land from 

production would presumably have some impact on farmers' cropping and land use decisions 

through changes in expected future agricultural prices. In their original forms, neither ASM nor 

TAMM included mechanisms for explaining intertemporal land management investments or the 

impacts of changing price expectations on investment behavior. And, since the models were 

independent, partial-equilibrium systems, there were no opportunities to reflect countervailing 

cross-sectoral price movements resulting from land shifts between the sectors. 

The initial FASOM model addressed these limitations by linking a simple intertemporal 

model of the forest sector with a version of the ASM model in a dynamic framework, allowing 

some portion of the land base in each sector to be shifted to the alternative use. Land could 

transfer between sectors based on its marginal profitability in all alternative forest and 

agricultural uses over the time horizon of the model. Management investment decisions, 

including harvest timing in forestry, in both sectors were made endogenous, so they too would be 

based on the expected profitability of an additional dollar spent on expanding future output (both 

timber and carbon, if valued monetarily). 

FASOM assumes intertemporal optimizing behavior by economic agents. The decision to 

continue growing a stand rather than harvesting it now is based on a comparison of the net 

present value of timber harvests from future periods and any GHG offsets obtained (not 

harvesting now) versus the net present value of harvesting now and replanting (or not replanting 

and shifting the land to agricultural use). Similarly, the afforestation decision would keep land in 

agriculture if it had a greater net present value there than in forestry, including any GHG 

monetary returns. This process establishes a land price equilibrium across the two sectors and, 

given the land base interaction, a link between contemporaneous commodity prices in the two 

sectors as well.
26 

2.1.5 Agricultural Greenhouse Gas Mitigation Modeling—ASMGHG 

While FASOM began work with GHG mitigation, it was basically limited in scope in 

coverage and response options. More specifically, FASOM only involved carbon stocks 

associated with trees, and wood products and to a lesser extent with land use change by 

incorporating an average level of carbon in forest and pasture land uses. Such an approach was 

not reflective of the spectrum of agricultural possibilities for GHG management. As a result, an 

EPA-funded project arose to widen the agricultural coverage of GHG management alternatives. 

This project manifested itself in the dissertation by Schneider (2000) and in the paper by McCarl 

and Schneider (2001) which expanded the ASM model as discussed earlier to include a detailed 

set of agricultural-related GHG management possibilities. That work expanded ASM to 

incorporate tillage change, land use exchange between pasture and crops, afforestation, 

fertilization alternatives, enteric fermentation, manure management, biofuels, fossil fuel use 

reduction, and rice land manipulation were included as well as a multigas framework. The 

resulting model was labeled ASMGHG. Again, the static equilibrium nature of ASMGHG and 

ASM omitted any modeling of the dynamic aspects of, particularly, the sequestration related 

strategies (forest and tillage) but also the dynamic market penetration restrictions caused by 

needed capital stock alterations to employ biofuels. 

2.1.6 Original FASOMGHG by Lee 

Given the dynamic and forest carbon sequestration coverage and the agricultural 

coverage in ASMGHG, it was decided to merge the agricultural alternatives into the 

FASOMGHG structure. This was manifest in the first version of FASOMGHG that was built in 

the context of Lee’s dissertation (2002). In that work, the agricultural model was expanded to 

have all the GHG management alternatives in ASMGHG with the additional coverage of 

dynamics. In particular, features were introduced for agricultural tillage options, wherein 

sequestration gains were only assumed to occur for 20 years, which is a simplification of the true 

soil dynamics believed to occur. Features were also introduced for biofuels reflective of the need 

to adapt power plants to biomass fuel usage. 

2.1.7 Project-Level GHG Mitigation Issues 

While the work was proceeding on FASOMGHG, there was emerging interest stimulated 

by US GHG policy to begin to look at GHG mitigation potential at the project (site) level, rather 

than at the national level. GHG projects could, in principle, be part of a network of voluntary 

programs or limited scale GHG cap-and-trade across sectors. In that context, attention was 

devoted toward the issues of project transactions cost, economic incentives above and beyond 
27 

cost differences, and possible reductions of project credits (discounts) for leakage of GHGs 

outside the project boundaries, possible impermanence of GHG benefits, non-additionality of 

project benefits, and uncertainty of project GHG outcomes. 

2.2 New developments in this FASOMGHG version 

Given the seven different endeavors above, an update of FASOMGHG was undertaken in 

2004 which led to the version documented herein. The main revisions in that effort were 

• updating of the biophysical and economic data, 

• complete restructuring of the computer implementation 

• expansion in the forest sector to include product as well as log markets, 

• incorporation of wood products processing, 

• expansion of the scope of agricultural sector GHG emission source and mitigation 

strategy coverage, 

• improvement of the modeling of agricultural carbon sequestration dynamics, 

• updating of the standing forest and wood product carbon accounting, 

• addition of carbon accounting related to forest use of fossil fuels 

• alteration of the model time step from 10 to five years, and 

• improvement of model execution time characteristics. 
28 

SECTION 2 FOUNDATIONS 
29 

3 CHAPTER 3 CONCEPTUAL SCOPE OF FASOMGHG 

Examining the role of forest and agricultural GHG mitigation in a dynamic setting 

requires an analytical framework that can depict the time path and GHG consequences of 

forestry and agricultural activity. FASOMGHG combines, for the US, component models of 

agricultural crop and livestock production, livestock feeding, agricultural processing, log 

production, forest processing, carbon sequestration, CO2/non-CO2 GHG gas emissions, wood 

product markets, agricultural markets, GHG payments, and land use to systematically capture the 

rich mix of biophysical and economic processes that will determine the technical, economic, and 

environmental implications of policy changes, climate change, and/or GHG mitigation 

opportunities. 

Operationally, FASOMGHG is a multiperiod, intertemporal, price-endogenous, 

mathematical programming model depicting land transfers and other resource allocations 

between and within the agricultural and forest sectors in the US. The model solution portrays 

simultaneous market equilibrium over an extended time, typically 70 to 100 years on a five year 

time step basis. The results from FASOMGHG yield a dynamic simulation of prices, production, 

management, consumption, GHG effects, and other environmental and economic indicators 

within these two sectors, under the scenario depicted in the model data. 

FASOMGHG’s key endogenous variables include: 

• commodity and factor prices, 

• production, consumption, export and import quantities, 

• land use allocations between sectors, 

• management strategy adoption, 

• resource use, 

• economic welfare measures, 

-- producer and consumer surplus, 

-- transfer payments, 

-- net welfare effects, 

• environmental impact indicators, 

-- GHG emission/absorption of carbon dioxide (CO2), methane (CH4), and nitrous 

oxide (N2O) 

-- surface, subsurface, and groundwater pollution for nitrogen, phosphorous, and 

soil erosion. 

In the following sections we provide initial details on the overall scope of FASOMGHG 

in terms of resources, production, processing, and commodity flows; land coverage; geographic 
30 

scope; market modeling; land allocation; GHG treatment; biofuels; use of a baseline; 

environmental indicators; dynamic scope; dynamic yield, cost, and demand updating.

3.1 Resources, Production, Processing, and Commodity Flows 

The basic conceptual framework of FASOMGHG is presented below (Figure 3-1). 

Land, water, labor, and national inputs (fertilizer, capital, etc.) resources are used by forest, crop 

(including biofuels feedstock), and livestock production. In turn, the raw, primary commodities 

are produced and some move directly to markets while others move to processing making 

secondary commodities, direct feeding, or are blended into blended feeds. In turn, then the 

primary, secondary, biofuel feedstock, and blended feeds go to domestic demand, biofuels 

production, exports, or livestock feeding. In addition, imports enter the market place. 

Figure 3-1. Overview of basic features modeled 

Removed to figures file 

3.2 Commodity Scope 

 There are several major groupings of agricultural and forest commodities depending on 

the sector, whether they are raw, processed, mixed for livestock feed or biofuels relevant. These 

commodity groups are 

• Raw crop, livestock, forestry, and biofuel feedstock primary commodities grown on the 

land (Table 3-1). 

• Processed, secondary commodities made from the raw crop, livestock, and wood 

products (Table 3-2) 

• Energy products made from biofuel feedstocks (also in Table 3-2) 

• Blended feeds for livestock consumption (Table 3-3) 

Agriculture and forestry commodities are quite frequently substitutable in demand. For 

example, sorghum is almost a perfect substitute for corn on a calorie for calorie basis in many 

uses and beet sugar is a perfect substitute for cane based sugar. Also, a number of feed grains are 

substitutes in terms of livestock feeding. FASOMGHG contains a set of processing activities 

which make secondary commodities. Secondary commodities are generally included in the 

model either to represent substitution or to depict demand for components of products. For 

example, processing possibilities for soybeans are included depicting soybeans being crushed 

into soybean meal and soybean oil because these secondary commodities frequently flow into 

different markets. Similar possibilities exist in the forest sector, for example, making paper from 
31 

pulp logs or using logging residues, thereby including in the model a large degree of demand 

substitution. 

Table 3-1. List of Raw, Primary Commodities 

Crop Items Units 

 Cotton 480-pound bales 

 Corn Bushels 

 Soybeans Bushels 

 SoftWhiteWheat Bushels 

 HardRedWinterWheat Bushels 

 DurhamWheat Bushels 

 HardRedSpringWheat Bushels 

 Sorghum Hundred pounds (CWT) 

 Rice CWT 

 Oats Bushels 

 Barley Bushels 

 Silage US tons 

 Hay US tons 

 Sugarcane US tons 

 Sugarbeet US tons 

 Potatoes CWT 

 TomatoFrsh Fresh tomatoes in 25-pound cartons 

 TomatoProc Processing tomatoes in US tons 

 OrangeFrsh75box Fresh market oranges in 75-pound boxes (California, Arizona) 

 OrangeFrsh90box Fresh market oranges in 90-pound boxes (Florida) 

 OrangeFrsh85box Fresh market oranges in 85-pound boxes (Texas) 

 OrangeProc75box Processing market oranges in 75-pound boxes (California, Arizona) 

 OrangeProc90box Processing market oranges in 90-pound boxes (Florida) 

 OrangeProc85box Processing market oranges in 85-pound boxes (Texas) 

 GrpfrtFrsh67box Fresh market grapefruit in 67-pound boxes (California, Arizona) 

 GrpfrtFrsh85box Fresh market grapefruit in 85-pound boxes (Florida) 

 GrpfrtFrsh80box Fresh market grapefruit in 80-pound boxes (Texas) 

 GrpfrtProc67box Processing market grapefruit in 67-pound boxes (California, Arizona) 

 GrpfrtProc85box Processing market grapefruit in 85-pound boxes (Florida) 

 GrpfrtProc80box Processing market grapefruit in 80-pound boxes (Texas) 

Livestock Items Units 

 NonFedSla 100 pounds nonfed beef on the hoof 

 FeedlotBeefSlaughter 100 pounds fed beef on the hoof will be reported in 1,000s 

 CalfSlaugh 100 pounds of calf on hoof 

 CullBeefCo 100 pounds of cull beef cow on hoof 

 Milk 100 pounds of raw milk 

 CullDairyCows 100 pounds of cull dairy cow 

 HogsforSlaughter 100 pounds live weight 

 FeederPig 100 pounds live weight 

 CullSow 100 pounds live weight 

 LambSlaugh 100 pounds live weight 

 CullEwes 100 pounds live weight 

 Wool Raw wool in pounds 
32 

 SteerCalve 100 pounds of steer calves 

 HeifCalve 100 pounds of heifer calves 

(continued) 

Table 3-1. List of Raw, Primary Commodities (continued) 

Livestock Items (continued) Units 

 StockedCalf 100 pounds of calves after first stocker phase ready to feed 

 StockedHCalf 100 pounds of heifer calves after first stocker phase ready to feed 

 StockedSCalf 100 pounds of steer calves after first stocker phase ready to feed 

 DairyCalves 100 pounds of dairy calves 

 StockedYearling 100 pounds of yearlings after second stocker phase ready to feed 

 StockedHYearl 100 pounds of heifer yearlings after second stocker phase ready to feed 

 StockedSYearl 100 pounds of steer yearlings after second stocker phase ready to feed 

 HorsesandMules Number of horses and mules in head 

 Eggs Dozens of eggs at farm level 

 Broilers 100 pounds live weight 

 Turkeys 100 pounds live weight 

Biofuel Feedstocks 

 SwitchGrass US tons 

 HybrdPoplar US tons 

 Willow US tons 

Logs From Timber Harvest 

 PVT_SWSLOG_WOODS Softwood privately-produced sawlog in 1,000 cu. ft. in the woods 

 PVT_HWSLOG_WOODS Hardwood privately-produced sawlog in 1,000 cu. ft. in the woods 

 PVT_SWPLOG_WOODS Softwood privately-produced pulplog in 1,000 cu. ft. in the woods 

 PVT_HWPLOG_WOODS Hardwood privately-produced pulplog in 1,000 cu. ft. in the woods 

 PVT_SWFLOG_WOODS Softwood privately produced fuellog in 1,000 cu. ft. in the woods 

 PVT_HWFLOG_WOODS Hardwood privately produced fuellog in 1,000 cu. ft. in the woods 

 PUB_SWSLOG_WOODS Softwood publicly produced sawlog in 1,000 cu. ft. in the woods 

 PUB_HWSLOG_WOODS Hardwood publicly produced sawlog in 1,000 cu. ft. in the woods 

 PUB_SWPLOG_WOODS Softwood publicly produced pulplog in 1,000 cu. ft. in the woods 

 PUB_HWPLOG_WOODS Hardwood publicly produced pulplog in 1,000 cu. ft. in the woods 

 PUB_SWFLOG_WOODS Softwood publicly produced fuellog in 1,000 cu. ft. in the woods 

 PUB_HWFLOG_WOODS Hardwood publicly produced fuellog in 1,000 cu. ft. in the woods 

 IMP_SWSLOG_WOODS Imported softwood sawlog in the woods 

 IMP_HWSLOG_WOODS Imported hardwood sawlog in the woods 

 IMP_SWPLOG_WOODS Imported softwood pulplog in the woods 

 IMP_HWPLOG_WOODS Imported hardwood pulplog in the woods 

 IMP_SWFLOG_WOODS Imported softwood fuellog in the woods 

 IMP_HWFLOG_WOODS Imported hardwood fuellog in the woods 

Logs From Timber Harvest 

(continued) Units 

 PVT_SWFLOG_MILL Softwood privately produced fuellog in 1,000 cu. ft. delivered to the mill 

 PVT_HWFLOG_MILL Hardwood privately produced fuellog in 1,000 cu. ft. delivered to the mill 

 PUB_SWSLOG_MILL Softwood publicly produced sawlog in 1,000 cu. ft. delivered to the mill 
33 

 PUB_HWSLOG_MILL Hardwood publicly produced sawlog in 1,000 cu. ft. delivered to the mill 

 PUB_SWPLOG_MILL Softwood publicly produced pulplog in 1,000 cu. ft. delivered to the mill 

 PUB_HWPLOG_MILL Hardwood publicly produced pulplog in 1,000 cu. ft. delivered to the mill 

 PUB_SWFLOG_MILL Softwood publicly produced fuellog in 1,000 cu. ft. delivered to the mill 

 PUB_HWFLOG_MILL Hardwood publicly produced fuellog in 1,000 cu. ft. delivered to the mill 

 IMP_SWSLOG_MILL Imported softwood sawlog delivered to the mill 

 IMP_HWSLOG_MILL Imported hardwood sawlog delivered to the mill 

 IMP_SWPLOG_MILL Imported softwood pulplog delivered to the mill 

 IMP_HWPLOG_MILL Imported hardwood pulplog delivered to the mill 

 IMP_SWFLOG_MILL Imported softwood fuellog delivered to the mill 

 IMP_HWFLOG_MILL Imported hardwood fuellog delivered to the mill 

Table 3-2. List of Processed, Secondary Commodities 

Crop Items Units 

 OrangeJuic 1,000 gallons at 42 brix 

 GrpfrtJuic 1,000 gallons at single strength equivalent 

 SoybeanMeal US tons 

 SoybeanOil Pounds of oil 

 HFCS Gallons 

 Beverages Gallons 

 Confection 100 pounds 

 Baking 100 pounds 

 Canning 100 pounds 

 RefSugar US tons 

 GlutenFeed 100 pounds 

 Starch 100 pounds 

 CornOil 100 gallons 

 CornSyrup Gallons 

 Dextrose 100 pounds 

 FrozenPot 100 pounds 

 DriedPot 100 pounds 

 ChipPot 100 pounds 

 CaneRefini 100 pounds 

Livestock Items 

 FedBeef 100 pounds fed beef carcass weight 

 NonFedBeef 100 pounds grass-fed beef carcass weight 

 Pork 100 pounds pork after dressing 

 Chicken 100 pounds on ready-to-cook basis 

 Turkey 100 pounds on ready-to-cook basis 

 WoolClean Pounds of clean wool 

 FluidMilk 100 pounds 

 Cream Pounds 

 SkimMilk Pounds 

 EvapCondM Pounds 

 NonFatDryM Pounds 

 Butter Pounds 
34 

 AmCheese Pounds 

 OtCheese Pounds 

 CottageChe Pounds 

 IceCream Pounds 

Biofuel Items 

 Ethanol Gallons 

 MktGasBlend Gallons 

 SubGasBlend Gallons 

 Tbtus Trillion BTUs 

Wood Products 

 SLUM Softwood lumber in millions board feet, lumber tally 

 SPLY Softwood plywood in millions square feet, 3/8 inch 

 OSB Oriented strand board (OSB) in millions square feet, 3/8 inch 

 HLUM Hardwood lumber in millions board feet, lumber tally 

 HPLY Hardwood plywood in millions square feet, 3/8 inch 

 SWPANEL Softwood used in Non-OSB reconstituted panel 

 HWPANEL Hardwood used in Non-OSB reconstituted panel 

 SWMISC Softwood miscellaneous products in million cu. ft. 

 HWMISC Hardwood miscellaneous products in million cu. ft. 

 SRESIDUES Softwood residues in 1,000,000 cu. m. 

 HRESIDUES Hardwood residues in 1,000,000 cu. m. 

 HWPULP Hardwood pulp in 1,000,000 cu. m. 

 SWPULP Softwood pulp in 1,000,000 cu. m. 

 AGRIFIBERLONG Agrifiber (long fiber—endog.) 

 AGRIFIBERSHORT Agrifiber (short fiber—endog.) 

 OLDNEWSPAPERS Old newspapers in 1,000,000 metric tonnes 

 OLDCORRUGATED Old corrugated in 1,000,000 metric tonnes 

 WASTEPAPER Mixed wastepaper in 1,000,000 metric tonnes 

 PULPSUBSTITUTE Pulp substitutes in 1,000,000 metric tonnes 

 HIGDEINKING Hi-grade deinking in 1,000,000 metric tonnes 

 NEWSPRINT Newsprint in 1,000,000 metric tonnes 

 UNCFREESHEET Unc. free sheet in 1,000,000 metric tonnes 

 CFREESHEET Coated free sheet in 1,000,000 metric tonnes 

 UNCROUNDWOOD Unc. roundwood in 1,000,000 metric tonnes 

 CROUNDWOOD Coated roundwood in 1,000,000 metric tonnes 

 TISSUE Tissue and sanitary in 1,000,000 metric tonnes 

 SPECIALTYPKG Specialty pkg. in 1,000,000 metric tonnes 

 KRAFTPKG Kraft pkg. in 1,000,000 metric tonnes 

 LINERBOARD Linerboard in 1,000,000 metric tonnes 

 CORRUGMED Corrug. medium in 1000000 metric tonnes 

 SBLBOARD Solid bl. board in 1000000 metric tonnes 

 RECBOARD Recycled board in 1000000 metric tonnes 

 CONSTPAPER Construc. paper and bd. in 1000000 metric tonnes 

 DISPULP Dissolving pulp in 1000000 metric tonnes 

 SWKMPULP Softwood kraft market pulp in 1000000 metric tonnes 

 HWKMPULP Hardwood kraft market pulp in 1000000 metric tonnes 

 RECMPULP Recycled market pulp in 1000000 metric tonnes 

 CTMPMPULP Chemi-thermomechanical market pulp in 1000000 metric tonnes 
35 

Table 3-3. List of Blended feeds 

Feed Items 

 StockPro0 Protein feed for stockers in 100 lbs (cwt) 

 CatGrain0 Blend of grains for cattle in 100 lbs (cwt) 

 HighProtCa Protein feed for cattle in 100 lbs (cwt) 

 CowGrain0 Blend of grains for cow calf operations in 100 lbs (cwt) 

 CowHiPro0 Protein feed for cow calf operations in 100 lbs (cwt) 

 FinGrain0 Blend of grains for pig finishing in 100 lbs (cwt) 

 FinProSwn0 Protein feed for pig finishing in 100 lbs (cwt) 

 FarGrain0 Blend of grains for farrowing operations in 100 lbs (cwt) 

 FarProSwn0 Protein feed for farrowing operations in 100 lbs (cwt) 

 FPGGrain0 Blend of grains for feeder pigs in 100 lbs (cwt) 

 FPGProSwn0 Protein feed for feeder pigs in 100 lbs (cwt) 

 DairyCon0 Blend of grains for dairy operations in 100 lbs (cwt) 

 BroilGrn0 Blend of grains for broilers in 100 lbs (cwt) 

 BroilPro0 Protein feed for broilers in 100 lbs (cwt) 

 TurkeyGrn0 Blend of grains for turkeys in 100 lbs (cwt) 

 TurkeyPro0 Protein feed for turkeys in 100 lbs (cwt) 

 EggGrain0 Blend of grains for eggs in 100 lbs (cwt) 

 EggPro0 Protein feed for eggs in 100 lbs (cwt) 

 SheepGrn0 Blend of grains for sheep in 100 lbs (cwt) 

 SheepPro0 Protein feed for sheep in 100 lbs (cwt) 

3.3 Geographic Coverage 

FASOMGHG covers forest and agricultural activity across the conterminous US, broken 

into 11 market regions meshed with 63 subregions for agricultural sector coverage. The 11 larger 

regions (see Table 3-4 and figure 3-2) are a consolidation of regional definitions that would 

otherwise differ if the forest and agricultural sectors were treated separately. The 11-region 

breakdown reflects the existence of regions for which there is agricultural activity but no 

forestry, and vice versa. In fact, forestry production occurs in nine of the larger 11 production 

regions, but agricultural sector activity can not be reasonably condensed to only these nine 

regions. For instance, the Northern Plains (NP) and Southwest (SW) regions reflect important 

differences in agricultural characteristics, but no forestry activity is included in either region. 

Likewise, there are important differences in the two Pacific Northwest regions (PNWW, PNWE) 

for forestry, but only the PNWE region is considered a significant producer of the agricultural 

commodities tracked in the model. 
36 

Figure 3-2. FASOMGHG Regions 

Removed to figure file 

Agriculture is explicitly modeled in all 63 regions (Table 3-5) for the initial 20 years in 

the model run to provide maximum regional detail for the near to intermediate term. But for 

model size control purposes, agriculture is collapsed back to 11 regions after the first 20 years of 

the model run. Each of the 63 regions is uniquely mapped to the overall 11 regions as specified 

in Table 3-64. Note that when land moves between sectors in the model during periods when the 

63 regions are active, that it moves on an 11 regions basis to and from the 63 regions in 

proportion to their initial land endowments. 

 

Table 3-4. FASOMGHG 11 Region Definitions 

Key Region States/Subregions 

CB Corn Belt All regions in Illinois, Indiana, Iowa, Missouri, Ohio 

NP Northern Plains Kansas, Nebraska, North Dakota, South Dakota 

LS Lake States Michigan, Minnesota, Wisconsin 

NE Northeast Connecticut, Delaware, Maine, Maryland, Massachusetts, New Hampshire, 

New Jersey, New York, Pennsylvania, Rhode Island, Vermont, West Virginia

PNWE Pacific Northwest-east side Oregon and Washington, east of the Cascade mountain range 

PNWW Pacific Northwest-west side Oregon and Washington, west of the Cascade mountain range 

PSW Pacific Southwest All regions in California 

RM Rocky Mountains Arizona, Colorado, Idaho, Montana, Eastern Oregon, Nevada, New Mexico, 

Utah, Eastern Washington, Wyoming 

SC South Central Alabama, Arkansas, Kentucky, Louisiana, Mississippi, Eastern Oklahoma, 

Tennessee, Eastern Texas (TxEast) 

SE Southeast Virginia, North Carolina, South Carolina, Georgia, Florida 

SW Southwest Western and Central Oklahoma, All of Texas but the Eastern Part -- Texas 

High Plains, Texas Rolling Plains, Texas Central Blacklands, Texas Edwards 

Plateau, Texas Coastal Bend, Texas South, TexasTrans Pecos 

Table 3-5 63 Regions Used in Agricultural Model 

State Substate Regions if Defined 

Alabama 

Arizona 

Arkansas 

California CaliforniaN, CaliforniaS 

Colorado 

Connecticut 

Delaware 

Florida 
37 

Georgia 

Idaho 

Illinois IllinoisN, IllinoisS 

Indiana IndianaN IndianaS 

Iowa IowaW, IowaCent, IowaNE, IowaS 

Kansas 

Kentucky 

Louisiana 

Maine 

Maryland 

Massachusetts 

Michigan 

Minnesota 

Mississippi 

Missouri 

Montana 

Nebraska 

Nevada 

NewHampshire 

NewJersey 

NewMexico 

NewYork 

NorthCarolina 

NorthDakota 

Ohio OhioNW, OhioS, OhioNE 

Oklahoma 

Oregon 

Pennsylvania 

RhodeIsland 

SouthCarolina 

SouthDakota 

Tennessee 

Texas 

Texas High Plains, Texas Rolling Plains, Texas Central 

Blacklands, Texas Edwards Plateau, Texas Coastal Bend, Texas 

South, TexasTrans Pecos, Texas East 

Utah 

Vermont 

Virginia 

Washington 

WestVirginia 

Wisconsin 

Wyoming 

The pulp and paper sector employs a slightly different (more aggregated) set of US 

regions than the 11 used by the agriculture and solid wood sectors, following the regional 

definition in the North American Pulp and Paper (NAPAP) model (Zhang et al, Ince). These are 

defined in Table 3-6. 
38 

Table 3-6 US Regions Used in Pulp and Paper Industry 

Key Region FASOMGHG Regions Included 

NO North NC and NE 

WEST West PNWW, PNWE, RM, and PSW 

SC South Central SC 

SE South East SE 

Modeling international trade in agriculture entails use of some other regional definitions 

outside of the US In particular, 27 foreign trading regions are employed as mapped in Figure 3-3 

and listed in table 3-7 below. The model’s forest sector considers explicit endogenous trade only 

with Canada. The Canadian regions employed are defined in Table 3-8. 

Table 3-7. Rest of World Production Trade Regions 

Key Region Counties Included 

1 WEST AFRICA Dahomey, Angola, Benin, Cameroon, Canary Island, Ghana, Guinea, 

Ivory Coast, Liberia, Mauritania, Niger, Nigeria, Senegal, Sierra Leone, 

Togo, Burkina, South W. Africa, Zaire 

2 NORTH AFRICA Algeria, Libya, Morocco, Tunisia 

3 EAST AFRICA Botswana, Malawi, Kenya, Mozambique, South Africa, Tanzania, 

Uganda, Zambia, Zimbabwe, Rwanda, Madagascar, Swaziland, Lesotho, 

Burundi 

4 EAST MED Egypt, Israel, Lebanon, Syria. 

5 RED SEA Ethiopia, Somalia, Sudan, Yemen. 

6 WEST ASIA Afghanistan, Bangladesh, Nepal, Pakistan, Sri Lanka, India. 

7 PERSIAN GULF Iran, Iraq, Kuwait, Saudi Arabia, Bahrain, Oman, Un Arab Em 

8 ADRIATIC Cyprus, Greece, Turkey. 

9 CHINA China 

10 SOUTHEAST ASIA Hong Kong, Indonesia, Malaysia, New Zealand, Okinawa, Philippines, 

Singapore, Thailand, Vietnam, Fr Pac Is, So Pac Is, Other Pac Is. 

11 JAPAN Japan 

12 SOUTH KOREA South Korea 

13 TAIWAN Taiwan 

14 EAST AMERICA Belize, Brazil, Costa Rica, El Salvador, Curacao, Guatemala, Honduras, 

Nicaragua, Panama, Paraguay, Suriname, Uruguay, Venezuela, Fr 

Guiana. 

15 CARRIBEAN Lee Wind Is, Bahamas, Barbados, Dominican Rep, Fr West Ind, Haiti, 

Trinidad, Jamaica. 

16 AUSTRALIA Australia 

17 N. CENTRAL EUROPE Austria, Belgium, Germany, Netherlands, Switzerland 

18 EAST BLOCK EUROPE Bulgaria, Czechoslovak, Hungary, Poland, Romania, Yugoslavia 

19 WESTERN EUROPE Italy, Malta, Portugal, Spain, Others 

20 ISLANDS Iceland, Ireland, U.K. 

21 SCANDINAVIA Denmark, Finland, Norway, Sweden 

22 CANADA Canada 

23 EAST MEXICO Mexico 

25 USSR Former USSR 

26 WEST AMERICA Bolivia, Chile, Colombia, Ecuador, Peru 
39 

27 BRAZIL Brazil 

28 ARGENTINA Argentina 

Figure 3-3. Non-US agricultural Regions Defined in Model

Removed to figures file 

Table 3-8. Canadian Regions used in Forest Sector Trade Modeling. 

 Key Region Provinces/countries 

CBCC Coastal British Columbia Coastal British Columbia 

CINT Interior Canada Interior British Columbia, 

Alberta, Saskatchewan, and 

Manitoba 

Regions used in 

Solidwood Sector 

CEST Eastern Canada The remainder of eastern 

Canada 

Regions used in Pulp CWEST Western Canada CBCC and CINT 

and Paper Sector CEAST Eastern Canada CEST 

Both the solid wood and fiber products sectors can also trade with an “off-shore” region. 

This is the aggregate of all off-shore trading areas. Both imports and exports to this region are 

exogenous and pre-specified before a run, except for softwood lumber imports in the solid wood 

sector. In the later case, an aggregate imports supply relation is employed to represent trade 

flows from these non-Canadian regions. 

3.4 Land base coverage 

FASOMGHG covers all crop land, pasture land and private timberland in production 

throughout the conterminous (“lower 48”) US. The remainder of this section describes the forest 

and agricultural land use definitions. The model’s treatment of land allocation decisions is 

described further below in the chapter. 

3.4.1 Agricultural land 

On the agricultural side, FASOMGHG separates land into 63 regions (Table 3-4) initially 

and 11 in later periods (as discussed in the following section). Four major types of land are 

specified. 

• Crop land is land suitable for crop production and is treated in four erodibility classes. 

The four erodibility classes are defined as follows. First, all crop land with USDA Land 

Capability Class III to VIII having a subclass of w (i.e., a wetness limitation for cropping) 

was grouped and labeled w3-8. The remaining crop land was divided into three groups 

according to its erodibility index (ei). The ei is either RKLS/T from the Universal Soil 
40 

Loss Equation (USLE) (Wischmeier and Smith, 1978) or WEQ/T from the Wind Erosion 

Equation, depending on whether wind or water erosion gives the larger ei (T, the soil loss 

tolerance level, is the maximum allowable erosion for sustained crop production. The 

three ei groups are: ei < 8.0 in loei; 8.0 <= ei < 20.0 in mdei; and ei ≥ 20.0 in svei. NRI 

data coupled with USDA National Agricultural Statistics Service (NASS) data on countylevel harvested acreage were used to specify land availability. 

• CRP land that is specified as land enrolled in the Conservation Reserve Program based 

on signups as of 2000. Land in the CRP is marginal crop land retired from production and 

converted to vegetative cover, such as grass, trees, or woody vegetation for the purpose 

of conserving soil, improving water quality, enhancing wildlife habitat, or producing 

other environmental benefits. 

• Pasture land is that suitable for livestock pasture. 

• AUM grazing supply is divided into public and private grazing on the subregional level. 

Public grazing is available at a constant price while private grazing can be obtained by an 

upward-sloping supply schedule. 

Agricultural land is allowed to move from the pasture land inventory into the crop land 

category and backwards. No more than 10 percent of the original endowment of pasture land can 

be converted to crop land on a regional over the whole time horizon. The conversion costs are set 

at the difference in the land rental rates between the alternative uses based on the assumed 

equilibration of land markets 

Land is also tracked by crop tillage system and irrigated/dryland status and the duration 

of time it has been in such a system to allow tracking of sequestered soil carbon and approach to 

a new soil carbon equilibrium after tillage change. 

3.4.2 Forestland 

Timberland refers to productive forestlands able to generate at least 20 cubic feet of live 

growing stock per acre per year and which are not reserved for uses other than timber production 

(e.g., wilderness use). Lands under forest cover that do not produce at least 20 cubic feet per 

year, called unproductive forestland, and timberland that is reserved for other uses are not 

considered part of the US timber base and are therefore not tracked by the model. In 

FASOMGHG, endogenous land use modeling is only done for privately held parcels, not 

publicly owned or managed timberlands. The only public land treatment is accounting for the 

quantity of timber cut from all US forestland owned and operated by any public entity as an 

exogenous assumption, and simulation of timber inventory levels for National Forest timberlands 

using exogenous timber harvest levels. In other words, the amount of public land in forests is not 

assumed to adjust to market conditions; rather, it is set by government administrative decree. 
41 

Private land in forestry is also treated according to its quality, and transferability between 

forestry and agricultural use. FASOMGHG includes three different site classes, as measures of 

forest productivity: 

• HIGH—high site productivity group (as defined in ATLAS), 

• MEDIUM—medium site productivity group; and 

• LOW—low site productivity group. 

The site groups were defined based on ATLAS inputs from the 1993 RPA Update 

(Haynes et al., 1995). Yields vary markedly by site groups. 

FASOMGHG also tracks land ownership including two private forest owner groups: 

forest industry (FI) and nonindustrial private forests (NIPF). The traditional definitions are used 

for these ownership groups, wherein industrial timberland owners are those that possess 

processing capacity for the timber, and NIPF owners do not. 

In terms of forest land, FASOMGHG tracks land in terms of the type of timber 

management, the species on the land, and the stand age. There are 18 different possible 

management intensity classes depending on whether thinning, partially cutting, passive 

management, some other management methods are used. The full spectrum of these management 

intensity classes is defined later in the forestry data chapter. There are also 25 different forest 

species types, which vary by region (e.g., Douglas fir and other species types in the West and 

planted pine, natural pine, and various hardwood types in the South), as defined in the forest data 

section below. In terms of stand age initially forest data and have forested stands are explicitly 

accounted for in five year cohorts in terms of the years it has occupied the land (not necessarily 

the tree age if older seedlings are transplanted in as is common in the South), with the age class 

scheme covering 0-4, 5-9, 10-14, etc., up to 95-00 and 100 plus years.

3.5 Production Modeling 

The production component includes agricultural crop and livestock operations, as well as 

private non-industrial and industrial forestry operations. Harvests from public forest lands are 

included in the model, but are treated as exogenously determined by the government. Production 

is modeled for the raw primary products listed in Table 3-6, except those imported. Production 

activity is depicted over a 70 to100-year period, with explicit accounting on a five year basis. 
42 

3.5.1 Agricultural and Biofuel feedstock Production 

Operationally, FASOMGHG contains an agricultural production model for the above 

listed primary crop, livestock, and biofuels feedstock commodities in each of the included five 

year periods. Agricultural crop, biofuels and livestock production competes for land, labor, AUM 

grazing, and irrigation water at the 63 or 11-region level, depending on the regional level for the 

included five year implementations (63 regions for the first 20 years and 11 thereafter). The cost 

of these and other inputs are included in the budgets for regional production variables. 

Budgets are present for the crop and biofuel feedstocks listed in Table 3-9. For each crop, 

production budgets are differentiated by region, tillage choice, fertilization alternative (three 

choices: 70, 85 and 100% of base levels), irrigated or dryland and crop land type (four as 

discussed in land use section above). Thousands of cropping production possibilities (budgets) 

represent agricultural production in each five year period. Biofuel feedstock possibilities are 

similar, except that irrigation is not an option. 

Table 3-9. Crops in FASOMGHG 

Crop Units 

Cotton Cotton in 1,000 acres 

Corn Corn in 1,000 acres 

Soybeans Soybeans in 1000 acres 

DurhamWheat Durham Wheat in 1000 acres 

HardRedSpringWheat Hard Red Spring Wheat in 1000 acres 

HardRedWinterWheat Hard Red Winter Wheat in 1000 acres 

SoftWhiteWheat Soft White Wheat in 1000 acres 

Sorghum Sorghum in 1000 acres 

Rice Rice in 1000 acres 

Oats Oats in 1000 acres 

Barley Barley in 1000 acres 

Silage Silage in 1000 acres 

Hay Other Hay in 1000 acres 

Alfalfa Alfalfa Hay in 1000 acres 

Sugarcane Sugar Cane in 1000 acres 

Sugarbeet Sugar Beets in 1000 acres 

Potatoes Potatoes in 1000 acres 

Fallow Fallow land in 1000 acres 

TomatoFrsh Tomatoes for fresh market in 1000 acres 

TomatoProc Tomatoes for processed market in 1000 acres 

OrangeFrsh Oranges for fresh market in 1000 acres 

OrangeProc Oranges for processed market in 1000 acres 

GrpFrtFrsh Grapefruit for fresh market in 1000 acres 

GrpFrtProc Grapefruit for fresh market in 1000 acres 

SwitchGrass Switch grass for biofuels 

HybrdPoplar Hybrid Poplar for biofuels 
43 

Willow Willow for biofuels 

Livestock production considers production of the animal types in Table 3-10. Livestock 

budgets are defined by region, animal type, enteric fermentation management alternative, manure 

management alternative, and feeding alternative. Hundreds of livestock production possibilities 

(budgets) represent agricultural production in each five year period. 

Table 3-10. Types of Animals in FASOMGHG 

Sheep Production of sheep in head 

CowCalf Cow calf production per cow 

FeedlotBeefYearlings Beef feeding of yearlings in units of head 

FeedlotBeefCalves Beef feeding of calves in units of head 

Dairy Dairy Production in units of cows 

HogFarrowtofinish Hog farrowing to finishing in unit of head of finished hog 

FeederPigProduction Feeder pig production in unit number of sows 

PigFinishing Pig finishing in unit of finished hog 

HorsesandMule Other livestock mainly horses in number of head 

SteerCalfStocker Stocker operation with steer calves in number of calves 

HeiferCalfStocker Stocker operation with heifer calves in number of calves 

SteerYearlingStocker Stocker operation with steer yearlings in number of yearlings 

HeiferYearlingStocker Stocker operation with heifer yearlings in number of yearlings 

produceTurkey Turkeys produced in units of birds reported in thousands 

Broiler Broilers produced in units of birds reported in thousands 

Egg Egg production on a 1 laying hen basis 

Supply curves for agricultural products, and GHG mitigation are implicitly generated 

within the system as the outcome of competitive market forces and market adjustments. This is 

in contrast to supply curves that are estimated from observed, historical data. This approach is 

useful in part because FASOMGHG could be employed to analyze conditions which fall well 

outside the range of historical observation (such as large scale tree-planting programs). 

3.5.2 Forest Production 

The forest production component of FASOMGHG depicts the use of existing private 

timberland1 as well as the reforestation decision on harvested land. Timberland is differentiated 

 

1Timberland is the subset of forestland that is capable of producing at least 20 cubic feet per acre per year of 

industrial wood at culmination of mean annual increment and is not withdrawn from timber harvesting or related 

timbering activities. 
44 

by region, the age cohort of trees,1 ownership class, cover type, site condition, management 

regime, and suitability of the land for agricultural use. These forestry activities produce the log 

products listed in Table 3-6 (primary product table). Decisions pertaining to timber management 

investment are endogenous. Actions on the inventory are depicted in a framework that allows 

timberland owners to institute management activities that alter the inventory consistent with 

maximizing the net present value of the returns from the activities. The timberland decisions for 

existing stands involve selecting the harvest age. Lands that are harvested and subsequently 

reforested or lands that are converted from agriculture to forestry (afforested) introduce decisions 

involving the choice of species type, management type, and future harvest age. 

3.6 Land Allocation 

Underlying the commodity production described above and the GHG consequences 

thereof is the decision by landowners on how much, where, and when to allocate land across the 

two sectors. Endogenous land allocation across sectors sets FASOMGHG (and FASOM) apart 

from other forest and agricultural sector models of the US The conceptual foundation for land 

allocation is described below. 

3.6.1 Scope for Land exchanges between sectors 

The basic structure of the land exchanges is portrayed in Figure 3-1. In terms of 

transferability between agriculture and forestry there are five land suitability classes: 

• FORONLY—includes timberland acres which can not be converted to agricultural uses; 

• FORCROP—includes acres which begin in timberland and which can be converted to 

crop land; 

• FORPAST—includes acres which begin in timberland and which can be converted to 

pasture land; 

• CROPFOR—includes acres which begin in crop and which can be converted to 

timberland; and 

• PASTFOR—includes acres which begin in pasture and which can be converted to 

timberland. 

Land can flow between the agricultural and forestry sectors or vice versa in the 

FORCROP, FORPAST, CROPFOR, and PASTFOR land suitability categories. Land 

movements in forestry are only allowed in the NIPF owner category. When land transfers from 

 

1Timberlands are grouped in 21 five year cohorts, 0 to 4 years, 5 to 9,..., up to 100+ years. Harvesting is assumed to 

occur at the midyear of the cohort. 
45 

forestry to agriculture, it requires an investment to clear stumps, level, and otherwise prepare the 

land for planting. Land moving from agriculture to forestry must be planted to forest and land 

movement from forestry occurs only upon timber harvest. Agricultural land can move to other 

uses during any of the five year model periods, but when afforested it begins in the youngest age 

cohort of timberland. 

When land moves from or to agricultural crops, it involves the high quality forest site 

class and moves in the erosion classes proportional to their existence in the region. Movements 

involving pasture come from the medium quality forest site class. Movements from pasture to 

timberland are also proportional across all erodibility classes. 

Land also moves into non-agricultural and non-forestry uses (e.g., shopping centers, 

housing, and other developed and infrastructural uses) based on exogenous estimates by Alig et 

al. (2004) and in proportion to the initial land endowments at exogenously specified rates. Land 

movement from forestry again occurs only upon timber harvest. 

Figure 3-1. Characterization of land movements 

Removed to file fasomGHGfigures

DROP (TAMM based) FROM FIGURE 

3.6.2 Nature of Land Supply 

In FASOMGHG, the initial land endowment is fixed. However, since land is allowed to 

move between forest and agriculture, agricultural production faces an endogenous excess land 

supply equation from forestry. Forestry production, in turn, faces an endogenous excess land 

supply equation from agriculture. Conservation Reserve Program (CRP) land is assumed to be 

permanently fixed at the initial levels, unless manipulated by a policy scenario. Animal Unit 

Month (AUM) grazing land supply is specified using an upward-sloping supply function 

reflecting the availability of more remote and less suitable lands. 

3.7 Non-Land Factor Modeling 

In addition to land, FASOMGHG depicts factor supply of water, labor, AUM grazing, 

other agricultural inputs in agriculture, as well as non-wood inputs in the forest sector. 
46 

On the agricultural side, water and labor are available in each of the 11 or 63 agricultural 

regions (recall agricultural regional definitions will generally aggregate from 63 to 11 regions 

after the first 20 years of model runs). Labor is available on an 11 region basis. Supply curves 

for all three items have a fixed price component and an upward sloping component, representing 

rising marginal costs of higher supply quantities. For water, the fixed price is available to a 

maximum quantity of federally provided agricultural water, while pumped water has an upward 

sloping supply curve and is subject to maximum availability. For AUMs, the fixed price is 

available to a maximum quantity of public grazing, while private grazing has an upward sloping 

supply curve and is subject to maximum availability. For agricultural labor, the fixed price is 

available to a maximum quantity of federally provided agricultural water, while pumped water 

has an upward sloping supply curve and is subject to maximum availability. Other inputs are 

assumed to be infinitely available at a fixed price (i.e., the agricultural sector is a price taker in 

these markets). 

On the forestry side, non-wood inputs are available on an upward sloping basis and 

include hauling, harvesting, and product processing costs. Other forest costs are assumed to be 

infinitely available at a fixed price. 

3.8 Product Processing Modeling 

As indicated above, raw product commodities are converted on both the agricultural and 

forestry sides into processed products. The processing activities in the model generally reflect a 

somewhat simplified view of the resources used in processing. They largely contain primary 

commodity usage, secondary commodity yield, and a level of cost. Thus, for example, in 

soybean crushing the processing activity uses one unit of soybeans and generates a given number 

of pounds of soybean meal and tons of soybean oil at a specified cost. The cost on the 

agricultural side is usually the observed price differential between the value of the outputs and 

the value of the inputs according to USDA Agricultural statistics (1990-2002). On the forestry 

side, the non-wood input supply curve provides the cost of processing wood. 

Wood product processing is always regionalized with different data in the 9 forest 

production regions and the Canadian regions. Agricultural processing is regionalized for 

biofuels, soybean crushing, wet milling, electricity generation from willow, switch grass and 

poplar and ethanol production from corn, willow, switch grass and poplar as will be discussed 

below. For the remaining agricultural items listed in Table 3-11, below the processing is done at 

a national level as discussed below. 
47 

Table 3-11. Agricultural Processing Alternatives 

Processing activity code Brief description

BroilChick Convert broilers to chicken meat 

ButterPow Make butter and non fat dry milk powder 

CaneRefine Convert raw cane sugar to refined sugar 

Chip-Pot Make potato chips 

ClCowSla Convert cull cow to non fed slaughter 

CleanWool Convert wool to clean wool 

Cottage Make cottage cheese 

DClfToBeef Convert cull dairy calf to non fed slaughter 

DCowSla Convert cull dairy cow to non fed slaughter 

DeHydr-Pot Make dehydrated potatoes 

EvapoMilk Make evaporated milk 

FluidMlk1 Make 2 percent milk 

FluidMlk2 Make skim milk 

Frozen-Pot Make frozen potatoes 

FSlatofBe Convert fed animal to fed slaughter 

Gluttosbm Substitute gluten feed for soybean meal 

HeiferYearlingSlaughter Slaughter a heifer yearling 

HogToPork Convert finished hogs to pork 

HybridpoplarToElec Make hybrid poplar into electricity 

HybridpoplarToEthanol Make hybrid poplar into ethanol 

IceCream1 Make ice cream alternative 1 

IceCream2 Make ice cream alternative 2 

JuiceGrpft Make grapefruit juice 

JuiceOrang Make orange juice 

makeAmCheese Make American cheese 

makeBaking Make sweetened baked goods 

makeBeverages Make sweetened beverages 

makeCanning Make sweetened canned goods 

makeConfection Make sweetened confectionaries 

makeCSyrup Make corn syrup 

makeEthanol Make ethanol 

makeHFCS Make high fructose corn syrup 

makeMktGasBlend Make unsubsidized liquid fuel blending gasoline & ethanol 

makeOtCheese Make other cheese 

makeSubGasBlend Make subsidized liquid fuel blending gasoline & ethanol 

makeDextrose Make dextrose 

NFSlatonF Convert non fed animal to non fed slaughter 

RefSugar1 Convert sugar cane to raw cane sugar 

RefSugar2 Convert sugar beets to refined sugar 

SowToPork Convert cull sow to pork 

SoyCrush1 Crush soybeans 

StockHeiferCalftoFeed Move stocked heifer calf into feedlot 

StockHeiferYearlingtoFeed Move stocked heifer yearling into feedlot 
48 

StockSteerCalftoFeed Move stocked steer calf into feedlot 

StockSteerYearlingtoFeed Move stocked steer yearling into feedlot 

SteerYearlingSlaughter Slaughter a steer yearling 

TurkeyProc Convert live turkeys to turkey meat 

SwitchgrassToElec Make switchgrass into electricity 

SwitchgrassToEthanol Make switchgrass into ethanol 

WetMill Wet mill corn 

WillowToElec Make willow into electricity 

WillowToEthanol Make willow into ethanol 

3.9 Market Modeling 

xxxRecommendation: This section could really benefit from a table that shows which 

products are represented by different supply regions in the US, whether demand is regional or 

national, whether international trade is included and, if so, how is international trade tracked 

regionally outside of the US 

The model solves by ensuring that each affected market is in equilibrium, wherein the 

quantity supplied equals the quantity demanded. This involves a mixture of implicit and explicit 

demand and supply curves in each five year period. Generally these involve 

• regional product supply, 

• national raw product demand, 

• regional or national processed commodity demand, 

• regional or national supply of processed commodities, 

• regional or national (depending on commodity) export demand 

• regional or national (depending on commodity) import supply, 

• regional feed supply and demand, 

• regional direct livestock demand, 

• interregional transport perfectly elastic supply, 

• international transport perfectly elastic supply and 

• country-specific excess demand and supply of rice, sorghum, corn, soybeans and the 5 

types of wheat 

On the forestry side, all commodities are produced regionally and are then transported to 

meet a national demand at a fixed transport cost. Canadian sawlog production is based on 

regional log supply curves and must be processed within the region of origin. The only exception 

is a small volume of log exports from Canada to the US and other regions which are treated as 

exogenous export flows from Canada and an exogenous import flow to the US. Endogenous 
49 

export flows from Canada include softwood lumber, OSB and all fiber products to the US. US 

exports to Canada are exogenous. 

On the agricultural side, corn, soybeans, four types of wheat, rice, and sorghum are 

modeled with US regional features and explicit demand in 27 foreign regions. The processed 

commodities of soybean meal, gluten feed, starch, and all livestock feeds are manufactured and 

used on a FASOMGHG 11 market region basis but go into national demand and international 

trade. 

3.10 GHG Treatment 

FASOMGHG quantifies the stocks of GHGs emitted from and sequestered by agriculture 

and forestry, plus the stock on lands in the model that are converted to nonagricultural, nonforest 

developed usages. In addition, the model tracks GHG emission reductions in other sectors caused 

by mitigation actions in the forest and agricultural sectors -- for example, reduced GHG 

emissions from fossil fuel use in the energy sector due to supply of renewable biofuel feedstocks 

from agriculture. 

As indicated above, GHGs tracked by the model include carbon dioxide (CO2) -- 

sometimes expressed in carbon (C) equivalent, methane (CH4), and nitrous oxide (N2O). The 

GHG accounting spans across both sectors and biofuels. A list of all the categories in the GHG 

accounting appears in Table 3-12 below. 

Table 3-12. List of All GHG Accounts in FASOMGHG 

Account Name Brief description 

Forest_ContinueSoil Carbon in forest soil of forests that remain forests 

Forest_AfforestSoil Carbon in forest soil of afforested forests 

Forest_ContinueLitUnd Carbon in litter and understory of forests that remain 

forests 

Forest_AfforestLitUnd Carbon in litter and understory of afforested forests 

Forest_ContinueTree Carbon in trees of forests that remain forests 

Forest_AfforestTree Carbon in trees of afforested forests 

Forest_USProduct Carbon in US consumed and produced wood products 

Forest_CANProduct Carbon in US consumed but Canadian produced wood 

products 

Forest_USExport Carbon in US produced but exported wood products 

Forest_USImport Carbon in US consumed but imported from non 

Canadian source 

Forest_USFuelWood Carbon in US consumed fuelwood 

Forest_USFuelResidue Carbon in US residue that is burned 

Carbon_For_Fuel Carbon emissions from forest use of fossil fuel 

Dev_ForestLand Carbon on forest land after it moved into developed use 

Dev_AgLand Carbon on agricultural land after it moved into 

developed use 
50 

AgSoil_Continue_Till Carbon on land moving continuing initial tillage 

Soil_AgToForest Carbon deductions when moving land between crops 

and forest 

AgSoil_Change_Till Carbon on land changing intensity of tillage 

AgSoil_ToFromPast Carbon on land changing between pasture and crop 

AgSoil_Pasture Carbon on land remaining as pasture 

AgSoil_IdlePasture Carbon on land that is idle pasture land 

Carbon_SoilCmix Soil carbon differences due to crop 

Carbon_AgFuel Carbon emissions from ag use of fossil fuel 

Carbon_Dryg Carbon emissions from grain drying 

Carbon_Fert Carbon emissions from fertilizer production 

Carbon_Pest Carbon emissions from pesticide production 

Carbon_Irrg Carbon emissions from irrigation water pumping 

Carbon_Ethl Carbon emission savings from ethanol production 

Carbon_CEth Carbon emission savings from cellulosic ethanol 

production 

Carbon_BioFuel Carbon emission savings from biofuel production 

Methane_Liquidmanagement Methane from Emission savings from improved manure 

technologies 

Methane_EntericFerment Methane from Enteric Fermentation 

Methane_Manure Methane from Manure Management 

Methane_RiceCult Methane from Rice Cultivation 

Methane_AgResid_Burn Methane from Agricultural Residue Burning 

Methane_BioFuel Methane emissions of biomass power plants below coal 

power plants 

Methane_Ethl Methane emission savings from Corn ethanol processing 

Methane_CEth Methane emission savings from cellulosic ethanol 

processing 

NitrousOxide_Manure Livestock Manure Practices 

NitrousOxide_Biofuel Nitrous oxide emissions of biomass power plants over 

coal power plants 

NitrousOxide_Ethl Nitrous oxide emission savings from Corn ethanol 

processing 

NitrousOxide_CEth Nitrous oxide emissions from cellulosic ethanol 

processing 

NitrousOxide_Fert N Fert Application Practices under Managed Soil 

Categories under AgSoilMgmt 

NitrousOxide_Sludge Emissions from sewage sludge used as crop fertilizer 

NitrousOxide_Nfixing Emissions from N fixing crops 

NitrousOxide_CropResid Emissions from Crop residue retention 

NitrousOxide_Histosoil Emissions from Temperate histosoil area 

NitrousOxide_Volat Indirect soils volatilization 

NitrousOxide_Leach Indirect soils Leaching Runoff 

NitrousOxide_AgResid_Burn Agricultural Residue Burning 

3.10.1 Forest GHG Accounts 

Forest GHG accounting includes carbon sequestered, carbon emitted, and fossil fuelrelated carbon emissions offset. Sequestration accounting encompasses carbon in standing trees, 

forest soils, forest understories and floors including woody debris, and wood products both in use 

and in landfills. The sequestration accounting involves both increases and reductions in stocks, 

with increases entered when land moves into the forest uses, trees grow, and products are placed 
51 

in long-lasting uses or landfills. Reductions arise when timber stands are harvested, land is 

migrated to agriculture or development, and products decay in their current uses. 

Forest-related emissions accounting counts the GHGs emitted when fossil fuels are 

combusted in forest production. Forest-related GHG offset accounting is done for the estimated 

amount of fossil fuel fuels that are saved when wood products are combusted in place of fossil 

fuels, particularly when milling residues are burned. In addition, wood products may be used as a 

biofuel to offset fossil fuel emissions, as discussed in the biofuels section below. 

Forest carbon accounts also include the carbon content of products imported into the US 

or exported out of the US. In particular there is accounting for products: 

• Processed in and coming from Canada, 

• Imported from other countries, and 

• Exported to other countries. 

These categories may or may not be included in an incentive scheme for GHG mitigation, 

as they will generally be accounted for elsewhere. Nonetheless, the accounts are included in the 

model in case they are needed for policy analysis. 

More detail on the data and models used to estimate forest carbon stock accumulation is 

included in Chapter 8. 

3.10.2 Agricultural GHG Accounts 

On the agricultural side, the main features of the GHG accounting are those listed in table 

3-13 below. Again, there is coverage of the emissions, sequestration, and offsets. Agricultural 

emissions arise from crop and livestock production, principally from: 

• fossil fuel use, 

• nitrogen fertilization usage, 

• rice production, 

• enteric fermentation, and 

• manure management and other categories that are not fully listed in table but are given in 

the previous table. 

Agricultural sequestration involves the amount of carbon sequestered in agricultural soils, 

due principally to choice of tillage, and irrigation along with changes to crop mix choice. 

Sequestration is also considered in terms of grasslands versus crop land or mixed usage, where 

crop land can be moved to pasture use or vice versa. The sequestration accounting can yield 
52 

either positive or negative quantities, depending upon the direction of tillage (conventional, low, 

or zero tillage) and irrigation choices, along with pasture land (grassland)/crop land land 

conversions. The sequestration accounting will also have a negative term when land moves out 

of agriculture into forestry or developed use. Although in the case of forestry, the loss in 

agricultural carbon will typically be more than offset by gains in forest carbon. 

Table 3-13. Mitigation strategies in FASOMGHG 

 GHG affected 

Mitigation strategy Strategy Nature CO2 CH4 N2O 

Biofuel production Offset X X X 

Crop mix alteration Emission, Sequestration X X 

Rice acreage reduction Emission X 

Crop fertilizer rate reduction Emission X X 

Other crop input alteration Emission X 

Crop tillage alteration Sequestration X 

Grassland conversion Sequestration X 

Irrigated /dry land conversion Emission X X 

Livestock management Emission X 

Livestock herd size alteration Emission X X 

Livestock system change Emission X X 

Liquid manure management Emission X X 

3.10.3 Biofuels 

Commodities that are endogenous can be used as feedstocks for biofuel production 

processes offsetting fossil fuel usage and their GHG emissions. Three forms of biofuel 

production are included. 

• Usage of switchgrass, poplar, willow, wood chips or mailing residues as inputs to electric 

generating power plants replacing coal usage. 

• Usage of corn, switchgrass, poplar, or willow for conversion to ethanol and replacement 

of carbon emissions from petroleum usage. 

• Usage of soybean oil or corn oil in the production of diesel fuel (xxxnote the above lists 

of commodities, GHG accounts, and processing alternatives does not reflect this). 
53 

In all these cases the GHG offset is the GHGs in the burning and producing the fossil fuel 

less the fossil fuel related emissions cost of producing the biofuel feedstock. The combustion 

emissions from the biofuels feedstock are not accounted as they are assumed to be offset by 

absorption of GHGs from the atmosphere by photosynthesis during plant growth. 

3.10.4 Land to Development 

FASOMGHG incorporates exogenous data that specify the rate of conversion of 

agriculture and forestry lands to nonagricultural and nonforestry developed uses. Simplified 

accounting is employed to estimate the carbon sequestered on these lands, as described in the 

GHG data sections of Chapter 13. 

3.10.5 Non-GHG Environmental Indicators 

FASOMGHG considers a number of environmental indicators above and beyond the 

GHG accounts. The main components are nitrogen and phosphorus runoff, soil erosion, 

irrigation water usage, and a number of descriptions of total resource use and activity within the 

agricultural and forestry sectors (total land use, total pasture use, manure load, livestock 

numbers, total afforestation, etc.). More information on these variables is provided in the Chapter 

on FASOMGHG output. 

3.11 Temporal Scope and Dynamics 

FASOMGHG is typically run as a 100-year model depicting land use, land transfers, and 

other resource allocations between and within the agricultural and forest sectors in the US The 

model solution portrays a multiperiod equilibrium on a five year time step basis. The results from 

FASOMGHG yield a dynamic simulation of prices, production, management, consumption, and 

GHG effects within these two sectors under the scenario depicted in the model data. 

FASOMGHG incorporates expectations of future prices. Farmers and timberland owners 

are able to foresee the consequences of their behavior (when they plant trees or crops) on future 

stumpage and agricultural product prices and incorporate that information into their behavior. 

FASOMGHG uses deterministic expectations, or "perfect foresight," whereby expected future 

prices and the prices that are realized in the future are identical. Net present value related profit 

maximizing behavior is assumed. 

The possibility of planting trees with a rotation length that would carry them beyond the 

explicit time frame of the model necessitates the specification of "terminal conditions". At the 
54 

time of tree planting, producers should anticipate a flow of costs and returns which justify stand 

establishment costs. The planting of a timber stand with an expected 30-year life in year 80 of a 

100-year projection is potentially problematic, however, because the anticipated harvest date is 

beyond the model time frame. A mechanism is needed to reflect the value of timber inventory 

carried beyond the explicit model time frame. This is done with "terminal conditions," which 

represent the projected net present value of an asset for all time periods beyond the end of the 

explicit model projection. Terminal conditions are resolved using downward sloping demand 

curves for the terminal inventory. 

Several types of terminal inventory are valued in FASOMGHG: a) initial timber stands 

that are not harvested during the projection; b) reforested stands remaining at the end of the 

projection; and c) agricultural land retained in agriculture. Specific valuation approaches for each 

of these elements are discussed chapters 7 and 8 below. 

3.12 Dynamic Yield, Cost, and Demand Updating 

Features have been added to FASOMGHG to reflect changes over time in market and 

production conditions. Different updating procedures are used in agriculture and forestry as 

explained in the chapters on the forest and agricultural submodels below.
55 

4 CHAPTER 4 ECONOMICS UNDERLYING FASOMGHG 

A number of basic economic principals are involved in forming FASOMGHG and 

provide the assumptions under which it simulates behavior. These are explained in this section 

4.1 Simulation of perfectly competitive behavior 

FASOMGHG employs an approach originally motivated by Enke (1951) and Samuelson 

(1952) that was later it was fully developed by Takayama and Judge (1973). as explained in the 

literature review by McCarl and Spreen (1980). In this approach, an optimization problem is 

defined and solved using a set of equations that specify attainment of an economic equilibrium. 

Underlying this mechanism is the First Fundamental Theorem of Welfare Economics, which 

dictates that an allocation of resources that maximizes producers’ profits, consumers' utility, and 

clears all markets, is Pareto Optimal (PO), an allocation which is at least as good as any other 

possible allocation. FASOMGHG is structured around the PO theoretical foundation and 

mathematical programming is used to maximize the sum of consumers' and producers’ surpluses, 

subject to a set of supply demand balances, and resource restrictions, to ensure that the PO 

condition is met. 

Mathematically, FASOMGHG solves an objective function to maximize net market 

surplus, represented by the area under the product demand function (an aggregate measure of 

consumer welfare) less the area under factor supply curves (an aggregate measure of producer 

costs). Such an approach involves solution of a nonlinear programming model and with 

endogenous product and factor prices. The resultant objective function value is consumers' plus 

producers' surplus. 

Figure 4.1 Objective function representation 

Removed to figure file 

The problem is now expressed in equation form. Suppose we have a demand curve 

Pd = f (Qd,) {xxxstart numbering the equations) 

and a supply curve 

Ps = f (Qs,)
56 

In turn, for a perfectly competitive market we would have a set of market equilibrium conditions 

requiring prices and quantities to equilibrate 

Pd = Ps 

Qd = Qs 

The mathematical programming approach to formulating such problems was motivated by 

Samuelson (1952), who suggested solving optimization problems whose first-order conditions constituted 

a system of equations characterizing an equilibrium. Suppose we follow this approach by first defining a 

system of equations, then posing the related optimization problem. In this case the equilibrium would 

simultaneously solve the equations 

d s

d s

d s

Q Q

and

f(Q ) f(Q )

or

P P

=

=

=

One should also recognize some possible peculiarities of the equilibrium. Namely it is possible 

that the markets could clear at zero quantity, in which case the supply price might be greater than or equal 

to the demand price. Thus, we can write the condition that the equilibrium price (P*

) is greater than or 

equal to the demand price 

* f(Qd ) ≤ P

Simultaneously, the market price may be less than the supply price, 

* f(Qs ) ≥ P

One can also argue that these two relations should only be inequalities when the quantity 

supplied or demanded equals zero. Namely, when the demand price is less than the equilibrium price, 

then no quantity should be demanded. Similarly, when the supply price is greater than the equilibrium 

price, then no quantity should be supplied. Simultaneously, when a non-zero quantity is supplied or 

demanded, then the equilibrium price should equal the supply or demand price. This relationship can be 

expressed through complementary slackness relations where 
57 

(f(Q ) - P ) Q 0

(f(Q ) - P ) Q 0

s

*

s

d

*

d

=

=

One should also recognize that the quantity supplied must be greater than or equal to the 

quantity demanded 

s Qd Q ≥ 

but, if the quantity supplied is strictly greater than the quantity demanded, then the equilibrium 

price should be zero. Mathematically this relationship is 

( Q Q )P 0 * − s + d =

Finally, we state nonnegativity conditions for price and quantities, 

Q , Q , P 0. *

d s ≥

The above equations are similar to Kuhn-Tucker conditions. In particular, if P*

 is taken to be a 

dual variable, then the above equation system is equivalent to the Kuhn-Tucker conditions of the 

following optimization model 

Q , Q 0

s.t. Q Q 0

Max f(Q ) Q f(Q ) Q

d s

d s

0

s s

0

d d

* Qs * Qd

≥

− ≤

− ∫ ∫ d d

Where the Lagrangian and Kuhn -- Tucker conditions are 
58 

, , 0

( ) 0 ( , , )

( ( ) ) 0 ( , , )

( ( ) ) 0 ( , , )

( ) 0 ( , , )

( ) 0 ( , , )

( ) 0 ( , , )

( , , ) f(Q ) Q f(Q ) Q ( )

* Qd * Qd

0

d d

0

d d

≥

=− − = ∂

∂

= − + = ∂

∂

= − = ∂

∂

=− + ≥

∂

∂

=− + ≤

∂

∂

= − ≤

∂

∂

= − − − ∫ ∫

λ

λ λ λ

λ λ

λ λ

λ

λ

λ λ

λ λ

λ λ

d d

d s

d

d s

s s s

d

d s

d d d

d

d s

d s

d s

s

d s

d

d

d s

d s d s

Q Q

Q Q Q

L Q Q

Q f Q Q Q

L Q Q

Q f Q Q Q

L Q Q

Q Q L Q Q

f Qs Q

L Q Q

f Q Q

L Q Q

L Q Q d d Q Q

and if P* is used in place of λ then the systems are mathematically the same. 

Thus, solving the optimization problem generates a solution which is an equilibrium. In 

this problem, the area under the demand curve above the price line yields consumers' surplus, 

while, the total revenue (price times quantity) less the area under the supply curve yields revenue 

minus production cost, or producers' surplus. 

4.1.1 Adding production 

The above presentation was restricted to a single commodity with explicit supply and 

demand curves. However, one can depict commodity demand for multiple products without 

explicit supply for those products, but rather with a production process and factor supply for 

inputs. Such models have exogenous factor supply and product demand curves, but implicit 

factor demand and product supply. Such a model can be expressed as follows. 
59 

() ()

β

β

β

β β β

β

β β

β

β β

Z , X , Q 0 for all i, h, k and

 b Q Y for all j and

- X a Q 0 for all i

s.t. Z - C Q 0 for all h

Max P Z dZ - P X dX

h i k

j

k

j k k

k

i i k k

k

h h k k

i i

i

X

0

h h si

h

Z

0

dh

h i

≥

≤

+ ≤

≤

∑

∑∑

∑∑

∑ ∫ ∑ ∫

This problem assumes that a number of different types of firms (β) are being modeled. 

Each firm has a finite set of production processes (k) which depict particular ways of combining 

fixed factors (j) with purchased factors (i) to produce commodities (h). The symbols in the 

formulation are: Pdh(Zh) is the inverse demand function for the hth commodity; Z h is the quantity 

of commodity h that is consumed; Psi (Xi) is the inverse supply curve for the ith purchased input; 

Xi is the quantity of the ith factor supplied; Qβk is the level of production process k undertaken by 

firm β; Chβk is the yield of output h from production process k; bjβk is the quantity of the jth

owned fixed factor used in producing Qβk; aiβk is the amount of the ith purchased factor used in 

producing Qβk and Yjβ is the endowment of the jth owned factor available to firm β. 

An investigation of the Kuhn-Tucker conditions would show that the shadow price on the 

first and second rows are, respectively, the demand and supply prices. The conditions for the Q 

variable indicates that production levels are set so the marginal value of the commodities 

produced is less than or equal to the marginal costs of the owned and fixed factors for each Qβk. 

The model formulation assumes that: 1) the supply and demand equations are integrable; 

and, 2) product demand and factor supply functions are truly exogenous to the model. 

The area under the product demand and factor supply functions makes the objective 

function equal consumers' plus producers' surplus, which is the net social benefit generated by 

the market exchange of these goods. The solution of the model generates equilibrium price and 

quantity for each output, and purchased input, along with the imputed values for the owned 

factors of production. 

The model formulation assumes that the sector is composed of many micro-units, none of 

which can individually influence output or factor prices. Each micro-unit supplies output at the 

point where marginal cost equals product price, and utilizes purchased inputs at the point where 

the marginal value product of each purchased input equals its market price. Thus, the sectoral 

supply of output schedule corresponds to an aggregate marginal cost schedule, and the sectoral 
60 

derived demand schedule for purchased inputs corresponds to the aggregate marginal value 

product schedule. Hence, the model does not take product supply or factor demand schedules as 

input, rather these schedules are derived internally based upon production possibilities, output 

demand and purchased input supply. 

The competitive behavior simulating properties of this formulation provides a powerful 

tool for policy simulation. Except in centrally planned economies, the government cannot dictate 

production patterns consistent with its objectives. This formulation recognizes the difference and 

possible conflict between government and producer objectives (see Candler, Fortuny, and 

McCarl 1981 for elaboration). The model allows policies to be specified, then simulated in terms 

of projected sectoral response to the policy change. The model does not assume participants 

respond to government wants; each producer optimally adjusts so as to maximize profits. 

Producer adjustment is endogenous to the model. 

4.2 Behavior over time using discounted NPV 

Given the modeling of multiyear timber production, FASOMGHG needs to handle 

economic returns over time. This is done by solving for multiple interlinked market equilibria in 

adjacent five year periods for the model duration, rather than for just one single period (as would 

be the case in a static equilibrium model). The FASOMGHG objective function depicts 

maximization of the net present value of producers' and consumers' surpluses, associated with 

production and price formation in competitive markets over time for both agricultural and wood 

products. In that sense, the first-order (Kuhn-Tucker) conditions for the choice variables in the 

model provide a set of optimization rules for economic agents to follow, leading to the 

establishment of a competitive equilibrium. 

Because these choices occur over time, the optimizing nature of the model holds that 

producers and consumers' have perfect foresight regarding future demand, yields, technologies, 

and prices. In other words, choices made at the beginning of the projection period are based on 

correct expectations of what the model predicts will occur in the future. 

Perfect foresight employs the assumption that agents are rational and respond with the 

best information they have available at the time. This draws on well-established economic 

theories about rational expectations (Muth 1961) and intertermporally efficient capital markets 

(Fama 1970). 
61 

4.2.1 Discounting 

The multiperiod nature of the economic problem requires transforming future revenues 

and costs to the present using a real (inflation-adjusted) annual discount rate. The default rate 

used is 4 percent, which is broadly consistent with opportunity costs of capital in agriculture and 

forestry. The default rate can be altered to test the sensitivity of model results to alternative 

discount rates. Higher discount rates devalue future revenue and cost streams. Because forestry is 

an enterprise with revenue streams that are deferred often several time periods beyond the 

incidence of initial establishment and ongoing management costs, forestry returns can generally 

be expected to be particularly sensitive to the chosen discount rate. Moreover, the discount rate 

can significantly affect the timing of land use, investment and harvest decisions with effects 

reaching broadly across both sectors in the model. 

4.2.2 Need for terminal conditions 

Given that the model is defined for a finite time period (e.g., 70-100 years), there will be 

immature trees of some age at the end of the time period modeled. If the model did not place a 

value on these forests, the optimizing nature of the model would be inclined to deplete all timber 

at the end of the projection period rather than leave it around for future harvests. Similarly, 

agricultural land values at the end of the period must also be considered to ensure that land is not 

inappropriately converted as a result of a perceived lack of opportunity cost. 

To counter these ending-period anomalies, terminal conditions are imposed on the model 

that value ending immature trees and land remaining in agriculture. FASOMGHG assumes that 

forest management is, from the last period onward, a continuous or constant flow process with a 

forest inventory that is fully regulated on rotations equivalent to those observed in the last time 

periods of the projection (see Adams et al. [1996]). Demand functions for timber are used in this 

period assuming that the fully regulated volume persists forever. The terminal value of land 

remaining in agriculture is formed by assuming that the last period persists forever. 

4.3 Dynamics of harvest 

FASOMGHG endogenizes the harvest date for a timber stand, assuming it is past an 

exogenously determined region-specific minimum harvest age. The harvest alternatives are 

differentiated by the model’s five year time periods. Thus a 40 year old Pacific Northwestwestside (PNWW) timber stand (which is beyond the minimum harvest age for that region) 

could be harvested now, five years from now, ten years from now, etc. The decision whether to 

harvest a stand or extend it until the next period depends on whether the discounted value of its 
62 

five year growth plus the value of any price change by extending the harvesting period exceeds 

the discounted cost of holding it into the next period, which consists of any realized production 

costs plus the difference in the opportunity cost of the land. The value of the timber when 

withheld from current harvesting is the price five years from now times the yield at that point. 

Naturally this is taken into account in the optimization for all the possible future harvest periods. 

4.4 Land exchanges 

FASOMGHG reflects the mobility of the land resource between the two sectors subject 

to controls for land quality/growing conditions, investments needed to mobilize land, and hurdle 

costs consistent with observed behavior. The land quality factors generally restrict some lands to 

only be in forest, due to topography or soil characteristics. Likewise, the growing conditions 

render some lands unsuitable for forest uses at all, particularly in the drier plains areas of the 

country, and would thus be suitable only for some agricultural uses. 

The investments to mobilize land from forest to agriculture generally involve stump 

clearing, leveling, etc. of forested lands and result in a three step depiction of land transformation 

processes. The hurdle costs reflect costs to move land between uses where for example it may 

take an income differential above and beyond the opportunity cost in agriculture to get 

agricultural producers to switch to forestry. Such evidence is based on the econometric findings 

of Lubowski, Plantinga and Stavins (xxxcite). 

Given these model attributes, the economic conditions for land movement are that when 

land moves into forestry, the net present value of the returns from one rotation in forestry plus 

the future value of forest land beyond the first rotation must be greater than the net present value 

of the land remaining in agriculture by at least the hurdle cost. For land moving from forest to 

agriculture, the net present value of land in agriculture must exceed returns to a rotation in 

forestry plus the future value of forested land by the investment cost to transfer land plus any 

hurdle cost (this term is currently set to zero). In both land transfer cases, the land moves 

between sectors until the markets equilibrate and the net present value plus the investment and 

market wedges are equal across the sectors for lands on the margin. Naturally, land movement 

does not occur if the differences in the land returns are less than the hurdle cost plus the land 

transformation investment costs. 

4.5 Commodity exchanges between sectors 

FASOMGHG also reflects movement of commodities between the forest and agriculture 

sectors, largely in the form of biofuels and short rotation woody crops. In particular, 
63 

agriculturally produced short rotation poplar can be chipped and move into pulp and paper 

production processes and milling residues, pulp logs and in some cases logging residues can 

move between sectors as raw material sources for finished products made in the other sector. 

4.6 Aggregation, Calibration profits, and mixes 

All economic models must deal with aggregation and calibration at some level, but these 

issues are particularly important in agricultural sector models where great heterogeneity of 

growing conditions, resource quality, market conditions, and management skills are present. The 

aggregation problem involves treating groups of producers operating over aggregated resource 

sets as homogeneous units. The calibration problem involves dealing with spatially disaggregate 

producers who are entrants in a single market but receive different prices. 

4.6.1 A discussion of calibration, aggregation and sectoral models 

Suppose we formulate an aggregate programming model that represents a group of farms 

in a region, as in Model 1. 

( )

(2) 0

(1) 

r - c x

≥

≤

x

Ax b

ST

MAX x

 Model 1 

Also suppose the true real-world situation on one of the farms represented in Model 1 is 

actually described as shown in Model 2. 

( )

(5) 0

(4) 

(3) 

r - c d - e x

≥

≤

≤

−

x

Dx f

Ax b

ST

MAX x x

 Model 2 

The notation in both models is: 

• x An aggregate vector of crop acreages. 

• r A vector of average revenue. 

• c Variable costs related to the crop acreage, which are included in both models. These 

costs normally include the costs reported in accounting statistics, such as fertilizer, seed, 

tilling, pesticide, energy and labor costs. 
64 

• d Variable costs taken into consideration by the farmer, which are not included in Model 

1. These may include marketing costs, for example. 

• e Variable costs that increase with increasing area of the crop and or revenue declines 

associated with the rate of decline in the yield with increasing area of the crop. These 

items occur due to increased disease pressure, marginally decreasing soil quality, etc. 

These items are taken into consideration by the farmer but are not included in Model 1. 

• A A matrix of technical coefficients, which are included in both models. 

• b A resource vector corresponding to matrix A. 

• D A matrix with technical coefficients, which are not included in Model 1. 

• f A resource vector corresponding to matrix D. 

As the models are described here, there are important differences. The underlying cause 

for the omissions in Model 1 is the lack of full information about farm resources and costs, 

transaction costs, incentives and market conditions. These differences make calibration and 

aggregation necessary. Adding relevant information to Model 1 could reduce the problem. One 

could imagine that if all relevant information were added, the model would not only calibrate 

correctly to current production, but also to all counterfactual scenarios, since the incentives and 

production possibility representation are correct. However, when a model is expanded from 

describing a few farms to the sector or society level, the costs of gathering and maintaining an 

adequate amount of information for all the included cases are enormous. 

The differences between the sector model in Model 1 and the real world as illustrated in 

Model 2 may be due to reasons discussed in the following subsections. 

4.6.1.1 Sector models typically depict groups of farms 

Usually, a large number of farms of a particular type in a geographical region such as a 

state or province are represented as a single typical farm. Thus, models contain, for example, a 

single submodel representing all corn-soybean farms in Iowa, or all dairy operations in Sweden, 

even though there may be hundreds or even thousands of such types of farms, each with different 

characteristics. The construction of such typical farms introduces aggregation, and is done as a 

result of data and model size considerations. 

4.6.1.2 Resource availability details 

Typically, there are submodels within sector models, and these are highly aggregated 

representations of the operations they depict. They involve annual land, labor and water 

availability without considering many, or sometimes any, of a large variety of farm-specific 

factors such as crop rotation, quality of labor, land type, implementation and tractor time 
65 

constraints. For example, in modeling an Indiana corn-soybean-wheat-silage farm, the farm level 

model employed by McCarl et al. (1977) had more than 200 production possibilities and more 

than 175 resource-related constraints. In contrast, FASOMGHG represents all of Indiana 

production, including livestock production potential, with less than two dozen production 

possibilities and a dozen constraints. Data and model size considerations force such an aggregate 

depiction. 

4.6.1.3 Sector models typically ignore certain market factors. 

Typically, more aggregate models depict regional producers and consumers' as if they 

traded a set of homogeneous commodities at a single commodity-specific price. However, it is 

commonly observed that prices for a single commodity such as hay vary within any region 

across the places in the region as well as by time of sale and commodity quality characteristics. 

Therefore, the notion of a single market price for a commodity is an abstraction of reality. 

4.6.1.4 Data availability forces aggregation on the modeler 

Typically, sector-modeling exercises requires the use (and possibly the development) of 

consistent data on a national basis. When trying to use or develop such data, one usually finds 

that crucial items such as crop production budgets are available for average or typical regional 

operations, but not for a large number of possible alternative enterprises. Confidentiality and the 

costs of finer data development generally preclude more detailed data sets. Price data are also 

typically averages over regions, days, sale contract terms and grades, as are consumption data. 

4.6.1.5 Differences exist between the producer problem and the model 

Models often depict profit maximization subject to resource constraints as the sole 

objective of the producer, excluding other potentially important factors. Examples of relevant 

excluded considerations include risk aversion, financial reserves, capital constraints, personal 

expectations concerning yields and prices, and non-market objectives that are important to the 

producer (e.g. stewardship, tradition, wildlife habitat provision). These are all difficult to 

measure and depict on an aggregate scale. 

4.6.1.6 Insufficient depiction of production possibilities in budgets 

The model’s producer level farm budgets give statistically based data describing 

production practices carried out at one point in time on average. This reflects practices as they 

were not how they could have been. Consequently, budgets do not give a full spectrum of 
66 

possible production responses. Also, time lags in budget availability (i.e. with those available 

being one or two years old) and geographical averaging may introduce bias in model response. 

4.6.1.7 Specialization and mathematical programming solutions 

Mathematical programming solutions, particularly those from linear programming 

models, tend to produce extremely specialized solutions (“corner solutions”), wherein only one 

activity might be selected from a wide range of options for a rather large segment or region of 

the model. Thus, model solutions may be generated which give regions as producing only part of 

the crop and livestock potential production which is actually common within the boundaries of 

the region. The extent of this problem will be determined by the number of production 

possibilities employed and by the richness of the constraint set and the embodied production 

possibilities. Because this single corner solution often runs counter to what is observed in the 

field, this sometimes introduces concerns about the model’s realism unless addressed by model 

design. 

4.6.1.8 Transaction costs are often omitted 

Many models are built on the basis of farm budgets, but then use consumer or regionallevel average prices to calculate economic returns. There are costs accruing in the marketing 

channel for handling and transport that are frequently not present in budgets, so there are often 

price differentials between farm level prices received and prices paid by consumers' which are 

not fully captured in models. 

4.6.2 Addressing the aggregation problem 

As indicated above, the aggregation problem involves depicting production responses 

across a group of producers as a single response. Namely, within a FASOMGHG agricultural 

subregion such as Oregon, each farmer is represented by a single aggregate set of production 

variables facing an aggregate quantity of land by type, water, labor, AUMS, etc. Such a situation 

clearly is a simplification of reality as producers in such regions face different climatological 

and other conditions. But availability of data and considerations of sheer model size make some 

degree of aggregation both desirable and necessary. In practice, virtually every national scale 

model contains simplifications of reality, omitting potentially important information which is 

taken into consideration by farmers when choosing a farm plan. However, the need to enhance a 

model’s sectoral, geographic, and temporal coverage and detail in a conceptually consistent 

manner requires such abstractions to be made. 
67 

Clearly time and data would not permit trying to depict the production system for all 

farms. Nor, if it were done once, could one afford to maintain such a data set over time. This 

raises the classic concern of aggregation. However, the usual objective in applying FASOMGHG 

and other similar models is to develop a representation of the production choices at a regional 

(then national) scale to gives an accurate and credible portrayal of how the region might respond 

to changes in policy. If, instead, the objective was to model how individual farms with highly 

specific characteristics would respond, a finer scale model would be necessary. The aggregate 

representation of FASOMGHG, though, should be designed so that it exhibits minimal 

differences between what would happen if we had a full regional representation vs. the more 

compact regional representation we choose to use. Such a choice obviously is hampered by the 

fact that we never know the full characteristics of the region. 

Agricultural economists have spent much time addressing aggregation issues, yielding 

two primary approaches to the problem. First, there are bottom-up theoretical and empirical 

investigations. Here one assumes s(he) has data on individual farms or firms and wishes to 

develop a representation which exhibits minimum bias (as typified by Day, 1963a,b, 1969a,b). 

Second, are the top down, more empirical approaches with theoretical justification. Here one 

assumes s(he) doesn’t know the data on the individual farms/firms but can get more aggregate 

data and wishes to appropriately use that data to represent activity for the population represented 

in the model. 

Some have tried empirical approaches motivated by Day’s bottom up work to classify 

farms into groups and develop models for those groups based on most limiting resources. In 

addition, formal pursuit of these approaches requires much more data than is typically available 

about crop choice and production economics for all of the farms in a region. This has led to the 

more general and loose empirical approach where one classifies farms in a region based on 

expert opinion, then generates models for those different farm classifications. Unfortunately, the 

Day based approach did not prove useful empirically and was not chosen for use in 

FASOMGHG. Farmers even under very similar conditions and crop mixes generally have 

different price expectations, equipment complements (resulting in different working rates), and 

different access to resources. 

The second (top down) approach is used in FASOMGHG. FASOMGHG requires a 

regional representative model to choose among a convex combination of typical crop mixes as 

will be illustrated in the agricultural modeling section below. The rationale behind this approach 

can be argued from two different standpoints. 
68 

4.6.2.1 Justification 1: Observed practices reflect constrained choices 

In production economics, duality theory asserts that supply equations can be identified by 

estimating the relationship between profit (or cost) and determining factors (such as prices), 

using theoretically based deduction. In agriculture, then, the supply function is implicitly 

revealed through the observed farm profit-seeking choices. 

Similarly, farm crop mix choices implicitly have embedded in them the farm’s full 

consideration of all production possibilities and the constraints imposed by rotation, resources, 

and other technical factors. As a consequence forcing a combination of observed crop mixes,

implicitly incorporates all firm production processes and constraints. 

4.6.2.2 Justification 2: Theory indicates use of approach solves problem 

The solution to a mathematical programming problem appears at what is called an 

extreme point. Such a point lies on the constraint boundary at an intersection point between 

separate constraints. Dantzig and Wolfe (1961) investigated solutions to problems which have a 

unifying regional market but contain individual submodels for every firm. They showed that the 

overall problem solution could be composed from the optimal crop mix solutions from the firmlevel problems without consideration of firm level constraints. They showed that the firms could 

be represented as a convex combination of solutions to firm problems, i.e., a convex combination 

of optimal crop mixes, which obey the firm-level constraints. 

This approach involves a reformulation of the programming model. The reformulation 

approach is based upon Dantzig and Wolfe decomposition and suggestions in McCarl (1982). 

Dantzig and Wolfe based their scheme on the property that the solution to a subproblem or group 

of subproblems will occur at the extreme points of the subproblem(s). Thus, one can reformulate 

the problem so that it contains the extreme point solutions from the subproblems. Formally this 

can be expressed as follows. Given the problem as expressed above 

() ()

β

β

β

β β β

β

β β

β

β β

Z , X , Q 0 for all i, h, k and

 b Q Y for all j and

- X a Q 0 for all i

s.t. Z - C Q 0 for all h

Max P Z dZ - P X dX

h i k

j

k

j k k

k

i i k k

k

h h k k

i i

i

X

0

h h si

h

Z

0

dh

h i

≥

≤

+ ≤

≤

∑

∑∑

∑∑

∑ ∫ ∑ ∫
69 

suppose we group the firms β into subsets rm(β) where rm depicts the mth aggregate firm 

grouping. In turn, suppose we have a set of s feasible solutions Q βk and add up their aggregate 

levels of production and input usage such that 

( )

( )

X a Q for all m i and s

Z C Q for all m h and s

s

i k k rm k

ms

i

s

h k k rm k

ms

h

, ,

, ,

β β β β

β β β β

= ∑ ∑

= ∑ ∑

∈

∈

This in turn can be used in the aggregate problem: 

() ()

Z , X , 0 for alli, h, m and s

 1 for all m

- X X 0 for alli

s.t. Z - Z 0 for all h

Max P Z dZ - P X dX

h i

s

ms

s

ms

i i

s

h h

i i

i

X

0

h h si

h

Z

0

dh

h i

≥

≤

+ ≤

≤

∑

∑∑

∑∑

∑ ∫ ∑ ∫

ms

m

ms

m

ms

λ

λ

λ

λ

This model differs in two major ways from those above. First, the firm response variables 

have data requirements not in terms of individual production possibilities, but rather in terms of 

total production and consumption of the sector wide outputs and inputs accumulated across the 

firms in each group. In addition, rather than using individual resource constraints we now require 

a convex combination of the total output/input vectors. This will be feasible in the subproblems 

since any combination of two feasible subproblem solutions is feasible. Implicitly these solutions 

contain all the firm level resource restrictions and production possibilities coded within them. 

The candidate solution vectors (i.e., the values of Xi

ms,Zhms) must be developed. These 

can be generated either by formally solving the linear programming subproblems for different 

prices or by selecting a historical set of observed feasible mixes or firms. This is discussed 

further in Onal and McCarl (1989, 1991). Furthermore crop mixes of individual firms are not 

needed but rather can use mixes from groups of firms such as all farms in a county. 

McCarl, Hamilton, and Adams (1985) investigated the effect of different representation 

schemes in a Midwest region study felt through changes in crop yields and resultant effects on 

regional welfare. That study looked at crop mixes derived from a set of 13 typical farm LP 

models as well as a set of crop mixes drawn out of the USDA Agricultural Statistics 

publications. A regional model based on the agricultural statistics crop mixes generated virtually 

the same information as the much more time and resource intensive linear programming 
70 

representative farm-based crop mixes, thereby providing evidence that aggregate data on crop 

choices are consistent with underlying profit-maximizing choices. 

There are some basic problems with this approach, however. First, the use of historical 

crop mixes does not constitute as rich a production possibility set as one would have with the full 

detail in a model which more completely represented individual units. Historical crop mixes are 

reflections of producer decisions in the face of prevailing prices. Thus the crop mixes will not be 

an accurate representation either if the expected prices confronted by the model are well outside 

the historical range or if the situation to be examined substantially revises the production 

possibilities. Önal and McCarl (1989) found that when the prices and product mixes were not 

substantially different, the historical mixes gave a solution very close to that produced by more 

disaggregated modeling schemes. Others have attempted to correct such problems by 

augmenting the historical crop mix information with expert opinion or survey information. 

Tanyeri-Abur et al., (1993) added additional crop mixes containing much less sugar when 

examining US sugar import policy. Apland and Jonasson (1992) followed a similar approach in 

eliminating oil crops. Schiable et al., (1999) added additional mixes from a farm survey in a 

study of farm policy revision, with the mixes being based on survey questions about reactions to 

policy revisions. 

Another problem with this approach is that it does not take account of changes in 

production costs, inputs and yields when crop mixes change. A farmer knows that crop yields 

depend very much on the land use the previous year. Furthermore, costs may also vary with the 

previous crop. Some crops assist in avoiding diseases, thereby reducing the need for pesticides or 

other crop protection, while other crops have the opposite effect. These cost and yield changes 

are not taken into account. 

4.6.2.3 Omitted costs -- profit calculation 

Producers scattered throughout the country all receive different prices because they sell 

goods at different times, in potentially different quality forms and at different distances from 

marketing channels. Economic theory addresses this with the Law of One Price. This theory 

posits that all price differences are caused by different transactions costs and that once these 

transaction costs are all taken into account, all goods trade at effectively the same price. For if 

the same good traded at different effective prices, there would be opportunities for agents to 

engage in arbitrage and profit merely by exchanging goods sold at different prices. Market forces 

tend to dissipate these arbitrage opportunities. 
71 

The notion of adjusting prices to adequately reflecting transaction costs causes problems 

when using production budgets as the source of input data. In particular production budgets do 

not typically contain marketing transactions costs. It also causes problems when the demand 

function price is based on national statistics, because there are regional markets with higher 

prices caused by extra transactions costs that would net out any nominal price differences across 

regions. 

The law of one price is assumed herein where the marginal returns from all production 

variables based on observed budgets are equated to the marginal costs plus missing cost items. 

FASOMGHG is structured based on farm production budgets and USDA Agricultural Statistics 

national average prices. In these budgets the prices received exhibit regional differentials. 

Furthermore, the USDA national average prices are also different. Under these circumstances, 

the decision was made to rely on the economic theory of competitive markets and structure the 

model so that the marginal cost of production at current levels of production equaled the 

marginal cost of production. This led to the missing costs calculation based on an idea originally 

expressed by Miller and Miller (xxxcite) and later utilized by Fajardo et al (1981). Each 

production and processing budget comes from actual production activity that was undertaken 

during the year that the budget was collected. When production budgets are collected, the data do 

not reflect the whole production possibility set, rather they reflect the actual production patterns. 

As such, in the base year one needs to assume that these goods are being produced optimally, 

given the price that prevails in the national market. Consequently, a transactions cost term is 

computed for each budget which equates the marginal value of its output and the marginal cost 

of input. Thus, for a corn production activity which uses land, labor, water and miscellaneous 

inputs, a profit term can be calculated which is equal to the base period corn price times base 

period corn yield minus the base period water price times the amount of water used minus the 

rental rate of land times land used minus the prevailing labor wage rate times labor used minus 

the sum of the other input prices times quantity used 

TC=Price*Yield-Factorcost*FactorUsage 

This cost term represents missing transaction costs. If one solves the model adding this 

cost term then when the shadow prices in the model equal the base period prices for crops and 

factors - this model has zero reduced costs. Consequently such a solution is a candidate solution 

in the FASOMGHG programming model. Summarizing this transactions cost is computed as a 

residual and then is added as a term in both the crop and livestock activities permitting the model 

to reproduce observed market prices and replicating regional pricing and production patterns. 
72 

SECTION 3: THE FASOMGHG PROGRAMMING MODEL 

This section presents discussion of the structure of the programming model within 

FASOMGHG. We will do this by highlighting model components including the forest sector 

submodel, the agricultural submodel, the GHG payment submodel and the intersectoral features 

this is not complete 
73 

5 CHAPTER 5: OVERALL FASOMGHG PROGRAMMING MODEL 

STRUCTURE 

Operationally, FASOMGHG is a dynamic, nonlinear, price endogenous, mathematical 

programming model. FASOMGHG is dynamic in that it solves for the simultaneous multimarket, multi-period equilibrium across all agricultural and wood product markets, for all time 

periods, and thus for the intertemporal, intersectoral land market equilibrium. FASOMGHG 

embodies a nonlinear objective function, representing the sum of producers' and consumers' 

surpluses in all of the included product and factor markets. It is price-endogenous because the 

prices of the products produced and the factors used in the two sectors are determined in the 

model solution. Finally, FASOMGHG is a mathematical programming model because it uses 

numerical optimization techniques to find the multi-market price and quantity vectors that 

simultaneously maximize the value of an objective function, subject to a set of constraints. The 

FASOMGHG equations characterize: (a) the transformation of resources into products over time; 

(b) initial and terminal conditions; (c) the availability of fixed resources; (d) generation of GHG 

net emissions; and (e) policy constraints. The first-order (Kuhn-Tucker) conditions for the choice 

variables provide a set of rules characterizing the establishment of a competitive equilibrium. 

An overview of the model is presented in three tableaus below: 

• One of which covers sectoral scope in a static sense 

• One of which is more aggregate but introduces the spatial/regional dimension 

• The last of which is more aggregate but introduces the intertemporal dimension. 

5.1 Static, single region portrayal 

The tableau within table 5-1 shows the full scope of the FASOMGHG programming 

model in a single region, single time period setting. Although the tableau is designed to illustrate 

the most important model features, the reader should be aware that there is substantially more to 

the model. The subsequent chapters provide additional detail, as does the GAMS code. 
74 

Table 5-1 Sample tableau illustrating full FASOMGHG model in a static setting without regional detail 

 Variables Equations 

Exist stand 

Reforest land 

Afforest land 

Wood production cost 

Manufacture wood prods 

Terminal manufacture 

Forest domestic transport 

Endog public supply (Can

a

Non-wood inputs 

Wood product demand 

Wood product export 

Wood product import 

Terminal for product dema

Crop land from ag 

Pasture land from ag 

Land to ag crop land 

Land to ag pasture land 

Move for to ag commod 

Move ag to for commod 

Initial tillage 

Change tillage 

Produce crops 

Produce livestock 

Agricultural processing 

Blend feed 

Sup water, AUMs Labor 

Welfare -pc -fdt -fds -fnw +fd +fe -fi +ft -alt -alt -flt -flt -fcm -acm -acc -alc -apc -afc -afs -Exist timberland +1 Bare forest land -1 +/-1 -1 +1 +1 Bare land from ag +1 -1 -1 Harvested log bal -fhe -fhr -fha +fpu -1 Min hardwoods +1 +1 +1 For production cost +fce +fcr +fca -1 Wood products bal +/-p +/- +1 +1 -1 +fm -fm For process capacity +1 +1 Mill residues bal +/-m +/-m Non-wood input bal +1 +1 -1 Terminal for inventory -te -tr -ta +fpu -1 Terminal for prods -1 +1 -1 +1 Initial crop land +1 Land that can change till +als -als -1 +/-1 +Tilled land +als -als -1 +/-1 +1 +Pasture land +1 -1 +pu -Crop balance -am +am -cy +cu +pc +fc Livestock balance +-ly +pl Processed ag commod +su +-py +fs Feed balance +fu -1 Water, AUMs, labor +cl +ll -1 Crop mix +1 Livestock mix +1 Max for land transfer -1 -1 +1 +1 Max ag land transfer +1 +1 -1 -1 GHG balance ce cr ca Cm -as -as as as ts tcs ce le pg d
75 

The tableau shows that the FASOMGHG programming model encompasses four 

submodels and an integrating objective function: 

• Forestry sector submodel – Covers forest sector production, manufacturing, input 

supply, consumption, interregional transport, international trade, and terminal inventory 

valuation. This submodel is represented by the tableau columns labeled Exist stand

through Terminal for product demand. The feasible solution values for the forestry 

submodel variables are limited by constraints on land; input/factor supply; log 

supply/demand balances; intermediate and final product balances; processing capacity; 

and terminal inventory valuation. This is represented by the tableau rows Exist 

Timberland through Terminal for prods. The forestry submodel also affects the GHG 

balance as is shown in the last row of the tableau. 

• Agricultural sector submodel – Covers agricultural sector crop and livestock 

production, processing, feed blending, factor supply, consumption, interregional transport 

and international trade including terminal valuation of land remaining in agriculture. This 

submodel is represented by the tableau columns labeled Initial tillage through Domestic 

ag transport. The feasible solution values for the agricultural submodel variables are 

limited by constraints on crop and pasture land; factor supply; supply/demand balances 

on crop, livestock, processed and blended feed products; and crop/livestock mixes. This 

is represented by the tableau rows Crop land through Livestock mix. The agricultural 

submodel also affects the GHG balance as is shown in the last row of the tableau. 

• Intersectoral transfers submodel – Covers transfers of land and commodities between 

the forestry and agricultural sectors. This submodel is represented by the tableau columns 

labeled Crop land from ag through Move ag to for commod. The first four columns depict 

land transfers and the last two commodity transfers. Land transfers are limited by the 

equations Max for land transfer and Max ag land transfer. The submodel variables have 

entries in the land availability and commodity balance equations within the forestry and 

agricultural submodels. 

• GHG submodel – Covers GHG accounting and payments to net GHG emission 

reductions from agriculture and forestry. The GHG accounts reflect sequestration 

activity, emission activity, and biofuel related offset activity. In the tableau, the GHG 

submodel is represented by the column GHG payment and the row GHG balance. The 

GHG balance row depicts the involvement of agricultural and forestry activities. In turn, 

given a policy or GHG price signal these submodels can employ different production 

possibilities to reduce net GHG emissions. 

• Integrating objective function – Net present value of consumers' and producers' surplus 

across all four submodels. This is maximized in the FASOMGHG solution. The 

objective function is the tableau row labeled Welfare. Positive contributions arise over 

time and in the terminal period in association: (a) the area underneath the demand curves 
76 

for domestic consumption and export of forestry and agricultural products; (b) the 

valuation of terminal forest inventory and (c) the GHG payments to net emission 

reductions. In turn, total cost is subtracted in the form of cost terms and the areas 

underneath supply curves. The upward sloping supply functions include (a) forestry nonwood inputs, (b) agriculture and forestry imports, and (c) agricultural factor supplies for 

water, AUMs, and labor. 

 Next we discuss components of each of the four submodels separately, including the 

submodel components within the objective function. 

5.1.1 Forestry sector submodel 

The forestry sector submodel depicts forestry production, processing, input supply, 

consumption, interregional transport, international trade, and terminal inventory valuation. This 

submodel is represented by the tableau columns labeled Exist stand through Terminal for 

product demand. The feasible solution values for the forestry submodel variables are limited by 

constraints on land; input/factor supply; log supply/demand balances; intermediate and final 

product balances; processing capacity; and terminal inventory valuation. This is represented by 

the tableau rows Exist Timberland through Terminal for prods. The forestry submodel also 

affects the GHG balance as is shown in the last row of the tableau. Next we discuss each variable 

(column) depicted in the tableau along with each equation (row). 

The variables in Tableau 5-1 that make up the forestry submodel are: 

• Exist stand -- Allocation of acres to forest production alternatives for stands that exist at 

the beginning of the model run. The variable involves determination of the time of 

harvest, with one possibility being that the stand ia never harvested. Forest stands are 

differentiated by region, land class (reflecting suitability for agriculture), site quality, type 

of forest stand (softwoods, hardwoods, planted pine, etc.), type of private forest owner 

(industrial or nonindustrial private), age of stand, and prior stand management (including 

prior fertilization, partial cut and thinning regimes). The variables reflect usage of forest 

land from the existing inventory. If clearcut, they yield an acre that can be reforested. 

They also fall into the hardwood minimum constraint provided that hardwoods are being 

grown. In periods of clearcut, thinning, or partial cut, they produce harvested logs 

depicted by fhe, while they incur production costs (fce) from the initial model time 

period up to the period of clearcut. If these stands are never harvested during the explicit 

model time periods or are partially cut, they yield terminal inventory equal to te. Finally, 

they enter the GHG balances between the first period and the period just before clearcut 

at the rate ce, reflecting: (a) GHG sequestration in soils, ecosystems, and standing timber 
77 

and (b) fossil fuel emissions incurred during production. Within the GAMS 

implementation these are the variables FORPRDEXIST. 

• Reforest land -- Acres allocated to reestablished forest on previously clearcut lands. They 

involve determination of harvest time (with never being a possibility), type of forest 

(softwoods, hardwoods, planted pine, etc.), and management applied (including possible 

fertilization, partial cut, and thinning regimes). These variables are defined by time of 

forest reestablishment, time of harvest, and land characteristics. The land characteristics 

involve region, land class in terms of suitability for agriculture, site quality, and type of 

forest owner. In turn, if clearcut, these stands yield acres that can be reforested. They also 

fall into the hardwood minimum constraint provided that hardwoods are being grown. In 

periods when the stand is clearcut harvested, thinned, or partially cut, they produce 

harvested logs depicted by fhr, while they incur production costs (fcr) across time from 

the establishment period to clearcut period or the model end. If these stands are not 

clearcut, they yield terminal inventory tr. Finally, they enter the GHG balances (cr) 

between time of stand establishment up to just before clearcut, reflecting sequestration, 

and fossil fuel emissions incurred during production. Within the GAMS implementation 

these are the variables FORPRDNEW. 

• Afforest land -- Afforestation of acres to forest production alternatives on land transferred 

from agriculture. They involve determination of harvest time, forest type (softwoods, 

hardwoods, planted pine, etc.), and management applied including possible choice of 

partial cut or thinning regime. These variables are defined for the time period of 

afforestation, clearcut harvest period, and land characteristics. Land is controlled by 

region, suitability for agriculture, and site quality (High or Medium). All afforested land 

is assumed to belong to nonindustrial private forest owners. The variables use one acre of 

land transferring in from agriculture. In turn, if clearcut, they yield an acre into the bare 

land equation. They also fall into the hardwood minimum constraint provided that 

hardwoods are being grown. When the stand is subjected to clearcut harvest, thinning, or 

partial cut, it produces harvested logs (fha), while incurring production costs (fca) from 

the periods of establishment through the clearcut period. If these stands are never clearcut 

harvested, they yield terminal inventory (ta). Finally, they enter the GHG balances (ca) 

during the periods between establishment up to just before the clearcut period, reflecting 

sequestration, and fossil fuel emissions incurred during production. Within the GAMS 

implementation these are the variables FORPRDNEWAFFOREST. 

• For production cost -- Total stand production costs in dollars by each region and time 

period. The variables equate with the costs incurred in the production cost balance 

equation and incur an objective function entry (pc). Within the GAMS implementation 

these are the variables FORPRDCOST.

• Manufacture wood prods -- Quantity of wood product manufacturing (processing) 

activity in units of product made by region, type of product, type of process, input mix, 
78 

and time period. These variables not only embody manufacturing, they also incorporate: 

(a) log harvest and forest to mill hauling, and (b) product transformation including 

downgrading of logs, such as from sawtimber to pulpwood. This variable is defined for 

all FASOMGHG wood product manufacturing regions, including those in Canada. Logs 

are used as inputs at the rate fpu, while wood products are produced and possibly used at 

the rate p, generating or using milling residues (m). Processing capacity is used. They 

also require one unit from the regional and process specific non-wood input balance, 

which in turn reflects an upward sloping supply curve of non-wood inputs. Finally, they 

enter the GHG balance (cm) in the period of wood product manufacture and all 

subsequent periods, reflecting carbon sequestered in manufactured wood products. 

Within the GAMS implementation these are the variables FORWDMANUFACT. 

• Terminal manufacture – Terminal-period activity of wood product manufacturing by 

region, wood product made, process, and input mix. The variables have the same 

characteristics as the above Manufacture wood prods variables, with the only real 

difference being that the logs come from the terminal inventory balance equation. Within 

the GAMS implementation these variables fall within FORWDMANUFACT. 

• Forest domestic transport -- Quantity of wood products transported between regions. The 

variable is defined by product type, originating region, destination region, and time 

period. They reflect transport cost in the objective function (fdt), while using one unit of 

wood product in the region of origin and supplying one unit into the region of destination. 

All regions are covered where wood products manufacture is defined, including those in 

Canada. Within the GAMS implementation these variables fall within 

FORWDTRANSPORT. 

• Exog public supply (Canada)—In Canada only, public supply (from provincial lands) of 

harvested logs by region, time period, and log type. They reflect cost of supply in the 

objective function (fds), and supply one unit of logs into the harvested log balance. 

Within the GAMS implementation these variables are named FORWDLOGSUPPLY. 

• Non-wood inputs -- Supply of non-wood input items for wood product manufacturing. 

They are defined by wood product, process, region, and time period. They depict an 

upward sloping supply curve for non-wood input items. Non-wood inputs include those 

for manufacturing inputs, harvest, and woods to mill hauling costs. The variables have 

objective function coefficients (fnw) reflecting subtraction of a term representing area 

underneath the non-wood input supply equation and supply one unit into the non-wood 

input balance equation. Within the GAMS implementation these are the variables 

FORWDNWCS. 

• Wood product demand -- Wood product demand by type of wood product at the US 

national level by time period. They represent a downward sloping demand curve. The 

variables fall into the objective function, with a term (fd) reflecting the area underneath 

the demand equation. They also reflect the withdrawal of one unit from the wood product 
79 

balance equation. Within the GAMS implementation these variables are cases within 

FORWDDEMAND. 

• Wood product import -- Import supply of wood products (softwood lumber from nonCanadian sources only) at the regional level by time period. They represent an upward 

sloping import supply curve. These are defined for each wood product manufacturing 

region. The variables fall into the objective function with the subtraction of a term (fi) 

reflecting the area underneath the import supply equation. They also add one unit to the 

wood product balance. Within the GAMS implementation these are within 

FORWDSUPPLY. 

• Terminal for product demand -- Terminal period demand for wood products at the US 

national level. They represent a downward sloping demand curve for future wood 

products, assuming all stands are subjected to perpetual even-aged management. The 

variables have an objective function term (ft) reflecting the area underneath the terminal 

demand equation. They withdraw one unit from the terminal wood product balance. 

Within the GAMS implementation these variables are cases within FORWDDEMAND. 

The equations portrayed in table 5-1 that are associated with the forest sector are: 

• Welfare -- Adds forest related net present value of consumers' and producers' surplus. 

The positive terms involve the area under the wood product demand curves for domestic 

consumption (fd), exports (fe), and terminal products (ft). The negative terms are of two 

different fundamental types. The first involves the area underneath explicit upward 

sloping supply curves for non-wood inputs (fnw) and wood products imports (fi). The 

second involves fixed per unit costs times quantities for stand production costs (pc), 

domestic transport (fdt), and public (Canadian) log supply (fds). Discounting provisions 

are included, as the model variables falling into the objective function embody a time 

dimension and consequently introduce income and cost streams arising in different time 

periods. Thus, they must be transformed into a common unit that we select to be year 

2002 dollars. To do this FASOMGHG incorporates two different discounting procedures. 

First, because all variables give the annual activity levels during each five year period, 

their objective function terms are transformed to give the present value of period 

spanning constant activity at that rate. That involves multiplying the term by a factor, 

where the factor used is present value of a five year annuity for all but the terminal 

period, where a perpetual annuity factor is used. Second, the terms for time periods 

beginning in year t are multiplied by the discount rate for year t relative to year 2000. The 

objective function is the GAMS implementation equation WELFAR. 

• Exist timberland – All acres in the initial inventory (preexisting stands) must be allocated 

to some form of management or reserved class. The stands are defined by region, land 

class in terms of suitability for agriculture, site quality, stand type (softwoods, 
80 

hardwoods, planted pine, etc.), owner type (industrial or nonindustrial private), stand age, 

and management (including possible fertilization, partial cut and thinning regimes). This 

row depicts the GAMS implementation equation FORINVENTORYA. 

• Bare forest land -- Balances clearcut timberland with its use of timberland for 

reforestation, transfer to agriculture, and transfer to developed use (fdev). The stands are 

defined by region, land class in terms of suitability for agriculture, site quality, type of 

eligible succeeding forest stand, and forest owner (industrial or nonindustrial private). 

Clearcut acreage comes from existing stands, previously reforested stands and previously 

afforested stands but only after their first afforested rotation. This row depicts the GAMS 

implementation equation FORLANDBALANCE. 

• Bare land from ag -- Balances agricultural land transferring into forestry with its use for 

afforestation. The stands are defined by region, land classes suitable for agriculture, and 

site quality (high, medium). This equation only treats afforested stands during their first 

rotation. Subsequent stands go into the bare forest land balance. This row depicts the 

GAMS implementation equation FORAFFORLANDBALANCE. 

• Harvested log bal -- Balances the harvested logs from private and public sources with 

their use in wood products manufacturing. The private logs come from existing stands 

(fhe), reforested stands (fhr), or afforested stands (fha). They include logs obtained from 

clearcut harvests, thinning, and partial cuts. Public logs come from exogenous US public 

lands cut (usps) and from the Endog public supply (Canada) variable that depicts upward 

sloping supply of Canadian logs. Wood products manufacturing uses logs at the rate fpu. 

These equations are defined by region, log type, and time period. This row depicts the 

GAMS implementation equations FORBALEXHRV (which covers clearcuts of existing 

stands), FORBALEXHPC (which covers thinning and partial cuts of existing stands), 

FORBALNEWHRV (which covers clearcuts of reforested and afforested stands), and

FORBALNEWHPC (which covers thinning and partial cuts of reforested and afforested 

stands). The GAMS implementation equation FORWDBALANCE for log commodities 

is also involved. 

• Min hardwoods -- Requires the standing hardwood area by owner to be greater than or 

equal to a minimum owner-specific acreage level (mh). The constraint is defined by 

region, type of forest owner, and time period. The GAMS implementation equation 

FORHARDWOODMIN is represented by this tableau row. 

• For production cost -- Balances the use of pre-harvest forest production cost items with 

their supply. The costs arise under management of existing (fce), reforested (fcr), and 

afforested (fca) stands. The equation is defined by log producing region and time period. 

This row depicts the GAMS implementation equation FORCOSTBAL. 

• Wood products bal -- Balances manufactured wood product supply and demand. These 

equations are defined by region, wood product (including logs), and time period. Supply 
81 

is obtained from wood products manufacturing at the rate of p plus incoming domestic 

transport and imports. The demand arises from intermediate product use by 

manufacturing (at a rate also depicted by p), and outgoing transport plus domestic 

demand and exogenous exports (exp). Finally, there are adjustments for commodity 

movements to and from agriculture. This row depicts the GAMS implementation 

equation FORWDBALANCE.

• For process capacity -- Imposes capacity limits on wood product manufacture. The 

capacity (fcap) is defined by time period, region, process, and wood product 

manufactured. This row depicts the GAMS implementation equations 

FORWDCAPACITY.

• Mill residues bal -- Balances milling residue supply and demand. These equations are 

defined by region, residue type, and time period. Milling residues are obtained from 

wood products manufacturing at the rate of m. Demand arises from intermediate product 

use by manufacturing (at a rate also depicted by m). This row depicts the GAMS 

implementation equations FORWDRESBAL.

• Non-wood input bal -- Balances wood product manufacturing activity with non-wood 

input supply. Non-wood input supply is from an upward sloping supply curve. The 

equation is defined by wood product, processing alternative, region, and time period. This 

row depicts the GAMS implementation equation FORWDNWCEQ.

• Terminal for inventory -- Balances logs in terminal forest stands (those that persist 

beyond the explicit model time period) with their use in terminal wood products 

manufacturing. These logs come from private lands that are either in existing stands (te), 

reforested stands (tr), or afforested stands (ta). Wood products manufacturing uses logs 

at the rate fpu. These equations are defined by region, log type, and time period. This row 

is in the GAMS implementation equation FORBALEXHRV.

• Terminal for prods -- Balances the terminal period supply and demand for manufactured 

wood products. Supply arises from wood products manufacturing at the rate of p plus 

incoming domestic transport and imports. Demand arises from intermediate product use 

by manufacturing (at a rate also depicted by p), outgoing transport, domestic demand, 

and exports. These equations are defined by region and wood product. This row depicts 

the GAMS implementation equation FORWDBALANCE.

• GHG balance -- Balances net GHG emissions by type of GHG account with the GHG 

payments variable. The equations incorporate terms that reflect sequestration in forests 

and wood products along with GHG emissions from fossil fuel use. The term ce reflects 

the GHG emissions and sequestration associated with the management of existing forests, 

while cr reflects that from reforestation and ca that from afforestation. The term cm

reflects carbon sequestered in wood products. GHG terms are also included, reflecting 
82 

effects for agriculture and land use change as discussed elsewhere. This row depicts the 

GAMS implementation equation GHGACCOUNTS. 

5.1.2 Agricultural sector submodel 

The agricultural sector submodel depicts crop and livestock production, processing, feed 

blending, factor supply, consumption, interregional transport, and international trade. This 

submodel is represented by the tableau columns Initial tillage through Domestic ag transport. 

The agricultural submodel incorporates constraints on crop and pasture land; factor supply; 

supply/demand balances for crop, livestock, processed and blended feed products; and 

crop/livestock mixes. This is represented by the tableau rows Crop land through Livestock mix. 

The agricultural submodel also affects the GHG balance, as shown in the last tableau row. Next, 

we discuss each variable (column) depicted in the tableau along with each equation (row). 

The variables in Tableau 5-1 that make up the agricultural sector submodel are: 

• Initial tillage -- Assigns initial crop land assignment to the existing inventory. The 

variables are defined by region, tillage system (conventional, minimum till, and no till), 

irrigation status (irrigated or dryland), and crop land quality type. The variables use land 

from the initial tillage balance and supply it for cropped use. They also enter the GHG 

balances (ts) during each subsequent period, reflecting the trajectory of soil sequestration. 

Within the GAMS implementation these are the variables AGINITIALTILL. 

• Change tillage -- Tillage system and irrigation status alterations. The variables are 

defined by region, beginning and ending tillage system (conventional, minimum till and 

no till), beginning and ending irrigation status (irrigated or dryland), and crop land 

quality type. These variables use land from the balance of land eligible to change tillage, 

including land crossing over from forestry (that is placed in as conventional dryland) and, 

in turn, supply it for cropping under a particular tillage system and irrigation status, while 

permitting it to change again in a later time period. They also enter the GHG balance 

(tcs) during the current and future periods, reflecting the trajectory of changes in soil 

sequestration. Within the GAMS implementation these are the variables 

AGCHANGETILL. 

• Produce crops -- Agricultural crop production alternatives. The variable gives acres 

harvested in a time period by crop, irrigation status (irrigated or dryland), tillage method 

(conventional, minimum tillage, and no till), and degree of fertilization (base level, 15% 

reduction, or 30% reduction). The land on which the crops are planted is differentiated 

by region and crop land quality type. The variables reflect: (a) usage of fixed price inputs 

(acc) in the objective function, (b) usage of an acre of tilled land, (c) yield of crop 

commodities (cy), (d) usage of labor and water (cl), and (e) a requirement for authorized 
83 

acreage from the crop mix. They enter the GHG balances (ce) reflecting net emissions 

involved with crop production, including those from fossil fuel and fertilizer use. Within 

the GAMS implementation these are the variables AGCROPBUDGET. 

• Produce livestock -- Livestock production alternatives. The variable gives the number of 

head by animal type, enteric fermentation alternative, and manure management 

alternative by region and time period. They reflect: (a) usage of fixed price inputs in the 

objective function (alc); (b) usage of pasture land (pu); (c) use of crop commodities for 

feed (cu); (d) livestock commodity yield (e.g., of milk) and intermediate product usage 

(e.g., calves used in feeding) at the rate ly per head; (e) agricultural processed commodity 

usage (su); (g) blended feeds usage (fu); (h) labor and AUM grazing usage (ll); and (i) a 

requirement for authorized animals from the livestock mix. They enter the GHG balance 

reflecting net emissions (le), including those from fossil fuel, enteric fermentation, and 

manure. Manure management alternatives are incorporated in an associated variable. 

Within the GAMS implementation these are the variables AGLVSTBUDGET and 

AGLVSTMANURE. 

• Agricultural processing -- Agricultural processing alternatives. They give the volume of 

agricultural processing manufacturing activity. The variable is differentiated by 

processing alternative, region, and time period. Some of the processing alternatives are 

only defined at the national level. The variables reflect: (a) usage of fixed price inputs in 

the objective function (apc); (b) usage of crop commodities (pc); (c) usage of livestock 

commodities (pl,); and (d) agricultural processed commodity production along with 

intermediate product usage (py). They enter the GHG balance (pg) reflecting emissions 

from fossil fuel usage and biofuel offsets. Within the GAMS implementation these are 

cases within the variables AGPROCESS and AGREGPROCESS. 

• Blend feed -- Feed blending alternatives. The variable involves determination of the 

number of units of blended feed manufactured by blending alternative. The variable is 

differentiated by feed type, blending alternative, region, and time period. The variables 

reflect: (a) fixed price input usage (afc) in the objective function; (b) crop commodity 

usage (fc); and (c) processed commodity usage (fs). Within the GAMS implementation 

these are cases within the variable AGREGPROCESS. 

• Sup water, AUMs, Labor -- Agricultural factor supply of water, labor, and AUM grazing. 

They give the amount supplied from fixed price and upward sloping supply curve 

portions. For water, this involves fixed price government owned, but leased, sources and 

an upward sloping supply curve for pumped, private, surface and ground water. For 

labor, this includes fixed price family and upward sloping hired labor supply. For AUM 

grazing, this includes fixed price AUMs available through grazing fees and AUMs 

available in an upward sloping fashion through private markets. The variable is 

differentiated by resource, type of source, region, and time period. The variables reflect: 

(a) the per unit fixed price or area underneath the supply curve relevant to the quantity of 
84 

the factors supplied in the objective function (afs); and (b) supply into the resource usage 

balance row. Within the GAMS implementation these are cases within the variable 

AGRESSUPPLY. 

• Crop/pasture exchange -- Transformation of crop land to and from pasture or grasslands. 

The variable gives acres transformed in each direction by region and time period. The 

variables reflect: (a) per acre fixed cost of transformation in the objective function(al); 

(b) supply or usage of crop land from the tilled land and can change tillage balances and 

(c) supply or usage of pasture land. These variables also enter the GHG balance, giving 

the trajectory of change in soil sequestration (ds), which is positive or negative depending 

on the direction of land use change. Within the GAMS implementation these are cases 

within the variable AGPASTLNDUSECHG. 

• Crop/livestock mix -- Choice among historically observed distributions within regions 

and livestock mix distributions across regions. The variable involves determination of the 

number of acres or head authorized within each observed mix. The crop mix variable is 

differentiated by region, historical alternative, and time period. The livestock mix 

variable is differentiated by historical alternative and time period. The variables reflect: 

(a) the share of the acreage of each crop in the total mix per unit of the alternative (cm); 

and (b) the share of the livestock herd by region in total mix per unit of the alternative 

(lm). Within the GAMS implementation these are the variables AGMIXR and

AGNATMIX. 

• Ag export -- Agricultural commodity exports. Two cases are defined. For commodities 

with explicit spatial trade modeling, the variable is differentiated by time period, 

commodity, and consuming country. In that case, associated transportation variables are 

also defined. Other commodities are defined only with a total excess demand equation 

facing the US and involve time period and commodity. Crop, livestock, and processed 

commodities can be exported. The variables reflect: (a) the area underneath the demand 

curve (ae) in the objective function; (b) transport costs when explicit trade is being 

modeled are also within ae; and (c) usage of the associated crop, livestock, or processed 

commodity. Within the GAMS implementation these are cases within the variables 

AGDEMAND and AGTRADE. 

• Ag import -- Agricultural commodities imported. Two cases are defined. For 

commodities with explicit spatial trade modeling, the variable is differentiated by time 

period, commodity, and producing country. In that case, associated transportation 

variables are also defined. Other commodities are defined only with a total excess supply 

equation facing the US and involve time period and commodity. Crop, livestock, and 

processed commodities can be imported. The variables reflect: (a) the area underneath the 

supply curve (ai) in the objective function; (b) transport costs when explicit trade is being 

modeled are also within ai; and (c) supply of the associated crop, livestock, or processed 
85 

commodity. Within the GAMS implementation these are cases within the variables 

AGSUPPLY and AGTRADE. 

• Ag domestic consumption -- Domestic consumption of agricultural commodities above 

and beyond those consumed as feed and as intermediate inputs to processing. The 

variable is differentiated by time period and commodity. Crop, livestock, and processed 

commodities can be consumed. The variables reflect: (a) the area underneath the demand 

curve (ad) in the objective function; and (b) usage of the associated crop, livestock, or 

processed commodity. Within the GAMS implementation these are cases within the 

variables AGDEMAND. 

• Domestic ag transport -- Transport of agricultural commodities. Movements are depicted 

between domestic regions or from domestic regions to the national market. The variable 

is differentiated by time period, commodity, region of origin, and region of destination 

including a national destination. Crop, livestock, and processed commodities can be 

moved. The variables reflect: (a) the cost of transport (adt) in the objective function; (b) 

the historic price differences between region and national markets (adt); and (c) usage in 

the region of origin and supply in the region of destination. Within the GAMS 

implementation these are cases within AGTRADE and AGTRANSPRIM. 

Because of space limitations, some of the agriculturally related FASOMGHG variables 

were not portrayed. This includes the usage of idle pasture/grasslands and the associated 

sequestration in the GAMS implementation variables AGIDLELANDPASTURE and 

AGUSEPASTURE. There is also weak portrayal of the international trade variables AGTRADE, 

the movement to national market variables AGTRANSPRIM, and the manure treatment 

variables AGLVSTMANURE. More on these variables appears within the agricultural model 

chapter below. 

The equations in Tableau 5-1 that make up the agricultural sector submodel are: 

• Welfare -- Adds agriculturally related net present value of consumers' and producers' 

surplus. The positive terms involve the area underneath the agricultural products demand 

curves (ad), and the area underneath the agricultural products export demand curves (ae). 

The negative terms components of total cost. They include the area underneath explicit 

upward sloping supply curves, which involves the area under the upward sloping factor 

supply curves (afs) that depict the supply of water, AUMs, and labor, and the area 

underneath the agricultural product import curves (ai). They also include the fixed price 

times quantity for costs of inputs used in crop production (acc), livestock production 

(alc), agricultural processing (apc), feed blending (afc), pasture to crop land 

transformations (ale), and agricultural domestic transportation (adt). Discounting 

provisions are also required. The model variables falling into the objective function 
86 

embody a time dimension and consequently introduce income and cost streams arising in 

different time periods. Thus, they must be transformed into a common unit, which we 

select to be year 2000 dollars. To do this, FASOMGHG incorporates two different 

discounting procedures. First, because all variables give the annual activity levels during 

each five year period, their objective function terms are transformed to give the present 

value of period spanning constant activity at that rate. That involves multiplying the term 

by a factor where the factor used is present value of a five year annuity for all but the 

final explicit period, where a perpetual annuity factor is used. Second, the terms for time 

periods beginning in year t are multiplied by the discount rate for year t relative to year 

2000. The objective function is the GAMS implementation equation WELFAR. 

• Crop land -- Limits the initial tillage allocation to the tillage inventory on hand. The land 

is defined by region, crop land quality, and tillage system employed (conventional, 

minimum tillage, no tillage). The tableau row has an exogenous land endowment (cl). 

This row depicts the GAMS implementation equations AGTILLSTART.

• Land that can change till -- Limits possible tillage changes in the face of the current 

inventory of tilled land, adjusted for the net changes due to forestry/crop or crop/pasture 

land exchanges. The land is defined by region, crop land quality, tillage system employed 

(conventional, minimum tillage, no tillage), and irrigation status (irrigated or dryland). 

The tableau row reflects exogenous migration of agricultural land into developed uses 

(cdev). The left hand side entries depict land changing tillage systems, land moving in 

and out of forestry, land moving between crop and pasture land, and land exchanging 

between tillage systems. This row depicts the GAMS implementation equations 

AGCANCHANGETILL.

• Tilled land -- Restricts use of crop land by tillage practice to the tillage inventory on hand 

by time period. The land is defined by region, crop land quality, tillage system employed 

(conventional, minimum tillage, no tillage), and irrigation status (irrigated or dryland). 

The entries depict the supply of tilled land from initial tillage, adjusted for tillage changes 

and land exchanges with forestry and pasture. This row depicts the GAMS 

implementation equations AGTILLUSE.

• Pasture land -- Limits pasture land use to the pasture land inventory by time period and 

region. The entries depict the endowment of pasture (pl), adjusted for exchanges with 

forest and crop land. An exogenous adjustment of land flowing into developed uses is 

also present, but is not explicitly reflected in the tableau. Two pasture land related 

equations are present, one of which accounts for the pasture used and the other which 

balances total pasture including the possibility of idled pasture land. This permits 

accounting for sequestration on any idled pasture land. This row depicts the GAMS 

implementation equations AGPASTLANDEXCHANGE and 

AGLANDPASTURETILLUSE.
87 

• Crop balance -- Balances crop commodity supply and use. The equation contains US 

regional, US national, and foreign country balances by commodity and time period. The 

entries depict the yields from crop production (cy), direct feed use by livestock 

production (cu), usage in processing (pc), and usage in feed blending (fc). The equation 

also includes domestic consumption, exports, supply from imports, and adjustments for 

incoming and outgoing interregional transport. This row depicts cases within the GAMS 

implementation equation AGPRODBAL.

• Livestock balance -- Balances livestock commodity supply and use. The equation 

contains US regional, US national, and conceivably foreign country balances by 

commodity and time period. The entries in the equation depict the yields of livestock 

from production (ly), direct use of some intermediate livestock categories like feeder pigs 

in livestock production (also depicted by ly), and usage in processing (pl). The equation 

also includes domestic consumption, exports, supply from imports, and adjustments for 

incoming and outgoing interregional transport. This row depicts cases within the GAMS 

implementation equations AGPRODBAL.

• Processed ag commod -- Balances processed agricultural commodity supply and use. The 

equation contains US regional, US national, and conceivably foreign country balances by 

commodity and time period. The entries depict the usage of processed commodities as 

feeds by livestock production (su), supply of processed commodities from agricultural 

processing (py), direct use of some intermediate processed commodities like cornstarch 

in HFCS manufacture by processing alternatives (also depicted by py), and usage in feed 

blending (fs). The equation also includes domestic consumption, exports, supply from 

imports, and adjustments for incoming and outgoing interregional transport. Finally, there 

are adjustments for commodity movements to and from forestry. This row depicts cases 

within the GAMS implementation equation AGPRODBAL.

• Feed balance -- Balances blended feed commodity supply and use. The equation contains 

US regional balances by blended feed commodity and time period. The entries in the 

equation depict the balance between usage of blended feed commodities by livestock 

production (fu) with the supply from the feed blending alternatives. This row depicts 

cases within the GAMS implementation equation AGPRODBAL.

• Water, AUMs, labor balance -- Balances usage of irrigation water, AUM grazing, and 

labor supply with their supply. Usage comes from crop (cl) and livestock (ll) production. 

The nature of the factor supply terms differs by resource. For water, a homogenous 

commodity acre feet of irrigation water is supplied by either fixed price governmentally 

owned, but leased, water or an upward sloping supply curve for pumped, private, surface 

and ground water. For labor, the homogeneous commodity hours of labor is supplied by 

either fixed price family sources or an upward sloping hired labor supply curve. For 

AUM grazing, the homogeneous commodity of one animal unit of grazing is supplied by 

either fixed price AUMs available through grazing fees or an upward sloping supply 
88 

curve of AUMs available through private markets. The equation is differentiated by 

region, factor, and time period. This row depicts the GAMS implementation equations 

AGRESBALANCE.

• Crop mix -- Balances acreage by crop in a region with the proportional occurrence of that 

crop in historically observed cropping patterns. The equation covers irrigation and 

dryland restictions for all crops that have been observed in crop mixes for the time 

periods. Generally, these constraints are defined within the first 20 years of the model 

run. The equations are present for aggregation purposes as discussed above. The equation 

balances the acres used in crop production possibilities with their supply from the crop 

mix alternatives (cm). Although not explicitly shown here, a convexity requirement is 

imposed that balances total acreage across all crops with the total acreage covered by the 

mixes. The equation is differentiated by region, crop, irrigation status, and time period. 

Simultaneously, a lower bound is imposed so that the acreage in the crop mix must be at 

least 90% of that in the historical mix. This row depicts the GAMS implementation 

equations AGCRPMIXUP and AGCRPMIXLO.

• Livestock mix -- Balances regional head by animal type with the proportional occurrence 

across regions in the US in historically observed livestock population patterns. The 

equation is defined for time periods in the first 20 years of the model run. The equations 

are present for aggregation purposes as discussed earlier. The equation reflects the need 

for a livestock head by the livestock production possibilities and its supply from the 

livestock mix alternatives (lm). The equation is differentiated by region, animal type, and 

time period. This row depicts the GAMS implementation equations 

AGLIVESTOCKMIXNAT.

• GHG balance -- Balances the GHGs by GHG account with GHG payments. These 

equations incorporate sequestration in soils, biofuel offsets, and emissions. The 

coefficients associated with crops involve sequestration associated with initial tillage (ts), 

tillage change (tcs), and land use change between crop land and pasture (ds). 

Sequestration accounting is also included within the term for changes in cropped acreage 

production (ce) when longer lived perennials are involved. Crop production related 

emissions are also included in the term ce and reflect emission's associated with: 

• Fossil fuels used in tillage, planting, harvesting, and other machinery operations 

• Crop drying 

• Irrigation 

• Histosoils 

• Nitrogen fertilization 

• Rice production 

• Fertilizer and pesticide manufacture 

• Residue burning 
89 

• Sewage sludge usage 

• Nitrogen fixing crops. 

Livestock related emissions associated with fossil fuel usage, enteric fermentation, and 

manure management are reflected in le. Emissions related to agricultural processing are 

reflected within pg. The coefficients pg also incorporate accounting for biofuel-related 

offsets when biofuel feedstocks are made into ethanol, diesel, or coal substitutes. GHG 

involvement from forestry operations and land use changes also appear. This row depicts 

the GAMS implementation equations GHGACCOUNTS. 

Although almost all of the FASOMGHG agriculturally related equations are shown in the 

tableau, there are a couple that are either not represented or are less than fully represented. This 

includes missing portrayals of equations imposing maximums on fixed price factor supplies 

(AGRESMAX), a manure related balance between livestock that can be managed with improved 

manure management systems and those treated by improved manure management systems 

(AGMANUREMGT), and a maximum transfer of pasture land to crop land 

AGMAXPASTURETOCROP. In addition, there are also less than detailed portrayals of lower 

bounds on participation in crop mixes AGCRPMIXLO, foreign trade balances within the 

AGPRODBAL equation, pasture land in use and idle pasture land in 

AGPASTLANDEXCHANGE and AGLANDPASTURETILLUSE. These cases are covered 

more extensively in the agricultural modeling chapter below. 

5.1.3 Intersectoral transfer submodel 

The intersectoral transfer submodel depicts movements of land and commodities between 

the forestry and agricultural sectors. This submodel is represented by the tableau columns labeled 

Crop land from ag through Move ag to for commod. The first four of these columns depict land 

transfers and the last two depict commodity transfers. Land transfers are limited by the equations 

Max for land transfer and Max ag land transfer. The explicit land balance or commodity balance 

rows are not treated within this submodel, rather the submodel variables have entries in the land 

availability and commodity balance equations within the forestry and agricultural sector 

submodels. Here we will first discuss the issue of land synchronization and then will turn 

attention to the tableau components. 

5.1.3.1 Land definition synchronization 

Before discussing the intersectoral transfer submodel features, it is important to discuss 

region and land type synchronization. Land in the forestry sector is defined at the 11 

FASOMGHG region geographic level, with quality dimensions including land classes relevant 
90 

for exchange with agriculture (FORCROP, CROPFOR, FORPAST, and PASTFOR) and three 

site productivity indices (high, medium, and low). On the agricultural side, the land base is 

defined on a 63 region basis in the first 20 modeled years and later on a FASOMGHG 11 region 

basis. In addition, while pasture land is defined as a single homogeneous commodity, crop land 

is not. Rather, crop land is differentiated into four crop land quality classes (w3-8, loei, mdei, and 

svei) and is also differentiated by tillage practice employed and irrigation status. 

To best model sequestration and control land movements, several assumptions are used to 

synchronize these disparate regional definitions. Briefly these assumptions are: 

• When crop land moves into forestry, it falls into the FORCROP class with high site 

productivity. 

• When pasture land moves into forestry, it falls into the FORPAST class with medium site 

productivity. 

• When crop land moves out of forestry, it comes from either the FORCROP or 

CROPFOR classes with high site productivity. 

• When pasture land moves out of forestry, it comes from either the FORPAST or 

PASTFOR classes with medium site productivity. 

• When crop land moves between forest and agriculture, it exchanges with the crop land 

quality differentiated lands in proportion to the original incidence of those lands in the 

crop land endowment data. This means that if the land in a region initially is 33% w3-8

and 67% mdei land, that the land moving in or out will be placed into or withdrawn from 

these two classes in the proportions 0.33 and 0.67. 

• When crop or pasture land moves between one of the FASOMGHG 11 regions into the 

agricultural sector during the periods in which the agricultural sector is disaggregated into 

63 subregions, that land moves into the subregions in proportion to the incidence in the 

initial distribution of subregional land. This procedures differs somewhat for crop and 

pasture land. 

• For pasture land, it moves in proportion to initial subregion shares of pasture land 

for subregions included in the larger regions. For example, suppose we consider 

land movements in the Pacific Southwest (PSW) region. Assume the initial 

endowment of land shows 20% of the PSW pasture land is in Southern California 

and 80% in Northern California. In that case, transferred pasture land would come 

from or be placed into the subregional pasture land balances at the rate of 0.2 

acres in Southern California and 0.8 acres in Northern California. 

• The crop land case is more complex because it must also synchronize with the 

crop land quality dimension. Namely, because crop land is subdivided into four 

crop land quality classes, the land exchanges need to be distributed across the four 

crop land classes while simultaneously falling across the contained subregions. In 
91 

our PSW example above, there would be eight subregion/quality cases. In turn, 

the land is distributed into those eight cases according to their observed 

proportions in the initial crop land endowment data. 

• When forest land exchanges with crop land, it always comes from or goes into the 

inventory of acres with dryland irrigation status that are conventionally tilled. The model 

can actually move land from or to other tillage/irrigation status cases by coupling the land 

transfer with a tillage change. 

• Although this discussion is centered on land transferring at the FASOMGHG 11 region 

level, not all such transfers are allowed. Namely, land transfers only occur in regions that 

have both agricultural and forestry production. This is true for only eight of the 

FASOMGHG 11 regions. 

Such procedures are not needed on the commodity side because the agricultural regional 

commodity model is always defined at the FASOMGHG 11 region level and the commodities 

can move on a one-to-one basis between comparable regions. 

5.1.3.2 Tableau components 

The variables in the intersectoral land transfer submodel are: 

• Crop land from ag -- Afforestation of agricultural crop land. Such land movements are 

defined at the FASOMGHG 11 region level by time period. They remove land (als) from 

the agricultural tilled land and can change tillage land balances and place it into the forest 

land balance. They incur a cost of land transformation (alt) in the objective function. 

They are limited by an exogenous maximum transfer limit (ac). They remove sequestered 

carbon from the GHG balance category for agricultural sequestration (as) by zeroing out 

the agricultural component for this acre (note sequestration accounting is then picked up 

by the afforestation and later possibly by reforestation variables). In turn, these 

movements are equated with a set of variables that move the transferring land into the 

FORCROP class with a HIGH site productivity classification into any of the possible 

types of succeeding forests. This tableau column represents cases within the GAMS 

implementation variables LANDFROMAG and CONVRTFROMAG. 

• Pasture land from ag -- Afforestation of agricultural pasture land. Such land movements 

are defined at the FASOMGHG 11 region level by time period. They remove land from 

the agricultural pasture land balances (als) and place it into the forest balance. They incur 

a cost of land transformation (alt) in the objective function. They are limited by an 

exogenous maximum transfer limit (ac). They remove sequestered carbon from the GHG 

balance (as) by zeroing out the agricultural component for this acre (note sequestration 

accounting is then picked up by the afforestation and later reforestation variables). In 

turn, these movements are equated with a set of variables that move the transferring land 
92 

into the FORPAST class with a MEDIUM site productivity classification for any of the 

possible types of succeeding forests. This tableau column represents cases within the 

GAMS implementation variables LANDFROMAG and CONVRTFROMAG. 

• Land to ag crop land -- Deforestation and land use change to agricultural cropping. Such 

land movements are defined at the FASOMGHG 11 region level by time period from the 

CROPFOR or FORCROP classes with a HIGH site productivity classification. They 

remove land from the forestry balance and subsequently place it into the agricultural 

Tilled land class, and land can change tillage balances at the rate als. They incur a cost of 

land transformation (flt) in the objective function. They are limited by an exogenous 

maximum transfer limit (ac) and add sequestered carbon to the GHG balance category for 

agricultural sequestration (as). This starts up the agricultural sequestration accounting for 

this acre (note sequestration accounting is dropped by the forestry component in the 

period before timber harvest). This tableau column represents cases within the GAMS 

implementation variables LANDTOAG and CONVRTTOAG. 

• Land to ag pasture -- Deforestation and land use change into agricultural pasture. Such 

land movements are defined at the FASOMGHG 11 region level by time period from the 

PASTFOR or FORPAST classes with a MEDIUM site productivity classification. They 

remove land from the forestry balance and place it into the agricultural pasture land 

balances at the rate als. They incur a cost of land transformation (flt) in the objective 

function. They are limited by an exogenous maximum transfer limit (ac). They remove 

sequestered carbon from forestry sequestration GHG balance at the rate as, starting up the 

agricultural sequestration component for this acre (note sequestration accounting is 

dropped by the forestry component in the period before timber harvest). This tableau 

column represents cases within the GAMS implementation variables LANDTOAG and 

CONVRTTOAG. 

• Move for to ag commod -- Movement of processed forestry commodities into the 

agricultural processed commodity balances. Commodity movements are defined at the 

FASOMGHG 11 region level by time period. They involve forestry commodities that are 

suitable as biofuel feedstocks. They incur cost of movement in the objective function at 

the rate acm. They remove commodities from the wood product balances at the rate fm

and place them into the agricultural commodity balances at the rate am. This tableau 

column represents cases within the GAMS implementation variables MOVCOMTOAG.

• Forest commodities moved from ag -- Movement of processed agricultural commodities 

into the wood product balances. Such commodity movements are defined at the 

FASOMGHG 11 region level by time period. They involve agricultural commodities that 

are suitable fiber resources for pulp and paper manufacturing processes. They incur cost 

of movement in the objective function at the rate fcm. They remove commodities from 

the agricultural commodity balances at the rate am and place them in the wood products 
93 

balance at the rate fm. This tableau column represents cases within the GAMS 

implementation variables MOVCOMFROMAG.

The equations in the tableau that are related to the intersectoral transfers are the sectoral 

specific balances as discussed in the forestry and agricultural sections above, along with the 

following two equations: 

• Max for land transfer -- Limit the maximum amount of forest land that can be transferred 

to agriculture and also defines adherence to cost function steps depicting increasing costs 

of land transformations as more land is transferred. They are defined by region for a total 

amount of land that could transfer across all time periods (ltf), with accounting in all 

subsequent time period so that it reflects the effects of past land transfers. This tableau 

row represents the GAMS implementation equations MAX_FOR_TO_AG_LAND and 

FOR_TO_AG_LANDTRNLIM. 

• Max ag land transfer -- Limit the maximum amount of agricultural land that can be 

transferred to forestry. They are defined by region for a total amount of land that could 

transfer across all time periods (lta), with an accounting in each subsequent time period 

so that it reflects the effects of past land transfers. This tableau row represents the GAMS 

implementation equations AG_TO_FOR_LANDTRNLIM. 

In the interests of space, the tableau does not portray the FASOMGHG equations that 

equate the variables LANDTOAG and LANDFROMAG that represent the land moving into and 

out of agriculture that are not differentiated by class, site productivity class, or type of possible 

forest successor with a set of the variables that do have such designations (CONVRTTOAG, 

CONVRTFROMAG). This involves the GAMS implementation equations TRNTOLDBAL and 

TRNFRLDBAL. 

5.1.4 GHG submodel 

The GHG submodel accounts for and reflects payments to net GHG emission reductions 

above those in the baseline from agriculture and forestry, including sequestration activity, 

emission activity, and biofuel related offset activity. In the tableau, the GHG submodel is 

represented by the column GHG payment and the row GHG balance. The GHG balance row 

depicts the involvement of agricultural and forestry activities. In turn, given a policy or GHG 

price signal, these submodels can employ different production possibilities to reduce net 

emissions. 

5.1.4.1 GHG payment variable 

The GHG payment variable reflects the cumulative amount of sequestration, emissions, 

or biofuel generated offsets by time period for each GHG account named above. This variable 
94 

can be either positive or negative and is equated with the quantity computed by the account 

specific GHG balance equations. The variable has an objective function coefficient that reflects 

the pricing of changes in this GHG account as portrayed by the term gp. This objective function 

term is somewhat complex, encompassing several different factors. Specifically it involves: 

• Computation of the net gain in the GHG account accrued since the last time period that is 

above and beyond the net gain in the baseline. This is done by incorporating the 

difference between the GHG payment variable in the current period and the variable 

value in the last period (GHGpaymentt - GHGpaymentt-1) to get the gain. Then we 

subtract off the difference in gain observed in a baseline by subtracting the baseline 

number for this period minus the baseline for the previous period (baselinet - baselinet-1). 

• Conversion of all accounts to a carbon dioxide equivalent basis by multiplying by the 

appropriate GWP. 

• Attaching the proper signs to emissions, offsets, and sequestration, specifically a negative 

sign to emissions and a positive to offsets and sequestration. This gets everything to the 

point that increases in the account would earn a positive payment. 

• Multiplying the individual account terms times a zero-one indicator that tells whether the 

GHG account is eligible for GHG payments from a policy standpoint. 

• Introducing discounting provisions to convert all dollar flows to a year 2000 net present 

value. This involves two stages. First, we multiply by an annuity factor that alters typical 

payments in each five year period to the net present value of total payments for that 

period. Then we multiply by a discount factor that reduces the value back to year 2000 

dollars. The annuity factor used is the value of a five year annuity for all time periods but 

the last explicit one in the model. In that period, the factor for present value of an infinite 

annuity is used, assuming that activity persists forever as is discussed under the topic of 

the integrating objective function just below. 

5.1.4.2 GHG balance equation 

The tableau row showing the GHG balance equation portrays the way the equation 

balances net GHG emissions by type of account with net GHG payments. These equations 

encompass GHG sequestration, emissions, and biofuel related offsets. The tableau portrayal for 

this equation is rather simplistic but within FASOMGHG it covers many different cases and 

mitigation options. Let us review these by submodel. 

• In the terms associated with the forestry submodel, the equations reflect sequestration in 

forest soils, ecosystems, and standing trees, along with sequestration in wood products 

and emissions from production related to fossil fuel use. The term ce reflects the GHG 

emissions and sequestration associated with the management of existing forests, while cr
95 

reflects that for reforested lands and ca for afforested lands. The term cm reflects carbon 

sequestered in wood products. 

• In the terms associated with the agricultural submodel, these equations incorporate effects 

on soil sequestration, biofuel offsets, and emissions. The coefficients associated with 

crops involve sequestration associated with initial tillage (ts), tillage change (tcs), and 

land use change between crop land and pasture (ds). Sequestration accounting is also 

included within the term for changes in cropped acreage production (ce) when longer 

lived perennials are involved. Crop production related emissions are also in the term ce

and reflect emission's associated with: 

• Fossil fuels used in tillage, planting, harvesting, and other machinery operations 

• Crop drying 

• Irrigation 

• Histosoils 

• Nitrogen fertilization 

• Rice production 

• Fertilizer and pesticide manufacture 

• Residue burning 

• Sewage sludge usage 

• Nitrogen fixing crops. 

Livestock related emissions associated with fossil fuel usage, enteric fermentation, and 

manure management are reflected in le. Emissions related to agricultural processing are 

reflected within pg. The coefficients pg also incorporate accounting for biofuel related 

offsets when biofuel feedstocks are made into ethanol, diesel, or coal substitutes. 

• In the intersectoral transfer part of the model, the coefficients ts reflect the amount of the 

carbon sequestration that is withdrawn from accounting in the agricultural sector when 

land moves from agriculture into forestry (where soil carbon accounting is then picked up 

within a forestry account). Likewise, these coefficients reflect the amount of 

sequestration that is added into the agricultural soil carbon accounting when land moves 

from the forest sector and is thus dropped from the forest sector soil accounting. 

This row depicts the GAMS implementation equations GHGACCOUNTS.

5.1.4.3 GHG mitigation alternatives portrayed 

Within these equations, there are numerous management alternatives to reduce net GHG 

emissions below baseline levels. These are referred to throughout the document as mitigation 

options and include forestry, agricultural, and biofuels options. 
96 

Forestry mitigation options include: 

• Management manipulations in the form of lengthened timber rotations or altered forest 

species choice. 

• Expanded usage of more intensive (higher input) management. 

• Expansions in forested area through conversion of agricultural lands into forest uses 

(afforestation). 

• Avoiding conversion of forested areas to agriculture (avoided deforestation). 

• Conversion of harvested wood into longer-lived wood products. 

• Utilization of techniques that embody less fossil fuel usage. 

• Usage of harvested wood to offset fossil fuel usage, employing it in electrical generation 

or other forms of biofuels. 

• Choice of management by region and site to introduce or manipulate forests on highly 

productive fast-growing sites to obtain higher timber yields and faster rates of carbon 

sequestration. 

Agricultural mitigation options include sequestration and emission management possibilities, 

where the sequestration ones include: 

• Deintensifying agricultural tillage. 

• Increasing the relative abundance of grasslands. 

• Altering the mix of annuals versus perennials, increasing the standing biomass through 

crop mix choice or crop management. 

While the agricultural emissions related ones include: 

• Lowering fossil fuel usage. 

• Lowering chemical usage, saving the GHG emissions obtained in producing them. 

• Reducing fertilization rates. 

• Manipulating enteric fermentation by altering ruminant livestock feeding and rate of gain. 

• Improving manure management. 

• Reducing the size of the livestock herd. 

• Lessening rice acreage. 

• Reducing legume acreage. 

• Manipulating crop mix, irrigated/ dryland use, regional, and soil type locations of crops. 

• Manipulating regional size and composition of the livestock herd, feed blend employed. 

• Manipulating consumption patterns, processing patterns, and import/export mixes. 

Biofuels feedstock related options involve agriculture and forestry provision of feedstocks that 

are in turn used to produce: 
97 

• Ethanol as a replacement for gasoline through the conversion of corn, sugar cane, 

switchgrass, poplar, and willow. 

• Electricity through use of milling residues, harvested wood, switchgrass, poplar, and/or 

willow as feedstocks as a substitute for coal. 

• Biodiesel from soybeans or corn, for use in transportation fuel. 

5.1.4.4 Other GHG related features 

A few clarifying comments are also in order on the nature of the way that FASOMGHG 

handles the GHG parts of the model: 

• An exogenously specified trajectory for GHG prices (expressed in carbon equivalents) is 

specified by five year period. Note that although this input can reflect increasing GHG 

prices over time, the model has perfect foresight and thus rising prices can alter current 

economic behavior in complex ways. 

• Incentive payments are not paid for the total stock of GHG emissions, offsets, or 

sequestration, but rather for deviations from the baseline. 

• FASOMGHG is initially run with a zero carbon equivalent price that is taken as the 

business-as-usual baseline. 

• Provisions are made to allow the user to include discounts on a national basis for any of 

the GHG accounts. These discounts are for permanence, leakage, additionality, and 

uncertainty. Each of these potential discount factors has a default value of zero. 

5.1.5 Integrating objective function 

The integrating objective function computes total consumers' and producers' surplus 

across all four submodels and is maximized in the FASOMGHG solution. The objective function 

is shown in the tableau row labeled Welfare. In this equation, we see positive contributions to 

welfare arising in association with: 

• Area underneath the domestic demand curves for forestry (fd) and agricultural (ad) 

products. 

• Area underneath the export demand curves for agricultural (ae) products. 

• Valuation of terminal forest inventory (ft). 

• GHG payments to net emissions reductions (gp). 

In turn, total cost is subtracted in the form of areas underneath supply curves and price 

times quantity for fixed price cost items. The area under the explicit upward sloping supply 

functions includes: 
98 

• Endogenous (Canadian) log supply 

• Forestry non-wood inputs (fnw). 

• Agricultural (ai) and forestry imports (fi). 

• Agricultural factor supplies for water, AUMs, and labor (afs). 

The total cost of the fixed price inputs, which is subtracted by taking price times quantity, is 

computed for: 

• Stand production (forest management) costs (pc). 

• Costs of domestic wood product transport (fdt). 

• Public log supply (fds). 

• Costs of land transformations from agriculture to forestry (alt). 

• Costs of land transformations from forest to agriculture (flt). 

• Costs of commodity movements from forest to agriculture (fcm). 

• Costs of commodity movements from agriculture to forestry (acm). 

• Costs of inputs used in crop production (acc). 

• Costs of inputs used in livestock production (alc). 

• Costs of inputs used in agricultural processing (apc). 

• Costs of inputs used in feed blending (afc). 

• Costs of land transformations between pasture and crop land (ale). 

• Agricultural domestic transportation costs (adt). 

Discounting provisions are also included. The model variables falling into the objective 

function embody a time dimension and consequently introduce income and cost streams arising 

in different time periods. Thus, they must be transformed into a common unit which we select to 

be year 2000 dollars. To do this, FASOMGHG incorporates two different discounting 

procedures. First, because all variables give the annual activity levels during each five year 

period, their objective function terms are transformed to give the present value of period 

spanning constant activity at that rate. That involves multiplying the term by a factor where the 

factor used is present value of a five year annuity for all but the terminal period in forestry and 

the last explicit period for agriculture and GHG payments. In those periods, a perpetual annuity 

factor is used. Second, the terms for time periods beginning in year t are multiplied by the 

discount rate for year t relative to year 2000. The objective function is the GAMS 

implementation equation WELFAR. 
99 

5.2 Aggregate spatial portrayal 

The tableau in table 5-1 portrays virtually the whole structure of the FASOMGHG 

programming model. However, because of a desire that it fit on a single page, it was constructed 

to represent a single aggregate region and a single aggregate time period. A companion tableau 

that reveals some regional details is shown in table 5-2. However, this again requires 

compromise to fit it on a single page. As consequence, we portray a two-region model but in the 

process need to aggregate or drop much of the forestry and agricultural sector submodel detail. 

Note this tableau omits many features in FASOMGHG and is designed to showcase the regional 

dimension. 

The variables in this tableau are 

• Reg forest production -- Acres of forest production across alternatives and inventories by 

region. This variable portrays forest production form existing, reforested, and afforested 

stands (the first three columns in table 5-1). The tableau shows that the regional forest 

production variable draws from the regionally specific timberland inventories while 

producing regional harvested logs (fh) and entering the national GHG balance to reflect 

sequestration and fossil fuel related emissions (fc). 

• Reg Manufacture wood -- Regionally specific wood products manufacturing activity. 

This column is a regionally enhanced depiction of the Manufacture wood prods column 

in table 5-1. This variable uses harvested logs from a regionally specific harvested log 

balance at the rate fpu, while producing goods into the regionalized wood products 

balance at the rate p and, if specified, using regional wood products as intermediate 

products to the production process (also part of p). It also requires the supply of nonwood inputs from the regional and process specific non-wood input balance. Finally, it 

enters the national GHG balance reflecting the fate of sequestered carbon in wood 

products at the rate cm. 

• Reg En. Public supply -- Supply of logs from regional public land harvesting (in Canada 

only). This column is a regionally enhanced depiction of the Endog public supply 

(Canada) column in table 5-1. This variable supplies harvested logs into the regional 

harvested log balance, while incurring a cost (fds) in the objective function. 

• Reg non-wood inputs -- Supply of non-wood input items as inputs into wood products 

manufacturing. These items are defined by region, process, and wood product. The nonwood input supply involves an upward sloping supply curve to reflect increasing regional 

costs of wood product manufacturing as the quantity manufactured increases. This 

column is a regionally enhanced depiction of the Non-wood inputs column in table 5-1. 

The non-wood input items are placed into a non-wood balance equation that reflects 
100 

regional processes and is product specific. The associated objective function term (fnw) 

gives the area underneath the non-wood input supply equation. 

• Reg wood products trade -- International imports and exports of manufactured wood 

products. This variable adds one unit of manufactured wood product into the regional 

balance when importing and withdraws one unit when exporting. It has an associated 

objective function cost term that adds the area under the regional and wood product 

specific export demand curve when exporting or subtracts the area under the regional and 

wood product specific import supply curve when importing. This column is an 

aggregation of the columns Forest import and Forest export in table 5-1 but also 

elaborates on their regional dimension, showing that they are defined in association with 

forest regions and not the national market. 

• Reg for com to nation -- Movements of manufactured wood products into the national 

market. This preserves model adherence with the law of one price. It withdraws one unit 

of a manufactured wood product from the regional balance and then enters it into the 

national wood product balance. This movement has an associated objective function cost 

term (fpd), which is the typical price difference between regional and national prices. 

This column is an elaboration on the column Forest domestic transport in table 5-1 and is 

one of the subcases contained within the GAMS implementation variable 

FORWDTRANSPORT. 

• Wood reg to reg -- Interregional movements of manufactured wood products. This 

variable withdraws one unit of a manufactured wood product from the originating region 

and then enters it into the destination region. In this movement, an interregional transport 

cost (fdt) is incurred in the objective function. This column is an elaboration on Forest 

domestic transport in table 5-1 and is contained within the GAMS implementation 

variable FORWDTRANSPORT. 

• Wood product demand -- National demand for manufactured wood products that involves 

a downward sloping demand curve. This variable withdraws one unit from the national 

wood product balance. It also reflects the area underneath the wood products demand 

curve (fd) in the objective function. This column is another portrayal of the Wood 

product demand column from table 5-1. 

• Reg Land from Ag -- Regional agricultural crop and pasture land moving into forestry for 

afforestation. This variable withdraws one unit of land from the regional agricultural land 

balance (possibly disaggregated by subregion and land quality class as discussed under 

the intersectoral transfer model above) and places it in the regional balance with the 

appropriate forest class. It also reflects the hurdle costs of land transformation (alt). This 

column is another portrayal of the columns Crop land from ag and Pasture land from ag

in table 5-1. 
101 

• Reg Land to ag -- Regional forest land being deforested and moving into agriculture for 

use as crop or pasture land. This variable withdraws one unit of land from the forestry 

bare land balance and moves it into the agricultural land balance (possibly disaggregated 

by subregion and land quality class as discussed under the intersectoral transfer model 

above). It also reflects the costs of land transformation (flt) for stump removal and other 

land clearing activities. This column is another portrayal of the Land to ag crop land and

Land to ag Pasture land columns in table 5-1. 

• Reg Produce crop/live -- Crop and livestock production by region. This portrays the 

columns Crop production and Livestock production as well as the tillage related columns

in table 5-1. The regional agricultural production variables draw from the regional 

agricultural land inventory (alu), while producing regionally differentiated crop (ac) and 

livestock (alp) commodities, possibly using some livestock as intermediate inputs (also 

within alp) and secondary/ blended feed commodities (as). It also uses water, AUMs, and 

labor (af). Finally, it enters the national GHG balance reflecting sequestration and 

emissions (ag). 

• Reg Ag processing/blend -- Regional agricultural processing and feed blending. This 

portrays the columns Agricultural processing and Feed blending in table 5-1. Regional 

agricultural processing and feed blending draws from the regional agricultural crop (pc) 

and livestock (pl) balances, while producing regional processed commodities (py) and 

possibly uses some processed commodities as intermediate inputs (also within py). 

Finally, it enters the national GHG balance, reflecting sequestration and emissions (pg). 

Not all processing is regionalized and in those cases this variable appears in association 

with the national commodity balance. 

• Reg water, AUMs Lab -- regional supply of water, AUMs, and labor. This column is a 

regionally enhanced depiction of the Sup water, AUMs, labor column in table 5-1. The 

factors are placed into regional and factor specific water, AUMs, and labor balance 

equations. An associated objective function term appears that gives the area underneath 

the upward sloping factor supply equation (fds). 

• Reg Ag trade -- International imports and exports of the agricultural products that are 

modeled with spatially explicit trade. This variable adds one unit of imported product 

into the regional balance when importing and withdraws one unit when exporting. It has 

an associated objective function term (s) that adds the area under the foreign country 

specific export demand curve when exporting or subtracts area under the country specific 

import supply curve when importing. This column is an aggregation of the columns Ag 

import and Ag export in table 5-1. It also elaborates on their regional dimension. 

Although not explicitly shown here, international transport between regions and foreign 

countries is also involved. 
102 

• Reg Move ag to nation -- Movement of agricultural crop, livestock, and processed 

commodities into the national market. This preserves model adherence with the law of 

one price. This variable withdraws one unit of a commodity from the regional balance 

and then enters it into the national market balance. This movement has an objective 

function cost term (fpd) that is the typical price difference between regional and national 

prices. This is an elaboration on the column Domestic ag transport in table 5-1. 

• Reg to reg ag transport -- Interregional movements of agricultural commodities. This 

variable withdraws one unit of a commodity from the originating region and then enters it 

into the destination region. This movement has an associated objective function transport 

cost term (adt). This column is an elaboration on the column Domestic ag transport in 

table 5-1. 

• Ag domestic consumption -- National demand for agricultural products. It involves a 

downward sloping demand curve. This variable withdraws one unit from the national 

commodity balance. It also reflects the area underneath the demand curve (ad). This 

column is another portrayal of the column Ag domestic consumption in table 5-1. 

• Ag trade -- International imports and exports of agricultural products that are modeled 

without spatially explicit trade. This variable adds one unit of the commodity into the 

national balance when importing and withdraws one unit when exporting. It has an 

objective function term (s) that adds the area under the rest of world excess demand curve 

when exporting or subtracts the area under the world excess import supply curve when 

importing. This column is an aggregation of the columns Ag import and Ag export in 

table 5-1. 

• GHG payments -- GHG payments by GHG account. Another portrayal of the GHG 

payment column in table 5-1. The objective function term (gp) reflects payments for 

GHG fluxes above the baseline and withdraws from the GHG balance equation. 

The equations in this tableau are: 

• Welfare -- Adds up consumers' and producers' surplus across the total programming 

model. The terms are discussed in the definition of the Welfare row in table 5-1. The 

portrayal here shows that many of the included items are regionally specific. 

• Reg Timberland -- Limits regional forest land use to land available. Regional lands can 

either come from the initial endowment (fl) or movements from agriculture. Land 

available is reduced by movements to agriculture. This equation aggregates several 

equations from table 5-1, encompassing Exist timberland, Bare forest land, and Bare 

land from ag. 

• Reg Harvested Logs -- Limits use of regional harvested logs to harvested logs available. 

Available harvested logs can come from either harvests in regional private forests (fh) or 

from regional exogenous public supply. Harvested logs are used by the regionalized 
103 

wood products manufacturing variables. This row portrays the Harvested log bal row in 

table 5-1. 

• Reg Wood Products -- Constrains regional use of manufactured wood products to the 

quantity available. Wood products are produced by regional wood products 

manufacturing (p) or can be imported. Regional wood products can be domestically 

transported, exported, or transferred to national demand. Wood products can also be used 

as intermediate products by manufacturing as also depicted by p. This portrays the Wood 

products bal row in table 5-1. 

• Reg Non-wood input -- Balances regional supply of non-wood input items with their use 

by wood products manufacturing. This portrays the Non-wood input bal row in table 5-1. 

• National wood products -- Balances national consumption of manufactured wood 

products with supply transferred in from the regions. This row establishes a national 

price that is translated to the regional prices, taking into account typical price differences. 

The row portrays the Wood products bal row in table 5-1. 

• Reg Ag land -- Constrains regional agricultural land use (alu) to land available. Regional 

lands either come from the initial endowment (cl) or movements from forestry and are 

reduced by movements to forestry. This equation aggregates Initial crop land, Land that 

can change still, Tilled land, and Pasture land from table 5-1. 

• Reg crop balance -- Constrains regional use of crop products to the quantity available. 

Available regional crops come from agricultural production (ap) or imports. Crop 

products are used by the regional agricultural processing and feed blending (pc) or can be 

exported. Regional crops can also be domestically transported, or transferred to the 

national demand. Crop products can be used directly as feeds by regional livestock as 

also depicted in ap. This tableau row portrays the Crop balance row in table 5-1. 

• Reg livestock balance -- Limits regional livestock product use to availability. Livestock 

come from agricultural production (alp) or imports. Livestock products are used by 

regional processing (pc) or export. Also regional livestock can be domestically 

transported, transferred to the national demand, or used as intermediate products by other 

livestock production possibilities, as also depicted in alp. This portrays the Livestock 

balance row in table 5-1. 

• Reg processed/feed -- Limits regional use of processed agricultural and blended feed 

products to the quantity available. Processed and blended feed products come from 

processing or feed blending (pl). Such products are used by the regional agricultural 

production at the rate as or can be moved to the national balance. These products can 

also be used as intermediate products by processing and feed blending possibilities as 

also depicted in py. This tableau row portrays an aggregation of the Processed ag 

commod and feed balance rows in table 5-1. 
104 

• Reg Wat, AUMs, Lab -- Balances regional supply of water, AUMs, and labor items with 

use by agricultural production. This tableau row portrays the Water, AUMs, labor row in 

table 5-1. 

• National ag products -- Balances national consumption of agricultural products with 

supply transferred in from regional balances. This tableau row establishes a national price 

that is then translated to regional prices, taking into account typical price differences. 

The aggregates the Crop balance, Livestock balance and Processed ag commod rows in 

table 5-1. 

• GHG balance -- Balances GHG accounts with their pricing. The net amount of GHG 

emissions arises from sequestration and emissions arising through forest production (fc); 

sequestration in wood products (cm); changes in sectoral sequestration when land 

transfers (as); net emissions from agricultural production (ag); and offsets/emissions 

from agricultural processing (pg). This row portrays the GHG balance row in table 5-1. 
105 

Table 5-2 Sample tableau illustrating full FASOMGHG model with regional detail but aggregate production 

 Variables Equations 

Reg 1 forest production 

Reg 1 Manufacture wood 

Reg 1 En. Public supply 

Reg 1 Non-wood inputs 

Reg 1 wood product trade 

Reg 1 for com to nation 

Reg 2 forest production 

Reg 2 Manufacture wood 

Reg 2 En. Public supply 

Reg 2 Non-wood inputs 

Reg 2 wood product trade 

Reg 2 for com to nation 

Wood reg 1 to reg 2 

Wood reg 2 to reg 1 

Wood product demand 

Reg 1 Land from Ag 

Reg 1 Land to ag 

Reg 2 Land from Ag 

Reg 2 Land to ag 

Reg 1 Produce crop/live 

Reg 1 Ag processing/blen

d

Reg 1 water, AUMs Lab 

Reg 1 trade 

Reg 1 Move ag to nation 

Reg 2 Produce crop/live 

Reg 2 Ag processing 

Reg 2 water, AUMs Lab 

Welfare -fds -fnw +/-t -fpd -fds -fnw +/-t -fpd -fdt -fdt +fd -alt -flt -alt -flt -ac -apc -afs +/-s -ad -ac -apc -afs Reg 1 Timberland +1 -1 +1 Reg 1 Harvested Logs -fh +fpu -1 Reg 1 Wood Products +/-p +/-1 +1 +1 -1 Reg 1 Non-wood input +1 -1 Reg 2 Timberland +1 -1 +1 Reg 2 Harvested Logs -fh +fpu -1 Reg 2 Wood Products +/-p +/-1 +1 -1 +1 Reg 2 Non-wood input +1 -1 National wood products -1 -1 +1 Reg 1 Ag land +1 -1 +alu Reg 1 Crop balance +-ap +pc +-1 +1 Reg 1 Livestock bal +-alp+pl +1 Reg 1 Processed/feed +as +-py +1 Reg 1 Wat, AUMs, Lab +af -1 Reg 2 Ag land +1 -1 +alu Reg 2 Crop balance -ap +pc Reg 2 Livestock bal +-alp+pl Reg 2 Processed/feed +as +-py Reg 2 Wat, AUMs, Lab +af -1 National ag products -1 GHG balance +fc +cm +fc +cm -as +as -as +as +ag +pg +ag +pg 
106 

5.3 Aggregate intertemporal portrayal 

The tableau in table 5-1 portrays virtually the whole structure of the FASOMGHG 

programming model. However, because we fit it on a single page we only represent a single 

aggregate region and time period. Table 5-3 provides a companion tableau that reveals 

intertemporal details. However, this again requires compromises to fit on a single page. As a 

consequence, we portray a three period, one region model but to do this we needed to aggregate 

or drop much of the forestry and agricultural sector submodel detail. Note this tableau omits 

many features in FASOMGHG and is designed to showcase the intertemporal dimension. Also, 

while not portrayed here, discounting provisions are included as discussed in the integrating 

objective function section above. 

The variables in this tableau are as follows: 

• Exist stand harvest in pd -- Management of existing forest stands across harvest date 

alternatives. This variable is an alternative portrayal of Exist stand in table 5-1. Table 5-3 

shows that the initial inventory (lf) can be managed using either different clearcut harvest 

dates (including never) or possibly partial cutting strategies. Upon harvest, stands yield 

logs at the rate fhe. When stands are not clearcut during the model explicit time period, 

they yield logs into the terminal log balance (te) that reflects long-term log yields under 

the assumptions of a fully regulated forest (using von Mantel’s formula as discussed 

below). In the GHG balance, the cumulative amount of sequestration (es) is entered only 

prior to clearcut harvest but not in the clearcut period (sequestration accounting is picked 

up under the subsequent use of the stand). Emissions accounting is also done for all 

periods to reflect cumulative emissions from that period until the model end and thus 

persists beyond the harvest period, but is not shown here. 

• Est forest land in a pd and harvest in pd -- Establishment of forests on lands that were 

previously forested or are from agriculture. This variable is defined over the periods in 

which the forest is established and harvested. This variable is an aggregate portrayal of 

the column Reforest stand and Afforest stand in the tableau in table 5-1. For illustrative 

purposes, the tableau portrays stands that can be harvested as soon as one period after 

planting (this is not true in the actual model). Forest establishment requires land from 

previous clearcuts or agriculture. That land can be used under one of a number of 

management alternatives involving either different clearcut harvest dates (possibly never) 

or partial cutting. Upon clearcut, thinning, or partial cut, stands yield harvested logs 

(fhe). When stands are not clearcut, logs are placed in the terminal log balance (te) that

reflects long-term log volume under the assumptions of full regulation. In the GHG 

balance, the tableau portrays sequestration showing that sequestration accounting is done 

from the establishment period up through the period immediately prior to harvest 
107 

(expecting sequestration accounting it to be picked up under the subsequent use of the 

stand). Also, while not shown here, emissions accounting is also done and persists 

beyond the harvest period. 

• Manufacture wood prods in pd -- Period specific wood products manufacturing activity. 

This column is a temporally enhanced depiction of Manufacture wood prods in table 5-1. 

This variable uses harvested logs in the manufacturing time period (fpu), while 

producing wood products (p) and, if specified, using intermediate products (also part of 

p). Finally, it enters the national GHG balance to reflect the fate of sequestered carbon in 

wood products from the time period of harvest through the end of the model period at the 

rate cm. 

• Wood product demand in pd -- National demand for manufactured wood products. This 

is another portrayal of the Wood product demand in table 5-1 but actually represents the 

entire wood products marketing part of the model that is greatly aggregated here. It 

involves a downward sloping demand curve. This variable withdraws manufactured 

wood products from the balance that is time period specific. The area underneath the 

wood products demand curve (fd) appears in the objective function. 

• Land from ag in pd -- Agricultural crop and pasture land moving into forestry for 

afforestation. This is an elaborated portrayal of Crop land from ag and Pasture land from 

ag in table 5-1. This variable withdraws land from the relevant agricultural land balance 

for the current and all subsequent time periods. It then places it in the corresponding 

balance for afforestation in that time period. It also reflects the hurdle costs of land 

transformation (alt). This variable enters the GHG balance, debiting the amount of 

agricultural soil carbon sequestered (as) for this and all subsequent time periods. In turn, 

that accounting will be picked up by the forestry establishment variables. 

• Land to ag in pd -- Deforestation and movement of land into agriculture for use as crop or 

pasture land. This is another portrayal of Land to ag crop land and Land to ag Pasture 

land in table 5-1. This variable withdraws land from the forest land class bare land 

balance and moves it into the corresponding agricultural balance for this and all 

subsequent periods. It also reflects the costs of land transformation (flt) for stump 

removal and other land clearing activities. This variable enters the GHG balance, 

augmenting the amount of agricultural soil carbon sequestered (as) for this and all 

subsequent time periods. 

• Initial tillage -- Initial allocation of agricultural lands to tillage systems at the model 

beginning. This variable uses land from the initial allocation (al) and makes it available 

for cropping under a particular tillage system. It enters the GHG balance as, beginning 

the agricultural soil carbon sequestration accounting in this and all subsequent periods. 

This is another portrayal of Initial tillage in table 5-1. 
108 

• Change tillage -- Alteration of tillage systems undertaken during a time period. This is 

elaboration on Change tillage in table 5-1. The variable uses land from the stock under a 

current tillage system and irrigation status. Such lands come from initial tillage 

allocation, land moving in from pasture or forestry (which moves into the conventional 

tilled, dryland stock), or prior tillage changes. It then makes that land available for 

cropping under an alternative tillage system and/or irrigation status. It enters the GHG 

balance (sc) for the current and all subsequent periods, reflecting a trajectory change in 

agricultural soil sequestration relative to the previously used tillage and irrigation system. 

This can be either positive or negative depending on whether tillage is made less or more 

intense. 

• Produce ag in pd -- Agricultural production across crop and livestock alternatives. This 

portrays Crop production and Livestock production in table 5-1. Agricultural production 

draws from the period specific land inventory (alu) while producing agricultural 

commodities (ay). It affects the national GHG balance to reflect sequestration and 

emissions (ag). These entries occur not only in the time period of activity but also in all 

subsequent time periods to reflect the cumulative nature of the FASOMGHG accounting 

of emissions and offsets. 

• Ag demand in pd -- Demand for agricultural commodities to reflect downward sloping 

demand. This is another portrayal of Ag domestic consumption in table 5-1 but is actually 

indicative of the broader modeling of agricultural commodity markets. This variable 

withdraws one unit of a commodity from the time period specific commodity balance and 

reflects the area underneath the demand curve (ad). 

• GHG payments in pd - GHG payments in a period. This is another portrayal of GHG 

payment in table 5-1. This variable has an objective function term (gp) that reflects 

payments for the difference in the GHG account between the time period at hand and the 

amount within the last time period, less the corresponding change in the baseline. 

The equations represented in this tableau are: 

• Welfare -- Consumers' and producers' surplus across the total programming model. 

These terms arise across time and thus the model incorporates discounting features as 

discussed in the integrating objective function section above. This corresponds to the 

table 5-1 row Welfare.

• Exist timberland -- Constrains usage of the existing forest land to that in the initial 

inventory (Lf). This equation portrays the table 5-1 row Exist timberland.

• Pd bare forest land -- Constrains the land used in establishing forest land use so it cannot 

exceed that coming from forest harvest or agriculture by time period. This is an 

aggregate portrayal of the table 5-1 rows Bare forest land and Bare land from ag. 
109 

• Pd harvested logs -- Limits period by period use of harvested logs to the harvested logs 

available. Harvested logs come from either management of private forests (fhe) or from 

unportrayed public supply. Harvested logs are used by time period specific wood 

products manufacturing. This portrays the Harvested log bal row in table 5-1. 

• Pd Wood Products -- Limits period by period use of manufactured wood products to the 

quantity of wood products available. Wood products are produced by period specific 

wood products manufacturing (p) or can be imported (not portrayed here). Wood 

products are then moved into markets but can also be used as intermediate products by 

the regional wood product manufacturing variables (also depicted in p). This reportrays 

the Wood products bal row in table 5-1. 

• Terminal for inventory -- Balances the perpetual even aged amount of logs from terminal 

standing forests (te) with their use (fu) by terminal manufacturing variables. This tableau 

row portrays the Terminal for inventory row in table 5-1. 

• Terminal Wood Products -- Balances use of terminal period manufactured wood products 

with quantity manufactured. The structure is the same as that discussed for the Terminal 

for products row above, except for the use of terminal period logs. This tableau row 

portrays the Terminal for products bal row in table 5-1. 

• Initial crop land -- Constrains the initial tillage and irrigation status assignment of 

agricultural land so it equals the initial land inventory available (cl). This represents the 

Initial crop land equation in table 5-1. 

• Pd Tilled ag land -- Constrains usage of agricultural land by time period, tillagesystem, 

and irrigation status to the available amount of land. The supply of such land comes from 

either the initial assignment of the land inventory, land changing tillage systems in the 

current or any previous time period, or land moving in from forestry (this movement is 

constrained so it only can move into the conventional tillage, dryland case). Such land is 

used either by cropping, changes into other tillage systems, or movement of land out to 

forestry (again only from the conventional, dryland case). The tillage changes can reflect 

either intensification or deintensification. This equation represents the Land that can 

change tillage and Tilled land rows in table 5-1. 

• Pd ag products -- Limits regional use of agricultural crop, livestock, processed products, 

and blended feeds to the quantity of those that are available. This tableau row portrays the 

Crop balance, Livestock balance, Processed ag commod and Feed balance rows in table 

5-1. 

• Pd GHG balance -- Balances the GHG accounts with their pricing by time period. This 

row portrays the GHG balance row in table 5-1. The coefficients as they are spread 

across the alternative time periods show the cumulative nature of the GHG accounting in 

FASOMGHG. 

Several major FASOMGHG features warrant discussion as they appear in this tableau: 
110 

• The contrast between the multi-year nature of the forestry production variables and the 

single year nature of the agricultural variables. In particular, notice how in the third 

column that the forestry variable takes initial land but does not release it for reforestation 

until the third period. On the other hand, in the agricultural columns notice how the 

periods are largely separable and the land balance repeats. Also, notice how in the land 

transfer activities that when land is withdrawn from the agricultural balances, it is 

withdrawn in the time period of transfer and all subsequent periods. 

• The stock accounting nature of GHG accounting. Namely, within the fifth forestry 

column note that the GHG balance emission and sequestration stream is multi-year in 

nature. These coefficients are cumulative and reflect the growing stock of sequestration. 

Also, on the agricultural side note that when emissions are encountered in the first time 

period, they also enter the balances for all subsequent periods, showing that 

FASOMGHG models the cumulative stock of emissions to the atmosphere 

• The nature of FASOMGHG soil carbon sequestration accounting. Notice that when a 

forest is harvested in a particular time, the sequestration related accounting in the GHG 

balance is only done up until the time period immediately before harvest. In turn, the soil 

carbon accounting is picked up when reforestation occurs underneath the reforestation 

variable, or by the land transfer variable when land moves to agriculture. In forestry, the 

net effect of this is that forest soil carbon sequestration accounting switches from the 

previous stand to the next stand in the period of harvest. This is done so as to permit the 

model to more accurately account for the loss of carbon when land use change occurs. 

• Synchronization of sequestration accounting across sectors. Soil sequestration 

accounting is done on both the agricultural and the forestry sides and is synchronized by 

the land transfer variables. Under those variables, when land transfers from agriculture to 

forestry, future sequestration on that land is removed from the agricultural accounts and 

will be picked up under the afforestation variable. Also, when land moves into 

agriculture, the sequestration accounting is entered from the period of movement until the 

model end. 

• The cumulative nature of agricultural soil carbon accounting. When land is committed to 

a particular tillage practice, accounting is done as if it remained in that tillage practice 

forever. Consequently, when land changes tillage, the model reflects the differences from 

the state being changed from. Also, when land moves to forestry, the model debits 

current and future sequestration to avoid double counting. 
111 

Table 5-3 Sample tableau illustrating FASOMGHG model in a dynamic setting without regional detail with aggr

 Variables Equations 

Exist Stand harv in pd 1 

Exist Stand harv in pd 2 

Exist Stand harv in pd 3 

Exist Stand harv never 

Exist partial cut 

Est forest Land in pd 1 harv in 2 

Est forest Land in pd 1 harv in 3 

Est forest Land in 1 harv never 

Est forest in pd 1 partial cut 

Manufacture wood prods in pd 1 

Wood product demand in period 

1

Est forest Land in pd 2 harv in 3 

Est forest Land in 2 harv never 

Est forest in pd 2 partial cut 

Manufacture wood prods in pd 2 

Wood product demand in period 

2

Est forest Land in 3 harv never 

Manufacture wood prods in pd 3 

Est forest in pd 3 partial cut 

Wood product demand in period 

3

Terminal Manufacture wood prod

Terminal Wood product demand 

Land from Ag in pd 1 

Land to Ag in pd 1 

Land from Ag in pd 2 

Land to Ag in pd 2 

Land from Ag in pd 3 

Land to Ag in pd 3 

Initial Tillage 

Change tillage in pd 1 

Produce ag in pd 1 

Ag demand in pd 1 

Change tillage in pd 2 

Produce ag in pd 2 

Welfare +fd +fd +fd +fd -alt -flt -alt -flt -alt -flt +ad Exist Timberland +1 +1 +1 +1 +1 Pd 1 Bare forest land -1 +1 +1 +1 +1 -1 +1 Pd 1 Harvested Logs -fhe -fhe +fpu Pd 1 Wood Products -p +1 Pd 2 Bare forest land -1 -1 +1 +1 +1 -1 +1 Pd 2 Harvested Logs -fhe -fhe -fhe -fhe +fu Pd 2 Wood Products -p +1 Pd 3 Bare forest land -1 -1 -1 +1 +1 -1 +1 Pd 3 Harvested Logs -fhe -fhe -fhe -fhe -fp -fhe +fu Pd 3 Wood Products -p +1 Terminal for inventory -te -te -te -te -te -te -te +fu Terminal for prods -p +1 Initial tilled land 1 Pd 1 Tilled Ag land +1 -1 -1 +/1 +alu Pd 1 Ag products -ay 1 Pd 2 Tilled Ag land +1 -1 +1 -1 -1 -1 +/1 +alPd 2 Ag products -ay Pd 3 Tilled Ag land +1 -1 +1 -1 +1 -1 -1 -1 -1 Pd 3 Ag products Pd 1 GHG balance es es es es fg fg fg fg cm -as +as as +/-scag Pd 2 GHG balance es es es fg fg fg cm fg fg cm -as +as -as +as as +/-scag +/-scag Pd 3 GHG balance es es fg fg cm fg cm fg cm -as +as -as +as -as +as as +/-scag +/-scag 
112 

6 CHAPTER 6 DESCRIPTION OF GREENHOUSE GAS MODELING 

Since GHG coverage is one of the core features of FASOMGHG, this chapter elaborates 

on the fundamentals of GHG modeling therein. 

6.1 GHG accounting in FASOMGHG 

FASOMGHG accounts for changes in agricultural and forestry sector related net GHG 

emissions within a number of categories. These categories can be classified into broad categories 

of those involved with forest, agriculture, and biofuels feedstocks. Coverage of these categories 

is described above in section 3.9.1. These items are strongly interactive within model solutions. 

For example, land moving from agriculture to forestry will change (a) agricultural sequestration 

and emissions, (b) sequestration gains from afforestation, (c) emissions from forest managementrelated fuel usage, and (d) eventual sequestration of carbon within wood products. Thus, the 

implications of GHG management-induced alterations span widely across activities within the 

model. The nature of these alterations are discussed below. 

6.2 Types of net GHG gains 

 Net GHG emissions can change due to altered GHG sequestration, rates of direct 

emissions and amounts of offsets generated. Each merits discussion. 

6.2.1 Carbon sequestration 

GHGs, generally in the form of carbon, can be sequestered in soils, standing trees, other 

vegetation, and in wood products. Sequestration refers to storage of the GHGs for more than one 

year. As a consequence, the sequestration definition used in the model for standing vegetation is 

limited to carbon storage in trees, understory and litter within both forests and plantations of 

woody biofuel feedstocks (poplar and willow) but excludes, for instance, carbon stored in 

annually cultivated crops. 

Carbon sequestration is also modeled within 

• Soils for lands in agricultural crop, and pasture lands 

• Soils in idled lands 

• Soils of land in forestry uses. 

• Harvested wood products 
113 

Finally, rough sequestration accounting is included for lands that move out of forestry 

and agricultural production into some form of developed usage such as housing, shopping 

centers, roads, etc. 

6.2.2 Direct GHG emissions 

FASOMGHG quantifies GHG emissions produced in the forestry and agricultural 

sectors. As described in Chapter 3, these emissions primarily arise from fossil fuel-related 

processes (e.g., energy consumption), livestock production, fertilization, and rice cultivation. 

However they also come from other smaller sources such as residue burning. One GHG source 

that potentially could be modeled as an emission, but is not, is emissions from land use change 

(e.g., deforestation or grassland conversion to crop land uses). Instead, these sources are 

accounted for in the model as reduced sequestration, although these are functionally equivalent 

to increased emissions. In particular, FASOMGHG depicts positive credits for sequestration and 

when the amount of carbon sequestered is reduced by harvesting forests or changing land uses. 

This in effect corresponds to an emission of the sequestered carbon and is thus “penalized” as a 

GHG emission debit. 

6.2.3 Biofuel offsets 

FASOMGHG can grant credits for activities which cause an offsetting reduction in GHG 

emissions by sources outside the model. These credits arise via the use of agricultural 

commodities as biofuel feedstocks for the production of three different types of energy. The 

energy types are 

• Electricity fueled by agricultural energy crops (switchgrass, willow and hybrid poplar), 

forest milling residues, or forest logs. 

• Ethanol from corn or agricultural energy crops, and 

• Diesel from oils derived from agricultural sources. 

The basic argument for granting credits for such activities involves the concept of carbon 

recycling. In particular, as agricultural or forest biomass grows, it absorbs carbon dioxide from 

the atmosphere through photosynthesis. The carbon removed from the atmosphere in this way is 

sequestered in standing biomass. In turn, when the biomass is harvested and turned into energy 

through combustion or chemical processes, the sequestered carbon is emitted and thereby returns 

to the atmosphere in the form of carbon dioxide. This basically means that the net effect on 

atmospheric carbon of growing biomass as a fuel source that is subsequently combusted is zero. 

In contrast, when fossil fuels are used to generate energy, the carbon that has been stored in 
114 

below-ground pools (and presumably would remain there forever were it not for its use as a fuel 

source) and is emitted to the atmosphere this leads to a net increase in atmospheric carbon 

concentration. Therefore, the substitution of biofuel feedstocks for fossil fuels can be viewed as 

decreasing the net carbon emissions. However, one also needs to account for the associated 

emissions of carbon or other GHGs that arise when the agricultural or forestry feedstocks are 

grown, transported and transformed into energy. 

6.3 Multi Gases and climatic forcing equivalency 

The multi-GHG impact of the agricultural and forestry sectors and possible manipulation 

of the atmospheric levels of these gases introduces multidimensional trade-offs between model 

variables, net GHG emissions, and the climate change implications thereof. In order to consider 

these trade-offs, the GHGes needed to be placed on a common footing. This is done through 

adoption of the 100-year global warming potential (GWP) concept and conversion of all gases to 

a carbon or carbon dioxide equivalent basis. 

GWPs compare the abilities of different GHGs to trap heat in the atmosphere. They are 

based on the radiative forcing (heat-absorbing ability) of each gas relative to that of CO2, as well 

as the decay rate of each gas relative to that of CO2. The GWP allows one to convert emissions 

of various GHGs into a common measure, which allows for aggregating the radiative impacts of 

various GHGs into a single measure denominated in CO2 or C equivalents. Extensive discuss ion 

of GWPs can be found in the documents of the Intergovernmental Panel on Climate Change 

(IPCC). In 2001, the IPCC updated its estimates of GWPs for key GHGs, but these estimates are 

still under debate. As a result, the FASOMGHG model uses the 1996 GWPs for the GHGs 

covered by the model, which are. 

• CO2 = 1 

• CH4 = 21 

• N2O = 310 

When carbon dioxide equivalent results are converted to a carbon equivalent basis, a 

transformation is done based on the molecular weight of carbon in the carbon dioxide. This 

means that the carbon dioxide equivalent quantities of gas are divided by 3.667 to compute the 

carbon equivalent quantities. 
115 

6.4 Including GHGs in Economic Incentive Scenarios 

Although FASOMGHG accounting considers all the categories of GHGs discussed 

above, it is possible that in specific implementation of the model that not all of the categories 

will be included in a GHG incentive scheme. In other words, the model tracks all GHG accounts 

but economic incentives may be applicable to only a subset of the accounts tracked in the model. 

FASOMGHG input contains parameters that authorize or de-authorize each of the individual 

accounts in terms of their eligibility for the GHG-related incentive payments and in terms of 

their use in the ultimate accounting done by the model 

6.4.1 Pricing GHG Increments 

FASOMGHG does not try to endogenize GHG prices. Rather it recognizes that the GHG 

prices will be exogenous to the agricultural and forestry sectors and takes a fixed GHG price on a 

carbon equivalent basis. This is a reasonable assumption given that approximately 84% of US 

GHG emissions arise in the energy sector, so it is clear the energy sector will play the primary 

role in price determination. FASOMGHG operates with an exogenously specified trajectory for 

carbon equivalent GHG prices by five year period. Although this input can reflect increasing 

GHG prices over time, users should note that the model has perfect foresight and thus rising 

prices can alter current economic behavior in complex ways. 

Although not implemented in the current FASOMGHG version, it would be simple to 

introduce policy targets in terms of the total quantity of net changes in GHGs. Also, one could be 

introduce incentive payments for amount of GHG mitigation practices (for example acres 

afforested) as opposed to payments for quantities of GHGs mitigated with relatively little effort. 

6.4.2 Use of a GHG Baseline 

FASOMGHG does not reflect incentive payments for the total stock of GHG emissions 

or sequestration, but rather for deviations from an emissions, offsets and sequestration baseline. 

Ordinarily, FASOMGHG is initially run with a zero carbon equivalent price. In turn the resultant 

GHG trajectory from that run is be used as the baseline in subsequent runs. This implies that 

FASOMGHG does not give mitigation credit for tillage changes, adoption of practices, 

afforestation, and other forest management manipulations that are observed in the absence of a 

GHG incentive program. Any GHG changes that occur in the baseline are considered businessas-usual (or BAU) changes to which GHG effects induced by a policy can be compared to gauge 

the effectiveness of the policy. However, this approach may lead to analytical difficulties when 

technologies to promote reductions in net GHG emissions that are profitable in the absence of 
116 

GHG incentives are introduced. Namely given the profit-maximizing foundations of the model, 

these activities would appear in the baseline and would therefore not be considered as additional 

GHG mitigation beyond BAU. This can be particularly of concern when observational data 

suggest that some of these “profitable” practices are not typically adopted in the field. Further 

research is needed on the occasional disconnect between apparent and actual profitability of 

different management practices. The baseline is defined in the array baseline 

6.4.3 Possible Inclusion of GHG Discounts 

Provisions are made to allow the user to include discounts on a national basis for any of 

the GHG accounts. The use of a discount indicates that only a portion of the GHG quantity in a 

particular account may be considered a recipient of incentive payments or counted as part of the 

mitigation total. Reasons for discounting GHG accounts generally include 

• Permanence: GHG emissions reduction or sequestration (more generally the latter) may 

be considered likely to be re-emitted in the future (beyond the time period that the model 

tracks), thereby indicating that the GHG benefits are only temporary. 

• Leakage: the GHG emission reductions or sequestration tracked by the model are offset 

by emissions increases outside the scope of the model. Therefore net GHG reductions are 

lower than the account would indicate. 

• Additionality: some of the GHG emission reductions and increased sequestration is 

considered part of the baseline, rather than induced by the policy. 

• Uncertainty: the GHG quantity effects projected are based on point estimates or 

averages. In reality, natural and economic factors could cause variation and deviations 

from the expected GHG effects that the model does not explicitly capture. Recipients of 

GHG payments will generally discount the value of payments based on their underlying 

uncertainty. 

Discounts related to each of these is permitted but all have a default value of zero in the 

table ghgdiscount in the file data_ghg.gms, meaning that no downward adjustments are made 

for the GHG quantities considered for payment or inclusion in the policy scenario. These factors 

are now described in more detail. 

6.4.3.1 Permanence 

In terms of permanence Kim, McCarl and Murray (2005) derive a permanence discount 

that is based on the time when an activity accumulates offsets, the possible reversal of the 

activity generating a loss of carbon credits in the future, and possible maintenance costs needed 
117 

to maintain the activity. They derive the permanence discount using a net present value 

framework that considers the relative value of nonpermanent GHG reduction with that of the 

perfect permanent GHG reduction. Such a discount is not necessary because, by its very nature, 

FASOMGHG is a multi-period net present value maximizing model that considers the exact 

same features that go into the derivation of the Kim, McCarl and Murray discount. As a 

consequence it's unlikely that the permanence discount needs to be used. 

6.4.3.2 Leakage 

In terms of leakage, Murray, McCarl and Lee (2004) derive a leakage discount based on 

the balance between GHG emission reductions stimulated with in a project area and the market 

induced emission gains stimulated outside of the project boundary. Murray, McCarl and Lee and 

Alig et al 1997 empirically demonstrate the leakage consequences of regional projects in the 

agricultural and forest sectors of the US both within other regions in the US and internationally. 

FASOMGHG, as a continental-scale US model, will consider US continental scale leakage 

because its GHG accounting is all inclusive or at least as close to such as we can make it. On the 

other hand, international leakage is not currently considered. Thus one needs to avoid double 

counting of domestic US leakage but may still need to include discounts that reflect international 

leakage. This is why the potential for adding such discounts is included in the model 

implementation. 

6.4.3.3 Additionality 

As mentioned above FASOMGHG incorporates a baseline and only pays for net GHG 

emission activity that occurs in addition to that in the baseline. An additionality discount as 

derived by McCarl reduces the creditable amount of GHG activity so that it only constitutes 

activity above and beyond that which would have occurred under business as usual i.e. that in 

the FASOMGHG baseline. As a consequence, it is unlikely that the additionality discount needs 

to be used. 

6.4.3.4 Uncertainty 

As mentioned above FASOMGHG treats net GHG emission activity as if it occurred at 

the average or point estimate level. An uncertainty discount as derived by McCarl and refined by 

Kim, McCarl and Butt (2005) reduce the creditable amount of GHG activity so that it constitutes 

a level of offsets expressed with a particular degree of certainty i.e. a 90% confidence interval as 

proposed by the Canadians in the Kyoto negotiations. Such a discount is not otherwise covered 

in FASOMGHG. 
118 

6.4.3.5 Avoid double-counting of discounts 

Care needs to be taken if imposing these discounts on a model run, as FASOMGHG 

endogenously treats facets of these items. For example, FASOMGHG 

• maximizes net present value, so it implicitly discounts for permanence; 

• operates at the US national scale, so it directly accounts for leakage at the national level; 

and 

• pays incentives on the difference between a baseline and the aggregate GHG trajectory 

for an account, so it generally considers additionality within the model structure. 

Why then include discounts? Mainly, the discounting scheme is present to permit 

introduction of measures of exogenous items, measures of leakage outside the US, uncertainty, 

and the possibility of treating projects where, for example, practices are forced in and payments 

are adjusted for these other factors. 

6.5 Which GHG categories count 

International negotiations regarding GHG emission crediting have revealed that it is 

certainly possible that not all activity that affects net GHG emissions will be eligible for GHG 

payments. Consequently, FASOMGHG allows users to specify payment eligibility of each of the 

alternative GHG accounts. For example, under the Kyoto Protocol to the United Nations 

Framework Convention on Climate Change, many types of enhanced forest management, and 

avoided deforestation among other things are apparently not be eligible for crediting. Similarly, 

in recent pieces of GHG legislation considered by the US Congress, various GHG components 

from forestry and agriculture are either explicitly excluded or treated as entities requiring special 

accounting. These types of limitations in policy scope can be accommodated by altering 

specification of payment eligibility. This is done in the data item willpayforghg in the file 

data_ghg.gms 

6.6 GHG mitigation alternatives in FASOMGHG 

Within the forest and agricultural sectors, as depicted, there are numerous management 

alternatives to reduce net GHG emissions below baseline levels. These are referred to throughout 

the document as mitigation options and are enumerated below. 

6.6.1 Forest mitigation 

The fundamental mechanisms within forestry that allow GHG mitigation are 
119 

• Forest management manipulations in the form of lengthened timber rotations or altered 

species choice. 

• Expanded usage of more intensive (higher input) management. For example one can 

employ improved tree varieties, fertilization, thinning, partial cutting, and a number of 

other management alternatives. 

• Expansions in forested area either through conversion of agricultural lands into forest 

uses (afforestation) or by avoiding conversion of forest areas into agriculture (avoided 

deforestation). 

• Conversion of harvested wood into longer-lived wood products. 

• Usage of techniques that embody less fossil fuel usage. 

• Usage of harvested wood to offset fossil fuel usage by employing it as a biofuel feedstock 

for electrical generation or some other forms of fossil fuel substitute. 

The principal GHG implications related to the above forestry manipulations involve 

manipulations of net sequestration and net emissions mainly altering carbon and carbon dioxide. 

In addition to the net mitigation pathways listed above, the net GHG emissions from forests can 

be altered by choice of regions and sites therein where management is altered. For example, one 

could choose to introduce forests on highly productive fast-growing sites to obtain higher yields 

and faster rates of carbon sequestration. 

6.6.2 Agricultural mitigation 

Agricultural mitigation can involve management manipulations that result in 

• Enhancements in soil carbon sequestration, 

• Reductions of GHG emissions, and 

• Offsets of emissions from fossil fuels 

Activities within this category can alter net emissions of the GHGs carbon/carbon 

dioxide, nitrous oxide, and methane. These two mitigation categories are now discussed in 

further detail. 

6.6.2.1 Agricultural carbon sequestration enhancement 

The enhancement of agricultural carbon sequestration involves management that 

increases the amount of carbon held in agricultural soils. The fundamental management 

manipulation mechanisms in this category involve alterations in: 
120 

• Intensity of agricultural tillage. This largely involves use of tillage alternatives that 

reduce the exposure of carbon in the soil to oxidation and allow larger soil aggregates to 

form. Such practices generally involve less soil disturbance. The practice also leaves crop 

residues on the soil, thereby potentially increasing carbon inputs. Tillage changes 

typically involve movement from more intensive tillage, such as moldboard plowing, to 

minimum or zero tillage practices. Additional emission reductions may also correspond 

with these tillage alterations because less-intensive tillage typically involves less direct 

fossil fuel use for tractors. However, there are also alterations in chemical usage (possibly 

increases in pesticide usage and alterations in rate of fertilization), which can then 

increase emissions from their manufacture and usage. FASOMGHG has the ability to 

track these indirectly induced GHG effects. 

• Relative abundance of grasslands. This involves shifting conventional crop lands into 

pasture/grazing lands or retiring crop lands from active agricultural usage, for example 

moving them into the Conservation Reserve Program (CRP). Again, this land movement 

involves reductions in soil disturbance and potential increase of carbon inputs and soil 

storage. 

• Mix of annuals versus perennials. Again, the basic mechanism involved here is the 

reduction in soil disturbance and a potential increase in carbon inputs to the soil but also 

includes an increase in the standing biomass.

6.6.2.2 Agricultural emissions reduction 

Agricultural activity is responsible for a large share of total anthropogenic emissions 

within several GHG categories. However, agricultural CO2 emissions related to fossil fuel usage 

are somewhat small, amounting to about 6-7% of the US total (EPA GHG Inventory, 2004). On 

the other hand, agricultural emissions of N2O, largely from fertilization and manure, approach 

50% of total US N2O emissions, while the agricultural emission share of methane (CH4) is also 

large (check % reported in Assessment Report) originating primarily from livestock herds, 

manure management, and rice cultivation. 

There are a number of management manipulations that alter the agricultural emissions 

profile. Briefly, the potential manipulations inherent in the structure of FASOMGHG are 

• Lowering fossil fuel usage -- agriculture can modify fossil fuel usage by changing tillage 

intensity, reducing the amount of water pumped for irrigation, reducing the usage of 

fossil fuels in grain drying, and otherwise manipulating the usage of fossil fuels in 

production. This reduces CO2 emissions. 
121 

• Lowering chemical usage -- agriculture can modify the usage of chemicals that require 

substantial amounts of fossil fuels in their production. This includes reductions in 

fertilizer and pesticide use. This reduces CO2emissions. 

• Reducing fertilization practices -- agriculture can reduce fertilization. This reduces the 

N2O emitted when nitrogen fertilizers are used as well as CH4 and CO2 emissions that are 

involved in fertilizer manufacture. 

• Reducing the size of the livestock herd -- livestock manure is the source of CH4 and 

N2O emissions. In addition, ruminant animals (cattle) are responsible for releases of CH4

through enteric fermentation. Thus reducing the size of the livestock herd can alter N2O 

and methane emissions. Herd size reductions also alter crop and grazing demand and 

thus, in turn, the entire emissions/sequestration profile involved with crop and grass 

production. 

• Manipulating ruminant livestock feeding and rate of gain -- cattle release CH4

through enteric fermentation. Methane release can be altered by either: (a) improving the 

quality of the diet (as discussed in Johnson et al, 2003a) or (b) by using additives such as 

BST to increase the rate of gain. 

• Improving manure management -- manure managed within wet handling systems leads 

to CH4 release through anaerobic decomposition. Manure is also a source of nitrous oxide 

emissions. One may alter the way manure is managed and resultant emission profiles 

using different practices including digesters. 

• Rice -- rice production generates CH4 through anaerobic decomposition within flooded 

rice fields. Within FASOMGHG the only mechanism for managing such emissions 

involves reductions in rice acreage. 

• Legumes -- certain nitrogen fixing legumes like soybeans and alfalfa fix nitrogen and 

subsequenty release N2O. Management may be used to alter these emissions by reducing 

the acreage of these crops. 

FASOMGHG also incoporates yet a broader set of emission reduction alternatives 

beyond those explicitly listed just above. These involve manipulations that have pervasive 

effects across the agricultural sector and include alterations in 

• crop mix 

• irrigated/dryland use 

• regional and soil type locations of crops 

• regional size and composition of the livestock herd 

• composition of feed blends 

• consumption patterns 

• processing patterns 
122 

• import/export mixes 

among many other possibilities. 

6.6.3 Biofuel production 

Energy sector activity is responsible for the lion's share of societal GHG emissions, with 

electricity production and petroleum combustion each responsible for about 40% of total US 

carbon/carbon dioxide emissions (better check this against the EPA inventory). Agriculture and 

forestry can offset energy-related emissions by providing feedstocks that can be used in energy 

production processes. As discussed above, such processes can greatly offset carbon emissions 

because the carbon present in the biofuel feedstocks which is inevitably released upon 

combustion would have come from the absorption of atmospheric carbon dioxide via 

photosynthetic processes during plant growth. As a consequence, the net emissions associated 

with biofuel combustion are those due to reduced emissions relative to the fossil fuels replaced 

by biofuel feedstock substitution. 

Briefly, the potential biofuel related management possibilities that are inherent in the 

structure of FASOMGHG are the production of 

• Ethanol as a replacement for gasoline through the conversion of corn, sugar cane, 

switchgrass, poplar and willow. 

• Electricity through use of milling residues, harvested wood, switchgrass, poplar and/or 

willow as feedstocks as a substitute for coal. 

• Biodiesel from soybeans or corn, for use in transportation fuel. 

6.7 Dynamics of GHG modeling 

Because FASOMGHG is a multi-period model, we needed to model the net GHG 

mitigation contributions of modeled activity over time. Different strategies were used to reflect 

these dynamic contributions depending on whether the activity of interest was sequestration, 

emissions reduction, or biofuel offsets. Here we chose to model the cumulative amounts of 

sequestration or emissions incurred during each model time period. Consequently, sequestration 

is modeled in terms of cumulative tons of carbon sequestered over time. For emissions and 

biofuel offsets, the cumulative amounts incurred in this and all previous time periods are 

reflected in each time period reflecting change in total climatic forcing. 
123 

6.7.1 Sequestration 

For sequestration activity, the model yields non-uniform quantities over time due to the 

generally accepted scientific premise that carbon sequestered in an ecosystem approaches a 

steady state equilibrium under any management alternative. Consequently, the rate of carbon 

sequestration uptake diminishes after some period of time and eventually dissipates to zero 

(sometimes called “saturation”) when the new equilibrium is reached (West and Post). This 

means that FASOMGHG produces unequal and ultimately diminishing sequestration 

contributions over time. Namely, the amount of carbon sequestered in forests depends on the 

timber growth and yield curves (which exhibit diminishing growth as stands become mature) 

along with assumptions derived from the FORCARB modeling system (see Chapter 13) 

regarding carbon sequestered in soils and forest understory,). Wood products also exhibit 

diminishing sequestration over time as products decay and re-release carbon to the atmosphere. 

On the agricultural side, soil carbon sequestration gains after a change in tillage practices were 

ultimately assumed to diminish to zero based on the findings of West and Post (200x). 

6.7.2 Emissions/Biofuel offsets 

Dynamic assumptions were also made about the contribution of emissions and biofuel 

offset activities. The assumption used is that the emissions incurred and emissions offset by 

biofuels persist forever (throughout the time period covered in the model). Therefore, GHG 

accounts in period 2 include emissions and offsets in that period and in period 1. Therefore, 

emissions reduction (below baseline) are treated as “permanent” in the model 

6.8 Programming model GHG implementation 

The ways that the GHG features discussed above enter into the programming model are 

summarized in this section using a time independent summary tableau and a more precise 

discussion of the objective function components of the GAMS implementation. Information on 

how agriculture and forestry generate entries in the GHG accounts will be covered in the sector 

specific modeling comments later in the document in Chapters 7 - 9. 

6.8.1 Tableau 

A summary tableau of the GHG portion of the model appears below. 
124 

Variables => 

Equations: 

Ag Production Forest production Seq Carbon Emit Carbon Emit N2O Emit CH4 Offset Carb 

 

Objective function + + +OCS -OCE -ON -OM +OCO 

Agric + < + 

Forest + < + 

Sequestered Carbon +SA +SF -1 = 0 

Emitted Carbon +EAC +EFC -1 = 0 

Emitted N2O +EAN -1 = 0 

Emitted CH4 +EAM -1 = 0 

Biofuel offset carbon +OAB +OFB -1 = 0 

This is a simplified tableau that depicts large parts of the model. The variables in this 

tableau are 

• Ag Production- Depicts numerous variables in the agricultural submodel. 

• Forest Production- Depict numerous variables in the forestry submodel. 

• Seq Carbon -- Cumulative net carbon sequestration by time period. The variable reflects 

both current activity and carryover sequestration from previous periods. This variable is 

contained within the AMOUNTGHGS variable in the model, which is defined for the 

carbon sequestration-related subset of the GHG types named above for each time period. 

• Emit Carbon -- Cumulative net carbon emissions by time period. The variable reflects 

not only current activity, but also emissions from previous periods (thereby implicitly 

assuming that the gases remain in the atmosphere for the duration of the time frame). 

This variable is contained within the GAMS implementation variable AMOUNTGHGS 

that is defined for the carbon emission related subset of the GHG types named above for 

each time period. 

• Emit N2O -- Cumulative nitrous oxide emissions by time period. This variable is 

contained within the GAMS implementation variable AMOUNTGHGS that is defined for 

the nitrous oxide-related subset of the GHG types named above for each time period. 

• Emit CH4 -- A variable that represents cumulative net methane emissions by time 

period. This variable is contained within the GAMS implementation variable 
125 

AMOUNTGHGS that is defined for the methane-related subset of the GHG types named 

above for each time period. 

• Offset Carbon -- Cumulative net GHG biofuel offsets by time period. This variable is 

contained within the GAMS implementation variable AMOUNTGHGS that is defined for 

the biofuel related subset of the GHG types named above for each time period. 

The equations in the tableau are 

• Objective function -- Algebraic expression for net producers' plus consumers' surplus in 

agriculture and forestry including GHG payments for the flux in the total GHG variables 

minus the corresponding flux in the baseline. In terms of the GHG payment component, 

credits are paid for gains in the sequestration and biofuel related offsets. Debits are 

imposed for gains in carbon, nitrous oxide and methane emissions. These terms involve 

the time discounted carbon equivalent price times the carbon equivalent quantities. Each 

of these is adjusted as needed for discounts and eligibility for program payments. 

• Agric -- Depicts numerous agricultural related constraints in the agriculture submodel. 

• Forest -- Depicts numerous market and resource forestry related constraints in the 

forestry submodel. 

• Sequestered Carbon -- Computes cumulative sequestration contributions during a time 

period for each sequestration-related GHG account and equates it with the total GHG 

sequestration variable (AMOUNTGHGS). This equation appears within the GAMS 

implementation equation GHGACCOUNTS that is defined for each sequestration 

account and time period. 

• Emitted Carbon -- Computes the cumulative carbon emissions during each period for 

each carbon emission related GHG account and equates it with the GHG carbon emission 

variable (AMOUNTGHGS). This equation appears within the GAMS implementation 

equation GHGACCOUNTS that is defined for each carbon emission related account and 

time period. 

• Emitted N2O -- Computes the change in cumulative nitrous oxide emissions from 

agriculture and forestry during each time period for each nitrous oxide-related GHG 

account with the total GHG nitrous oxide emission variable (AMOUNTGHGS). This 

equation appears within the GAMS implementation equation GHGACCOUNTS that is 

defined for each nitrous oxide emission related account and time period. 

• Emitted CH4 -- Computes the change in cumulative methane emissions during each time 

period for each methane related GHG account and equates it with the total GHG methane 

emission variable (AMOUNTGHGS). This equation appears within the GAMS 

implementation equation GHGACCOUNTS that is defined for each methane emission 

related account and time period. 
126 

• Biofuel offset carbon Emitted CH4 -- Computes the change in cumulative biofuels 

offsets during each time period for each biofuel related GHG account and equates it with 

the total GHG biofuel offset variable (AMOUNTGHGS). This equation appears within 

the GAMS implementation equation GHGACCOUNTS that is defined for each biofuel 

offset related account and time period. 

The terms within the tableau are: 

OCS -- Net present value of payments for a change in the number of tons of carbon 

dioxide sequestered within each carbon sequestration account computed as the 

change from the last period less the change in the baseline. This equals the carbon 

dioxide equivalent price times an indicator of whether or not this particular 

sequestration category is eligible for payments adjusted for discounts and net 

present value concerns. 

OCE -- Net present value of the costs for a change in the number of tons of carbon 

dioxide emitted within each carbon emission account computed as the change 

from the last period less the change in the baseline. This equals the carbon 

equivalent price times an indicator of whether or not this particular emission 

category incurs costs adjusted for discounts and net present value concerns. 

ON --Net present value of the costs for a change in the number of tons of nitrous oxide 

emitted within each nitrous oxide emission-related account computed as the 

change from the last period less the change in the baseline. The price equals the 

global warming potential factor for converting nitrous oxide to carbon dioxide 

equivalent times the carbon dioxide equivalent price times an indicator of whether 

or not this particular emission category incurs costs adjusted for discounts and net 

present value concerns. 

OCE -- Net present value of the costs incurred for a change in the number of tons of 

methane emitted within each methane-related account computed as the change 

from the last period less the change in the baseline. This equals the global 

warming potential for converting methane to carbon equivalent times the carbon 

dioxide equivalent price times an indicator of whether or not this particular 

emission category incurs costs adjusted for discounts and net present value 

concerns. 

OCO -- Net present value of payments for a change in the number of tons of carbon 

offset by use of biofuel feedstocks within each biofuel-related account computed 

as the change from the last period less the change in the baseline. This equals the 

global warming potential for the gas at hand times the carbon dioxide equivalent 

price times an indicator of whether or not this particular biofuel category is 

eligible for payments adjusted for discounts and net present value concerns. 

SA -- Net sequestration contribution by agricultural management alternatives to each 

sequestration category in each modeled time period. This represents activities 

widely across the agricultural submodel and involves current and past 

management possibilities involving tillage change and land use change. 

SF -- Net sequestration contribution by forestry management alternatives in each time 

period to each sequestration category for in each model time period. This 
127 

represents activities widely across the forestry submodel and involves current and 

past management possibilities involving harvest date alterations, forestry 

replanting, forest management, afforestation and deforestation. 

EAC -- Net carbon emission contribution by agricultural management alternatives to 

each carbon emission category in each modeled time period. This represents 

activities widely spread across the agricultural submodel and involves current and 

past management possibilities involving fossil fuel use, crop mix and input 

manufacture. 

EFC -- Net carbon emission contribution by forestry management alternatives in each 

time period to each carbon emission category in each model time period. This 

represents activities widely spread across the forestry submodel and involves 

current and past management possibilities involving fossil fuel use. 

EAN -- Net methane emission contribution by agricultural management alternatives to 

each methane emission category in each modeled time period. This represents 

activities widely spread across the agricultural submodel and involves current and 

past management possibilities including fertilization, livestock herd size, and 

manure management. 

OAM -- Net methane emission contribution by agricultural management alternatives to 

each methane emission category in each modeled time period. This represents 

activities spread widely across the agricultural submodel and involves current and 

past management possibilities involving livestock herd size, feeding, manure 

management and rice acreage. 

EAB -- Net carbon offset contribution by agricultural biofuel feedstock usage 

management alternatives to each biofuel related emission category in each 

modeled time period. This represents activities widely spread across the 

agricultural submodel and involves current and past management possibilities 

involving agricultural feedstocks for ethanol, biodiesel and biofuel fired power 

plants. 

EFB -- Net carbon offset contribution by forestry-generated biofuel feedstock usage 

management alternatives to each biofuel related emission category in each 

modeled time period. This represents activities widely spread across the forestry 

submodel and involves current and past management possibilities involving forest 

feedstock fired power plants. 

6.8.2 GAMS implementation 

The GHG implementation is carried into the GAMS implementation equations in two 

main locations: the objective function and the GHG balance equation. The main GHG variable is 

AMOUNTGHGS(periods,ghgtype) that is the amount of emission, sequestration or offset by 

GHG account (the set ghgtype) and time period. 

6.8.2.1 GHG part of objective function 

The objective function of FASOMGHG is the equation WELFAR. In that equation the 

following terms can be found 
128 

+scaldifag* 

 sum(period, 

 +disc(period)*wtannuity(period) 

 *willpaycarbon(period) 

 *carbonprice(period) 

 *sum(ghgclassify(ghggas,activeghgtype), 

 willpayforghg(activeghgtype) 

 *gwp(ghggas) 

 *([ (AMOUNTGHGS(period,activeghgtype)-AMOUNTGHGS(period-1,activeghgtype) 

 $(date(period) > firstyear)) 

 -(baseline(period,activeghgtype) -baseline(period-1,activeghgtype) 

 $(date(period) > firstyear))] 

 *prod(discountsource, 

 (1-ghgdiscount(activeghgtype,discountsource))))) 

The terms excluding the GAMS operators sum and prod herein are 

scaldifag -- an indicator of scaling currently set to one 

period -- current period being addressed

disc(period) -- discount rate for current period 

wtannuity(period) -- annuity weight for annual amount over length of current period

willpaycarbon(period) -- indicates whether GHG payment program in place this period 

carbonprice(period) -- carbon equivalent price per ton in this period

ghgclassify(ghggas,activeghgtype) - indicates the GHG gas involved with this account 

ghggas—type of GHG -- carbon, carbon dioxide, nitrous oxide or methane

activeghgtype -- GHG account as listed above

willpayforghg(activeghgtype) -- payment or cost eligibility for this account (0, +1 or -1) 

gwp(ghggas) -- global warming potential

AMOUNTGHGS(period,activeghgtype) -- endogenous variable giving amount of GHG 

account by period where period-1 references the amount in the previous period 

baseline(period,activeghgtype) -- baseline amount of this GHG account by period where 

period-1 references the amount in the previous period 

discountsource -- types of discounts applied -- additivity, permanence, additionality and 

uncertainty 

(1-ghgdiscount(activeghgtype,discountsource)) -- quantity fully paid for relative to a 

discount 

The net result of all this is the amount of GHG (AMOUNTGHGS) as it deviates from 

amount in the previous period less the change in the baseline (baseline) is computed. Then that 

amount is adjusted downward for market discounts (1-ghgdiscount). In turn the result is 

converted to carbon dioxide equivalent by multiplying by gwp. Then the result is multiplied by 
129 

the carbon equivalent price (carbonprice). Subsequently, we adjust for whether this account is 

eligible and whether it is a sequestration credit, offset credit or emission cost (willpaycarbon). 

Finally we multiply by a facto that adjusts from an annual to an annuity basis (wtannuity) then 

discount back to present value (disc). This is summed over all time periods and GHG accounts to 

form the total net emission change objective function contribution. The term is also scaled so it 

matches the other parts of the objective function (scaldifag) 

6.8.2.2 GHG equations 

In the model the GHG amounts by account are summed up in the equation 

GHGACCOUNTS(currentperiod,activeghgtype). This involves many forest, agricultural and 

intersectoral land movement terms. Discussion of them is provided in Chapters 7-9. 
130 

7 CHAPTER 7 FOREST SECTOR SUBMODEL 

Here we detail the way the forest sector submodel covers important forest sector 

characteristics. To do this we first overview the forest sector submodel. Then we illustrate 

model subcomponents that address key forest sector characteristics. Later we present an 

algebraic representation of the whole forestry submodel. 

7.1 Whole forest model overview 

A broad overview of the forestry submodel appears in the tableau within table 7-1. This 

tableau shows the key forest sector features involved with 

• Forest harvest

• Forest stand establishment

• Wood products manufacturing

• Wood products demand

• Domestic wood product transport

• International trade in wood products

• Forest land resources

• Forest non-wood inputs 

The tableau also shows interaction with other sectors including land moving in and out 

from agriculture and land movement to development. Finally, it illustrates GHG involvement.
131 

Table 7-1 Sample tableau illustrating forest sector submodel aspects 

 Variables Equations 

Clearcut exist stand 

Partial cut exist stand 

Reforest land 

Afforest land 

Timber production cost 

Manu. US wood prod 

Terminal manufacture 

Manufacture Canada wood prod 

Canadian harvest 

Canadian transport 

Domestic transport 

Public supply Non-wood inputs 

Land from ag 

Land to ag 

US Wood product demand 

Wood products import 

Canadian product demand 

Welfare -1 -k -a -b -c -d -e -f g -n h Exist timberland 1 1 Harvested clearcut forest land -1 +/-1 -1 1 Land from ag 1 -1 US harvested logs -he -hp -hr -ha y Canada harvested logs Y -1 Production cost ce cp Cr ce -1 US manufactured wood prods -1 -1 +/- -1 1 -1 Canada manufactured wood prods -1 1 1 Milling residues +/- +/- +/- Non-wood input 1 1 1 -1 Terminal inventory -te -tp -tr -ta Y Terminal manufactured wood products -1 GHG balance ce cp cr ca cm 
132 

The equations (rows) in the tableau are: 

• Welfare -- The sum of consumers' and producers' surplus net of transport and other costs. 

This is the forestry component of the objective function that is maximized to find the 

market equilibrium solution. The terms incorporated fall into several classes. Areas 

underneath demand curves appear in association with the variables labeled Wood product 

demand, Wood product export and Terminal product demand. These depict positive 

contributions to the objective function. The objective function term associated with the 

variable GHG payments give the GHG payments and are also a positive contribution to 

the objective function. Simultaneously the objective function contains terms that subtract 

the area underneath the supply curves for Non-wood input items, and Wood product 

import. The terms associated with the variables Production cost, Canadian transport, 

Domestic transport, Land from ag, and Land to ag give the costs of purchasing items 

involved in the total production, processing land transformation, and commodity 

movement that are assumed to be available at a fixed price. The GAMS implementation 

equation WELFAR is represented by this tableau row. 

• Exist timberland -- Limits use of the initial forest inventory in acres to the amount of 

inventory available. All existing stands at the start of the problem are allocated to some 

management regime (including no management or reserved). This equation is defined by 

age of stand (the GAMS set cohort), FASOMGHG log producing region (logregions), 

land suitability class (class), type of forest owner (pvtlogowner), type of forest stand 

(type), site index (site) and type of management to which the stand has been subjected 

(MgtIntensity). The GAMS implementation equation FORINVENTORYA is represented 

by this tableau row. 

• Harvested clearcut forest land -- Balances land obtained from clearcut timber harvest 

with its subsequent use for reforestation or land use change. The land use change 

possibilities are movements to agriculture or movement to developed use. Afforestation is 

a potential source of land but only after the first rotation. The variable constitutes both a 

supply and a use (+/-) of land. Bare land is consumed by forest establishment and upon 

harvest is released for subsequent reuse. This equation is defined by log producing region 

(logregions), land suitability class (class), forest owner (pvtlogowner), type of 

succeeding forest stand (sucessorgroup), site index (site) and time period (period). The 

GAMS implementation equation FORLANDBALANCE is represented by this tableau 

row. 

• Land from ag -- Balances land coming into forestry from agriculture with afforestation 

for the first forest rotation. All subsequent rotations afforested lands are handled within 

the Harvested clearcut forest land balance as reforestation. This equation is defined by 

log producing region (logregions), land suitability class (class), forest owner 
133 

(pvtlogowner), site index (site) and time period (period). The GAMS implementation 

equation FORAFFORLANDBALANCE is represented by this tableau row. 

• US harvested logs -- Balances logs harvested with their use in wood products 

manufacturing. Harvested logs arise from existing stands, reforested stands, and 

afforested stands under clearcut management and thinning or partial cut harvest regimes. 

Logs cut from public lands also enter as an exogenous supply source (usps). This 

equation is defined by time period (period), log producing region (logregions), forest 

owner (pvtlogowner), and log type (logproducts). Cases within the GAMS 

implementation equations FORBALEXHRV, FORBALEXHPC, FORBALNEWHRV, 

FORBALNEWHPC, and FORWDBALANCE are represented by this tableau row. 

• Canada logs -- Balances logs obtained from Canadian harvest (that varies with log price) 

with Canadian wood product manufacture. This equation is defined by time period 

(period), Canadian region (reg), forest owner (pvtlogowner), and product type 

(logproducts). Cases within the GAMS implementation equations FORWDBALANCE

are represented by this tableau row. 

• Timber production cost -- Computes total forest production cost across a number of 

categories such as establishment and fertilization and equates it with the forest production 

cost variable. This equation is defined by time period (period), and log producing region 

(logregions). The GAMS implementation equations FORCOSTBAL are represented by 

this tableau row. 

• US manufactured wood products -- Balances wood product production with 

consumption. Wood products come from from wood product manufacturing plus imports 

from Canada and off-shore. Consumption comes from domestic demand, exports and 

intermediate product use. This equation is defined by time period (period), wood 

manufacturing region (activewoodregions), and product type (woodproducts). Cases 

within the GAMS implementation equations FORWDBALANCE are represented by this 

tableau row. 

• Canada manufactured wood prods -- Balances the product yield from Canadian 

manufacturing with Canadian consumption and exports to the US. This equation is 

defined by time period (period), Canadian region (activewoodregions), and product type 

(woodproducts). Cases within the GAMS implementation equations FORWDBALANCE

are represented by this tableau row. 

• Milling residues -- Balances the supply of milling residues with their use in further 

manufacturing and is designated separately for US and Canadian conditions. This 

equation is defined by wood manufacturing region (activewoodregions), residue type 

(residues) and time period (period). Cases within the GAMS implementation equations 

FORWDRESBAL are represented by this tableau row. 
134 

• Non-wood input -- Associates non-wood inputs with manufacturing activity. Non-wood 

inputs encompass costs of log harvest and hauling to mills along with the costs of nonwood inputs used in manufacturing. The cost of supply of non-wood inputs vary with the 

volume. This equation is defined by type of non-wood input being supplied 

(woodsupplytype), wood manufacturing region (activewoodregions), product being 

manufactured (woodproducts) and time period (period). Cases within the GAMS 

implementation equations FORWDNWCEQ are represented by this tableau row. 

• Terminal inventory -- Computes the log volume that would be obtained under a perpetual 

even-aged management system from unharvested timber stands in inventory at the end of 

the explicit model time frame and balances that with terminal period wood products 

manufacturing. This equation is defined for the terminal (period "9999") period by log 

producing region (logregions), forest owner (pvtlogowner), and product type 

(logproducts). Cases within the GAMS implementation equations FORBALEXHRV, 

FORBALNEWHRV, and FORWDBALANCE are represented by this tableau row.

• Terminal wood products -- Balances the wood products obtained from processing with 

consumption for the perpetual terminal period. This equation is defined for the "9999" 

time period, by wood manufacturing region (activewoodregions), and product type 

(woodproducts). Cases within the GAMS implementation equations FORWDBALANCE

are represented by this tableau row. 

• GHG balance -- Computes forest-related GHG emissions and sequestration from forest 

soils, litter, and understory; growing trees; and wood products. This includes the fossil 

fuel related emissions from forest production. Net payments to fluxes in GHGs are 

computed in the objective function. This equation is defined by time period (period), and 

GHG account (ghgtype). Cases within the GAMS implementation equations 

GHGACCOUNTS are represented by this tableau row. 

The variables (columns) in the tableau are 

• Clearcut exist stand -- Clearcuts/even-aged management of existing stands. Alternatives 

alliow variance in harvest age, thinning and management intensity. The variable requires 

land in the initial inventory and production cost inputs while generating harvested logs 

and affecting the GHG balance. Upon harvest, land is released for subsequent 

reforestation or land use change. This variable is defined by harvest period (period), 

stand age (cohort), log producing region (logregions), land suitability class (class), forest 

owner (pvtlogowner), forest type (type), site index (site), management applied 

(mgtintensity), and possible subsidy-related policy (policy). Cases within the GAMS 

implementation variable FORPRDEXIST are represented by this tableau column. 

• Partial cut exist stand -- Partial cutting of existing stands. The variable uses land from the 

inventory and production cost inputs while generating harvested logs and affecting the 
135 

GHG balance. Land allocated to partial cutting can be maintained in partial cutting or 

clearcut harvested and shifted to even-aged management in subsequent periods. Land 

allocated to partial cutting is not released for subsequent reforestation or land use change 

after a partial cut. This variable is defined by eventual harvest period (period -- which can 

be never), stand age (cohort), log producing region (logregions), land suitability class 

(class), forest owner (pvtlogowner), forest type (type), site index (site), partial cut related 

management practice applied (mgtintensity), and possible subsidy-related policy (policy). 

Cases within the GAMS implementation variable FORPRDEXIST are represented by 

this tableau column. 

• Reforest Land -- Establishment of forests on previously forested land. While not fully 

represented here such stands have a choice of an array of management intensities nd 

harvest methods. Bare land that was previously in forest is required as are forest 

production cost inputs. Harvested logs are generated and an entry placed in the GHG 

balance. This land, when clearcut, is released for subsequent reforestation or land use 

change. This variable is defined by stand establishment period (period), eventual harvest 

period (period -- which can be never), log producing region (logregions), land suitability 

class (class), forest owner (pvtlogowner), forest type (type), site index (site), management 

practice applied (mgtintensity), and possible subsidy-related policy (policy). Cases within 

the GAMS implementation variable FORPRDNEW are represented by this tableau 

column. 

• Afforest Land -- Establishment of forests on land transferring from agricultural crops or 

pasture. Land is classed as afforestation for the first forest rotation only. Although not 

fully represented here such stands have a choice of harvest age, choice of cutting regime 

including whether or not they're managed through thinning, partial cut or clearcut 

systems and choices of management intensity. After the first forest rotation this land is 

then treated within the reforest land variable. The variable requires land from agriculture 

and production cost inputs while generating harvested logs and affecting the GHG 

balance. This land, if clearcut, is released for subsequent reforestation or land use change. 

This variable is defined by stand establishment period (oldperiod), eventual harvest 

period (period -- which can be never), log producing region (logregions), land suitability 

class (class), forest owner (pvtlogowner), stand type (type), site index (site), management 

practice applied (mgtintensity), and possible subsidy-related policy (policy). Cases within 

the GAMS implementation variable FORPRDNEWAFFOREST are represented by this 

tableau column. 

• Production cost -- Costs forest production (silvicultural) activities in the objective 

function. This variable is defined by log producing region (logregions) and time period 

(period). Cases within the GAMS implementation variable FORPRDCOST are 

represented by this tableau column. 
136 

• Manufacture US wood products -- Wood products manufacturing. Several functions are 

encompassed by this variable, including transformation of logs into intermediate 

products, transformations of intermediate products into final wood products; and 

downgrading of logs into lower use classes. The variable requires logs, milling residues 

and/or immediate products along with non-wood production costs. They generate 

intermediate products, milling residues and final products. They enter the fate of the 

sequestered carbon in harvested wood products into the GHG balance. This variable is 

defined by time period (period), wood producing region (activewoodregions), product 

being manufactured (woodproduct), process being used (process), and input mix 

(inputmix). Cases within the GAMS implementation variable FORWDMANUFACT are 

represented by this tableau column. 

• Terminal wood products manufacture -- Wood manufacturing in the terminal period. 

This is essentially identical to the just discussed Manufacture US wood products variable 

but deals with the logs and products available in the terminal period. This variable is 

defined for the terminal time period ("9999"), wood producing region 

(activewoodregions), product being manufactured (woodproduct), process being used 

(process), and input mix (inputmix). Cases within the GAMS implementation variable 

FORWDMANUFACT are represented by this tableau column. 

• Manufacture Canada wood -- Canadian wood manufacturing. This essentially identical to 

the Manufacture US wood products variable but deals with logs and products generated 

in Canada. This variable is defined by time period (period), Canadian wood producing 

region (activewoodregions), product being manufactured (woodproduct), process being 

used (process), and input mix (inputmix). Cases within the GAMS implementation 

variable FORWDMANUFACT are represented by this tableau column. 

• Canadian transport -- Movement of Canadian-produced wood products into US markets. 

Goods are used from the Canadian wood products balance and supplied into US regional 

balances while incurring transport cost in the objective function. This variable is defined 

by Canadian region of origin (activewoodregions), region of destination 

(activewoodregions2), wood product involved (woodproducts) and time period (period). 

Cases within the GAMS implementation variable FORWDTRANSPORT are represented 

by this tableau column. 

• Domestic transport -- Interregional transport of US-produced wood products. Goods are 

used from the wood products balance equation for the region of origin and are supplied 

into the region of destination while incurring transport cost in the objective function. This 

variable is defined by region of origin (activewoodregions), region of destination 

(activewoodregions2), wood product involved (woodproducts) and time period (period). 

Cases within the GAMS implementation variable FORWDTRANSPORT are represented 

by this tableau column. 
137 

• Public supply -- Logs harvested from public lands. Harvested logs are supplied and incur 

a cost equal to the log price. This variable is defined by region (activewoodregions), log 

type (logproducts) and time period (period). Cases within the GAMS implementation 

variables FORWDLOGSUPPLY are represented by this tableau column. 

• Non-wood inputs -- Supply of non-wood inputs to log harvest and hauling and wood 

products manufacture according to an upward sloping supply cost schedule. The variable 

supplies one unit into the non-wood input equation and has the area underneath the nonwood supply equation in the objective function. This variable is defined by type of supply 

(woodsupplytype), manufacturing region (activewoodregions), wood product being made 

(woodproducts), time period (period) and step (steps). Cases within the GAMS 

implementation variables FORWDNWCS are represented by this tableau column. 

• Land from ag -- Land use change from agriculture to forestry. Land is drawn on the 

agricultural side from either the pasture or crop land equations and is placed into the 

forestry equation at a hurdle cost. This land can only be used by the Afforest Land

variable. This variable is defined by log producing region (logregions), land class (class), 

and time period (period). Cases within the GAMS implementation variables 

LANDFROMAG and CONVRTFROMAG are represented by this tableau column. 

• Land to ag -- Land use change from forestry into agriculture. Land is withdrawn on the 

forestry side from the land available for reforestation and placed into the agricultural crop 

or pasture land balances incurring a land transformation cost. This variable is defined by 

log producing region (logregions), land class (class), cost step (three), and time period 

(period). Cases within the GAMS implementation variables LANDTOAG and

CONVRTTOAG are represented by this tableau column. 

• Wood Product demand -- Domestic demand for wood products in US markets. The 

variable withdraws from the wood products balance and contains an objective function 

term that equals the area underneath the demand curve. This variable is defined by region 

(activewoodregions), wood product involved (woodproducts), and time period (period). 

Cases within the GAMS implementation variables FORWDDEMAND are represented 

by this tableau column. 

• Wood product export -- Export demand for wood products from US markets. The 

variable withdraws one unit from the wood products balance equation and contains an 

objective function term that equals the area underneath the product specific export 

demand curve. This variable is defined by region (activewoodregions), wood product 

involved (woodproducts), and time period (period). Cases within the GAMS 

implementation variables FORWDDEMAND are represented by this tableau column. 

• Wood Products import -- Import supply of wood products into US markets. The variable 

adds into the wood products balance equation and contains an objective function term 

that equals the negative of the area underneath the product specific supply curve. This 
138 

variable is defined by region (activewoodregions), wood product involved 

(woodproducts), and time period (period). Cases within the GAMS implementation 

variables FORWDSUPPLY are represented by this tableau column. 

• Terminal product demand -- Demand for wood products in the terminal period. This 

variable is essentially identical to all of the domestic and export demand variables above 

but deals with products produced in the terminal period. This variable is defined by type 

of demand (wooddemandtype), region (activewoodregions), and wood product involved 

(woodproducts). Cases within the GAMS implementation variables FORWDDEMAND 

are represented by this tableau column. 

• GHG payments -- Payments or taxes for changes in net GHG emissions above those in 

the baseline by inventory account. This variable is defined by time period (period), and 

GHG account (ghgtype). Cases within the GAMS implementation variables 

GHGACCOUNTS are represented by this tableau column. 

The parameters in the tableau are: 

a -- the per unit transport costs of moving wood products from Canada into the US 

b -- the per unit transport costs of moving US wood products between regions 

c -- the per uit price of public timper supply 

d -- the area underneath the supply curve for US non-wood inputs which includes nonwood items used in wood products manufacture along with hauling and harvest 

for log movements from the woods to manufacturing facilities 

e -- the hurdle costs of moving land from agriculture 

f -- the land transformation costs involved in moving previously forested land into 

agriculture 

g -- the area underneath the demand curves for US wood products 

m -- the area underneath the export demand curves for exports of US wood products 

n -- the area underneath the supply curves for imports into the US of wood products 

h -- the area underneath the Canadian demand curves for wood products 

i -- the area underneath wood products demand curves in the terminal period 

j -- the per unit payments/taxes that apply to changes above those in the baseline for net 

GHG emissions 

l -- the amount of land in the initial forest inventory by type of stand 

dev -- the amount of land moving out of the forest inventory into developed uses 

exp -- the amount of exported wood products (exogenous) 

he -- the volume of logs obtained per acre of harvested existing forest 

hp -- the volume of logs obtained per acre of partially cut existing forest 

hr -- the volume of logs obtained per acre of clearcut or partially cut reforested forest 

ha -- the volume of logs obtained per acre of clearcut or partially cut afforested forest 

during the first rotation 

y -- the amount of logs used in the manufacture of one unit of intermediate or final 

manufactured wood product 

usps -- the exogenously specified amount of logs obtained from US publically owned 

forests 
139 

candem – Canadian demand 

OSexprts – Canadian off shore exports 

ce -- the net carbon emission profile in a number of accounts from existing forests 

including the sequestration increment and the fossil fuel consumption related 

emissions 

cp -- the net carbon emission profile in a number of accounts from partially cut forests 

including the sequestration increment and the fossil fuel consumption related 

emissions 

cr -- the net carbon emission profile in a number of accounts from reforested forests 

including the sequestration increment and the fossil fuel consumption related 

emissions 

ca -- the net carbon emission profile in a number of accounts from afforested forests 

including the sequestration increment and the fossil fuel consumption related 

emissions 

cm -- the fate of carbon sequestered in wood products 

+/- -- indicates that the coefficient in this location can either be positive or negative in 

sign 

te -- terminal period log yield from management of any unharvested existing forests 

according to a perpetual even-aged management scheme 

tp -- terminal period log yield from management of any unharvested existing partially cut 

forests according to a perpetual even-aged management scheme 

tr -- terminal period log yield from management of any unharvested reforested forests 

according to a perpetual even-aged management scheme 

ta -- terminal period log yield from management of any unharvested afforested forests 

according to a perpetual even-aged management scheme 

7.2 Model elements 

In this section we further highlight key forest sector characteristics and the ways that the 

FASOMGHG model structure accommodates them. 

7.2.1 Stand representation 

Forest stands3 grow at differential rates due to differences in management, site quality, 

ownership, climate, tree age and tree species. The FASOMGHG forest stand and inventory 

representation reflects these characteristics on current timberland and potentially afforested land 

in the contiguous 48 states (Alig et al. 1998) under private ownership. Pubic lands are treated 

exogenously. Private timberland is characterized by: 

• Geographic region (nine as in figure 3.xx), 

 

3 We deal with aggregates representing strata that cover relatively large areas; for example, by region, ownership, 

forest type, etc.. For simplicity, we will term them modeled “stands” as is common in forestry discussions. 
140 

• Type of land owner (private lands only- two owners) 

• Land use suitability for transfer to or from agriculture (5 groups), 

• Forest types (ten) as defined below, 

• Site productivity potential for wood volume growth (three levels) as defined below, 

• Management intensity (23 timber management regimes applied to the area) as defined 

below, and 

• Five year age cohorts up to 100+ years of age. 

7.2.1.1 Regions 

Forest production occurs in 9 of the 11 regions used in FASOMGHG to depict the lower 

48 states (table 3-1). While timber production is represented in all 9 of these regions, the major 

producing regions are (a) the Pacific Northwest west of the Cascade Mountain Range (PNWW); 

(b) the South Central (SC) and (c) the South East (SE). National Forest timber and Canadian 

production are also represented but with exogenous harvest levels. 

7.2.1.2 Land owner 

The only forested stands explicitly represented are those owned by private parties. Two 

ownership classes are defined 

• Forest industry (FI) --private lands owned by companies or individuals operating wood 

manufacturing plants. 

• Non industrial private forest --private lands owned by individuals or companies who do 

not operate wood manufacturing plants. 

7.2.1.3 Land use suitability 

Five land suitability classes are used in tracking timberland: 

FORONLY -- Timberland acres that are not suitable for conversion to agricultural uses; 

FORCROP -- Acres that begin in timberland but could be converted to crop land uses 

FORPAST -- Acres that begin in timberland but could be converted to pasture uses 

CROPFOR -- Acres that begin in crop land uses but are converted to timberland. All 

afforested crop land is in this category and after conversion into forest can be 

returned to agricultural crop land later in the model time frame. 

PASTFOR -- Acres that begin in pasture land uses but are converted to timberland. All 

afforested pasture land is in this category and after conversion into forest can be 

returned to agricultural pasture later in the model time frame. 
141 

The classification name identifies the type of allowed land use changes. The second part 

identifies the type of use for which the land is potentially suited for conversion (crop, pasture, or 

forest only) and by the prior use (first part of name). For example, FORCROP is land that was in 

forest cover and is suitable for conversion to crop land. 

7.2.1.4 Forest type 

Ten forest types are defined. These are listed in Table 7-2. The definitions used in all 

regions but the SC, SE, and PNWW are limited to HARD and SOFT. In the SC and SE regions 

the definitions BOT_HARD, UP_HARD, NAT_PINE, OAK_PINE, and PLNT_PINE are used. 

The three definitions DOUG_FIR, OTH_SWDS, and HARDWOODS are used in the PNWW 

region. 

Table 7-2 Forest types used in the model 

Forest Type Description 

SOFT Broad softwood forest type 

HARD Broad hardwood forest type 

BOT_HARD Bottomland hardwood forest type 

UP_HARD Upland hardwood forest type 

NAT_PINE Natural pine forest type 

OAK_PINE Oak-pine forest type 

PLNT_PINE Planted pine forest type 

DOUG_FIR Douglas-fir forest type 

OTH_SWDS Representative softwood forest type, excluding Doug-fir 

HARDWOODS Composite hardwood forest type for the PNWW region 

7.2.1.5 Site productivity 

Three site productivity types are defined. These are based on a classification of 

forestland in terms of potential annual cubic-foot volume growth per acre at culmination of mean 

annual increment in fully-stocked natural stands (Smith et al. 2001). Specific productivity ranges 

can vary by region and an example for the South is given in Table 7-3 below. 

Table 7-3 Timberland site classes for the South 

Site Class Cubic feet per acre per year 

LO 20-49 cubic feet 

MED 50-84 cubic feet 

HI 85+ cubic feet 
142 

7.2.1.6 Management intensity classes 

We allow several different levels of timber management intensity for newly regenerated 

timber stands. These management intensity classes (MICs) were largely derived from the MICs 

developed for modeling by the Aggregate TimberLand Analysis System (ATLAS) (Mills and 

Kincaid, 1992) in the 2000 RPA Timber Assessment (Haynes, 2003, Mills and Zhou, 2003). The 

number and type of MICs vary by region, forest type, and site class. The largest numbers are in 

the SC, SE and PNWW where the bulk of the nation's timber harvest originates. In other regions, 

two relatively low intensity levels of timber management are used that approximate the regional 

forms of timber management: passive (PASSIVE) -- depicting no management intervention of 

any type between timber harvests of naturally-regenerated aggregates; and low (LO) -- custodial 

timber management of naturally-regenerated aggregates (Adams et al. 1996). 

The management options in the South and PNWW regions involve a combination of 

harvest method -- (clearcut or partial cutting) and silvacultural practices including thinning. The 

management alternatives are listed in table 7-4. 

Table 7-4 Forest management intensity codes (MICs) used 

MIC Code Description 

AFFOR Afforestation of bottomland hardwood (SE and SC) 

AFFOR_CB Afforestation of hardwood and softwood forest types (CB) 

LO Natural regeneration (or afforestation) with low management 

NAT_REGEN Natural regeneration with low management (PNWW) 

NAT_REGEN_PART_CUT_HI Partial cutting with high level of management (PNWW) 

NAT_REGEN_PART_CUT_LO Partial cutting with medium level of management (PNWW) 

NAT_REGEN_PART_CUT_MED Partial cutting with low level of management (PNWW) 

NAT_REGEN_THIN Natural regeneration with a commercial thin (PNWW) 

PART_CUT_HI Partial cutting with medium level of management (SE and SC) 

PART_CUT_HI+ Partial cutting with high level of management (SE and SC) 

PART_CUT_LO Partial cutting with low level of management (SE and SC) 

PASSIVE Passive management (minimal amount of management) 

PLANT Plant with no intermediate treatments (PNWW) 

PLANT_THIN Plant with medium level of management (PNWW) 

PLANT+ Plant with high level of management (PNWW) 

PLNT_HI Planted pine with high level of management (SE and SC) 

PLNT_HI_THIN Planted pine with commercial thin and high level of management (SE and SC) 

PLNT_LO_THIN Planted pine with commercial thin and no intermediate treatments (SE and SC) 

PLNT_MED Planted pine with medium level of management (SE and SC) 
143 

PLNT_MED_THIN Planted pine with commercial thin and medium level of management (SE and SC) 

RESERVED Reserved from harvest 

SHORT_ROTSWDS Short rotation softwoods with high level of management (SE and SC) 

TRAD_PLNT_PINE Planted pine with no intermediate treatments (SE and SC) 

Additional details and supporting data relative to these alternatives are described in 

Section xx.2. 

7.2.1.7 Cohorts 

For an even-aged stand, a FASOMGHG stand is characterized by a range of ages for the 

trees therein. Even-aged stands are those where 70% or more of the tree stocking falls within a 

30-year grouping. We use five-year cohorts to classify even-aged stands, to provide indications 

about how long different stands have occupied the land. In the South the first year of occupancy 

is commonly trees that are older as trees are transplanted in at older ages. The cohorts for land 

occupancy are 0-4, 5-9, 10-14, 14-19 and so on in five year intervals up to 95-99 and 100+. We 

do not differentiate between age groups beyond 100 years. 

7.2.2 Initial inventory 

The initial forest inventory was developed using inventory data from the Forest Service's 

2000 RPA Timber Assessment (Haynes, 2003). Each stratum is represented by the number of 

timberland acres it contains. Inventories on public lands are not explicitly modeled and public 

timber harvests in the US are taken as exogenous. We do not model or project the Canadian 

timber inventory on public (provincial) or private lands. 

The basic constraint in the model reflecting the initial inventory requires that all of the 

inventory acreage of stands in existence at the start of the model projection be allocated to the 

management variables for existing stands across harvest possibilities. In the GAMS 

implementation this is the FORINVENTORYA equation which is defined for each stand as 

FORINVENTORYA(cohort,allreg,class,pvtlogowner,type,site,MgtIntensity) where the sets are 

cohort -- tree age cohort 

allreg -- log producing region 

class -- land suitability for agriculture or forestry 

pvtlogowner -- type of private owner 

type -- forest type 

site -- site productivity class 

mgtintensity -- management intensity class 
144 

These areas are allocated to either timber harvest in some current or future period or a 

never harvest possibility using the FORPRDEXIST variable, which is defined in GAMS with set 

dependency as follows: 

FORPRDEXIST(allperiods,cohort,allreg,class,pvtlogowner,type,site,MgtIntensity,policy). 

The sets contained herein beyond those defined just above are 

allperiods -- the period in which the stand is clearcut harvested (2000,2005,2010,...) one 

possibility for which is never (9999) 

policy -- the policy under which these acres are managed, which is generally the BASE, 

but could be another definition when subsidy or other policy programs are being 

simulated. 

The basics of the GAMS implementation of this equation is 

+ sum((period,policy), 

FORPRDEXIST(period,cohort,reg,class,pvtlogowner,type,site,MgtIntensity,policy))) 

 = invent(cohort,reg,class,pvtlogowner,type,site,MgtIntensity) 

This requires that the area cut from pre-existing timberlands across the different harvest periods 

under the available policies equal the existing (or initial period) acres in the inventory. 

Empirically, the inventory data in the GAMS parameter invent give the acreage in 1000 acres.

Thus, the units of FORPRDEXIST are also in 1000 acres. 

Note that existing stands allocated to a partial cutting regimes can be clearcut (if it is 

optimal to do so) and replanted to some new even-aged or partial cutting regime, or they may 

remain in partial cutting for the entire projection (with the clearcut harvest period being “never”). 

This permits stands to move back and forth between even and partial cutting regimes. 

7.2.3 The new and existing stands distinction plus isnew/isnewexist 

A very important distinction in the model is the difference between new and existing 

stands and the accompanying use of the sets isnew and isexist. 

7.2.3.1 New versus existing stands 

Timberland areas are differentiated into "existing" and "new" activities, depending on 

whether the timber stand was present in the initial inventory or was created during the course of 

the projection. By definition a new stand does not exist at the beginning of a model run but rather 

will come into the inventory only upon the reforestation of a harvested existing stand or upon the 

afforestation of land moving over from agriculture. Yields for existing stands are in existyld for 
145 

clearcuts and existyldpc for thinning and partial cuts. The associated variable is 

FORPRDEXIST(period,cohort,allreg,class,pvtlogowner,type,site,mgtintensity,policy). Note 

that the only time dependent set used in the definition of this variable is the time of harvest 

which is identified by the set period in the definition above but also includes 9999 for the never 

clearcut possibility. Yields for existing stands are in newyld for clearcuts and newyldpc for 

thinning and partial cuts. The associated variable is 

FORPRDNEW(period,when,allreg,class,pvtlogowner,type,site,mgtintensity,policy) for 

reforested stands and 

FORPRDNEWAFFOREST(periods,when,allreg,class,pvtlogowner,type,site,MgtIntensity,polic

y) for the first rotation of an afforested stand. Two time dependent sets are used in the definition 

of these variables. One is the time of stand establishment which is identified by the set period in 

the definition above. The other is the time of harvest of the stand which is identified by the set 

when giving how long after planting that harvest occurs. 

7.2.3.2 Isnew and isexist 

Two multidimensional sets are associated with the new and existing stand definitions that 

are used to indicate when stands may potentially exist in the inventory. These are isnew and 

isexist and have all the same dimensions as the variables above except for the harvest dimension. 

These sets have active (non-zero) elements only when a stand truly either exists (having 

inventory, yield and cost) or has the capability to exist through afforestation or reforestation of a 

harvested existing stand along with accompanying yield and cost data. These multidimensional 

sets are calculated based on the model data in the GAMS file model_update.gms. They are 

repeatedly used in calculations to limit the number of variables or constraints that the model 

generates. For example, we need not create a variable for the 60-year old age class in the initial 

inventory if there are no 60-year old acres in the starting inventory. Furthermore the 

FORINVENTORYA constraint requires that all acres in the initial inventory be allocated to 

some management regime. In the definition of this constraint below, by means of the isexist set, 

the FORPRDEXIST variable is created only for those cohorts, region, land classes, owners, 

forest types, sites, management intensities, and simulation policies for which there is actually 

some land in the initial inventory: 

sum(period, 

 sum(isexist(period,cohort,reg,class,pvtlogowner,type,site,mgtintensity,policy), 

FORPRDEXIST(period9999,cohort,reg,class,pvtlogowner,type,site,MgtIntensity,policy)) 

 =e= 

 invent(cohort,reg,class,pvtlogowner,type,site,MgtIntensity); 

where use of isexist limits attention only to potentially viable stands. 
146 

7.2.4 Forest management representation 

Land management decisions for timberland owners simulated each period are: 1) 

whether to harvest a forest stand or keep it for another period; 2) whether to replant a harvested 

stand in trees (i.e., reforestation) or move it out of forest production (i.e., deforestation) 

converting it to developed or agricultural uses; 3) what forest type and timber management 

option to select if the land is planted in trees; and 4) what to do with the land if it is converted to 

agricultural use as will be discussed in the agricultural section below. These decisions are based 

on the relative profitability of land in its various competing alternative uses over the life-span of 

foreseeable choices. 

FASOMGHG represents 23 alternative timber MIC regimes to depict potential responses 

to changes in policy or market conditions. These MICs represent silvicultural practices now 

being used or those that might be applied to future stands. MICs encompass the use of 

• regeneration (natural or planted), 

• stand density control (precommercial or commercial thinning), 

• fertilization, and 

• method of harvest (partial cutting, clearcutting or reserved from harvest). 

MICs represent a regional average response for a particular forest type and site class. These 

MICs are initially populated with timberland inventory data as described later in Section xx.2, 

using guidelines from the 2000 RPA Timber Assessment (Haynes, 2003). 

The basic way MICs appear in the forest sector model (excluding those dealing with 

harvest alternatives that are discussed in the harvest section just below) is portrayed in a 

simplified manner in table 7-5. 

Table 7-5 Tableau depicting forest management intensity alternatives 
147 

Manage stand with Passive MIC Manage stand with Lo MIC Manage stand with Higher MIC Log demand Total cost 

Timberland 1 1 1 = L 

Harvested logs -typassive -tylo -tyhigher +1 = 0 

Production cost +cstlo +csthigher -1 = 0 

Where 

L represents the initial inventory of land in the forest stand. 

typassive is the log yield under use of the passive management alternative 

tylo is the log yield under use of the lo management alternative 

tyhigher is the log yield under use of the higher management alternative 

cstlo is the cost incurred under use of the lo management alternative 

csthigher is the cost incurred under use of the higher management alternative 

The basic way MICs appear in the forest sector model (excluding those dealing with 

harvest alternatives that are discussed in the harvest section just below) is portrayed in a 

simplified manner in table 7-5. 

Three variables represent these possibilities and are 

FORPRDEXIST(period,cohort,allreg,class,pvtlogowner,type,site,mgtintensity,policy) for 

existing stands, 

FORPRDNEW(period,when,allreg,class,pvtlogowner,type,site,mgtintensity,policy) for 

reforested stands and 

FORPRDNEWAFFOREST(periods,when,allreg,class,pvtlogowner,type,site,mgtintensity,polic

y) for afforested stands. Within these variables the mgtintensity dimension represents the MIC 

alternatives. The data giving yield differences are resident in the GAMS parameters existyld, 

newyld, existyldpc and newyldpc as will be discussed in the section on stand growth below. The 

cost data are resident in the GAMS parameters existforestcost and newforestcost as discussed 

below. 
148 

7.2.5 Forest Establishment and Growing Costs 

Cost estimates for stand establishment and intermediate treatments are resident in the 

parameters existforestcost(allperiods,cohort,allreg,class,type,mgtintensity,manage) and 

newforestcost(when,allreg,class,type,mgtintensity,manage) in the files data_forexistcost.gms

and data_fornewcost.gms, where the set when tells when management practices are applied 

relative to the date of planting. The manage set gives the alternative management cost items with 

the categories in that data being listed in table 7-6. 

Table 7-6 Timber Management Costs 

Cost 

category Definition Units 

EST Stand Establishment (site preparation and if 

applicable, planting and seedling costs) 

2002 Dollars/acre 

DEC Decadal (aggregated periodic management costs 

including management plan, boundary 

maintenance, survey and cruising, and fire 

protection) 

2002 Dollars/acre/Decade 

HRB Herbicide Treatment 2002 Dollars/acre 

FRT Fertilizer Treatment 2002 Dollars/acre 

PCT Precommercial Thinning 2002 Dollars/acre 

RXF Prescribed Fire 2002 Dollars/acre 

Grow Sum of Period Costs 2002 Dollars/acre 

These cost estimates are included in the forest production cost equation that is defined as 

FORCOSTBAL(reg,period) by region and time period. The equation has terms that multiply 

these per acre costs times stand acreage and adds this up into the variable 

FORPRDCOST(reg,period) that in turn enters the objective function. The tableau in the 

previous section illustrates the way the cost data enter the model. 

Terms were entered for costs associated with land use change for converting timberland 

to crop land or pasture land. Three levels of costs were used to represent a step function or 

increasing marginal costs of conversion as more timberland is converted. These data are resident 

in the parameter CONVERT(allreg,class,convdat,three) that is defined in the file 

data_forconvert.gms. The convdat set has elements (1) ccost that gives the cost per acre 

converted, and (2) cquan that gives the maximum number of acres that can be converted at this 

cost. Note these data vary by land suitability for agricultural use and region. These data are 

entered directly into the objective function (WELFAR) and are applied to the land conversion 
149 

variable LANDTOAG(reg,class,period,three) that tells how much acreage is converted from 

forest to agriculture by region, land suitability class, time period in each of the three steps. This 

will be further discussed and illustrated in the chapter below on intersectoral transfers. 

7.2.6 Stand Growth 

Harvest age is allowed to vary and thus the growth of existing and regenerated/afforested 

stands must be modeled. Timber growth and yield data are included for existing stands, 

reforested stands, and afforested lands that track the volume of wood in each unharvested stand 

which in turn is used in computing forest carbon sequestration. These data indicate the wood 

volume per acre in unharvested timber stands for each timber stand strata (e.g., a stand giving 

location, forest type, management intensity class, etc.) by age cohort. The data used are derived 

largely from the USDA Forest Service RPA modeling system (see Haynes (2003)). 

Move next 2 paragraphs to data section? 

More specifically, they are mostly based on yield tables resident in the ATLAS model 

(Mills and Kincaid 1992) version employed for the 2000 RPA Assessment, but are augmented 

with Pacific Northwest Westside timber yields developed by Alig et al. 2005 using the Forest 

Vegetation Simulator (Stage 1973). 

Existing stand yield projections for each inventory cell are projected relative to a base 

yield, based on ATLAS estimates and a relative density approach described by Mills and Kincaid 

(1992). A set of base yield tables was derived for each forest type within each region from the 

FIA plot data. Moving from initial inventory estimates to future levels requires growth and yield 

estimates over time, which was also done by adopting ATLAS estimates (Mills and Kincaid 

1992). These estimates add the dimension of time so that each aggregate is represented in every 

five-year period for 100 years. These data permit FASOMGHG to update the regional inventory 

levels by owner, land use suitability, forest type/species, site class, management regime, and age 

for each time period in the model. This general technique was used in past RPA Assessments 

(Mills and Kincaid 1992) and the use of empirical growth rates embodies the effects of historical 

and recent timber management and disturbances. 

Once a cohort is harvested in FASOMGHG, the land can be regenerated. Regeneration 

yields are the potential yields for regenerated stands by region, land suitability class, owner, 

forest type, site class, management intensity class, and age cohort. Upon regeneration, 

FASOMGHG assigns a new MIC. Timber growth by MIC differs by region, forest type, site 

class, and age cohort. 
150 

Move next few paragraphs to data section? 

Assumptions pertaining to initial stocking for a regenerated stand are based on the 

ATLAS modeling for the 2000 RPA Timber Assessment, and regeneration stocking ratios can 

differ by forest type, MIC, and site class (Mills and Kincaid, Haynes 2003). Stocking 

considerations also include "operational falldown," which took into account wind-damaged 

timber, breakage during harvesting, and other losses during management activities (Alig et al. 

2005). 

The ATLAS modeling process specifies no specific climate scenarios. Implicitly, all 

timber yields based on FIA field data incorporate past climate trends and this can affect future 

projections. Using scenarios to examine sensitivity of timber market projections to timber yield 

inputs, McCarl et al. (2001) analyze the impacts of different assumptions about yield effects 

from climate change. 

For the Pacific Northwest west side, the FVS model was used to estimate timber yields, 

tapping into the same FIA data base as for the ATLAS-modeling. The FVS model draws upon 

FIA plot data and uses local growth rates to adjust model timber growth relationships. The FIA 

data provide a tree list, required for simulating an existing stand. Timber growth and yield 

predictions are dependent on interactions between trees within a timber stand. The FVS model 

can portray timber yields for a relatively wide variety of forest types and for both even-aged and 

partial cutting stand structures (Stage 1973). 

The timber growth and yield data are in the GAMS parameters 

existyld(period,cohort,logregions,class,pvtlogowner,type,site,MgtIntensity,logproducts) and 

newyld(when,logregions,class,pvtlogowner,type,site,MgtIntensity,logproducts). The yield of 

harvested logs for stands that are thinned or partially cut are resident in 

existyldpc(period,cohort,logregions,class,pvtlogowner,type,site,MgtIntensity,logproducts) and 

newyldpc(when,logregions,class,pvtlogowner,type,site,MgtIntensity,logproducts). These data 

come from the files data_forexist.gms, data_fornew.gms, data_forexistpc.gms and 

data_fornewpc.gms. 

7.2.7 Harvest representation 

The earlier version of FASOM used a forest inventory projection approach involving 

Johnson and Scheurman's (1977) "model II" with fixed yield relations that varied with 

management input. FASOMGHG still employs a model II structure for the even-aged portions of 

the forest, but also allows allocation of forest land to partial cutting or uneven-aged management 
151 

regimes (using Johnson and Scheurman's "model I" scheme). This basic structure is portrayed in 

a simplified manner in table 7-7. 

Table 7-7 Tableau depicting forest clearcut harvesting alternatives Clearcut in T1 Clearcut in T2 Clearcut in T3 Clearcut in T4 Clearcut in T3 with thin in T1 Clearcut in T4 with thin in T1 Partial cut in T1 and T3 Log demand 

Timberland 1 1 1 1 1 1 1 = L 

Harvested Logs in T1 -cc1 -th1 -th1 -pc1 + =0 

Harvested Logs in T2 -cc2 + =0 

Harvested Logs in T3 -cc3 -ct3 -pc3 + =0 

Harvested Logs in T4 -cc4 -ct4 + =0 

where 

Tn represents time period n and indexes five year periods.

L represents the land in the forest stand. 

ccn is the yield obtain from a clearcut operation in time period n 

thn is the yield obtained from thinning operations in time period n 

ctn is the yield obtained from a clearcut operation in time period n on a stand that was 

previously thinned 

pcn is the yield obtained from a partial cutting harvest operation in time period n. 

The table columns broadly depict the harvest alternatives which are clearcut, thin then 

clearcut and partial cut (which can also be combined with a clearcut). The first four variables 

show harvest age alternatives for a clearcut. The data in ccn arises from the timber growth and 

yield tables and would reveal an increasing volume of growth as harvest is delayed. The fifth and 

sixth variables show thinning combined with clearcut where ctn would differ from ccn because of 

the effects of thinning. The last harvest variable shows a partial cutting regime which yields 

periodic harvested logs pcn but is not in general clearcut at the end. More on the harvest 

alternatives is given in the sub sections just below. 
152 

Three variables represent these possibilities and are 

FORPRDEXIST(period,cohort,allreg,class,pvtlogowner,type,site,mgtintensity,policy) for 

existing stands, 

FORPRDNEW(period,when,allreg,class,pvtlogowner,type,site,mgtintensity,policy) for 

reforested stands and 

FORPRDNEWAFFOREST(periods,when,allreg,class,pvtlogowner,type,site,mgtintensity,polic

y) for afforested stands. 

Within these variables the period dimension of the FORPRDEXIST variable gives 

harvest time and could include a never case. Simarly the when dimension of the FORPRDNEW 

and FORPRDNEWAFFOREST variables depicts harvest age (being plus25, plus30, plus35, ... 

never). 

7.2.7.1 Even-aged Timber Management 

In representing even-aged management, FASOMGHG assumes all of the trees in a stand 

are removed when clearcutting, and in turn allocates all of the growing space to subsequent 

regeneration or land use change. In all forest regions, there are at least two even-aged MIC 

alternatives for regenerated aggregates. These include the passive and lo alternatives. 

The passive MIC refers to a stand that receives little management intervention of any 

kind between harvests of naturally regenerated trees. A lo MIC refers to custodial management 

(where timberland receives management such as forest protection and elimination of grazing by 

livestock) of naturally regenerated trees. Additional MICs are present in the SC, SE, and 

PNWW, representing stand establishment and intermediate management, followed by a clearcut 

final harvest. In addition to final harvests, commercial thinnings can occur. A relatively intensive 

example of an even-aged MIC for the South would involve site preparation and establishment of 

a pine plantation using genetically-improved tree stock, commercially thinning in later years, and 

then final harvest at ages beyond 20 years of age. A mathematical description for an even-aged 

scheduling structure is given by Adams et al. (1996), emphasizing the forest sector and 

illustrating the interperiod link of existing, new or regenerated, and terminal timber stands. 

Move? The passive MIC was added to the ATLAS-based MICs to represent cases where 

the landowner accepts whatever type and rate of regeneration occurs naturally (Adams et al. 

1996), modeled as growing under even-aged conditions. Relative to the lo MIC, where 

timberland receives a low level of timber management, such as forest protection and elimination 

of grazing by livestock, future merchantable timber yields for the passive MIC are lagged ten 
153 

years and reduced 10% relative to those for low MIC timber yields for that same region, forest 

type, and site class. 

7.2.7.2 Partial cutting timber management 

In modeling timber management by partial cutting, we broadly represent the periodic 

removal of mature trees, leaving immature trees to grow, thereby allocating a portion of the 

growing space to regeneration but none to land use change unless a terminal clearcut is chosen. 

In contrast, we assume removal of all trees when harvesting an even-aged stand with all of 

growing space reallocated to regeneration or land use change. We model regimes of multipleentry partial harvests over long time periods. 

Partial cutting MICs are represented in the SE, SC and PNWW regions. In the SC and SE 

regions, partial cutting takes place in four forest types: natural pine, oak-pine, upland hardwood, 

and bottomland hardwood. The partial cutting MICs for the region include low, high, and highplus regimes. In the PNWW, partial cutting MICs are represented for the Douglas-fir and Other 

Softwood types. 

7.2.7.3 Minimum harvest age 

Minimum harvest age restrictions are used to represent lower limits of merchantablity of 

stands, ages below which there is insufficient merchantable volume ina stand to justify 

commercial entry. Eliminating activites for stands below the minimum harvest age also helps to 

reduce model size, since timber harvesting isnot allowed and the generation of a number of 

variables is suppressed. They are based on observations of merchantable age thresholds drawn 

from the ATLAS inputs used in the 2000 RPA Timber Assessment (Haynes 2003). Minimum 

harvest ages vary by region, owner, site class, forest type, and MIC. The original data appear in 

the minharv2(allreg,allowner,type,mgtintensity,site) GAMS parameter in the 

data_forminiharv.gms file. 

7.2.8 Reforestation, Afforestation and Deforestation 

When timber on existing even-aged forested lands is harvested, all trees are assumed to 

be removed and the resultant treeless bare land may be either: 

• reforested 

• transferred to agriculture 

• transferred to a developed use. 
154 

In addition, in any period land may be transferred in from agriculture and afforested. This 

is controlled within the 

FORLANDBALANCE(reg,class,pvtlogowner,successorgroup,site,period) equation. In each 

five-year period, potentially reforestable acres (in the FORPRDNEW variable) plus timberland 

transferred out to agriculture (in the CONVRTTOAG variable) or development are balanced (in 

the regdevelopmentfor data) with the land available from timber harvest arising from existing, 

reforested, and afforested stands(respectively in the FORPRDEXIST, FORPRDNEW and 

FORPRDNEWAFFOREST variables). Similarly, potentially afforested acres (in the 

FORPRDNEWAFFOREST variable) are balanced with lands in-migrating from agriculture (in 

the CONVRTTOAG). When timberland is reforested or afforested, the model selects an MIC and 

an optimal future harvest date. These acres are then retained in the forest base until their harvest 

date, at which time another reforestation or land use decision is made. 

Afforestation activity is assumed to only occur for nonindustrial private ownerships and 

only into the medium and high site classes. Consistent with other studies and long-term trends 

(see Haynes, 2003, for a discussion of these trends), we also assume that there will be little or no 

loss of industrial land to non-forest developemtn. Thus, the timberland area for forest industry in 

the FASOMGHG modeling is assumed to remain constant in the baseline case, by region over 

the projection period. That is, all forest industry timberland is placed in the "FORONLY" land 

suitability class, where it remains over the projection. 

Decisions regarding the characteristics and timing of private areas afforested, reforested, 

or converted to agricultural use are endogenous. The choice of investment levels in intermediate 

treatments or timber management are also consistent with a wealth-maximizing objective, in 

contrast to external determination of management investment decisions as in most past studies 

(e.g., Haynes 2003). 

Table 7-8 Tableau depicting afforestation, reforestation and deforestation 
155 

Clearcut Exist Stand in T1 Clearcut Exist Stand in T1+k Reforest Land in T1 then Clearcut in T1+k Reforest Land in T1+k then Clearcut in T1+2k Afforest Land in T1 then Clearcut in T1+k Land from Ag in T1 Land to Ag in T1 Log demand Ag activity in year T1

Exist Timberland 1 1 = L 

Bare land in T1 -1 1 1 = -dev1

Bare land from ag in T1 1 -1 = 0 

Bare land in T1+k -1 -1 1 -1 = -dev1+k

Harvested Logs in T1 -he1 + =0 

Harvested Logs in T1+k -he1+k -hr1+k -ha1+k + =0 

Ag land in T1 1 -1 + =A 

where 

Tn -- represents time period n and indexes the five year periods. 

K -- is the rotation age for new stands (note this is fixed only for display purposes)

L -- represents the initial inventory of lands in existing forest stands. 

hen -- is the yield obtained from a clearcut operation on an existing stand in time period n 

hrn -- is the yield obtained from a clearcut operation on a reforested stand in time period n 

han -- is the yield obtained from a clearcut operation on afforested stand in time period n 

A -- is available agricultural land 

devn -- is the private NIPF land moving to developed use in time period n 

The columns in table 7-8 broadly depict the variables and associated equations for 

production and harvest of existing, reforested, and afforested stands. The first two variables 

(representing the variable FORPRDEXIST) allow choice of varying harvest ages for clearcut of 

existing stands. The first constraint restricts the use of the existing stands to the available 

inventory. 

The next two variables represent reforestation activity (the model variable 

FORPRDNEW). The first of these depicts reforestation in the first time period with subsequent 
156 

harvest k time periods later. Note that such early reforestation can only follow harvested existing 

stands. The second reforestation variable represents the possibility for reforestation of land after 

a previous forest rotation in a time period (T1+k) long enough after the model starts that initially 

reforested stands have enough time to become mature and eligible for harvest. This reforestation 

activity (that in T1+k) can follow after existing, reforested, and afforested stands. Reforestation 

activity following existing stands must remain unharvested up until the time period at issue (1+k 

in this case). When reforestation activity (that in T1+k) follows a previously reforested stand (i.e., 

one from T1), the preceding reforested stand has to have been endogenously planted or naturally 

regenerated in an earlier model time period and have achieved sufficient maturity to make it 

eligible for harvest by the time period at question. When reforestation activity follows an 

afforested stand, it must have the same characteristics in terms of being planted earlier and now 

being eligible for harvest as mentioned above when following a reforested stand, but can only be 

placed on land moving over from agriculture in the time period at question as imposed by the 

third constraint. 

The fifth variable in the tableau depicts afforestation (in the model variable 

FORPRDNEWAFFOREST). This variable is only defined for the first tree planting rotation 

after land moves over from agriculture. The variable requires land coming from agriculture and 

upon harvest puts land into the same category as any other harvested stand becoming eligible for 

subsequent reforestation. 

The sequencing relationships, in terms of enforcing what stands other stands can follow, 

are represented by the second and third equations in the tableau. In the GAMS implementation 

this is the FORLANDBALANCE equation. That equation also requires that land be harvested 

and diverted to developed uses. 

The final four equations depict land moving to and from agriculture, wood product 

processing/demand, and agricultural land use and will be discussed below. 

7.2.8.1 Species succession 

One feature of the rotation aspects of reforestation involves species succession. We 

restrict reforestation activity so that only certain species can succeed other species. This prevents 

the model from having for example upland hardwood succeed bottomland hardwoods. Currently 

a restriction is in place that only allows the same forest type to succeed the original forest type. 

In the longer run this will be relaxed. 
157 

7.2.8.2 Developed use 

Exogenous data on movement of forested land to developed uses were included to 

account for timberland converted to development. Deforestation for the purpose of development 

(e.g., urban use of land) is handled by exogenous land transfers out of forestry. Projections were 

obtained from land use modeling for the 2000 Resources Planning Act (RPA) Timber 

Assessment (Alig et al. 2003, Haynes 2003) and updated to reflect current development 

estimates (Alig et al. 2004). A key part of the development projections are expected changes for 

population and personal income by state (Alig et al. 2004). 

7.2.9 Wood products 

Earlier versions of FASOM and essentially all past dynamic models of the forest sector 

(Johnson and Scheurman, 1977; Berck, 1979; Sedjo and Lyon (1990), Adams et al (1996), 

Sohngen et al, 1999; Shillinger et al, 2003) have used a single market level formulation, the 

markets for logs, with a single demand region, multiple supply regions, and limited 

differentiation between types of products and species. These approaches were computationally 

tractable and required relatively limited data to calibrate, but it was difficult to use them to model 

the impact of changes in product trade, trade restrictions or exchange rates; shifts in determinants 

of demand for processed products (such as housing activity or GDP growth); or changes in the 

technology of wood products processing. Accounting for carbon stored in product pools was also 

cumbersome in these models, requiring fixed assumptions about log breakdown into specific 

product proportions regardless of log prices or changes in the log market. 

FASOMGHG overcomes many of these difficulties by incorporating multiple market 

levels in the forest sector (logs, intermediate products and final products) in the form of a 

manufacturing sector that transforms logs and their intermediate products into final products. It 

explicitly includes such manufacturing in both the US an Canada (the US’s principal wood 

products trading partner). Harvest of an acre of timberland involves the simultaneous production 

of some mix of softwood and hardwood logs (sawlogs, pulpwood, and fuelwood; see glossary). 

The composition of this product mix varies across regions, site classes, forest types, and age 

cohorts and changes over time as stands age. Proportions also change between MICs. 

Downward substitution of logs is allowed. Sawlogs can be substituted for pulpwood, and 

pulpwood, in turn, can be substituted for fuelwood, provided that the prices of sawlogs and 

pulpwood, respectively, fall to low enough levels. This "down grading" or inter-product 

substitution is technically realistic and prevents the price of pulpwood from rising above that of 

sawlogs and the price of fuelwood from rising above that of pulpwood. 
158 

Logs in turn are processed into products. The full sequence of transformations from trees 

to products is illustrated in Figure 7-1. 

Figure 7-1. Flows of wood and products in forest sector of FASOMGHG. 

With this additional market and product detail, the forest sector includes a full materials 

balance, accounting for all wood flows from forest to final products. 

7.2.9.1 Log and solid wood products 

Table 7-9 lists the classes of harvested logs and wood products at the mill represented in 

FASOMGHG. Harvested logs are identified as either softwood or hardwood species and as 

sawtimber, pulpwood or fuelwood. Sawtimber is processed into one of the solid wood products, 

with the exception of OSB (oriented strandboard) which is classified as a structural panel but 

uses pulpwood as its fiber source. Quantities and prices of lumber, softwood plywood and OSB 

are determined endogenously in the model. Demands for, and production of, hardwood plywood, 

other nonstructural panels and miscellaneous products are determined outside the model. Two 

classes of residue by-products are produced by solid wood products milling and may be 

transferred to pulping, used as fuel, or left unutilized. Product classification and treatment in the 

solid wood sector follow the TAMM model format (Adams and Haynes, 1996). 

FIBER PRODUCTS 

STUMPAGE (TIMBER)ÆLOGSÆPROCESSED PRODUCTS 

SOLID WOOD 

(LUMBER, STRUCTURAL 

PANELS, ETC.. 

RESIDUES 
159 

Table 7-9 Classes of forest sector products by market level and processing sector 

Timber and Logs Solid Wood Products Fiber Products 

Softwood sawtimber Using Sawtimber Recycled fiber

Softwood pulpwood Softwood lumber Old newspapers 

Softwood fuelwood Softwood plywood Old corrugated 

Hardwood sawtimber Hardwood lumber Wastepaper (mixed) 

Hardwood pulpwood Pulp substitute 

Hardwood fuelwood Using Pulpwood High quality deinking 

 OSB 

 Primary Products

By-products Newsprint 

 Softwood residues Uncoated freesheet 

 Hardwood residues Coated freesheet 

 Uncoated groundwood 

 Coated groundwood 

Exogenous Products Tissue 

 Hardwood plywood Specialty packaging 

 Nonstructural panels Kraft packaging 

Miscellaneous products Linerboard 

 Corrugating medium 

 Special bleachedboard 

 Recycled board 

 Construction paper 

 Dissolving pulp 

 

 Market pulps

 Softwood kraft market pulp 

 Hardwood kraft market pulp 

 Recycled chemi-mechanical pulp 

 CTMP pulp 

Note: production and consumption volumes of “exogenous” products are determined outside the model. 

All other volumes determined by market simulation within the model. 

7.2.9.2 Pulp and fiber products 

In the fiber products sector, supplies of recycled fiber are classed in five groups. Old 

newsprint, old corrugated containers and mixed wastepaper generally originate at consumption 

or distribution points. High quality deinking and pulp substitutes arise from printing plants and 

box/container makers. Fourteen classes of primary paper and paperboard products are identified, 

including a dissolving pulp category (used in photographic film and fabric production). The 

model also employs four classes of market pulps varying with the pulping process and fiber input 

mix. All of the primary product quantities and prices are determined endogenously in the model. 

Product classification and treatment in the fiber products sector follow the NAPAP model format 

(Zhang et al, 1993; Ince, 1994). 
160 

7.2.10 Log and intermediate processing 

Wood product manufacture is explicitly modeled. Figure 7-2 illustrates the flows of wood 

from forest to manufacture. The inventory accounting at the far left relates exclusively to the 

growing stock volume that is measured in the basic FIA inventory data (see preceding sections 

for a discussion of the inventory data). The non-growing stock volumes are estimated as 

proportions of the total wood volume used in processing (regardless of source) on a productspecific basis. The split into solidwood, pulpwood and fuelwood is consistent with the product 

composition of the timber inventory (sawtimber, pulpwood and fuelwood). As noted above, logs 

can also be “downgraded” to the next most valuable use: so sawlogs can be used as pulpwood 

and pulpwood as fuelwood. Output in product units at the far right side of the diagram is 

computed by means of fixed product conversion coefficients (product units/unit of wood input). 

The residue/roundwood mix shown for pulp products is determined by the wood requirements of 

the available pulping processes and the relative values of residue used in pulping and energy 

generation. 

Processing is represented via the variable 

FORWDMANUFACT(period,activewoodregions,woodproduct,process,inputmix) that 

represents manufacture of a particular woodproduct via a particular process using a particular

mix of intermediate products or logs (inputmix) in a region during a time period. Input 

requirements in terms of intermediate products and logs are given in table 

woodmancoefs(activewoodregions,woodproducts2,woodproduct,Process,inputmix,period)

which tells how much of each of the other products (woodproducts2) are used to manufacture 

one unit of a specific woodproduct in a specific region (activewoodregions) via the technology 

mix (Process,inputmix). These production conditions can vary with time period. The data are 

specified in the file data_formcoefs.gms. The log, intermediate and final products are controlled 

by balance equatios so use cannot exceed supply in the constraint FORWDBALANCE. In 

addition, residues are accounted for in the constraint 

FORWDRESIDUES(activewoodregions,residues,period) and recycled paper in the equation

FORWDRECSUPPLY(activewoodregions,woodproducts,period). 

Manufacturing is also subject to the capacity constraints 

FORWDCAPACITY(activewoodregions,woodproducts,process,period) that are defined by

region, product and process in a period. The capacity data are in the GAMS parameter 

woodcap(activewoodregions,woodproducts,process,period) which are input via the file 

data_forcapacity.gms. 
161 

Figure 7-2. Wood flows in the forest sector of FASOMGHG.

Removed to figures file 

The tableau in table 7-10 summarizes the treatment and disposition of wood and product 

volumes in the forest sector of FASOMGHG. 
162 

Table 7-10 Tableau depicting treatment and disposition of wood products 

Stand harvest 

Sawlogs to mill 

Pulpwood logs to mill 

Downgrade sawlogs to pulpwood 

Manufacture lumber 

Manufacture Plywood 

Chip a pulpwood log 

Make paper from chips and recycled fiber 

Make OSB from chips 

Move residue into pulpwood Non-wood input 

Sell products 

Welfare - -nwc + Harvested sawlog balance - +1 = 0 Harvested pulpwood log balance - +1 = 0 Mill sawlog balance -1 +1 +sls +slp + = public sawlogs Mill pulpwood log balance -1 -1 +1 = public pulpwood Lumber balance -1 + = 0 Plywood balance -1 + = 0 OSB balance -1 + = 0 Paper product balance -1 + = 0 Chipped log balance -yp +pr +po -1 = 0 Recycled fiber balance +pf - = 0 Milling residues balance -yrs -yrp +1 = 0 Paper manufacturing capacity +1 < capacity Sawlog harvest and haul non-wood input +1 - = 0 Pulplog harvest and haul non-wood input +1 - = 0 Paper non-wood input +1 - = 0 
163 

where 

nwc is the non-wood input function for log hauling and paper manufacture 

sls is the use of saw logs to manufacture one unit of saw timber 

slp is the use of saw logs to manufacture one unit of plywood 

psl is the exogenous supply of public and other saw logs 

ppl is the exogenous supply of public and other pulp logs 

yp is the yield of wood chips from one unit of pulp logs 

pr is the use of wood chips to manufacture one unit of paper 

pf is the use of recycled fiber to manufacture one unit of paper 

po is the use of wood chips to manufacture one unit of OSB 

yrs is the use of milling reside when manufacturing one unit of saw timber 

yrp is the use of milling reside when manufacturing one unit of ply wood 

cap is paper making capacity 

The columns in the table broadly depict the variables and associated equations for wood 

products manufacturing and log downgrading. The first variable represents forest harvest and the 

output of harvested logs as discussed above. All of the remaining variables except the last two 

reflect activities at wood products manufacturing facilities and are represented in the variable 

FORWDMANUFACT(period,region,woodproduct,process,inputmix) of the GAMS 

implementation. Such variables indicate the level of manufacturing related activity during a 

period by region in terms of the number of units of a particular wood product (woodproduct) 

being made with a particular process and input mix. 

Several aspects of the model are illustrated in this tableau. 

• There is a distinction made between logs in the woods and logs at the manufacturing 

facility. This is done through use of a variable within the manufacturing portion of the 

model that reflects transformation of logs with status (location) “in the woods” to logs 

with status “at the mill”. 

• The log to manufacturing facility transformation also uses non-wood inputs for 

harvesting and hauling. These are grouped under the non-wood input portion of the 

model in the GAMS implementation variable 

FORWDNWCS(woodsupplytype,activewoodregions,woodproducts,period9999,steps)

that in general depict an upward sloping supply function for such non-wood inputs. 

• FASOMGHG includes the potential for downgrading logs. In the example tableau the 

variable Downgrade sawlogs to pulpwood shows transformation of sawlogs into 

pulpwood logs. This will only be done when the value of the sawlogs has been driven 

down to equal the value of the pulpwood logs. 

• When solid wood products like lumber and plywood are made, then one obtains the 

byproduct milling residues. 
164 

• Some products are transformed within the model. For example pulpwood logs are 

converted into chips in the Chip pulpwood variable. 

• Milling residues can be substituted for pulpwood and in turn go into the paper or OSB 

manufacturing processes. 

• Competing uses are reflected for alternative inputs. For example, in the tableau sawlogs 

can go into either lumber or plywood manufacture while the chips from pulpwood logs 

can go into either a pulp and paper operation or OSB manufacture. 

• Manufacturing activities in general use non-wood inputs and incur costs. 

• Manufacturing activities are potentially subject to capacity constraints. 

• Manufacturing capacity is accounted by processing alternatives across all input mixes. 

• The non-wood inputs differ by process and input mix. 

• Paper does not have non-wood inputs that vary with output volume rather they are 

constant on a per unit basis. 

• Alternative processes and input mixes can be used as illustrated in table 7-11 that depicts 

an example for paper. This tableau shows two processes for making paper from wood 

chips (roundwood and residues) and recycled fibers each having two alternatives 

involving different mixes of inputs. 

• Total chip supply comprises chipped pulpwood logs and residues generated in the 

manufacture of solid wood products. 

• OSB competes with fiber products (paper) for chips. 

• Capacity is reckoned at the process level, since a given process can be adapted to either 

of the input mixes. 
165 

Table 7-11 Tableau illustrating alternative processes and input mixes in the case of paper 

Manufacture lumber 

Manufacture Plywood 

Chip a pulpwood log 

Make paper from chips and recycled fiber process 1, input mix A 

Make paper from chips and recycled fiber process 1, input mix B 

Make paper from chips and recycled fiber process 2, input mix AA 

Make paper from chips and recycled fiber process 2, input mix BB 

Make OSB from chips 

Move residue into pulpwood 

Non-wood input 

Sell products 

Paper products -1 -1 -1 -1 + = 0 Chipped logs -yp +pr1a +pr1b +pr2aa +pr2bb +po -1 = 0 Recycled fiber +pf1a +pf1b +pf2aa +pf2bb - = 0 Milling residues -yrs -yrp +1 = 0 Paper capacity process 1 +1 +1 < capacity 1 Paper capacity process 2 +1 +1 ≤ capacity 2 Paper non-wood inputs -pc1a -pc1b -pc2aa -pc2bb 1 = 0 
166 

7.2.11 Harvest, hauling and processing costs 

The fiber products sector, drawn from NAPAP, is modeled exclusively as a fixed 

coefficients production process. Total production costs for any given product can be computed as 

the sum across all inputs (factor use per unit of product output times the cost per unit of factor) 

times the level of output. There are no factors whose unit costs vary with the volume consumed 

or whose use per unit of output is not constant. In the solidwood sector, drawn from TAMM, 

output is assumed to be a fixed multiple of wood input, but the relationship between output and 

non-wood inputs varies with the level of output. Assuming quasi-fixed capital inputs, the 

production function for a specific product would appear as: 

NEED EQUATION NUMBERS 

min[ , ( , , , , )] Q = rWW f X1 X 2 K X n K

Where 

Q is output 

rw is the product recovery factor for wood (output per unit input or Q = rwW) 

W is the volume of wood input 

Xi are the non-wood variable inputs, and 

K is quasi-fixed capital. 

The function f can be viewed as an aggregator function for the other inputs, and the two 

groups of factors, W and (Xi, K) are weakly separable. In this case, and assuming that the 

aggregator function (f) can be approximated by a quadratic form, it can be shown that the 

inverse (price-dependent) product supply curve can be written as: 

P = F(Q, K) + (1/rw)Pw

where 

P is product price 

Pw is wood input price, and 

F(Q, K) is a linear function of output, quasi-fixed capital and the prices of all other 

inputs. 

As a result, the area under the product supply curve (total variable costs) can be shown to 

be: ∫∫ ∫ PdQ = F( where the first term on the right side is the total variable Q,K)dQ + PW dW

cost arising from use of the non-wood inputs and the second term is the area under the timber or 

log supply curve. The first term is called “non-wood input” in TAMM (and FASOMGHG) as 

shown in equation [7._ ] above. It includes all non-wood inputs to log processing at the mill 

(labor, energy, and other) and all harvest and transport costs from woods to mill. The second 

term on the right is the cost of timber and is represented in the model objective by the 

“management cost” terms in equation [7.__]. 
167 

Coefficients for the non-wood input equations are found in the GAMS data item 

WOODnwcost(WOODsdtype,allreg,alli,allperiods,params) in the FASOMGHG input file 

data_forsupdem.gms. Non-wood input equations vary by product (WOODsdtype) region 

(allreg) and period. Total non-wood inputs are computed in the FASOMGHG constraint 

FORWDNWCEQ(woodsupplytype,allreg,alli,allperiods).

7.2.12 Other sources of log supply 

Not all of the timber harvest and logs in the model are generated from the private land 

inventory and harvesting process. Exogenous supplies come from National Forests and other 

public timberlands in the US and, in Canada harvests from provincial and private lands are 

represented by price-sensitive supply relations 

7.2.12.1 US Public log supplies 

Harvests of logs from public lands in the US are treated as exogenous in FASOMGHG. 

Policies that determine harvests on these lands are based on an array of public and environmental 

concerns and generally do not consider prices or developments in log and product markets. 

These volumes are incorporated in the input file data_forlogsupdem.gms in the GAMS data item 

WOODlogsup(WOODsdtype,allreg,allowner,alli,allperiods,params) 

US public harvests are the intercept terms (params) for the appropriate region and owner 

(NF or OG). In the model solution process these preset volumes are transferred in each period to 

the variable FORWDSUPPLY(woodsupplytype,allreg,alli,allperiods) in the equation 

FORWDLOGSUPEQ(woodsupplytype,activewoodregions,allowner,woodproducts,period9999) 

7.2.12.2 Canadian log supplies 

Log supplies in Canada derive primarily from public lands (termed “Crown” lands) 

governed by the individual provinces with a small volume coming from private lands. Harvests 

may vary over time based on extraction and delivery costs and hence with market log prices. 

These supplies are represented by a set of (log price sensitive) delivered log supply equations for 

both sawlogs and pulpwood. The supply equation coefficients are input through the same files 

and variables as the US public supplies described above. The area under the Canadian log supply 

curves are deducted from the overall model objective function. The actual current period harvest 

volumes from Canadian forests are computed in the equation 

FORWDLOGSUPEQ(woodsupplytype,activewoodregions,allowner,woodproducts,period9999)

by summing the volumes linked to the active steps included in the current period solution. 
168 

7.2.12.3 Other log supply 

Small volumes of logs are also imported to the US for processing from Canadian and 

non-Canadian sources. These volumes are treated as exogenous in FASOMGHG. They also enter 

the model via the data_forlogsupdem.gms in the same table as the other supplies discussed 

above.

7.2.13 Wood product movement and markets 

FASOMGHG permits interregional commodity movements for certain commodities in 

certain directions using the variable 

FORWDTRANSPORT(activewoodregions2,activewoodregions,woodproduct,period) that 

depicts movement of a particular product (woodproduct) between a source region

(activewoodregions2) and a destination region (activewoodregions) during a time period. Such 

movements are restricted on a bilateral and product flow basis to ensure that model behavior 

does not drift too far from historically observed product flow patterns.4 Notes on the types of 

restrictions imposed appear in the sections just below. 

The data defining when flows are allowed are resident in the data in the parameter 

woodtranscost(activewoodregions2,activewoodregions,woodproducts). Shipments are only 

allowed when the woodtranscost data are non zero. The movement variable incurs costs in the 

objective function (WELFAR) and uses commodities within the 

FORWDBALANCE(activewoodregions,woodproducts,period) equation. 

7.2.13.1 Logs and residues 

With certain exceptions, logs are not permitted to flow between regions. Because logs are 

expensive to transport, actual interregional log flows are relatively limited. Where larger flows 

are observed, the volumes originate near the borders of regions and move to immediately 

adjacent border areas in other regions. We rule out most of these flows to maintain better control 

of regional production (and harvest) behavior. The cases excepted include shipments of 

hardwood pulpwood and other logs from northern US regions to eastern Canada and hardwood 

log shipments from the east to the PSW region for both processing and export. Residues are also 

permitted to move from the northern US into eastern Canada. 

 

4 For an extensive discussion of problems in tracking bilateral trade flows between regions in the forest sector and 

potential solutions see Kallio, Dykstra and Binkley (1987). 
169 

7.2.14 International trade 

Wood product sector trade modeling is handled differentially depending on whether the 

trade is with Canada or with other countries. 

7.2.14.1 Canada 

Canadian demand and supply regions are included but we do not attempt to model 

bilateral trade flows with the US in both directions. The model uses only a single US and 

Canadian national demand region for wood products. Product movements from Canadian 

producing regions to the US demand center are endogenous and subject to appropriate transport 

costs, exchange rates and tariffs. Solid wood demand in Canada is treated as exogenous and 

varies over time according to projections in the 2000 RPA Timber Assessment (Haynes, 2003). 

Solid wood exports from the US to Canada are exogenous. Fiber products demand in Canada is 

price sensitive but fiber products exports from the US to Canada are treated as exogenous. 

Tariffs are set at "current" (2003) levels. The projected Canadian-US exchange rate (a real rate 

since the model employs deflated prices for all goods) also follows trends in the 2000 RPA 

Timber Assessment. 

7.2.14.2 Other regions 

With the exception of US imports of softwood lumber, the Canadian and US regions are 

modeled so that they trade wood products with other world regions. This trade is specified as 

exogenous regionally-specific volumes. Base case projections follow trends in the 2000 RPA 

Timber Assessment. Data are entered via the GAMS data array 

WOODsupdem(WOODsdtype,allreg,alli,allperiods,params) in the file Data_forsupdem.gms. 

Softwood lumber imports into the US from non-Canadian sources are based on an import 

supply function drawn from the 2000 RPA Timber Assessment (Haynes 2003). The function 

shifts over time according to the base scenario in the Timber Assessment. Slope and intercepts 

for the linear functions are entered via 

WOODsupdem(WOODsdtype,allreg,alli,allperiods,params) in the file Data_forsupdem.gms. 

7.2.15 Wood product prices 

FASOMGHG incorporates price dependent demand relations for softwood lumber, 

softwood plywood, hardwood lumber, OSB and a number of fiber products. The relations for 

non-fiber products were derived by aggregating TAMM annual demand relations. Demand 

relations for the 14 classes of primary fiber products were derived from NAPAP. 
170 

The basic set of FASOMGHG relations comes from the TAMM-NAPAP "base case" as 

described in the 2000 RPA Timber Assessment (Haynes, 2003). The solidwood demand relations 

are linear, except for hardwood lumber that uses a constant elasticity form. All of the fiber 

products demand curves are of the constant elasticity form. These curves shift over time 

following the TAMM and NAPAP procedures. Alternative projection scenarios that would 

influence the intertemporal development of demand (e.g., changes in the projections of 

macroeconomic activity or price trends of substitute goods) require re-derivation of the 

FASOMGHG demand curves by making an appropriate TAMM-NAPAP run and extracting then 

reaggregating new demand relations. 

The demand curves for the final consumption of timber products are incorporated into 

FASOMGHG at a national level. In addition, the forest manufacturing sector utilizes many 

products as intermediate inputs all on a regional basis. Similarly both international and 

interregional trade are specified on a regional basis. FASOMGHG thus generates wood product 

prices at both the regional and national levels. Goods flow from regions into national demand at 

a cost equal to the historically observed price difference. This is done within the 

FORWDTRANSPORT variable. 

7.2.16 Price expectations 

FASOMGHG incorporates the multi-period path of future prices. Farmers and timberland 

owners are able to foresee the consequences of their behavior (when they plant trees or crops) on 

future stumpage and agricultural product prices and incorporate that information into their 

behavior. The FASOMGHG model uses deterministic expectations, or "perfect foresight", 

whereby expected future prices and the prices that are realized in the future are identical. 

7.2.17 Timing issues 

FASOMGHG is fundamentally designed to simulate forest and agricultural sector activity 

over time. Thus, it must have a dynamic representation. In particular, it was judged essential 

that FASOMGHG reflect the substantial time lag between the establishment of a timber stand 

and its harvest. In addition the GHG consequences of pursuing certain types of forestry actions 

differ over time and thus are dynamic. As a consequence FASOMGHG is designed to depict 

activity over a long time period, approaching 100 years in its current form. 

A related issue is the number of explicit time periods that should be reflected within this 

total 100 year horizon. In the original FASOM version (Adams et al. 1996), time was represented 

in ten year intervals. Experience with subsequent model analysis sometimes suggested that ten 
171 

year intervals were too long. This was particularly true in terms of harvest rotations in the South 

which can be as short as 20 years. Restricting rotations to ten year intervals like 20 or 30 or 40 

years was constraining. As a consequence FASOMGHG is set up based on a five year time step 

allowing portrayal of Southern harvest options at 20, 25 and 30 year periods Naturally there is a 

trade-off in the model between the number of explicit time periods (given a 100-year projection 

period) and model size. 

Forestry activities are assumed identical in each year of a five year period as are activities 

in forest manufacturing and harvest. These cases were treated as if they generated constant costs 

and returns during each year of a five year period. The only exception is that certain forestry 

costs that occur only once during a rotation, e.g., regeneration costs, were not annualized. 

7.2.17.1 Annuities and time periods 

The forestry model returns and costs are assumed to represent typical activity during each 

year of a five year period (running from year 0 to year 4). Thus, forest returns in each explicit 

period were treated as a continuing annual series of five equal amounts discounted to the start of 

each period under the assumption that the same level of returns arise in each year of the period. 

In the terminal period returns arising in all subsequent years (beyond the end of the projection) 

were treated as an infinite annuity as will be discussed in the next section. Thus the period 

specific annuity factor dp 

for 9999 1

and

for 0 1

(1 )

1 4

0

= =

≤ ≤ − + =∑=

p

r

d

p P

r

d

p

t

p t

Where 

r is the discount rate for period p as defined in the GAMS parameter discrate in 

data_basicsets.gms and typically reset in the file model_structure.gms 

P is the last time period plus one as is defined in the set called period9999 in 

data_basicsets.gms and may be reset in the file model_structure.gms. 

In turn, the forestry part of the objective function is 

p p

P

p

p

d ForWel

r

W ∑= + = 0

5 (1 )

1

where 
172 

W is the net present value of forestry welfare. 

dp is the period specific annuity factor which is contained in the model in the array 

Annuitywt(periods,"forestry") as computed at the top of the 

model_structure.gms file. 

p identifies the five year time period. 

ForWelp represents the multi term forestry consumers' and producers' surplus objective 

function in multi year time period p. 

The term involving (1+r) exponentiated to the 5p provides a discount factor to take the net 

present value of the returns in each time period back to the first model period. Multiplying by 

period-specific annuity factor dp converts the returns in each five year period to net present value 

in the dollars of the first year in each period. All of this is implemented in the WELFAR

equation within the file model_structure.gms

7.2.17.2 Discounting forestry returns after the projection period

Values arising in the forest sector beyond the terminal period are handled as an annuity. 

Harvest volumes are computed using von Mantel’s formula as discussed below. Discounted net 

surpluses from this harvest are computed at the end of the final model projection period (using 

the standard form for the present value of an infinite annual payment, 1/r). The end of projection 

values are then discounted to the start of the projection. 

7.2.18 Markets over time 

FASOMGHG reflects changes over time in market and production conditions. In the 

forest sector, changes in basic projection conditions are all-time based and specified outside of 

the model. Demand relations for solid wood and fiber products shift over time, based on TAMM 

and NAPAP projections (see Chapter 2) for a specific RPA case. For the FASOMGHG base case 

and many of the alternative GHG policy analyses, we employ the 2000 RPA Timber Assessment 

BASE case (Haynes, 2003). Other RPA scenarios can also be used as appropriate for the specific 

FASOMGHG application. Shifts over time in non-wood production costs, recovery rates for 

solid wood products, Canadian delivered wood costs, all trade with countries or regions other 

than Canada, and non-Canadian softwood lumber import supply are derived in the same way. 

Unlike some past intertemporal models in the forest sector (for example, Sedjo and Lyon, 

1990; Sohngen et al, 1999), FASOMGHG does not assume an independent time-based 

improvement in timber yields. Following the approach of the 2000 RPA Timber Assessment 

(Haynes, 2003), aggregate yields can improve over time based on adoption of the more intensive, 

and higher yielding, timber management intensity classes on larger areas of the timberland base. 
173 

Thus, a unit of area allocated to a specific MIC in period t of the projection will promise the 

same yields at harvest as a unit allocated to the same MIC in any other period. Aggregate yields 

improve as more area is allocated to the more intensive regimes. 

7.2.19 Valuing terminal standing inventory 

The possibility of planting trees with a rotation length which would carry them beyond 

the explicit model time frame necessitates valuation of the standing inventory existing in the 

terminal projection period. At the time of planting, producers should anticipate a flow of costs 

and returns which justify stand establishment costs. The planting of a stand with an expected 30 

year life in year 80 of a 100-year projection is potentially problematic, however, because the 

anticipated harvest date is beyond the model time frame. The mechanism reflecting the value of 

inventory involves specification of "terminal conditions" that represent the projected net present 

value for all time periods beyond the end of the model projection. Terminal conditions are 

resolved by computing the potential future even-flow of harvest from the terminal inventory and 

valuing this harvest using appropriate prices from downward sloping product demand curves and 

forested stands associated timber management and production costs. 

Terminal period inventories are valued in both forest and agricultural sectors assuming 

perpetual, steady state management following the last year of the time horizon. In the forest 

sector, we used von Mantel's formula to estimate the perpetual yield of a fully regulated forest 

with volume equal to the model's terminal inventory at the end of the final period (see details in 

Chapter 14). The resultant yields were placed in time period 9999 and the full manufacturing, 

timber consumption and movement structure was also defined in that period. Demand relations 

for forestry in all periods beyond the end of the projection were taken to be the same as those in 

the final period. Thus terminal period prices, costs and revenues vary with level of output. 

Deducting costs, the resulting streams of net returns were treated as constant perpetual series. 

7.2.20 GHG involvement 

Management decisions involving the forestry sector have implications for net GHG 

emissions. We account for a number of the GHG implications are accounted for. Specifically the 

forest-related GHG accounts tracked are listed in table 7-12. These include GHG increments of 

six major types 

• sequestration increments in forest soils 

• sequestration increments in forest litter and understory or more generally the forest 

ecosystem not including trees and soils 
174 

• sequestration involved in standing trees 

• sequestration in wood products 

• biofuel offsets when wood products are burned 

• carbon emissions when fossil fuels are used in forest production 

These appear in the GHGACCOUNTS equation that is defined for each period wherein 

coefficients appear for the forest production and manufacturing variables (see the tableau in table 

7-13 where the accounts are collapsed into one row). Specifically, carbon accounting is done in 

association with the FORPRDEXIST, FORPRDNEW and FORPRDNEWAFFOREST forest 

production variables as well as with the FORWDMANUFACT wood product manufacturing 

variable. The accounting appearing underneath the forest production variables involves the 

sequestration in soils; litter and understory; and standing trees along with the emission 

accounting for forest production use of fossil fuels. 

Forest production sequestration accounting is broken into 2 parts: one for continuing 

forests and one for first rotation forests established on lands coming over from agriculture. The 

reason for this is that the amount of carbon sequestered in forest soils can change dramatically 

between the beginning state of lands just transferring from agriculture and that observed on 

forest lands after progression to a mature forest 

The accounting underneath the manufacturing variables involves the carbon sequestered 

in wood products and the fate of those products over time. This contains a number of accounts 

because the model explicitly portrays manufacturing activity in Canada and it is questionable 

whether it would be appropriate to include Canadian generated carbon offsets in US carbon 

accounting. It is anticipated that the Canadian carbon will not be counted in US payment 

schemes and as a consequence it is kept in a separate account to allow for its removal or unlikely 

addition. 

Table 7-12. Forest related GHG accounts 

Account Name Brief description 

Forest_ContinueSoil Carbon in forest soil of forests that remain forests 

Forest_AfforestSoil Carbon in forest soil of afforested forests 

Forest_ContinueLitUnd Carbon in litter and understory of forests that remain 

forests 

Forest_AfforestLitUnd Carbon in litter and understory of afforested forests 

Forest_ContinueTree Carbon in trees of forests that remain forests 

Forest_AfforestTree Carbon in trees of afforested forests 

Forest_USProduct Carbon in US consumed and produced wood products 

Forest_CANProduct Carbon in US consumed but Canadian produced wood 

products 
175 

Forest_USExport Carbon in US produced but exported wood products 

Forest_USImport Carbon in US consumed but imported from non 

Canadian source 

Forest_USFuelWood Carbon in US consumed fuelwood 

Forest_USFuelResidue Carbon in US residue that is burned 

Carbon_For_Fuel Carbon emissions from forest use of fossil fuel 

Dev_ForestLand Carbon on forest land after it moved into developed use 
176 

Table 7-13 Sample tableau illustrating forest related GHG model aspects 

Clearcut Exist Stand in T1 

Clearcut Exist Stand in T1+k 

Reforest Land in T1 then Clearcut in T1+k 

Reforest Land in T1+k then Clearcut in T1+2k 

Afforest Land in T1 then Clearcut in T1+k 

Manufacture wood products in T1 

Manufacture wood products in T1+k 

Land from Ag in T1 

Land to Ag in T1 

Product demand 

GHG payments 

Bare land in T1 -1 1 1 = -dev1 

Bare land from ag in T1 1 -1 = 0 Exist Timberland 1 1 = L Bare land in T1+k -1 -1 1 -1 = -dev1+k Harvested Logs in T1 -he1 y = 0 Harvested Logs in T1+k -he1+k -hr1+k -ha1+k y = 0 Wood Products in T1 -1 + = 0 Wood Products in T1+k -1 + = 0 GHG in T1 cse1 csn1 cp1 + = -cdev1 

GHG in T2 cse2 csn2 cp2 + = -cdev2 GHG in T1+k csn1 csa1 cp1+k cp1 + = -cdev1+k GHG in T1+2k cp1+2k cp2 + = -cdev1+2
177 

where 

Tn represents time period n and indexes the five year periods. 

k is the rotation age for new stands (note this is fixed only for display purposes) 

devn is the amount of land moving into developed uses in time period n 

L is the amount of land in existing stands at the model beginning 

hen is the yield of logs from harvesting an existing stand in time period n 

hrn is the yield of logs from harvesting an afforested stand in time period n. 

han if the yield of logs from harvesting a reforested stand in time period n. 

y is the amount of logs needed to yield one unit of final wood product 

csen is the carbon sequestered less the net fossil fuel related emissions from an existing 

stand in the time period n 

csnn is the carbon sequestered less the net fossil fuel related emissions from a 

reforested stand in the time period n 

csan is the carbon sequestered less the net fossil fuel related emissions from an 

afforested stand in the time period n 

cpn is the amount of carbon sequestered in wood products n time periods after the 

wood product was manufactured.

cdevn is the cumulative amount of carbon sequestered in all lands that moved from 

forestry into developed use in this and all previous periods 

Several things can be observed from this tableau about the FASOMGHG conventions for 

GHG accounting: 

• Forest production accounting is done from the period of forest establishment (or the first 

model period for preexisting stands) up until the last time period before the period of 

forest clearcut harvest. Accounting in the clearcut harvest period is picked up by the next 

production variable in the rotation and in the manufacturing variable. This is done 

because when land switches to agriculture its residual carbon characteristics would be 

quite different than if it were maintained in forestry. By doing our accounting in the next 

rotation variable we know where the land went. Thus continuing forest carbon accounting 

is done under the reforestation variable for forests and under the agricultural variables 

when land use changes. 

• Carbon sequestered in wood products is accounted for underneath the forest 

manufacturing variable. The reason for this is that on manufacturing we know the country 

origin of the logs and can appropriately credit that carbon. We cannot do this underneath 

the consumption variables as, for example, 30% of US softwood lumber consumption is 
178 

of Canadian origin and one should likely not credit the carbon in that wood to US 

accounts. 

• Carbon accounting differs for afforested and reforested stands. This is done simply to be 

able to track the rather large gain in soil carbon that is encountered during the first 

rotation. 

Details on how all the carbon sequestration numbers are computed in the model are 

presented in the forest GHG related data section below. 

7.2.21 Non-market management considerations 

Inside FASOMGHG several model features are present to accommodate the fact that 

management of some forest land responds to an array of amenity and non-market forces. The 

first involves the notion of “limited management response” where some regions (those outside of 

the SC, SE, and PNWW) have limited management intensity choices. Second public lands 

harvest is totally exogenous. Third some timberlands can only be managed under a partial 

harvest regime. Fourth, we introduce a restriction that a given amount of forest land will always 

contain hardwoods. The FORHARDWOODMIN constraint imposes this limit, always requiring 

a minimum percentage of the forest lands to be in hardwoods in a region for each time period. 

Finally there is provision in the model for a limit on reforestation timber investment that can be 

used to restrict model solutions to mimic historical levels and patterns of regeneration investment 

spending. In earlier versions of FASOM, this constraint was used experimentally to limit 

investment by nonindustrial private forest land owners (Adams et al, 1998). This is implemented 

in the constraint FORSTICKY. 

7.3 Algebraic model 

The general form of the forest sector model is illustrated in the following mathematical 

representation. Notation for some dimensions (such as time or product) has been dropped in 

some cases to simplify the exposition. Thus these relations should be viewed as representative of 

the general form of the model. We have also suppressed notation showing currency conversion 

via the exchange rate and any tariffs between the US and Canada. All monetary units are treated 

as US dollars. 

7.3.1 Objective Function. 

In the forestry portion of FASOMGHG the principal decision variables include the 

harvest and management of existing and newly regegerated or afforested timberland (X, N, AF), 
179 

production of manufactured products (Y), levels of manufactured product demand (D), 

interregional transportation of logs and products (T), and aggregate shipments from producing 

regions (S). The forestry portion of the FASOMGHG objective function involves maximization 

of the discounted sum of producers' and consumers' surplus, less the costs of timber supplies 

from Canada that vary with volume harvested, less the costs of volume-sensitive non-wood 

inputs, transportation, manufacturing inputs, and forest management. In equation 7.___ total 

willingness to pay is computed under the product demand curves [Pik(.)]. An array of costs are 

then deducted: Canadian wood costs [Cik(.)], the area under the marginal cost curves of those 

inputs whose costs vary with output [NWCik(.)], transportation costs [Tjik], non-wood costs for 

those inputs (labor, materials, energy in solidwood production) whose total does not vary with 

output [YCikpx], and the costs of forest management, such as planting and fertilization [MC]. 

Finally, because the projection is made for a finite time period (to year TMAX), we add 

an estimate of net surpluses in all periods beyond the end of the projection [TERM]. We assume 

that at the end of the final period the forest is fully regulated on a fixed rotation age (ROT 

measured in years). We compute the total volume of timber in the forest at that point, INV, and 

approximate the periodic sustained yield harvest volume (TERMCUT) using von Mantel's 

formula (see Davis and Johnson, 1987), where TERMCUT = 2 INV / (ROT / 5). The 

TERMCUT volume is then used to estimate production volumes and costs, surpluses in the 

demand relations, and ultimately a net surplus per future period [denoted TERM]. The 

discounted value at time TMAX of an infinite series of future payments occurring every ROT 

years is TERM/[(1+r)ROT - 1] which is then brought forward to the start of the projection. 

NEED EQUATION NUMBERS -- -I’M NOT SURE HOW TO ADD THEM 

() ()

TERM(1 r) /[(1 r) 1]

{MC(i, o, t, m)[X(i, o, t, m) N(i, o, a, t, m) AF(i, o, a, t, m)]}(1 r)

T TC Y YC

( P D dD C S dS NWC Y dY

TMAX ROT

t

o m

ikpx

xpk i

jik ikpx

ki j

jik

ikpx

x p

ikpx

k i

Y

0

ik ik ik

k i

S

0

k k ik

k

D

0

ik

TMAX

{S,

MAX

T,D,Y,X,N,AF} t 1

+ + + −

− + + +

− −

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− −

−

−

=

∑∑∑

∑∑∑ ∑∑∑∑

∑ ∑∫ ∑∑∫ ∑∑∫ ∑∑

i
180 

7.3.2 Constraints 

Constraints relate to manufacturing activities, treatment of the forest inventory, and land 

transfers to and from agriculture. Given their complexity, we do not show the GHG accounting 

relations. 

7.3.2.1 Manufacturing capacity limitations. 

Output can not exceed capacity. Capacities are defined at the process level within each 

product. 

o

ikp

x

∑Yikpx ≤ K for region i, process p and product k 

7.3.2.2 Residue generation at processing facilities. 

Residues are generated primarily at solid wood manufacturing facilities and may be 

transferred to other manufacturing processes, such a fiber products, burned to generate energy, or 

sent to land fills. 

= ∑∑∑

xpk

Ric YikpxGikc for region i and product c 

7.3.2.3 Supply of recycled paper products. 

The fraction of a particular type of paper or paperboard recovered from the consumption 

stream is a fraction that may vary over time up to some maximum set by considerations of 

contamination of the stream, geographic dispersal, and mixing of the desired grade with other 

grades. 

l

l

Sikt = ∑μ iklt D for region i and product k 

7.3.2.4 Materials balance 

In region i, the sum of shipments received plus harvests plus residues generated in 

manufacturing plus internal supplies (from products with explicit supply relations) plus 

production less demand (consumption) less use in manufacturing less shipment out of the region 
181 

must be greater than zero. This is a general expression, listing all types of sources and uses. Not 

all of the terms are non-zero for every commodity. 

∑ +∑ + + +∑∑ − −∑∑∑ −∑ ≥ 0

j

ijk

xpl

ik ilpx iklpx

x p

ik ik ikpx

o

iok

j

Tjik H R S Y D Y M T 

for region i and product k 

7.3.2.5 Harvest balances 

The volume of harvest is defined as a function of the areas allocated to various 

management intensity classes, harvest times and associated yields. All stands are managed under 

some management intensity class (MIC) or silvicultural regime (denoted by the set m below), 

either even-aged without thinning (the subset m’ of all regimes), even-aged with thinning, or 

partial cutting (both combined in the subset mo

 of all regimes). 

∑∑

∑ ∑ ∑

>

+ <

+

= + − +

t m

H

N

H o

X

m mt a

N

iok

X i o m V k m N i o a m V k m

H X i o t m V k m N i o a t m V k t a m

τ

ν

τ τ τ τ 0[ ( , , , ) ( , , ) ( , , , , ) ( , , )]

( , , , ) ( , ) ( , , , , ) ( , , )

0 0 0

 

for region i, owner o and product k. 

Stands managed on an even-aged basis with thinning and stands managed on a partial 

cutting basis (MIC ∈ mo) produce harvest volumes at their preset thinning or partial cut times 

(i.e., times prior to their clearcut age if any, or τ > t in the notation below). Stands may be shifted 

between MICs during the projection. Land initially managed on an even-aged (clearcut) basis 

with no thinning can be harvested and replanted on a regime involving partial cutting (with an 

appropriate delay to the time of first partial cut). Stands initially enrolled in a partial cutting 

regime can be clearcut harvested, replanted and managed on an even-aged basis in subsequent 

periods. Thus the initial set of harvest yields in equation 7.___ involve summations over the full 

set of MICs (m) to cumulate the volume from all types of stands that might be clearcut in a given 

period. The second set of terms cumulate volumes from partial cuts or thinnings. 
182 

7.3.2.6 Management allocation of initial areas. 

All timberland areas that exist at the start of the projection are allocated to some MIC 

based on inventory data and owner surveys. These areas must then be allocated to a harvest in 

some period. Note that existing stands allocated to a partial cutting regime can be clearcut (if it is 

optimal to do so) and replanted to some new even or partial cutting regime at some point in the 

future or they may remain in partial cutting for the entire projection (t = never). So stands can 

move back and forth between even and partial cutting regimes. 

∑ = t

X ( for region i, owner o and MIC m i,o,t,m) A(i,o,m)

7.3.2.7 Reforestation of clearcut areas. 

No more area can be reforested in period t than is clearcut harvested from existing, 

afforested or new stands in that period adjusted for any loss of land from agriculture and less any 

land that shifts to developed uses. Again, stands in partial cutting regimes can be clearcut at 

some point in the projection and regenerated to either an even or partial cutting regime. Land 

transferred from agriculture must be afforested in the period transferred and these areas are 

considered in a separate constraint (see constraint h). 

∑ ∑

∑ ∑ ∑ ∑

+ − −

≤ +

+ <

> + + <

m' t a v

m' m l t v a v t

N(i, o, a, t, m') LTA(i, o, t) DL(i, o, t)

N(i, o, t, l, m') X(i, o, t, m') AF(i, o, a, t, m')

 for region i, owner o, period t 

7.3.2.8 Afforestation. 

Land that moves to forestry from agriculture must be planted in the period it shifts uses. 

It may be allocated to even and partial cutting regimes. 

AF(i,o,t,m) LFA(i,o,t) m

∑ = for region i, owner o and period t 

7.3.3 Symbol definition 

Sets 

i,j sets of forest regions 
183 

k,l,c sets of wood product commodities 

m = [mo

,m’] the set of possible management intensity class assignments, where mo

comprises even-aged thinning or partial cutting options and m’ options involving 

only clearcutting. Areas allocated to partial cutting may be clearcut in a period 

when no partial cut is scheduled. They then enter the regeneration pool and may 

be replanted to a partial cutting or any other regime. 

o set of forest owners 

p set of wood product production processes 

x set of wood product manufacturing input mixes 

Coefficients (Parameters) 

μiklt fraction of recycled paper product k recovered in region i, period t from paper 

products l (in some cases several types of paper products can contribute to a given 

class of recycled paper) 

Gikc generation of residue commodity c during manufacture a unit of commodity k in 

region i. 

Kikp manufacturing capacity for process p, commodity k in region i. 

Miklpx consumption of commodity l to manufacture a unit of commodity k utilizing 

production process p and input mix x in region i. 

TCjix cost of transporting a unit of commodity k from region j to region i. 

YCikpx cost of manufacturing a unit of commodity k utilizing production process p and 

input mix x in region i. 

Variables and functions 

A(i,o,m) initial (exogenous) area in region i, ownership o, and MIC m 

AF(i,o,a,t) land that is afforested in period a and scheduled to be harvested i period t 

> a in region i, owner o 

Cik(Sik) cost-dependent supply function for commodity k in region i 

Dik demand variable for commodity k region i. 

DL(i,o,t) forest land lost to developed uses in region i, owner o, period t 

H(i,o,k,t) harvest volume for log commodity k by owner o in region i, period t. 

LFA(i,o,t) land transferred from agriculture to forestry in region i, owner o, period t 

LTA(i,o,t) land transferred from forestry to agriculture in region i, owner o, period t 

MC(i,o,t,m) forest management costs per unit are for land in region i, owner o, under 

MIC m 

N(i,o,a,t,m) forest land planted in period a and harvested again in period t, in region i 

owner o in MIC m—termed “new” areas since they are created after the start of 

the projection. A stand regenerated to a partial cutting (or thinning) regime will be 

subject to the partial harvests (r thinnings) until period t when it is clearcut and 

regenerated. A partial cut stand may be scheduled for harvest in t = never, so 

retained in the partial cut regime until the end of the projection. 
184 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∑∑

x p

NWCik Yikpx non-wood input function for commodity k region i. Non-wood 

inputs for commodity k depend on the quantity of k produced. 

Pk(Dk) price-dependent demand function for commodity k 

Rik residue generation per unit of commodity k, region i

ROT rotation age on which forests are assumed to be managed in periods after the end 

of the projection (t > TMAX) 

Sikt supply of commodity k region i

Tjik transport of commodity k from region j to region i

TERM periodic net surplus in periods after TMAX 

TMAX length of projection period 

V(k,m’), VN

(k,t-a,m’), VX

H(k,t,mo

), VN

H(k,t,mo

) are volumes of product k per acre on 

timberland managed in even-aged MICs in the initial stands (V), under even-aged 

MICs in new stands (VN

), and under partial cutting and thinning in new and 

existing stands (VX

H, VNH).

X(i,o,t,m) forest land in region i, owner o that existed at the start of the projection 

that is allocated to some MIC (m) and is scheduled to be cut in period t. Stands in 

partial cutting regimes may be retained in those regimes for the entire projection 

(t = never) or clearcut and regenerated to any other feasible regime. 

Yikpx manufacture of commodity k utilizing production process p and input mix x in 

region i. 
185 

8 CHAPTER 8 AG SECTOR MODELING DETAILS 

FASOMGHG contains an adaptation of the ASM model (Chang et al) and the ASMGHG 

variant (Schneider, McCarl and Schneider) as a submodel. This model is wholely included as a 

submodel in FASOMGHG appearing in each explicit time period. This agricultural sector 

submodel depicts crop and livestock production and agricultural processing using key land, 

water, labor, and forage inputs as well as product trade. 

The agricultural sector submodel simulates the effects of changes in agricultural 

resources and market conditions on prices, quantities produced, consumers' and producers' 

surplus, exports, imports, and processing. The submodel considers production, processing, 

domestic consumption, imports, exports, and input procurement. The submodel distinguishes 

between primary and secondary commodities, with primary commodities being those directly 

produced by farms and secondary commodities being those involving processing. 

For agricultural production the US is disaggregated into either 63 or 11 geographical 

subregions depending on time period. Each subregion possesses different endowments of land, 

labor, irrigation water and AUM grazing, as well as crop and livestock yields. The supply sector 

allocates these regional factors across a set of regional crop and livestock budgets and a set of 

processing budgets which use commodities as inputs. There are more than 1200 production 

possibilities (budgets) representing agricultural production in each time period. These include 

field crop, livestock, and biofuel feedstock production. The field crop variables are also divided 

into irrigated and dryland production according to the irrigation water and production 

possibilities available in each region. There are also import supply functions from the rest of the 

world for a number of commodities. The demand sector of the model is constituted by the 

intermediate use of all the primary and secondary commodities, domestic consumption, and 

exports. 

Secondary commodities are produced by processing variables. They include soybean 

crushing, corn wet-milling, potato processing, sweetener manufacturing, mixing of various 

livestock and poultry feeds, and the conversion of livestock and milk into consumable meat and 

dairy products. The processing cost is generally calculated as the difference between its price and 

the costs of the primary commodity inputs. 
186 

Primary and secondary commodities are consumed at the national level according to 

constant elasticity demand functions. The areas under these demand functions represent total 

willingness to pay for agricultural products. The difference between total willingness to pay and 

production and processing costs is equal to the sum of producers' and consumers' surpluses. 

Maximization of the sum of these surpluses constitutes the agricultural sector objective function. 

The basic relations in the agricultural sector model are treated as if they represent typical 

repeating activity in each year of each time period. Demand and supply components are updated 

between time periods by means of projected growth rates in yield, processing efficiency, 

domestic demand, exports, and imports. 

The agricultural related land use decision simulated in FASOMGHG is that, in each 

period, owners of agricultural land can decide: 1) whether to keep an acre of land in agricultural 

production or change land use to afforestation; 2) what crop/liversock mix to plant/rear/harvest, 

if the land stays in agriculture; and 3) what type of timber management to select, if the land is to 

be planted in trees. These decisions are made entirely on the basis of relative profitability of land 

in its various competing alternative uses over the life-span of the foreseeable choices (for land in 

either crops or trees). 

Here we 

• discuss the basic scope of the agricultural sector representation 

• present an overview tableau 

• delve into model details showing key features 

8.1 Scope of agricultural sector representation 

8.1.1 Regional Disaggregation 

The model operates with two levels of regional disaggregation. The fundamental unit of 

disaggregation is 63 state and/or substate subregions. These smaller subregions uniquely fall into 

one of the 11 FASOMGHG larger regions. A listing of the aggregate and more disaggregated 

regions are given in Tables 3-1 and 3-2 respectively. 
187 

8.1.2 Characterizing the landscape and the sector 

8.1.2.1 Land 

Agricultural land is defined into two fundamental types: crop and pasture land. Four crop 

land quality classes are defined as follows. First, all crop land with USDA Land Capability Class 

III to VIII having a subclass of "w", i.e., a wetness limitation for cropping, was grouped and 

labeled 

w3-8 wet lands. 

The remaining crop land was divided into three groups according to its erodibility index (ei). The 

ei is either RKLS/T from the Universal Soil Loss Equation (USLE) (Wischmeier and Smith, 

1978) or WEQ/T from the Wind Erosion Equation, depending on whether wind or water erosion 

gives the larger ei ("T", the soil loss tolerance level, is the maximum allowable erosion for 

sustained crop production. The three ei groups are: 

Loei land has ei < 8.0; 

Mdei land has 8.0 <= ei < 20.0 

Svei land has ei >= 20.0 in "svei". 

8.1.2.2 Crops 

A set of crops is modeled that depicts the majority of agricultural land use. These are 

listed in Table 3-9 and include 

Food grains: wheat (4 types) and rice 

Feed grains: corn, oats, barley, sorghum 

Cotton 

Soybeans 

Sugar crops: beets and cane 

Potatoes 

Citrus: oranges and grapefruit 

Tomatoes 

Hay 

Silage 

Biofuel feed stocks: switch grass, hybrid poplar and willow. 
188 

8.1.2.3 Animals 

A set of animal types are modeled that collectively represent the majority of the resources 

used by livestock. These are listed in Table 3-10 and includes 

Sheep 

Beef cattle at the cow calf, stocker and feedlot stages 

Dairy cattle 

Hogs at the feeder pig, farrow to finish and finishing stages 

Poultry 

Turkeys 

Broilers 

Egg layers 

Horses and mules 

8.1.3 Commodities 

8.1.3.1 Primary Commodities 

There are 56 primary agricultural commodities AS listed in Table 3-6. The primary 

commodities depict the majority of total agricultural production, land use and economic value. 

They can be grouped into crops, livestock and biofuels related commodities. 

The crop commodities are 

Food grains: wheat (durham, soft red winter, hard red winter hard red spring) and rice 

Feed grains: corn, oats, barley, sorghum 

Cotton 

Soybeans 

Sugar crops: beets and cane 

Potatoes (fresh and processed) 

Citrus: oranges and grapefruit (fresh and processed by box size) 

Tomatoes (fresh and processed) 

Hay 

Silage 

Biofuel feed stocks: switch grass, hybrid poplar and willow. 

The livestock commodities by animal grouping are 

Sheep (lambs for slaughter, cull ewes, wool) 

Beef cattle 

Cow calf (calves for slaughter, cull beef cows, steer calves, heifer calves) 
189 

Stocker (nonfed slaughter, stocked calves, stocked heifer calves, stocked steer 

calves, stocked yearling, stocked heifer yearling, stocked steer yearling) 

Feedlot (fed beef slaughter) 

Dairy cattle (milk, cull dairy cows, dairy calves) 

Hogs 

Feederpig (cull sows, feeder pigs) 

Farrow to finish (cull sows, hogs for slaughter) 

Finishing stages (hogs for slaughter) 

Poultry 

Turkeys (turkey for slaughter) 

Broilers (chicken for slaughter) 

Eggs 

Horses and mules 

8.1.3.2 Secondary commodities 

The FASOMGHG agricultural submodel incorporates processing of primary 

commodities into secondary commodities. Table 3-7 lists the 39 secondary commodities that are 

created by processing. These commodities are chosen based on their linkages to agriculture. 

Some primary commodities are inputs to processing activities yielding these secondary commodities. Certain secondary products (by-products) are in turn inputs to agricultural livestock 

production or feed blending. These can be broken into crop, livestock and biofuels related items. 

The crop related secondary items by major class are: 

Processed citrus products -- orange juice, grapefruit juice 

Crushed soybean products -- soybean meal, soybean oil 

Corn wet milling products -- high fructose corn syrup, gluten feed, corn starch, corn oil, 

corn syrup, dextrose 

Sweetened products -- beverages, confection, baking, canning 

Refined sugar items-- refined sugar, refined cane 

Potato products -- frozen potatoes, dried potatoes, potato chips 

 

The livestock related items by major class are: 

Meat items 

Beef -- fed beef, non fed beef 

Pork 

Chicken 

Turkey 

Clean wool 
190 

Dairy products -- fluid milk, cream, skim milk, evaporated condensed milk, non fat dry 

milk, butter, american cheese, other cheese, cottage cheese, ice cream 

The biofuels related items are: 

Ethanol 

Blended gasoline that contains ethanol (subsidized and unsubsidized) 

Biodiesel 

Electricity generated with biofuels feedstocks in terms of BTU content of feedstock 

8.1.3.3 Blended feeds 

The agricultural submodel incorporates mixing of feeds for livestock consumption. Table 

3-8 lists the 20 blended feed categories. Grouped by major animal type these are 

Beef 

Cow calf -- cow calf grain, cow calf protein supplement 

Stockers -- stocker protein supplement 

Feedlot -- cattle grain, high protein cattle feed 

Hogs 

Feeder pig -- farrowing grain, farrowing protein feed, feeder pig grain, feeder pig 

protein 

Farrow-finish— farrowing grain, farrowing protein feed, feeder pig grain, feeder 

pig protein, finishing grain, finishing protein feed 

Finishing -- finishing grain, finishing protein feed 

Dairy -- Dairy concentrate 

Poultry 

Broilers -- broiler grain, broiler protein feed 

Turkeys-- turkey grain, turkey protein feed 

Egg layers-- egg layer grain, egg layer protein feed 

Sheep -- sheep grain, sheep protein feed 

8.1.4 Non land inputs 

In the model there is modeling of water, labor, animal unit month grazing, national inputs 

and blended feed inputs. 

8.1.4.1 Water 

The water supply is divided into fixed price supply (generally public surface waater) and 

pumped upward sloping supply (generally ground or private surface water) components. The 

fixed price water is available for a constant price up to a maximum quatity. The pumped upward 
191 

sloping water is provided according to a supply schedule where increasing amounts of water are 

available for higher prices. 

8.1.4.2 Labor 

The labor input includes two components: family labor and hired labor. The family labor 

is available at a fixed reservation wage up to a maximum amount. The hired labor is based on an 

inducement wage rate which is higher than the reservation wage and a supply function from 

thereon. 

8.1.4.3 Grazing in AUMS 

Grazing land supply is provided on an animal unit month (AUM) basis. Its supply is 

divided into public and private sources. Public grazing is available at a constant price (a grazing 

fee) up to a maximum availability. Private grazing is supplied according to an upward-sloping 

supply schedule. 

8.1.4.4 National Inputs 

The model represets use of 168 national inputs. They are listed in the file 

data_aginputname.gms. These are specified in dollar terms so they are homogeneous within 

each calss; for example, ten dollars worth of nitrogen, twenty dollars worth of repair cost. They 

include things like fertilizer expenditures by fertilizer type, pesticide expenditures use by type, 

chemical expenditures, energy expenditures, equipment expenditures, custom operator 

expenditures, feed additive expenditures, capital expenditures, interest costs, and animal health 

expenditures among many other items. 

8.1.4.5 Blended and other feed 

Crops are not only outputs but are also inputs for direct use by livestock or in feed 

blending processes. In addition the blended feeds as listed above are intermediate inputs to 

livestock production. Some of the secondary commodities like gluten feed and soybean meal are 

also directly used as inputs to livestock production and are used in feed blending procedures. 

8.1.5 Agricultural Production 

Crops and livestock can be produced. 
192 

8.1.5.1 Crops 

The crop production set is defined at the 63 region level and currently includes more than 

1200 production possibilities (budgets). Yields, costs and input usare rates vary by region. These 

include major field crop production, livestock production, and biofuel feedstock production. In 

addition they are defined across multiple land types (the four defined above), irrigation 

possibilities (irrigated and dryland), fertilization alternatives (3 alternatives -- base fertilization 

then 15% and 30% reductions from the base) and tillage alternatives (3 alternatives -- 

conventional, minimum and no till). Yield, water use, and erosion data for these alternatives are 

defined based on runs of the EPIC crop growth simulator. 

8.1.5.2 Livestock 

Livestock production alternatives are defined for the 63 regions for the animal types 

defined above. In addition some alternative production possibilities are defined that alter feed 

and land inputs. 

8.1.6 Agricultural Processing 

The processing activities generally reflect a simplified processing representation 

concentrating on the commodities used. They largely depict primary/secondary commodity 

usage, secondary commodity yield and a level of cost. Thus, for example, the soybean crushing 

processing activity uses one unit of soybeans and generates a given number of pounds of 

soybean meal and tons of soybean oil at a cost. The cost is usually the observed price differential 

between the value of the outputs and the value of the raw commodities used where both are 

valued at observed prices. 

Processing activities are defined partially at a regional level and partially at a national 

level largely depending on market conditions for the crop and livestock primary commodities. 

The regional activities are listed below in Tale 8-1 followed by a list of the national commodities 

(Table 8-2). 

Table 8-1 Processing activities that are defined on a regional basis 

Regional activity code Brief description

SoyCrush1 Crush soybeans 

WetMill Wet mill corn 
193 

Gluttosbm Substitute gluten feed for soybean meal 

SwitchgrassToElec Make switchgrass into electricity 

HybridpoplarToElec Make hybrid poplar into electricity 

WillowToElec Make willow into electricity 

SwitchgrassToEthanol Make switchgrass into ethanol 

HybridpoplarToEthanol Make hybrid poplar into ethanol 

WillowToEthanol Make willow into ethanol 

MakeBiodiesel Make biodiesel 

Table 8-2 Processing activities that are defined on a national basis 

National activity code Brief description 

makeAmCheese Make American cheese 

makeOtCheese Make other cheese 

ButterPow Make butter and non fat dry milk powder 

FluidMlk1 Make two percent milk 

FluidMlk2 Make skim milk 

EvapoMilk Make evaporated milk 

IceCream1 Make ice cream alternative 1 

IceCream2 Make ice cream alternative 2 

Cottage Make cottage cheese 

makeHFCS Make high fructose corn syrup 

makeCSyrup Make corn syrup 

makeBeverages Make sweetened beverages 

makeConfection Make sweetened confectionaries 

makeBaking Make sweetened baked goods 

makeCanning Make sweetened canned goods 

makeEthanol Make ethanol from corn 

makeMktGasBlend Make unsubsidized liquid fuel blending gasoline & ethanol 

makeSubGasBlend Make subsidized liquid fuel blending gasoline & ethanol 

makeDextrose Make dextrose 

CleanWool Convert wool to clean wool 

RefSugar1 Convert sugar cane to raw cane sugar 

RefSugar2 Convert sugar beets to refined sugar 

CaneRefine Convert raw cane sugar to refined sugar 

HogToPork Convert finished hogs to pork 

BroilChick Convert broilers to chicken meat 

TurkeyProc Convert live turkeys to turkey meat 

SowToPork Convert cull sow to pork 

ClCowSla Convert cull cow to non fed slaughter 

DCowSla Convert cull dairy cow to non fed slaughter 

NFSlatonF Convert non fed animal to non fed slaughter 

FSlatofBe Convert fed animal to fed slaughter 
194 

DClfToBeef Convert cull dairy calf to non fed slaughter 

StockSteerCalftoFeed Move stocked steer calf into feedlot 

StockHeiferCalftoFeed Move stocked heifer calf into feedlot 

StockSteerYearlingtoFeed Move stocked steer yearling into feedlot 

StockHeiferYearlingtoFeed Move stocked heifer yearling into feedlot 

HeiferYearlingSlaughter Slaughter a heifer yearling 

SteerYearlingSlaughter Slaughter a steer yearling 

Frozen-Pot Make frozen potatoes 

DeHydr-Pot Make dehydrated potatoes 

CHIP-POT Make potato chips 

JuiceOrang Make orange juice 

JuiceGrpft Make grapefruit juice 

8.1.7 Feed blending 

FASOMGHG depicts the blending of 20 different types of feeds that, in turn, are used 

within the livestock production alternatives. For each feed, a number of blending alternatives are 

specified. The feed alternatives, their names and a list of the alternative blending formula names 

are given in table 8-3. The alternative names are only presented to depict how much diversity is 

allowed for the blend of any one feed. 

The optimal feed composition is a convex combination of the blending alternatives. 

These alternatives are regionally specific allowing the optimal feed blend to adapt to the relative 

regional abundance and price of the commodities used in the feed blend. The data specifying the 

feed alternatives are regionally adapted. For example, blending alternatives in regions where 

sorghum is produced reflect substitution possibilities of sorghum for corn. Table 8-3 lists the 

codes for the feeds, provides brief description and the blending alternatives defined. 

Table 8-3 Feed blended and alternatives that make them 
195 

Feed Code Feed description Blending alternatives 

StockPro0 Protein feed for stockers stkpromix0, stkpromix2 

CatGrain0 Blend of grains for finishing cattle 

beefbases, beefalt1s, beefalt2s, beefalt3s, beefalt4s, beefalt5s,beefalt6s, beefalt7s, 

beefbasew, beefalt1w, beefalt2w, beefalt3w,beefalt4w, beefalt5w, beefalt6w, 

beefalt7w, beefbaset, beefalt4t, beefalt5t, beefalt6t, beefalt7t, beefbased, beefalt1d, 

beefalt2d, beefalt3d, beefalt4d, beefalt5d, beefalt6d, beefalt7d 

HighProtCa Protein feed for finishing cattle catpro1, catpro3 

CowGrain0 Blend of grains for cow calf operations 

cowbases, cowalt1s, cowalt2s, cowalt3s, cowalt4s, cowalt5s, cowalt6s, cowalt7s, 

cowbasew, cowalt1w, cowalt2w, cowalt3w, cowalt4w, cowalt5w, cowalt6w, 

cowalt7w, cowbaset, cowalt4t, cowalt5t, cowalt6t, cowalt7t, cowbased, cowalt1d, 

cowalt2d, cowalt3d, cowalt4d, cowalt5d, cowalt6d, cowalt7d 

CowHiPro0 Protein feed for cow calf operations Cowpromix0, cowpromix2 

FinGrain0 Blend of grains for pig finishing 

basemix1s, alt1mix1s, alt2mix1s, alt3mix1s, alt4mix1s, alt5mix1s, alt6mix1s, 

alt7mix1s, basemix1w, alt1mix1w, alt2mix1w, alt3mix1w, alt4mix1w, alt5mix1w, 

alt6mix1w, alt7mix1w, basemix1t, alt1mix1t, alt2mix1t, alt3mix1t, alt4mix1t, 

alt5mix1t, alt6mix1t, alt7mix1t, basemix1d, alt1mix1d, alt2mix1d, alt3mix1d, 

alt4mix1d, alt5mix1d, alt6mix1d, alt7mix1d 

FinProSwn0 Protein feed for pig finishing finpromix0, finpromix6 

FarGrain0 Blend of grains for farrowing operations 

hogbases, hogalt1s, hogalt2s, hogalt3s, hogalt4s, hogalt5s, hogalt6s, hogalt7s, 

hogbasew, hogalt1w, hogalt2w, hogalt3w, hogalt4w, hogalt5w, hogalt6w, hogalt7w, 

hogbaset, hogalt1t, hogalt2t, hogalt3t, hogalt4t, hogalt5t, hogalt6t, hogalt7t, hogbased, 

hogalt1d, hogalt2d, hogalt3d, hogalt4d, hogalt5d, hogalt6d, hogalt7d 

FarProSwn0 Protein feed for farrowing operations farpromix0, farpromix6 

FPGGrain0 Blend of grains for feeder pigs 

basemix2s, alt1mix2s, alt2mix2s, alt3mix2s, alt4mix2s, alt5mix2s, alt6mix2s, 

alt7mix2s, basemix2w, alt1mix2w, alt2mix2w, alt3mix2w, alt4mix2w, alt5mix2w, 

alt6mix2w, alt7mix2w, basemix2t, alt1mix2t, alt2mix2t, alt3mix2t, alt4mix2t, 

alt5mix2t, alt6mix2t, alt7mix2t, basemix2d, alt1mix2d, alt2mix2d, alt3mix2d, 

alt4mix2d, alt5mix2d, alt6mix2d, alt7mix2d 

FPGProSwn0 Protein feed for feeder pigs fdppromix0, fdppromix6 

DairyCon0 Blend of grains for dairy operations 

dairybases, dairyalt1s, dairyalt2s, dairyalt3s, dairyalt4s, dairyalt5s, dairyalt6s, 

dairyalt7s, dairybasew, dairyalt1w, dairyalt2w, dairyalt3w, dairyalt4w, dairyalt5w, 

dairyalt6w, dairyalt7w, dairybaset, dairyalt1t, dairyalt2t, dairyalt3t, dairyalt4t, 

dairyalt5t, dairyalt6t, dairyalt7t, dairybased, dairyalt1d, dairyalt2d, dairyalt3d, 

dairyalt4d, dairyalt5d, dairyalt6d, dairyalt7d 

BroilGrn0 Blend of grains for broilers 

brobases, broalt1s, broalt2s, broalt3s, broalt4s, broalt5s, broalt6s, broalt7s, brobasew, 

broalt1w, broalt2w, broalt3w, broalt4w, broalt5w, broalt6w, broalt7w, brobaset, 

broalt4t, broalt5t, brobased, broalt1d, broalt2d, broalt3d, broalt4d, broalt5d, broalt6d, 

broalt7d 

BroilPro0 Protein feed for broilers brlpromix0, brlpromix4 

TurkeyGrn0 Blend of grains for turkeys 

polbases, polalt1s, polalt2s, polalt3s, polalt4s, polalt5s, polalt6s, polalt7s, polbasew, 

polalt1w, polalt2w, polalt3w, polalt4w, polalt5w, polalt6w, polalt7w, polbaset, 

polalt4t, polalt5t, polbased, polalt1d, polalt2d, polalt3d, polalt4d, polalt5d, polalt6d, 

polalt7d 

TurkeyPro0 Protein feed for turkeys trkpromix0, trkpromix4 

EggGrain0 Blend of grains for eggs 

eggbases, eggalt1s, eggalt2s, eggalt3s, eggalt4s, eggalt5s, eggalt6s, eggalt7s, 

eggbasew, eggalt1w, eggalt2w, eggalt3w, eggalt4w, eggalt5w, eggalt6w, eggalt7w, 

eggbaset, eggalt4t, eggalt5t, eggbased, eggalt1d, eggalt2d, eggalt3d, eggalt4d, 

eggalt5d, eggalt6d, eggalt7d 

EggPro0 Protein feed for eggs eggpromix0, eggpromix5 

SheepGrn0 Blend of grains for sheep 

bases, alt1s, alt2s, alt3s, alt4s, alt5s, alt6s, alt7s, basew, alt1w, alt2w, alt3w, alt4w, 

alt5w, alt6w, alt7w, baset, alt1t, alt2t, alt3t, alt4t, alt5t, alt6t, alt7t, based, alt1d, alt2d, 

alt3d, alt4d, alt5d, alt6d, alt7d 

SheepPro0 Protein feed for sheep shppromix0, shppromix2 

8.1.8 Commodity Markets 
196 

The commodity market representation generally contains multiple possibilities for 

consumption and supply of a commodity. The consumption possibilities include domestic 

consumption, and exports along with intermediate product use. The intermediate product use 

possibilities include direct consumption by livestock (i.e. silage use in a dairy), use in livestock 

feed blends (i.e. corn in a hog finishing grain blend), or use as an input to processing (i.e. 

soybeans as an input to a soybean crushing operation). The supply possibilities include domestic 

production (i.e. corn from farm production), yields from processing (i.e. distillers grain from wet 

milling), yields from feed blending (i.e. blended hog finishing grain mix), and imports. 

Markets are either regionalized or national. The regionalized markets are present for only 

a subset of the commodities while all commodities are subject to a national market at least for 

domestic consumption. The primary commodities with regional markets are listed in table 8-4 

while the secondary commodities with such markets are listed in table 8-5 and blended feeds in 

table 8-6. 

Table 8-4 Primary commodities with regional markets 

FASOMGHG Code Brief Description 

Corn Corn in bushels 

Soybeans Soybeans in bushels 

SoftWhiteWheat Soft White wheat in bushels 

HardRedWinterWheat Hard Red Winter Wheat in bushels 

DurhamWheat Durham Wheat in bushels 

HardRedSpringWheat Hard Red Spring Wheat in bushels 

Sorghum Sorghum in cwt 

Rice Rice in cwt 

Silage Silage in US tons 

Hay Hay in US tons 

SwitchGrass Switch grass in US tons 

HybrdPoplar Hybrid poplar in US tons 

Willow Willow in US tons 

Table 8-5 Secondary commodities with regional markets 

FASMGHG Code Brief Description 

SoybeanMeal Soybean Meal in US tons 

GlutenFeed Gluten Feed in 100 lbs 

Table 8-6 Blended feed commodities with regional markets 
197 

FASMGHG Code Brief Description 

StockPro0 Protein feed for stockers in 100 lbs (cwt) 

CatGrain0 Blend of grains for cattle in 100 lbs (cwt) 

HighProtCa Protein feed for cattle in 100 lbs (cwt) 

CowGrain0 Blend of grains for cow calf operations in 100 lbs (cwt) 

CowHiPro0 Protein feed for cow calf operations in 100 lbs (cwt) 

FinGrain0 Blend of grains for pig finishing in 100 lbs (cwt) 

FinProSwn0 Protein feed for pig finishing in 100 lbs (cwt) 

FarGrain0 Blend of grains for farrowing operations in 100 lbs (cwt) 

FarProSwn0 Protein feed for farrowing operations in 100 lbs (cwt) 

FPGGrain0 Blend of grains for feeder pigs in 100 lbs (cwt) 

FPGProSwn0 Protein feed for feeder pigs in 100 lbs (cwt) 

DairyCon0 Blend of grains for dairy operations in 100 lbs (cwt) 

BroilGrn0 Blend of grains for broilers in 100 lbs (cwt) 

BroilPro0 Protein feed for broilers in 100 lbs (cwt) 

TurkeyGrn0 Blend of grains for turkeys in 100 lbs (cwt) 

TurkeyPro0 Protein feed for turkeys in 100 lbs (cwt) 

EggGrain0 Blend of grains for eggs in 100 lbs (cwt) 

EggPro0 Protein feed for eggs in 100 lbs (cwt) 

SheepGrn0 Blend of grains for sheep in 100 lbs (cwt) 

SheepPro0 Protein feed for sheep in 100 lbs (cwt) 

When both regional and national markets are defined for a commodity FASOMGHG 

reflects a movement from the regional market to the national market at the cost of the historically 

observed region to nation price differential. When a commodity has a regional market then 

domestic transport becomes a source of consumption where goods can be moved outside the 

region and a source of supply when goods are moved into a region. 

8.1.9 International Trade 

Three types of agricultural commodity trade arrangements are represented. Agricultural 

primary and secondary commodities may be portrayed 

• With trade occurring in explicit international markets using a Takayama and Judge style, 

spatial equilibrium submodel that portrays country/regional level excess demand on 

behalf of a set of foreign countries/regions, excess supply on behalf of a set of foreign 

countries/regions and interregional trade between the foreign regions themselves and with 

the US. 

• With the US facing a single excess supply and or excess demand relationship on behalf of 

the rest of the world or 

• Without being subject to international trade. 
198 

8.1.9.1 Spatially traded commodities 

When commodities are subject to explicit spatial interregional trade with spatial 

equilibrium submodels, then trading is portrayed with the 27 countries/foreign regions listed in 

table 3-7. In those countries/foreign regions, there are explicit supply and demand functions. 

Table 8-7 gives the commodities that are traded and the countries/regions which supply and 

demand them in the model. Note when a country supplies it can either export to another explicit 

country or to the US. Similarly, demand in a country/region can be met from either imports from 

other countries or from the US. 

Table 8-7 Commodities that are traded and the countries/regions involved 

FASOMGHG Code Exporting countries Importing countries 

Corn Others, S-Africa, China, 

Argentina 

SW-Euro, E-Europe, E-Medit, N-Africa, E-Africa, Pers-GF, SE-Asia, 

Taiwan, S-Korea, Japan, Adriatic, Caribbean, E-Mexico, ESAmerica, WS-America, Indonesia, KoreaRep, Thailand, Canada 

Soybeans Argentina, Brazil NC-Euro, E-Europe, USSR, N-Africa, SE-Asia, Taiwan, S-Korea, 

Japan, China, E-Mexico 

SoftWhiteWheat Australia, EEC, Canada SW-Euro, USSR, E-Medit, N-Africa, W-Africa, S-Africa, Red-Sea, 

Pers-GF, SE-Asia, W-Asia, Taiwan, S-Korea, Japan, China, EMexico, ES-America, WS-America, Brazil, Bangladesh, Indonesia, 

KoreaRep, Pakistan, Philippine, Thailand, Vietnam 

HardRedWinterWheat Argentina, Australia, 

Canada 

SW-Euro, USSR, E-Medit, N-Africa, W-Africa, S-Africa, Red-Sea, 

Pers-GF, SE-Asia, W-Asia, Taiwan, S-Korea, Japan, China, EMexico, ES-America, WS-America, Brazil, Bangladesh, Indonesia, 

KoreaRep, Pakistan, Philippine, Thailand, Vietnam 

DurhamWheat EEC, Canada SW-Euro, USSR, N-Africa, S-Africa, SE-Asia, Taiwan, S-Korea, 

Japan, ES-America, WS-America, Brazil, Bangladesh, Indonesia, 

KoreaRep, Pakistan, Philippine, Thailand, Vietnam 

HardRedSpringWheat Australia, Canada SW-Euro, USSR, E-Medit, N-Africa, W-Africa, S-Africa, Red-Sea, 

Pers-GF, SE-Asia, W-Asia, Taiwan, S-Korea, Japan, China, ESAmerica, WS-America, Brazil, Bangladesh, Indonesia, KoreaRep, 

Pakistan, Philippine, Thailand, Vietnam 

Sorghum Others, Red-Sea, China, 

Argentina, Australia 

NC-Euro, E-Medit, Taiwan, S-Korea, Japan, E-Mexico 

Rice Others, China, ESAmerica, Argentina, 

Australia, India, 

Myanmar, Pakistan, 

Thailand, Vietnam 

Others, SW-Euro, E-Europe, USSR, E-Medit, W-Africa, S-Africa, 

Red-Sea, Pers-GF, SE-Asia, W-Asia, S-Korea, Japan, Adriatic, 

Caribbean, E-Mexico, WS-America, Brazil, Bangladesh, Indonesia, 

KoreaRep, Philippine, Canada 
199 

8.1.9.2 Excess supply/demand commodities 

When US trade is subject to just excess import supply and export demand functions, then 

the curves represent the level of total rest of world exports and imports that are faced at the 

national US market level. The commodities treated by this arrangement are listed in table 8-8. 

Table 8-8 Commodities with rest of world export or import possibilities 

FASOMGHG Code Imported into the US Exported from the US 

Cotton - X 

Oats X X 

Barley - X 

Sugarcane X X 

Potatoes X X 

TomatoFrsh X X 

TomatoProc X X 

OrangeFrsh75box X X 

GrpfrtFrsh85box X X 

Eggs X X 

OrangeJuic X X 

GrpfrtJuic X X 

SoybeanMeal - X 

SoybeanOil - X 

HFCS - X 

Confection X 

GlutenFeed - X 

FrozenPot X X 

DriedPot X X 

ChipPot - X 

CaneRefini X 

FedBeef - X 

NonFedBeef X 

Pork X X 

Chicken - X 

Turkey - X 

WoolClean X X 

EvapCondM X X 

NonFatDryM X X 

Butter X X 

AmCheese X X 

OtCheese X X 
200 

8.1.9.3 Commodities without trade 

Commodities without explicit trade are generally specified as such because either the 

trade numbers are small or the commodity is not traded. These include the commodities listed in 

the table 8-9 below and all of the blended feeds. 

Table 8-9 Commodities without international trade possibilities 

FASOMGHG 

Code 

Silage 

Hay 

Sugarbeet 

OrangeFrsh90box 

OrangeFrsh85box 

OrangeProc75box 

OrangeProc90box 

OrangeProc85box 

GrpfrtFrsh67box 

GrpfrtFrsh80box 

GrpfrtProc67box 

GrpfrtProc85box 

GrpfrtProc80box 

SwitchGrass 

HybrdPoplar 

Willow 

NonFedSla 

FeedlotBeefSlaughter 

CalfSlaugh 

CullBeefCo 

Milk 

CullDairyCows 

HogsforSlaughter 

FeederPig 

CullSow 

LambSlaugh 

CullEwes 

Wool 

SteerCalve 

HeifCalve 

StockedCalf 

StockedHCalf 

StockedSCalf 
201 

DairyCalves 

StockedYearling 

StockedHYearl 

StockedSYearl 

HorsesandMules 

Broilers 

Turkeys 

Beverages 

Baking 

Canning 

RefSugar 

CornStarch 

CornOil 

CornSyrup 

Dextrose 

FluidMilk 

Cream 

SkimMilk 

CottageChe 

IceCream 

Ethanol 

MktGasBlend 

SubGasBlend 

Tbtus 

8.2 Tableau overview 

An overview of the agricultural submodel that is repeatedly included in FASOMGHG is 

given in Table 8-10. The columns represent variables, while the rows represent equations (e.g., 

resource constraints). This tableau shows a single period, single region version of the agricultural 

submodel. 

This submodel maximizes welfare in the form of areas beneath the demand curves less 

than the areas beneath the explicit supply curves less other costs. This maximization occurs 

subject to 

• Resource limits for land, water, labor, and AUM grazing 

• Cconstraints on crop and livestock mixes 

• Bbalances on primary, secondary and blended feed commodities 

• GHG balances 
202 

The types of constraints are defined more precisely below. 

In maximizing this objective the main manipulatable variables are: 

• Crop production 

• Livestock production 

• Feed blending 

• Land transformation 

• Agricultural processing 

• Domestic consumption 

• Exports 

• Imports 

• GHG related payments. 

These variables are defined more precisely below. 

This single period submodel will be contained within any full FASOMGHG 

programming model multiple times with an instance occurring within every time period. The 

submodel is assumed to represent typical activity within each time period and the objective 

function contribution is treated as constant annuity during each of these generally five year 

periods. The submodel for the final time period is treated as if that level of activity were to 

persist forever. 

8.2.1 Equations defined 

The equations within this tableau are: 

• Welfare -- Adds up agricultural consumers' plus producers' surplus. This consists of the 

area underneath the product demand curves arising from domestic consumption, exports 

and international consumption less the areas under the explicit supply curves from 

imports and international consumption on the product side along with labor, water and 

AUMs on the factor side. In addition, total cost is subtracted under a set of assumed 

infinitely elastic, fixed price supply curves of agricultural inputs used within crop and 

livestock production, processing, land transformation and transportation. We also add in 

the payments/taxes associated with net GHG emissions. The WELFAR GAMS 

implementation equation is represented by this tableau row. 
203 

• Crop land -- Limits crop land usage by tillage system to that available. The land use is 

limited to the initial agricultural endowment of crop land adjusted for land use chages to 

and from pasture and forest land. The land is used by the tillage choice variables. Limits 

on crop land use are defined on a subregional basis in periods when subregions are being 

used and on a regional basis otherwise. Cases within the AGTILLSTART and 

AGCANCHANGETILL GAMS implementation equations are represented by this 

tableau row. 

• Tillage supply -- Limits acreage of each tillage system in use within the cropping 

variables to the acreage produced by the tillage choice variables. Limits crop land use by 

tillage system on a subregional basis when subregions are defined. Cases within the 

AGTILLUSE GAMS implementation equations are represented by this tableau row. 

• Pasture Land -- Limits pasture land use to that available. The availability is the initial 

amount of agricultural pasture land adjusted for transformations to and from crop and 

forest land. This land is used by the livestock production variables. Limits pasture land 

use on a subregional basis when subregions are defined and regions otherwise. Cases 

within the AGPASTLANDEXCHANGE and AGLANDPASTURE GAMS 

implementation equations are represented by this tableau row. 

• AUM Grazing -- Limits the usage of grazing land on an animal unit month (AUM) basis 

to that available. The grazing land is used by livestock production. The supply comes 

from a mixture of fixed price supply and upward sloping supply. This is defined on a 

subregional basis when subregions are being used for agricultural production. Cases 

within the AGRESBALANCE GAMS implementation equations are represented by this 

tableau row. 

• Max Pub AUM -- Limits the maximum availability of fixed price AUM grazing largely 

reflecting public supply through grazing fees. Limits AUM grazing use on a subregional 

basis when subregions are being used for agricultural production. Cases within the 

AGRESMAX GAMS implementation equation are represented by this tableau row. 

• Water -- Limits the water use to that available. The water is used by crop production. The 

water available comes from a mixture of sources. One is fixed price water (from BLM 

and other sources) that is only available up to a maximum quantity. The other is upward 

sloping supply curve component representing pumped water from ground and private 

surface water sources. Limits water use on a subregional basis when subregions are being 

used for agricultural production. Cases within the AGRESBALANCE GAMS 

implementation equations are represented by this tableau row. 

• Fixed Water -- Limits the amount of fixed price water to a maximum quantity. Limits 

fixed water availability on a subregional basis when subregions are being used for 
204 

agricultural production. Cases within the AGRESMAX GAMS implementation equations 

are represented by this tableau row. 

• Labor -- Limits the labor used to that available. Labor is used by the crop and livestock 

production variables. The labor available comes from a mixture of fixed price family 

labor that is available up to a maximum quantity and an upward sloping supply curve 

component of hired labor. The limits control the labor market at the geographic level of 

the 11 FASOMGHG regions. Cases within the AGRESBALANCE GAMS 

implementation equations are represented by this tableau row. 

• Family Labor -- Limits the maximum availability of fixed price family labor again an 11 

FASOMGHG region basis. Cases within the AGRESMAX GAMS implementation 

equations are represented by this tableau row. 

• Primary Products -- Balances primary product usage so it cannot exceed primary product 

availability. Primary product usage arises through the combined effects of processing 

usage, feed blending usage, direct usage by livestock, domestic consumption, exports 

through the excess demand formulation and international trade. Availability comes from 

crop and livestock production and imports either from the excess supply formulation or 

the explicit international trade component. This constraint is defined on an 11 region 

basis when the commodity is regionalized and on a national basis. Cases within the 

AGPRODBAL GAMS implementation equations are represented by this tableau row. 

• Secondary Products -- Balances processed or secondary product usage so it cannot 

exceed secondary product availability. Secondary product usage arises through the 

combined effects of processing usage, feed blending usage, direct usage by livestock, 

domestic consumption, or exports. Availability coses from processing. This constraint is 

defined possibly on an 11 region basis and always on a national basis depending on the 

commodity. Cases within the AGPRODBAL GAMS implementation equations are 

represented by this tableau row. 

• International mkt -- Balances foreign country/region markets do thir demand and 

outgoing international transportation is less than demand and incoming transport. The 

constraint is defined for the commodities which have explicit spatial international market 

modeling. Cases within the AGPRODBAL GAMS implementation equations are 

represented by this tableau row. 

• Blended feed -- Balances the usage of blended feeds with the amount produced. The 

constraint is defined on an 11 region basis. Cases within the AGPRODBAL GAMS 

implementation equations are represented by this tableau row. 

• Herd size -- Balances herd size for animals that can be treated with improved manure 

management against the number of animals treated with improved manure management 
205 

possibilities. The constraint is defined only for the categories of livestock that can be 

subjected to improved manure management for GHG emission reduction purposes. 

Limits the herd size on a subregional basis when subregions are being used for 

agricultural production. The AGMANUREMGT GAMS implementation equations are 

represented by this tableau row. 

• Crop Mix -- Balances acreage by crop against the acreage allowed by the crop mix 

possibilities. The constraint is defined for each crop in the crop mixes on both an irrigated 

and total crop land basis. The geographic basis is the same as the active regional 

definition being used for agricultural production during a time period. The 

AGCRPMIXUP and AGCRPMIXLO GAMS implementation equations are represented 

by this tableau row. 

• Crop mix convex -- Forces a convex combination of the crop mixes. The geographic 

basis is the same as the active regional definition being used for agricultural production 

during a time period. The GAMS implementation equations AGCRPMIXTOT are 

represented by this tableau row. 

• Livestock Mix -- Balances the number of head by livestock against the distribution of 

head allowed by the livestock mix possibilities. The constraint is defined for each type of 

livestock for which a livestock mix is defined. The geographic basis is the same as the 

active regional definition being used for agricultural production during a time period. The 

AGLIVESTOCKMIXNAT GAMS implementation equations are represented by this 

tableau row. 

• GHG net emissions -- Accumulates net GHG emissions by category and balances against 

the GHG payment variable by GHG account. That variable equals the total net emissions 

and is unrestricted in sign reflecting a possible net emission reduction available for 

payment and/or an emissions increase subject to emission payments. Net emission 

increments arise from sequestration possibilities under tillage choice, emissions related to 

crop or livestock production, savings from manure management, and emissions or offsets 

from agricultural processing (that includes biofuel feedstock usage). Forest and pasture 

sequestration is also accounted under the tillage choice and land use change variables. 

The GHGACCOUNTS GAMS implementation equations are represented by this tableau 

row. 

• Forest land -- Forestry land use balance as explained in the forestry section above. 

8.2.2 Variables defined 

The variables present in the tableau are 
206 

• Tillage Choice -- Choice between tillage alternatives. They use crop land and supply 

tilled land for use in the crop production variables. They also have sequestration 

implications that fall in the GHG balance equations. Their presence allows for depiction 

of the dynamic trajectory of carbon sequestration under changes in tillage systems. These 

variables are defined for each crop land quality type, irrigation/dryland status and tillage 

alternative. These variables are defined on a subregional or regional basis depending on 

time period. The AGINITIALTILL and AGCHANGETILL GAMS implementation 

variables are represented by this tableau column. 

• Crop Production -- Crop production possibilities. They use inputs as reflected within the 

objective function coefficient, tilled crop land, water, and labor while producing crop 

products. They also require land that falls within the allowed crop mixes and enter the 

GHG balance. In the GHG balance equation they enter several accounts including fossil 

fuel usage related emissions, nitrous oxide emissions and sequestration alterations by 

type of crop. They are defined by crop, crop land type, irrigation/dryland choice, 

fertilization alternative, and tillage alternative. These variables are defined on a 

subregional or regional basis depending on time period. The AGCROPBUDGET GAMS 

implementation variables are represented by this tableau column. 

• Livestock Production -- Livestock production possibilities. They use inputs as reflected 

within the objective function coefficient, use pasture land, and use labor while producing 

livestock products. They also use some primary and secondary products directly as feed 

or intermediate animals (e.g. feeder pigs to finishing) and use blended feeds. They require 

that the animal distribution falls within the selected livestock mix, make animals 

available for improved manure management and enter the GHG balance. In the GHG 

balance, they enter several accounts including fossil fuel usage related emissions, enteric 

fermentation emissions and manure emissions. They are defined by animal type, 

livestock management alternative, and enteric fermentation alternative. These variables 

are defined on a subregional or regional basis depending on time period. The 

AGLVSTBUDGET GAMS implementation variables are represented by this tableau 

column. 

• Manure Management -- Choice of improved manure management systems. They incur 

cost in the objective function, require that animals are present that can be treated and 

offset manure related emissions in the GHG balance. These variables are defined by type 

of animal and manure management system type. Geographically, they are defined on a 

subregional or regional basis depending on time period. The AGLVSTMANURE GAMS 

implementation variables are represented by this tableau column. 
207 

• Feed Blending -- Blending of livestock feeds from a number of different alternative 

formulas utilizing primary and secondary commodities. The resultant feeds are supplied 

for eventual consumption by the livestock production variables. These variables are 

defined by feed and feed blending alternative. Geographically they are defined on an 11 

region basis. Cases within the AGREGPROCESS GAMS implementation variables are 

represented by this tableau column. 

• Crop Mix -- Choice between a set of historically observed crop mixes. They implicitly 

represent many omitted resource constraints and other considerations. The variables 

supply a proportion of the land suitable for each different type of crop either on an 

irrigated or total crop acreage basis and enter the crop mix convexity equation. These 

variables are defined for a number of historical alternatives for irrigated crops and for 

total crops. Geographically they are defined on a subregional or regional basis depending 

on time period. The AGMIXR GAMS implementation variables are represented by this 

tableau column. 

• Livestock Mix -- Choice between a set of historically observed livestock herd regional 

distributions by type of animal. They implicitly represent many omitted resource 

constraints and other considerations. These variables supply a proportion of the herd that 

appears in each region or subregion. These variables are defined by type of animal for 

each of a number of historical alternatives for livestock regional distributions. 

Geographically they are defined on a subregional or regional basis depending on time 

period. The AGNATMIX GAMS implementation variables are represented by this 

tableau column. 

• Land to forest -- Land use change of crop or pasture land into forestry. When shifting 

crop land these variables reflect removal of land from the crop land constraints and 

supply into the forest land balance. When crop land is being shifted the entries in the 

subregion and land quality subcases contain coefficients that are proportional to their 

initial relative abundance. When pasture land is being shifted the coefficients reflect the 

removal of an acre from the pasture land equation and its supply into the forest land 

equation. These variables are defined far a single crop land and a pasture land case. 

Geographically they are defined on an 11 region basis. The LANDFROMAG and 

CONVRTFROMAG GAMS implementation variables are represented by this tableau 

column. 

• Land from forest -- Land use change (deforestation) from forest land into crop or pasture 

land. These variables reflect supply of land into the agricultural land constraints and use 

of land from the forest land availability constraint. When crop land is being shifted the 

entries in the subregion and land quality subcases of the crop land equations contain 
208 

coefficients that are proportional to their initial relative abundance. When pasture land is 

being shifted the coefficients reflect the addition of one acre into the pasture land 

equation and its withdrawal from forest land. These variables are defined for a single 

crop land and a pasture land case. Geographically they are defined on an 11 region basis. 

The LANDTOAG and CONVRTTOAG GAMS implementation variables are represented 

by this tableau column. 

• Land to pasture -- Land use change of crop land into pasture land. These variables reflect 

removal of land from crop land equations with coefficients that are proportional to their 

initial relative abundance in supply by quality type and then supply into the single 

homogeneous pasture land equation. These variables are defined geographically on the 

same basis as it is agricultural production by time period. Cases within the 

AGPASTLNDUSECHG GAMS implementation variables are represented by this tableau 

column. 

• Land from pasture -- Land use change of pasture land into crop land. These variables 

reflect the supply of land into the subregion and land quality subcases of the crop land 

equations in a fashion proportional to their initial relative abundance and withdrawal 

from the pasture land equation. These variables are defined geographically on the same 

basis as it is agricultural production by time period. Cases within the 

AGPASTLNDUSECHG GAMS implementation variables are represented by this tableau 

column. 

• AUM Supply -- Supply of AUM grazing from public and private sources. The publically 

supplied AUMs are assumed to be available at a fixed price (a grazinf fee) up to a 

maximum quantity. The private sources are supplied according to a supply function. The 

variables reflect the area under the supply function in the objective function, a supply into 

the AUM grazing equation and the use of any applicable maximum. These variables are 

defined on a subregional basis when subregions are being used for agricultural 

production. Cases within the AGRESSUPPLY and AGRESSEPSUPPLY GAMS 

implementation variables are represented by this tableau column. 

• Water Supply -- Supply of water from fixed price and pumped sources. The fixed price 

supplied water is assumed to be available at a fixed price up to a maximum quantity and 

largely reflects the surface water supplied by the government (e.g. BLM water). The 

pumped sources are supplied according to a supply function. They represent private 

surface water markets and ground water. The variables reflect the area under the supply 

function in the objective function, a supply into the water equation and the use of any 

applicable maximum. These variables are defined on the regional basis being used for 
209 

agricultural production. Cases within the AGRESSUPPLY and AGRESSEPSUPPLY

GAMS implementation variables are represented by this tableau column. 

• Labor Supply -- Supply of labor from family and hired sources. The family labor is 

assumed to be available at a fixed reservation wage up to a maximum quantity. The hired 

labor is supplied according to a supply function. The variables reflect the area under the 

supply function in the objective function, a supply into the labor balance equation and the 

use of any applicable maximum. These variables are defined on an 11 region basis 

reflecting pooled regional labor markets. Cases within the AGRESSUPPLY and

AGRESSEPSUPPLY GAMS implementation variables are represented by this tableau 

column. 

• Processing -- Agricultural processing activity that transforms primary commodities into 

secondary commodities. The variables reflect the cost of processing in the objective 

function, the use of primary and some secondary products as inputs to processing and the 

creation of processed secondary products. The processing variables also enter the GHG 

balances reflecting GHG emissions from inputs used in processing and GHG offsets 

when they represent transformation of biofuel feedstocks into forms of bioenergy. These 

variables are defined by processing alternative and geographically are defined on either 

an 11 region or a national basis depending on the secondary commodity being 

manufactured. The AGPROCESS and cases within the AGREGPROCESS GAMS 

implementation variables are represented by this tableau column. 

• Domestic Demand -- Domestic consumption of primary and secondary commodities. 

This includes the disappearance of commodities to the public, supermarkets or movement 

into processing alternatives that are not formally included in FASOMGHG. The variables 

have the area underneath the demand curve in the objective function and reflect a 

withdrawal of the commodity from the relevant primary or secondary balance at the 

national level. These variables are defined by commodity on a national basis. Cases 

within the AGDEMAND and the AGDEMANDS GAMS implementation variables are 

represented by this tableau column. 

• Export Demand -- Export of goods which are specified with explicit rest of world excess 

demand equations. The variables have the area underneath the excess demand curve in 

the objective function and reflect withdrawal of the commodity from the relevant primary 

or secondary balance at the national level. These variables are defined by commodity on 

a national basis. Cases within the AGDEMAND and the AGDEMANDS GAMS 

implementation variables are represented by this tableau column. 

• Import Supply -- Import of goods which are specified with explicit rest of world excess 

supply equations. The variables have the negative of the area underneath the import 
210 

excess supply curve in the objective function and reflect supply of the commodity into 

the primary or secondary balance. These variables are defined by commodity on a 

national basis. Cases within the AGSUPPLY and the AGSUPPLYS GAMS 

implementation variables are represented by this tableau column. 

• International trade -- International transport between the US and foreign countries/regions 

and in between foreign countries/regions. These variables are defined for all pairs of 

movements allowed in the data between the US and foreign countries/regions and 

between the foreign countries/regions and themselves. The AGTRADE GAMS 

implementation variables are represented by this tableau column. 

• Int. demand/supply -- Import and export of goods which are specified with explicit 

foreign country/region excess supply or demand equations. The variables have the area 

underneath the country level export excess demand or import excess supply curve in the 

objective function and reflect addition/withdrawal of the commodity in the foreign 

country/region commodity balance. These variables are defined by commodity for each 

relevant foreign country/region basis. Cases within the AGDEMAND, AGDEMANDS, 

AGSUPPLY, and AGSUPPLYS GAMS implementation variables are represented by this 

tableau column. 

• GHG Payment -- Payments/taxes on net changes in GHG emissions. These variables are 

defined for each of the GHG accounts. Cases within the AMOUNTGHGS GAMS 

implementation variables are represented by this tableau column. 
211 

Table 8-10. Agricultural model tabular overview for a single period and region 

Tillage Choice 

Crop Production 

Livestock Production 

Manure management 

Feed Blending 

Crop Mix 

Livetock Mix 

Land to forest 

Land from forest 

Land to pasture 

Land from pasture 

AUM Supply 

Water Supply 

Labor Supply 

Processing 

Domestic Demand 

Export Demand 

Import Supply 

International trade 

Welfare -cc -lc -mc -pc -ac -wc -lbc -prc +di +ei -ii -tc 

Crop land +1 +1 -1 +1 -1 Tillage supply -1 +1 Pasture Land +lu +1 -1 -1 +1 AUM Grazing +lg -1 Max Pub AUM +1 Water +cw -1 Fixed Water +1 Labor +cl +ll -1 Family Labor +1 Primary Products -cp +/-lp +fp +pp +1 +1 -1 +/Secondary Products +ls +fs +/-ps +1 +1 -1 International mkt -/+Blended feed +lf -1 Herd size +1 -1 Crop Mix +1 -mxc Crop mix convex +1 -mxs1 

Livestock Mix +1 -la GHG balance -ts +ce +le -me -as +as +/-pg Forest land -1 1 
212 

8.2.3 Coefficient definitions 

The coefficients in the model are 

cc -- the per acre cost of crop production which is the sum of the cost of using fixed price 

inputs 

lc -- the per head cost of livestock production which is the sum of the cost of using fixed 

price inputs 

mc -- the costs of the improved manure management systems 

pc -- the cost of transforming pasture land into crop land 

ac -- the area under the AUM supply curve 

wc -- the area under the water supply curve 

lbc -- the area under the labor supply curve 

prc -- the cost of processing 

di -- the area under the domestic demand curve 

ei -- the area under the export demand curve 

ii -- the area under the excess import supply curve 

tc -- the cost of international transport 

isd -- the area under the foreign excess demand and supply curves times minus one if this 

is an excess supply curve 

gp -- the GHG payment rate 

cla -- the amount of crop land initially available 

lu -- pasture land use per head of livestock 

pla -- the amount of pasture land initially available 

lg -- the AUM grazing land requirement per head of livestock 

paum -- maximum availability of public AUMs 

cw -- the use of irrigation water per acre cropped 

pwat -- maximum availability of fixed price water 

cl -- the use of labor per acre of crop land 

ll -- the use of labor per head of livestock 

plab -- maximum availability of family labor 

cp -- the primary product production per acre of crops 

lp -- primary product production from livestock production and the primary products 

(crops directly fed) consumed directly in livestock production 

fp -- use of primary products in blending one unit of feed 

pp -- use of primary products per unit of processing 

ls -- use of secondary products (soybean meal) directly in livestock production 

fs -- use of secondary products in feed blending and the yield of the blended feeds 

ps -- secondary product use in processing and the secondary product yield 

lf -- usage of blended feed per head of livestock 

mxc -- amount of each crop in the crop mix 

mxs -- amount of all crops in the mix 
213 

la -- proportional amount of livestock in each active agricultural region during a period 

ts -- sequestration under a tillage system per acre 

ce -- emissions of GHGs by crop and GHG category 

le -- emissions of GHGs by animal type and GHG category 

me -- manure emissions offset per unit of emission system 

pg -- processing net GHG emissions per unit of processing 

as -- sequestration removed or added when land use change to or from forestry occurs 

fl -- initial forest land 

8.3 Details on features of the agricultural model 

Now we show how particular aspects of agriculture are represented within the 

FASOMGHG programming model structure. 

8.3.1 Crop production modeling 

Table 8-11 portrays the FASOMGHG crop production model in a simplified one region, 

one time period, setting. The crop production alternatives vary by crop, crop land qualtity type, 

irrigated/dryland choice, fertilizer use and tillage system. It also shows the imposed relationships 

between the tillage choice and the crop production variables. Namely, in order to produce crops 

under a tillage system tilled acres must be supplied under that tillage system (where as discussed 

above there are three in the model). The tillage system choice variables are seperated to permit 

modeling of the dynamics of carbon sequestration under alterations in tillage systems (as 

discussed in the section immediately below). The tillage variables defined are both an initial 

tillage and a tillage change variable. The initial tillage variable is only defined for the first period 

and enters the GHG balance supplying a profile of current and future levels of carbon 

sequestration. The tillage change variables are defined for each time period and alter the GHG 

balance profile of sequestration from that time period to the end of the model. 

The GHG balance entries for the production variable reflects production based emissions 

due to 

• Changes in sequestration when longer lived perennials are involved. 

• Fossil fuels used in tillage, planting, harvesting and other machinery operations 

• Crop drying 

• Irrigation 

• Histosoils 
214 

• Nitrogen fertilization 

• Rice production 

• Fertilizer and pesticide manufacture 

• Residue burning 

• Sewage sludge usage 

• Nitrogen fixing crops. 

Now let us turn attention to a more precise definition of the tableau contents. The 

equations in this table 8-11 are 

• Welfare -- Consumers' and producers' surplus. In this function the crop cost terms vary 

with crop and input usage. The GAMS implementation equation WELFAR is represented 

by this tableau row. 

• Initial acres -- Limits initial starting amount of crop land to the initial inventory as 

allocated across irrigation status, tillage method employed and land type. The crop land 

usage by the initial tillage variables summed across the irrigation possibilities is 

constrained to not exceed the land by tillage class and type initially available. 

Geographically, this equation is defined on the same basis as is crop production and 

varies by time period. The GAMS implementation equation AGTILLSTART is 

represented by this tableau row. 

• Tilled acres -- Balances amount of tilled acres with its use by tillage system, irrigation 

status, land type and time period. The land is used by the crop production variables 

supplied by either the initial tillage or the tillage change variables. Within these equations 

tillage changes are reflected where in an acre moves from one tillage type on one type of 

irrigated or dryland acreage to another tillage type possibly with a different irrigation 

status. Geographically this equation is defined on the same basis as is crop production. 

The constraint is defined for each explicit time period. The GAMS implementation 

equation AGTILLUSE is represented by these taleau rows. 

• Can change till -- Limits the amount of tilled acres that can change tillage status. It is 

defined by tillage system, irrigation status and land type giving acres available to change 

the tillage during a particular time period. The land is supplied by the additional tillage 

choice and later the switch tillage variables. It is used by the tillage change variables. 

These equations are used to cause land changed into a tillage type to remain in that tillage 

type for a minimum amount of time before changing again. This restriction is enforced on 

all tillage changes after the initial choice. Geographically, this equation is defined on the 

same basis as is crop production. The constraint is defined for each explicit time period. 
215 

The GAMS implementation equation AGCANCHANGETILL is represented by this 

tableau row. 

• Water -- Limits water use to water availability. Water availability modeling is portrayed 

in a simplistic fashion here and is more accurately and extensively discussed elsewhere. 

Within this constraint water use is restricted to irrigated crops. The coefficients for water 

use vary by crop and tillage system. Geographically, this equation is defined on the same 

basis as is crop production. The constraint is defined for each explicit time period. Cases 

within the AGRESBALANCE and AGRESMAX GAMS implementation equations are 

represented by this tableau row. 

• Labor -- Limits labor use to labor availability. Labor availability modeling is portrayed in 

a simplistic fashion here and is more accurately and extensively discussed elsewhere. The 

coefficients for labor use vary by crop and tillage system. Geographically, this equation is 

defined on the 11 region basis. The constraint is defined for each explicit time period. 

Cases within the AGRESBALANCE and AGRESMAX GAMS implementation 

equations are represented by this tableau row. 

• Primary Products -- Balances commodity supply with use. This constraint reflects yields 

from crop production and the disappearance of commodities in the marketplace. The 

constraint is defined for each crop commodity and can be defined either on a regional or 

national basis. Generally the commodities defined on a regional basis are those that are 

internationally traded, used in livestock feeds or used as biofuel feedstocks. The 

constraint is defined for each explicit time period. Cases within the AGPRODBAL 

GAMS implementation equations are represented by this tableau row. 

• Fertilizer -- this is not actually a FASOMGHG equation but is included for expositional 

purposes. This illustrates that fertilizer coefficients generally reflect changing amounts of 

fertilizer usage across crop and fertilizer strategies. These coefficients are collapsed into 

the objective function row by multiplying usage rates by fertilizer prices. Calculations 

within the implementation equation WELFAR are represented within this tableau row. 

• GHG balance -- Net GHG emissions, sequestration and offsets from crop and tillage 

system usage and production are balanced with their eventual pricing. The constraint is 

defined for each GHG account on a national basis. Under crop production we have 

emissions from crop production associated with: (a) sequestration when longer lived 

perennials are involved; (b) fossil fuels used in tillage, planting, harvesting and other 

machinery operations; (c) crop drying; (d) irrigation; (e) histosoils; (f) nitrogen 

fertilization; (g) rice production; (h) fertilizer and pesticide manufacture; (i) residue 

burning; (j) sewage sludge usage; and (k) nitrogen fixing crops. Under the initial tillage 

system choice we have the sequestration trajectory for a particular tillage system. Under 
216 

the change till variable we have changes in the sequestration trajectory when tillage 

systems are altered. Under the land to and from pasture or forestry we reflect alterations 

in sequestration as moving land into crops removes it from the forest and pasture use 

GHG accounting and thus reflects a loss over there and a gain here. The constraint is 

defined for each explicit time period. Cases within the GHGACCOUNTS GAMS 

implementation equations are represented by this tableau row. 

• Forest/Pasture land -- Land drawn from either the pasture or forest land parts of the 

model. It is more extensively discussed elsewhere. 

The variables in table 8-11 are 

• Crop production -- Acreage by crop land type allocated to each crop by fertilization 

strategy (of which there are three -- 70%, 85% and 100% of base levels), the three tillage 

alternatives, and dryland or irrigated status. The variable uses cost items, land by tillage 

status, water, labor and fertilizer. It creates a crop yield in the crop commodity balance 

row and has GHG net emission implications. Geographically the production variables are 

defined on a subregion or regional basis depending on the agricultural regions used in a 

particular time period. The variable is defined for each explicit time period. The 

AGCROPBUDGET GAMS implementation variables are represented by this tableau 

column. 

• Initial till -- Assignment of initial agricultural land to tillage system and irrigation status. 

These variables use land from the initial allocation equation and supply it for crop 

production and also allow tillage change. Geographically these variables are defined on 

the same regional basis as are the crop production variables. The variable is defined for 

only for the first time period. The AGINITIALTILL GAMS implementation variables 

are represented by this tableau column. 

• Switch tillage -- Tillage switches. Land is switched from one tillage system and 

irrigation status alternative to another. These variables use land from the period by period 

tillage availability equation and supply it into another. They require land suitable for a 

tillage change. Geographically these variables are defined on the same regional basis as 

are the crop production variables. The variable is defined for each time period. The 

AGCHANGETILL GAMS implementation variables are represented by this tableau 

column. 

• Transform in land -- Land use change from pasture or forest land. These variables use 

land from pasture or forests and supply land across the different crop land quality types 

and subregions in a region. Land only moves into the conventional tillage, dryland 
217 

category. Geographically, these variables are defined only for a move of all crop land not 

by land type and only at a FASOMGHG 11 region level. The coefficients under these 

variables reflect the relative abundance of land by type and subregion. Thus, if 50% of 

the land in the PSW region were in Northern California and 50% in Southern California 

and each of those subregion that equal proportion of type 1 and type 2 land, then there 

would be four coefficients equaling -0.25's in the tableau in the tilled land available 

equation. The variable is defined for all of the time periods. Cases within the 

LANDTOAG and CONVRTTOAG GAMS implementation variables are represented by 

this tableau column. 

• Transform out land -- Land use change to pasture or forest land. These variables supply 

land to pasture or forests and use land across the different crop land quality types and 

subregions in a region. Land only moves from the conventional tillage, dryland category. 

Geographically, these variables are defined only for a move of all crop land not by crop 

land quality type and only at a FASOMGHG 11 region level. The coefficients are the 

same as discussed under the transform in land variables discussed just above. The 

variable is defined for all of the time periods. Cases within the LANDFROMAG and

CONVRTFROMAG implementation variables are represented by this tableau column. 

• Commodity market -- Aggregate representation of the commodity markets as discussed 

elsewhere. 

• GHG Payment -- GHG net emission payment submodel as discussed elsewhere. Cases 

within the AMOUNTGHGS GAMS implementation variables are represented by this 

tableau column. 

Coefficients within table 8-11 are 

cc -- cost of crop production which varies with crop management, crop, region, land type, 

and time period. 

clt - cost of land transformation 

cla -- initial endowment of land by land type and tillage system 

cw -- water use by crop production which varies with crop management, crop, region, 

land type, and time period. 

awater -- water availability and actually an indicator of a more complex water supply 

model structure 

cl -- labor use by crop production which varies with crop management, crop, region, land 

type, and time period. 

alabor -- labor availability and actually an indicator of a more complex labor supply 

model structure 

cp -- yield from crop production which varies with crop management, crop, region, land 

type, and time period. 
218 

cf -- fertilizer use by crop production which varies with crop management, crop, region, 

land type, and time period. 

ce -- net GHG emissions by crop production which varies with crop management, crop, 

region, land type, and time period. 

cs -- net GHG sequestration by crop tillage system which varies with tillage system, 

irrigation alternative, region, and land type. 

oland -- land in pasture and forests and an indicator of other submodels using those lands. 
219 

Table 8-11 Tableau illustrating static crop production and tillage choice 

Crop 1 low fert, conv till, dry land type 1 

Crop 1 normal fert, conv till, dry land type 1 

Crop 1 low fertilizer, min till, dry land type 1 

Crop 1 normal fert, min till, dry land type 1 

Crop 1 low fert, conv till, dry land type 1 

Crop 1 normal fert, conv. till, dry land type 1 

Crop 1 low fertilizer, min till, dry land type 1 

Crop 1 normal fert, min till, dry land type 1 

Initial till conv on dry land type 1 

Initial till min on dry land type 1 

Initial till conv on irrigated land type 1 

Initial till min on irrigated land type 1 

Switch conv dry to minimum dry land type 1 

Switch conv dry to minimum irrig land type 1 

Crop 1 low fert, conv till, dry land type 2 

Initial till conv on dry land type 2 

Transform in land 

Transform out land 

Commodity market 

GHG Payment 

Welfare -------- - -

l

-

l

+ + 

Initial acres conventional land type 1 +

1

+

1

 

Initial acres minimum till land type 1 +

1

+

1

 

Initial acres minimum till land type 2 +

1

 

Tilled acres dryland conventional land type 1 +

1

+1

 -1 +

1

+1

-

lt

+lt1

 

Tilled acres dryland minimum till land type 1 +

1

+1

 -1 -1 

Tilled acres irrigated conventional land type 1 +

1

+1

 -1 

Tilled acres irrigated minimum till land type 1 +

1

+1

 -1 -1 

Tilled acres dryland conventional land type 2 +

1

-1 -

lt

+lt2

 

Can change till dryland conventional land type 1 -1 -1 +

1

+1

 

Water ++++ Labor +

cl

+cl

+cl

+cl

+cl

+cl

+cl

+cl

+

cl

 

Primary Products -------- - +

1

 

Fertilizer +

f

+

f

+

f

+

f

+

f

+

f

+

f

+

f

+

f

GHG balance ++++++++ - - - - - - +- -1 Forest/Pasture land +

1

-1 
220 

8.3.1.1 Tillage choice 

While table 8-11 illustrates several important features regarding crop production, tillage 

choice and tillage system change, the dynamics of these features are not shown therein. 

Consequently, table 8-12 was created to illustrate the dynamic features of tillage change across 

the land related variables/constraints and the GHG balance. A number of key points are 

illustrated: 

• The initial tillage choice variable supplies land for use by crop production in the initial 

and all future time periods. Thus, when land initially is conventionally tilled then the 

initial tillage variable provides conventionally tilled into the land available for crop 

production equations in time periods 1, 2, 3 and all subsequent periods. Simultaneously, 

these variables supply acreage into the land that can be subjected to a change from 

conventional tillage in the current and subsequent periods. 

• The initial tillage variable provides a current and future carbon sequestration trajectory. 

This incorporates the dynamics of tillage based sequestration reflecting accumulation and 

attainment of a new equilibrium where carbon gains effectively saturate. 

• The tillage change tillage variables use land from a previous tillage status and move it 

into its new tillage status. In the tableau that when land is changed from conventional 

tillage to minimum till we have +1 in the conventional row and -1 in the minimum tillage 

row. 

• The model can reflect both tillage intensification and deintensification with this tableau 

containing changes back from minimum tillage to conventional tillage. 

• The tillage change variables enter the GHG balance for the current and future periods 

altering the sequestration profile with coefficients that reflect the sequestration 

differences observed when the tillage system is altered. These coefficients can be either 

positive or negative depending on whether the tillage intensity tillage is being increased 

or decreased. Data from the EPIC or CENTURY crop simulation models are used to 

specify such numbers. 

• When a tillage change is pursued in a period it uses up available acreage from the 

constraint on land permitted to have a tillage change in that period and all subsequent 

periods. This can be seen in the constraints for periods 1 and 3. 

• The source of land available for a tillage change can either be from (a) initial tillage 

choice, (b) current or past land use changes from forest or pasture or (c) from a tillage 

change in previous period. 
221 

• When tillage is changed that the land is made available for subsequent tillage changes 

only with a lag. For example, in the tableau, when tillage is altered in time period 1 the 

land does not become available for subsequent changes until time period 3. The reason 

for use of such a restriction is that it allows us to accurately portray sequestration 

dynamics including the approach to saturation. We employ the assumption that once 

tillage is changed it cannot be altered again for a minimum of 20 years. 

• Table 8-12 shows the differences in the way the model handles land use between the 

forest and agricultural sectors. 

• Fundamentally in the forest sector the land use change variables do not try to reflect 

the multi-period implications of land transfers in the forest land equation. Rather this 

is handled within the multi-period forestry production variables. 

• When the land is moved into agriculture then we must reflect multi-period 

implications across the agricultural submodels for each FASOMGHG time periods. 

Thus when land is moved in time period 1 it makes land available for cropping use in 

time periods 1, 2, and 3. 

• We restrict land movements so they can only come into or out of the conventionally tilled 

dryland case. Land can in turn be moved into other tillage or irrigation systems since the 

model allows an immediate tillage change. 

• When land is moved in a period it only supplies land in later periods. 

• The GHG accounts are dynamic and are stocks not flows. 

• Thus, we have payments for the GHG accounts in each time period. 

• We accumulate GHG emissions. This means that emissions in the first time period 

also enter the GHG balance in the second and subsequent time periods. 

• The net effect of cropping on the GHG balance involves both crop production effects and 

tillage effects. The tillage effects are initially composed of the sequestration profile 

arising from the initial tillage choice variable. But these effects can be subsequently 

corrected as tillage changes are put into place employing the tillage switch variable. Such 

tillage changes can reflect either intensification or deintensification. 

Now suppose we turn our attention to a more formal definition of structural elements. 

The equations in this tableau are: 

• Welfare -- the welfare equation as discussed above. The GAMS implementation equation 

WELFAR is represented by this tableau row. 
222 

• Initial acres -- Limits initial acreage by type of tillage system to that available as has been 

discussed above. This has region, land type, and tillage system dimensions. The GAMS 

implementation equation AGTILLSTART is represented by this tableau row. 

• Tilled acres -- Balances use and supply of acres by tillage system and irrigation status. 

This land is used by crop production. In the tableau this is portrayed in a simplistic 

fashion but actually would have regional, land type, irrigated/dryland, and tillage system 

dimensions as well as time period. The GAMS implementation equation AGTILLUSE is 

represented by this tableau row. 

• Can change till -- Controls the amount of acreage that can be subjected to a tillage system 

change. This is used to facilitate carbon accounting and reduce model size. Tillage 

system changes may only occur after the land has been subjected to that tillage system for 

20 years so that we may assume that the sequestration quantity is mature. This constraint 

that same dimensions as detailed acreage constraint just above. The GAMS 

implementation equation AGCANCHANGETILL is represented by this tableau row. 

• GHG balance -- Adds up the cumulative stock of GHG emissions, sequestration and 

offsets and balances it against the GHG payments variable. This constraint is defined for 

the various GHG accounts in all time periods. Cases within the GHGACCOUNTS

GAMS implementation equations are represented by this tableau row. 

• Forest land -- the constraint that reflects the land availability in land use within the 

forestry model as discussed above. 

The variables in this tableau are 

• Crop prod. -- Amount of crop production undertaken as discussed above. This variable is 

defined by region, crop, land type, tillage system, fertilization alternative, 

irrigation/dryland and time period. These variables use land by tillage system that is 

available in the time period for which the cropping variable is defined. The 

AGCROPBUDGET GAMS implementation variables are represented by this tableau 

column. 

• Initial tillage -- Amount of land initially entering each of tillage/irrigation system 

possibility by region. These variables use land from the initial tillage limit equation, then 

supply land for use by cropping in each subsequent time period, supply land available to 

switch tillage in each subsequent time period and reflect the initial sequestration profile 

in the GHG balance equations. The AGINITIALTILL GAMS implementation variables 

are represented by this tableau column. 

• Switch tillage -- Amount of land switching from and to each of the tillage/irrigation 

system possibilities by region. These variables use land from the tilled acreage equation 
223 

for the tillage system and irrigation possibility that land will be switched from then 

supply it into the corresponding equation for the new tillage system and irrigation status. 

They also use land on which tillage may switched and subsequently supply land on which 

tillage can be switched in the future with some lag as discussed above. They enter the 

GHG balance equations reflecting the dynamic shift in the sequestration trajectory 

relative to the tillage and irrigation system combination from which land is being 

withdrawn. The AGCHANGETILL GAMS implementation variables are represented by 

this tableau column. 

• Transfer land -- Amount of land use change from forestry both from and to pasture and 

forestry. These variables use land from the previous land use balance equation and place 

acreage into the balance for the conventional tillage system under dryland status. They 

also permit both immediate and subsequent switches from the tillage/irrigation system 

combination. Much more about these variables is discussed above and more will appear 

in the next chapter. Cases within the LANDTOAG and CONVRTTOAG GAMS 

implementation variables are represented by this tableau column. 

• GHG Payment -- Net GHG payments as has been discussed above. Cases within the 

AMOUNTGHGS GAMS implementation variables are represented by this tableau 

column. 

The coefficients in this tableau meriting definition are 

cc -- the carbon sequestration trajectory under conventional tillage and the chosen 

irrigation alternative that varies by region, land type, tillage system and elapsed 

time since the beginning of the model. 

cm -- the carbon sequestration trajectory under minimum tillage and the chosen irrigation 

alternative that varies by region, land type, tillage system and elapsed time since 

the beginning of the model. 

cg -- change in the carbon sequestration trajectory when switching from conventional 

tillage under the chosen irrigation status to minimum tillage under another 

irrigation status that varies by region, land type, tillage system, irrigation status 

and elapsed time since the switch. 

cl -- change in the carbon sequestration trajectory when switching from minimum tillage 

under the chosen irrigation status to conventional tillage under another irrigation 

status that varies by region, land type, tillage system, irrigation status and elapsed 

time since the switch. 

as -- change in sequestration when land moves in that aloso would be matched by losses 

in pasture soil accounting.
224 

Table 8-12 Tableau illustrating dynamics of tillage choice 

Crop prod. dryland conv. till period 1 

Crop prod dryland min. till period 1 

Crop prod. dryland conv. till period 2 

Crop prod dryland min. till period 2 

Crop prod. dryland conv. till period 3 

Crop prod dryland min. till period 3 

Initial till conv on dryland 

Initial till min on dryland 

Switch conv dry to min dry period 1 

Switch min. till dry to conv. pd 1 

Switch conv dry to min dry period 2 

Switch min. till dry to conv. pd 2 

Switch conv dry to min dry period 3 

Switch min. till dry to conv. pd 3 

Transfer land into crops period 1 

Transfer land into crops period 2 

Transfer land into crops period 3 

GHG Payment in period 1 

GHG Payment in period 2 

GHG Payment in period 3 

Welfare - - - - - - + + + Initial acres conventional +1 Initial acres minimum till +1 Tilled acres dryland conventional period 1 +1 -1 +1 -1 -1 Tilled acres dryland minimum till period 1 +1 -1 -1 +1 Tilled acres dryland conventional period 2 +1 -1 +1 -1 +1 -1 -1 -1 Tilled acres dryland minimum till period 2 +1 -1 -1 +1 -1 +1 Tilled acres dryland conventional period 3 +1 -1 +1 -1 +1 -1 +1 -1 -1 -1 -1 Tilled acres dryland minimum till period 3 +1 -1 -1 +1 -1 +1 -1 +1 Can change till dryland conventional land period 1 -1 +1 -1 Can change till dryland minimum till period 1 -1 +1 Can change till dryland conventional land period 2 -1 +1 -1 -1 Can change till dryland minimum till period 2 -1 +1 Can change till dryland conventional land period 3 -1 -1 +1 -1 -1 -1 Can change till dryland minimum till period 3 -1 -1 +1 GHG balance period 1 + + +cc +cm +cg -cl +as -1 GHG balance period 2 + + + + +cc +cm +cg -cl +cg -cl +as +as -1 GHG balance period 3 + + + + + + +cc +cm +cg -cl +cg -cl +cg -cl +as +as +as -1 Forest land in period 1 +1 Forest land in period 2 +1 Forest land in period 3 

 +1 

 
225 

8.3.1.2 Land transfer dynamics 

When crop land is transferred in or out it possesses a number of notable characteristics 

that deserve mention. Namely when crop land transfers out to pasture in a particular time period 

that land is removed from crop land use and made available for pasture not only in the time 

period of transfer, but also in all subsequent periods. Furthermore, when land transfers out of the 

land quality differentiated crop land into the single homogeneous category pasture land it is 

assumed to transfer in a distribution proportion to the way the different qualities of crop land 

were initially populated. In particular, if initially 25% of the land in a region fell into the wetland 

category then when land transfers from crop land the transferred acre will withdraw 25% of an 

acre from the wetland category along with 75% of an acre from the other three quality classes in 

appropriate proportions. 

Similar practices are employed when land transfers into crop land from pasture. Namely 

land it is removed in the time period of the transfer and all subsequent time periods. Furthermore, 

land is placed into the various crop land land quality accounts in proportion to the initial 

proportional shares by land quality class. 

When crop land transfers occur from and to forestry, the land flows come from and to the 

high quality forest site index. Land moving in supplies crop land in the current and all 

subsequent time periods and withdraws land from the CROPFOR or FORCROP categories. 

When land transfers out from crop land it goes into the balance for afforested land in the 

CROPFOR forest land category. Crop land is also removed from or added to the agricultural 

crop land balance in the time period of transfer and all subsequent time periods. Transfers are 

again in proportion to the initial population distribution across land quality classes. 

8.3.1.3 Crop mixes 

As discussed above, aggregation problems are avoided by requiring the crops in a region 

to fall within the mix of crops observed. The model is constrained so that for each area the crop 

mix falls within one of those observed in the past 40 years. Both irrigated and dryland mixes are 

present. The way the crop mixes are implemented is illustrated in table 8-13. This table employs 

example numbers in representing how the crop mixes constrain the feasible levels of the crop 

production variables. In particular, concentrating for the moment only on the total acreage crop 

mix constraints, notice how the first four crop production variables require that acres be available 
226 

for the particular crop being grown in the total acres crop mix by crop constraint. Note that it 

also uses acreage from the total crop acres convexity equation. 

The crop mix variables depict historical alternatives of which two contrived ones are 

shown. These make acreage available for each crop in the total crop mix by crop equations. 

These variables also make the sum of the acreage across all crops in the mix available in the total 

crop mix convexity equation. Collectively, the intersection of these constraints makes the only 

feasible cropping alternatives to have somewhere between 30% (30/100) and 25% (60/150) of 

the acreage devoted to crop 1 with the rest devoted to crop 2. 

In the more general model the crop mix constraints cover all of the crops excluding the 

biofuels which have not historically been produced. There are also almost 35 crop mix 

alternatives for each region and the data within the tableau are drawn from historical records and 

are in the file data_agcropmix.gms. 

Broadening our examination to cover both the total acreage and irrigated acreage crop 

mix restricutions that are imposed in FASOMGHG, note that the total acreage crop mix 

constraints imposes the crop mixes for the sum of dryland plus irrigated dryland acreage while 

the irrigated mix constraints only act on the irrigated crop production possibilities. 

More formally the equations in this tableau are 

• Tillage supply -- Limits the acreage of each tillage system in use within the cropping 

variables to the acreage produced by the tillage choice variables. Limits crop land use by 

tillage system on a subregional basis when subregions are defined. Cases within the 

AGTILLUSE GAMS implementation equations are represented by this tableau row. 

• Total acres crop mix by crop -- Balances the acreage by crop against the total acreage 

allowed by the crop mix possibilities. The constraint is defined for each relevant crop on 

a total careage by crop basis. The geographic basis is the same as the definition being 

used for crop production during each time period. Cases within the AGCRPMIXUP and

AGCRPMIXLO GAMS implementation equations are represented by this tableau row. 

• Crop mix convexity -- Forces a convex combination of the total acres covered of a crop 

in the mix. The geographic basis is the same as that used for crop production during a 

time period. Cases within the GAMS implementation equations AGCRPMIXTOT are 

represented by this tableau row. 
227 

• Irrigated acres crop mix by crop -- Balances acreage by crop against the total irrigated 

acreage allowed by the crop mix possibilities. The constraint is defined for each relevant 

crop on a total irrigated crop land use basis. The geographic basis is the same as is being 

used for crop production during a time period. Cases within the AGCRPMIXUP and

AGCRPMIXLO GAMS implementation equations are represented by this tableau row. 

• Irrigated acres crop mix convexity -- Forces a convex combination of the irrigated acres 

crop mix by crop. The geographic basis is the same as is being used for crop production 

during a time period. Cases within the GAMS implementation equations 

AGCRPMIXTOT are represented by this tableau row. 

The variables in this tableau are 

• Crop Production -- Crop production possibilities. They use tilled crop land and also 

require land that falls within the appropriate crop mix and crop mix convexity constraints. 

They are defined by crop, crop land quality type, irrigation/dryland choice, fertilization 

alternative, and tillage alternative. These variables are defined on a subregional or 

regional basis depending on time period. The AGCROPBUDGET GAMS 

implementation variables are represented by this tableau column. 

• Total acreage crop mix -- Choice across a set of historically observed crop mixes. They 

implicitly represent many omitted resource constraints and other considerations. The 

variables supply a proportion of the land suitable for each different type of crop and the 

total acres across all crops in the crop mix convexity equation. These variables are 

defined for a number of historical alternatives for total regional/subregional crop acreage. 

Geographically they are defined on a subregional or regional basis depending on time 

period. Cases within the AGMIXR GAMS implementation variables are represented by 

this tableau column. 

• Irrigated acreage crop mix -- Choice across a set of historically observed irrigated crop 

mixes. They implicitly represent many omitted resource constraints and other 

considerations. The variables supply a proportion of the land suitable for each different 

type of irrigated crop and the total irrigated acres across all crops into the crop mix 

convexity equation. These variables are defined for a number of historical alternatives for 

total regional/subregional irrigated crop acreage. Geographically they are defined on a 

subregional or regional basis depending on time period. Cases within the AGMIXR and 

AGMIXR2 GAMS implementation variables are represented by this tableau column. 
228 

Coefficients appearing within this tableau are purely illustrative and are actually drawn 

from the crop mix data in the GAMS file data_agcropmix.gms from 1970 to 2002. 

Table 8-13 Tableau illustrating crop mix modeling Crop prod. Crop 1 dryland Crop prod. Crop 1 irrigated Crop prod. Crop 2 dryland Crop prod. Crop 2 irrigated Total crop mix alternative 1 Total crop mix alternative 1 

Irrigated crop mix alternative 1 Irrigated crop mix alternative 1 

 

Tilled acres dryland 

Tilled acres irrigated +1 +1 < 0 

Total acres mix -- crop 1 +1 +1 -30 -60 = 0 

Total acres mix -- crop 2 +1 +1 -70 -90 = 0 

Convexity for total acres mix +1 +1 +1 +1 -100 -150 = 0 

Irrigated acres mix -- crop 1 +1 -20 -20 = 0 

Irrigated acres mix -- crop 2 +1 -20 -30 = 0 

Convexity for irrigated acres mix +1 +1 -40 -50 = 0 

8.3.2 Livestock production/Feed blending 

The other major agricultural production component involves livestock production and 

associated feed blending. Table 8-14 provides a simplified but somewhat comprehensive 

example of the livestock production and feed blending component again on a single period, 

single region basis. There we portray the basic livestock related agricultural resources of pasture, 

labor, and AUM grazing along with raw crop commodities and blended feeds. We also see 

multiple types of livestock being produced generating multiple products, some of which are 

intermediate products into further livestock production. For example, feeder pigs are produced as 

an intermediate input to a hog finishing operation. The tableau also contains examples of enteric 

fermentation alternatives for dairy and methane related manure management alternatives. 

Another feature illustrated in the model is livestock feed blending and use. The livestock 

production alternatives directly use primary crop commodities like corn and sorghum as feeds 

but also use blended feeds as illustrated in the case of egg grain feed. The feed blending process 
229 

is also shown using crop commodities. The tableau shows two alternative variables that each 

make egg layer blended grain feed which both incur some degree of costs and use different 

amounts of crop commodities to blend the homogeneous commodity egg layer grain feed. This 

reflects commodity substitution depending on the relative prices of the commodities used. 

The tableau also illustrates livestock production involvement in the GHG accounting 

balances. Livestock generate direct emissions related to factors such as fossil fuel usage but also 

have emissions related to enteric fermentation and manure while being involved with pasture 

land sequestration. The pasture land sequestration involves accounting of the cumulative 

sequestration on pasture land in use and idle pasture land. In terms of enteric fermentation, there 

are multiple production possibilities for selected livestock types that alter feed additives, feeding 

patterns and usage of pasture based on the alternatives discussed in Johnson et al. For manure 

management we use EPA data to represent alternative manure management systems and the 

potential of altering methane emissions for animals produced with wet manure handling systems 

- hogs and dairy. 

Resource usage patterns in the tableau illustrate several animal dependent FASOMGHG 

characteristics. In particular, while all livestock production systems can potentially use all 

resources, the data do not reflect this. For example, in the pasture land and AUM grazing cases 

only the more extensive operations are shown to use such. Similarly, the blended feeds are 

tailored to certain types of animals and are not used by others. Finally, things like enteric 

fermentation and manure management only apply to certain classes of animals. 

Now suppose we turn attention to a more formal definition of the tableau contents. The 

equations in the tableau are: 

• Welfare -- the welfare equation that is maximized as discussed above. The subcomponent 

regarding livestock includes usage of variable inputs by livestock production along with 

the costs of manure management, feed blending, and land transformations. The tableau 

also crudely shows the objective function contributions that occur in the product market, 

the costs of factor supply and the payments to net changes in the GHG accounts. The 

GAMS implementation equation WELFAR is represented by this tableau row. 

• Pasture land -- Balances the disposition of pasture land by fate and with the supply of 

pasture land from the initial endowment less the net effect of transformations from/to 

forests and crops. In terms of pasture land disposition, both the active use of pasture land 
230 

by livestock and idle pasture land are considered. This allows accounting for 

sequestration on both used and idled land. Geographically, this equation is defined for 

each time period on the same regional basis as is agricultural production across time 

periods. The GAMS implementation equation AGPASTLANDEXCHANGE is 

represented by this tableau row. 

• Pasture land in use -- Balances pasture land used by livestock with pasture land in use 

variables. This allows accounting for sequestration on pasture land whether it is idled or 

not. Geographically, this equation is defined on the same regional basis as is agricultural 

production. The GAMS implementation equation AGLANDPASTURE is represented by 

this tableau row. 

• Labor -- Balances labor used by livestock production with labor supply as will be 

discussed below. This equation is defined for 11 FASOMGHG regions for each time 

period. Cases within the GAMS implementation equation AGRESBALANCE are 

represented by this tableau row. 

• Grazing -- Balances AUM grazing used by livestock production variables with AUM 

grazing supply as discussed below. Geographically, this equation is defined on the same 

regional basis as is agricultural production. Cases within the GAMS implementation 

equation AGRESBALANCE are represented by this tableau row. 

• Commodity balance -- Balances usage against supply for the primary, secondary and 

blended feed commodities. The commodities covered include crops, livestock 

intermediate products (feeder pigs, calves, etc.), livestock final primary products (e.g. 

eggs, raw milk, fed hogs, cull sows), secondary products and blended feeds (egg layer 

grain feed). Only a simplified portrayal of the product market is present here that 

ordinarily would include processing, domestic consumption, imports, exports and 

international trade. The tableau shows how livestock activities can be involved in 

producing and using the commodity in an equation. For example, in the feeder pig 

commodity balance we see production of feeder pigs by the feeder pig production activity 

and their use in the hog finishing activity. This equation is defined for each of the 

FASOMGHG time periods and for each primary, secondary and blended feed commodity 

on a national or regional basis. Generally a regional basis is used for the crops used in 

feeding, blended feeds, and intermediate livestock products. The GAMS implementation 

equation AGPRODBAL is represented by this tableau row. 

• Head for manure management -- Limits the number of head that can be subject to 

improved manure management to the number of head produced under the production 

variables and the proportional share of wet manure management systems that could be 

improved. This equation is defined by animal type subject to wet manure management 
231 

(swine and dairy) and for multiple manure management system alteration possibilities 

based on applicable percentage of the herd. Geographically this equation is defined on the 

same regional basis as is agricultural production. The GAMS implementation equation 

AGMANUREMGT is represented by this tableau row. 

• Livestock mix -- Controls the regional distribution of livestock around the country. This 

will be elaborated on below. This equation is defined by type of animal on the same 

regional basis as is agricultural production. The GAMS implementation equation 

AGLIVESTOCKMIXNAT is represented by this tableau row. 

• Crop/forest land - Represents the cropping and forestry parts of the model as discussed 

under those sections in this and the previous chapter. 

• Maximum land to crop -- Limits the quantity of pasture land that can be transformed to 

crops based on land suitability. Again this constraint is defined for all time periods on the 

same geographical basis as is agricultural production. The GAMS implementation 

equation AGMAXPASTURETOCROP is represented by this tableau row. 

• GHG balance -- Adds cumulative GHG emissions, sequestration stock and biofuel related 

offsets then balances that sum against the GHG payments variable. This constraint is 

defined for various GHG accounts including the ones highlighted here. The livestock 

related ones involve enteric fermentation, manure management and pasture sequestration. 

For manure management this shows that the management alternatives offset the 

emissions from base levels where the net effect is their difference. The equation is 

defined for all explicit time periods in FASOMGHG on the same regional basis as is 

livestock production. Cases within the GHGACCOUNTS GAMS implementation 

equation are represented by this tableau row. 

The variables appearing in this tableau are 

• Livestock Production -- Livestock production possibilities. They use inputs as reflected 

within the objective function coefficient, pasture land, labor and AUM grazing while 

producing primary products like eggs, feeder pigs, and finished hogs. They also use some 

intermediate livestock products as inputs to higher order livestock production processes. 

Feeds including crop commodities and blended feeds are used along with, while not 

shown here, secondary products (like soybean meal). They also require that the animal 

distribution falls within the selected livestock mix, make animals available for improved 

manure management and enter the GHG balance. In the GHG balance equation, the 

livestock production variables enter various accounts including fossil fuel usage related 

emissions, enteric fermentation related emissions and manure emissions. They are 

defined by animal type, livestock management alternative, and enteric fermentation 
232 

alternative. These variables are defined on a subregional or regional basis depending on 

time period. The AGLVSTBUDGET GAMS implementation variables are represented by 

this tableau column. 

• Manure Management -- Employment of improved manure management systems. They 

incur cost in the objective function, require animals that can be treated, limit the number 

of animals treated by each system to a maximum and offset manure related emissions in 

the GHG balance. These variables are defined by type of animal and manure management 

system type. Geographically they are defined on a subregional or regional basis 

depending on time period. The AGLVSTMANURE GAMS implementation variables are 

represented by this tableau column. 

• Feed Blending -- Blending of livestock feeds via a number of different alternative 

formulas. Primary and secondary commodities are used according to the formula. The 

resultant feeds are supplied for livestock consumption. These variables are defined by 

feed and feed blending alternative. Geographically, they are defined on an 11 region basis 

by time period. Cases within the AGREGPROCESS GAMS implementation variables 

are represented by this tableau column. 

• Livestock Mix -- Choice between a set of historically observed livestock herd regional 

distributions by type of animal. They implicitly represent many omitted resource 

constraints and other considerations. These variables supply a proportion of the herd that 

appears in each region or subregion. These variables are defined by type of animal for 

each of a number of historical alternatives for livestock regional distributions. 

Geographically they are defined on the same basis as is livestock production. The 

AGNATMIX GAMS implementation variables are represented by this tableau column. 

• Use pasture -- Amount of pasture land used by livestock. These variables are equated 

with the use computed underneath the livestock production variables and fall into the 

pasture land sequestration GHG balance equations. The variables are defined for each of 

the FASOMGHG time periods and on the same regional basis as is agricultural 

production. The GAMS AGUSEPASTURE variables are represented by this tableau 

column. 

• Land to forest/crop land -- Land use change from pasture to crop land or forests. These 

variables withdraw from the pasture land equations and supply into the crop or forest land 

equations as discussed in the crop and forest modeling sections. Land movement to crop 

land is subject to a maximum suitability restriction and a transformation cost. GHG 

accounting entries remove sequestration from the pasture land account and if moving to 

crop land place sequestration into the crop land sequestration account. These variables 

are defined geographically on the same basis as is agricultural production by time period. 
233 

Cases within the AGPASTLNDUSECHG, LANDFROMAG and CONVRTFROMAG

GAMS implementation variables are represented by this tableau column. 

• Land from forest/crop land -- Land use change to pasture from crop or forest land. These 

variables reflect supply into the pasture land equations and withdrawal of land from the 

crop land or forest land equations as discussed in the crop land and forest modeling 

sections. GHG accounting entries place sequestration into the pasture land account and if 

moving from crop land remove sequestration from the crop land sequestration account. 

These variables are defined geographically on the same basis as it is agricultural 

production and by time period. Cases within the AGPASTLNDUSECHG, LANDTOAG

and CONVRTTOAG GAMS implementation variables are represented by this tableau 

column. 

• Idle pasture -- Amount of pasture land in the inventory that is idle. These variables are 

equated with pasture land available less the use by livestock activities and fall into the 

pasture land sequestration GHG balance equations. The variables are defined for each of 

the FASOMGHG time periods and on the same regional basis as is agricultural 

production. The GAMS AGIDLELANDPASTURE variables are represented by this 

tableau column 

• Resource Supply -- Supply of labor and AUM grazing. The variables reflect the cost of 

the supply in the objective function, a supply into the appropriate resource equation and 

the use of any applicable maximum. These variables are defined on a subregional or 

regional basis depending on time period and item being supplied. Cases within the 

AGRESSUPPLY and AGRESSEPSUPPLY GAMS implementation variables are 

represented by this tableau column. 

• Product market -- these variables represent the more general product market as discussed 

above and below. 

• GHG Payment -- Net GHG payments as discussed above. Cases within the 

AMOUNTGHGS GAMS implementation variables are represented by this tableau 

column. 

The coefficients appearing in this tableau are 

cl -- the costs of livestock production which is the sum of the variable inputs used times 

their prices plus any other cost factors 

cm -- the cost of alternative manure management systems 

cb -- the cost of feed blending including the cost of any commodities consumed that are 

not explicitly modeled 
234 

clt -- the cost of land transformation particularly those for transforming pasture land into 

crop land 

apast -- the initial availability of agricultural pasture land 

lu -- livestock usage of pasture land 

lb -- livestock usage of labor 

lg -- livestock usage of AUM grazing 

ldf -- livestock usage of primary crop commodities directly for feed usage 

bc -- feed blending usage of primary crop and while not shown here secondary processed 

commodities 

y -- the yield of primary commodity from production of a livestock alternative 

iu -- the intermediate usage of livestock primary commodities as inputs to higher order 

livestock production alternatives 

fu -- the usage of blended feed commodities as inputs to livestock production alternatives 

lm -- the proportional distribution of the livestock herd by region or subregion for this 

animal type and particular livestock herd distribution mix alternative. 

ee -- enteric fermentation emissions by animal 

me -- manure related emissions by animal under base manure management 

cm -- reduction in manure related emissions obtained when treating a given number of 

animals under a given manure management alternativemaxtran -- maximum 

regional amount of land that can be transferred from pasture land to crop land at 

the model initiation 

le -- other GHG emissions by animal 
235 

Table 8-14 Tableau illustrating livestock production and feed blending 

Produce eggs 

Produce feeder pigs 

Farrow to finish 

Finish hogs 

Cow calf 

Dairy base production 

Dairy with enteric 

Dairy manure manage 1 

Dairy manure manage 2 

Blend Egg grain diet 1 

Blend Egg grain diet 2 

Blend other feeds 

Livestock mix 

Use pasture 

Land into crops or forest 

Land from crops or forest 

Idle pasture 

Commodity Mkt 

Welfare -cl -cl -cl -cl -cl -cl -cl -cm -cm -cb -cb -cb -clt -clt + Pasture land +1 +1 -1 +1 Pasture land in use +lu +lu +lu -1 Labor +lb +lb +lb +lb +lb +lb +lb Grazing +lg +lg +lg Commodity balance – Corn +ldf +ldf +ldf +ldf +ldf +ldf +ldf +bc +bc +bc + Commodity balance – Sorghum +ldf +ldf +ldf +ldf +ldf +ldf +ldf +bc +bc +bc + Commodity balance – Eggs -y + Commodity balance -- Raw milk -y -y + Commodity balance – Calves -y Commodity balance -- Feeder pigs -y +iu Commodity balance - Finished hogs -y -y + Commodity balance - Cull sows -y -y + Commodity balance Egg protein mix +fu -1 Commodity balance Egg grain mix +fu -1 -1 Commodity bal Other blended feeds +fu +fu +fu +fu +fu +fu -1 Head for manure manag – dairy -1 -1 +1 +1 Livestock mix +1 +1 +1 +1 +1 +1 +1 -lm Crop/forest land -1 +1 Maximum land to crop -1 +1 GHG balance enteric +ee +ee +ee GHG balance manure +me +me +me +me +me +me +me -cm -cm GHG balance pasture sequestration +ps +ps GHG balance other +le +le +le +le +le +le +le 
236 

8.3.2.1 Livestock mixes 

An important FASOMGHG element involves the way that the livestock mixes influence 

the regional distribution of livestock production. Years ago experience with the ASM 

predecessor during Burton's Ph.D. thesis indicated that the model had difficulties with 

developing an appropriate interregional allocation of livestock. Cases were found where the 

model solution reflected production of all the hogs in the whole model in the state of Georgia. 

Subsequently, a livestock mix regional distribution approach was incorporated that required the 

livestock herd to be distributed across the country in a fashion consistent with the historic 

interregional herd distribution. Interregional distributions are included from the last 30+ years. 

Table 8-15 portrays the interrelationship between livestock production and the livestock 

mixes. The tableau illustrates two regions for two types of animals with two alternative mixes for 

each livestock type. Livestock production in a region requires that a mix be adopted that reflects 

production of that type of livestock in that region. Each livestock mix alternative implies 

particular interregional distribution of the herd. The mix contraint involves the sum of the 

animals across all regional alternatives for that animal type. This constraint implicitly considers 

omitted processing and production capacity constraints along with other factors which are behind 

the interregional livestock distribution. 

Now suppose we turn attention to a more formal definition of the tableau contents. The 

equations therein are: 

• Livestock resources -- Land, labor and AUM grazing resources faced by livestock 

production as discussed above. These equations are defined for the same geographic 

regions as are agricultural production. 

• Livestock mix -- Control the regional distribution of livestock around the country. This 

equation is defined by type of animal and time period on the same regional basis as is 

agricultural production. The GAMS implementation equation AGLIVESTOCKMIXNAT

is represented by this tableau row. 

The variables appearing in this tableau are 

• Livestock Production -- Livestock production possibilities. These use resources and 

require animal specific livestock mixes. They are defined by animal type, livestock 
237 

management alternative, and enteric fermentation alternative. These variables are defined 

on a subregional or regional basis depending on time period. The AGLVSTBUDGET

GAMS implementation variables are represented by this tableau column. 

• Livestock Mix -- Choice between a set of historically observed livestock herd regional 

distributions by type of animal and time period. They implicitly represent many omitted 

resource constraints and other considerations. These variables supply a proportion of the 

herd in each region or subregion. These variables are defined by type of animal for each 

of a number of historical alternatives for livestock regional distributions. Geographically 

they are defined on a subregional or regional basis depending on time period. The 

AGNATMIX GAMS implementation variables are represented by this tableau column. 

Coefficients appearing within this tableau are purely illustrative and are actually drawn 

from the livestock mix data from the GAMS file data_agnatmix.gms from 1970 to 2002. 

Table 8-15 Tableau illustrating livestock mix modeling Livestock prod. region 1 animal type 1 base Livestock prod. region 1 animal type 1 enteric Livestock prod. region 1 animal type 2 Livestock prod. region 2 animal type 1 base 

Livestock prod. region 2 animal type 1 enteric Livestock prod. region 2 animal type 2 Livestock mix alt animal type 1 alternative 1 Livestock mix alt animal type 1 alternative 2 Livestock mix alt animal type 1 alternative 1 Livestock mix alt animal type 1 alternative 2 

 

Livestock production resources region 1 + + + < + 

Livestock production resources region 2 + + + < + 

Livestock mix -- animal 1, region 1 +1 +1 -30 -60 = 0 

Livestock mix -- animal 1, region 2 +1 +1 -70 -90 = 0 

Livestock mix -- animal 1, region 1 +1 -20 -20 = 0 

Livestock mix -- animal 1, region 2 +1 -20 -30 = 0 

8.3.2.2 Dynamics 
238 

The livestock submodel has the same dynamic characteristics as does the crop model. 

Namely, livestock activity in each of the five year FASOMGHG periods is assumed to be 

repeated at the same annual level for each year in the five year period. There is no dependency 

between adjacent five year periods other than through land transfers. 

Land transfers are modeled with dynamic characteristics as discussed above relative to 

the agricultural cropping submodel. Namely, when pasture land is transferred to crop land in a 

particular time period that land is removed from pasture land use and made available for 

cropping not only in the time period of transfer, but also in all subsequent periods. Furthermore, 

when land transfers out of the single homogeneous category pasture land into the land quality 

differentiated crop land it is assumed to transfer in a distribution proportion to the way the 

different qualities of crop land were initially populated. In particular, if initially 25% of the land 

in a region fell into the wetland category then when land transfers into crop land the transferred 

pasture land acre will supply 25% of an acre into the wetland category along with 75% of an acre 

into the other three quality classes in appropriate proportions. 

Similar practices are also employed when land transfers from crop land into pasture land. 

Namely, when the model transfers an acre from crop land into pasture land it is removed in the 

time period of the transfer and all subsequent time periods. Furthermore, land is withdrawn from 

the various crop land land quality accounts in proportion to the initial proportional shares by land 

quality class. 

When pasture land transfers occur from and to forestry, the land flows come from and to 

the medium quality forest site index. Land moving in supplies pasture land in the current and all 

subsequent time periods and precludes reforestation of land in the PASTFOR and FORPAST 

forest land categories. When land transfers out from pasture land it goes into the balance for 

afforested land in the PASTFOR forest land category. Pasture land is also removed from the 

agricultural pasture land balance in the time period of transfer and all subsequent time periods. 

8.3.3 Processing and feed blending 

Agricultural processing and feed blending is modeled to reflect commodity substitution 

possibililities or to reflect demand for different product forms. In terms of substitution 

agriculture commodities are frequently substitutable as inputs to the production of other products 

or in blended feeds. For example, beet sugar is a perfect substitute for cane based sugar while 
239 

sorghum can be substituted for corn in feed blending. In terms of demand for different product 

forms, agricultural products are frequently processed into a mix of secondary products. For 

example, soybeans are crushed into soybean meal and soybean oil which face different markets. 

The set odf processing alternatives used was selected to reflect important processing substitution 

and demand form possibilities. 

Some of the processing alternatives are modeled on a regional basis some on a national 

basis. The processing alternatives represented on a national basis and the commodities they 

manufacture and use are listed in table 8-16 below. The regional processing alternatives are 

listed in table 8-17. 

Table 8-16 National processing alternatives and the commodities they involve 

FASOMGHG name for national 

processing alternative 

Secondary product 

manufactured 

Primary and secondary commodities 

used in manufacture 

makeAmCheese AmCheese Cream, SkimMilk 

makeOtCheese OtCheese Cream, SkimMilk 

makeHFCS HFCS CornStarch 

makeBeverages Beverages HFCS, RefSugar 

makeConfection Confection HFCS, RefSugar 

makeBaking Baking HFCS, RefSugar 

makeCanning Canning HFCS, RefSugar 

makeEthanol Ethanol CornStarch 

makeMktGasBlend MktGasBlend Ethanol 

makeSubGasBlend SubGasBlend Ethanol 

makeDextrose Dextrose CornStarch 

StockSteerCalftoFeed StockedCalf StockedSCalf 

StockHeiferCalftoFeed StockedCalf StockedHCalf 

StockSteerYearlingtoFeed StockedYearling StockedSYearl 

StockHeiferYearlingtoFeed StockedYearling StockedHYearl 

HeiferYearlingSlaughter NonFedSla StockedHYearl 

SteerYearlingSlaughter NonFedSla StockedSYearl 

NFSlatonF NonFedBeef NonFedSla 

FSlatofBe FedBeef FeedlotBeefSlaughter 

DClfToBeef SteerCalve DairyCalves 

CleanWool WoolClean Wool 

makeCSyrup CornSyrup CornStarch 

RefSugar1 CaneRefini Sugarcane 

RefSugar2 RefSugar Sugarbeet 

CaneRefine RefSugar CaneRefini 

HogToPork Pork HogsforSlaughter 

BroilChick Chicken Broilers 
240 

TurkeyProc Turkey Turkeys 

SowToPork Pork CullSow 

ButterPow NonFatDryM, Butter Milk 

FluidMlk1 FluidMilk, Cream Milk 

EvapoMilk EvapCondM Milk 

FluidMlk2 Cream, SkimMilk Milk 

IceCream1 IceCream Milk, Cream, NonFatDryM 

IceCream2 IceCream Milk, Cream, SkimMilk 

Cottage CottageChe Milk, Cream, SkimMilk 

Frozen-Pot FrozenPot Potatoes 

DeHydr-Pot DriedPot Potatoes 

CHIP-POT ChipPot Potatoes 

JuiceOrang OrangeJuic OrangeProc90box 

JuiceGrpft GrpfrtJuic GrpfrtProc85box 

Table 8-17 Regional non feed blending processing alternatives and the commodities they 

involve 

FASOMGHG name for 

regional non feed processing 

alternative 

Secondary product 

manufactured 

Primary and secondary 

commodities used in 

manufacture 

SoyCrush1 SoybeanMeal, SoybeanOil Soybeans 

WetMill 

GlutenFeed, CornStarch, 

CornOil Corn 

Gluttosbm SoybeanMeal GlutenFeed 

SwitchgrassToElec Tbtus SwitchGrass 

HybridpoplarToElec Tbtus HybrdPoplar 

WillowToElec Tbtus Willow 

SwitchgrassToEthanol Ethanol SwitchGrass 

HybridpoplarToEthanol Ethanol HybrdPoplar 

WillowToEthanol Ethanol Willow 

In addition livestock feed blending is embedded within the regional processing activities 

and involves the products, alternatives and inputs identified in Table 8-18. Details on this 

blending are presented in the section on livestock feeding above. 

Table 8-18 Regional feed blending processing alternatives and the feeds made plus 

commodities they involve 

FASOMGHG name for regional feed processing 

alternatives that blend this feed 

Blended feed 

product 

manufactured 

Primary and secondary 

commodities used in 

manufacture 

stkpromix0, stkpromix2 StockPro0 SoybeanMeal 

beefbases, beefalt1s, beefalt2s, beefalt3s, CatGrain0 Corn, SoftWhiteWheat, 
241 

beefalt4s, beefalt5s, beefalt6s, beefalt7s, 

beefbasew, beefalt1w, beefalt2w, beefalt3w, 

beefalt4w, beefalt5w, beefalt6w, beefalt7w, 

beefbaset, beefalt4t, beefalt5t, beefalt6t, beefalt7t, 

beefbased, beefalt1d, beefalt2d, beefalt3d, 

beefalt4d, beefalt5d, beefalt6d, beefalt7d 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

catpro1, catpro3 HighProtCa SoybeanMeal 

cowbases, cowalt1s, cowalt2s, cowalt3s, 

cowalt4s, cowalt5s, cowalt6s, cowalt7s, 

cowbasew, cowalt1w, cowalt2w, cowalt3w, 

cowalt4w, cowalt5w, cowalt6w, cowalt7w, 

cowbaset, cowalt4t, cowalt5t, cowalt6t, cowalt7t, 

cowbased, cowalt1d, cowalt2d, cowalt3d, 

cowalt4d, cowalt5d, cowalt6d, cowalt7d 

CowGrain0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

cowpromix0, cowpromix2 CowHiPro0 SoybeanMeal 

basemix1s, alt1mix1s, alt2mix1s, alt3mix1s, 

alt4mix1s, alt5mix1s, alt6mix1s, alt7mix1s, 

basemix1w, alt1mix1w, alt2mix1w, alt3mix1w, 

alt4mix1w, alt5mix1w, alt6mix1w, alt7mix1w, 

basemix1t, alt1mix1t, alt2mix1t, alt3mix1t, 

alt4mix1t, alt5mix1t, alt6mix1t, alt7mix1t, 

basemix1d, alt1mix1d, alt2mix1d, alt3mix1d, 

alt4mix1d, alt5mix1d, alt6mix1d, alt7mix1d 

FinGrain0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

finpromix0, finpromix6 FinProSwn0 SoybeanMeal 

hogbases, hogalt1s, hogalt2s, hogalt3s, hogalt4s, 

hogalt5s, hogalt6s, hogalt7s, hogbasew, 

hogalt1w, hogalt2w, hogalt3w, hogalt4w, 

hogalt5w, hogalt6w, hogalt7w, hogbaset, 

hogalt1t, hogalt2t, hogalt3t, hogalt4t, hogalt5t, 

hogalt6t, hogalt7t, hogbased, hogalt1d, hogalt2d, 

hogalt3d, hogalt4d, hogalt5d, hogalt6d, hogalt7d 

FarGrain0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

farpromix0, farpromix6 FarProSwn0 SoybeanMeal 

basemix2s, alt1mix2s, alt2mix2s, alt3mix2s, 

alt4mix2s, alt5mix2s, alt6mix2s, alt7mix2s, 

basemix2w, alt1mix2w, alt2mix2w, alt3mix2w, 

alt4mix2w, alt5mix2w, alt6mix2w, alt7mix2w, 

basemix2t, alt1mix2t, alt2mix2t, alt3mix2t, 

alt4mix2t, alt5mix2t, alt6mix2t, alt7mix2t, 

basemix2d, alt1mix2d, alt2mix2d, alt3mix2d, 

alt4mix2d, alt5mix2d, alt6mix2d, alt7mix2d 

FPGGrain0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

fdppromix0, fdppromix6 FPGProSwn0 SoybeanMeal 

dairybases, dairyalt1s, dairyalt2s, dairyalt3s, 

dairyalt4s, dairyalt5s, dairyalt6s, dairyalt7s, 

dairybasew, dairyalt1w, dairyalt2w, dairyalt3w, 

dairyalt4w, dairyalt5w, dairyalt6w, dairyalt7w, 

dairybaset, dairyalt1t, dairyalt2t, dairyalt3t, 

dairyalt4t, dairyalt5t, dairyalt6t, dairyalt7t, 

dairybased, dairyalt1d, dairyalt2d, dairyalt3d, 

dairyalt4d, dairyalt5d, dairyalt6d, dairyalt7d 

DairyCon0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

brobases, broalt1s, broalt2s, broalt3s, broalt4s, 

broalt5s, broalt6s, broalt7s, brobasew, broalt1w, 

broalt2w, broalt3w, broalt4w, broalt5w, broalt6w, 

BroilGrn0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 
242 

broalt7w, brobaset, broalt4t, broalt5t, brobased, 

broalt1d, broalt2d, broalt3d, broalt4d, broalt5d, 

broalt6d, broalt7d 

HardRedSpringWheat, 

Sorghum, Barley 

brlpromix0, brlpromix4 BroilPro0 SoybeanMeal 

polbases, polalt1s, polalt2s, polalt3s, polalt4s, 

polalt5s, polalt6s, polalt7s, polbasew, polalt1w, 

polalt2w, polalt3w, polalt4w, polalt5w, polalt6w, 

polalt7w, polbaset, polalt4t, polalt5t, polbased, 

polalt1d, polalt2d, polalt3d, polalt4d, polalt5d, 

polalt6d, polalt7d 

TurkeyGrn0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

trkpromix0, trkpromix4 TurkeyPro0 SoybeanMeal 

eggbases, eggalt1s, eggalt2s, eggalt3s, eggalt4s, 

eggalt5s, eggalt6s, eggalt7s, eggbasew, eggalt1w, 

eggalt2w, eggalt3w, eggalt4w, eggalt5w, 

eggalt6w, eggalt7w, eggbaset, eggalt4t, eggalt5t, 

eggbased, eggalt1d, eggalt2d, eggalt3d, eggalt4d, 

eggalt5d, eggalt6d, eggalt7d 

EggGrain0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

eggpromix0, eggpromix5 EggPro0 SoybeanMeal 

bases, alt1s, alt2s, alt3s, alt4s, alt5s, alt6s, alt7s, 

basew, alt1w, alt2w, alt3w, alt4w, alt5w, alt6w, 

alt7w, baset, alt1t, alt2t, alt3t, alt4t, alt5t, alt6t, 

alt7t, based, alt1d, alt2d, alt3d, alt4d, alt5d, alt6d, 

alt7d 

SheepGrn0 Corn, SoftWhiteWheat, 

HardRedWinterWheat, 

DurhamWheat, 

HardRedSpringWheat, 

Sorghum, Barley 

shppromix0, shppromix2 SheepPro0 SoybeanMeal 

Processing activity modeling in FASOMGHG is relatively simplistic largely concentrating 

on: 

• Primary and secondary commodity usage, 

• Secondary or blended feed commodity yield and 

• All other costs. 

Thus, for example, in portraying soybean crushing the FASOMGHG processing activity 

uses one unit of soybeans and generates a given number of pounds of soybean meal and tons of 

soybean oil at a cost. The cost is usually the observed price differential between the value of the 

outputs and the value of the inputs according to Agricultural Statistics. The tableau in table 8-19 

portrays elements of processing: 
243 

Table 8-19 Tableau illustrating processing Wet mill corns Crush soybeans First stage cane refinancing Cane sugar to sugar Refine sugar beets 

Make fluid milk Slaughter fed beef Make HFCS Make confectionaries with sugar Make confectionaries with HFCS Substitute gluten feed for soy meal Commodity Mkt 

 

Welfare -c -c -c -c -c -c -c -c -c -c -c + 

Commodity balance -- Corn +ci + ≤ 0 

Commodity balance -- Soybeans +ci + ≤ 0 

Commodity balance -- Sugarcane +ci + ≤ 0 

Commodity balance -- Sugar beets +ci + ≤ 0 

Commodity balance -- Feedlot beef +ci + ≤ 0 

Commodity balance -- Raw milk +ci + ≤ 0 

Commodity balance -- Soybean meal -cy -cy + ≤ 0 

Commodity balance -- Soybean oil -cy + ≤ 0 

Commodity balance -- Refined cane -cy +ci + ≤ 0 

Commodity balance -- Refined sugar -cy -cy +ci + ≤ 0 

Commodity balance -- Fluid milk -cy + ≤ 0 

Commodity balance -- Cream -cy + ≤ 0 

Commodity balance -- Corn starch -cy +ci + ≤ 0 

Commodity balance -- Gluten feed -cy +ci + ≤ 0 

Commodity balance -- Corn oil -cy + ≤ 0 

Commodity balance -- HFCS -cy +ci + ≤ 0 

Commodity balance -- Fed beef -cy + ≤ 0 

Commodity balance -- Confectionaries -cy -cy + ≤ 0 

where the equations depicted are 

• Welfare -- the welfare objective function that is maximized as discussed above. In this 

function the processing cost terms vary with product created, along with primary and 

secondary commodity usage. The GAMS implementation equation WELFAR is 

represented by this tableau row. 

• Commodity balance -- Balances usage against supply for the primary, secondary and 

blended feed commodities. The commodities depicted in the tableau include 

• primary commodities from crops (corn, soybeans), and livestock (feedlot beef, raw 

milk) 

• secondary products created by processing (soybean meal through soybean crushing or 

confectionaries throuch use of sweetners) 
244 

Only a portion of the variables appearing within these equations are portrayed here as for 

example the product market that ordinarily would include processing, domestic 

consumption, imports, exports and international trade. The tableau shows how livestock 

activities can be involved in producing and using the commodity in an equation. This 

equation is defined for each time periods and for each primary, secondary and blended 

feed commodity on a national or regional basis. Generally a regional basis is used for the 

crops used in feeding, blended feeds, and intermediate livestock products. The GAMS 

implementation equation AGPRODBAL is represented by this tableau row. 

The variables in this tableau are 

• Processing -- Amount of agricultural processing activity. Such activity transforms 

primary commodities into secondary commodities. The variables reflect processing cost 

in the objective function, use of primary and some secondary products as inputs to the 

production process and eventual creation of processed secondary products. These 

variables are defined by processing alternative and on either an 11 region or a national 

basis depending on the secondary commodity being manufactured. The AGPROCESS 

and cases within the AGREGPROCESS GAMS implementation variables are 

represented by this tableau column. 

• Commodity market -- Supply and consumption markets for the commodities. 

The terms in this tableau are 

• c -- the per unit costs of agricultural processing 

• ci -- the per unit usage of commodities by agricultural processing 

• cy -- the per unit yield of secondary commodities by agricultural processing 

Generally the processing activities reflect the usage of primary and some intermediate 

secondary commodities as inputs to the production of other secondary commodities. For 

example, in the tableau we see processing alternatives that involve 

• Usage of primary commodities (though the rows for corn through raw milk) and resultant 

conversion into some mixture of secondary commodities (i.e., soybeans to soybean meal 

and oil). 

• Usage of a single primary commodity and its transformation through use of the fixed 

coefficient into a related to secondary commodity (i.e., the tableau illustrates conversion 

of beef on the hoof to carcass beef and conversion of sugar cane to raw cane sugar). 

Incorporation of this type of processing allows us to represent production of the raw 
245 

commodities at farm gate prices and then consumption of processed commodities in 

common units like carcass weight of pork, fed beef, chicken or turkey. 

• Use of secondary commodities to create other secondary commodities like the use of 

cornstarch to create HFCS. 

• Use of more than one possible mixture of input commodities to create the same final 

secondary commodity. For example the tableau illustrates manufacture of confectionaries 

using HFCS or refined sugar as a sweetener 

The processing activities are also used to implement the regional feed blends as listed in 

the table above and the livestock production section. 

8.3.4 Factor markets 

Three fundamental approaches are taken to agricultural factor market modeling. Each 

approach applies to different types of factors. These approaches and the markets to which they 

apply are 

• Land modeling of crop and pasture land 

• Water, AUM grazing and labor factor supply that includes explicit factor supply curves 

• Purchased inputs that are assumed made available according to an infinitely elastic, fixed 

price, supply curve 

Each will be discussed separately 

8.3.4.1 Land modeling of crop and pasture land 

The land markets have been discussed above and will be more extensively discussed in 

the chapter on intersectoral land and commodity movements below. The only statement we will 

make here is that these land markets are subject to a fixed total availability of land but with the 

possibilities of land use change between crop, pasture and forest usages. Developed usage also 

constitutes an added demand. 

8.3.4.2 Water, AUM grazing and labor which have explicit factor supply curves 

Explicit supply curves are present for irrigation water, AUM grazing and labor. The 

supply curves have two components 

• A component of factor supply at a fixed price up to a maximum availability 

• A component of factor supply according to an upward sloping supply curve 

Table 8-20 shows an overview of this availability while details regarding the individual markets 

for irrigation water, AUM grazing and labor are discussed in sections just below. 
246 

The equations in this tableau are 

• Welfare - Adds up the quantity that is maximized when the FASOMGHG programming 

model is solved. The quantity added up consists of the area underneath the product 

demand curves arising from consumption less the areas under the import supply curves 

along with the area under the labor, water and AUMs factor supplies. The factor supply 

related objective function terms reflect the two factor supply components. The first 

involves price times quantity for the fixed price factor supplies. The second consists of 

the area underneath the upward sloping factor supply for that factor. In addition price 

times quantity is subtracted for a set of other agricultural inputs used within crop, 

livestock, and processed product production. We also add in net GHG payments. The 

WELFAR GAMS implementation equation is represented by this tableau row. 

• Crop land -- Limits crop land usage to that available. The land use is limited to the initial 

agricultural endowment of crop land adjusted for transformations to and from pasture 

land and transformations to and from forest land as discussed above. This is defined on a 

subregional basis when subregions are defined across tillage systems. Cases within the 

AGTILLSTART, AGTILLUSE and AGCANCHANGETILL GAMS implementation 

equations are represented by this tableau row. 

• Pasture Land -- Limits pasture land usage to that available. The availability is the initial 

amount of agricultural pasture land adjusted for transformations to and from crop land 

and transformations to and from forest land. This land is used by the livestock production 

variables. Limits pasture land use on a subregional basis when subregions are defined. 

Cases within the AGPASTLANDEXCHANGE and AGLANDPASTURE GAMS 

implementation equations are represented by this tableau row. 

• AUM Grazing -- Limits the usage of grazing land to that made available on an animal 

unit month (AUM) basis. AUMs are used by livestock production. Supply comes from a 

mixture of public fixed price supply and private upward sloping supply. This is defined 

on a subregional basis when subregions are defined. Cases within the AGRESBALANCE

GAMS implementation equations are represented by this tableau row. 

• Max fixed price AUMs -- Limits the maximum availability of fixed price AUM grazing. 

Limits use on a subregional basis when subregions are defined. Cases within the 

AGRESMAX GAMS implementation equations are represented by this tableau row. 

• Water -- Limits irrigation water use to that available. Irrigation water is used by crop 

production. The water available comes from a mixture of fixed price water (from BLM 

and other sources) that available up to a maximum quantity and an upward sloping supply 

curve component representing pumped water from ground and private surface water 

sources. Limits use on a subregional basis when subregions are defined. Cases within the 

AGRESBALANCE implementation equations are represented by this tableau row. 
247 

• Fixed Water -- Limits the amount of fixed price water to a maximum quantity. Limits 

fixed water availability on a subregional basis when subregions are defined. Cases within 

the AGRESMAX GAMS implementation equations are represented by this tableau row. 

• Labor -- Limits labor used to that available. Labor is used by the crop and livestock 

production. Labor available comes from both fixed price family labor that is available up 

to a maximum quantity and an upward sloping supply curve component of hired labor. 

Limits use an an 11 FASOMGHG region basis. Cases within the AGRESBALANCE

GAMS implementation equations are represented by this tableau row. 

• Family Labor -- Limits maximum availability of fixed price family labor. The constraint 

limits family labor availability on an 11 FASOMGHG region basis. Cases within the 

AGRESMAX GAMS implementation equations are represented by this tableau row. 

• Primary Products -- Balances primary product usage so it cannot exceed primary product 

availability. Primary product usage arises through the combined effects of processing 

usage, feed blending usage, direct feed usage by livestock, domestic consumption, 

exports through the excess demand formulation and international trade. Availability 

comes from crop and livestock production plus imports either from the excess supply 

formulation or the explicit international trade component. This constraint is defined on 

either an 11 region or a national basis depending on the commodity. Cases within the 

AGPRODBAL GAMS implementation equations are represented by this tableau row. 

• Secondary Products -- Balances processed product usage so it cannot exceed availability. 

Processed product usage arises through processing, feed blending, direct feeding to 

livestock, domestic consumption, or exports. This constraint is defined on either an 11 

region or national basis depending on the commodity. Cases within the AGPRODBAL

GAMS implementation equations are represented by this tableau row. 

• National inputs -- Balances national input usage for inputs that are assumed infinitely 

available at fixed price with supply. National input usage arises through the combined 

effects of crop, livestock and processed product production. The constraint is defined on 

a national basis and is generally not included in the model but rather collapsed into the 

objective function unless a maximum national input limit is specified. Cases within either 

the WELFAR or AGPROCESSMAXPURCHINPUT GAMS implementation equations 

are represented by this tableau row 

The variables within this tableau are 

• Crop Production -- Crop production possibilities. They use inputs that are infinite elastic 

in supply as reflected within the objective function coefficient while also using crop land, 

irrigation water, and labor. They produce primary crop products. These variables are 

defined on a subregional or regional basis depending on time period. The 

AGCROPBUDGET implementation variables are represented by this tableau column. 
248 

• Livestock Production -- Livestock production possibilities. They use inputs that are 

infinite elastic in supply as reflected within the objective function coefficient while using 

AUM grazing, pasture land, and labor. The produce primary livestock products. They 

also use some primary and secondary products directly as feed or intermediate animal 

inputs and use blended feeds. These variables are defined on a subregional or regional 

basis depending on time period. The AGLVSTBUDGET GAMS implementation 

variables are represented by this tableau column. 

• Fixed price Water Supply -- Supply of irrigation water that is fixed in price. That water is 

assumed to be available at the fixed price up to a maximum quantity and largely reflects 

the surface water supplied by the government like that from the BLM. The variables 

reflect the fixed price of such supply in the objective function and supply into the water 

equation. They are subject to maximum availability. These variables are defined on a 

subregional or regional basis depending on time period. Cases within the 

AGRESSUPPLY implementation variables are represented by this tableau column. 

• Upward sloping water supply -- Supply of irrigation water from an upward sloping 

supply curve. That water largely reflects private surface water and pumped ground water. 

The variables reflect the negative of the area under the supply curve in the objective 

function and supply into the water equation. They are subject to maximum availability. 

These variables are defined on a subregional or regional basis depending on time period. 

Cases within the AGRESSUPPLY implementation variables are represented by this 

tableau column. 

• Fixed price AUM grazing supply -- Supply of AUM grazing that is fixed in price. This 

AUM grazing is assumed to be available at a fixed price up to a maximum quantity and 

largely reflects the AUM grazing supplied by the government through grazing fees. The 

variables reflect the fixed price of the supply in the objective function and a supply into 

the AUM grazing equation. They are subject to a maximum availability. These variables 

are defined on a subregional or regional basis depending on time period. Cases within the 

AGRESSUPPLY implementation variables are represented by this tableau column. 

• Upward sloping AUM grazing supply -- Supply of AUM grazing from an upward sloping 

supply curve. That water largely reflects private market AUMs. The variables reflect the 

area under the supply curve in the objective function and a supply into the AUM grazing 

equation. They are subject to a maximum availability. These variables are defined on a 

subregional or regional basis depending on time period. Cases within the 

AGRESSUPPLY implementation variables are represented by this tableau column. 

• Processing -- Amount of processing activity. The variables reflect the cost of processing 

in the objective function, the use of primary and some secondary products as inputs to the 

production process and the eventual creation of processed secondary products. These 

variables are defined by processing alternative and geographically are defined on either 
249 

an 11 region or a national basis depending on the commodity being manufactured. The 

AGPROCESS and cases within the AGREGPROCESS GAMS implementation variables 

are represented by this tableau column. 

• Family Labor Supply -- Supply of labor from family sources. The family labor is 

assumed to be available at a fixed reservation wage to up to a maximum quantity. The 

variables reflect the reservation wage as a cost of the supply in the objective function, a 

supply into the labor balance equation and use against the applicable maximum. These 

variables are defined on an 11 region basis reflecting pooled regional labor markets. 

Cases within the AGRESSUPPLY implementation variables are represented 

• Hired Labor Supply -- Supply of labor from hired sources. Hired labor is supplied 

according to a supply function. The variables reflect the area under the supply curve in 

the objective function and a supply into the labor balance equation. These variables are 

defined on an 11 region basis reflecting pooled regional labor markets. Cases within the 

AGRESSUPPLY GAMS implementation variables are represented by this column. 

• National input supply -- Supply of fixed price national inputs on a national basis. These 

inputs are assumed to be infinitely available at a fixed price. They are balanced against 

the usage of these national inputs in crop, livestock and processed product production. 

The portrayal in the tableau is purely conceptual as these items are calculated into the 

objective function cost terms for the production and processing variables 

• Commodity Market -- this tableau column represents the more general commodity 

market including domestic consumption, exports and imports. 

The coefficients in the model are 

• cc -- the per acre cost of crop production which is the sum of the cost of using fixed price 

inputs 

• lc -- the per head cost of livestock production which is the sum of the cost of using fixed 

price inputs 

• wf - the per unit to price of the fixed price water supply 

• wi - the area under the upward sloping water supply curve 

• ac - the per unit price for the fixed price AUM supply 

• ai - the area under the AUM supply curves 

• cp - the per unit cost of processing 

• lw - the reservation wage for family labor 

• li - the area under the hired labor supply curve 

• cw - the use of irrigation water by crops 

• Fpw - maximum availability of fixed price water 

• lg - the AUM grazing land requirement per head of livestock 
250 

• Fpa - maximum availability of fixed price AUMs 

• clb - the use of labor per acre of crop production 

• alb - the use of labor per head of livestock production 

• fpl - maximum availability of fixed price labor 

• cy - the primary product production per acre of crop production 

• lny - accounts on a per head of livestock basis for the primary product production and the 

primary products (crops directly fed) consumed directly in livestock production 

• pp - use of primary products per unit of processing 

• ps -- accounts on a per unit of processing basis for the secondary yield from processing 

• ci -- usage of national inputs per acre of crop production 

• li -- usage of national inputs per head of livestock production 

• pi -- usage of national inputs per unit of processing 

Components of this tableau merit explanation as discussed below. 
251 

Table 8-20 Tableau illustrating factor supply 

Crop production -- subregion 1 

Livestock production -- subregion 1 

Fixed price water -- subregion 1 

Supply curve water -- subregion 1 

Fixed price AUMS -- subregion 1 

Supply curve AUMS -- subregion 1 

Crop production -- subregion 2 

Livestock production -- subregion 2 

Fixed price water -- subregion 2 

Supply curve water -- subregion 2 

Fixed price AUMS -- subregion 2 

Supply curve AUMS -- subregion 2 

Processing -- FASOMGHG region 

Family labor -- FASOMGHG region 

Supply curve labor -- FAS region National input supply 

Commodity Mkt 

Welfare -cc -lc -cp -wf -wi -ac -ai -cc -lc -cp -wf -wi -ac -ai -cp -lw -li -1 + Crop land - subregion 1 +1 < Pasture land - subregion 1 +li < Water - subregion 1 +cw -1 -1 < Max fixed price water -- subregion 1 +1 < AUM grazing - subregion 1 +lg -1 -1 < Max fixed price AUMs -- subregion 1 +1 < Crop land - subregion 2 +cl < Pasture land - subregion 2 +li < Water - subregion 2 +cw -1 -1 < Max fixed price water -- subregion 2 +1 < AUM grazing - subregion 2 +lg -1 -1 -1 < Max fixed price AUMs -- subregion 2 +1 < Labor -- FASOMGHG region +clb +alb +clb +alb -1 -1 < Max family labor -- FASOMGHG regi +1 < Primary Commodities -- FAS. region -cy -lny -cy -lny +pp + < Secondary Commodities -- FAS. region +ls +ls -ps + < National inputs +ci +li +ci +li +pi -1 + < 
252 

8.3.4.2.1 Irrigation water supply 

In the irrigation water market, the fixed price component represents water available at a 

fixed price generally up to a maximum availability. That fixed price water depicts that made 

available largely through governmentally owned and distributed water that exists in the western 

US. The upward sloping supply curve component reflects the availability of privately traded 

surface and ground water where increasing use across that market causes increased pumping 

costs and water prices. 

These variables are defined by agricultural region and make water available that is a 

available for any irrigation use in the region. They enter the objective function reflecting cost or 

the area underneath the supply curve. The fixed price water use also enters the row imposing 

maximum availability. GHG accounting associated with irrigation water pumping is not modeled 

in association with these variables, rather it is included in association with crop production. 

8.3.4.2.2 AUM grazing supply 

In the AUM grazing market, the fixed price component represents AUM grazing 

available at a fixed price generally up to a maximum availability. Such grazing represents that 

made available largely through grazing fees on governmentally owned lands in the western US. 

The upward sloping supply curve component reflects the availability of privately traded AUM 

grazing where increasing use increases AUM grazing rental rates. 

These variables are defined by agricultural region and make AUM grazing available that 

is available for any AUM grazing use by livestock in the region. They enter the objective 

function reflecting the fixed per unit cost or the area underneath the supply curve. They also 

potentially enter the row imposing maximum availability. 

8.3.5 Labor supply 

In the labor market, the fixed price component is designed to represent family labor 

available at a fixed reservation wage below which the family will not work. This reservation 

wage is generally set at one half the prevailing hired labor rate. Family labor is assumed to be 

available at this reservation wage up to a maximum availability. The upward sloping supply 

curve component reflects the availability of hired labor where increasing use across the market 

leads to higher wages. 
253 

These variables are defined at the level of the 11 FASOMGHG market regions and make 

labor available across all subregions in each market region. That labor is assumed to be available 

for any and all production related agricultural labor use in the region. 

The variables enter the objective function reflecting the reservation wage or the area 

underneath the hired labor supply curve. They also potentially enter the row imposing maximum 

availability. 

8.3.5.1 Purchased input supply 

Numerous inputs are made available at a fixed price. Potentially these could be subject to 

a maximum availability constraint but none are currently so constrained. These include fossil 

fuels, fertilizer, capital, sutom operations and a number of other categories as listed in the file in 

data_aginputname.gms. 

These variables are defined on a national basis in the units of dollars spent and make the 

input available for usage anywhere across the nation. They enter the objective function reflecting 

cost and are generally computed into objective function coefficients for the production activities. 

They also potentially enter a row imposing maximum availability. GHG accounting associated 

with fertilizer and fossil fuel use is modeled in association with crop and livestock production. 

8.3.6 Commodity consumption and markets 

An overview of the commodity market model structure is presented in table 8-21. That 

tableau portrays the sources of market supply and demand. These include 

• Domestic supply from production 

• Domestic interregional transportation 

• International transportation 

• Domestic demand 

• Exports 

• Imports 

• Processing utilization and production 

Commodities are sometimes subject to regional markets and are always subject to a 

national market. The tableau shows one case of each. For a commodity subject to a regional 

market, supply arises from production in subregions contained within that region, yields from 

processing and incoming transport from other regions as well as incoming transport from other 

countries (if the commodity is subject to a spatially explicit transportation trade representation). 
254 

Sources of regional demand include outgoing transport to other US regions, processing, outgoing 

transport to foreign countries (again if the spatially explicit trade modeling is present for the 

commodity) and transfer to the national market. 

At the national market level for the regionalized commodities the supply is that 

transferred in from the regions. On the other hand for commodities without regional markets 

supply arises directly from the production variables. Under either case at the national level we 

see national demand, export demand and import supply as defined by excess supply and demand 

equations along with usage by national level processing. More about the explicit international 

trade model appears in the next section. 

The equations in this tableau are: 

• Welfare -- the consumers' and producers' surplus objective function that is maximized. In 

terms of the commodity market features, this incorporates the areas under the domestic 

and export demand functions less the areas under the import supply and foreign country 

supply curves. Transport costs are also sutracted. Many other terms like production and 

processing costs are also included. The GAMS implementation equation WELFAR is 

represented in this tableau row. 

• Commodity balance -- Balances regionalized commodities in the US regions. These 

balances balance usage of commodities controlled on a regional basis (as listed above) 

with supply. Namely usage by processing, trade with other US regions, trade to other 

countries, direct use by production (not shown here but discussed in the livestock section 

above) and transfer to the national market does not exceed regional production, regional 

processing yield and incoming domestic/international transport. The constraint is defined 

at the FASOMGHG 11 region level. Cases within the AGPRODBAL GAMS 

implementation equations are represented by this tableau row. 

• Commodity balance -- National balances for regionalized commodities. These insure that 

consumption of commodities controlled on a regional basis (as listed above) balances 

against national demand. At the national level the source of supply is incoming 

movements from regions as well as imports when imports of this commodity are 

represented as if the total US faced a single excess supply equation for imports. National 

demand consists of domestic demand and export demand when exports are not spatially 

explicit. The constraint is defined for all of those commodities that are depicted on a 

regional basis. Cases within the AGPRODBAL GAMS implementation equations are 

represented by this tableau row. 

• Commodity balance -- Balances spatially explicitly traded commodities in foreign 

countries. These balances insure that usage of commodities subject to spatially explicit 

international trade modeling (as listed above) balance at the foreign country/region level. 
255 

Namely, demand from consumption in the foreign country, trade to US regions, trade to 

other foreign countries (not exquisitely shown here), is constrained so it does not exceed 

supply coming from the country excess supply equation, incoming shipments from the 

US and incoming shipments from other foreign countries. The constraint is defined for 

those commodities that are subject to spatially explicit trade modeling at the 

FASOMGHG 27 foreign country/region level. Cases within the AGPRODBAL GAMS 

implementation equations are represented by this tableau row. 

• Commodity balance -- National balance for national commodities. These balances insure 

that usage of commodities controlled on a national basis (as listed above) balance against 

demand. The source of supply is regional production and processing yields, plus possible 

imports from the total US faced excess supply equation for imports. National demand 

consists of domestic demand, use of inputs by processing and export demand from an 

explicit rest of world excess demand equation. The constraint is defined for all 

commodities depicted on a national basis. Cases within the AGPRODBAL GAMS 

implementation equations are represented by this tableau row. 

The variables depicted in this tableau are 

• Production -- All crop and livestock production. These variables produce and possibly 

use commodities while incurring costs in the objective function. The commodities 

produced are either placed in the regional or national balances depending upon whether 

or not the commodity market is regionalized. The individual components are discussed in 

crop and livestock sections above. 

• Transport of commodity to other US regions -- Flow of commodities between US 

regions. These are only defined for commodities subject to regional market modeling. 

These variables have a per unit transport cost in the objective function and reflect 

commodity usage from the region of origin plusa supply into the region of destination. 

Movement is modeled between the 11 FASOMGHG regions for each regionalized 

commodity. Cases within the GAMS implementation variable AGTRADE are depicted 

by this tableau column. 

• Transport of regional commodities to and from foreign countries -- Flow of commodities 

between US regions and foreign countries/regions. They are only defined for 

commodities that are subject to spatially explicit international trade modeling. These 

variables have per unit transport cost in the objective function and reflect a usage of the 

commodity in the US or foreign region where the shipment originates plus a supply into 

the destination region. This international trade is modeled between the 11 FASOMGHG 

regions and 27 foreign countries/regions. Cases within the GAMS implementation 

variable AGTRADE are depicted by this tableau column. 

• Regional processing -- Regional processing amounts across the 11 FASOMGHG regions. 

These variables have per unit processing costs in the objective function and reflect usage 
256 

of primary/secondary commodities as well as a supply of secondary commodities into the 

regional or national balances depending on the regionalization of the subject 

commodities. Cases within the GAMS implementation variable AGREGPROCESS are 

defined by this tableau column 

• Regional commodity to national market -- Movement of commodities from the 11 

FASOMGHG regions to the national market. These variables have an objective function 

coefficient that equals per unit observed regional to national price differentials.They 

reflect withdrawal from the regional commodity balance and addition into the national 

balance. These variables are defined for movements from the 11 FASOMGHG regions 

for the regionalized commodities. Cases within the GAMS implementation variable 

AGTRANSPRIM are defined by this tableau column 

• Domestic demand -- Demand for national and regionalized commodities. National market 

demand for all commodities whether they be regionalized or nationalized. These 

variables have the area underneath the demand curve in the objective function and reflect 

usage of primary/secondary commodities from the national balance. These variables are 

defined for all commodities with domestic demand curves. Cases within the GAMS 

implementation variable AGDEMAND are defined by this tableau column 

• Export demand -- Exports of commodities without explicit spatial trade modeling. Export 

market demand for all commodities that are modeled such that the US faces an aggregate 

rest of world excess demand equation. These variables have the area underneath the rest 

of world excess demand curve in the objective function and reflect usage of commodities 

from the US national balance. These variables are defined all the commodities for which 

explicit excess demand curves are defined. Cases within the GAMS implementation 

variable AGDEMAND are defined by this tableau column. 

• Import supply -- Imports of commodities without explicit spatial trade modeling. Import 

market supply for all commodities that are modeled such that the US faces an aggregate 

rest of world excess supply equation. These variables subtract the area underneath the rest 

of world excess supply curve in the objective function and reflect supply of 

primary/secondary commodities into the national balance. These variables are defined all 

the commodities for which explicit excess supply curves are defined. Cases within the 

GAMS implementation variable AGSUPPLY are defined by this tableau column 

• Processing -- Levels of processing for alternatives defined on a national basis. These 

variables have per unit processing costs in the objective function and reflect usage of 

primary/secondary commodities as well as supply of secondary commodities into the 

national balances. These variables are defined for the relevant processing alternatives. 

Cases within the GAMS implementation variable AGPROCESS are defined by this 

tableau column. 
257 

• Foreign country demand -- Foreign country level demand for commodities with explicit 

spatial trade. These variables have the area underneath the country level excess demand 

curve in the objective function and reflect use of commodities from the country level 

balance. These variables are defined all the commodities subject to spatially explicit 

international trade modeling for the countries with excess demand curves. Cases within 

the GAMS implementation variable AGDEMAND are defined by this tableau column 

• Foreign country supply -- Foreign country level supply for commodities with explicit 

spatial trade. These variables subtract the area underneath the country level excess supply 

curve in the objective function and reflect supply of thes commodities into the country 

level balance. These variables are defined all the commodities subject to spatially explicit 

international trade modeling for the countries with excess supply curves. Cases within the 

GAMS implementation variable AGSUPPLY are defined by this tableau column 

The coefficients in these equations are 

c -- per unit cost of production 

tc -- per unit costs of domestic interregional transportation 

ti -- per unit cost of international transportation from US regions to foreign regions 

pc -- per unit processing costs 

pd -- per unit price differences between the prices in US regions and the US national 

price 

di - the area underneath the national domestic demand curve 

ei -- the area underneath the explicit rest of world export demand curve 

Ii -- the area underneath the explicit rest of world import supply 

xi - the area underneath the country specific excess demand curve 

si -- the area underneath the country specific excess supply curve 

y -- production of commodities 

+/- -- a symbol representing use and creation of commodities by processing 

Several characteristics merit discussion 

• Only selected commodities are modeled with regional markets, all are modeled with 

national markets. Only commodities subject to spatially explicit trade, livestock feeds and 

biofuel feedstocks are regionalized as listed above table 8-4 through 8-6. The rest of the 

commodities are nationalized. 

• Not all commodities are subject to national demand some are just produced and used as 

intermediate products. 

• More details on the spatially explicit international trade modeling appear in the next 

section. 

• Not all commodities are subject to international trade. Some are just limited to US 

exports but are not treated as commodities that can be imported when imports have not 

recently been observed. Others are subject only to imports but are not allowed to be 
258 

exported where US exports have not recently been observed. Yet others are only 

intermediate commodities are not traded at all. 
259 

Table 8-21 Tableau illustrating commodity markets 

Production regional commodity -- region 1 

Production national commodity -- region 1 

Transport regional commodity to region 2 

Transport t regional commodity o countries 

Transport regional commodity from countries 

Processing -- region 1 

Regional commodity to national market 

Production regional commodity -- region 2 

Production national commodity -- region 2 

Transport regional commodity to region 1 

Transport t regional commodity o countries 

Transport f regional commodity from countries 

Processing -- region 2 

Regional commodity to national market National demand for regional commodity National demand for national commodity National processing National exports National imports 

Welfare -c -c -tc -ti -ti -pc -pd -c -c -tc -ti -ti -pc -pd +di +di -pc +ei -ii Regional Commodity -- reg 1 -y +1 +1 -1 +/-r +1 -1 Regional Commodity -- reg 2 -1 -y +1 +1 -1 +/-r +1 Reg Commodity – foreign country -1 +1 -1 +1 Reg commodity National balance -1 -1 +1 +/- National commodity balance -y +/-n -y +/-n +1 +/- +1 -1 
260 

8.3.7 Spatial international trade and interaction with domestic regions 

Some commodities are modeled with spatially explicit international trade. Specifically 

spatial equilibrium submodels ala Takayama and Judge are incorporated for eight commodities -- 

hard red winter wheat, hard red spring wheat, durham wheat, soft white winter wheat, corn, 

sorghum, rice, and soybeans. These spatial equailibrium submodels depict movement of the 

subject commodities between the 11 FASOMGHG market regions and the 27 foreign 

countries/regions as named in table 3-7. Across these foreign countries/regions we have supply 

and demand curves for these commodities. Naturally not all regions are both suppliers and 

demanders. The tableau in Table 8-22 overviews the FASOMGHG spatial trade submodel 

features as they interact with the domestic market regions. 

The equations in this tableau are 

• Welfare -- The consumers' and producers' surplus objective function that is maximized. 

In terms of the spatial commodity market features, this function incorporates some purely 

domestic terms including the costs for domestic production, domestic interregional 

transport and movements from regions to the domestic national market along with the 

area underneath the domestic demand curves. The objective function also includes 

international terms accounting for transport cost from domestic to the international 

markets, the area underneath the international supply curves, the costs of moving from 

international regions to US regions, the costs of moving from international regions to 

other international regions and the area underneath the international demand curves. 

Domestic GHG payments are also included. The GAMS implementation equation 

WELFAR is represented in this tableau row. 

• Commodity balance- US regional -- Balances usage of commodities with supply on a US 

regional basis. Namely, as discussed above, usage through trade with other US regions, 

consumption in national markets, and exports to other countries, along with domestic 

usage through processing and feeding (not shown here but discussed in the livestock and 

processing sections above) does not exceed supply. Supply arises from regional 

production, incoming domestic interregional transport and incoming international 

transport. The constraint is defined for those commodities that are depicted with spatially 

explicit trade characteristics at the FASOMGHG 11 region level. Cases within the 

AGPRODBAL GAMS implementation equations are represented by this tableau row. 

• Commodity balance- National -- Balances usage of against demand at the national level. 

At the national level the source of supply is incoming movements from the regions. The 

constraint is defined for all commodities that are subject to regional modeling including 
261 

all spatially traded ones. Cases within the AGPRODBAL GAMS implementation 

equations are represented by this tableau row. 

• Commodity balance- Foreign countries -- Insures that commodities balance at the foreign 

country/region level. Demand from consumption in the foreign country, trade to US 

regions, plus trade to other foreign countries is constrained so it does not exceed supply 

coming from foreign country/region level supply curves, incoming shipments from US 

regions and incoming shipments from other foreign countries. The constraint is defined 

for those commodities that are subject to spatially explicit trade modeling at the 

FASOMGHG 27 foreign country/region level. Cases within the AGPRODBAL GAMS 

implementation equations are represented by this tableau row. 

• GHG balance -- Balances GHG payments with net emissions. The most notable thing 

about this constraint in the context of spatially explicit trade is the absence of any entries 

in association with the international supply and demand. FASOMGHG only models 

domestic GHG accounts. Cases within the GHGACCOUNTS GAMS implementation 

equations are represented by this tableau row. 

The variables depicted in this tableau are 

• Production -- Aggregate crop and livestock production. This component is extensively 

discussed in the crop and livestock submodel sections above. These variables produce 

commodities while incurring costs in the objective function. The commodities produced 

that are subject to this spatially explicit trade modeling are always placed in regional 

balances. 

• Transport of commodity to other US regions -- Flow of commodities between US 

regions. These variables incur transport cost in the objective function and reflect 

commodity usage in the region where the shipment originates plus supply into the 

destination region. Movement is modeled between the 11 FASOMGHG regions. Cases 

within the implementation variable AGTRADE are depicted by this tableau column. 

• Transport of commodities from US regions to foreign countries -- Flow of commodities 

from US regions into importing foreign countries/regions. These variables incur transport 

cost in the objective function and reflect usage in the originating US region then supply 

into the destination foreign country/region. Trade is modeled between the 11 

FASOMGHG regions and 27 foreign countries/regions where the US exports that 

commodity and the foreign country demands that commodity. Cases within the GAMS 

implementation variable AGTRADE are depicted by this tableau column. 

• Regional commodity to national market -- Movement of commodities from the 11 

FASOMGHG regions to the US national market as discussed above. Cases within the 

GAMS implementation variable AGTRANSPRIM are defined by this tableau column 
262 

• Domestic demand -- National market demand as discussed above. Cases within the 

GAMS implementation variable AGDEMAND are defined by this tableau column. 

• Foreign country supply -- Country level excess supply for all commodities that are 

modeled with spatially explicit international trade. These variables have the area 

underneath the country level excess supply curve in the objective function and reflect 

supply of commodities into the country level balance. These variables are defined all the 

commodities subject to spatially explicit international trade modeling for the countries 

with excess supply curves. Cases within the GAMS implementation variable 

AGSUPPLY are defined by this tableau column 

• Transport of commodities to US regions from foreign countries -- Flow of commodities 

into US regions from exporting foreign countries/regions. These variables incur per unit 

transport cost in the objective function and reflect a usage of the commodity in the 

originating foreign country/region plus supply into the US destination region. Trade is 

modeled between the 11 FASOMGHG regions and 27 foreign countries/regions for each 

commodity for cases where the US imports that commodity and the foreign country 

supplies that commodity. Cases within the GAMS implementation variable AGTRADE

are depicted by this tableau column. 

• Transport of commodities between foreign countries -- Flow of commodities between 

foreign countries/regions. These variables incur transport cost in the objective function 

and reflect usage in the originating foreign countrys plus supply into the destination 

region. This international trade is modeled between pairs of the 27 foreign 

countries/regions when transport costs are defined and when a country of origin is a 

supplier and the country of destination is a demander. Cases within the GAMS 

implementation variable AGTRADE are depicted by this tableau column. 

• Foreign country demand -- spatially traded commodities -- Country level excess demand. 

These variables have the area underneath the country level excess demand curve in the 

objective function and reflect use of the commoditiy from the country level balance. 

These variables are defined for the countries with excess demand curves. Cases within 

the GAMS implementation variable AGDEMAND are defined by this tableau column. 

• GHG Payment -- Net GHG payments in the model as has been discussed above. Cases 

within the AMOUNTGHGS GAMS implementation variables are represented by this 

tableau column. 

The coefficients in this tableau are 

c -- the costs of crop production 

dt -- the cost of domestic interregional transport 

pd -- domestic price differences between regional and national markets 

i -- the area underneath the domestic demand curve 

it -- transport cost for moving goods from domestic to international regions or vice versa 
263 

is -- the area underneath the foreign country supply curve 

ic -- transport cost for moving goods between international regions 

id -- the area underneath the foreign country/region demand curves 

g -- GHG payments 

y -- production yields 

+/- -- a portrayal of coefficients of various sign in the GHG balance 

Several features of this spatially explicit trade model merit mention 

• As mentioned above the spatially explicit trade modeling is only done for select 

commodities in the model. 

• Trade for other commodities generally is represented with excess supply and demand 

functions that face the total US on a rest of world basis as is discussed in the section on 

commodity markets above. 

• Not all US regions are involved with the export and/or import of each commodity. 

Shipments to foreign countries only occur where they have been observed in the past. In 

particular, landlocked US regions generally transport commodities to regions with ports 

who in turn export to the foreign countries/regions. For example exports to Asia are more 

likely to come from the West Coast and do not originate directly from the Corn Belt. 

• Not all foreign regions are suppliers or demanders of a commodity. Generally the foreign 

regions are a supplier, a demander or neither. Some regions simply do not produce 

particular commodities, are self-sufficient or are not significantly involved in 

international trade. 

• Most of the data behind this model for the elasticities used in the supply and demand 

equations are based on the USDA SWOPSIM model. Transport data comes from some 

efforts by Dr. Stephen Fuller and associates at Texas A&M. Data on quantities and prices 

come from a mixture of USDA, World Bank and FAO sources. 
264 

Table 8-22 Tableau illustrating spatially explicit trade and relation to domestic regions Production region 1 Production region 2 Domestic transport region 1 to region 2 Domestic transport region 2 to region 1 Move from region 1 to US National market Move from region 2 to US National market US national market International transport from US region 1 to country 2 International transport from US region 2 to country 2 International supply country 1 International transport from country 1 to US region 1 International transport from country 1 to US region 2 International transport from country 1 to country 2 International Demand in country 2 

GHG payments 

 

Welfare -c -c -dt -dt -pd -pd +i -it -it -is -it -it -ic +id +g 

Commodity balance -- US region 1 -y +1 -1 +1 +1 -1 < 0 

Commodity balance -- US region 2 -y -1 +1 +1 +1 -1 < 0 

Commodity balance -- US national -1 -1 +1 < 0 

Commodity balance -- country 1 -1 +1 +1 +1 < 0 

Commodity balance -- country 2 -1 -1 -1 _1 < 0 

GHG fossil emissions +/- +/- +1 = 0 

8.3.8 Biofuels 

One of the key potential GHG mitigation strategies involves offsetting fossil fuel based 

carbon emissions by providing biofuels feedstocks that after conversion can prodiide proucts that 

replace gasoline, diesel and/or coal for electric power plants. Table 8-23 shows a tableau that 

overviews the biofuel submodel. 

The equations in this tableau are 

• Welfare -- the consumers' and producers' surplus objective function that is maximized. In 

terms of the biofuel feedstock features, this incorporates the cost of feedstock production 

whether it involves traditional crops like corn or specialized energy crops like willow, 

hybrid poplar, or switchgrass. The costs of processing in and commodity movement from 

the forest sector also appear. The objective function also includes the costs of utilizing 

biofuel feedstocks that integrate hauling and transformation costs to a point at which the 

resultant product is perfectly substitutable with the fossil energy source. These costs 

occur in association with processing variables. Finally, the objective function 

incorporates demand coefficients that reflect the prices received when generating ethanol 

and biofuel feedstocks for electricity generation. In these cases, the demand curves are 
265 

currently assumed to be infinitely elastic at a fixed price but could be specified as 

downward sloping in the future. The GAMS implementation equation WELFAR is 

represented in this tableau row. 

• Commodity balance of raw commodities -- Balances usage of biofuel feedstock 

commodities with their supplies. Namely, usage by processing, transfer to forestry as a 

fiber source, other direct use by production plus other forms of 

demand/production/processing/export (which really only occurs for corn) does not 

exceed regional production, plus transfers from forest processing. The constraint is 

defined for all of the biofuel feedstock commodities at the FASOMGHG 11 region level. 

Cases within the AGPRODBAL GAMS implementation equations are represented by this 

tableau row. 

• Commodity balance of processed agricultural commodities -- Balances usage of 

byproducts that can be utilized as biofuel feedstocks with supply of those byproducts. 

Namely usage by processing of cornstarch, corn oil and soybean oil does not exceed 

regional processing yields. The constraint is defined at the FASOMGHG 11 region level. 

Cases within the AGPRODBAL GAMS implementation equations are represented by this 

tableau row. 

• Commodity balance of energy replacements -- Balances usage of ethanol, biodiesel and 

power plant feedstocks with supply of those products arising directly through raw product 

production, transfer from forest processing and yields from agricultural processing. The 

constraint is defined at the FASOMGHG 11 region level. Cases within the 

AGPRODBAL GAMS implementation equations are represented by this tableau row. 

• Commodity balance of other commodities -- Balances usage of byproducts generated 

during the biofuel production process with supply of those byproducts. Namely usage of 

byproducts like brewers grain (that is produced during the wet milling process from 

which the cornstarch is produced and in turn used in ethanol production) does not exceed 

regional processing yield. The constraint is defined at the FASOMGHG 11 region level. 

Cases within the AGPRODBAL GAMS implementation equations are represented by this 

tableau row. 

• Wood products -- Balances usage of logs and milling residues in the forestry sector with 

quantities available. This constraint is a marker for the broader forestry submodel as 

extensively discussed in above forestry model section. 

• Maximum energy penetration limits -- Limits maximum market penetration of fossil fuel 

replacements. More explanation regarding these constraints appears after the definition of 

the coefficients below. These equations are defined at the national level for ethanol and at 

the FASOMGHG 11 region level for biofuel power plants. They are imposed either as 

upper bounds on the AGDEMAND GAMS implementation variable and/or through limits 
266 

on the usage of inputs within the AGPROCESSMAXPURCHINPUT GAMS 

implementation equation. 

• GHG balance of fossil and non-CO2 emissions -- Balances GHG emissions generated 

through the feedstock production use of fossil fuel, fertilizer and other inputs with net 

payments therefore. In the biofuel feedstock context this involves accounting for the 

emissions from fossil fuel, fertilizer, etc. used during biofuel feedstock production plus 

any energy used in transport and processing. Cases within the GAMS implementation 

equation GHGACCOUNTS are depicted by this tableau row. 

• GHG balance of energy offsets, carbon and non-CO2 -- Net GHG emissions savings 

generated through the replacement of combustion of fossil fuel by biofuel feedstocks. 

This will be discussed following the definition of the coefficients below. Cases within the 

GAMS implementation equation GHGACCOUNTS are depicted by this tableau row. 

The variables depicted in this tableau are 

• Biofuel feedstock production -- Acres devoted to biofuel feedstock production. These 

variables produce commodities while incurring costs in the objective function and 

generate GHG emissions due to the use of fossil fuel, fertilizer and other agricultural 

inputs. Sequestration is also present as described in the crop submodel section above. As 

discussed in the crop section above they also use crop land, tilled land, irrigation water 

and labor. The biofuel feedstock commodities produced are placed in regional balances. 

These variables are defined by crop, region, fertilizer use, tillage practice, crop land type, 

and irrigation status. Cases within the AGCROPBUDGET GAMS implementation 

variables are represented by this tableau column. 

• Forest processing -- Processes in the forest sector that generate logs and/or milling 

residues that can be used as biofuel feedstocks. More on these features are covered in the 

forestry chapter above. 

• Agricultural processing -- Biofuel feedstock generation. Processing activities that 

generate secondary commodities that can be used as biofuel feedstocks. These include 

corn wet milling and soybean crushing. These variables use raw commodities and 

agricultural inputs while generating a secondary commodity that can be used as a biofuel 

feedstock like corn starch along with other commodities like brewers grain. They also 

utilize agricultural inputs and generate fossil fuel related GHG emissions. These variables 

are defined on a FASOMGHG 11 region. Cases within the AGREGPROCESS variables 

are represented by this tableau column. 

• Agricultural processing that generates ethanol. Several processing activities generate 

ethanol from biofuel feedstocks. These include conversion of cornstarch into ethanol 

along with cellulosic ethanol generation from switchgrass, hybrid poplar and willow. 

These variables use raw commodities or cornstarch along with agricultural inputs while 
267 

generating ethanol. They also generate fossil fuel related GHG emissions and generate 

gasoline replacement based GHG offsets. These variables are defined on a FASOMGHG 

11 region basis. Cases within the AGREGPROCESS variables are represented by this 

tableau column. 

• Agricultural processing that generates coal replacements for use in electricity generation. 

Processing activities that generate biofuel feedstocks capable of substituting for coal 

within electricity generation. These include use of energy crops and products from the 

forest sector and all the costs of the transforming them to the point that they are 

substitutes on a BTU heat unit basis for coal as an input to a power plant. These variables 

use raw biofuel feedstocks or forest commodities along with agricultural inputs reflecting 

hauling and other costs while generating BTUs of replacement feedstock. They also 

generate fossil fuel related GHG emissions and generate coal usage based GHG offsets. 

These variables are defined on a FASOMGHG 11 region basis for the relevant types of 

processing alternatives. Cases within the AGREGPROCESS variables are represented by 

this tableau column. 

• Demand for ethanol in gasoline blends -- Demand for agriculturally based ethanol 

blended into a liquid fuel mix that is or is not subject to the full extent of fuel taxes as a 

potential implicit subsidy. The unsubsidized possibility is included to raise the possibility 

of unsubsidized gasoline blends when large expansions in ethanol production are 

realized. The variable has an objective function coefficient that reflects a fixed price, and 

withdraws ethanol from the processed commodity balance row. The subsidized 

alternative is subject to an upper bound set at the current level of subsidized ethanol 

production. The variable is defined on a national basis over time for each of the two 

ethanol subsidy possibilities. Cases within the GAMS implementation variable 

AGDEMAND are represented by this tableau column. 

• Demand for electricity feedstock in tbtus -- Demand for agriculturally based feedstocks to 

power plants in trillion btus. The variable has an objective function coefficient that 

reflects the area underneath a fixed price demand curve, withdraws the feedstock in 

thermal units (trillion BTUs) from a commodity balance row. The variable is defined on a 

national basis over time. Cases within the GAMS implementation variable AGDEMAND

are represented by this tableau column. 

• GHG payments/taxes -- Net GHG payments as has been discussed above. Cases within 

the AMOUNTGHGS GAMS implementation variables are represented by this tableau 

column. 

The coefficients in these equations are 

c -- per unit cost of agricultural production 

pr -- per unit cost of forestry processing 
268 

r -- per unit cost of agricultural processes that make biofuel feedstocks into replacements 

for fossil fuels 

i -- per unit prices for commodities that replace fossil fuels 

y -- per unit yield of biofuel feedstock 

u -- per unit usage of raw commodities in processing 

p -- per unit yield of secondary biofuel feedstocks or energy commodity replacements 

Eth -- maximum quantity of subsidized ethanol that can be sold 

Elec -- maximum quantity of biofuel feedstock coal replacement that can penetrate the 

marketplace over time 

ce -- carbon emissions from crop production 

pe -- carbon emissions from agricultural processing 

co -- carbon offsets generated when making biofuel feedstock based replacements for 

coal in electricity generation 

go -- carbon offsets generated when making biofuel feedstock based replacements for 

gasoline 

ne -- non-CO2 emissions from crop production 

pn -- non-CO2 emissions from agricultural processing 

gn -- non-CO2 offsets generated when making biofuel feedstock based replacements for 

coal in electricity generation 

no -- non-CO2 offsets generated when making biofuel feedstock based replacements for 

gasoline 

Several features of the biofuel model merit discussion. 

• The biofuels feedstocks model is resident within the agricultural sector and as a 

consequence is an annual representation of activity that will be constant across a five year 

period. 

• The commodities involve include forestry and agricultural commodities. 

• The possible rate of substitution for energy commodities is subject to market penetration 

constraints. Two forms of such constraints are defined. 

• The ethanol one is included to preclude the possibility of a ten or more fold increase 

in ethanol production that by default is subject to the degree of implicit subsidization 

that is present within current policy in the form of gasoline tax forgiveness. This 

obviously is a policy decision. This maximum is specified in the commodsupdem

table for the commodity SubGasBlend in the file data_agsupdem.gms. 

• Market penetration constraints that limit the amount of biofuel feedstock that can be 

used in generating electricity. The motivation for this constraint is that biofuel 

feedstocks can only be used in electricity generation if (a) new plants are constructed 

with biofuel capabilities which this depends on the rates of (1) demand growth and 

(2) existing plant depreciation; or (b) the retrofit of existing plants so they can use 

biofuel feedstocks. Such processes all take time and require substantial investments. 

Forecasted projections of electricity market biofeedstock penetration rates were taken 
269 

from the Haq's work at the Energy Information Agency and are present in the 

BioMktPenReg table in the file data_agbiomass.gms. 

• The net effect on GHG net emissions from biofuel feedstock usage involves the offset of 

the emissions from replaced fossil fuel that would have been combusted less the costs of 

the emissions incurred in biofuel feedstock production and processing. 

• Biofuel feedstock offsets not only affect carbon, but also methane and nitrous oxide 

based on lifecycle accounting results found in the literature. The data on these emissions 

offsets are present in the regionalprocess table in the data_agprocessregional.gms file 

for the biofuel feedstock related processing alternatives. 

• The coefficients giving the amount of emissions offset when biofuel feedstocks replace 

fossil fuel are based on the fact that when growing the feedstocks absorb atmospheric 

carbon dioxide through photosynthetic processes and store them in the body of the 

feedstock in the form of carbon. In turn, when that feedstock or derivative products 

thereof are combusted as energy substitutes then the absorbed carbon is reemitted to the 

atmosphere. However, the net gowing and processing energy is often substantially less 

than the magnitude of the fossil fuel combustion emissions. As consequence the 

emissions from combustion can be either zero or greatly reduced as these emissions are 

offset by the photosynthetic absorption. The data on these emissions offsets are present in 

the regionalprocess table in the data_agprocessregional.gms file for the biofuel 

feedstock related processing alternatives. 

Table 8-23 Tableau illustrating biofuels production 
270 

Production corn Production energy crop Forest processing Wet mill corn Process corn into ethanol Process energy crop into ethanol Process energy crop into electricity Process forest residues and chips to elec Demand subsidized ethanol in gas Demand for unsubsidized ethanol in gas Demand for electricity in tbtus GHG payments 

 

Welfare -c -c -pr -r -r -r -r -r +i +i +i + 

Commodity balance - corn -y 1 < 0 

Commodity balance -- energy crops -y +u +u < 0 

Commodity balance -- corn starch -p +uu < 0 

Commodity balance -- brewers grain -p < 0 

Commodity balance -- ethanol -p -p 1 1 < 0 

Commodity balance -- electricity -p -p < 0 

Wood products + < 0 

Forest milling residues and chips -y +u < 0 

Max subsidized ethanol 1 < Eth 

Max electricity penetration +1 +1 < Elec 

GHG fossil emissions ce ce pe pe pe pe Pe -1 = 0 

GHG coal offset co Co -1 = 0 

GHG gasoline offset go go -1 = 0 

GHG non co2 emissions ne ne pn pn pn pn Pn -1 = 0 

GHG non co2 offset gn gn no No -1 = 0 

8.3.9 Time 

Operating the agricultural submodel in conjunction with the forestry submodel raises a 

number of dynamic issues. These are discussed in this section. In particular, since the forestry 

model spans many years and the agricultural model is a shorter-term equilibrium model, then 

there are issues of coordinating the two submodels, equating welfare across them, updating 

agricultural activity over time and ltreating and valuation in the terminal period. 

8.3.9.1 Coordinating the agriculture and forestry submodels 

The forestry sector submodel is a multi-period model such that when a forest stand is 

established it may be 30 to 50 years before that stand is harvested. On the other hand, the 

agriculture model depicts cropping and livestock activity in a typical equilibrium year assuming 

that the same activity persists over a five year time period. The dynamics of any perennial crop 

or livestock possibilities (excepting the sequestration implications of tillage and land use change) 
271 

are assumed to be able to worked out in each typical five year period. The general way this 

works is summarized in the discussion surrounding the chapter 9 table 9-1. 

8.3.9.2 Discounting and annuities 

The agricultural model is assumed to represent typical activity during each year of a five 

year period (running from year 0 to year 4). Thus, agricultural returns in each period excepting 

the last one were treated as if they were a continuing annual series of five equal amounts 

discounted to the first period's dollars. In the last period the returns were treated as if they were 

an infinite annuity as will be discussed in the next section. Thus the period specific annuity 

factor dp 

p P

r

d

p P

r

d

p

t

p t

= =

≤ <

+ =∑=

for 1

and

for 1

(1 )

1 4

0

where 

r is the discount rate for period p as defined in the GAMS parameter discrate in 

data_basicsets.gms as is typically reset in the file model_structure.gms 

P is the last time period as is defined in the set called period in data_basicsets.gms and 

may be reset in model_structure.gms. 

In turn the agricultural part of the objective function is 

p p

p

p

d AgWel

r

W ∑= + =

5

0

5 (1 )

1

where 

W is the net present value of agricultural welfare 

dp is the period specific annuity factor which is contained in the model in the array 

Annuitywt(periods,"agriculture") as computed at the top of the 

model_structure.gms file 

p identifies the five year time period 

AgWelp represents the multi term agricultural consumers' and producers' surplus 

objective function in multi year time period p 

• The term involving (1+r) exponentiated to the 5p provides a discount factor to take the 

net present value of the returns in each time period back to the first model period. 
272 

• Multiplying by period specific annuity factor dp converts the returns in each five year 

period to net present value in the dollars of the first year in each period. 

• All of this is implemented in the WELFAR equation within the file model_structure.gms

8.3.9.3 Terminal period agricultural land use valuation

While the model structure readily treats net returns from the uses of agricultural lands 

along with the net returns to existing and regenerated forest stands during the explicit 

FASOMGHG periods, additional provisions are required to accommodate net returns beyond the 

end of the projection period. 

Because land values in any use reflect the present value of an infinite stream of future net 

returns, it is theoretically inappropriate to ignore land values at the end of our finite projection 

period. In practical terms, some rotation ages in the forest sector can be as long as 90 years and 

omission of terminal conditions or terminal land values could lead the model to fail to replant 

after initial harvest, perhaps as soon as the third decade in the solution. In turn, adding valuation 

of such existing stands in terms of their future returns beyond the explicit model time periods 

requires that one also value agricultural land in continuing agricultural use beyond the explicit 

model time periods. If this is not done the model would simply transform agriculture lands into 

forestry to capture net returns beyond the explicit model time horizon. 

Terminal conditions in forestry are handled as constant perpetual using von Mantel's 

formula as discussed in chapter 7. In the agricultural sector, activity in the last period is treated 

as if it continues forever. This is done using the mathematical relation that 

t r r t

1

(1 )

1

0

= + ∑

∞

=

which explains why this is the annuity factor used in the final explicit model period. 

8.3.9.4 Updating yields, demand levels and other factors over time 

Features have been added to FASOMGHG to reflect market and production condition 

changes over time. In the agricultural sector submodel, there are exogenously specified growth 

rates in yields, domestic demand, imports and exports for the major commodities. Also rates of 

change are specified for the quantities available of and prices for crop land, pasture, AUMS, 

labor, and water as well as the prices of inputs. Finally, there are features that update the usage of 

inputs when yields change within the crop and livestock budgets. 
273 

The basic mechanism for updating falls into two classes. There are items that are updated 

based on time and those updated based on yield changes. The time-updated items include yield 

levels, demand, import levels, and supplies and quantities of available inputs. In all cases, these 

are updated by a formula (1+ ri)

t

 where ri is the annual rate of change for item i. The ri terms 

have been estimated by either using 40 years of agricultural statistics to determine the annual 

percentage rate at which those items have increased over time, or by computing rates from the 

USDA Economic Research Service’s Agricultural Outlook projections (1990-2002). The data 

specifying the rates of change appear in the file data_agdynamic.gms. 

The model then takes the base quantities and the elapsed time to the future year for which 

desired data are needed and multiplies the base quantity by (1+ ri)

t-base to update yields, demand 

quantities, etc. in the file data_agdynamic.gms. It is important to observe that both yields and 

demand are being updated. It is also important to be careful in balancing rates of growth in 

demand across uses. For example, one might want to change the rate of growth in corn 

disappearance. To do this, one needs to consider export demand, domestic demand, and feeding 

dimensions, all of which are treated in various functions. 

The other major updating feature involves input adjustments related to yield levels. Such 

updating is done for crop input uses, crop profits, livestock feed use, and livestock profits. The 

procedure used here employs an elasticity term that gives the percentage response of input usage 

to a percentage change in yield. Input usage is changed by the percentage change in yield times 

that elasticity. Elasticities are based on three different assumptions. First, based on results 

derived by Robert Evenson (xxx cite), the elasticities for inputs for which we have no data are set 

at 0.5. This includes crop and livestock profits, as well as, in some cases, other crop inputs. 

Second, the elasticity of input change with respect to crops has been derived from a 1five year 

period from the mid 70's to the early 90's based on USDA FEDS budgets. During this period, the 

percentage change in input usage per percent change in yields is explicitly calculated and then 

used in specifying the elasticity. When such data are not available, 0.5 is used. Third, livestock 

feed use is assumed to be directly proportional to yield increases. Thus, if there is a 10% increase 

in milk output, there is a 10% increase in assumed feed consumption. All of this is done in the 

file data_agdynamic.gms 

The overall updating procedure, then, is to use the rate of change data to project all the 

demand, yield, import, and export figures for each of the FASOMGHG five year time periods 

and is implemented in the file data_agdynamic.gms. Subsequently, based on the yields, input 

uses in the production budgets are updated using the elasticity of input use change with respect to 

yield change times the projected yield change and this is implemented in model_structure.gms. 
274 

8.3.10 Varying regional granularity over time 

FASOMGHG can be quite large. As a consequence, the agricultural submodel is 

designed so that it can operate with varying degrees of geographic aggregation across the 

different modeled time periods. In particular, the 63 subregion representation can be used at the 

beginning and then reduced to an 11 region representation. This is controlled by the yessub

GAMS parameter which 

• when set to one brings in the 63 subregion representation and 

• when set to zero causes FASOMGHG to operate continually at the 11 region level. 

When yessub is set to one the GAMS array yesdis(period) defines the time periods for which 

agricultural subregions will be used. Both of these items are defined at the beginning of the 

model_structure.gms file. Currently, the empirical set up causes the disaggregate subregions to 

be used in the first 20 years. 

This strategy is employed to deliver detailed solutions at the beginning of the time frame 

while making computer solutions faster and reflecting the future consequences of early 

decisions. In terms of model structure, this involves aggregating the future consequences of any 

subregional decisions that influence resource availability or use into the corresponding 

FASOMGHG 11 regions. This is illustrated in the tableau in table 8-24. There we illustrate the 

altered regional granularity in a two period setting where in the early time period we have 4 

subregions and in a later time period we have 2 aggregate regions where subregions 1 and 2 fall 

into region A while subregions 3 and 4 fall into region B. 

The equations in this tableau are 

• Pasture Land -- Limits the pasture land use to that available. The availability is the initial 

amount of agricultural pasture land adjusted for land use change. Only the transformation 

case to crop land is shown here, but in the full FASOMGHG equations, there would also 

be transformations to and from forest land plus a crop land to pasture case. This land is 

used by the livestock production variables. Initially the pasture land use limits are defined 

on a subregional basis as shown in time period 1. However later its regional basis so it 

limits land use on larger regional basis as shown in period 2. Cases within the 

AGPASTLANDEXCHANGE and AGLANDPASTURE GAMS implementation 

equations are represented by this tableau row. 

• Crop land -- Limits crop land usage by tillage system to that available by crop land 

quality type. The land use is limited to the initial crop land endowment adjusted for land 

use change. Only the transformation case from pasture is shown here, but in the full 
275 

FASOMGHG there would be transformations to and from forest land plus a crop land to 

pasture case. Limits crop land use on a subregional basis when subregional basis when 

subregions are defined as shown in time period 1. However its regional basis is later 

altered so it limits land use on larger region basis as shown in period 2. Cases within the 

AGTILLSTART, AGTILLUSE and AGCANCHANGETILL GAMS implementation 

equations are represented by this tableau row. 

The variables in this tableau are: 

• Land from pasture -- Shifting of pasture land into crop land. These variables reflect the 

supply of land by geographic region from the single homogeneous pasture land equation 

into the land quality subcases in the crop land equations. The coefficients reflecting 

supply are proportional to their initial relative abundance of quality types in supply. 

These variables are defined geographically on the same basis as is agricultural production 

by time period. Thus in this illustration they are defined for subregions in the first period 

but only for the FASOMGHG 11 regions in the second period. Cases within the 

AGPASTLNDUSECHG GAMS implementation variables are represented by this tableau 

column. 

• Crop prod. -- Amount of crop production undertaken as discussed above. This variable 

would have dimensions of region, crop, land type, tillage system, fertilization alternative, 

irrigation/dryland and time period. The AGCROPBUDGET GAMS implementation 

variables are represented by this tableau column. The AGINITIALTILL and 

AGCHANGETILL GAMS implementation variables would also be involved. 

The coefficients in this tableau are 

p -- Pasture usage per head of livestock production 

L -- initial endowment of crop and pasture land 

a1 -- proportional share of crop land in land quality class 1 in the initial land endowment 

data 

a2 -- proportional share of crop land in land quality class 2 in the initial land endowment 

data 

Several comments are in order regarding this representation 

• The tableau only portrays the geographic granularity related procedures in terms of land 

use change from pasture to crop land. Similar procedures are used with transformation of 

land from and to other sources as well as with tillage change. 

• Transformations from crop land to pasture are treated identically to the pasture to crop 

land case above but with all the signs flipped. 
276 

• Land transfers from forest to agriculture always come from a forest land inventory that is 

defined by the FASOMGHG 11 regions but can go into a 63 region agriculture. 

Consequently these must be meshed. When needed this is done by supplying land into the 

subregions in a manner proportional to the share of each subregion within the original 

agricultural land data by FASOMGHG region as discussed above or in chapter 9 below. 

In later time periods this land transfers on a one-to-one basis between the corresponding 

forest and agricultural regions. Naturally when moving to crop land the land coefficients 

are distributed proportionately to the incidence of the crop land quality types in the initial 

land endowment. 

• Transformations from crop land to forest are treated identically to the forest to crop land 

case with all the signs flipped. 

• Agricultural tillage transformations that occur in a particular subregion will supply and 

use the appropriate tilled land case in the appropriate more aggregate region in the later 

time periods. 

• Crop and livestock budget data are aggregated into the larger regions using weighted 

acerages the 1992 crop and livestock mixes. Facotr suppliy prices are aggregated using 

endowment weighted averages. 
277 

Table 8-24 Tableau with varying regional granularity 

Transfer pasture to crop subregion 1 period 1 

Transfer pasture to crop subregion 2 period 1 

Transfer pasture to crop subregion 3 period 1 

Transfer pasture to crop subregion 4 period 1 

Produce livestock pd 1 subreg 1 

Produce crops pd 1 subreg 1 land type 1 

Produce crops pd 1 subreg 1 land type 1 

Produce livestock pd 1 subreg 2 

Produce crops pd 1 subreg 2 land type 1 

Produce crops pd 1 subreg 2 land type 1 

Produce livestock pd 1 subreg 3 

Produce crops pd 1 subreg 3 land type 1 

Produce livestock pd 1 subreg 4 

Produce crops pd 1 subreg 4 land type 1 

Transfer pasture to crop region A period 1 

Transfer pasture to crop region B period 1 

Produce livestock pd 1 region A 

Produce crops pd 1 region A land type 1 

Produce crops pd 1 region A land type 1 

Pasture land subregion 1 in period 1 +1 +p Crop land subregion 1 type 1 in period 1 -a1 +1 Crop land subregion 1 type 2 in period 1 -a2 +1 Pasture land subregion 2 in period 1 +1 +p Crop land subregion 2 type 1 in period 1 -a1 +1 Crop land subregion 2 type 2 in period 1 -a2 +1 Pasture land subregion 3 in period 1 +1 +p Crop land subregion 3 type 1 in period 1 -a1 +1 Pasture land subregion 4 in period 1 +1 +p Crop land subregion 4 type 1 in period 1 -a1 +1 Pasture land region A in period 2 +1 +1 +1 +p Crop land region A type 1 in period 2 -a1 -a1 -a1 +1 Crop land region A type 2 in period 2 -a2 -a2 -a2 +1 Pasture land region B in period 2 +1 +1 +1 Crop land region B type 1 in period 2 -a1 -a1 -a1 
278 

8.3.11 Environmental accounts 

A number of environmental accounts are computed mostly in association with crop land 

production. These include the amount of 

• wind and water erosion 

• fertilizer use 

• pesticide use 

• fertilizer run off 

and a number of other items. 

Most of these data come from EPIC crop simulator runs that were done at the level of 

crop production possibilities. The remaining data come from the crop production budgets. These 

environmental accounts will be added up in the report writer but are not formally incorporated 

within the FASOMGHG programming model. 
279 

9 CHAPTER 9 FOREST AND AGRICULTURE LINKAGES 

The agricultural and forestry submodels are largely independent. However, commodity 

and land market linkages are present in FASOMGHG. These involve: 

• intersectoral land transfers, and 

• intersectoral commodity transfers. 

When making such linkages, efforts are required to: 

• synchronize different geographies, and 

• synchronize time using discounting and annuities. 

The model also reflects: 

• Intersectoral tradeoffs under policies. 

Each will be discussed in this chapter. 

9.1 Intersectoral land transfers 

Land can be used within either the agricultural or the forestry sectors. When a forested 

stand is clearcut, the resultant land now devoid of trees can be reforested, transferred to 

agriculture, or transferred to developed use. In addition, land now in agricultural production can 

be transferred into forest. Thus, in each time period, land balances are present in both the 

forestry and agricultural submodels and model variables depict the active decision whether to 

change land use from or to the other sector. Naturally, this also requires that the other sector be 

defined in the region at hand (this is not true for the PNWW, NP, and SW regions) and that land 

suitable for movement to the other sector exists (FORCROP, CROPFOR, CROPPAST or 

PASTFOR). The land use change decisions embody a number of modeling features and dynamic 

considerations as we discuss here. 

The model is basically designed to consider whether the net present value of the future 

returns to land in the other sector outweigh those earned if land remains in the sector plus any 

adjustment costs involved with land transfers. If this is the case, then land will transfer and this 

rate of transfer will continue until the land markets equilibrate such that the value of the marginal 

acre in either sector differs by no more than the transfer costs. In forestry, this calculation 

considers the returns to reestablishing a stand plus the value of all future stands that would 

succeed the stand now being considered and the terminal value of any unharvested trees at model 

end. On the agricultural side, this considers the returns to land in cropping and/or livestock uses 
280 

in the current plus all future periods including the final, perpetual one. In both cases land use 

changes may occur now or any time in the future and may include more than one change with for 

example agricultural land migrating to a forest use for a rotation then back to agriculture. 

A tableau that reflects such decisions appears in table 9-1. There we see that multi-period 

forest variables that only enter the land markets in periods when a forest stand is being 

established or upon clearcut harvest. On the agricultural side, the agricultural submodel is an 

annual equilibrium model that repeatedly occurs in each of the five year periods. When land 

moves into the agricultural sector, the land transfer variables supply land into either 

• crop land under conventional tillage in a dryland state or 

• pasture land 

from the period of transfer through the end of the explicit time period. The land is then used in 

period-specific agricultural variables. This multi-period supply is employed to reflect a land use 

decision that looks at current and future returns to land, along with performing the needed 

synchronization with the multiple submodels representing single period equilibrium agricultural 

production. 

In this tableau, when land transfers sectors, we see that costs are encountered. On the 

forestry side, as discussed in Chapter 7, the costs of outgoing transfers face a three-step 

escalating cost schedule, where a given amount of land can transfer at an initial cost, but then as 

more and more land transfers the costs rise. The costs of this land transfer from forest to 

agriculture reflect the costs of stump clearing and other needed activities required to get the land 

ready for agricultural production. On the agricultural side, we have a specified hurdle cost of 

moving agricultural land to forestry plus establishment costs that are present in the production 

cost data in the forest submodel. These hurdle costs largely reflect a cost above and beyond the 

direct income difference that arises because one is moving from an annual income agricultural 

regime to a regime where returns are earned in the more distant future only after a lag for tree 

growth. 

The equations in this tableau are 

• Welfare -- Adds up total consumers' and producers' surplus across the two sectors and 

time periods using a net present value approach less any intersectoral adjustment costs. 

This tableau row represents the GAMS implementation equation WELFAR. 

• Forest land -- Balances land within the forest sector with its transfer and use. Land 

supply includes the land obtained from clearcut harvest plus land coming from 

agriculture. Land use includes its subsequent use for reforestation or land use change. 
281 

The land use changes allowed are movements to agriculture or movement to developed 

use. This equation is defined by log producing region (logregions), land suitability class 

(class), forest owner (pvtlogowner), type of succeeding forest stand (sucessorgroup), site 

index (site), and time period (period). The GAMS implementation equations 

FORLANDBALANCE and FORAFFORLANDBALANCE are represented by this 

tableau row. 

• Forest resources -- Represents the production cost, non-wood input, and manufacturing 

capacity resources in the forest submodel as discussed in chapter 7. 

• Forest terminal valuation -- Values standing forest inventory that exists beyond the 

explicit model time frame as discussed in chapter 7. 

• Agricultural land -- Balances land supply within the agricultural sector with its use. 

Supply includes the land initially in agriculture plus land coming from forestry. Use 

within agriculture involves that for cropping or livestock. Other uses are the land use 

changes allowed as movements to forestry or movement to developed use. Adjustments 

are also made for land use change involving transfers between crop and pasture land. 

This equation is defined by agricultural region/subregion (agregion), land type including 

land quality (aglandtype), and time period (period) for conventional tillage when dealing 

with crop land. The GAMS implementation equations PASTLANDEXCHANGE and 

AGCANCHANGETILL are represented by this tableau row. The GAMS implementation 

equations AGLANDPASTURE, AGMAXPASTURETOCROP, AGTILLSTART, and

AGTILLUSE are also involved.

• Agricultural resources -- Represents the water, AUMs, and labor agricultural submodel 

features as discussed in chapter 8. 

• GHG balance -- the GHG balance as discussed above. In this case, it shows additions and 

subtractions for the GHG balance to account for land moving to and from the forest soil 

sequestration accounts. 

The variables in this tableau are 

• Establish and harvest forest stand -- Clearcuts of existing stands and establishment of 

forests on previously forested or agricultural land. Note the variables reflect an 

establishment and harvesting (clearcut) time period. Cases within the GAMS 

implementation variables FORPRDEXIST, FORPRDNEW, 

FORPRDNEWAFFOREST are represented by this tableau column. Also implicit are the 

remainder of the forest sector variables discussed in chapter 7 that involve cost, wood 

product manufacturing, trade, domestic consumption, and transport. 

• Forest terminal inventory -- Valuation of terminal inventory that reflects the net present 

value of stands carried beyond the explicit model time period. This is discussed in 

chapter 7. 

• Ag production -- Agricultural land use by crop and livestock production. Note that the 

variables are defined for each time period. Cases within the GAMS implementation 

variables AGCROPBUDGET and AGLVSTBUDGET are represented by this tableau 

column. Also implicit are the remainder of the agricultural sector submodel as in chapter 

8 involving cost, processing, trade, domestic consumption, and transport. 

• Land from forest to ag -- Land use change of crop or pasture land into forestry. When 

changing land use, these variables reflect removal of land from the agricultural 
282 

constraints in the current and all future time periods. They supply land into the constraint 

governing bare land available for afforestation. When crop land is being shifted, the 

entries in the equations for agricultural subregion and land quality differentiated crop 

land contain coefficients that are proportional to the initial relative abundance of that 

subregion's endowment of that quality of land in total region. When pasture land is being 

shifted, the coefficients reflect the removal of one acre from the forest land equation and 

supply into the pasture land equations proportional to the pasture share in the subregion at 

hand as it falls in the total region. These variables are defined for a movement of one acre 

of forest land. Geographically, they are defined on an 11 region basis. The 

LANDFROMAG and CONVRTFROMAG GAMS implementation variables are 

represented by this tableau column. 

• Land from forest to ag -- Land use change of forest land into crop or pasture land. When 

changing land use, these variables reflect placement of land into the agricultural 

constraints in the current and all future time periods. They draw land from that 

represented by the constraint governing bare land for reforestation. When crop land is 

shifted, the entries in the equations for agricultural subregion and land quality 

differentiated crop land contain coefficients that enter land in a fashion proportional to 

the initial relative abundance of that subregion's endowment of that quality of land in the 

total subject region. When pasture land is being shifted, the coefficients reflect the 

addition of land into the pasture land equations according to the pasture share in the 

subregion at hand as it falls in the total region. It also withdraws land from the forest 

land equation. These variables are defined for a movement of one acre of crop or pasture 

quality land from forestry. Geographically, they are defined on an 11 region basis. The 

LANDTOAG and CONVRTTOAG GAMS implementation variables are represented by 

this tableau column. 

• GHG payments -- Net GHG net payments as discussed above 

The coefficients in this tableau of are 

f -- cost, returns, and welfare generated in the forestry sector model across its many 

variables 

i -- valuation of the terminal inventory in the form of area under product demand 

functions less production and manufacturing costs 

a -- cost, returns, and welfare generated in the agricultural submodel across its many 

variables 

ft --costs for transformation of forest land to agricultural land use 

at -- costs for transformation of agricultural land to forest land use 

g -- payments to net GHG increments as discussed above 

Lnd -- initial forest land endowment 

w -- forest land resource usage 

fr -- forest resources available 

fi -- forest standing inventory that persists beyond the last explicit model time period 

Agln -- agricultural land endowment 

S -- agricultural resource usage per unit production 

Agr -- agricultural resource endowment 

fse -- net GHG emissions by the forest sector 
283 

ase -- net GHG emissions by the agricultural sector 

sq --agricultural sequestration lost (gained) when land use changes to forest (from forest) 

Several features of the intersectoral land use change component of FASOMGHG merit 

additional comment: 

• Land transferred to and from agriculture can shift uses more than once over the projection 

period, constrained in part by minimum harvest ages for timber. For example, timberland 

may be converted to agriculture for several time periods, and then could then shift back to 

timberland in a subsequent time period or vice versa. 

• The inventory of agricultural lands contains some lands that are not suitable for forestry 

or agriculture because of climatic or topographical conditions. 

• The types of forest that could be established on agricultural lands and the associated yield 

characteristics differ by region. 

• Land only moves into and out of the category of land owned by nonindustrial private 

forest (NIPF) owners, in the land suitability classes for which land could start in forest 

and could potentially be converted to crop land and pasture land. 

• Given that the forestry model is a multi-period model, such that when a forest stand is 

established, it may be 30 to 50 years before that stand is harvested. On the other hand, the 

agriculture model depicts cropping and livestock activity in a typical equilibrium year 

assuming that the same activity persists over a five year time period. This necessitates 

that the transfer variables remove or add agricultural land from/into all current and future 

land balances. 
284 

Table 9-1 Tableau illustrating dynamic meshing of forest and agriculture submodels 

T 

Multi year forest production in periods 1-3 

Multi year forest production in periods 2-4 

Multi year forest production in periods 3-terminal 

Multi year forest production in periods 4-terminal 

Forest terminal inventory 

Ag production in period 1 

Ag production in period 2 

Ag production in period 3 

Ag production in period 4 

Land from forest to ag period 1 

Land from forest to ag period 2 

Land from forest to ag period 3 

Land from forest to ag period 4 

Land from ag to forest period 1 

Land from ag to forest period 2 

Land from ag to forest period 3 

Land from ag to forest period 4 

GHG payment period 1 

GHG payment period 2 

GHG payment period 3 

GHG payment period 4 

Welfare f f f f i a a a A -ft -ft -ft -ft -at -at -at -at +g +g +g +g Forest land period 1 +1 +1 -1 Forest resources period 1 +w Forest land period 2 +1 +1 -1 Forest resources period 2 +w +w Forest land period 3 -1 +1 +1 -1 Forest resources period 3 +w +w +w Forest land period 4 -1 +1 +1 -1 Forest resources period 4 +w +w +w Forest terminal valuation -fi -fi 1 Agricultural land period 1 +1 -1 +1 Agricultural resources period +s Agricultural land period 2 +1 -1 -1 +1 +1 Agricultural resources period +s Agricultural land period 3 +1 -1 -1 -1 +1 +1 +1 Agricultural resources period +s Agricultural land period 4 +1 -1 -1 -1 -1 +1 +1 +1 +1 Agricultural resources period +s GHG balance period 1 +fse +ase +sq -sq -1 GHG balance period 2 +fse +fse +ase +ase +sq +sq -sq -sq -1 GHG balance period 3 +fse +fse +fse +ase +ase +ase +sq +sq +sq -sq -sq -sq -1 GHG balance period 4 +fse 

+fse +fse 

+fse +ase +ase

+ase

+ase +sq

+sq +sq +sq -sq -sq -sq -sq -1 
285 

9.2 Intersectoral commodity transfers 

A limited number of commodities can shift from the agricultural commodity balances 

called AGPRODBAL to the forestry commodity balances called FORWDBALANCE. These 

commodities must be defined on a regional basis in agriculture. The GAMS implementation 

variable that is involved with this commodity that it is called MOVCOMTOAG for forest 

commodities moved into the agricultural sector submodel and MOVCOMFRAG for agricultural 

commodities that are moved into the forest sector submodel. The specific commodities that can 

move are: 

• The agricultural commodity hybrid poplar that can be transformed into the commodity 

AGRIFIBERSHORT. 

• The forestry commodity commodities pulp logs and milling residues that can move into 

the agricultural hybrid poplar and willow balances then enter into processing activities to 

produce ethanol or electricity. 

These commodities move at a cost on a regional commodity specific basis in any time 

period. 

9.3 Synchronizing different geographies 

The agricultural and forestry sector submodel potentially each contain different 

geographies within the land base and log/crop/livestock production possibility set. Namely, in 

the initial time periods, the agricultural sector submodel operates at the 63 subregion level then 

later on an 11 region basis as discussed in Chapter 8. Simultaneously, the forestry model 

continually operates on an 11 region basis. This necessitates a procedure to place land transfers 

in appropriate places and stop the model from cherry picking where it would move the worst 

land from one sector into the best land in the other sector. To achieve this we require movement 

to always be in one fixed pattern by land type. Thus when land moves between the 11 region 

forest model and the 63 region agricultural model a synchronization procedure is used as is 

rather extensively explained in Chapter 8. 

A limited number of commodities can shift from the agricultural commodity balances, 

called AGPRODBAL, to the forestry commodity balances, called FORWDBALANCE. These 

commodities must be defined on a regional basis in agriculture. The GAMS implementation 

variable that is involved with this commodity is called MOVCOMTOAG for forest commodities 

moved into the agricultural sector submodel, and MOVCOMFRAG for agricultural commodities 

that are moved into the forest sector submodel. The specific commodities that can move are: 
286 

• The agricultural commodity hybrid poplar that can be transformed into the commodity 

AGRIFIBERSHORT, and 

• The forestry commodities pulp logs and milling residues that can move into the 

agricultural hybrid poplar and willow balances. In turn these enter into processing 

activities to produce ethanol or electricity. 

These commodities move at a cost on a regional commodity specific basis in any time 

period. 

9.4 Synchronizing different geographies 

The agricultural and forestry sector submodels potentially each contain different 

geographies within the land base and log/crop/livestock production possibility set. Namely, in 

the initial time periods, the agricultural sector submodel operates at the 63 subregion level and 

then later at an 11 region level, as discussed in Chapter 8. Simultaneously, the forestry submodel 

continually operates on an 11 region basis. This necessitates a procedure to place land transfers 

in appropriate places and stop the model from cherry picking where it would move the worst 

land from one sector into the best land in the other sector. To achieve this, we require movement 

to always be in one fixed pattern by land type. Thus, when land moves between the 11 region 

forest model and the 63 region agricultural model, a synchronization procedure is used as is 

rather extensively explained in Chapter 8. 

Briefly, this procedure affects one acre in a forestry region and fractions of that acre as 

they fall in the contained subregions (those that fall within the FASOMGHG region involved in 

the land transfer). These fractions are derived from a subregion’s proportion of the total land in 

each region. The proportions are based on the initial inventory data and vary by type of land 

being transferred (e.g., crop or pasture). For example, if the PSW initial land area is apportioned 

80% in Northern California and 20% in Southern California, then in the transfer of one acre of 

forest land to agriculture for the PSW forest land balance, it would be assigned so that 0.8 acre is 

added to the Northern California agricultural land balance and 0.2 acre in the Southern California 

balance. For crop land this would be further subdivided to reflect the incidence of land across 

quality types. 

Also note the geographic basis for agricultural lands varies by time period. In the later 

time periods, the agricultural model reverts to the same 11 region definition for crop and 

livestock production as is used for log production in the forest model, so land transfers on a one 

to one basis. For crop land, this still would be subdivided to reflect, in this case, regional 

incidence of land across quality types. 
287 

9.5 Synchronizing time -- discounting and annuities 

The dynamic characteristics of the submodels for GHG payments, agricultural sector, and 

forestry sector are somewhat different. This requires model features to synchronize the sectoral 

objective functions, as well as some alterations in the interpretations of levels of activity within 

the model time periods. Efforts were made in the forestry and agricultural submodels to represent 

typical steady-state activity in each year during a five year period. 

On the forestry side, this necessitated model features regarding the volume of logs 

obtained from a harvested acre. Mainly, the harvested acreage gives the total acreage harvested 

during each five year period and if one multiplies that acreage by the per acre yield, one would 

get the total volume of logs across the five year period. To convert this to an annual amount, the 

yield terms were divided by five under the assumption that the acres harvested are cut at an equal 

rate in each year of the five year period. This is done in the GAMS implementation equations 

FORBALEXHRV, FORBALEXHPC, FORBALNEWHRV, and FORBALNEWHPC. In turn, 

this annualized volume is entered into the wood products balance equation 

(FORWDBALANCE) via the harvested log variables FOREXHARVEST, FOREXHARVPC, 

FORNEWHARVEST, and FORNEWHARVPC. This leads to the processing and demand 

portions of the forest submodel having annualized amounts in a five year period. Also, the cost 

data for forestry were usually specified as annual costs, and in the case of the variable cost items, 

were adjusted to be average annual cost during a five year period. In turn, the forest returns were 

treated as constant annuities across the five year period and were multiplied by annuity factors. 

Subsequently, the returns across each of the five year periods were each multiplied by the 

relevant discount rate to adjust back to net present value on the basis of the first model time 

period. This is more precisely discussed in Chapter 7. 

 On the agricultural side the agricultural model represents typical activity during each 

year of a five year period. Thus, agricultural returns in each time period were also treated as a 

continuing annual annuity and were multiplied by a net present value for an annuity factor. This 

is more precisely discussed in Chapter 8. 

The GHG payment part of the model was also treated with net preset value terms but was 

not converted to an annuity. 

Therefore, the composite net present value returns were formed as the: 

• Net present value of the agricultural submodel 

• Plus the net present value of the forestry submodels 
288 

• Less the net present value of land transfers 

• Less the net present value of the commodity transfers 

• Plus the net present value of the GHG payments 

and this in total forms the composite objective function WELFAR. 

9.6 Intersectoral tradeoffs under policies 

FASOMGHG is solved with a composite objective function that spans across the GHG, 

agricultural sector, forestry sector, and intersectoral transfer submodels. When policies are 

imposed that provide incentives or require adjustments, the unifying force of the objective 

function causes the model to consider the possibility of adjusting activity anywhere within the 

forestry and agricultural sectors as well as the amount of land transfers and commodity 

movements. Such activities are also adjusted temporally and geographically. In turn, the model 

reequilibrates the land, commodity, and factor markets across all sectors, time periods, and 

geographic locations. 
289 

10 CHAPTER 10 APPROACHES USED TO INSURE TRACTABILITY 

A number of features are used in the model to make it solve better or be asier to use. 

These include the use of 

• Handling the supply and demand curves 

• Seperable programming and associated steps for the supply and demand curves 

• Crop and livestock mix relaxation 

• Geographic expansion/collapse 

• Time horizon and terminal conditions 

• Substituting Memory for Time 

• Arificial variable addition to insure feasibility 

• Right hand side perturbation to avoid degenerate cycling 

10.1 Handling the demand and supply curves 

Given the dynamic nature of the supply and demand curves where they shifted out over 

time we felt a need to specify the demand and supply curves by passing them though a known 

point. We also found a need to handle the limits of integration so as to avoid numerical 

problems with large demand curve related integrals. This introduces a number of features are 

used in the context of handling the curves which merit discussion. We will present this in the 

context of a demand curve but make comments relative to a supply curve. 

10.1.1 Demand and supply curve form 
290 

In FASOMGHG most of the demand and supply curves are assumed to be of the cost 

elasticity form (a few are assumed to be linear in the forestry sector) 

P = P(Q) = F Q1/E 

where F is a constant and E the elasticity. 

10.1.2 Passing the curve through a known point 

The curves are set up so they pass through a given price quantity point (starting with the 

base year price and quantity and then later a quanity with a quantity growing at the historically 

observed rate and the price falling at the historically projected rate as discussed in the dynamic 

setion of the agricultural model chapter) with a given elasticity. Assume 

Pˆ , Qˆ is the price and quantity point that the curve will pass through 

 E is the assumed elasticity of the curve 

In turn given the assumed form 

P = F Q1/E 

The we may solve for the unknown value of F getting 

F = Pˆ Qˆ -1/E

which renders the original curve of the form 

Q ) ˆ P (Q/ P = ˆ 1/E

This curve form is used as it improves the numerical accuracy attributes as forming the 

ratio Q over Qˆ and then exponentiating is subject to less round off error than would be 

individual exponentiations. It also facilitates gridpoint approximation as will be discussed 

below. 

10.1.3 Integrating the functions 

The formation of the objective function requires integration under the curves. The general 

form of the area under these curves is P(Q) dQ

Q*

a

∫ where 
291 

a and Q*

 give the limits of integration with Q* being the incumbent variable value in the 

model solution. 

P(Q) gives the invese demand or supply curve 

Q the quantity over which the area curve is swept. 

When this curve is integrated one gets 

Q) evaluated at Q and a ˆ (Q/ Pˆ * )

E

1 (1+

)

E

1 (1+

or 

) E

1 (1+

)

E

1 (1+

) E

1 (1+ *

)

E

1 (1+

Q) ˆ ( / Pˆ Q) ˆ (Q / Pˆ − a

For supply cases we use a lower integration limit of zero (a=0) and the term involving a 

drops out. However, for demand curves this is but is problemantic for demand cases as zero 

cannot be used since zero to a negative power is undefined so we must use a non zero lower 

limit. This involves truncating the evaluation as discussed next. 

10.1.4 Truncating the demand evaluation 

As stated just above we need a non zero lower limit for the demand curve integration. 

We choose this to both yield a defined value of the integral and to avoid numnerical problems. 

In particular, the consant elasticity demand curves become asymptotic to the axis as the quanity 

approaches zero. Thus, given inelastic curves for small limits of integration (Q* and a) one gets 

very large areas. This makes for very large welfare measures and objective function values. To 

avoid this we truncated the curve at the lower limit of integration. This was done by establishing 

a truncation factor at the larger of the quantity that is 1/10th of Qˆ or the quantity that raises the 

price to 10 times Pˆ . Given this truncation factor is K Qˆ the integration was reexpressed so that it 

is of the form 

Pˆ (Q/Qˆ ) dQ

Q*

Q/ ˆ

1/E ∫

K

which after integration becomes 

)

E

1 (1+

) E

1 (1+

) E

1 (1+ *

)

E

1 (1+

Pˆ Q) ˆ (Q / Pˆ − K
292 

This is the formula that is used in the model. Note this formula requires that E cannot 

equal the numerical value of minus one as the denominator becomes undefined. This particular 

formulation has a couple of implications. 

• The quantity cannot fall below 1/K times the base quantity that the curve is passed 

through. But assuming the demand curve is properly formed this is quite an unusual 

occurrence as going to 1/10th the quantity or 10 times the price is generally unexpected. 

• The area under the demand curve is not as large as one might get as one might truly 

integrated the curve out from zero as a very large block near the axis is cut off. 

10.2 Adopting separable programming 

Early experience with the nonlinear version of FASOM indicated that it would take a 

great deal of solution time, often measured in days to get a single solution. Thus was deemed to 

be unsatisfactory and we decided to see if formulation modifications would speed this up. We 

also have such a large model that in sheer size it strains or is beyond the capability of many 

available nonlinear solvers. As a consequence, we use a technique called seperable 

programming that allows the model to be approximated as a linear program. As a result given an 

advanced basis FASOMGHG now can be solved in less than an hour for many cases. 

In FASOMGHG the demand and supply curves are based on own price elasticities only. 

This generates an objective function which in mathematical programming terms is separable. A 

well known result is that such a problem may be reformulated using a Taylor series 

approximation (Miller, 1963, Hadley 1964). We discuss this approach herein. 

Approaches to nonlinear problems often utilize approximations. Such approximations 

may be either one-time or iterative (see McCarl and Spreen (1980) for a discussion of the 

differences). Seperable programming is a one time approximation and uses grid points, 

representing the inherent nonlinear phenomena as a discrete series of linearized steps. 

Furthermore, normal speerable programming requires a special solver that requires the adjacent 

grid points be employed. But given that we use downward sloping demand and upward sloping 

supply means we are doing seperable programming on concave functions. In turn, Hadley shows 

that adjacency will be a property of a linear programming solution and thus does not need to be 

specially handled. 

Separable programming deals with problems in which the functions may be of any 

nonlinear form, but must be separable into functions of a single variable. For example, in a two 
293 

variable case, the functions f(x,y) must be decomposable into h(x) + g(y). Separable 

programming is usually considered a nonlinear programming technique (Hadley, 1964); but is 

commonly used in an LP setting. The most commonly used form of separable programming that 

is employed here arose originally with Charnes and Lemke, and was extended by Miller(1963). 

The formulation yields an LP whenever the objective function terms are concave and the feasible 

set is convex (Hadley, 1964, p. 124). 

Separable programming relies on a set of grid points and constructs an approximation 

between these points. The approximation is setup so that the approximated value arises from a 

first order Taylor series expansion equaling the value at the base point plus the slope divided by 

the difference from the base point. Suppose we wish to approximate the function at point X 

which falls between approximating points. This can be expressed algebraically for approximating 

the term f(X) with the term F(X) at the point X that falls between the grid points Xk ˆ and Xk 1 ˆ +

by the formula 

( ) ( ) k

k 1 k

k k 1

k Xˆ X - X ) Xˆ ˆ (

X ) ˆ X ) f( ˆ f( Xˆ f(X) F(X) f −

− ≅ = +

+

+

Now suppose we write X as a convex combination of Xk ˆ and Xk 1 ˆ + using some new variables 

, 0

1

X Xˆ Xˆ

k 1

k 1

k k 1 k 1

≥

+ =

= +

+

+

+ +

k

k

k

λ λ

λ λ

λ λ

where λk and λk+1 are the new variables and give the the amount of the kth and k+1st

approximation points used. 

Substituting this relationship for X as a function of λ and the grid points into the above 

appproximating equation for F(X) we get the equation 

( ) ( ) ( ) k 1 Xk 1 ˆ X f ˆ F X f ≅ λk + λk+ +

where the function value is approximated by a convex combination of the function evaluated at 

the two adjacent grid points. This can be represented by a LP problem. Namely given the 

separable nonlinear problem (where in the context of FASOMGHG the f(X) terms are the 

nonlinear expressions for area under demand and supply curves) 
294 

( )

 X 0

s.t. a X b , for all i

Max f X

j

i

j

ij j

j

j j

≥

∑ ≤

∑

and we may form the approximating problem 

λ μ

λ

λ

λ

μ

μ

μ

μ

μ μ

μ

μ μ

0 for all j and

1 for all j

X b , for all i ˆ s.t. a

X ) ˆ Max f (

j

j

i

j

j ij j

j

j j j

≥

=

≤

∑

∑∑

∑∑

where X jμ ˆ is the th μ approximating point for Xj and 

= ∑u

j λ jμXjμ X ˆ

This formulation involves a change of variables. The variables λjμ give the amount of the 

μ

th grid point used in the approximation of the jth variable. The term ( ) j X jμ ˆ f gives the values of 

the objective function (area under the curves) evaluated at the grid points. The new constraints 

on the λ variables cause a convex combination of the grid points to be chosen for each variable 

approximated. The demand functions must be downward sloping and the supply functions 

upward sloping, otherwise the nonzero λ's in the solution will not necessarily be adjacent; and 

the approximation will not work properly (Hadley, 1964). 

In FASOMGHG, uniformly this is entered for all of the nonlinear objective function 

terms. What is involved for a demand curve is to select a set of points that surround the expected 

level of demand name defining a grid of such points. In turn, then we form the approximation 

using those points. We also alter the model definition slightly so it is as follows: Given the 

model 

( )

 X 0

s.t. a X b , for all i

Max f X

j

i

j

ij j

j

j j

≥

∑ ≤

∑
295 

We alter it to include a new variable XS that is equated to X but only has the sperable objective 

function preserving the original X variable in the problem. 

( )

X , XS 0 for alli

X XS 0 for all j

. . a X b for all i

f XS

j j

j j

i

j

ij j

j

j j

≥

− =

∑ ≤

∑

s t

Max

Then we apply our approximation to this problem 

u

s t

Max XS

X , 0 for all j and

1 for all j

XS 0 for all j X ˆ

. . a X b for all i

) ˆ f (

j j

j

j j j

i

j

ij j

j

j j j

≥

≤

− =

≤

∑

∑

∑

∑∑

μ

μ

μ

μ

μ μ

μ

μ μ

λ

λ

λ

λ

where the gridpoints XSjμ ˆ are selected to surround the expected numerical values of the supply 

and demand quantities. In FASOMGHG, this is used to allow the original demand and supply 

variables to remain in the problem (for example AGDEMAND) involves introduction of a new 

variable with an approximated nonlinear objective function term. The new variable is of the 

same dimension as the variable for which the term is being approximates plus the grid point 

dimension (AGDEMANDS that has same dimension as AGDEMAND plus the added dimension 

step). The naming then is the same as the original variable with an S and the step dimension 

added. 

The FASOMGHG formulation uses grid points around the expected value of X to 

approximate the associated functions. Such grid points should provide a reasonable 

approximation of the function in the domain of the answer, including points both close to the 

expected answer as well as points depicting functional extremes (Geoffrion (1977) discusses the 
296 

importance of the extreme points). Even spacing of the grid points is not required. Thus, one 

could approximate a curve at the points 10, 2, 1, 0.95, 0.50, 0.10, 0.02 and 0.01. We will discuss 

formation of the grid points below. 

10.3 Selecting grid points 

As shown above the integral of the subject curves for the demand curve cases is 

)

E

1 (1+

)

E

1 (1+

)

E

1 (1+ *

)

E

1 (1+

Pˆ Q) ˆ (Q / Pˆ −

− K

wherein the second term is merely a constant and for the supply curve cases this is 

) E

1 (1+ *

)

E

1 (1+

Q) ˆ (Q / Pˆ

Thus the general term we need to approximate in the objective function is of the form just above. 

Now in choosing grid points for the decision variable Q we may either specify alternative ratios 

of Qˆ Q /

* where * Q equals the base value of Qˆ times the gridpoint factor M and M=1 gives the 

base value. We choose to do the latter. Namely given the following demand related model 

component 

Q for all j Q K ˆ 

s.t. a Q b , for all i

Q ) ˆ (Q /

Pˆ

Max

j j j

i

j

ij j

j

) E

1 (1+

j j ) E

1 (1+

j j

j

≥

∑ ≤

∑

Where the 

j subscript identifies the jth commodity 

Pj

ˆ , Qj ˆ is the price quantiy point the demand curve is passed though 

Qj is the level of demand for which we wish an integral 

Kj is the truncation lower level on demand as a proportion of Qj ˆ

The constraint ∑

j

ijQj a ≤ bi is simply an indicator of the rest of the model 

 We add in the new variable QS which merely has the nonlinear terms 
297 

Q , QS 0 for all j

Q for all j QS K ˆ

Q QS 0 for all j

. . a Q b for all i

Q ) ˆ (QS /

Pˆ

j j

j j j

j j

i

j

ij j

j

) E

1 (1+

j j ) E

1 (1+

j j

j

≥

≥

− =

∑ ≤

∑

s t

Max

Then we specify values of grid points Mju as ratios of j Qj ˆ QS /

ju ju Qj ˆ QS / M = ˆ or ju ju Qj ˆ QS M * ˆ =

And we introduce the seperable programming step variable λ and a convexity constraint 

Q , 0

1 for all j

Q for all j ˆ K ˆ

0 for all j Q ˆ

. . a Q b for all i

(M )

Pˆ

j ju

u

ju

j j

u

ju ju

u

j ju ju

i

j

ij j

u

) E

1 (1+

ju ) E

1 (1+

j j

j

≥

=

≥

− =

≤

∑

∑

∑

∑

∑∑

λ

λ

λ

λ

λ

j

j

j

ju

M Q

M Q

s t

Max

This is what is done in the FASOMGHG objective function with several small variants 

• The term involving the Kj truncation factor is dropped as the first gridpoint value is that 

factor and it is impossible for demand to be smaller than that given the formulation. 

• The objective function has a constant added to it to take care of the truncation of the area 

as discussed above. 

• For supply curves all is as above but no truncation factor is used. However the lowest 

gridpoint does supply a lower bound on the level of supply. 

• We actually use elasticity dependent grid points with lower quantity spreads for more 

inelastic curves. 

• The gridpoints are specified in the file model_seperable.gms and are resident in the 

arrays qincag and qincwood for the forest and agricultural parts of the model 

respectively. 
298 

• The number of grid points is determined by the size of the set step. 

• The grid approximation variables corresponding to λ in the above conceptual model are 

FORWDNWCS 

FORWDDEMANDS 

FORWDSUPPLYS 

FORWDLOGSUPPLYS 

AGDEMANDS 

AGSUPPLYS 

AGRESSEPSUPPLY 

The identities linking these to the original variables are defined for all cases but the nonwood input case (FORWDNWCS) which is defined originally with steps present and are 

FORWDSUPEQ 

FORWDSUPPLY 

FORWDDEMEQ 

FORWDLOGSUPEQ 

AGSDIDENTITY 

AGRESIDENTITY

Convexty is imposed in 

FORWDNWCCONVEX 

FORWDSCONVEX 

FORWDDCONVEX 

FORWDSLOGCONVEX 

AGSDCONVEX 

AGRESCONVEX 

10.4 Crop and livestock mixes – concept and relaxation 

Crop and livestock mixes are used in the model to prevent difficulties with aggregation 

and preventing extreme regional specialization. The conceptual reason for and theory behind the 

use of mixes is discussed in chapter 5. Their use in irrigated and total crop modeling and their 

risk in livestock context is discussed in Chapter 8. Numerical aspects of the implementation of 

mixes are discussed here. 

Some additional mix related features were included in FASOMGHG to facilitate 

numerical solutions and to relax the stringency of the mix restrictions as time advances. These 

involve 

• Treating the crop mixes as upper and lower limits 

• Relaxing the mixes in later time periods 

These are discussed in the sections just below. 
299 

10.4.1 Upper and lower limits 

The crop mixes are treated as upper and lower bounds on the acreage of crops that can be 

ground. In particular the crop acreage must fall in a range between 90% and 100% of the crop 

the acreage from the mix. This allows some slight relaxation of the mixes to facilitate the model 

from not getting into a numerically infeasable situation. This is implemented by defining an 

upper (AGCRPMIXUP) and lower bound (AGCRPMIXLO) constraint on the mix as well as a 

constraint that requires that the total acreage is the crops covered equals the total acreage in the 

mix (AGCRPMIXTOT). 

10.4.2 Temporal relaxation 

The crop and livestock mixes are a particularly dense and difficult part of the model. 

Their imposition is somewhat questionable for distant future time periods. Namely new 

technological developments may significantly alter the production possibility set (e.g. 80 years 

ago soybeans were not produced in any significant quantities in the US and are now a major 

crop). In response to these observations, the decision was made to set up the empirical 

FASOMGHG programming model with the crop and livestock mixes only for time periods in the 

first 20 years, then drop them for the remaining explicit time periods. That means that solutions 

for periods beyond 2020 will show a higher degree of specialization. Such a decision makes 

FASOMGHG easier to solve, and reduces the future influence of the crop and livestock mix 

constraints. These mixes are maintained in the first 20 years as we felt that yielded the most 

realistic and detailed solutions for those time periods. 

10.5 Geographic expansion/collapse 

The FASOMGHG 63 subregion agricultural production representation creates a large 

submodel and makes FASOMGHG hard to solve. In the interests of improved solution 

efficiency, this level of detail was only maintained for the first 20 years. Subsequently, the 

agricultural sector production representation was aggregated to an 11 region basis but still 

represented the full diversity of production possibilities. The data for prices, production budgets, 

transport costs, etc. defining the aggregate 11 regions was formed as a weighted average across 

the 63 region data set where the weighting was by quanitiy of acreage or associated item in each 

region weighted up from the subregions in that region. The data on resource availability is a 

simple sum across the subregions data in that regions. This means that production is represented 

in the PSW region is initially modeled in Northern and Southern California but then later this is 
300 

aggregated to the total PSW region with the same set of crop and livestock production 

possibilities but aggregated data. This was done to facilitate model solution with details retained 

in the initial years to yield the most detailed and realistic information as possible in the first 20 

years. 

10.6 Time horizon and terminal conditions 

The decision on how FASOMGHG should represent the passage of time and 

management alternatives over time greatly affects the tractability of the resultant programming 

model. Conceptually, one should depict land-use decision making particularly that involving 

forest planting dates and rotation lengths as if the decision maker was considering returns over 

an infinite time horizon. Such consideration is necessary to avoid the incidence of biased 

behavior within the model solution. For example if we were to only consider 50 years one would 

undoubtedly find solutions where no timber stands were planted that could not be harvested 

within the 50 year period. Further such a solution would reflected little timber being established 

after year 30 and almost everything scheduled for harvest somewhere in the explicit time periods 

modeled. However while it is desirable to reflect infinitely long time periods, the model easily 

becomes too large to be tractable. It is also difficult to obey the conventional dynamic rule that 

one should depict a long enough time period that a lengthening of that explicit time period does 

not affect the solution in the initial model time periods that are of decision-making focus. 

Experience with FASOMGHG showed we could not do this and generate a model that would 

solve in reasonable time. As a consequence and the FASOMGHG strategy involved three time 

period related considerations 

• How long the model goes i.e. how long a time period is explicitly depicted 

• How fine the resolution is within that explicit time period. 

• How to value land and assets in unharvested timber stands or in agriculture at the end of 

the explicit model time period. 

Regarding these questions, the FASOMGHG implementers generally felt that the explicit 

model time periods had to be extended until so they were enough to get about two full rotations 

represented for stands with the longest expected rotation lengths. Given the longest rotations are 

in the neighborhood of 40 of 50 years, our choice has usually been to depict 100 years. 

Simultaneously, while going 100 years it's also important to have a fine enough disaggregation 
301 

of time periods to adequately represent harvest possibilities for the shortest rotation forest stands. 

This involves rotations in the South for pulpwood production in the neighborhood of 20 to 30 

years. In the face of this and experience with an earlier 10-year granularity version we decided 

to represent five-year granularity. Consequently the FASOMGHG programming model 

explicitly represents 100 years of production in 20 explicit five year periods. 

We also need to value ending inventory of unharvested forest stands and continuing land 

use in agriculture. To provide such valuation, FASOMGHG is structured under the assumption 

that forest management is, from the last period onward, a continuous or constant flow process 

with a forest inventory that is fully regulated at typical rotation lengths observed for the region 

(see Adams et al. [1996]). The terminal value of land remaining in agriculture is formed by 

assuming that the last period persists forever. In both cases, demand curves are used to reflect 

diminishing valuation as the ending inventory or allocation of agricultural land increases. 

10.7 Substituting Memory for Time 

One strategy used to ensure tractability is to pre-calculate items that take substantial time 

to compute and are complex, repetitive, and never or infrequently changing. This is done by 

precalculating such items into arrays then only the results in the formulation. For example we 

precalculate the conditions indicating whixh forest stands exist and place them into the isexist

and isnew tuples for later use in the model. Similarly, we pre-calculate stand level forest cost 

elements across a number of cost categories. This placing summary calculations into memory 

then only using the saved results in the model set up. 

10.8 Artificial variable addition to insure feasibility 

The ability to specify lower bounds on particular forest or agricultural product 

consumption levels raises the specter that empirical programming model realizations may be set 

up that are infeasible. As a consequence, a number of artificial variables are permanently 

resident in the model formulation that permit satisfaction of minimum consumption constraints 

even though it's not technically possible. In turn, when these artificails are in solution indicating 

that some of the minimum consumption levels cannot be satisfied their presence distorts the 

market clearing producy and factor shadow prices allowing one to diagnose the cause of the 

model infeasibility. For a conceptual discussion of this issue along with examples see McCarl. 
302 

10.9 Right hand side perturbation to avoid degenerate cycling 

One concern that emerged in the 1950s and 60s involved the possibility of degenerate 

cycling within mathematical programming computer algorithms and subsequent failure. Some of 

the literature recommended one avoid this problem through perturbation of the right hand sides 

(adding small numbers). Experience over the years has found this is helpful with particular 

solvers (note we are currently using CPLEX which does this automatically and makes the 

procedure we describe next somewhat unnecessary). Such a perturbation is permanently 

implemented in FASOMGHG. For example in many of the supply demand balance constraints 

that ordinarily would have zeros on the right hand sides theye actually implemented with small 

numbers on the right hand side. These numbers are selected so that they do not significantly bias 

the solution results ( i.e. we do not care about an extra 1/10th of a bushel of corn in the face of a 

9 billion bushel corn crop) but make the problem easier to solve. These generally involve a 

parameter called twid.
303 

11 CHAPTER 10 MODELING OF EFFECTS OF CLIMATIC CHANGE 

*** 
304 

12 CHAPTER 11 MODELING LAGGED PRODUCTION RESTRICTIONS 
305 
306 

SECTION 4: DATA SPECIFICATON 

This section presents discussion of the procedures used in specifying the data used. 

For starters, we can use the recently expanded write-up from the Assessment Report 

which follows the basic structure below (I will send separately). But we will need to be more 

detailed than that for SAB review. So, for a first pass, provide a fair amount of detail about the 

underlying data (NASS, FIA, ...) and models (TAMM, ATLAS, Century, EPIC, FORCARB,...) 

as possible. If this proves unwieldy, we will develop a strategy for assigning details to 

appendices later. 
307 

13 CHAPTER 12 GHG DATA SPECIFICATION 

Bruce, please note that Ch 13 is titled "GHG Data Specification" but only includes our stuff on 

forest Carbon. Also, where do we report on the data that J Chmelik collected on fuel-related emissions 

from forestry?

13.1 Forest Carbon Detail 

The carbon sector is designed to provide an accounting system for major carbon pools in 

private timberland and crop land. It is structured so that a variety of policy instruments can be 

evaluated including constraints for total carbon pools or the rate of accumulation of carbon form 

year to year. These constraints can be consistent with a variety of policy instruments that may 

vary carbon management by region, owner, land class, etc. In addition, FASOMGHG’s can 

evaluate the effects of GHG payment policy. 

The basic functions of the carbon accounting component of the FASOMGHG include: 

• carbon accumulation in trees, understory, forest floor, and soil on existing forest stands in 

the existing private timberland inventory during the simulation period, 

• carbon accumulation in trees, understory, forest floor, and soil on reforested and 

afforested stands during the simulation period, 

• carbon losses over time associated with harvested logs transformed into wood or paper 

products, and 

• carbon profiles for land transferring between forests and agriculture and developed land 

uses. 

As shown in Figure 13-1, the forest carbon accounting is separated into two fundamental 

parts: (1) the accumulation of carbon as forested stands mature prior to harvest and (2) the 

disposition of carbon into various pools after the point of harvest. We discuss each component 

below and provide details of the calculations and data sources. 
308 

Figure 13-1. Forest Carbon Accounting 

Soil

Trees

Forest floor

and coarse

woody debris

Understory

Reforest or

Deforest?

Reforest

Product 

Disposition

Deforest

t = 0,...,T T = Harvest T,T+1,...

Carbon accumulation before harvest Carbon disposition 

after harvest

Afforestation

Disposition

of site C after

deforestation

C removed

from site

C remaining

onsite

13.2 Carbon Accumulation Before Harvest 

This section outlines the carbon accumulation process on three types of land: existing 

forest land, agricultural land that is converted to forest land, and forest land that continues to be 

used as forest land after initial harvests. Within each land type, carbon accumulates in four 

carbon pools: 

• Trees, 

• Understory, 

• Forest Floor and Coarse Woody Debris, and 

• Soil 
309 

Figure 13-2. Carbon Accumulation Before Harvest 

13.2.1 Trees 

Onsite carbon accounting closely mirrors the FORCARB system employed by the USFS 

in their periodic aggregate assessments of forest carbon sequestration. The onsite carbon 

accounting in FORCARB has been developed over the years by USFS researchers Richard 

Birdsey, Linda Heath, and Jim Smith. Most recently, Smith et al 2003 have revised the tree 

carbon component of the system to more flexibly express carbon in terms of (live and dead) 

biomass density equations. 

In FASOMGHG, tree carbon on land is a function of three factors: 1) merchantable 

volume, 2) the ratio of growing stock volume to merchantable volume, 3) and parameters of a 

forest volume-to-biomass model developed by USFS researchers (Smith, et al, 2003). 

Merchantable volume, by age, on each representative stand is obtained form the timber growth 

and yield tables in the model described in Chapter X. The volume factors and biomass model 

Carbon 

Accumulation 

Before Harvest 

Land Type 

• Existing Forest Land 

• Afforested Land (Crop/Pasture to 

Forest) First Rotation

Carbon Pools 

• Tree 

• Understory 

• Forest Floor and Coarse Woody Debris 
310 

parameters vary by species and region and are obtained from Birdsey (1996) and Smith, et al 

(2003). The corresponding equations, variable descriptions, units, and sources used to compute 

tree carbon are described below. 

13.2.1.1 Total Growing Stock Volume in Standing Trees 

The key input for the forest volume-to-biomass model is the total timber volume in 

standing trees. This value is expressed using the following approach: 

VT

 = VM*F*1,000/UA [1] 

The variables in this equation are defined in Table 13-1. 

Table 13-1. Total Timber Volume Variables and Parameters 

Symbol Description Units Source Comment 

VT Total timber volume m3/ha Calculated Volume must be expressed 

in m3/ha to be used in 

Forest volume-to-biomass 

model. 

VM Merchantable timber volume 1,000 

ft3

/acre 

Growth and yield tables 

from timber inventory data. 

(see Chapter X) 

F Conversion factor: 

merchantable to total timber 

volume 

 -- Birdsey 1996, specific values 

displayed in Table 2 

Assumed constant over 

age. 

UA Units conversion factor 14.29 m3

/ha = 14.29 ft3/acre 

The conversion factors (F) for Equation (1) are differentiated by region and species and 

are reported in Table 13-2. 

Table 13-2. Total Volume Conversion Factors by Region and Forest Type 

FASOMGHG Region Softwood Hardwood 

North East 2.193 2.14 

Lake States 2.514 2.418 

Corn Belt 2.601 2.651 

South East 1.682 2.233 

South Central 1.786 2.896 

Rocky Mountain 2.254 2.214 

Pacific Northwest-west 1.675 2.279 

Pacific Northwest-east 1.675 2.279 

Pacific Southwest 1.675 2.279 

Source: Birdsey(1996 a,b)). This work cites the earlier work of Birdsey (1992a and b), on which some of the initial 

carbon calculations are based. Selected values from Tables 1.2 and 1.3. 
311 

13.2.1.2 Live and Standing Dead Trees 

Carbon in live and standing dead trees is calculated using the parameters of the forest 

volume-to-biomass model equations for live and dead tree mass densities (above- and 

belowground) in Smith, et al (2003). The parameters used are weighted parameters for the 

FASOMGHG region/forest type designations. Forest land area data reported by RPA (Miles, 

2003) are used to calculated the appropriate weights. Birdsey’s assumption that mass of wood is 

approximately 50 percent carbon is used to derive the associated levels of carbon (Birdsey, 

[1992]). 

DL

 = Fw × (Gvbw + (1-exp(-VT)/Hvbw)) [2] 

DD = DL

 × Avbw × exp(-((VT/Bw)^Cvbw)) [3] 

CR

 = (DL + DD)/UB × 0.5 [4] 

Table 13-3. Tree Carbon Variables and Parameters 

Symbol Description Units Source 

DL Live-tree mass density (aboveand belowground) Mg/ha Calculated 

DD Dead-tree mass density 

(above- and belowground) 

Mg/ha Calculated 

CR Total tree carbon Mg/ac Calculated 

VT

 Total timber volume m3/ha See Equation (1) 

Fvbw,Gvbw, 

Hvbw

Weighted live tree density 

parameters from volume-tobiomass equations 

 -- Smith et al (2003) Table 7 

weighted by forest land area 

data from RPA (Miles, 2003) 

Tables 5 and 6. 

We report values in Table 3a. 

Avbw,Bvbw, 

Cvbw

Weighted dead tree mass 

density parameters from 

volume-to-biomass equations 

 -- Smith et al (2003) Table 8 

weighted by forest land area 

data from RPA (Miles, 2003) 

Tables 5 and 6. 

We report values in Table 3a. 

UB

 Units conversion factor 1 hectare (ha) = 2.471 acres -- 

The weighted parameters used are reported in Table 3a. 
312 

Table 13-3a. FASOMGHG Live and Dead Tree Density Parameters 

FASOMGHG GHG 

Region 

FASOMGHG 

GHG 

Forest Type Owner A B C F G H 

Cornbelt Hardwood Public 0.4130 222.20 0.977 406.6 0.0570 248.4 

Cornbelt Hardwood Private 0.2540 234.02 1.038 377.2 0.0590 224.3 

Cornbelt Softwood Public 0.2500 241.43 0.691 409.0 0.0480 319.0 

Cornbelt Softwood Private 0.2500 241.43 0.691 409.0 0.0480 319.0 

Lake States Hardwood Public 0.4130 222.20 0.977 406.6 0.0570 248.4 

Lake States Hardwood Private 0.2540 234.02 1.038 377.2 0.0590 224.3 

Lake States Softwood Public 0.2500 241.43 0.691 409.0 0.0480 319.0 

Lake States Softwood Private 0.2500 241.43 0.691 409.0 0.0480 319.0 

Northeast Hardwood Public 0.0910 354.15 2.156 522.4 0.0380 348.3 

Northeast Hardwood Private 0.0910 354.15 2.156 451.8 0.0480 284.7 

Northeast Softwood Public 0.1330 228.25 1.368 354.1 0.0390 208.6 

Northeast Softwood Private 0.1330 228.25 1.368 354.1 0.0390 208.6 

Rocky Mountain Hardwood Public 0.3400 1095.89 2.478 1097.5 0.1070 996.0 

Rocky Mountain Hardwood Private 0.3400 1095.89 2.478 1097.5 0.1070 996.0 

Rocky Mountain Softwood Public 5.8740 50.10 0.296 795.4 0.0520 725-1 

Rocky Mountain Softwood Private 5.9280 11.21 0.258 809.1 0.0500 733.2 

Pacific Southwest Hardwood Public 1.0480 2.67 0.230 1463.7 1119.4 

Pacific Southwest Hardwood Private 1.0480 2.67 0.230 1463.7 1119.4 

Pacific Southwest Softwood Public 1.1940 688.79 0.308 1581.9 0.0150 1745-3 

Pacific Southwest Softwood Private 1.1940 688.79 0.308 1581.9 0.0150 1745-3 

Pacific Northwest 

West Douglas Fir Public 0.2840 848.73 0.379 5062.8 0.0050 6830.2 

Pacific Northwest 

West Douglas Fir Private 0.2840 848.73 0.379 1191.2 0.0190 1251.2 

Pacific Northwest 

West Hardwood Public 0.6790 1.84 0.179 9977.5 0.0060 12560.4 

Pacific Northwest 

West Hardwood Private 0.6790 1.84 0.179 9977.5 0.0060 12560.4 

Pacific Northwest 

West Other Softwoods Public 0.5130 320.98 0.225 4902.2 0.0090 7325.7 

Pacific Northwest 

West Other Softwoods Private 0.5130 320.98 0.225 4728.3 0.0100 7048.4 

Pacific Northwest 

West Softwood Public 0.2840 848.73 0.379 5062.8 0.0050 6830.2 

Pacific Northwest 

West Softwood Private 0.2840 848.73 0.379 1191.2 0.0190 1251.2 

Pacific Northwest 

East Hardwood Public 0.9230 1.00 0.585 614.0 0.0530 660.4 

Pacific Northwest 

East Hardwood Private 0.9230 1.00 0.585 614.0 0.0530 660.4 

 (continued)
313 

Table 13-3a (continued) 

FASOMGHG GHG 

Region 

FASOMGHG 

GHG 

Forest Type Owner A B C F G H 

Pacific Northwest 

East Softwood Public 3.2290 32.94 0.246 2137.6 0.0040 2768.8 

Pacific Northwest 

East Softwood Private 1.5960 111.35 0.415 444.7 0.0160 393.4 

South Central 

Bottomland 

Hardwood Public 0.3290 30.12 0.305 313.5 0.1020 147.9 

South Central 

Bottomland 

Hardwood Private 0.1490 145.42 0.484 314.5 0.1090 174.9 

South Central Hardwood Public 0.3290 30.12 0.305 313.5 0.1020 147.9 

South Central Hardwood Private 0.1490 145.42 0.484 314.5 0.1090 174.9 

South Central Natural Pine Public 0.0470 974.52 1.355 363.1 0.1130 480.0 

South Central Natural Pine Private 0.0550 424.29 1.901 358.3 0.0940 421.9 

South Central Oak Pine Public 0.0620 835.98 0.892 282.3 0.0900 197.4 

South Central Oak Pine Private 0.0620 835.98 0.892 282.3 0.0900 197.4 

South Central Planted Pine Public 0.0630 5137.75 0.136 161.8 0.1400 116.1 

South Central Planted Pine Private 0.0630 5137.75 0.136 161.8 0.1400 116.1 

South Central Softwood Public 0.0550 3056.14 0.745 262.5 0.1260 298.1 

South Central Softwood Private 0.0590 2781.02 1.018 260.1 0.1170 269.0 

South Central 

Upland 

Hardwood Public 0.0620 313.09 2.438 241.0 0.0970 141.4 

South Central 

Upland 

Hardwood Private 0.0670 315.70 1.314 193.5 0.1520 112.8 

Southeast 

Bottomland 

Hardwood Public 0.0770 347.43 1.104 429.2 0.0570 291.6 

Southeast 

Bottomland 

Hardwood Private 0.0770 347.43 1.104 963.2 0.0260 800.4 

Southeast Hardwood Public 0.0770 347.43 1.104 429.2 0.0570 291.6 

Southeast Hardwood Private 0.0770 347.43 1.104 963.2 0.0260 800.4 

Southeast Natural Pine Public 0.0510 826.84 1.353 1213.0 0.0140 1610.1 

Southeast Natural Pine Private 0.0510 826.84 1.353 356.4 0.0430 340.9 

Southeast Oak Pine Public 0.0510 826.84 1.353 420.1 0.0350 309.8 

Southeast Oak Pine Private 0.0510 826.84 1.353 420.1 0.0350 309.8 

Southeast Planted Pine Public 0.0510 826.84 1.353 226.4 0.0670 183.7 

Southeast Planted Pine Private 0.0510 826.84 1.353 226.4 0.0670 183.7 

Southeast Softwood Public 0.0510 826.84 1.353 719.7 0.0400 896.9 

Southeast Softwood Private 0.0510 826.84 1.353 291.4 0.0550 262.3 

Southeast 

Upland 

Hardwood Public 0.0770 347.43 1.104 342.3 0.0900 261.8 

Southeast 

Upland 

Hardwood Private 0.0770 347.43 1.104 352.6 0.0610 285.8 

Source: Author calculations using Smith et al (2003) and forest land area data from RPA (Miles, 2003). 

As noted in Smith, et al (2004b), correction factors should be applied to the biomass 

model when the distribution of volume of an area is unknown. However, FASOMGHG 
314 

aggregates data by age class which means that volumes are narrowly distributed. As a result, 

there is no need to apply these factors within FASOMGHG (Smith, 2004a). 

13.2.2 Understory 

Understory vegetation comprises the smallest component of total carbon stock and 

includes all live vegetation except trees larger than seedlings. FASOMGHG makes the 

assumption that understory carbon is a fixed fraction of live tree carbon and uses published ratios 

reported in US EPA (2003) as the basis for these calculations. Weighted ratios for FASOMGHG 

regions/forest types are created using forest land area data reported by RPA (Miles, 2003). 

CU = DL

/UB × 0.5*RUw [5] 

The variables in this equation are defined in Table 13-4. The weighted parameters used 

are reported in Table 13-4a. 

Table 13-4. Understory Carbon Variables and Parameters 

Symbol Description Units Source 

CU Total Understory Carbon Mg/ac Calculated 

DL Live-tree mass density (above- and 

belowground) 

Mg/ha See Eq.2 

UB

 Units conversion factor 1 hectare (ha) = 2.471 

acres 

 -- 

RUw Weighted ratio of understory 

carbon to live tree carbon 

percent EPA (2003) Table O-2 weighted 

by forest land area data from 

RPA (Miles, 2003) Tables 5 and 

6. 

Table 13-4a. Weighted Ratio of Understory to Live Tree Carbon (Percent) 

FASOMGHG 

REGION Softwood Hardwood 

Planted 

Pine 

Natural 

Pine 

Oak 

Pine 

Douglas 

Fir 

Bottomland 

Hardwood 

Upland 

Hardwood 

Other 

Softwoods

North East 2.6 2.2 NA NA NA NA NA NA NA 

Lake States 2.1 2.4 NA NA NA NA NA NA NA 

Corn Belt 2.1 2.4 NA NA NA NA NA NA NA 

South East NA NA 6.8 6.8 4.4 NA 2.2 4.4 NA 

South Central NA NA 5.9 5.9 4.4 NA 2.2 3.7 NA 

Rocky Mountain 5.7 9.2 NA NA NA NA NA NA NA 

Pacific Northwest- NA 4.5 NA NA NA 2.0 NA NA 3.2 
315 

West 

Pacific NorthwestEast 

3.0 4.5 NA NA NA NA NA NA NA 

Pacific Southwest 5.0 2.9 NA NA NA NA NA NA NA 

Source: Author calculations using EPA (2003) and forest land area data from RPA (Miles, 2003). 

13.2.3 Forest Floor and Coarse Woody Debris 

Forest floor carbon constitutes the third largest carbon storage pool, but is much smaller 

than tree or soil carbon pools. Smith and Heath (2002) have recently developed a model 

estimating forest floor carbon mass and it forms the basis for forest floor carbon estimates in 

FASOMGHG. The model’s definition of forest floor excludes coarse woody debris materials, 

that is, pieces of down dead wood that are not attached to trees. In order to account for this 

material, coarse woody debris is assumed to be a fixed fraction of live tree carbon and is added 

to the forest floor carbon values generated by Smith and Heath’s forest floor model. Figure 13-3 

describes the essential components of these calculations. 
316 

Figure 13-3. Carbon Accumulation in Forest Floor and Coarse Woody Debris 

The model for net accumulation of forest floor carbon is a continuous and increasing 

function of age. The rate of accumulation eventually approaches zero (i.e. and a steady state level 

of forest carbon reached): 

CFFA = (Affw × Age)/(Bffw + Age) × UB

 [6] 

The variables in this equation are defined in Table 13-5a. 

Carbon Pool: 

Forest Floor Carbon and Coarse 

Woody Debris 

Forest Floor 

Decay 

• Existing Forest Land 

• Reforested Land 

(Forest to Forest,) 

Coarse Woody 

Debris 

• Existing Forest Land, 

Afforested Land 

(Agriculture to 

Forest), and 

Reforested Land 

(Forest to Forest) Forest Floor 

Accumulation 

• Existing Forest Land 

• Afforested Land 

(Agriculture to Forest) 
317 

Table 13-5a. Forest Floor Carbon Variables and Parameters: Net Accumulation 

Symbol Description Units Source 

CFFA Total Forest Floor 

Carbon net accumulation 

Mg/ac Calculated 

Age Age of Stand Years -- 

Affw,Bffw Weighted forest floor 

carbon model coefficients 

 -- Smith and Heath 

(2002) Table 4 

weighted by forest 

land area data from 

RPA (Miles, 2003) 

Tables 5 and 6. We 

report values in Table 

6a. 

UB

 Units conversion factor 1 hectare (ha) = 2.471 acres -- 

Forest floor carbon mass following clearcutting is assumed to begin at a mature forest 

level of carbon and decay is described using exponential function of time and average mature 

forest floor carbon mass: 

CFFR = (Cffw × exp-(Age/Dffw)) × UB [7] 

Since this equation accounts for decay of forest floor carbon mass existing prior to 

clearcut, this equation only applies to land with existing forests or land that is reforested. Land 

that has moved from agriculture to forestry does not include this calculation during the first 

rotation. 

The variables in this equation are defined in Table 13-5b. 

Table 13-5b. Forest Floor Carbon Variables and Parameters: Decay of Forest Floor 

Carbon Mass Existing Prior to Clearcut 

Symbol Description Units Source 

CFFR Total Forest Floor 

Carbon, residual 

Mg/ac Calculated 

Age Age of Stand Years -- 

Cffw,Dffw Weighted forest floor 

carbon mass coefficients 

 -- Smith and Heath (2002) Table 4 

weighted by forest land area data from 

RPA (Miles, 2003) Tables 5 and 6. We 

report values in Table 6a. 

UB

 Units conversion factor 1 hectare (ha) = 2.471 

acres 
318 

The weighted parameters used are reported in Table 13-5c. 

Table 13-5c. Forest Floor Carbon Model Coefficients Weighted by Forest Land Area Data 

from RPA 

Region Forest Type A B C D 

Cornbelt Hardwood 37.1 88.8 17.7 9.1 

Cornbelt Softwood 43.9 43.8 25-1 8.4 

Great Plains Hardwood 34.8 34.7 30.6 14.9 

Great Plains Softwood 43.9 87.3 24.1 24.1 

Lake States Hardwood 37.1 88.8 17.7 9.1 

Lake States Softwood 43.9 43.8 25-1 8.4 

Northeast Hardwood 37.1 88.8 17.7 9.1 

Northeast Softwood 43.9 43.8 25-1 8.4 

Rocky Mountain Hardwood 34.8 34.7 30.6 14.9 

Rocky Mountain Softwood 43.9 87.3 24.1 24.1 

Pacific Southwest Hardwood 34.8 34.7 30.6 14.9 

Pacific Southwest Softwood 43.9 87.3 24.1 24.1 

Pacific Northwest West Hardwood 53.9 44.3 29.5 16.0 

Pacific Northwest East Hardwood 53.9 44.3 29.5 16.0 

South Central Bottomland Hardwood 15-3 61.0 6.1 3.2 

South Central Natural Pine 20.4 27.1 12.2 3.8 

South Central Oak Pine 20.4 27.1 12.2 3.8 

South Central Planted Pine 20.4 27.1 12.2 3.8 

South Central Upland Hardwood 15-3 61.0 6.1 3.2 

Southeast Bottomland Hardwood 15-3 61.0 6.1 3.2 

Southeast Natural Pine 20.4 27.1 12.2 3.8 

Southeast Oak Pine 20.4 27.1 12.2 3.8 

Southeast Planted Pine 20.4 27.1 12.2 3.8 

Southeast Upland Hardwood 15-3 61.0 6.1 3.2 

Southwest Hardwood 34.8 34.7 30.6 14.9 

Southwest Softwood 43.9 87.3 24.1 24.1 

Source: Author calculations using Smith and Heath (2002) and forest land area data from RPA (Miles, 2003). 

As noted above, Smith and Heath’s model definition of forest floor excludes coarse 

woody debris materials, that is, pieces of dead wood that are not attached to trees. This is large 

woody material fallen or cut and left form live and standing dead trees with a diameter of at least 

7.5 cm (Smith, 2004). To account for effects of growth, mortality, disturbance, and decay of 

carbon in this material, coarse woody debris is assumed to be a fixed fraction of tree carbon. 

Published ratios of coarse woody debris carbon to live tree carbon reported in US EPA (2003) 

and weighted ratios for FASOMGHG regions/forest types using forest land area data reported by 

RPA (Miles, 2003). The weighted ratios used are reported in Table 13-6. 
319 

Table 13-6. Weighted Ratio of Coarse Woody Debris (CWD) to Live Tree Carbon 

(Percent) 

FASOMGHG 

REGION Softwood Hardwood 

Planted 

Pine 

Natural 

Pine 

Oak 

Pine 

Douglas 

Fir 

Bottomland 

Hardwood 

Upland 

Hardwood 

Other 

Softwoods

North East 12.3 11.2 NA NA NA NA NA NA NA 

Lake States 14.1 10.8 NA NA NA NA NA NA NA 

Corn Belt 14.1 10.8 NA NA NA NA NA NA NA 

South East NA NA 23.9 23.9 17.3 NA 21.8 24.3 NA 

South Central NA NA 18.6 18.6 17.3 NA 15.7 15.0 NA 

Rocky 

Mountain 

12.6 26.7 NA NA NA NA NA NA NA 

Pacific 

NorthwestWest 

NA 3.9 NA NA NA 11.9 NA NA 15.4 

Pacific 

Northwest-East 

14.8 3.9 NA NA NA NA NA NA NA 

Pacific SW 13.0 11.4 NA NA NA NA NA NA NA 

Source: Author calculations using EPA (2003) and forest land area data from RPA (Miles, 2003). 

13.2.4 Soil 

Soil carbon is the second-largest carbon pool of carbon. Treatment of soil carbon follows 

Birdsey (1996) and recent work by Heath, Birdsey, and Williams (2004). FASOMGHG, 

computes soil carbon profiles using soil carbon data over time from Birdsey (1996). The 

regression specifies soil carbon and a function of age (see equation 8). The variables and 

parameters are reported in Table 13-7. The results of these regressions for land transferring from 

crops or pasture to forest in Tables 13-7a and 13-7b. 

CS = (A + Bt + Ct2

)/ UC [8] 

Table 13-7. Soil Carbon Variables and Parameters 

Symbol Description Units Source 

CS Total Soil Carbon Mg/ac Regression equation calculate using 

data from Birdsey (1996) 

A Regression Intercept 1,000 lbs per ac -- 

B Regression Co-efficient for 

t 

1,000 lbs per ac -- 

C Regression Co-efficient for 

t

2

1,000 lbs per ac -- 

t Age of Stand Years -- 

UC Units conversion factor 1,000 lbs per acre = 2.205 Mg/ac -- 
320 

Table 13-7a. Soil Carbon Profile for Land Moving From Crops to Forestry by Region: 

Regressions Based On Birdsey (1996) (1,000 lbs/ac) 

Region Forest Type 

Intercept 

(A) 

t 

(B) 

t2 

(C) 

Southeast Planted Pine 32.2 0.827 -0.004 

Southcentral Planted Pine 31.6 0.810 -0.004 

Northeast White-red-jack-pine, Spruce- Fir 68.5 1.473 -0.005 

Lake States White-red-jack-pine, Spruce- Fir 55.0 1.220 -0.005 

Central States White-red-jack-pine, OakHickory 35-2 0.770 -0.003 

Rocky Mountain Planted Pine 34.2 0.754 -0.003 

Pacific Planted Pine, Douglas-Fir 41.4 0.897 -0.003 

Table 13-7b. Soil Carbon Profile for Land Moving From Pasture to Forestry by Region: 

Regressions Based On Birdsey (1996) (1,000 lbs/ac) 

Region Forest Type 

Intercept 

(A) 

t 

(B) 

t2 

(C) 

Southeast Planted Pine 45.0 0.626 -0.003 

Southcentral Planted Pine 44.0 0.610 -0.003 

Northeast White-red-jack-pine, SpruceFir 93.9 1.159 -0.005 

Lake States White-red-jack-pine, SpruceFir 75.8 0.938 -0.004 

Central States White-red-jack-pine, OakHickory 48.5 0.586 -0.002 

Rocky Mountain Planted Pine 46.7 0.600 -0.003 

Pacific Planted Pine, Douglas-Fir 56.7 0.696 -0.003 

As Heath, et al (2004) note, little change in soil carbon occurs if forests are regenerated 

immediately after harvest. As a result, FASOMGHG assumes soil carbon on a reforested stand 

remains at a steady-state value. Currently, the age that this value is reached is assumed to be the 

minimum harvest age for FASOMGHG region/forest type (see Chapter X). This assumption is 

generally consistent with the ages at which steady-state levels of soil carbon are achieved in 

Birdsey (Birdsey, 1996). 

CS = A + Agemin + Agemin

 2 [9a] 

For example, a reforested softwood stand in the southeast with a minimum harvest age of 

50 years would have a soil carbon value of : 
321 

CS = [32.2 + 50 × (0.827) + 502 × (-0.004)]/2.205 = (32.2 + 41.4 -- 10)/2.205 = 28.8 Mg/ac 

[9b]

Afforested land coming from crop or pasture use start with the initial soil carbon value 

reported by Century -- -- -- and begin accumulating soil carbon until a steady-state is attained 

(again assumed to be the minimum harvest age for the FASOMGHG region/forest type). The 

soil carbon profile for an afforested stand use the regression coefficients in Tables 13a and 13b: 

CS = Century Ag Soil Carbon Value × ((B/A)t +(B/A)t2,) 

Using this approach, FASOMGHG soil carbon values are consistent with the levels of 

soil carbon existing at the time of land use conversion and rates of soil carbon accumulation 

reported by Birdsey (1996). 

13.3 Carbon disposition after harvest 

This section describes how FASOMGHG physically tracks the fate of carbon, after 

harvest. Figure 13-4 provides a schematic of the disposition of carbon after harvest and points on 

the critical path are described. To calculate carbon in harvested logs, cubic feet of roundwood 

(the units in which timber is quantified in the model) is converted into metric tons of carbon 

using factors reported in Skog and Nicholson (2000) (see Table 13-10). These factors vary by 

region and are reported for logs coming from an aggregate softwood and hardwood stand. They 

exclude carbon in logging residue left onsite. Logging residue is tracked separately in the forest 

floor carbon pool described above in Section 9.1.2.3. 

Harvested logs removed from site are converted into three types of outputs through 

primary manufacturing processes: FASOMGHG wood and paper products, mill residue, and 

fuel wood. The fate of each of these types is discussed in turn below. 

Table 13-8. Carbon per unit of Roundwood, by Region (lbs/ft3) 

Skog and Nicholson Region FASOMGHG Region Softwood Log Hardwood Log 

North East North East 12.15 19.21 

North Central Lake States 12.55 17.33 

North Central Corn Belt 12.55 17.33 

South East South East 16.90 19.82 
322 

South Central South Central 16.90 19.82 

Rocky Mountain (Average of North 

and South) 

Rocky Mountain 13.36 11.87 

Pacific North West-west Pacific North West-west 15-11 11.76 

Pacific North West-east Pacific North West-east 13.29 11.76 

Pacific Southwest Pacific Southwest 15-11 11.76 

Source: Skog and Nicholson. 2000, Table 5-1. 
323 

Figure 13-4. Carbon Disposition after Harvest 

13.3.1 Wood and Paper Products 

FASOMGHG contains the following 13 wood and paper products: 

Softwood sawlogs for export, 

Carbon Disposition After 

Harvest 

Harvested Logs Removed from 

site 

Primary FASOMGHG 

Manufacturing 

Wood and Paper Products (i = 

1,...13) Section 8.1.3.1 

Mill Residue 

Section 8.1.3.2 

Fuelwood 

Section 8.1.3.3 

Logging Residue 

Down Dead Wood (Coarse Woody 

Debris) 

Accounted for in on-site module 

Wood and Paper Product 

Disposition Over Time 

Section 8.1.3.1 

Emission Fuel Offset 

Emission 

In-product or Landfill 

Section 8.1.3.1.2 

Secondary Manufacturing 
324 

Hardwood sawlogs for export, 

Softwood lumber, 

Softwood plywood, 

Oriented strand board, 

Hardwood lumber, 

Hardwood plywood, 

Softwood miscellaneous products, 

Hardwood miscellaneous products, 

Softwood used in non-OSB reconstituted panel, 

Hardwood used in non-OSB reconstituted panel, 

Softwood pulpwood, and 

Hardwood pulpwood. 

The previous FASOMGHG model handled product and other offsite carbon pools using a 

method developed in the early 1990s by Row and Phelps (Row and Phelps, 1991). The USFS 

has since modified their approach to product accounting using the work of Skog and Nicholson 

(2000). The distribution of product carbon changes over time and FASOMGHG tracks the fate of 

product carbon for each end-use using two pools: carbon remaining in-product and carbon 

leaving the product (see Figure 13-5). Carbon that leaves the product ultimately makes its way to 

emissions or is permanently sequestered in landfills. 
325 

Figure 13-5. Wood and Paper Product Carbon Disposition 

Total Carbon in Wood and Paper 

Products 

Emission

Carbon

remaining in 

product

Landfill 

Landfill

(Permanent) 

Landfill

(Temporary) 

Carbon

leaving

product 
326 

13.3.1.1 Fraction Remaining in Product 

Skog and Nicholson’s model (2000) specifies a half-life values for a set of end-use 

categories (see Table 13-8). The half life represents the time it takes for approximately half of 

the product to decompose. For example, carbon store in paper products have a short life with 50 

percent of carbon decomposing in 2 years. In order to map these end uses to FASOMGHG wood 

and paper products and compute the appropriate weighted half-life, FASOMGHG uses the end 

use weights reported in Table 13-10. For example, softwood pulpwood is only used in paper end 

uses (weight=1.0). Therefore the half life for this FASOMGHG product is 2 years. 
327 

Table 13-10. Distribution of FASOMGHG Wood and Paper Products Across End-Uses (Percent) 

FASOMGHG Product 

Skog End Use Categories 

Softwood 

Sawlogs for 

Export 

Hardwood 

Sawlogs for 

Export 

Softwood 

Lumber 

Softwood 

Plywood 

Oriented Strand 

Board 

Hardwood 

Lumber 

Hardwood 

Plywood 

Softwood 

Miscellaneous 

Products 

Hardwood 

Miscellaneous 

Products 

Softwood Used 

in Non-OSB 

Reconstituted 

Panel 

Hardwood Used 

iNOSB 

New Residential Construction Single family 0.33 0.04 0.33 0.33 0.58 0.04 0.13 0.33 0.04 0.13 0.1Multifamily 0.03 0.00 0.03 0.03 0.05 0.00 0.02 0.03 0.00 0.02 0.0Mobile homes 0.04 0.00 0.04 0.04 0.06 0.00 0.04 0.04 0.00 0.04 0.0Residential upkeep & improvement 

0.25 0.04 0.25 0.24 0.16 0.04 0.11 0.25 0.04 0.11 0.1

New Nonresidential ConstructionAll except railroads 0.08 0.03 0.08 0.09 0.07 0.03 0.05 0.08 0.03 0.05 0.05 Railroad ties 0.00 0.05 0.00 0.00 0.00 0.05 0.00 0.00 0.05 0.00 0.00 Railcar repair 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.00 0.00 Manufacturing Household furniture 0.02 0.24 0.02 0.05 0.00 0.24 0.14 0.02 0.24 0.14 0.14 Commercial furniture 0.00 0.05 0.00 0.05 0.01 0.05 0.22 0.00 0.05 0.22 0.22 Other manufactured 0.04 0.10 0.04 0.08 0.02 0.10 0.09 0.04 0.10 0.09 0.09 Shipping Wooden containers 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.01 0.01 0.01 Pallets 0.04 0.35 0.04 0.03 0.00 0.35 0.00 0.04 0.35 0.00 0.00 Dunnage etc. 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.00 0.00 Other 0.13 0.01 0.13 0.01 0.04 0.01 0.14 0.13 0.01 0.14 0.14 Exports 0.03 0.08 0.03 0.04 0.01 0.08 0.05 0.03 0.08 0.05 0.05 Paper 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Total 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 
328 

Table 13-9. Half Life for Products in End Uses 

End Use or Product Half Life in Years 

Paper 2 

New residential construction 

Single family 100 

Multifamily 70 

Mobile homes 12 

Residential upkeep & improvement 30 

New nonresidential construction 

All ex. railroads 67 

Railroad ties 12 

Railcar repair 12 

Manufacturing 

Household furniture 30 

Commercial furniture 30 

Other products 12 

Shipping 

Wooden containers 6 

Pallets 6 

Dunnage etc. 6 

Other uses for lumber and panels 12 

Uses for other industrial timber products 12 

Exports 12 

To compute the fraction of carbon remaining in one unit of FASOMGHG products, the 

HWP model uses the data on the distribution of product across end-uses (Table 13-8), and an 

exponential decay function: 

FP

= ∑ [SiFP

 t-1 × exp(-ln(2)/HL× t)] [10] 

The variables in this equation are defined in Table 13-11. 

Table 13-11. Product Carbon Parameters 

Symbol Description Units Source 

FP Fraction of Carbon remaining in-product 

for one unit of FASOMGHG product. 

Percent Calculated 

Si Share of product in end use i. Table 9 

FP

t-1 Fraction of carbon remaining in-product 

from the previous period 

Percent -- 
329 

HL End-Use Half Life Years See Table 8 

T Time Years 

13.3.1.2 Fate of Carbon Leaving Wood and Paper Products 

Carbon leaving the product pool moves to either the emissions pool or landfill pool. Skog 

and Nicholson’s HWP model (2000) assumes that 67 percent of carbon leaving the wood product 

pool goes to landfills. Similarly 34 percent of carbon leaving the paper product pool goes to 

landfills. The remaining shares for each product are immediately released back to the atmosphere 

(emissions) 

Once in landfills, the HWP model tracks carbon using permanent and temporary landfill 

pools. Carbon in permanent landfills is not released back to the atmosphere and remains 

sequestered in landfills forever. Carbon in temporary landfills decays and is eventually released 

to the atmosphere. The HWP model assumes approximately 77 percent of the wood product 

going into landfills remains permanently sequestered. Only 44 percent of paper product remains 

permanently sequestered. Finally, carbon in temporary landfills eventually is released to the 

atmosphere. The HWP model uses an exponential decay function for the degradable fraction 

landfill carbon and specifies a half-life value of 14 years for wood and paper products. 

13.3.2 Disposition of Mill Residue 

FASOMGHG also tracks the fate of mill residue using two pools: Mill residue used as an 

intermediate input for wood and paper products and burned at the mill (see Figure 13-6). Carbon 

in mill residues that make it to product are tracked using the appropriate product carbon profile 

described above. Residue used for other uses is tracked in the following manner. First, the 

fraction of other mill residue that is used for fuel is computed using data from Table 41 of the 

Forest Resources of the US, 1997 (Smith, et al, 1997). These fractions are reported in Table 13-

12. Currently 1/3 of burned mill residue is used to offset fossil fuels. Currently, each unit of mill 

residue burned for energy purposes is assumed to get one unit of carbon offset credit. The model 

parameters can be modified to not assign a credit for residue burning for energy production. 

Table 13-12. Fraction of Mill Residue Burned 

Softwood Percent 
330 

Northeast 40% 

Lake States 75% 

Corn Belt 75% 

Southcentral 81% 

Southeast 75% 

Rocky Mountain 79% 

Pacific Northwest-West 97% 

Pacific Northwest-East 97% 

Pacific Southwest 85% 

Hardwood 

Northeast 44% 

Lake States 56% 

Corn Belt 56% 

Southcentral 76% 

Southeast 82% 

Rocky Mountain 19% 

Pacific Northwest-West 78% 

Pacific Northwest-East 78% 

Pacific Southwest 100% 

Figure 13-6. Disposition of Carbon in Mill Residue 

Removed to file fasomGHGfigures
331 

13.3.3 Disposition of Fuelwood 

Harvested fuel logs and the associated carbon are used as to produce energy at mills (see 

Figure 13-7). The default assumption holds that 100 percent of fuel wood burned in the 

sawtimber and pulpwood production process are used to offset fossil fuels. The assumption can 

be modified down as far as zero percent at the discretion of the model scenario. 

Mill Residue 

Intermediate Input Other Use 

Burned 

Emission 

Burned 

Offset 

Wood and Paper 

Product Accounting 

Burned Other 

(emission) 
332 

Figure 13-7. Disposition of Carbon in Fuelwood 

Removed to file fasomGHGfigures

13.4 Disposition of Site Carbon after Deforestation 

In FASOMGHG, land used in forestry can move to agriculture or developed use. 

When land moves from forestry one of these uses, three carbon pools are tracked (see 

Figure 13-8): 

Residual forest floor carbon 

Soil Carbon in agriculture 

Soil Carbon in developed use 

For agriculture and developed land uses, the path of residual forest floor carbon stock is 

assumed to be the same as for the forest floor carbon profile after a harvest (see Eq [7]) above. 

This model of decay is based on the average forest floor of mature forests and regional averages 

for decay rates as described in Smith and Heath (2002). 

Fuelwood 

Burned 

Emission

Offset 
333 

Absent better date for transition paths of soil carbon, the following approaches are used. 

For forestry switching to agriculture, soil carbon levels are assumed to be consistent with century 

ag soil data and do not vary over time. For forestry switching to developed land use, we assume 

the soil carbon levels are consistent with the steady-state value of the minimum harvest age and 

use the data in Tables 13a and 13b to derive the soil carbon level this level does not vary with 

time. 

Figure 13-8. Disposition of Site Carbon after Deforestation 

Years in Agriculture or Developed 

Residual Forest Floor 

Soil 

Total 

M
334 

14 CHAPTER 14 FOREST SECTOR DATA DETAIL (ADAMS AND ALIG) 

The forest sector of FASOMGHG is patterned in large part after the basic structures of the 

TAMM, NAPAP, ATLAS, and AREACHANGE models. Data for the various demand and supply 

processes in the sector come primarily from the most recent versions of these models as described by 

Haynes (2003) for the U. S. Forest Service's 2000 RPA Timber Assessment and from forest inventory 

data collected by the Forest Service's Forest Inventory and Analysis groups.This chapter describes forest 

sector key models and data sources. Terms are defined in a Glossary in the Appendix. 

Modeling of timberland dynamics in the forest sector component of the FASOMGHG model is 

based largely on the USDA Forest Service modeling system for conducting national periodic assessments 

of the nation's forests and related renewable resources under the Resources Planning Act (RPA) (Haynes 

2003). Data for the different components are derived primarily from the 2000 RPA Timber Assessment. 

Next, we describe key models and data sources below. For more information on the RPA modeling 

framework see Haynes (2003). 

The general modeling framework used for the 2000 RPA Timber Assessment has evolved over 

the past 20 years to fill needs for greater geographic and product specificity in the timber resource 

projections and now consists of a set of linked submodels. The Timber Assessment Market Model 

(TAMM) embraces the solid wood products sector and also provides the linkage between product markets 

(solid wood and pulpwood) and the timber inventory (Adams and Haynes 1996). The North American 

Pulp and Paper Model (NAPAP) is a model of the paper and board sector, with detailed treatment of fiber 

supply (recycled, roundwood, and short-rotation woody crops) (Ince 1999). The Aggregate Timberland 

Assessment System (ATLAS) is a structure for projecting timber inventory over time (Mills and Kincaid 

1992). The AREACHANGE model explains the shifting of land between forest and non-forest uses and 

among forest types (Alig et al. 1990, Alig et al. 2003). 

14.1 Changes in Timberland Area 

14.1.1 Timberland Inventory Representation 

Timberland by region in the FASOMGHG model is represented by aggregates, based on 

combinations of strata presented in Table 14.2.1.1. The sources and format of associated data 

representing timberland strata are discussed next. 

To provide perspective, 358 million acres of private timberland existed in the US in 1997 

(table 14.2.1.1-2) (Smith et al. 2001). One-half of the private timberland acres are in the South. 
335 

In addition, 80 percent of the private timberland area is held by nonindustrial private forest 

(NIPF)owners, although a large percentage of forest land in the Pacific Northwest is owned by 

the forest industry (see glossary for definitions). The area of National Forest timberland in the 

contiguous 48 states is 93 million acres, while other public timberland covers another 41 million 

acres. Finally, hardwood species are the predominant forest species group in the East while 

softwood species are the primary forest species group in the West. 

Modeling of timberland dynamics in the forest sector component of the FASOMGHG 

model is based largely on the USDA Forest Service modeling system for conducting national 

periodic assessments of the nation’s forests and related renewable resources under the Resources 

Planning Act (RPA) (Haynes 2003). Data for the different components are derived primarily 

from the 2000 RPA Timber Assessment. Next, we describe key models and data sources below. 

Terms are defined in a Glossary in the Appendix, and for more information on the RPA 

modeling framework see Haynes (2003). 

The general modeling framework used for the 2000 RPA Timber Assessment has evolved 

over the past 20 years to fill needs for greater geographic and product specificity in the timber 

resource projections and now consists of linked models (Haynes 2003). A key model is the 

Timber Assessment Market Model (TAMM) that embraces the solid wood products sector and 

also provides the linkage between product markets (solid wood and pulpwood) and the timber 

inventory (Adams and Haynes 1996). The North American Pulp and Paper Model (NAPAP) is a 

model of the paper and board sector, with detailed treatment of fiber supply (recycled, 

roundwood, and short-rotation woody crops) (Ince 1999). The Aggregate Timberland 

Assessment System (ATLAS) is a structure for projecting timber inventory over time (Mills and 

Kincaid 1992). The AREACHANGE model explains the shifting of land between forest and nonforest uses and among forest types (Alig et al. 1990, Alig et al. 2003). 

The RPA system of models is an example of a bioeconomic model, as it combines 

representations of both biological and economic processes. Major links among the models have 

evolved over time, and the modular structure facilitated development of a forest sector 

foundation for the FASOMGHG model. For example, timber harvest estimates lead to 

adjustments in timber inventories, given changes in forest growth and timberland area. Such 

adjustments in the FASOMGHG model are based on perfect foresight and economic optimality 

conditions, but draw upon very similar input data sets for initial inventory estimates and timber 

growth and yield. In ATLAS modeling, allocation of acres to MICs is exogenous or pre-set, 

governed in part by externally developed scenarios of prospective future private and National 

Forest timber management decisions. In the FASOMGHG model, allocation of acres in the 
336 

future to MICs is endogenous, sensitive to market elements such as prices and costs. This 

background can be useful to bear in mind when viewing output from the respective forest sector 

modeling systems. Below we describe related RPA models and supporting data by the modeling 

categories used in Section 7.1. 

The 504 million acres of US timberland contain almost one trillion cubic feet of timber 

(Smith et al. 2001). About half of that growing stock volume is on private timberlands (table 

14.2.1.1-2). The majority of private timberland is within the eastern US, with most of that in the 

South. The Eastern regions have much more private timberland area and timber volume in the 

younger age classes. For example, 22% of timberland area in the East has stands with trees less 

than 20 years of age, in contrast to 12% for the West (Smith et al. 2001, Alig 2005). Timberland 

is managed differently by ownership, and the Western regions in the FASOMGHG model 

contain relatively more public timberland, 65% compared to 15% in the East. 

The majority of public timberland is located in the Pacific Northwest and Rocky 

Mountain regions. The RM region has 48 million acres of timberland, more than twice as much 

as the Pacific Northwest region. However, timber volumes per acre are typically higher in the 

more productive Pacific Northwest, with its timber volume of 155 billion cubic feet exceeding 

that for the Rocky Mountain region (140 billion cubic feet). 

Timberland on various public ownerships—including Federal, state, and local public 

owners—represented 29% of the US timberland and provided 11% of US timber removals in 

1997 (Smith et al. 2001). Timber inventories on National Forests are represented in the current 

model but timber management and harvest decisions are exogenous or pre-selected. 

Representation of the timber inventory facilitates carbon accounting on the National Forest 

timberland. Timber inventories on other public timberlands are currently not represented but 

their timber harvests are taken as exogenous.5

Nontimberland, forestland constitutes about 30% of the forest land in the US. These lands 

include some withdrawn from timber harvest activities (e.g., wilderness) and low productivity 

lands (e.g., pinyon-juniper lands). Such forestland is stocked with at least 10% forest cover (see 

Glossary). Also included are forest areas adjacent to urban and built up lands. Although the land 

area in this category is large, data pertaining to site quality and inventory structure are generally 

 

5 National Forest timberland inventories are drawn from the RPA Assessment process and it is anticipated that 

consistent data for other public inventories will be ready in the near future. 
337 

unavailable. Thus, timber harvest on this land is taken as exogenous, and changes in forest 

inventory volumes or structure are not accounted for in the FASOMGHG model. 

Timberland described above represents about four-fifths of forest land in the contiguous 

48 states. Forest land is any land with at least 10 percent tree cover and timberland is that subset of 

forest land that has the capability to grow at least 20 cubic feet per acre per year of commercial 

timber products and is not legally withdrawn from timber harvest activities (see glossary in 

Appendix). Inventory information for non-timberland forest land, which is largely in public 

ownership, is not as complete as for timberland, and this precludes developing a comparable 

inventory (e.g., site class and inventory structure) of such lands in the FASOMGHG model. Such 

forest land contains a considerable amount of designated wilderness and low productivity land 

(e.g., pinyon-juniper), so that their exclusion represents a small part of commodity production. 

The expected direction of future policies will also likely place increasing weight on the 

management of such lands for non-market benefits. Next, we summarize how timberland is 

stratified in the FASMGHG modeling. 

Each region in FASOMGHG possesses a different endowment of land and timber yields. 

Nine regions are used to represent the productive land base in the forest and agriculture sectors: 

Northeast, Lake States, Corn Belt, Southeast, South Central, Rocky Mountains, Pacific 

Northwest Westside, Pacific Northwest Eastside, and Pacific Southwest (Adams et al. 1996) (see 

earlier figure 3.10). Two additional regions that contain insignificant timberland areas (from a 

national perspective) fill out the agriculture side: the Northern and Southern Great Plains. 

The stratum for land suitability was added beyond what was used in the ATLAS 

modeling. To enable the modeling of land exchanges, five land suitability classes were defined: 

FORONLY, FORCROP, FORPAST, CROPFOR, and PASTFOR. For the land use suitability 

classification, referred to as LAND CLASS in subsequent discussion, we used classes for crop or 

pasture plus a "forest only" class that can not shift use. On the agricultural side, acres by region 

that could potentially be converted from crop or pasture land to forest land were included in the 

CROPFOR and PASTFOR land classes, respectively, based on National Resource Inventory data 

of the USDA Natural Resources Conservation Service (1989, 2001) and the study by Moulton 

and Richards (1990). In the forestry inventory, acres that could be converted from forest to crop 

or pasture use were included in the FORCROP and FORPAST classes, respectively. Acres 

suitable for transferring between agriculture and forestry use were assigned to high and medium 

site classes. All other private timberland acres, which were not eligible for transferring between 

sectors, were assigned to the FORONLY land class. 
338 

Definitions of the private owner groups are the traditional ones, where industrial owners 

are integrated in some way to processing facilities and NIPF owners are not. Native American 

lands are included in the latter group.6 National Forest inventory is represented, but public timber 

harvests from those lands and other public lands (e.g., State timberlands) are treated as 

exogenous. Timberland on the other public ownership (e.g., State timberlands) is not included, 

although their harvest levels are exogenous inputs based on a policy input. 

Two or more forest type groups by region are used to reflect variations in timber yields, 

financial returns, and other attributes (e.g., forest carbon). In all regions except the SC, SE, and 

PNWW, two broad forest types-softwoods (SOFT) and hardwoods (HARD)-are used. In the 

Southern regions, five forest types were drawn directly from the 2000 RPA Timber Assessment 

(Haynes 2003): planted pine, natural pine, oak-pine, upland hardwood, and bottomland 

hardwood. For the Pacific Northwest Westside, the three forest types are Douglas-fir, other 

softwoods, and hardwoods. 

FASOMGHG employs four different species types in all regions except the SC, SE, and 

PNWW: 1) SOFTSOFT -- softwood forest type in current and subsequent model periods; 2) 

HARDHARD -- hardwood forest type in current and subsequent model periods; 3) HARDSOFT 

-- hardwood forest type that is naturally regenerated or replanted to softwood type; and 4) 

SOFTHARD -- softwood forest type that is regenerated or replanted to hardwood type. 

In the South, 25 forest type classes are used, based on combinations of the following five 

forest types reported by FIA (Smith et al. 2001): planted pine, naturally-regenerated pine, oakpine, upland hardwoods, and bottomland hardwoods. An example is upland hardwoods-planted 

pine, where planted pine exists in the current model period after following upland hardwoods 

that covered an aggregate in the preceding model time period. Some forest type combinations or 

pathways are excluded, such as upland hardwood-bottomland hardwoods because of site 

considerations (table 14.2.1.1-3). For afforestation opportunities, table 14.2.1.1-4 lists forest 

types by region. I THOUGHT WE DROPPED THIS

In the Pacific Northwest Westside, nine forest type classes are used for existing and 

regenerated stands, based on combinations of the following three forest types: Douglas-fir, other 

softwoods, and hardwoods. An example forest type class is Hardwoods-Douglas-fir, where 

 

6 Native American timberlands were included with the "other public" ownership in the ATLAS modeling in the 

2000 RPA Timber Assessment. Thus, comparisons of timberland areas and timber volumes by ownerships 

reflect such differences. 
339 

Douglas-fir exists in the current model period after following hardwoods that covered the 

aggregate in the preceding model time period. 

The site productivity classification scheme is based on potential annual cubic-foot 

volume growth at culmination of mean annual increment in fully stocked natural stands (Haynes 

2003). Inventory data allowed differentiation of timberlands into three site classes (low, medium, 

and high) in the two southern regions and the Pacific Northwest Westside. Elsewhere, limited 

data only allowed identifying a single average site class. 

Timber yields can vary markedly by site groups. For the three site classes in the SC, SE, 

and PNWW, measures of forest productivity are: 1) HIGH -- High site productivity group (as 

defined in ATLAS); 2) MEDIUM -- Medium site productivity group; and 3) LOW -- low site 

productivity group. The site groups were defined based on ATLAS inputs from the 2000 RPA 

Timber Assessment (Haynes 2003). Productivity ranges can vary by region. For the South, the 

HIGH site group produced at least 85+ cubic feet/acre/year at culmination of MAI. The 

MEDIUM site group produced 50-84 cubic feet/acre/year while the LOW site group produced 

20-49 cubic feet/acre/year. In the Pacific Northwest-Westside region, the site groups were 

defined for Hemlock and other species. For Hemlock, the HIGH site group can produce at least 

225+ cubic feet/acre/year at culmination of MAI. The MEDIUM site group can produce 120-224 

cubic feet/acre/year, while the LOW site group can produce 20-119 cubic feet/acre/year. For all 

other species, the HIGH site group produced at least 165+ cubic feet/acre/year; the MEDIUM 

site group 120-164 cubic feet/acre/year; and the LOW site group produced 20-119 cubic 

feet/acre/year. 

An average or medium site class was assigned for National Forest timberland across 

regions and for private timberland in regions other than the Southeast, South Central, and Pacific 

Northwest Westside. An exception is use of an average or medium site class for bottomland and 

upland hardwood forest type groups in the Southern regions. THE SITE PRODUCTIVITY 

GROUPS CAN’T VARY BY SPECIES!!!

Five year age cohorts were developed for trees on timberland in the FASOMGHG 

model, based on ATLAS information and FIA estimates. Five year age classes were used by 

ATLAS for the two southern regions, and this facilitated assigning acres within ATLAS age 

classes to appropriate FASOMGHG age cohorts. ATLAS assignment of acres to age classes for 

the Southern regions included having the first year age cohort class represent years 0-7. Class 2 

represents ages 8-12, class 3 represents 13-17 years of age and so on until the terminal cohort 18 

that spans aggregates five years and older. 
340 

For the Pacific Northwest Westside, age cohorts are separated into 21 five year classes. 

Age cohort 1 (0-4 years of age) comprises the first class, 2 (5-9) comprises the second age class 

and so on until age cohort 21, which is comprised of aggregates aged 100 and older. In regions 

outside the SC, SE, and PNWW, ATLAS age classes are in ten-year intervals and start in year 1 

(0-9) and continue with year 2 (10-19), and so on until age class 10 that contains aggregates 90 

years and older. In these regions, the ten year age classes were separated into five year age 

cohorts to align with the Southern and Pacific Northwest Westside regions. 

WHAT ABOUT REGIONS OUTSIDE THE PNWW AND SOUTH. 

I THOUGHT WE WEREN’T GOING TO TALK ABOUT THE NF 

INVENTORIES SINCE THEY’RE NOT IN TH E MODEL??? 

Inventory acres of existing National Forest timberland from ATLAS were complied into 

FASOMGHG input tables in the same way as described above for private timberland. National 

Forest data from ATLAS modeling was also stratified the same as ATLAS private timberland 

data (Mills and Zhou 2003). Acres were classified by region, land class, owner, forest type, site 

class, MIC, and age cohort. Southern National Forest data were provided in five year increments, 

while areas outside the South were represented by ten-year age intervals. Forest types were 

aggregated into softwood and hardwood groups for all regions. Each stand in the inventory was 

assigned a medium site class, because no site detail is provided in ATLAS for National Forest 

timberland (Mills and Zhou 2003). National Forest inventory data were not broken out by land 

class, as timberland is assumed not to be eligible for conversion to other land uses. 

14.1.2 Land Base Adjustments 

Transfers of land between the agriculture and forest sectors are endogenous in the 

FASOMGHG model. Exogenous projections of the conversion of timberland and agricultural 

land to developed uses are drawn from modeling by Alig et al. (2004). Population and personal 

income are key drivers in the model (table 14.2.1.1-5). 

The projections of conversions to urban and developed uses were drawn from a synthesis 

of findings from RPA-based land use studies, a study by Alig et al. (2003), and analysis of the 

1997 National Resource Inventory (NRI) data. Because conversion and development of 

farmland, forests, and other open space accelerated during the 1990s, FASOMGHG estimates of 

deforestation were updated from statistical and econometric analyses of data by Alig et al. 

(2003). We also drew upon analyses of developed area trends and projections prepared by 

Plantinga and Lubowski as part of the 2005 RPA Assessment Update (Alig and Plantinga 2004), 
341 

based on NRI data. In addition, we examined trend data for forest area compiled for the 2000 

RPA Assessment by the USDA Forest Service. 

For the contiguous United States, each developed area is designated by State, and is 

assumed to come out of existing FASOMGHG land suitability classes (e.g., FORCROP) in 

proportion to what exists currently. The proportion that each state contributed to total 

development in the contiguous United States was based on data from the National Resources 

Inventory by the USDA Natural Resources Conservation Service (2001). Deforested acres are 

assumed to exit the timberland base by age cohort in proportion to the existing distribution of 

total NIPF timberland area by age cohort. 

Consistent with the early FASOM work (Adams et al. 1996), FASOMGHG projects no 

significant net change in timberland area for forest industry ownerships. By assumption, this 

means that the amount of NIPF timberland acquired by forest industry will offset the conversion 

of some forest industry land to urban and developed uses. Thus, developed land use movements 

in the modeling were restricted to NIPF owners. 

Another exogenous land transfer into forestry is tree planting due to government 

programs. Tree planting due to government programs was enrolled each time period by region, 

for reforestation and afforestation. Estimates were based on RPA land base analyses (Alig et al. 

2003), tree planting reports from the State and Private Forestry branch of the USDA Forest 

Service (1998), a study by Kline et al. (2002), and personal communication with State and 

Private Forestry staff. Historically, most of the government-subsidized US tree planting has been 

in the South, mainly involving pine plantations. For example, in 1998, about 80% of all US land 

planted in trees was in the South, represented by the Southeast and South Central regions in the 

FASOMGHG modeling (see figure 3.xx in earlier chapter). 

14.2 Forest Inventory 

Forest inventory data representing the private timberland base consists of the area by 

strata described earlier and the merchantable timber volume per acre. Each stratum is represented 

by the number of timberland acres and the growing stock timber volume per unit area (in cubic 

feet per acre) it contains. FASOMGHG inventory data were derived from the ATLAS inventory 

estimates for the 2000 RPA Assessment (Haynes 2003). The ATLAS data sets are based on 

approximately 180,000 permanent ground plots maintained by regional FIA units of the USDA 

Forest Service (Smith et al. 2001). Example FIA surveys for one State are the last periodic 

surveys for western Oregon (Azuma et al. 1997) and eastern Oregon (Azuma et al. 2002). More 
342 

information on FIA surveys can be obtained from the national FIA Web site (http://fia.fs.fed.us), 

including description of its 76-year history as the nation’s forest census dating back to the 

McSweeny/McNary Act of 1928. Over its history, FIA units have continuously monitored the 

extent, condition, and trends of our nation’s forests, and in recent decades have played an 

important role in supporting the periodic RPA Assessment and by extension helping support the 

FASOMGHG modeling. 

The timberland base in the FASOMGHG model consists of inventory area and timber 

volumes per acre for private ownerships and National Forests, based on compiled data from 

inventory plots maintained by regional FIA units of the USDA Forest Service (Smith et al. 

2001). The FIA surveys conducted by the USDA Forest Service are designed to provide 

objective and scientifically credible information on key forest attributes, such as forest stocks, 

growth, harvest, and mortality. Related data are collected on region, forest ownership category 

(e.g., forest industry vs. nonindustrial private forests), and cover type (e.g., planted pine), by 

using a sample of around 180,000 permanent plots. The FIA inventories provide consistent forest 

inventory data for the Nation back to 1953 (Smith et al. 2001). The FIA inventories measure 

approximately one field plot for every 6,000 acres of forest land in most regions. 

14.2.1 Even-aged Forest Inventory 

A key determinant of what timber volumes will grow in the various timberland strata of 

the inventory are current and possible future timber management regimes, referred to here as 

timber management intensity classes (MICs). MICs representing regimes or packages of 

silvicultural practices now being used and those that might be applied to future stands were 

developed for the 2000 RPA Timber Assessment in collaboration with the American Forest and 

Paper Association, the Southern Forest Resources Assessment Consortium, and State Forestry 

agencies in different regions (Haynes 2003). MICs describe the methods of regeneration (natural 

or planted), stand density control (precommercial or commercial thinning), fertilization, and 

method of harvest (partial cutting or clearcutting). Another class is area reserved from harvest. 

The MICs represents a regional average response for a particular forest type and site class. 

We use two broad representations of timber management: even-aged and partial cutting. 

In partial cutting, we remove typically only the mature trees, leaving the immature trees to grow, 

thereby allocating a portion of the growing space to regeneration. To contrast, we remove all of 

the trees when harvesting an even-aged stand in order to allocate all of the growing space to 

regeneration. For example, when growing southern pine plantations for timber, an even-aged 

management scheme is represented. 
343 

At its most basic level, ATLAS uses an “even-age” model of the timber inventory, in 

representing the inventory as a collection of age classes. ATLAS advances acres through the age 

classes over time to simulate the growth and progression of timberland aggregates. Throughout a 

projection, each unit of area, or cell, can be identified by attributes or strata. The projection 

mechanism in ATLAS moves each aggregate cell along an independent timber yield trajectory. 

The timber yield estimation process projects cell volumes period to period in a fashion consistent 

with the timberland inventory age classes. The timber yield tables and associated yield projection 

inputs required for the growth models were derived from FIA field data, from cooperative 

research and consultation with private forest land owners, and from previous studies (Haynes 

2003). The FIA field data describe forest conditions at a plot level, which are aggregated to 

regional levels by strata to combine a broad mix of conditions. The even-aged characterization 

used by ATLAS gives way, in effect, to a multi-age model where age classes might alternatively 

be thought of as growth classes. 

For the 2000 RPA Timber Assessment, the most detailed representation of the timberland 

inventory was for the key timber supply regions of the SC, SE, and PNWW. Examples of added 

detail for these regions are the site classes described above and the timber management intensity 

classes described in the next section. Timberland data in those two regions were further stratified 

by three site productivity classes and up to 12 timber management intensity classes (table 

14.2.2.1). Thus, the most detailed set of timberland attributes used to identify a unit of private 

timberland inventory would be region, owner, forest type, site productivity class, management 

intensity classes, and age. Timber resource data for National Forests were stratified into three 

management intensity classes. 

For all regions other than the SC, SE, and PNWW, the FASOMGHG model uses two 

MICs that dictate how timberland aggregates are managed: 1) passive -- lowest management 

intensity; and 2) low -- low management intensity class. The "passive" MIC refers to very little 

management intervention between harvests of naturally regenerated aggregates. The low MIC 

refers to custodial management of naturally regenerated aggregates, and may include protection 

measures such as fencing but no significant intermediate treatments such as fertilization or 

precommercial thinning. 

The passive MIC was added in the FASOMGHG model beyond the ATLAS-based MICs 

to represent future harvested acres that are totally passively managed, where the owner accepts 

whatever type and rate of regeneration occurs naturally. Relative to the low MIC, where 

timberland receives a low-level of timber management, such as forest protection and elimination 
344 

of grazing by livestock, future merchantable timber yields for the passive MIC are lagged ten 

years. 

Allocation of the existing or initial timberland inventory by MIC in the FASOMGHG 

model is based on the ATLAS distribution by region, owner, forest type group, and site class. 

The ATLAS information in the 2000 RPA Timber Assessment was updated in collaboration with 

the American Forest and Paper Association, State Foresters (Moffat et al. 1998), and the 

Southern Forest Resources Assessment Consortium (Haynes 2003). In the South, forest industry 

surveys for the RPA Timber Assessment were compiled by the American Forest and Paper 

Association, while the responses from State Foresters were compiled at North Carolina State 

University (Moffat et al. 1998). A similar process was used in the West for forest industry lands 

(Adams et al. 1992). 

For the SC, SE, and PNWW in the FASOMGHG model, an expanded set of MICs is 

modeled. The southern MICs are drawn from the ATLAS-based ones, in some cases involving 

combining or collapsing into the fewer number of FASOMGHG ones. In the Pacific NorthwestWestside, the MICs were based on studies by Adams et al. (1992, 2002), supplemented by 

current literature and expert opinion. Specific treatment regimes (e.g., timing of intermediate 

treatment) were assigned to each individual MIC using the same sources from which MICs were 

derived. In the Southeast and South Central regions, Siry’s study (1998) was used to determine 

timing of planted pine treatments, including such treatments as commercial thinning and 

fertilization. Herbicide treatment in these scenarios was assumed to be conducted with 

fertilization at time of thinning. Timings of pre-commercial thinning and partial cuts were 

obtained from Mills (2003). For treatment information for short-rotation planted pine, 

information was obtained from the study by Siry (2002). Prescribed burning timing and 

treatment practices were estimated from Devos (1999). The Pacific Northwest-Westside 

treatment regime was developed using information from Adams et al. (2002) and the Oregon 

Department of Forestry’s 1998 surveys of management regime activities applied by industrial 

and non-industrial private forest landowners. 

Ten MICs were developed for the Southern regions, with the most for pine plantations 

(table 14.2.2.1). Representative MICs from ATLAS were chosen based on their relative amount 

of acres in production and estimated future production. The MICs for the Southeast and South 

Central regions are identical with respect to treatment prescriptions. To further validate the 

selected planted pine MICs, given planted pines’ relative importance in timber production in the 

South, the ability for each MIC to generate positive returns was evaluated. Each planted pine 

MIC did produce positive net present values across the South (Siry 2002). 
345 

Six MICs were developed for the Douglas-fir forest type group in the Pacific Northwest 

Westside region (table 14.2.2.1), expanded beyond what was simulated in the first-generation 

FASOMGHG model for this important timber producing region. The MICs incorporate two 

types of regeneration (natural, planting), commercial and pre-commercial thinning, and 

fertilization. 

All afforested land in the FASOMGHG model is represented by even-aged timber 

management. For afforested land in regions other than the South, such afforestation aggregates 

can be managed using a low MIC, where agricultural lands revert to naturally-regenerated 

softwood timberland. After forest establishment, the timberland is managed in a low intensity 

manner, similar to that for the low MIC for regenerated timberland in the region. 

In the South, active afforestation is simulated. Agricultural lands are planted to pines and 

can then be managed using one of two MICs: medium afforestation management, for minimal 

management before timber harvest in planted aggregates under even-aged management; and 

high—beyond the medium level, this involves use of genetically improved stock, fertilization 

and/or other intermediate stand treatments. 

The South and Corn Belt are the only two regions having afforested hardwood 

aggregates. In the South, bottomland hardwood planting options in the Southeast and South 

Central regions follow from recent emphasis on bottomland hardwood restoration (Amacher et 

al. 1997; Huang et al. 2003; Shabman and Zepp 2000; Stranturf et al. 2000). Hardwood 

afforestation opportunities also appear significant in the Corn Belt, with the relatively productive 

land. For other regions, active hardwood afforestation is not simulated because of a lack of 

significant amount of historic hardwood planting. 

Treatments for afforested bottomland hardwoods were derived from the literature 

(Amacher et al. 1997). Information on specific treatments for the bottomland hardwood 

afforestation was limited, especially regarding individual silvicultural treatments and timing 

within an MIC. Amacher et al. (1997) point out there is no current published work that 

establishes the financial feasibility of thinning bottomland hardwood stands. Based on this 

information, only intermediate treatments of herbicide and fertilizer were included in the 

afforestation of bottomland hardwoods. 

14.2.2 Partial cutting Intensity Classes 

An advance beyond the first-generation modeling of the forest sector in the FASOMGHG 

model (Adams et al. 1996) is the introduction of partial cutting representation of timber 
346 

management for selected regions. Partial cutting MICs on private timberland are modeled in the 

Southern and Pacific Northwest Westside regions. A partial cutting MIC is used in all regions for 

the modeling of National Forest inventory. In partial cutting, we remove typically only the 

mature trees, leaving the immature trees to grow, thereby allocating a portion of the growing 

space to regeneration. Such partial cutting in practice can arise from various landowner 

objectives and setting, including landowner adherence to traditional silvicultural practices 

recommended by forestry professionals, retaining greater structural diversity in the forest, 

avoiding reforestation requirements set by regulations, promoting aesthetic values, or other 

reasons. Thus, existing practices on the ground can involve variable retention harvests, and a mix 

of silvicultural systems and other approaches reflecting economic and operational constraints. 

Our broad representation of partial cutting timber management draws upon related modeling 

tested in the 2000 RPA Timber Assessment (Haynes 2003, Mills and Zhou 2003) and regional 

studies (e.g., Adams et al. 2002). 

Partial cutting can take place in the Southern regions in forest types other than planted 

pine: natural pine, oak-pine, upland hardwood, and bottomland hardwood. This partial cutting 

timber management is described as low intensity selective harvest by Haynes (2003). More than 

75 million acres of natural pine, oak-pine, bottomland hardwood, and upland hardwood in the 

South Central and Southeast are managed under partial cutting, based on representation in 

ATLAS modeling for the 2000 RPA Timber Assessment (Mills 2003). The MIC set in the 

FASMGHG model for the two southern regions includes three partial cut regimes: low, high, 

and high-plus (Alig et al. 2005). The high-plus partial cut MIC only applies to natural pine stands 

in the existing inventory, but can be applied to all four naturally-regenerated forest types 

concerning regenerated or "New" yield estimates. 

Based on ATLAS harvesting patterns, partial cut activity was limited to four entries for 

an aggregate over the 100-year FASOMGHG projection horizon. This restricts existing stands 

that enter FASOMGHG at older ages in receiving only one or two partial cutting treatments 

before the 100-year mark. If existing aggregates persist beyond 90 years, they can be clearcut 

and regenerated back under multiple MIC options. This restriction is related to ATLAS 

aggregated partial cutting data, where activity ceases after approximately year 90. The timing of 

the initial harvest varies by site class (Alig et al. 2005). 

In the Pacific Northwest Westside region, partial cutting MIC’s on private timberland are 

used in the Douglas-fir and other softwoods forest types, with three MIC’s: low, medium, and 

high. Natural regeneration for each partial cutting aggregate is simulated in these MICs. The 

initiation age and length of cutting intervals with growing stock removals for the low-MIC 
347 

partial cutting varies with site class. As in the South, volume thresholds are used with the Forest 

Vegetation Simulator model (Crookston and Stage 1999, Crookston and Havis 2002; Stage 

1973), based on observable volume patterns in the aggregated ATLAS partial cut information 

(Alig et al. 2005). 

In the Pacific Northwest Westside, treatment of existing stands under the three partial cut 

MICs is the same as described in the regenerated projections, except that the age of existing 

stands is used as the harvest initiation criterion. Aggregates with low site index, for instance, will 

have partial cutting from above if the stand age is at least 35 and removal of 25% of the trees 7 

inches dbh and higher will result in one thousand cubic feet of timber. For medium site index 

stands, a removal will occur if the aggregate age is 30, and for high site index stands age must be 

at least 25. 

Partial cutting is also an option for National Forest timberland aggregates. National 

Forest timberland was allocated to three MICs in ATLAS, in a pre-set manner, and we applied 

that information in developing the corresponding input sets for the FASOMGHG model. The 

MICs include a low intensity one with no treatments, a low partial cut MIC, and a reserved MIC. 

Across the nine forest regions, two forest types (softwoods and hardwoods) are represented by 

these MICs. The regional inventories on National Forest timberlands were simulated using these 

MICs, but in contrast to private timberlands, the allocation of acres by MIC and timber harvest 

levels are pre-set or exogenous. 

14.3 Timber growth and yield 

The FASOMGHG model requires projected yields for existing aggregates, reforested 

aggregates, and afforested aggregates. Timber yields can vary markedly by MIC, as shown in the 

example in figure 14.2.3 for planted pine yields in the South. 

14.3.1 Existing Aggregates of Private Timberland 

Estimates of existing aggregate yields were obtained from the ATLAS model used for the 

2000 RPA Timber Assessment (Haynes 2003, Mills and Zhou 2003), except for the Pacific 

Northwest Westside region (discussed below). The ATLAS model provides empirically-based 

yields per acre based on USDA Forest Service FIA plot data. Yields for each RPA region are 

presented by age class, forest type, site class, and management intensity class. Timber yields by 

site class and region were assumed to be equivalent for FORONLY, FORCROP, and FORPAST 

land suitability classes. 
348 

Under even-aged management, timber yields for existing and reforested stands in the low 

management intensity class were derived from ATLAS base yield tables. These cases involve 

use of ATLAS’s "approach to normal" or relative density equations and regeneration stocking 

ratios as described by Mills and Kincaid (1992) and Mills and Zhou (2003). The base yields are 

based on a set of measurements from permanent FIA sample plots. Timber growth and yield 

parameters used in the ATLAS modeling are developed from the FIA data. The use of empirical 

growth rates embodies the effects of historical and recent management practices and 

disturbances, the latter including fire if it occurred. The ATLAS approach estimates net timber 

growth by age for each regional forest type. Timber yields are then an accumulation of net 

annual growth. 

Commercial thinning volumes under even-aged timber management are part of some of 

the MICs in the Southeast, South Central, and Pacific Northwest Westside regions, in addition to 

final harvest volumes for aggregates under even-aged MICs. Commercial thinning yields are the 

commercial volumes removed from an aggregate in the intermediate period between forest 

establishment and final harvest. Commercial thinning yields are estimated for particular MICs in 

existing, regenerated, and afforested stands. Commercial thinning volumes for the Southeast and 

South Central regions are based on ATLAS modeling. 

Timber yields for passively managed aggregates are lagged ten years relative to those for 

the corresponding low MIC group. In FASOMGHG, all timber yields are assumed to remain 

constant after 100 years. Stocking considerations also include “operational falldown,” which 

took into account wind-damaged timber, breakage during harvesting, and other real-world 

factors. 

Under partial cutting timber management, timber yields for the partial cut MICs in the 

South are based on ATLAS’s approach (Mills 2003), where partial timber harvests remove a 

portion of the timber volume to mimic a forest stand subject to multiple harvest entries. Partially 

cut stands in the South were aggregated into the three partial cut regimes to estimate existing 

stand yields. Removals of growing stock in partial cutting MICs take place at scheduled intervals 

(Alig et al. 2005), with a certain percentage of an aggregate’s volume removed each interval. 

Harvests can be delayed if total harvestable volume falls below a threshold merchantable level in 

any of these intervals (Alig et al. 2005). In that period, the stand is not harvested, and the stand is 

then harvested in the subsequent interval if the threshold criterion is met. Threshold timber 

harvest volumes by region were based on information from partial cutting activity totals in 

ATLAS. Thresholds are specified that define minimum amounts of harvestable growing stock 

volume by region before harvest is implemented. 
349 

For the Pacific Northwest Westside, the Forest Vegetation Simulator (FVS) (Stage 1973, 

Teck et al. 1997) was used to incorporate a recently completed FIA periodic survey for Western 

Washington, in estimating timber yields for existing and regenerated aggregates. FIA databases 

for western Oregon and western Washington were used to populate plot and tree list files 

required for projecting timber growth and yield with the FVS model (Alig et al. 2005). The FVS 

model allows more direct estimation of timber yields by sawtimber and pulpwood proportions, 

compared to the first-generation approach of obtaining (non-modeled) estimates from FIA 

sources (Adams et al. 1996). The FVS model follows the Prognosis Model developed in the 

1970s and has been applied in a number of applications by others (e.g., Crookston and Stage 

1999), and associated information or guidelines were drawn upon in developing yields that 

reflect current timber management and anticipated regeneration options. 

FVS estimates of timber yields for existing stands are based on FIA data, used in input 

form as tree lists. Timber growth and yield projections are dependent on interactions between 

trees within stands. The FIA samples of current growth or increment are used to project 

yields for existing stands, reflecting unique variations in site and environment not 

represented in the FVS parameters. <<<<WHAT IS THIS????? Some or all of the following 

information is used, depending in part on the geographic variants of the FVS model (Crookston 

and Stage 1999): site conditions (e.g., site index, stand density index or basal area maximums, 

elevation), characteristics of each tree measured in the inventory (e.g., species, tree height, 

current diameter at breast height), and other information (e.g., tree history code, crown ratio). For 

example, species is used in FVS to index the various growth models. 

14.3.2 New or regenerated aggregates of private timberland 

New stands can result either from reforestation or regeneration of timberland, or from 

afforestation of agricultural land. Except for the Pacific Northwest Westside, estimation of 

regenerated yield estimates is based on similar ATLAS modeling or related studies, with 

adjustments for regeneration stocking assumptions. The initial volume for a regenerated stand in 

ATLAS is determined by the base timber yield table and an input parameter termed the 

regeneration stocking proportion (Mills and Kincaid 1992). This regeneration stocking 

proportion is assigned upon entry into the first or zero age class for an ATLAS aggregate, 

depending upon the region, owner, forest type, and site class combination. Timber stocking in 

subsequent periods (or age classes as the aggregate moves through time) is based on the stocking 

trajectory that the aggregate was assigned at time of regeneration. 
350 

For example, regenerated stands in the medium or high MICs and afforested stands were 

assumed to be fully stocked relative to either ATLAS or Birdsey (1996) reference or base yields. 

For low MIC timberland, new stands were modeled as stocked as a percentage of fully stocked, 

based on corresponding ATLAS estimates. Likewise, their timber yield estimates are based on 

use of ATLAS’s relative density equations by region (Mills and Kincaid 1992). As with existing 

stands, timber yields for regenerated stands allocated to a passive MIC are lagged ten-years 

relative to those for the low MIC group (i.e., ten year relative regeneration lag). 

For partial cut MICs in the South, regenerated yield tables were created using yield 

estimates from the counterpart ATLAS modeling, drawn from guidelines reported by Haynes 

(2003). Partial cut yields are estimated for the naturally-regenerated types: natural pine, oakpine, bottomland hardwood, and upland hardwood. 

For the Pacific Northwest Westside region, regenerated yields were obtained from the 

FVS model (Alig et al. 2005). Partial cut yields estimated by the FVS model for the Pacific 

Northwest Westside are based on similar interval and threshold volume guidelines as in the case 

of existing yields. 

14.3.3 Afforested aggregates 

Afforestation only occurs on NIPF land in the model, and can involve either tree planting 

or natural reversion of agricultural lands. For planted afforestation cases, resulting aggregates 

were assumed to be fully stocked. Regions likely to experience significant amounts of 

afforestation are based on estimates by Birdsey (1996) for planted pine, and by Amacher et al. 

1997; Huang et al. 2003; Shabman and Zepp 2000; and Stranturf et al. 2000 for bottomland 

hardwood restoration trends. The mix of forest species within a region comprising a planted 

forest types was determined using Birdsey's (1996) estimates of forest types planted by state, 

national tree planting data (USDA Forest Service 1998) and expert opinion. 

In the Southeast and South Central regions, planted pine afforestation yields were based 

on Birdsey’s estimates (1996) for planted southern pines. These planted pine yields are 

represented in the medium and high FASOMGHG site classes for pasture and crop land, 

respectively. 

Bottomland afforestation yields for the South Central region were derived using average 

yields for three forest type groups comprising afforested bottomland hardwoods (Murray et al. 

2002) and timber yields from Murray’s study (2003) for planted bottomland hardwoods. 
351 

Non-planted afforestation yields were derived from Birdsey (1996) and Moulton and 

Richards (1990). Birdsey gives yields (cubic feet per acre) by Moulton and Richards (1990) 

region and forest type for crop and pasture land. All afforested acres were assumed to be fully 

stocked in terms of ATLAS yield standards. Thus, yields were derived directly from Birdsey's 

yield tables for those regions in which only one species was planted. Weighted afforestation 

yields were derived for the Northeast and Pacific Southwest regions based on planting 

percentages by forest type given in Birdsey (1996) and tree planting statistics (USDA Forest 

Service 1998). Crop land planted to forest was assigned a high FASOMGHG site class while 

acres planted on pasture land were assigned a medium site class. 

14.4 Harvest 

As background, annual removals of growing stock on US timberland are approximately 

16 billion cubic feet (Smith et al. 2001). The majority of this volume, 10 billion, comes from the 

Southern regions. The bulk of volume in these regions (95%) is harvested on private land. Of 

this, 69% comes from NIPF timberland. National Forests provided 5% of the annual harvest and 

all public land (including National Forest) makes up 10% of the national annual harvest (1.7 

billion). In FASOMGHG, the public timber harvest is exogenous. 

In FASOMGHG, harvest of an acre of timberland involves the simultaneous production 

of some mix of softwood and hardwood timber volume. In FASOMGHG, this is translated 

hardwood and softwood products (sawlogs, pulpwood, and fuelwood) that are described next. 

Percentages of growing stock timber volumes are assigned to three product types -- 

sawlogs, pulpwood, and fuelwood, by softwoods and hardwoods. This results in six possible 

product classes: 1) SAWTSW -- Softwood sawtimber products; 2) PULPSW -- softwood 

pulpwood products; 3) FUELSW -- Softwood fuelwood products; 4) SAWTHW -- Hardwood 

sawtimber products; 5) PULPHW -- Hardwood pulpwood products; and 6) FUELHW -- 

Hardwood fuelwood products. The percentages of growing stock volume allocated to different 

products can vary by region, forest type, site class, MIC, and by age class. The estimates were 

obtained from the regional FIA units, with most based on analysis of available FIA data and 

expert opinions of analysts in each region.7 For example, in the South, estimates were checked 

against similar product proportion tables (Siry 2003), and validated by Southern FIA personnel 

 

7 For the Pacific Northwest Westside, the Forest Vegetation Simulator provided estimates 

by size class that were useful for product characterization. 
352 

(Johnson 2003). For the West, Morgan (2003) provided expert opinions for some product 

proportions. 

The product mix changes over time, as the stand ages, and between rotations if the 

management regime (intensity) changes. Downward substitution (use of a log "normally" 

destined for a higher valued product in a "normally" lower valued application) is allowed when 

the price spread between pairs of products is eliminated. Sawlogs can be substituted for 

pulpwood and pulpwood, in turn, can be substituted for fuelwood, provided that the prices of 

sawlogs and pulpwood, respectively, fall low enough to become competitive substitutes for 

pulpwood and fuelwood. 

14.5 Costs 

To produce up-to-date cost estimates, a literature review of land conversion, forest 

establishment, and timber stand management costs was conducted for the nation. Special 

attention was paid to the cost information pertinent to the Southeast, South Central, and Pacific 

Northwest Westside regions because of their relative importance in timber production (Haynes 

2003). Taxes were not included in the forestry costs in order to keep them consistent with cost 

accounting on the agricultural side of FASOMGHG. 

14.5.1 Land Conversion 

Sources of land conversion costs were various Economic Research Service studies (e.g., 

Daugherty 1982) and expert opinion. However, most of the formal studies were dated, with most 

conducted before the 1980s and before significant changes in conversion technology, and so 

were augmented by expert opinion. 

Costs are represented in each region by step functions to reflect increasing costs, as the 

percent of land base being converted increases. Costs for land conversion in a region are less 

expensive for the initial 10 percent of land converted and subsequently higher for the next 50 

percent, and even more so for the final 40 percent. This reflects the increasing marginal cost of 

land conversion due to varying topography, moisture, and other factors. 

Land conversion costs include those for land clearing, wind rowing, and burning, and any 

necessary leveling and removing large chunks of woody debris for seedbed preparation. Any 

timberland converted to agricultural land is assumed to occur after harvest of any merchantable 

trees, and 75% of timber volume removed in land clearing is assumed to be hauled to market 
353 

(Adams et al. 1996). Taxes were not included in the forestry costs in order to keep them 

consistent with cost accounting on the longer-standing agricultural side of FASOMGHG. 

Constraints on the amount of timberland that could be converted to agricultural uses were 

derived from data from the Natural Resource Inventory by the Natural Resources Conservation 

Service (2001), pertaining to NIPF timberland with medium or high potential for conversion to 

crop land and pasture land. The data were checked against that for NRI prime farmland, 

representing forest, pasture land, crop land, rangeland, or other minor land uses that have good 

potential for cultivated crops (e.g., slope less than 5%, not excessively eroded, not wetlands, 

etc.). The published NRI data do not identify forestland qualifying as prime crop land below our 

FASOMGHG region, thus allocation of prime crop land by forest type, MIC, and age cohort is 

by assumption (proportional to what is in the highest forestry site group). 

The equation for land conversion cost includes land conversion, windrowing, burning, 

and leveling and stump removal costs. Cost estimates from the first-generation FASOM 

modeling (Adams et al. 1996) were updated in the case of conversion costs. These cost estimates 

were updated from 1990 to 2002 dollars using the US Bureau of Labor Statistics (2003) Producer 

Price Index for all commodities. 

Another important portion of the conversion cost information is estimates of acres of 

available prime crop land and pasture land in each state that are currently under the cover of 

forestland (USDA NRCS 2001). NRI data (1997 national survey) were used to estimate these 

land areas. To determine the proportion of forested crop land and pasture land available in each 

state, the ratio of “active” crop and pasture land was used to disaggregate the total prime 

agricultural land in forest cover. The amount of crop and pasture land eligible for conversion to 

timberland was established using information from Moulton and Richards (1990), as was done in 

the previous FASOM model. One stipulation from the first FASOM model is that reforestation 

establishment costs must be greater than or equal to crop to forest or pasture to forest conversion 

establishment costs (Adams et al. 1996). 

14.5.2 Forest establishment costs 

Forest establishment costs include those for site preparation, tree seedlings, and tree 

planting. Intermediate timber management costs include those for precommercial thinning, 

prescribed burning, fertilization, and any other practices between stand establishment and 

harvest. Establishment costs vary by FASOMGHG land class, with generally higher costs for 
354 

reforested acres, such as those for FORONLY acres, and lower costs for afforesting CROPFOR 

and PASTFOR acres. 

For regional averages of forest establishment in the South, Forest Farmer reports cost 

trends every 2-3 years in the Manual Edition. Cost estimates and trends over the period 1952-

1994 were reported for specific forestry practices common to the South (Dubois et al. 1999, 

2000, 2003). These cost data are based on surveys of forest industry, consultants, and public 

agencies, and most are on a per acre basis. Those practices with a high percentage of labor 

experienced the greatest cost increases (e.g., Dubois et al. 1999). A comparable regional 

synthesis of establishment and management costs does not exist for the Pacific Northwest, 

however. 

Updated cost functions were used from the previous FASOM model to estimate 

establishment and growing costs on a per acre basis (Adams et al. 1996). Establishment costs for 

naturally regenerated stands include site preparation costs, but significantly less than for planted 

stands. Sources for updated cost estimates included Dubois (2003) and Cathcart (2003), 

primarily for establishment of planted stands in the Southern regions and Pacific Northwest 

Westside, respectively. 

Establishment costs in the case of conversion from crop land or pasture land to forest are 

lower than for regeneration on timberland, because of lower site preparation costs. By land type, 

site preparation costs were weighted according to the difference in establishment costs between 

forest and crop or pasture land in Moulton and Richards (1990). 

Cost adjustments pertaining to forest type conversions included adding 10% for costs of 

prescribed burning and herbicide treatments for conversions of forest types across softwood and 

hardwood bounds (Adams et al.1996). Costs were only increased 10% for one period, and then 

reverted back to the standard decadal cost for the type and region. Also, prescribed fire was not 

allowed on stands of mixed oak-pine or hardwood (Devos 1999). 

14.5.3 Timber growing costs 

Timber growing costs include costs of thinning, prescribed burning, fertilization, and 

general periodic maintenance. For the Southeast and South Central regions, information by 

Dubois et al. (2000) pertaining to cost and cost trends for forestry practices in the South 

represented the most complete source. The associated documentation is published on a regular 

periodic basis and encompasses a variety of timber stand treatment and cruising costs. Cost 

estimates from this survey were obtained for 12 Southern states and included private firms and 
355 

public agencies. Additional sources were used in estimating costs for naturally regenerated pine, 

oak-pine, and upland and bottomland hardwoods (Amacher et al. 1997; Bates et al. 2003; Huang 

et al. 2003; McKee 1987; Stranturf et al. 2000; Shabman and Zepp 2000; Siry 2002; Vasievich 

1983). 

Literature pertaining to timber outside the South was used to estimate costs for the Pacific 

Northwest-Westside and the remaining regions. According to Floyd et al. (2000), “Growing 

costs are surveyed in the South, but no comparable survey is conducted in the West.” Limited 

region-specific information was obtained for the Pacific Northwest-Westside using a survey of 

professional foresters in Oregon, while other resources were used to estimating costs for the 

remaining regions (Cathcart 2003; Moulton and Richards 1990; Vasievich 1983). 

Growing costs for passive and low MIC aggregates are for management plans, boundary 

maintenance, survey and cruising, and fire protection. For medium and high MICs, intermediate 

treatment costs can also include precommercial thinning, fertilization, herbicide application, and 

prescribed burning. It is assumed that before reforestation or afforestation activities take place, 

landowners have a clear definition of their boundaries (e.g., historical fencing, fire breaks, etc.) 

and reasonable access to their land (e.g., established roads, drainage, etc.) Intermediate treatment 

costs were weighted for regional differences, unless the costs were directly from the region in 

question (Moulton and Richards 1990). 

The periodic growing costs are applied every time period until the harvest takes place, 

while the other intermediate treatments are applied only as indicated by the specified timing in 

the governing MIC (e.g., precommercial thinning at age 15). Prescribed fire is not incorporated 

into specific MIC’s or linked to the decadal costs of timber management, but implemented on a 

infrequent periodic basis, given the relatively small number of acres burned and the declining 

trend to do so on private lands (Haines et al. 2001). Prescribed fire has been excluded from the 

PNWW stands based on expert opinions from the Oregon Department of Forestry and 

Weyerhaeuser Company. 

Table 14.2.1.1 Forest sector inventory strata used in the FASOMGHG Model 

Mccarl why is this table so empty looking 

Region Land Suitability 

Class Owner Site Class Age Cohort Forest type 

Management 

Intensity 

Corn Belt Forest Only Forest Industry High 5 year See Table 

14.2.1.1-

See Table 

14.2.2.1 
356 

3 

Lake States Crop land to 

Forest 

Nonindustrial 

Private 

Medium 

Northeast Pasture land to 

Forest 

 Low 

Pacific 

NorthwestEastside 

Forest to Crop 

land 

 

Pacific 

NorthwestWestside 

Forest to 

Pasture land 

 

Pacific 

Southwest 

 

Rocky Mountain 

South Central 

Southeast 

Table 14.2.1.1-2 Initial Private Timberland Inventory by Region (circa 2000) 

FASOMGHG Region 

Private Timberland 

Area (million acres) 

Softwood Volume 

(billion cubic feet) 

Hardwood Volume 

(billion cubic feet) 

North East 69.320 27.366 76.380 

Lake States 30.333 8.494 29.855 

Corn Belt 27.544 1.087 27.074 

South East 75.430 44.418 61.289 

South Central 104.778 44.639 70.187 

Rocky Mountain 21.125 20.914 5.002 

Pacific North West 17.580 38.862 8.660 

Pacific Southwest 7.437 18.308 5.755 

Source: Smith et al. (2001); timber volumes are growing stock component (see glossary). The historical statistics 

(Smith et al. 2001) do not separate out the Westside and Eastside for the Pacific Northwest. 
357 

Table 14.2.1.1-3 Forest type pathways in FASOMGHG, by region. 

Allowable Forest Type Pathways During Reforestation 

Region Forest Type and MIC Pathways 

South Central and 

Southeast Planted Pine MIC Planted Pine: Conversion allowed on Natural Pine, OakPine, Upland Hardwood, and Bottomland Hardwood 

Natural Regeneration - Natural 

Pine MIC 

Natural Pine: Conversion allowed from existing Natural 

Pine, Planted Pine, and Oak-Pine 

Natural Regeneration - Oak-Pine 

MIC 

Oak-Pine: Conversion allowed from existing Natural 

Pine, Planted Pine, and Oak-Pine 

Natural Regeneration - Upland 

Hardwood MIC 

Upland Hardwood: Conversion allowed from existing 

Natural Pine, Planted Pine, Oak-Pine, and Upland 

Hardwood 

Natural Regeneration - 

Bottomland Hardwood MIC 

Bottomland Hardwood: Conversion allowed from 

existing Natural Pine, Planted Pine, Oak-Pine, and 

Bottomland Hardwood 

Corn Belt, Lake State, 

and North East 

Natural Regeneration - Softwood 

MIC 

Softwood: Conversion allowed form existing Softwood 

only 

Natural Regeneration - 

Hardwood MIC 

Hardwood: Conversion allowed from existing Hardwood 

and Softwood 

Pacific Northwest 

Eastside, Pacific 

Southwest, and Rocky 

Mountain 

Natural Regeneration - Softwood 

MIC 

Softwood: Conversion allowed from existing Softwood 

only 

Natural Regeneration - 

Hardwood MIC 

Hardwood: Conversion allowed from existing Hardwood 

only 

Pacific Northwest 

Westside 

Natural Regeneration - Douglasfir MIC Douglas-fir: Conversion allowed from Douglas-fir and 

Other Softwoods 

 Planted - Douglas-fir MIC Douglas-fir: Conversion allowed from Douglas-fir, Other 

Softwoods, and Hardwoods 

Natural - Regeneration Other 

Softwood MIC 

Other Softwood: Conversion allowed from Douglas-fir 

and Other Softwoods 

 Planted -Other Softwood MIC Other Softwood: Conversion allowed from Douglas-fir, 

Other Softwoods, and Hardwoods 

Natural Regeneration and 

Planted -Hardwood MIC 

Hardwood: Conversion allowed from Douglas-fir, Other 

Softwood, and Hardwood 

Allowable Forest Type Pathways During Afforestation 

South Central and 

Southeast Planted Afforestation MIC Planted Pine and Bottomland Hardwood 

Corn Belt Planted and Non-planted 

Afforestation MIC Softwood and Hardwood 

Lake State, North East 

Pacific Northwest 

Eastside, Pacific 

Southwest, and Rocky 

Mountain 

Non-planted Afforestation MIC Softwood Only 
358 

Table 14.2.1.1-4 Forest type possibilities in afforestation in FASOMGHG, by region 

Region Forest Type Source

 

Corn Belt Hardwood and Softwood Adams 1996 

Lake States Softwood Adams 1996 

Northeast Softwood Adams 1996 

Pacific Northwest-Eastside Softwood Adams 1996 

Pacific Northwest-Westside Douglas fir, other softwoods, hardwoods Adams 1996 

Pacific Southwest Softwood Adams 1996 

Rocky Mountains Softwood Adams 1996 

South Central Southern pine (Pinus spp.) 

Bottomland Hardwood (for example, 

cottonwood, ash, oak, etc.) 

Birdsey 1996 

Murray 2003 

Southeast Southern pine (Pinus spp.) 

Bottomland Hardwood (for example, 

cottonwood, ash, oak, etc.) 

Table 14.2.1-5. Exogenous projected acres (million ac.) of developed land in 2025, by 

region 

Region 

Developed 

Area, 

1997 

Projected 

Developed Area, 

2025 

Projected population 

Increase, 1997 to 2025 

(%) 

Northeast 14.6 25-2 13 

South 26.4 46.2 49 

Northern Midwest 21.4 38.6 20 

Southern Midwest 15.5 28.0 45 

Great Plains 4.8 8.3 25 

Southwest 5-3 9.9 80 

Pacific Northwest 4.0 7.4 54 

California 5.5 10.8 44 

48 contiguous state Total 97.6 174.3 

Percent of continental US area 

developed 5-2% 9.2% 

Note: Projections based on population and per capita income growth projected by NPA 

Data Services (Alig et al. 2004). 
359 

Figure 14.2.3 Example of timber yields for different MICs: Planted Pine on Forest 

Industry High-Site Timberland in the South Central Region 

Removed to figures file 

Table 14.2.2.1 Timber management intensity classes (MICs) in the FASOMGHG Model 

Region Forest type ATLAS MIC FASOMGHG MIC Management Intensity 

Southeast Planted Pine 1 TRAD_PLNT_ PINE Traditional

and Planted Pine 4 PLNT_LO_THIN LO Thin 

South Central Planted Pine 5 PLNT_MED Medium 

 Planted Pine 6 PLNT_MED_THIN Medium Thin 

 Planted Pine 7 PLNT_HI High 

 Planted Pine 10 PLNT_HI_THIN High-Plus Thin 

 Planted Pine 11 SHORT_ROTSWDS Short Rotation Softwoods 

 Planted Pine 12 RESERVED Reserved 

 Natural Pine N/A PASSIVE Passive 

 Natural Pine FI 1 & NIPF 2 PART_CUT_LO Partial Cut LO 

 Natural Pine FI 3 & NIPF 1 LO LO 

 Natural Pine 4 PART_CUT_HI Partial Cut HI 

 Natural Pine 6 PART_CUT_HI+ Partial Cut HI-Plus 

 Natural Pine 12 RESERVED Reserved 

 Oak-Pine N/A PASSIVE Passive 

 Oak-Pine FI 1 & NIPF 2 PART_CUT_LO Partial Cut LO 

 Oak-Pine FI 3 & NIPF 1 LO LO 

 Oak-Pine 4 PART_CUT_HI Partial Cut HI 

 Oak-Pine 6 PART_CUT_HI+ Partial Cut HI-Plus 

 Oak-Pine 12 RESERVED Reserved 

 Upland Hardwoods. N/A PASSIVE Passive 

 Upland Hardwoods. FI 1 & NIPF 2 PART_CUT_LO Partial Cut LO 

 Upland Hardwoods. FI 3 & NIPF 1 LO LO 

 Upland Hardwoods. 4 PART_CUT_HI Partial Cut HI 

 Upland Hardwoods. 6 PART_CUT_HI+ Partial Cut HI-Plus 

 Upland Hardwoods. 12 RESERVED Reserved 

Bottomland 

Hardwoods. 

N/A PASSIVE Passive 

Bottomland 

Hardwoods. 

FI 1 & NIPF 2 PART_CUT_LO Partial Cut LO 

Bottomland 

Hardwoods. 

FI 3 & NIPF 1 LO LO 

Bottomland 

Hardwoods. 

4 PART_CUT_HI Partial Cut HI 

Bottomland 

Hardwoods 

6 PART_CUT_HI+ Partial Cut HI-Plus 

Bottomland 

Hardwoods. 

N/A AFFOR Afforestation 
360 

Bottomland 

Hardwoods. 

12 RESERVED Reserved 

Pacific Northwest- Douglas-fir N/A PASSIVE Passive 

Westside Douglas-fir N/A NAT_REGEN Natural Regeneration 

 Douglas-fir N/A NAT_REGEN_THIN Natural Regeneration 

Thin 

 Douglas-fir N/A PLANT Plant 

 Douglas-fir N/A PLANT_THIN Plant Thin 

 Douglas-fir N/A PLANT+ Plant Plus 

 Douglas-fir N/A NAT_REGEN_PART_CU

T_LO 

Natural Regeneration 

Plus PC LO 

 Douglas-fir N/A NAT_REGEN_PART_CU

T_MED 

Natural Regeneration 

Plus PC ME 

 Douglas-fir N/A NAT_REGEN_PART_CU

T_HI 

Natural Regeneration 

Plus PC HI 

 Douglas-fir N/A RESERVED Reserved 

 Other Softwood N/A PASSIVE Passive 

 Other Softwood N/A NAT_REGEN Natural Regeneration 

 Other Softwood N/A PLANT Plant 

 Other Softwood N/A PLANT_THIN Plant Thin 

 Other Softwood N/A NAT_REGEN_PART_CU

T_LO 

Natural Regeneration 

Plus PC LO 

 Other Softwood N/A NAT_REGEN_PART_CU

T_MED 

Natural Regeneration 

Plus PC ME 

 Other Softwood N/A NAT_REGEN_PART_CU

T_HI 

Natural Regeneration 

Plus PC HI 

 Other Softwood N/A RESERVED Reserved 

Pacific Northwest- Hardwoods N/A PASSIVE Passive 

Westside Hardwoods N/A NAT_REGEN Natural Regeneration 

 Hardwoods N/A PLANT Plant 

 Hardwoods N/A RESERVED Reserved 

Other Regions Hardwood N/A PASSIVE Passive 

 Softwood N/A PASSIVE Passive 

 Hardwood 1 LO General Low 

 Softwood 1 LO General Low 

 Hardwood N/A AFFOR Afforestation (Corn Belt 

Only) 

 Softwood N/A AFFOR Afforestation (Corn Belt 

Only) 

National Forest Hardwood N/A PASSIVE Passive 

 Softwood N/A PASSIVE Passive 

 Hardwood 1 LO Low 

 Softwood 1 LO Low 

 Hardwood 2 LO_PART_CUT Low Partial Cut 

 Softwood 2 LO_PART_CUT Low Partial Cut 

 Hardwood 12 RESERVED Reserved 

 Softwood 12 RESERVED Reserved 

Forest type FASOMGHG Type ATLAS Numerical Equivalent 

Planted Pine PLNT_PINE 1 

Natural Pine NAT_PINE 2 

Oak-Pine OAK_PINE 3 

Upland Hardwood UP_HARD 4 
361 

Bottomland Hardwood BOT_HARD 5 

Douglas-fir (PNWW) DOUG_FIR 1 

Other Softwood (PNWW) OTH_SWDS 2 

Hardwood (PNWW) HARDS 3 

Softwood SOFT 1 

Hardwood HARD 2 
362 

14.6 Forest processed Commodities 

Logs at the mill are converted to product volumes according to sets of recovery or conversion 

coefficients that vary by region and product, and in some cases by time as well. Table 14-__ gives 

examples of these coefficients for the endogenous solidwood products in the starting period (2000) and 

for 2045 as derived from the TAMM model. These are the solidwood volumes (logs at the mill) in cubic 

feet required to produce one unit of the particular product. In the case of OSB the proportions of wood 

input coming from softwoods and from roundwood (as opposed to milling residues) must also be 

specified. OSB uses pulpwood rather than sawlogs as log input. Use of non-wood inputs (labor, energy, 

and other variable factors) is represented in the non-wood input relations described below. The model 

does not employ conversion or recovery factors for non-wood inputs. 

Table 14-___. Examples of recovery coefficients for softwood lumber, softwood plywood, 

hardwood lumber and OSB by region and period from FASOMGHG forest 

sector: volume of wood required to produce one unit of the product. 

SOFTWOOD 

LUMBER 

SOFTWOOD 

PLYWOOD HARDWOOD LUMBER 

OSB 

(Oriented Strand board) 

 WW SC WW SC LS SC LS SC 

 CF,LS/ BF,LT CF,LS/SF,3/8" CF,LS/BF,LT CF,LS/SF,3/8" 

2000 0.105 0.133 0.060 0.053 0.172 0.184 0.056 0.056 

2045 0.100 0.118 0.059 0.052 0.172 0.184 0.056 0.056 

 

FRACTION 

SOFTWOOD 

2000 0.100 0.800 

2045 0.100 1.000 

 

FRACTION 

ROUNDWOOD 

2000 0.950 0.900 

2045 0.950 0.900 

Note: CF,LS is cubic foot, log scale; BF,LT is board foot lumber tall; SF,3/8” is square foot, 3/8” thick. 

In the fiber products sector, similar recovery coefficients are employed to describe the amounts of 

pulpwood, recovered papers, and market pulp used per tonne of paper product produced. This is 

illustrated in Tables 14-___ and 14-___ for newsprint in the NE region and linerboard in the SC region. 

(see separate files newsprint coefficients sec 14.2.doc and linearboard coefficients sec 14.2.doc) In Table 

14-___ there are four alternative newsprint production processes each with two alternative input mixes. 

For linerboard (Table 14-___) there are three alternative production processes with two to three 

alternative input mixes. 
363 
364 

Table 14.___. Fiber input requirements (pulpwood, recovered papers, and market pulp) and costs of other inputs for newsprint 

in the NE region for four alternative production processes and several alternative input mixes. The newsprint product is 100% 

fiber [from NAPAP, Ince (1994)]. 

Process and Input Mix SOFTWOOD PULPWOOD HARDWOOD PULPWOOD 

1 - Integrated to Roundwood (GW) & Chemical Pulp (75/25) tonne/tonne m3/tonne tonne/tonne m3/tonne 

 1 - Max. Softwood (100%) 1.319 3.959 - 

 2 - Min. Softwood (90% in GW; 50% in Chem. Pulp) 0.979 2.938 0.335 0.880 

2 - Integrated to TMP Pulp, using some Mkt. Pulp (90/10) 

 1 - Max. Softwood (100%) 1.000 3.002 - 

 2 - Min. Softwood (90% in TMP; 50% in Chem. Pulp) 0.900 2.702 0.100 0.263 

3 - Integrated to Deinked Recycled Pulp (100%) 

 1 - ONP only - - 

 2 - ONP & Mixed - - 

4 - Integrated to CTMP Pulp (100%) 

 1 - Max Softwood (100%) 1.111 3.336 - 

 2 - Min. Softwood (90%) 1.000 3.002 0.111 0.292 

 RECOVERED PAPERS 

 Pulp Hi Grd 

 ONP OCC Mixed Subs. Deink 

 tonne/tonne 

1 - Integrated to Roundwood & Chemical Pulp (75/25) 

 1 - Max. Softwood (100%) - - - - - 

 2 - Min. Softwood (90% in GW; 50% in Chem. Pulp) - - - - - 

2 - Integrated to TMP Pulp, using some Mkt. Pulp (90/10) 

 1 - Max. Softwood (100%) - - - - - 

 2 - Min. Softwood (90% in TMP; 50% in Chem. Pulp) - - - - - 

3 - Integrated to Deinked Recycled Pulp (100%) 

 1 - ONP only 1.176 - - - - 

 2 - ONP & Mixed 0.882 - 0.385 - - 

4 - Integrated to CTMP Pulp (100%) 

 1 - Max Softwood (100%) - - - - - 

 2 - Min. Softwood (90%) - - - - - 

 MARKET PULP 

 Soft Kraft Hard Kraft Recycled CTMP 

OTHER 

COSTS 

 tonne/tonne $/tonne 

1 - Integrated to Roundwood & Chemical Pulp (75/25) 

 1 - Max. Softwood (100%) - - - - 382.80 

 2 - Min. Softwood (90% in GW; 50% in Chem. Pulp) - - - - 379.32 

2 - Integrated to TMP Pulp, using some Mkt. Pulp (90/10) 

 1 - Max. Softwood (100%) 0.111 - - - 336.40 

 2 - Min. Softwood (90% in TMP; 50% in Chem. Pulp) 0.056 0.056 - - 336.40 

3 - Integrated to Deinked Recycled Pulp (100%) 

 1 - ONP only - - - - 348.00 

 2 - ONP & Mixed - - - - 348.00 

4 - Integrated to CTMP Pulp (100%) 
365 

 1 - Max Softwood (100%) - - - - 359.60 

 2 - Min. Softwood (90%) - - - - 359.60 
366 

Table 14.___. Fiber input requirements (pulpwood, recovered papers, and market pulp) and costs of other inputs for linerboard in the SC region for three 

alternative processes and several alternative input mixes. The linerboard product is 99% fiber and 1% filler [from NAPAP, Ince (1994)]. 

 SOFTWOOD PULPWOOD HARDWOOD PULPWOOD 

Process and Input Mix tonne/tonne m3/tonne tonne/tonne m3/tonne 

1 - Older press technology integrated to Unbl. Kraft 

 1 - Max. Softwood (100%) & no recycled 1.904 4.266 - 

 2 - Max. Softwood & Max. recycled (10% OCC) 1.713 3.840 - 

 3 - Max. Hardwood (5%) & no recycled 1.809 4.053 0.095 0.175 

2 – New press technology integrated to Unbl. Kraft 

 1 - Max. Softwood (100%) & no recycled 1.768 3.961 - 

 2 - Max. Softwood & Max. recycled (25% OCC) 1.326 2.971 - 

 3 - Max. Hardwood (30%) & no recycled 1.238 2.773 0.530 0.976 

3 - Based on Recycled Fiber 

 1 - Using Old Corrugated - - 

 2 - Max. use of lower grades - - 

 RECOVERED PAPERS 

 Pulp Hi Grd 

ONP OCC Mixed Subs. Deink 

tonne/tonne 

1 - Older press technology integrated to Unbl. Kraft 

 1 - Max. Softwood (100%) & no recycled - - - - - 

 2 - Max. Softwood & Max. recycled (10% OCC) - 0.104 - - - 

 3 - Max. Hardwood (5%) & no recycled - - - - - 

2 - New press technology integrated to Unbl. Kraft 

 1 - Max. Softwood (100%) & no recycled - - - - - 

 2 - Max. Softwood & Max. recycled (25% OCC) - 0.261 - - - 

 3 - Max. Hardwood (30%) & no recycled - - - - - 

3 - Based on Recycled Fiber 

 1 - Using Old Corrugated - 1.042 - - - 

 2 - Max. use of lower grades (20%ONP) 0.248 0.834 - - - 

 MARKET PULP 

Softwood Hardwood 

Kraft Kraft Recycled CTMP 

OTHER 

COSTS 

tonne/tonne $/tonne 

1 - Older press technology integrated to Unbl. Kraft 

 1 - Max. Softwood (100%) & no recycled - - - - 214.60 

 2 - Max. Softwood & Max. recycled (10% OCC) - - - - 214.60 

 3 - Max. Hardwood (5%) & no recycled - - - - 212.28 

2 - New press technology integrated to Unbl. Kraft 

 1 - Max. Softwood (100%) & no recycled - - - - 197.200 

 2 - Max. Softwood & Max. recycled (25% OCC) - - - - 197.200 

 3 - Max. Hardwood (30%) & no recycled - - - - 193.720 

3 - Based on Recycled Fiber 

 1 - Using Old Corrugated - - - - 191.400 

 2 - Max. use of lower grades (20%ONP) - - - - 197.200 

Note: OCC is old corrugated containers. 
367 

14.7 Forest Processing 

Growing stock removals are computed by adjusting the total volume of wood processed 

for a specific product to: (i) remove the “non-growing stock” portion of the volume; and (ii) 

account for the loss in volume to logging residues and “other removals” not reflected in product 

outputs. “Other removals” comprise unutilized wood volume from cut or killed growing stock, 

from cultural operations such as precommercial thinnings or from timberland clearing. These 

several factors were derived from TAMM model input for the 2000 RPA Timber Assessment. Their 

original source was Forest Service estimates of roundwood products harvest by species, source (growing 

stock and non-growing stock) and product type (sawlog, veneer log, pulpwood, etc.) and logging residue 

generation by region and species (Smith et al, 2001; tables 39 and 40, pages 154-162). Table 14-__ gives 

a summary of factors of all types for all products. There is no variation over time. The adjustment process 

is described in the following equation: 

where 

FNGS is the fraction of non-growing stock volume in the total wood volume that reaches 

a mill, 

OREMS is the fraction of volume not extracted from the site in other removals, 

LOGRES is the fraction of growing stock removals left as logging residue on the site, and 

Table 14-__. Logging residues (LOGRES), other removals (OREMS) and non-growing stock (FNGS) fractions 

by region and product. 

Definitions 

below PNWW PNWE PSW RM 

LS & 

CB NE SC SE 

HLOGRES 0.0419 0.1290 0.0909 0.0593 0.1047 0.1212 0.1372 0.1378 

SLOGRES 0.0457 0.0675 0.0909 0.0908 0.0414 0.0516 0.0596 0.0605 

HOREMS 0.0040 0.0040 0.0013 0.0000 0.0816 0.0000 0.1351 0.1652 

SOREMS 0.0004 0.0004 0.0000 0.0000 0.0353 0.0000 0.0504 0.0604 

HSFNGS 0.0008 0.0008 0.0000 0.0906 0.0960 0.1162 0.0941 0.0560 

SSFNGS 0.0313 0.0313 0.0816 0.0757 0.0299 0.1994 0.0258 0.0243 

HVFNGS 0.2370 0.0467 0.0000 0.0000 0.0916 0.1155 0.0243 0.0094 

SVFNGS 0.0860 0.0860 0.2364 0.0063 0.0972 0.1995 0.0281 0.0222 

HPFNGS 0.8470 0.0530 0.7626 0.0000 0.1762 0.1816 0.1210 0.1034 

SPFNGS 0.1653 0.1653 0.0000 0.2851 0.1121 0.2182 0.0797 0.1063 

HRPFNGS 0.8470 0.0000 0.7626 0.0089 0.2333 0.1815 0.1305 0.1110 

SRPFNGS 0.1566 0.1566 0.0000 0.2851 0.2979 0.2179 0.1345 0.1225 

HOPFNGS 0.0000 0.0000 0.0000 0.0418 0.6613 0.2577 0.3401 0.2487 

SOPFNGS 0.0098 0.0098 0.0330 0.3189 0.1084 0.3361 0.1213 0.1393 

HFFNGS 0.3140 0.9350 0.8360 0.9400 0.8280 0.8610 0.4900 0.4470 

SFFNGS 0.3590 0.7490 0.5260 0.9710 0.6500 0.9060 0.3930 0.4560 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−

− + = (1 LOGRES )(1 FNGS )(1 OREMS ) GrowingStock Removals Total Removals

region,product

region,product region,product

region,product region,product
368 

Initial letters H and S in names indicate hardwood and softwood species. For the non-growing stock fractions 

(FNGS), the first letters denote the product: HS, HV, HP, HRP, HOP and HF denote sawlogs (S), veneer logs 

(V), pulpwood (P), reconstituted panels including OSB (RP), other solid wood products (OP) and fuelwood (F), 

respectively, for hardwood species. Names are similar for softwoods with a preceeding S. 

14.7.1 Forest non-wood input (solid wood products only)

As noted in section 7.1.8, TAMM’s assumption of weak separability between wood and nonwood inputs (and its specific fixed coefficients technology assumption about wood use) makes it possible 

to write the inverse supply functions for the solidwood products as in equation 7.__, Pp = F(Q, K) + 

(1/rw)Pw. The full supply representation in TAMM is as follows (note that a quadratic form is assumed for 

the aggregator function f in equation 7.__ which yields a linear profit function and linear product supply 

and factor demand functions): 

Qp = asp + bsp[Pp + PRESp -- (L&Hp + Pw)/rwp] + cspOCp + dspKp,t-1 

where 

asp, bsp, csp, and dsp are coefficients estimated by econometric methods, 

PRESp is residue revenue for product p, 

L&Hp is log and haul cost (forest-to-mill costs measured per unit of log input) which 

varies by product p, 

OCp are all other costs, 

Pp and Pw are the prices of product and wood input, respectively, and 

Kp,t-1 is start-of-period capacity (the measure of quasi-fixed capital used in TAMM). 

Residues are treated as a fixed proportion by-product, so residue revenues are added to product price. 

Delivered wood costs are the sum of timber (stumpage, Pw) and delivery (log and haul, L&Hp) costs. 

Solving for Pp, 

 

Pp = -asp/bsp - PRESp + L&Hp/rwp - (csp/bsp)OCp - (dsp/bsp)Kp,t-1 + (1/ bsp)Qp + Pw/rwp

so the non-wood input term (F(Q,K) in equation 7.__) is 

NWCp = -asp/bsp - PRESp + L&Hp/rw - (csp/bsp)OCp - (dsp/bsp)Kp,t-1 + (1/ bsp)Qp 

which varies with the level of output and also over time as recovery (rwp) and other components vary. 

Elasticities of non-wood inputs with respect to output and of total supply with respect to product price are 

shown in Table 14-___ for the 2000-2004 period. Non-wood inputs are highly sensitive to shifts in output 

for softwood lumber in interior and eastern Canada, for OSB in Canada and for hardwood lumber 

production in all of the eastern US regions. 
369 

Table 14-___ Elasticities of non-wood inputs with respect to output and of supply with respect to product 

price by region and product for the initial (2000-2004) model projection period. 

 Softwood Lumber Softwood Plywood OSB Hardwood Lumber 

Nonwood 

inputs Own Price 

Nonwood 

inputs Own Price 

Nonwood 

inputs Own Price 

Nonwood 

inputs Own Price 

PNWW 0.453 0.611 0.423 1.013 

PNWE 0.320 0.345 0.459 0.910 

PSW 0.089 1.481 

RM 0.396 0.500 0.424 0.910 0.841 

LS 0.213 0.820 1.281 

CB 1.281 

8.059 0.206 

NE 1.111 0.280 0.847 7.041 0.254 

SC 0.821 0.561 0.568 0.811 1.658 3.117 0.364 

SE 0.496 0.766 1.194 0.529 1.665 

0.204 

2.309 0.472 

CBCC 0.399 0.935 

CINT 2.147 0.447 

CEST 3.955 0.492 

2.716 0.193 

 

Projections of log and haul costs were derived from the 2000 RPA Timber Assessment. Projected 

residue revenues and capacity in these equations were also taken initially from the TAMM projections. 

These latter variables are determined within the FASOMGHG framework (as shadow prices of the 

residue balance constraints and from the endogenous capacity variables). 

14.8 Wood products Demand 

14.8.1 Solid Wood Products 

Demands for softwood lumber, softwood plywood and OSB are the sum of demands in 

their several “end-uses.” An end-use is a specific group of applications, for example, single 

family housing, manufacturing, shipping, etc. The FASOMGHG equations are derived by 

aggregating annual relations across end-uses for each of the products from TAMM. The original 

end-use demand equations are base on the technology diffusion model developed by Spelter 

(1984, 1985, 1992). In simplified form the model can be written as in equations 14.__ through 

14.__. 

NEED EQUATION NUMBERS 

i,s,t

i,p,t i,s,t

t t 1

t

i i i

M

i 1

i

P

P P

T T

) T

b Q M U exp(

Q Q

− = +

= −

=

−

=

∑
370 

where 

Q is total demand for a product (e.g., softwood lumber), 

Qi is demand in the ith end-use, 

Mi is a measure of the output of the ith end-use (for example, floor area of single family 

housing starts), 

Ui is the maximum use of the solidwood product per unit of output of end-use category i, 

b is a parameter to be estimated, and 

Pi,p,t and Pi,s,t are the prices (put-in-place) of the solidwood product (p) and its substitute 

(s) in end-use category i in period t. 

Price “put-in-place” refers to the cost of the product per unit of application, including the 

costs of all additional or related inputs needed to produce one unit of output of the application. 

For example, the cost put-in-place of OSB used in wall sheathing in a single family home 

includes the cost of the panel itself as well as the labor and fasteners needed to install it. The 

costs are measured per unit of end-use output, in this case, per square foot of floor area in a 

single family housing unit. If we assume fixed coefficients production in their manufacture, the 

put-in-place units can be viewed as “composite inputs” with a different technology for the solid 

wood product and the substitute (see Chambers, 1988). The notion of “diffusion” arises in this 

context because the response of demand to shifting relative prices of solidwood products and 

substitutes is gradual as the cumulative price ratio variable T changes over time. For further 

details of the underlying methodology see Adams and Haynes (1996). Adams et al (1992) 

provide a further discussion and application of this approach to derived demand for factors based 

on composite inputs and specific technology assumptions. 

The demand for hardwood lumber was also extracted from TAMM. It was developed 

using an approach similar to that employed for the other solidwood products but did not include 

the cumulative (diffusion) price ratio term. Demand is broken out by end-use category dependent 

on the relative prices put-in-place of hardwood lumber and a representative substitute product. 

Periodic (5-year) equations were cumulated from the annual estimates in TAMM. See Adams 

and Haynes (1996) for further details of the hardwood sector. 

Demand elasticities for the four endogenous solid wood products are shown in Table 

14.__ for the average of the 1980’s and 1990’s and for the initial 2000-2004 period. The 

elasticity of softwood plywood rises sharply after the 1990’s in the face of competition from 

OSB and rapid increases in its consumption. Consistent with the diffusion approach, the 

elasticity of OSB demand drops sharply as its market share grows. 

Table 14-__ Demand elasticities for solid wood products derived from TAMM projection. 

 Softwood Softwood OSB Hardwood 
371 

Lumber Plywood Lumber 

1980's-1990's -0.10 -0.10 -0.36 -0.60 

2000-2004 -0.21 -0.55 -0.05 -0.51 

Fiber products demand relations are of the constant elasticity form (see Zhang et 

al(1993,1996); Ince, 1994) and shift over time in response to changes in GDP per capita, 

population, and the prices of substitute goods. Table 14-__ summarizes the own price elasticities 

of demand for the US and Canada. 

Table 14-__ Elasticities of demand by fiber 

product for the US and Canada from 

NAPAP (Zhang et al(1993,1996); Ince, 

1994) 

Type of Paper or Pulp US Canada 

Newsprint -0.22 -0.2 

Uncoated. Free Sheet -0.47 -0.2 

Coated Free Sheet -0.40 -0.2 

Uncoated Roundwood -0.54 -0.2 

Coated Roundwood -0.40 -0.2 

Tissue & Sanitary -0.26 -0.6 

Specialty Packaging -0.23 -0.6 

Kraft Packaging -0.54 -0.6 

Linerboard -0.29 -0.7 

Corrugating Medium -0.43 -0.7 

Solid Bleached Board -0.29 -0.7 

Recycled Board -0.40 -0.7 

Construction Pap. & 

Bd. -0.58 -0.7 

Dissolving Pulp -0.26 -0.7 

14.9 International Trade in Wood products 

The US has been a net importer of wood products (on a roundwood volume equivalent 

basis) for the past 50 years. Softwood lumber trade with Canada has received much attention in 

recent years, but net imports of other classes of products have also grown markedly. In the past, 

Canada has been the largest source of US imports of both solid wood and fiber products. This 

dominance has declined somewhat in the past two decades as some European and southern 

hemisphere countries have entered the softwood lumber and panel trade and an array of nations 

and regions have expanded exports in paper and paperboard products. 

In the FASOMGHG forest sector, trade flows from Canada to the US are endogenous for 

softwood lumber, OSB, all 14 classes of fiber products and softwood pulpwood and residues. 

The solidwood sector also incorporates an import supply relation for softwood lumber shipments 
372 

from non-Canadian sources. All other trade flows, both with Canada and the rest of the world, 

are exogenous and specified consistent with the Base case trade scenario assumptions in the 2000 

RPA Timber Assessment. 

14.9.1 Canada 

14.9.1.1 Exchange rates and tariffs 

Canada comprises three endogenous producing regions in the solidwood sector and two 

in the fiber products sector. There is one demand center in the US and one in Canada for fiber 

products. Canadian demand for solidwood products is exogenous and there is a single demand 

center in the US for solidwood products. Thus in both solid wood and fiber products Canada is 

treated as an excess supply region, shipping products to the US, while shipments from the US to 

Canada are exogenous. In the endogenous cases, trade moves in response to relative costs and 

prices subject to exchange rate assumptions and any tariffs. Exchange rate history and 

projections (from the 2000 RPA Timber Assessment) are shown in Figure 14.___. Note that this 

is the real exchange rate defined as: 

Real exchange rate=Nominal exchange rate*relative prices in trading countries. 

In the present case the real exchange rate is computed as 

($US/$C)(CPPI/USPPI), 

where CPPI and USPPI are the Canadian and US all commodity producer price indexes, 

respectively. 

Figure 14.2. Real US/Canadian exchange rate 1950-2003 with projections to 2050 from 2000 

RPA Timber Assessment.

Removed to figures file 

US tariffs (or effective tariffs) on softwood lumber imported from Canada have varied 

markedly over the past decade. In the base FASOMGHG projection we assume continuation of 

the current (2003-2004) tariff structure amounting to approximately at 27.2% rate ad valorem

(see Adams, 2003, for a discussion of the effects of changing tariffs on trade and timber 

resources in the context of the TAMM model). US tariffs on fiber products are limited and have 

been quite stable over the past several decades. They are ignored in the base case analysis. 
373 

14.9.1.2 Canadian timber supply 

While there is a small area of private timberland in Canada, the bulk of the timberland 

base is held and managed by the provinces. The volume of timber offered for sale (or annual 

allowable cut, AAC) from these lands, like their public counterparts in the US discussed below, 

is determined by processes independent of timber prices (and often management costs). In 

addition, the current timber inventory and timber growth and yield data for Canada do not allow 

the construction of a compact timber inventory projection model (such as ATLAS) as was 

possible for the US. As a consequence the “supplies” of sawtimber and pulpwood in Canada are 

represented by: (i) a set of delivered wood cost relationships developed in the TAMM and 

NAPAP models and (ii) specific assumptions about future trends in the AACs in response to 

various political pressures in Canada. 

Delivered wood cost relations for sawtimber derive from historical analysis of costs and 

wood volumes. The constant elasticity relations have own-price elasticities of delivered wood 

volumes of 1.22 for the BC Coast region, 0.67 for the Canadian interior region, and 1.33 for 

eastern Canada. The relations do no shift over time. Canadian roundwood pulpwood supply is 

represented by a combined minimum price (harvest and haul cost) and quantity upper bound. 

Volume is available at the fixed price up to the bound. Roundwood pulpwood has accounted for 

only about 40% of the total pulpwood receipts at mills (roundwood + residues) in the past. 

Projections, based on assumptions in the 2000 RPA Timber Assessment, envision that it will 

continue to provide a similar proportion in the future remaining in the neighborhood of recent 

harvest levels (about 35 million m3). Residues from lumber mills provide the remaining 60% of 

pulpwood receipts and are determined within the model. 

Public forest lands in Canada face an array of pressures to broaden the objectives for their 

management, to limit harvests to sustainable levels and to provide land for native peoples. As a 

result, AACs have been falling in some provinces, and in the British Columbia Coast and Interior 

Canadian regions actual or realized harvest has fallen as well. This is, at present, an highly 

controversial issue in Canada, and the extent and timing of any future reductions in allowable cut 

and harvest are uncertain. The base projection, following assumptions in the 2000 RPA Timber 

Assessment, assumes that harvest restrictions will continue in western provinces and be enacted 

in eastern provinces within the next decade, gradually reducing softwood sawtimber harvest and 

exports of softwood lumber to the US. Only softwood sawtimber harvests are affected by these 

limitations. 
374 

In the BC Coast region it is assumed that allowable softwood sawtimber harvest will 

continue its decline of the past decade and will rise no higher than 400 million ft3

. In the 

Canadian Interior region it was assumed that softwood sawtimber harvest by 2010 will rise no 

higher than the peak level observed in 1992 (some 2.0 billion ft3

 per year). Between 2010 to 

2020 this limit is reduced to the lowest harvest level observed in the decade of the 1990's 

(roughly 1.75 billion ft3

 per year) and remains there for the rest of the projection. In the Eastern 

Canadian region, where AAC's are at present substantially higher than harvest, it was assumed 

that harvest would increase no more than 15 percent above approximate 1999 levels (to about 2.6 

billion ft3

 per year) in the period to 2010. Between 2010 and 2020 the limit falls back to roughly 

the average level observed during the 1990s (about 2.0 billion cubic feet per year) 

. 

1975 1980 1985 1990 1995 2000 2005

0%

10%

20%

30%

40%

Percent of US Consumption

CANADA

OTHER

Figure 14-1. Share of Canadian and non-Canadian imports in US softwood 

lumber consumption. 
375 

14.9.1.3 Other world regions 

Trade with non-Canadian countries and regions is treated as exogenous except for import 

flows of softwood lumber. Over the period from 1993 to 2003, non-Canadian softwood lumber 

imports grew from 0.5% of US consumption to 3.2%, a volume gain of more than 1.5 billion 

board feet. As shown in Figure 14.__, non-Canadian imports have accounted for the continued 

growth in the share of imports in US consumption while the Canadian share has stabilized. In 

light of this past growth, and prospects for continued expansion in the future, we included the 

TAMM estimate of non-Canadian import supply in the FASOMGHG solid wood sector. This is 

a constant elasticity function with an own price elasticity of 1.5 established on a judgmental 

basis. The import supply curve shifts (exogenously) over time based on Forest Service estimates 

of future supply potential from these sources. In the 2000 RPA Timber Assessment, this 

approach led to projected non-Canadian softwood lumber imports of 7.3 billion board feet by 

2020 and 10.5 billion feet by 2050. 

14.10 Public land harvests 

Timber harvest from public lands in the US is established by an array of policy-making 

processes varying from the state-local to the federal level. In general, however, harvest 

determination--the so-called "allowable sale quantity" or volume offered for sale--is independent 

of market price for timber and may be unrelated as well to levels of timber inventory and growth. 

As a consequence we treat public timber harvests as exogenous in FASOMGHG, with future 

projections for the base case derived from 2000 RPA Timber Assessment base assumptions. 

Historical and projected volumes of sawtimber are shown in Figure 14-__ for the US totals. The 

modest increase in national forest harvest reflects assumptions of expanded restoration thinning 

programs in western states but only toward the levels allowed under current management 

direction. The impacts of any implementation of the Healthy Forests Restoration Act of 2003 are 

not reflected in these volumes 
376 

s.

0

1

2

3

4

5

6

7

8

9

10

1960 1980 2000 2020 2040 2060

BILLION CUBIC FEET PER 5-YEAR PERIOD

NATIONAL FORESTS

OTHER GOVERNMENT

Figure 14-3. Sawtimber harvests on national forests and other government lands in 

the US: estimated actual levels 1975-2000, projections from 2000 RPA Timber 

Assessment. 
377 

15 CHAPTER 14 AGRICULTURE SECTOR ECONOMIC DETAIL (MCCARL) 

15.1.1 Commodities disappearance 

15.1.2 Production budgets 

15.1.2.1 Crops 

15.1.2.2 Livestock 

15.1.3 Factor supply 

15.1.3.1 land 

15.1.4 types 

The availability on these two types of land was derived from USDA NAS county 

reporting and Agricultural Statistics. The regional prices for land were derived from the 

information in Farm Real Estate Market Developments. Cash rental prices of land were used to 

reflect annual opportunity costs to the owners. The third land type is AUM grazing land. The 

AUM supply is divided into public and private grazing on the subregional level. Public grazing is 

available at a constant price while private grazing can be obtained by an upward-sloping supply 

schedule. Information on public grazing comes from the Grazing Statistical Summary by USDA 

Forest Service and Public Land Statistics by the Bureau of Land Management in the US 

Department of the Interior. Private grazing information comes from the estimates in An Analysis 

of the Range Forage Situation in the US: 1989-2040 by L.A. Joyce. Information on grazing fees 

originates from Estimating Forage Values for Grazing National Forest Lands by W.F. Hahn et al. 

and the Bureau of Land Management. 

Three major types of land are specified. The first one (type 1) is land suitable for crop 

production. Depending on ASM version, crop land may be treated as a single type or in four 

erodibility classes. The second land type (type 2) is suitable for pasture or grazing. The 

availability on these two types of land by states or regions was derived from Agricultural 

Statistics. The regional prices of these land were derived from the information in Farm Real 

Estate Market Developments. Cash rental prices of land were used to reflect annual opportunity 

costs to the owners. The third land type is AUM grazing land. The AUM supply is divided into 

public and private grazing on the subregional level. Public grazing is available at a constant price 

while private grazing can be obtained by a upward- sloping supply schedule. Information on 
378 

public grazing comes from the Grazing Statistical Summary by USDA Forest Service and Public 

Land Statistics by the Bureau of Land Management in the US Department of the Interior. Private 

grazing information comes from the estimates in An Analysis of the Range Forage Situation in 

the United States: 1989-2040 by L.A. Joyce. Information on grazing fees originates from 

Estimating Forage Values for Grazing National Forest Lands by W.F. Hahn, et al. and the 

Bureau of Land Management. 

Conservation Reserve Program (CRP) acres, signups 1 through 9, were subtracted from 

the crop land base by subarea and crop land class. Available CRP data did not allow a direct 

allocation of enrolled acres by FASOMGHG crop land class. However, USDA analysis (Osborn 

et al., 1992) of the available data provided guidelines for allocation of the CRP by ASM crop 

land classes indicating that about 25 percent of the CRP enrollment went into non-highly 

erodible land (ei < 8.0). In turn, land was allocated so the CRP proportion in svei and mdei could 

not exceed 75 percent; likewise, restrict for each subarea that only 75 percent of svei and mdei 

could be in the CRP. First, CRP was allocated into svei and mdei, proportional to their 

occurrence in total land, until either 75 percent of the CRP was allocated or 75 percent of svei 

and mdei devoted to CRP. Then, the remainder of the CRP was allocated to loei and w3-8 

proportionate to their occurrence in the region. 

The labor input also include two components: family labor and hired labor. The model 

requires specification of a maximal amount of family labor available, and a reservation wage for 

family labor. The additional labor to be hired is based on an inducement wage rate which is 

higher than the reservation wage. The regional information about the quantities and wages was 

obtained from Farm Labor. 

The water input is also divided into fixed (or surface) and variable available (or pumped 

ground) water and is supplied at the subregion level. The fixed water is available for a constant 

price but the amount of variable water is provided according to a supply schedule where 

increasing amounts of water are available for higher prices. The information on water came from 

USDA and NASS sources who used the Farm and Ranch Irrigation Survey and other government 

sources in its formation. 

The labor input also include two components: family labor and hired labor. The model 

requires specification of a maximal amount of family labor available, and a reservation wage for 

family labor. The additional labor to be hired is based on an inducement wage rate which is 

higher than the reservation wage. The regional information about the quantities and wages was 

obtained from Farm Labor. 
379 

The water input is also divided into fixed (or surface) and variable available (or pumped 

ground) water and is supplied at the subregion level. The fixed water is available for a constant 

price but the amount of variable water is provided according to a supply schedule where 

increasing amounts of water are available for higher prices. The information on water came from 

USDA and NASS sources who used the Farm and Ranch Irrigation Survey and other government 

sources in its formation. 

15.1.4.1 AUMs 

15.1.4.2 labor 

15.1.4.3 water 

15.1.4.4 Other inputs 

15.1.5 Crop mixes 

15.1.6 Livestock mixes 

15.1.7 Agricultural Product Demand 

Both supply and demand information (i.e., prices, quantities, slopes and/or elasticities) 

are required in the model. The total supply consists of domestic production from all agricultural 

regions and imports. Total demand is made up of domestic and foreign (or export) components. 

Domestic demand includes food consumption, CCC stock, livestock feed and processing. 

Transportation costs to the market are included in the supply budget. Livestock feed and 

processing demands are endogenously determined. The prices and quantity data came from 

Agricultural Statistics, Agricultural Prices Annual Summary, and Livestock and Meat Statistics 

Supplement. Elasticity, slope, and other information came from Baumes, Burton, Tanyeri-Abur 

and Bob House in the USDA. 

15.1.8 International Trade in Agricultural Products 

15.1.9 Biofuels: additional detail 

Two opportunities — Ethanol and biofuel for power plants 
380 

Biomass production for power plant use required several new production possibilities be 

added: 

Diversion of mill residues from traditional pulp and paper or other uses; 

Collection of logging residue or harvest of whole trees for chipping, and shipment to a 

power plant; 

Production and hauling of switch grass and short rotation woody crops for biomass 

Treatment of power plant use of biomass to the point where the energy in biomass is on 

an equivalent basis with the energy from coal; (100 mega watt plant) Ira Shavel, Mark Shenckel 

and Bob Shackleton made up numbers for this) 

Treatment of the possible use of wood chips from short rotation woody crops for pulp 

and paper production. 

15.1.10 Non-CO2 Environmental Indicators (McCarl) 

15.1.10.1 Natural resource use (land, water,...) 

15.1.10.2 Nutrient loadings (N,P,K, erosion,...) 

15.1.10.3 Pesticide loadings 

c) Cross-Sector Land Interaction (McCarl) 

d) GHG Accounting 

i) Forest Sector GHG Accounting (Murray & Depro) 

ii) Agriculture Sector GHG Accounting (McCarl) 

e) Non-CO2 Environmental Indicators (McCarl) 

i) Natural resource use (land, water,...) 

ii) Nutrient loadings (N,P,K, erosion,...) 

4) Model Baseline (McCarl, Adams, Alig) 
381 

Describe the process by which the model baseline is constructed and simulated (and 

compared to other projections?) 

a) Economic variable projections (note: FASOMGHG doesn't normally present 

absolute levels for these, but indices relative to the baseline. For baseline purposes, could index 

based of bas year value, 2000?) 

i) Forest sector 

(1) Prices 

(2) Quantities: production,consumption, trade 

ii) Agriculture Sector 

(1) Prices 

(2) Quantities: production,consumption, trade 

b) Land use projections 

i) Timberland 

ii) Crop land 

iii) Pasture land 

iv) Other 

c) GHG projections 

i) Forest sector 

(1) Carbon sequestered in forests 

(2) Carbon sequestered in products 

ii) Agriculture sector 

(1) Carbon sequestered in soils 

(2) Non-CO2 emissions 

(3) CO2 emissions from fossil fuel use 

(a) On-farm 

(b) Upstream / input use? 

(4) Biofuel offsets 
382 

SECTION 5: FASOMGHG OUTPUT AND VALIDATION 
383 

16 CHAPTER 15 BROAD CATEGORIZATIONS OF OUTPUT 

The FASOMGHG solution is addressed here both in terms of the information it yields 

and its economic properties. The FASOMGHG objective function involves the maximization of 

the present value of consumers' plus producers' surpluses net of transport and capacity costs. It 

depicts (assumes), therefore, a multi-period simulation of economic activity in competitive 

sectors under perfect foresight of future price conditions. The sizes of timberland holdings are 

assumed to be small enough that owners do not individually affect prices but are knowledgeable 

of future wood product prices and land opportunity costs. Harvest decisions are made so that 

stands are harvested at the point where the (marginal present) value of wood and carbon growth 

(if priced) is no larger than the (present value of) marginal costs of maintaining the stand plus the 

marginal opportunity cost of holding the land in the current stand for an additional period (the 

present value of future rotations). In addition, land will shift into forestry from agriculture if the 

expected returns in forestry exceed the returns in agriculture over the remaining time periods in 

the model plus the terminal values. The decision regarding transferring land to agriculture would 

involve the opposite considerations. 

The solution to the nonlinear programming problem provides information in eight areas: 

3⁄4 Consumers' and producers' welfare 

3⁄4 Agricultural production and prices 

3⁄4 Forest area and inventory volumes 

3⁄4 Harvest levels and prices 

3⁄4 Wood product output and prices 

3⁄4 Land and forest asset values 

3⁄4 Carbon sequestration amounts and "prices" 

3⁄4 Land transfers 

Appendix D gives a definition of output items from a current version of FASOMGHG. 
384 
385 

• Consumer and producer welfare -- As previously stated, the FASOMGHG objective 

function represents the net present value of consumers' and producers' surpluses in the 

two sectors. Consumers' surplus is calculated in both sectors. Producers' surplus is 

calculated regionally. Thus, the model produces information about the distribution of the 

present and future values of consumers' and producers' surpluses over both space and 

time. 

• Agricultural production and prices -- FASOMGHG provides regional level information 

about the market-clearing production and price levels for all of the ASM commodities by 

time period. Regional production levels for crops can be further broken down into 

average yield levels and acreage harvested. Price levels for agricultural products are 

endogenous in FASOMGHG. 

• Agricultural factor use and prices -- Tree planting programs have the potential to reduce 

input use by farmers. Annual management costs associated with tree plantations are 

considerably below agricultural production costs. Sufficiently large reductions in input 

use by farmers may cause the prices of some inputs, such as hired labor and water, to 

decrease. FASOMGHG contains input supply curves for land and hired labor. 

Consequently, price (and cost) impacts on these inputs are an output of FASOMGHG. 

The impacts of reductions in the use of other inputs can be measured, in aggregate, in 

terms of cost decreases to farmers, or as revenue decreases to input suppliers (on the 

other side of the balance sheet). 

• Forest inventory levels -- For each ten year period in the simulation, FASOMGHG 

reports regional inventory levels by owner, land use suitability, forest type/species, site 

class, management regime, and age -- in other words, by each of the dimensions that 

characterizes a representative inventory aggregate in the model. 

• Harvest levels and prices -- Harvest levels are provided by FASOMGHG at the same 

level of detail as other inventory statistics. Prices may be examined at either the national 

or regional levels. 

• Wood product output and prices -- Levels of wood product output levels, by period, are 

provided for each of the three products (sawlogs, pulp, and fuelwood), at least by region 

and forest-type. Price levels for these products are endogenous. 

• Land and forest asset values -- Because FASOMGHG simulates the competition between 

forest and agricultural activities for land, FASOMGHG produces information about 

marginal land and forest asset values over time. Marginal land values for agricultural and 

forestland can be determined from shadow prices for the equations representing the 

potential reforested land balance and agricultural land balance. Asset values for regional 

inventories can be calculated from this information using information about volumes per 

acre from the solution to the NLP. 

• Carbon sequestration amounts and prices -- FASOMGHG produces region- and nationallevel information about the total amount of carbon in storage in each period and the 
386 

storage rate (i.e., change in storage) during each period. If carbon is "forced" into the 

model, then FASOMGHG will generate an estimate of the shadow price associated with 

that requirement, provided that the constraint is binding. 

• Land transfers -- An important feature of FASOMGHG is the intersectoral linkage 

between agriculture and forestry. FASOMGHG was designed so that transfers of land 

between sectors would occur endogenously within the model as a result of intertemporal 

economic forces. Thus, an important output of FASOMGHG is the listing of land 

transfers in each time period. These transfers are shown by region, land class, and sector 

(from - to) for each time period. 

FASOMGHG’s key endogenous variables include 

• commodity and factor prices; 

• production and export and import quantities; 

• land use; 

• management strategy adoption; 

• resource use; 

• economic welfare measures: 

producer and consumer surplus, 

transfer payments, 

net welfare effects, 

• environmental impact indicators; 

GHG emission/absorption (CO2, CH4, N2O), and 

surface, subsurface, and groundwater pollution for nitrogen, phosphorous, and 

soil erosion. 
387 

17 CHAPTER 16 GAMS IMPLEMENTATION 

This appendix details the structure and sequence of the files that make up the 

FASOMGHG model. FASOMGHG is implemented in the GAMS algebraic modeling language 

(Brooke et al. 1988, McCarl, 2005). The model is made up of a number of files. This is done to 

allow separation of distinctly different types of data and to allow disciplinary experts to work on 

selected parts of the model. Functionally the program can be divided several ways. The division 

we describe separate files into categories according to whether they involve data, data 

calculations, model specification, analysis execution and report writing and/or model support. 

Distinctions will also be made between unifying files, forestry files, agricultural files and carbon 

files. 

17.1 File Structure 

Table 17-1 gives an alphabetic list of each of the FASOMGHG files. These files may also 

be classified in terms of their function and aim. A listing of the files, along those lines, is given 

below in Table 17-2. 

Table 17-1. Alphabetic list and brief description of the FASOMGHG files 

Filename Description 

allofit.gms -- integrates the data files for FASOMGHG 

calc_agcondition.gms-- calculates where production is located 

calc_aggregate.gms -- aggregates subregion ag data to regions 

calc_agliveghg.gms-- calculates livestock GHG emission factors 

calc_agsetup.gms -- calculates data for ag model setup mainly the profit calculations 

calc_fixregs.gms-- calculates regional incidence of types of production 

carbon_compute.gms -- computes forestry stand carbon data 

cplex.opt -- option file for CPLEX solver 

data_agall.gms—unifies all agricultural data 

data_agbiomass.gms-- data on moving wood products into biofuels 

data_agcemission_rawdata.gms-- data on agricultural emissions 

data_agcostname.gms -- defines agricultural cost item names 

data_agcropbudsoil.gms-- data giving agricultural crop budgets 

data_agcropmix.gms -- data on agricultural crop mix 

data_agdevelopment.gms-- contains data on ag land moving to developed use 

data_agdynamic.gms-- data on agricultural yield and other dynamic growth 

data_agelectricemit.gms-- data on emissions when generating electricity with coal 

data_agfeedprocess.gms -- defines names of feed blend alternatives 

data_agfeeds.gms -- defines agricultural blended feed commodity names 
388 

data_agghglivestock.gms-- data on GHGs from manure and enteric fermentation 

data_agghgmitigate.gms-- data on biofuels combustion and fossil fuel emissions 

data_agghgnonco2.gms-- data on agricultural nonco2 emissions and management 

data_agghgreglivestock.gms-- data on manure and enteric ferment management 

data_agghgsoil.gms-- data on initial tillage practices by soils 

data_aginputname.gms -- defines agricultural input item names 

data_aginputprice.gms -- data for prices of agricultural inputs 

data_aglivebuds.gms-- data giving agricultural livestock budgets 

data_agmisc.gms-- data on population by region used in welfare allocation 

data_agnatmix.gms-- data on agricultural crop mix 

data_agprimary.gms -- defines agricultural primary commodity names 

data_agprocess.gms-- data on national agricultural processing 

data_agprocessregional.gms-- data on regional agricultural processing 

data_agprocessset.gms -- defines the name of the agricultural processing alternatives 

data_agresource.gms-- data on initial land and labor, water and AUMS supply 

data_agsecondary.gms -- defines agricultural secondary commodity names 

data_agsoilcarb.gms-- data on CENTURY and EPIC soil carbon sequestration 

data_agsubreg.gms -- names of the agricultural subregions 

data_agsubregtoreg.gms -- defines how subregions fall into regions 

data_agsupdem.gms -- data for agricultural commodity demand, export and import 

data_agtransport.gms-- data on transportation 

data_basicsets.gms -- defines the basic regional and time sets 

data_carbon_biomassmodel.csv -- tree biomass data for carbon accounts 

data_carbon_trees.gms -- brings in all tree carbon data 

data_carbon_weightbyrpaland.csv -- carbon weighting data 

data_carbon_undercwd.csv—understory data for carbon accounting 

data_fasomreg.gms -- names of the FASOMGHG overall regions 

data_forall.gms -- integrates all the forest data 

data_forcanval.gms -- contains US Canada trade and stumpage supply adjusters 

data_forcapacity.gms -- contains wood product manufacturing capacities 

data_forconvert.gms -- contains cost per acre to convert to agriculture use 

data_fordevelopment.gms -- contains data on forest land moving to developed use 

data_forexist.gms -- contains the timber growth and yield curves for existing forests 

data_forexistcost.gms -- contains cost for existing stands 

data_forexistpc.gms-- contains the partial cut and thin yields for existing forests 

data_forfuelusage.gms -- -- contains forest fossil fuel use for production 

data_forinvent.gms -- contains the initial forest inventory data 

data_forlogsupdem.gms -- contains public and Canada log supply/demand 

data_formcoefs.gms -- contains wood product manufacturing data 

data_forminiharv.gms -- contains minimum harvest ages for stands 

data_fornew.gms -- contains timber growth and yield for afforested and reforested stands 

data_fornewcost.gms -- contains cost for afforested and reforested stands 

data_fornewpc.gms -- contains the partial cut and thin yields for new forests 

data_forproducts.gms -- defines the wood product commodity names 

data_forrecycle.gms -- contains wood product related recycling data 

data_forrotationage.gms-- contains typical rotation ages for stands 

data_forsticky.gms -- contains investment cost limits for establishing new stands 
389 

data_forsupdem.gms -- contains wood product supply and demand curves 

data_ghg.gms -- defines a number of items about GHG coverage 

data_ghgtype.gms -- defines the names of the GHG accounts in the model 

data_landtransfer.gms -- collects all forest to and from ag land transfer data 

model_bounds.gms-- defines upper and lower bounds for model 

model_scale.gms -- defines scaling factors for model 

model_seperable.gms -- contains data to set up grid point approximations 

model_setup.gms -- sets up miscellaneous model related parameters 

model_structure.gms -- defines model structure and initially solves 

model_update.gms—updates incidence of forest stands and ag crops 

policy_model.gms -- contains data about policy setup of model 

report_agcal.gms -- computes single run agricultural report 

report_carboncal.gms -- computes single run GHG report 

report_comparecal.gms -- computes comparative run report 

report_comparesetup.gms-- sets up parameters for a cross scenario report 

report_finalcal.gms -- displays cross scenario report 

report_forcal.gms -- computes single run forestry report 

report_forresultsput.gms -- saves forestry report in put files 

report_ghgtype.gms -- computes single run GHG report 

report_onerun.gms -- does report writing on solutions 

report_runsummarytables.gms -- computes cross run summary report 

report_setup.gms -- sets up parameters for a single run report 
390 

Table 17-2. File grouping by major model component 

Sector or Data Model Report Function Data Calculation Specification Writing Forest Sector data_forall.gms Model_update.gms model_bounds.gms report data_forcapacity.gms carbon_compute.gms model_seperable.gms report data_forcanval.gms calc_fixregs.gms model_scale.gms 

data_forconvert.gms model_setup.gms data_fordevelopment.gms model_structure.gms 

data_forexist.gms data_forexistcost.gms data_forexistpc.gms data_forfuelusage.gms data_forinvent.gms data_forlogsupdem.gms data_formcoefs.gms data_forminiharv.gms data_fornew.gms data_fornewpc.gms data_fornewcost.gms data_forproducts.gms data_forrecycle.gms data_forrotationage.gms data_forsticky.gms data_forsupdem.gms policy_model.gms Agricultural Sector data_agall.gms calc_agcondition.gms model_bounds.gms reportdata_agcostname.gms calc_aggregate.gms model_seperable.gms data_agbiomass.gms calc_agliveghg.gms model_scale.gms data_agcemission_rawdata.gms calc_agsetup.gms model_setup.gms data_agcropbudsoil.gms calc_fixregs.gms model_structure.gms data_agcropmix.gms 
391 

data_agdevelopment.gms data_agdynamic.gms data_agelectricemit.gms data_agfeedprocess.gms data_agfeeds.gms data_agghglivestock.gms data_agghgmitigate.gms data_agghgnonco2.gms data_agghgreglivestock.gms data_agghgsoil.gms data_aginputname.gms data_aginputprice.gms data_aglivebuds.gms data_agmisc.gms data_agnatmix.gms data_agprimary.gms data_agprocess.gms data_agprocessregional.gms data_agprocessset.gms data_agresource.gms data_agsecondary.gms data_agsoilcarb.gms data_agsubreg.gms data_agsubregtoreg.gms data_agsupdem.gms data_agtransport.gms policy_model.gms GHG model data_agbiomass.gms calc_agliveghg.gms reportdata_agghglivestock.gms carbon_compute.gms report_ghgtype.gms data_agghgmitigate.gms data_agghgnonco2.gms data_agghgreglivestock.gms data_agghgsoil.gms  data_carbon_biomassmodel.csv  data_carbon_trees.gms  data_carbon_weightbyrpaland.csv  data_carbon_undercwd.csv  data_agelectricemit.gms  data_ghgtype.gms  data_ghg.gms  data_ghgtype.gms 
392 

Unifying allofit.gms model_update.gms model_bounds.gms report data_basicsets.gms calc_fixregs.gms model_seperable.gms report_compar data_fasomreg.gms model_scale.gms report_compar data_landtransfer.gms model_setup.gms report_finalcal policy_model.gms model_structure.gms report cplex.opt report
393 

17.2 Run File Sequence and Control Switches 

The basic method is to run three files, largely in sequence using the file aaab.gms for the 

large model or aaa.gms for a small version. The files run are in the order given below, with a 

brief description of their function. 

Allofit.gms Includes all agricultural, forestry, and carbon data as well as 

associated data calculations 

Model_structure.gms Defines the FASOMGHG optimization model 

Report_onerun.gms Report writer 

Users may also use an advanced basis in the case of problem cold starts. Using the GDX 

savepoint option and the later loadpoint writes and incorporates that basis. 

FASOMGHG contains two switches that may be set which alter the type of model being 

analyzed. These are set at the top of the FAMODEL but may be reset anywhere below that point. 

These switches and their functions are: 

YESAG A switch which controls whether the ag model is generated. A nonzero value 

activates the ag model while a zero value suppresses it. 

YESFOR A switch which controls whether the forestry model is generated. A nonzero value 

activates the forestry model while a zero value suppresses it. When both YESFOR 

and YESAG are nonzero the full linked FASOMGHG two sector model is solved. 
394 

17.3 File Functions and Sequence 

As previously stated, there are five files executed by the batch file. These files call 

various associated files and control the model setup, solution, and output processes. These files 

are discussed further below. 
395 

Detailed Specifications for Each Main File 

ALLOFIT.GMS

This file includes all the FASOMGHG data. The 

include files: 

 data_basicsets.gms -- defines the basic regional and time sets 

 data_fasomreg.gms -- names of the FASOMGHG overall regions 

data_agsubreg.gms -- names of the agricultural subregions 

 data_agsubregtoreg.gms -- defines how subregions fall into regions 

 data_agprimary.gms -- defines agricultural primary commodity names 

 data_agsecondary.gms -- defines agricultural secondary commodity names 

 data_agfeeds.gms -- defines agricultural blended feed commodity names 

 data_forproducts.gms -- defines the wood product commodity names 

 data_aginputname.gms -- defines agricultural input item names 

 data_agcostname.gms -- defines agricultural cost item names 

 data_ghgtype.gms -- defines the names of the GHG accounts 

 data_agprocessset.gms -- defines the name of the agricultural processing 

alternatives 

 data_agfeedprocess.gms -- defines names of feed blend alternatives 

 data_ghg.gms -- defines a number of items about GHG coverage 

 data_ghgtype.gms gms -- defines the names of the GHG accounts in the model 

 data_forall.gms -- integrates all the forest data 

 data_forproducts.gms -- defines the wood product commodity names 

 data_forinvent.gms -- contains the initial forest inventory data 

 data_forexist.gms -- contains the timber growth and yield curves for 

existing forests 

 data_forexistpc.gms-- contains the partial cut and thin yields for existing 

forests 
396 

 data_fornew.gms -- contains timber growth and yield for afforested and 

reforested stands 

 data_fornewpc.gms -- contains the partial cut and thin yields for new 

forests 

 data_fornewcost.gms -- contains cost for afforested and reforested stands 

 data_forexistcost.gms -- contains cost for existing stands 

 data_forminiharv.gms -- contains minimum harvest ages for stands 

 data_forrotationage.gms-- contains typical rotation ages for stands 

 data_forfuelusage.gms -- -- contains forest fossil fuel use for production 

 data_forsticky.gms -- contains investment cost limits for establishing new 

stands 

 data_forsupdem.gms -- contains wood product supply and demand curves 

 data_forlogsupdem.gms -- contains public and Canada log supply/demand 

 data_forcapacity.gms -- contains wood product manufacturing capacities 

 data_formcoefs.gms -- contains wood product manufacturing data 

 data_forcanval.gms -- contains US Canada trade and stumpage supply 

adjusters 

 data_forrecycle.gms -- contains wood product related recycling data 

 data_agall.gms -- unifies all agricultural data 

 data_agprimary.gms -- defines agricultural primary commodity names 

 data_agsecondary.gms -- defines agricultural secondary commodity names 

 data_agfeeds.gms -- defines agricultural blended feed commodity 

names 

 data_agfeeds.gms -- defines agricultural blended feed commodity names 

 data_agcostname.gms -- defines agricultural cost item names 

 data_aginputname.gms -- defines agricultural input item names 

 data_agprocessset.gms -- defines names of the agricultural processing 

alternatives 

 data_agfeedprocess.gms -- defines names of feed blend alternatives 
397 

 data_agfeedprocess.gms -- defines names of feed blend alternatives 

 data_agsupdem.gms -- data for agricultural commodity demand, export and 

import 

 data_aginputprice.gms -- data for prices of agricultural inputs 

 data_agcropmix.gms -- data on agricultural crop mix 

 data_agnatmix.gms-- data on agricultural crop mix 

 data_agresource.gms-- data on initial land and labor, water and AUMS 

supply 

 data_agcropbudsoil.gms-- data giving agricultural crop budgets 

 calc_fixregs.gms-- calculates regional incidence of types of production 

 data_aglivebuds.gms-- data giving agricultural livestock budgets 

 data_agprocess.gms-- data on national agricultural processing 

 data_agprocessregional.gms-- data on regional agricultural processing 

 data_agtransport.gms-- data on transportation 

 data_agbiomass.gms-- data on moving wood products into biofuels 

 data_agmisc.gms-- data on population by region used in welfare allocation 

 data_agghgmitigate.gms-- data on biofuels combustion and fossil fuel 

emissions 

 data_agelectricemit.gms-- data on emissions when generating electricity 

with coal 

 data_agghglivestock.gms-- data on GHGs from manure and enteric 

fermentation 

 data_agghgreglivestock.gms-- data on manure and enteric ferment 

management 

 data_agghgsoil.gms-- data on initial tillage practices by soils 

 data_agcemission_rawdata.gms-- data on agricultural emissions 

 data_agsoilcarb.gms-- data on CENTURY and EPIC soil carbon 

sequestration 
398 

 data_agghgnonco2.gms-- data on agricultural nonco2 emissions and 

management 

 calc_agcondition.gms-- calculates where production is located 

 calc_agliveghg.gms-- calculates livestock GHG emission factors 

 data_agdynamic.gms-- data on agricultural yield and other dynamic growth 

 calc_fixregs.gms-- calculates regional incidence of types of production 

 data_landtransfer.gms -- collects all forest to and from ag land transfer data 

 data_forconvert.gms -- contains cost per acre to convert to agriculture use 

 data_fordevelopment.gms -- contains data on forest land moving to 

developed use 

 data_agdevelopment.gms-- contains data on ag land moving to developed 

use 

 policy_model.gms -- contains data about policy setup of model 

 model_seperable.gms -- contains data to set up grid point approximations 

 calc_agsetup.gms -- calculates data for ag model setup mainly the profit 

calculations 

 model_setup.gms -- sets up miscellaneous model related parameters 

 model_update.gms—updates incidence of forest stands and ag crops 

 model_update.gms—updates incidence of forest stands and ag crops 

 calc_aggregate.gms -- aggregates subregion ag data to regions 

 data_carbon_trees.gms -- brings in all tree carbon data 

 data_carbon_weightbyrpaland.csv -- carbon weighting data 

 data_carbon_biomassmodel.csv -- tree biomass data for carbon accounts 

 data_carbon_undercwd.csv—understory data for carbon accounting 

 carbon_compute.gms -- computes forestry stand carbon data 

model_structure.gms 

This file defines model structure and initially solves 
399 

include files: 

 model_scale.gms -- defines scaling factors for model 

 model_bounds.gms-- defines upper and lower bounds for model 

 calc_fixregs.gms-- calculates regional incidence of types of production 

 model_update.gms—updates incidence of forest stands and ag crops 

report_onerun.gms 

This file does report writing on solutions 

include files: 

 report_setup.gms -- sets up parameters for a single run report 

 report_comparesetup.gms-- sets up parameters for a cross scenario report 

 report_agcal.gms -- computes single run agricultural report 

 report_forcal.gms -- computes single run forestry report 

 report_forresultsput.gms -- saves forestry report in put files 

 report_carboncal.gms -- computes single run GHG report 

 report_ghgtype.gms -- computes single run GHG report 

 report_comparecal.gms -- computes comparative run report 

 report_runsummarytables.gms -- computes cross run summary report 

 report_finalcal.gms -- displays cross scenario report 

17.4 Flow Chart of Model Segments 

 

Primary file 

Secondary file that is included 

in primary file 

File that is included in secondary 

file 
400 

allofit_fasom.gms < data_basicsets.gms << data_fasomreg.gms 

 << data_fasomreg.gms 

 << data_fasomreg.gms 

 << data_agsubreg.gms 

 << data_agsubregtoreg.gms 

 < data_agprimary.gms 

 < data_agsecondary.gms << data_agfeeds.gms 

 < data_forproducts.gms 

 < data_aginputname.gms 

 < data_agcostname.gms 

 < data_ghgtype.gms 

 < data_agprocessset.gms << data_agfeedprocess.gms 

 < data_ghg.gms << data_ghgtype.gms 

 < data_forall.gms << data_forproducts.gms 

 << data_forinvent.gms 

 << data_forexist.gms 

 << data_forexistpc.gms 

 << data_fornew.gms 

 << data_fornewpc.gms 

 << data_fornewcost.gms 

 << data_forexistcost.gms 

 << data_forminiharv.gms 

 << data_forrotationage.gms 

 << data_forfuelusage.gms 

 << data_forsticky.gms 

 << Data_forsupdem.gms 

 << data_forlogsupdem.gms 

 << data_forcapacity.gms 

 << data_formcoefs.gms 

 << data_forcanval.gms 

 << Data_forRecycle.gms 

 < data_agall.gms << data_agprimary.gms 

 << data_agsecondary.gms 

 << data_agfeeds.gms 

 << data_agfeeds.gms 
401 

 << data_agcostname.gms 

 << data_aginputname.gms 

 << data_agprocessset.gms 

 << data_agfeedprocess.gms 

 << data_agfeedprocess.gms 

 << data_agsupdem.gms 

 << data_aginputprice.gms 

 << data_agcropmix.gms 

 << data_agnatmix.gms 

 << data_agresource.gms 

 << data_agcropbudsoil.gms 

 << calc_fixregs.gms 

 << data_aglivebuds.gms 

 << data_agprocess.gms 

 << data_agprocessregional.gms 

 << data_agtransport.gms 

 << data_agbiomass.gms 

 << data_agmisc.gms 

 << data_agghgmitigate.gms 

 << data_agelectricemit.gms 

 << data_agghglivestock.gms 

 << data_agghgreglivestock.gms 

 << data_agghgsoil.gms 

 << data_agcemission_rawdata.gms 

 << data_agsoilcarb.gms 

 << data_agghgnonco2.gms 

 << calc_agcondition.gms 

 << calc_agliveghg.gms 

 << data_agdynamic.gms 

 < calc_fixregs.gms 

 < data_landtransfer.gms << data_forconvert.gms 

 << data_fordevelopment.gms 

 << data_agdevelopment.gms 

 < policy_model.gms 

 < model_seperable.gms 
402 

 < calc_agsetup.gms 

 < model_setup.gms << model_update.gms 

 < model_update.gms 

 < calc_aggregate.gms 

 < data_carbon_trees.gms << data_carbon_weightbyrpaland.csv

 << data_carbon_biomassmodel.csv 

 << data_carbon_undercwd.csv 

 < carbon_compute.gms 

model_structure.gms < model_scale.gms 

 < model_bounds.gms 

 < calc_fixregs.gms 

 < model_update.gms 

report_onerun.gms < report_setup.gms 

 < report_comparesetup.gms 

 < report_agcal.gms 

 < report_forcal.gms 

 < report_forresultsput.gms 

 < report_carboncal.gms 

 < report_ghgtype.gms 

 < report_comparecal.gms 

 < report_runsummarytables.gms 

 < report_finalcal.gms 
403 

SECTION 6: FASOMGHG APPLICATIONS AND FUTURE PLANS 
404 

18 CHAPTER 17 VALIDATION 
405 

19 CHAPTER 18 POLICY APPLICATIONS 

A core objective of FASOMGHG is to provide a tool for simulating the effects of various 

policy scenarios on a wide range of economic and environmental outcomes in the US forest and 

agricultural sectors. This section provides an overview of the types of policies that can be 

addressed by FASOMGHG, the basic procedures to follow to analyze policies using the model, 

and examples of policy-relevant studies that have been or could be performed using the model. 

19.1 Types of policies and problems that can be evaluated using FASOMGHG 

At its inception as FASOM, the primary focus of the modeling system was to evaluate 

carbon sequestration policies in the US forest and agricultural sectors to support wide-ranging 

assessments of climate change mitigation strategies. As the model has evolved to FASOMGHG, 

it provides a more complete assessment of GHG mitigation options in forestry and, in particular, 

agriculture. Moreover, the model is well-suited to work via integration with other models to 

assess the impacts of climate change on forestry and agriculture. Therefore, the relevance for 

GHG and climate policy has become even stronger. However, because of its breadth of coverage 

and depth of sectoral detail, FASOMGHG can be used to evaluate a wide range of policy issues 

other than GHGs and climate change. Indeed, most any type of policy affecting resource use or 

terms of trade in forestry and agriculture can, in principle, be evaluated by the model. Such 

examples may include trade policy, non-climate environmental policy, technical change, and 

resource conservation issues. 

Table 18-1 includes a list of selected publications addressing various policy issues with 

FASOMGHG or its predecessor FASOM. The list does not include the numerous policy 

applications using ASMGHG or ASM. For a more complete and periodically updated references 

to related publications and policy applications of FASOMGHG and ASMGHG, consult Dr. B.A. 

McCarl’s website (http://agecon2.tamu.edu/people/faculty/mccarl-bruce/). 

Table 18.1 Selected Policy Applications of FASOM or FASOMGHG 
406 

Policies analyzed Publication 

GHG Mitigation 

Lee, H-C, B.A. McCarl, D. Gillig, and B. Murray. Forthcoming. “US Agriculture 

and Forestry Greenhouse Mitigation Over Time.” In Rural Lands, Agriculture 

and Climate beyond 2015: Usage and Management Responses, F. Brouwer and 

B.A. McCarl (eds.), Dordrect, The Netherlands: Kluwer Academic Publishers. 

 Gillig, D., B.A. McCarl, and R.D. Sands, "Integrating Agricultural and Forestry 

GHG Mitigation Response into General Economy Frameworks: Developing a 

Family of Response Functions," Mitigation and Adaptation Strategies for Global 

Change, vol. 9,iss. 3(July), pp. 241-259, 2004. 

 Murray, B.C., B.A. McCarl, and H-C. Lee, "Estimating Leakage From Forest 

Carbon Sequestration Programs," Land Economics, 80(1), 109-124, 2004. 

Murray, B.C. and B.A. McCarl, US Potential for increasing forest Carbon sinks 

above business-as-usual scenarios: an economic analysis, Prepared for the InterAgency working group on land use and forest sinks, under the direction of the 

US Environmental Protection Agency, 2000.

 Adams, D.M., R.J. Alig., B.A. McCarl, J.M. Callaway and S.M. Winnett, 

"Minimum Cost Strategies for Sequestering Carbon in Forests", Land 

Economics, 75(3), 360-374, 1999. 

 Alig, R.J., D.M. Adams, B.A. McCarl, and Haynes, R.W., ”Evaluation of Effects 

of Forestry and Agricultural Policies on Forest Carbon and Markets”, in S. Fox, 

and R.A. Mickler (eds) Chapter 41 of The Productivity and Sustainability of 

Southern Forest Ecosystems in a Changing Environment, Springer : New York, 

1998, pp 755-776 

 Alig, R.J., D.M. Adams, B.A. McCarl, J.M. Callaway, and S.M. Winnett, 

“Assessing Effects of Mitigation Strategies for Global Climate Change Within an 

Intertemporal Model of the US Forest and Agriculture Sectors”, Environment 

and Resource Economics,9: 259-274 1997 

Climate Change

Impacts and 

Adaptation

 Alig, R.J., D.M. Adams, and B.A. McCarl, "Projecting Impacts of Global 

Climate Change on the US Forest and Agriculture Sectors and Carbon 

Budgets," Forest Ecology and Management, 169, 3-14, 2003. 

 Reilly, J.M., J. Hrubovcak, J. Graham, D.G. Abler, R. Darwin, S.E. Hollinger, 

R.C. Izaurralde, S. Jagtap, J.W. Jones, J. Kimble, B.A. McCarl, L.O. Mearns, 

D.S. Ojima, E.A. Paul, K. Paustian, S.J. Riha, N.J. Rosenberg, C. Rosenzweig, 

and F. Tubiello, Changing Climate and Changing Agriculture: Report of the 

Agricultural Sector Assessment Team, US National Assessment, prepared as part 

of USGCRP National Assessment of Climate Variability, Cambridge University 

Press, 2002. 
407 

(Was this FASOM or ASM?) 

 Irland, L. C., D.M. Adams, R.J. Alig, C. J. Betz, C.C. Chen, M. Hutchins, B.A. 

McCarl, K. Skog and B. L. Sohngen, "Assessing Socioeconomic Impacts of 

Climate Change on U. S. Forests, Wood-Product Markets and Forest 

Recreation", BioScience, 51(9) September, 753-764, 2001. 

 McCarl, B.A., D.M. Burton, D.M. Adams, R.J. Alig and C.C. Chen, "Effects of 

Global Climate Change on the US Forest Sector: Response Functions Derived 

from a Dynamic Resource and Market Simulator", Climate Research, 15(3), 195-

205, 2000. 

McCarl, B.A., D. Burton, D.M. Adams, and R.J. Alig, “Economic Dimensions of 

Climate Change Impacts on Southern Forests”, in S. Fox, and R.A. Mickler (eds) 

Chapter 42 of The Productivity and Sustainability of Southern Forest Ecosystems 

in a Changing Environment, Springer: New York, 1998 pp 777-794 

General 

sector 

policies 

and 

trends 

 McCarl, B.A., D.M. Adams, R.J. Alig and J.T. Chmelik, "Analysis of Biomass 

Fueled Electrical Power plants: Implications in the Agricultural and Forestry 

Sectors", Annals of Operations Research, 94, 37-55, 2000. 

 Alig, R.J., B.A. McCarl, D.M. Adams and P.J. Ince, "Economic Potential of 

Short-Rotation Woody Crops on Agricultural Land for Pulp Fiber Production in 

the United States", Forest Products Journal, April, 67-74, 2000. 

 Adams, D.M., R.J.Alig., B.A. McCarl, S.M. Winnett and J.M. Callaway, "The 

Effects of Factor Supply Assumptions on Intertemporal Timber Supply 

Behavior: The Cases of Investable Funds and Land", Canadian Journal of Forest 

Research, 28(2), 239-47, 1998. 

 Alig R.J., D.M. Adams and B.A. McCarl, "Ecological and Economic Impacts of 

Forest Policies: Interactions Across Forestry and Agriculture", Ecological 

Economics, 27, 63-78, 1998. 

 Alig, R.J., D.M. Adams and B.A. McCarl, "Impacts of Incorporating Land 

Exchanges Between Forestry and Agriculture in Sector Models", Journal of 

Agricultural and Applied Economics, 30(2), 389-401, 1998. 

 Adams, D.M., R.J. Alig, B.A. McCarl, J.M. Callaway and S.M. Winnett, “An 

Analysis of the Impacts of Public Timber Harvest Policies on Private Forest 

Management in the US ", Forest Science, 42(3), 343-358, 1996 

The following subsections briefly review the types of policies that the model can be used 

to examine. 
408 

19.2 Climate Analysis 

Climate policy is a major driver behind the development of FASOMGHG. The model is 

unique in its ability to combine data and models of GHG emissions and sequestration with data 

and models of economic activity in the US forest and agricultural sectors. This provides an 

integrated view of the joint GHG and economic effects of climate scenarios, economic policies, 

and combinations thereof. 

Climate policy is oft divided into distinct elements: impacts, adaptation, and mitigation. 

The IPCC followed this taxonomy in developing their Third Assessment Report (IPCC 2001), 

with separate documents for (1) Mitigation, and (2) Impacts, Vulnerability, and Adaptation. 

FASOMGHG can be used to address these basic elements if climate policy, as described below. 

19.2.1 GHG Mitigation 

As indicated above, the original impetus for FASOM was to evaluate carbon 

sequestration in from land use change between agriculture and forestry and changes in forest 

management practices. By keeping carbon accounts across the landscape, the model can quantify 

the amount of carbon sequestered (stored) in forest and agricultural ecosystems under both 

baseline (business-as-usual) conditions and under specific policies to induce additional 

sequestration. The difference in carbon sequestered with the policies and without the policies 

(baseline) can be viewed as a measure of GHG mitigation within these sectors. 

However, as has been described throughout the detailed chapters on model structure and 

data, FASOM’s evolution to FASOMGHG has substantially expanded the model’s ability to 

examine GHG mitigation strategies in forestry and agriculture. FASOMGHG enhancements 

(since the original version of FASOM) include the following 

• Carbon sequestration in agriculture 

• Fossil fuel mitigation through agricultural practices 

• Mitigation of non-CO2 GHGs from agriculture 

• Biofuel offsets 

Thus, the model has evolved from one which specialized primarily in carbon sequestration 

through land use change and forestry to one that provides more comprehensive coverage of GHG 

mitigation in forestry and agriculture. Table 18-2 identifies the model’s coverage of broad 

mitigation strategies, specific activities, and targeted gases. 
409 

 

Table 18-2: Broad GHG Mitigation Strategies Covered in FASOMGHG 

Strategy 

Mitigation Activities Tracked in 

FASOMGHG 

Target 

GHG 

Afforestation Convert agricultural lands to forest CO2

Forest management Lengthen timber harvest rotation 

Increase forest management intensity 

Forest preservation 

Avoid deforestation 

CO2

Agricultural soil carbon 

sequestration 

Crop tillage change 

Crop mix change 

Crop fertilization change 

Grassland conversion 

CO2

Fossil fuel mitigation from crop 

production 

Crop tillage change 

Crop mix change 

Crop input change 

Irrigated/dry land mix change 

CO2

Agricultural CH4 and N2O 

mitigation 

Crop tillage change 

Crop mix change 

Crop input change 

Irrigated/dry land mix change 

Enteric fermentation control 

Livestock herd size change 

Livestock system change 

Manure management 

Rice acreage change 

CH4

N2O 

Biofuel offsets Produce crops for biofuel use CO2

The coverage and structure of the model provides analytical capabilities to address the following 

policy questions 

• What will be the net emissions of GHGs from US forestry and agriculture over time if no 

mitigation policies are put in place (business-as-usual)? 

• How much GHG mitigation can be generated by the US forest and agricultural sectors if 

various economic incentives are put in place? 

• What strategies and gases have the highest mitigation potential and lowest costs? 

• How are GHG mitigation opportunities distributed across regions? 

• How do GHG reductions from mitigation actions change over time, especially given the 

potential for re-releases of carbon sequestered in forests and soils? 

• What are the direct and indirect consequences of mitigation policies that are limited in 

their coverage of activities, regions, or time periods? Indirect consequences could include 

leakage or reversal of GHG reduction benefits. 
410 

• How will changes in land use and management brought about by a GHG mitigation 

incentive program affect the production and prices of forest and agricultural 

commodities? 

• How will changes in commodity production and prices affect the welfare of commodity 

producers and consumers? 

• What ancillary (non-GHG) environmental effects (e.g., water quality, habitat) could 

occur as a result of GHG mitigation actions on the landscape? Are these co-benefits or 

ancillary costs of mitigation strategies? 

Table 18-1 provides some examples of publications using FASOM or FASOMGHG to 

address GHG mitigation policy issues such as those raised above. 

Examples of the type and nature of mitigation results that can be produced are presented 

below. These examples draw from a common set of analytic scenarios imposed on FASOMGHG 

that simulate responses to a hypothetical prices offered for GHG mitigation. Such a system could 

be viewed as part of an emissions trading mechanism for GHGs, though no such system 

currently exists, Responses are evaluated at GHG prices ranging from $1-50 per tonne of CO2

equivalent. 

[note: I am pasting in results from the yet unpublished EPA Assessment Report here. If 

this report gets published, we should cite accordingly. If it does not, then we should perhaps set 

up the scenarios here and present them here as the only published outlet] 

19.2.1.1 Land Use Projection 

Figure 18-1 depicts how FASOMGHG projects land allocation across major groups in 

2025 under the baseline scenario (price of $0) and prices of $1, $5, $15, $30 and $50 per tonne 

CO2. The figure suggests that land use effects in 2025 are small except at prices greater than $15. 

Figure 18-1 
411 

Land Use in 2025 at Different 

GHG Price Levels 

0

50

100

150

200

250

300

350

400

450

MM acres

$0* $1 $5 $15 $30 $

Cropland Pasture

Timberland (private) Biofuel Land

*Baseline 

Notes: $ represent price per tonne, CO2 Eq. 

Quantities are in million acres. 

Figure 18-2 shows how one land use, timberland, changes over time at a relatively high 

GHG price ($50 per tonne). In this simulation, the initial rise in timberland reverts to baseline 

levels after several time periods. The commodity market feedbacks and other technological 

factors drive this land use reversion. 

Figure 18-2 

Timberland Area over Time: $50/t 

CO2 Eq. vs. Baseline 

0

100

200

300

400

500

2010 2030 2050 2070 2090

Year

Land Area (MMha)

Baseline

$50/Mg

19.2.1.2 GHG Mitigation Supply Function 
412 

In economics, a supply function conveys the relationship between the price of a good and 

the quantity that is supplied. In this case, the good in question is GHG mitigation and the price is 

the price per tonne of mitigated GHG. Figure 18-3 shows this relationship over the $1-50 per 

tonne CO2 price range. The supply function is decomposed into the broad mitigation strategies 

identified in Table 18-2. We see here that different strategies dominate at different prices. 

GHG Mitigation Supply Function from National GHG Mitigation Totals by Activity 

Quantities are Tg CO2 Eq. per year net emissions reduction below baseline, annualized over the time 

period 2010--2110. 

Emission Reduction in Tg CO2 Equivalent

$/t CO2 Eq.

$0

$10

$20

$30

$40

$50

$60

0 500 1,000 1,500 2,000 2,500

Afforestation

Forest management

Agricultural soil carbon

sequestration

Fossil fuel mitigation from

crop production

Agricultural CH4 and N2O

mitigation

Biofuel offsets

All activities

19.2.1.3 Cumulative Mitigation over Time 

It is important to see how mitigation may vary over time, as policy targets and other 

factors may vary as well. Figure 18-4 tracks the cumulative total of mitigation quantity from the 

time the policy is implemented (in this case, the Year 2010) on out for 100 years at two different 

GHG prices. Inspection of the figure shows that the cumulative effect of forest carbon 

sequestration options (afforestation and forest management) rises at first and then falls, as the 

carbon sequestered in the initial years is later released through harvesting and land use change. 

Figure 18-4 
413 

Cumulative GHG Mitigation over Time 

Quantities are Tg CO2 Eq. cumulative net emissions reduction below baseline. 

 $15/t CO2 Eq. Constant Real Price

0

5,000

10,000

15,000

20,000

25,000

30,000

Tg CO2 Eq.

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

Year

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100

Year

Tg CO2 Eq.

0

20,000

40,000

60,000

80,000

100,000

Biofuel offsets

Crop management FF mitigation

Ag CH4 and N2O

Forest management

Afforestation

Ag soil C sequestration

Biofuel offsets

Crop management FF mitigation

Ag CH4 and N2O

Forest management

Afforestation

Ag soil C sequestration

 $30/t CO2 Eq. Constant Real Price

2015 2025 2055

2015 2025 2055

19.2.1.4 Targeting Activities and Regions 

The regional distribution of GHG mitigation opportunities may have important policy 

implications for legislators and developers of policies targeted to increase GHG mitigation in 

forestry and agriculture. For a variety of reasons, mitigation programs may need to be more 

limited in scope than one that pays for all mitigation activities and all gases. Consequently, it 

may be useful for policy targeting to use FASOMGHG to generate rankings of the top mitigation 

options by region-activity combination as indicated in Table 18-3. 
414 

Table 18-2: GHG Mitigation Quantity Ranking by Region--Activity Combination: Ranks 

are Based on Mitigation Quantities Annualized Over the Period 2010--2110 

GHG Constant Price Scenario ($/t CO2 Eq.) 

Region Activities $1 $5 $15 $30 $50 

SC Forest management 1 1 1 3 3 

CB Agricultural soil carbon sequestration 2 2 4 7 10 

LS Agricultural soil carbon sequestration 3 3 6 

GP Agricultural soil carbon sequestration 4 5 7 

SW Fossil fuel mitigation from crop production 5 7 

RM Agricultural soil carbon sequestration 6 8 

SC Fossil fuel mitigation from crop production 7 6 8 10 

NE Agricultural soil carbon sequestration 8 9 

CB Fossil fuel mitigation from crop production 9 10 

CB Agricultural CH4 and N2O mitigation 10 

SE Forest management 4 3 6 8 

SC Afforestation 2 1 2 

NE Biofuel offsets 5 4 5 

RM Afforestation 9 

SW Agricultural soil carbon sequestration 10 

CB Afforestation 2 1 

SE Biofuel offsets 5 4 

SC Biofuel offsets 8 6 

CB Biofuel offsets 9 7 

LS Afforestation 9 

19.2.2 Climate Change Impacts and Adaptation 

The model’s forest and agricultural sector activity and outcomes are driven by the 

biophysical productivity of the landscape. The economic returns to a particular land use or 

management practices are driven by the physical yields that can be generated. Clearly, climate is 

a significant factor in determining these yields in both the forest and agricultural sectors. For 

instance, geo-specific changes in temperature, precipitation, and CO2 concentrations over time 

(the “greenhouse effect”) can affect the level and distribution of forest and agricultural yield 

potential. FASOMGHG can simulate farmers and foresters adapt to these climate-driven yield 

changes in yield by altering land uses and management practices. Accounting for these 

adaptations, the model can show how changes in climate ultimately impact the economic wellbeing of producers and consumers' in the forest and agricultural sectors. 

In order for FASOMGHG to simulate future climate change scenarios, it must be 

integrated into a broader framework that includes global circulation models (GCM’s) that project 

future climate change and biophysical models that translate climate change to yield changes in 

forestry and agriculture. Such an integration was performed as part of the US National 

Assessment Synthesis Team (2001) report analyzing possible climate change impacts on 

forestry, agriculture and other sectors, wherein FASOM was linked with GCM model scenarios 

from the Hadley Centre (UK) and The Canadian Centre climate models and corresponding 
415 

simulations from biophysical models such as Century (Parton, 1996) and TEM (Melillo et al 

1993). 

The NAST analyses showed how future climate change scenarios could affect aggregate 

productivity of US forests and agricultural lands, thereby affect resource allocation across and 

within the sectors, i.e., adaptations such as land use change, crops planted, and changes in 

management practices. The climate-induced changes and the adaptations they engender have 

economic consequences for the sectors in question, affecting the levels of output and prices for 

timber and agricultural commodities and the welfare of producers and consumers' in these 

sectors. For example, climate change impacts on the forest sector are reported for the FASOM 

scenarios run for the NAST report in Irland et al (2001). Under scenarios showing a climate 

change-induced increase in aggregate forest productivity, timber output rises, prices fall, 

consumers' are made better off and producers are made worse off. FASOMGHG can show how 

these effects vary by region within the US, by climate scenario (Hadley or Canadian) and by 

biophysical model employed for gauging productivity effects (Century or TEM). 

Insert figures here from NAST Ch. 17, Fig 8 and 9 or something like that? 

(http://www.usgcrp.gov/usgcrp/Library/nationalassessment/17Forests.pdf) 

19.3 General Land Use, Forest, and Agricultural Policies and Trends 

There is a long history of policies operating at the US national and regional levels that try 

to modify the way land is used, encourage certain management practices, set targets for 

commodity production levels, and achieve other environmental, economic, and social policy 

objectives. FASOMGHG’s broad coverage and sectoral detail make it useful for examining a 

wide range of these policies. Policy options are evaluated in term below. 

19.3.1 Land Use 

The inclusion of land allocation mechanisms in FASOMGHG allows for exploration of 

land allocation responses to changes in policy, market, or other conditions. Some of the subjects 

for analysis have included or could include 

• Tree planting on marginal agricultural lands 

• Grassland conversion 

• Effect of urbanization on land use and commodity production 

• Land use response to technological and environmental change 
416 

• Zoning and other land use restrictions at the regional level 

As an example, Alig et al (1997) found that a policy targeting the conversion of roughly 5 

million acres of agricultural land to forest without offering counter-incentives (or disincentives) 

for keeping land in forest, caused a substantial shifting of land from forest back to agriculture. 

[Bruce or Ralph, please check and see if I got this right. Its been a while BCM} 

19.3.2 Forest sector 

The analytical framework and data of FASOMGHG allow it to explore a variety of 

resource allocation and policy issues in the forest sector including 

• Private forest management incentives 

• Forest conservation/preservation 

• Variations in allowable timber harvests on public lands 

• Wood products trade policy between US and Canada 

• Effects of advances in technology, such as genetic improvements in forest stock 

• Expanded use of management practices to reduce fire risks (e.g., thinning) 

• Land transfers between owner groups (forest industry, nonindustrial private, public) 

For example, FASOMGHG has been used to examine how recent technical advances in 

short rotation forestry might effect the level, price, and regional distribution of pulpwood timber 

harvests and corresponding land use responses (Alig et al 2000). Additionally, the model has 

been used to examine interregional land allocation and forest management responses to regionspecific public timber harvest policies (Adams et al 1996, Murray et al 2004). 

19.3.3 Agricultural sector 

US agricultural policy is far-reaching and has many dimensions. Much agricultural policy 

is encompassed in periodic revisions of the Farm Bill and its many provisions affecting 

commodity support programs, conservation, environmental protection, and rural income support. 

Specific aspects to consider in agricultural sector policy analysis may be 

• Conservation/land retirement programs such as the Conservation Reserve Program 

(CRP) 

• Programs to enhance environmental quality and sustainable development in agriculture 

(e.g., EQUIP) 

• Commodity loan programs 
417 

• Commodity promotion programs 

• Technological change in agriculture 

• Genetic improvements in seed stock 

• Water use restrictions 

• Agricultural trade policy 

• Environmental regulations in agricultural production 

[FASOM pubs haven’t spoken to these issues per se. Unless the following is based on 

FASOM ... Callaway, J.M. and B.A. McCarl, “The Economic Consequences of Substituting 

Carbon for Crop Subsidies in United States' Agriculture”, Environmental and Resource 

Economics, 7,15-43, 1996] 

19.3.4 Bio-Energy Analysis 

Although biofuel production is typically considered part of a GHG mitigation strategy, it 

can also be considered a component of energy policy. As a renewable resource, biofuels have 

attracted attention as a potentially sustainable source of energy supply. FASOMGHG 

incorporates the costs of biofuel production and the size of subsidy necessary for it to out 

compete conventional fossil fuels. Studies such as McCarl et al (2000) have used FASOMGHG 

to estimate the economic potential for biofuel production in the agricultural and forest sectors to 

meet growing energy demands. 

[more here] 
418 

20 CHAPTER 18 UNCERTAINTIES, CAVEATS, AND FUTURE PLANS 

(McCarl and Adams) 
419 

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SECTION 8: APPENDICES 

21 APPENDIX: GLOSSARY OF FORESTRY TERMS 

Afforestation The establishment of a forest or stand in an area where the preceding vegetation or 

land use was not forest. 

Age cohort An interval into which the age range of trees is divided for classification or use. Five 

year intervals are used. 

Crop land -- Land used for the production of adapted crops for harvest, including row crops, 

small grain crops, hay crops, nursery crops, orchard crops, and other specialty crops. The 

land may be used continuously for these crops, or they may be grown in rotation with 

grasses and legumes. 

Cull tree -- A live tree, 5.0-inches in diameter at breast height (d.b.h.) or larger, that is 

unmerchantable for sawlogs now or prospectively because of rot, roughness, or species. 

(See definitions for rotten and rough trees). 

Diameter class -- A classification of trees based on diameter outside bark measured at breast 

height (4 1/2 feet above ground). The common abbreviation for "diameter at breast 

height" is d.b.h. With 2-inch diameter classes, the 6-inch class, for example, includes 

trees 5.0 through 6.9 inches d.b.h. 

Douglas-fir subregion -- The area in the states of Oregon and Washington that is west of the 

crest of the Cascade Range (also called Pacific Northwest Westside). 

Farmer-owned lands Lands owned by a person who operates a farm, either doing the work 

themselves or directly supervising the work. 

Fiber products -- Products made with largely intact plant fibers (or wood fibers) derived 

primarily from pulpwood, pulpwood chips, and recovered paper, such as wood pulp, 

paper or paperboard products, and also (in this publication) products made primarily from 

pulpwood roundwood, such as oriented strand board, but not including other panel 

products made primarily from fine wood residues, sawdust or bark. 

Forest industry (FI) -- A diverse group of manufacturers that harvest, process, and use timber 

products in their final products. Activities include the harvesting of the timber resource; 

conversion of logs to primary timber products, such as lumber, plywood, and wood pulp; 

and the conversion of primary timber products to secondary or final products, such as 

pallets, furniture, and paper products. 
440 

Forest land -- Land at least 10 percent stocked by forest trees of any size, including land that 

formerly had such tree cover and that will be naturally or artificially regenerated. Forest 

land includes transition zones, such as areas between heavily forested and nonforested 

lands that are at least 10 percent stocked with forest trees, and forest areas adjacent to 

urban and built-up lands. Also included are pinyon-juniper and chaparral areas in the 

West, and afforested areas. The minimum area for classification of forest land is 1 acre. 

Roadside, streamside, and shelterbelt strips of timber must have a minimum crown width 

of 120 feet to qualify as forest land. Unimproved roads and trails, streams, and clearings 

in forest areas are classified as forest if less than 120 feet in width. 

Forest management type A classification of timberland based on the species and source of trees 

forming a plurality of live trees present. 

Forest Inventory and Analysis (FIA) Regional forest survey units of the USDA Forest Service. 

See Smith et al. (2001) for examples of the types of data collected and compiled. 

Forest inventory types A classification of forest land based on the species forming a plurality of 

the live-tree stocking. Major forest type groups recognized in the timber assessment 

include: 

Natural pine A southern management type representing stands that (a) have not been artificially 

regenerated, (b) are classed as a pine or other softwood forest type, and in which 50 

percent or more of the naturally established stand is loblolly pine, slash pine, shortleaf 

pine, longleaf pine, or other southern pines singly or in combination. Common associates 

include oak, hickory, and gum. 

Planted pine A southern management type representing forests in which 50 percent or more of 

the stand is loblolly pine, slash pine, shortleaf pine, longleaf pine, or other southern pines 

that have been established by planting or direct seeding. 

Lowland hardwoods (bottomland hardwoods) -- A southern management type composed of 

forests in which 50 percent or more of the stand is tupelo, blackgum, sweetgum, oak, and 

southern cypress, singly or in combination, and southern pine makes up less than 25 

percent. Common associates include cottonwood, willow, oak, elm, hackberry, and 

maple. This type is found on the alluvial flood plains of the Mississippi and other 

southern rivers. May also be called bottomland hardwood. 

Oak-pine A southern management type composed of forests in which 50 percent or more of the 

stand is hardwood, usually upland oaks, and southern pines make up 25 to 49 percent of 

the stocking. Common associates include upland oak-shortleaf pine in the foothills and 

plateaus; mixed hardwood-loblolly pine on moist sites; and scrub oak-longleaf pine in the 

sand hills of the Carolinas, Georgia, and Florida. Other associates include gum, hickory, 

and yellow-poplar. May also be called mixed pine-hardwood. 
441 

Douglas-fir -- Forests in which Douglas-fir composes a plurality of the stocking. Common 

associates include western hemlock, western redcedar, the true firs, redwood, ponderosa 

pine, and larch. 

Hemlock-Sitka spruce -- Forests in which western hemlock, Sitka spruce, or both compose a 

plurality of the stocking. Common associates include Douglas-fir, silver fir, and western 

redcedar. 

Upland hardwoods -- A southern management type composed of stands that have at least 10 

percent stocking and classed as an oak-hickory or maple-beech-birch forest type. 

Common associates include yellow-poplar, elm, maple, and black walnut. 

Fuelwood -- Wood used by conversion to some form of energy, primarily residential use. 

Growing stock -- A classification of timber inventory that includes live trees of commercial 

species meeting specified standards of quality or vigor. Cull trees are excluded. When 

associated with volume, includes only trees 5.0 inches d.b.h. and larger. 

Hardwood -- A dicotyledonous (nonconiferous) tree, usually broad leaved and deciduous. 

Harvest (a) An intermediate or final cutting that extracts salable trees. (b) The volume of 

roundwood harvested from both growing-stock and nongrowing-stock sources that is 

extracted from harvest sites. 

Highly erodible crop land -- All crop land in land capability classes (classifications used by the 

Soil Conservation Service to rate the suitability of soils for agricultural production) 3e, 

4e, 6e, and 7e. 

Industrial wood -- All commercial roundwood products except fuelwood. 

Land area -- (a) Bureau of the Census: The area of dry land and land temporarily or partly 

covered by water, such as marshes, swamps, and river food plains; streams, sloughs, 

estuaries, and canals less than 1/8 statute mile wide; and lakes, reservoirs, and ponds less 

than 40 acres in area. (b) Forest Inventory and Analysis: same as (a) except that the 

minimum width of streams, etc., is 120 feet, and the minimum size of lakes, etc., is 1 

acre. This latter definition is the one used in the forest sector work. 

Live cull -- A classification that includes live, cull trees. When associated with volume, it is the 

net volume in live, cull trees that are 5.0 inches d.b.h. and larger. 

Logging residues -- The unused portions of growing-stock trees cut or killed by logging and left 

in the woods. 
442 

Managed plantations -- Stands of trees established by artificial means (e.g., planting or direct 

seeding) composed primarily of single or related species, treated to have uniform 

structure and age class, and projected to receive at least minimal treatment for growth 

enhancement. 

Management intensities -- Timber growth and yield catagories developed to represent the 

development of stands under various improved management practices (i.e., genetic 

improvement, stocking control, fertilization, commercial thins, etc.). 

Net annual growth -- The average annual net increase in the volume of trees during the period 

between inventories. Components include the increment in net volume of trees at the 

beginning of the specific year surviving to its end, plus the net volume of trees reaching 

the minimum size class during the year, minus the volume of trees that died during the 

year, and minus the net volume of trees that became cull trees during the year. 

Net volume in cubic feet -- The gross volume in cubic feet less deductions for rot, roughness, 

and poor form. Volume is computed for the central stem from a 1-foot tall stump to a 

minimum 4.0-inch top diameter outside bark, or to the point where the central stem 

breaks into limbs. 

Nonforest land -- Land that has never supported forests and lands formerly forested where use 

of timber management is precluded by development for other uses. (Note: Includes area 

used for crops, improved pasture, residential areas, city parks, improved roads of any 

width and adjoining clearings, powerline clearings of any width, and 1- to 40-acre areas 

of water classified by the Bureau of the Census as land. If intermingled in forest areas, 

unimproved roads and nonforest strips must be more than 120 feet wide, and clearings, 

etc., more than 1 acre in size, to qualify as nonforest land). 

Nongrowing stock -- A classification of inventory that includes all trees not meeting the 

standards for growing stock. 

Nonindustrial private forest (NIPF) -- An ownership class of private forest lands whose owner 

does not primarily operate wood-using plants (distinguished from land owned by forest 

industry). 

Nonsawtimber timber -- Timber that is not used by sawmills or veneer mills, but is used in the 

manufacture of pulp, paper, OSB, various nonstructural panels, or used for fuelwood. 

Nonstocked areas -- Timberland less than 10 percent stocked with growing-stock trees. 
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Oriented strand board (OSB) -- An engineered structural-use panel made from wood strands 

that are cut longitudinally from small-diameter logs or pulpwood roundwood. The strands 

have a high length-to-thickness ratio and are bonded together with waterproof resin under 

heat and pressure. The strands are oriented along the length or width of the panel in 

alternating layers to take advantage of the inherent longitudinal fiber strength of wood. 

The panels are used in construction for roof, wall, and floor sheathing and for the web for 

prefabricated wood I-joists. 

Other forest land -- Forest land other than timberland and productive reserved forest land. It 

includes reserved forest land, and available land that is incapable of producing annually 

20 cubic feet per acre of industrial wood under natural conditions because of adverse site 

conditions such as sterile soils, dry climate, poor drainage, high elevation, steepness, or 

rockiness. Urban forest land is also included that, owing to its location, is considered 

unavailable for sustained timber harvesting. 

Other land -- Nonforest land less the area in streams, sloughs, estuaries, and canals between 120 

and 660 feet and lakes, reservoirs, and ponds between 1 and 40 acres in area (i.e., 

nonforest land less non-Census water area). 

Other removals -- Unutilized wood volume from cut or otherwise killed growing stock, from 

cultural operations such as precommercial thinnings, or from timberland clearing. Does 

not include volume removed from inventory through reclassification of timberland to 

productive reserved timberland. 

Other sources -- Sources of roundwood products that are nongrowing stock. These include 

salvable dead trees, rough and rotten trees, trees of noncommercial species, trees less than 

5.0 inches d.b.h., tops, and roundwood harvested from nonforest land (e.g., fence rows). 

Ownership -- Categories of property owners: a combination of persons; a legal entity such as a 

corporation, partnership, club, or trust; or a public agency. All parcels of land in the US 

are assigned to one of the categories of ownership. 

Plantation -- See managed plantation. 

Poletimber -- Live trees at least 5.0 inches in diameter, but smaller than sawtimber trees (9.0 

inches or greater). 

Ponderosa pine subregion -- The area in the states of Oregon and Washington that is east of the 

crest of the Cascade Range, (also called Pacific Northwest East). 

Private Ownerships: 

Forest industry (FI) -- An ownership class of private lands owned by companies that grow 

timber for industrial use and own wood processing facilities. 
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Nonindustrial private forest (NIPF) -- An ownership class of private lands where the owner 

does not operate wood-use plants. This includes lands owned by operators of farms, lands 

owned by private individuals, and lands owned by private corporations. 

Native American-(a) Lands held in trust by the US or states for Native American tribes or 

individual Native Americans. (b) Lands owned in fee by Native American tribes whether 

subject to federal or state restrictions against alienation or not. Since 1990, these lands are 

grouped with other private lands in the NIPF ownership group. 

Productivity class -- A classification of forest land in terms of potential annual cubic-foot 

volume growth per acre at culmination of mean annual increment in fully stocked natural 

stands. 

Public ownerships: 

Federal -- An ownership class of public lands owned by the US Government. 

National forest -- An ownership class of federal lands, designated by Executive order or statute 

as national forests or purchase units, and other lands under the administration of the 

Forest Service including experimental areas and Bankhead-Jones Title III lands. 

Other public -- An ownership class that includes all public lands except national forest. This 

category generally includes federal, state, county, and municipal ownerships. 

Pulpwood -- Roundwood, wood chips, or wood residues that are the wood raw materials used 

for the production of wood pulp or the roundwood inputs for reconstituted panels (such as 

oriented strand board). 

Reserved timberland -- Forest land withdrawn from timber use through statute, administrative 

regulation, or designation without regard to protective status. 

Residues -- Bark and woody materials that are generated in primary wood-using mills when 

roundwood products are converted to other products. Examples are slabs, edgings, 

trimmings, miscuts, sawdust, shavings, veneer cores and clippings, and pulp screenings. 

Includes bark residues and wood residues (both coarse and fine materials) but excludes 

logging residues. 

Removals -- The net volume of growing-stock trees removed from the inventory by harvesting; 

cultural operations, such as timber stand improvement or land clearing; or changes in 

land use. 

Rotten tree -- A live tree of commercial species that does not contain a sawlog now or 

prospectively, primarily because of rot (i.e., when rot accounts for more than 50 percent 

of the total cull volume). 
445 

Rough tree -- (a) A live tree of commercial species that does not contain a sawlog now or 

prospectively, primarily because of roughness (i.e., a sound tree that is culled because of 

such factors as poor form, splits, or cracks affecting more than 50 percent of its total cull 

volume); or (b) a live tree of noncommercial species. 

Roundwood -- Logs, bolts, or other round sections cut from growing-stock and nongrowingstock sources such as trees smaller than 5.0 inches d.b.h.; stumps, tops, and limbs of 

growing stock trees; rough and rotten trees; dead trees; and trees that grow on land other 

than timberland. 

Roundwood equivalent -- The volume of logs or other round products required to produce 

given quantities of lumber, plywood, wood pulp, paper, or other similar products, after 

deducting the proportion of wood raw material input that is obtained not from logs or 

roundwood but from plant byproducts or recycled wood fiber (from recovered paper). 

Sawlog -- A log meeting minimum standards of diameter, length, and defect, including logs at 

least 8 feet long, sound and straight, and with a minimum diameter inside bark of 6 

inches for softwoods and 8 inches for hardwoods, or meeting other combinations of size 

and defect specified by regional standards. A log usually used in the manufacture of 

lumber and plywood. 

Sawtimber -- Stands at least 10 percent occupied with growing-stock trees, with half or more of 

total stocking in sawtimber or poletimber trees, and with sawtimber stocking at least 

equal to poletimber stocking. 

Sawtimber trees -- Live trees containing at least one 12-foot saw log or two noncontiguous 8-

foot logs, and meeting regional specifications for freedom from defect. Softwood trees 

must be at least 9.0 inches d.b.h., and hardwood trees must be at least 11.0 inches d.b.h. 

Site productivity class -- A classification of forest lands in terms of inherent capacity to grow 

crops of industrial wood. The class identifies the average potential growth in cubic feet 

per acre per year and is based on the culmination of mean annual increment of fully 

stocked natural stands. An example for the South is given next. 

High sites -- Land capable of growing at least 85 cubic feet of wood per acre per year. 

Medium sites -- Land capable of growing 50 to 85 cubic feet of wood per acre per year. 

Low sites -- Land capable of growing 20 to 49 cubic feet of wood per acre per year. 

Softwood -- A coniferous tree, usually evergreen, having needles or scalelike leaves. 

Stocking -- The degree of occupancy of land by trees, measured by basal area or number of trees 

by size and spacing, or both, compared to a stocking standard; i.e., the basal area or 

number of trees, or both, required to fully use the growth potential of the land. 
446 

Stumpage -- Standing timber (trees) in the forest. 

Stumpage price -- The price paid for standing timber (trees) in the forest. Usually expressed as 

dollars per thousand board feet, log scale. 

Succession -- A series of dynamic changes by which one community succeeds another through 

stages leading to potential natural community or climax. Forest type transition is a related 

but broader concept that includes the possibility of changes due to human influences, 

such as disturbances that can lead to different seral stages (Alig and Butler 2004). 

Timber supplies -- The volumes of roundwood actually harvested, range of volume available for 

harvest at varying price levels, or future volumes estimated to be harvested at market 

equilibrium. Includes roundwood from growing-stock and nongrowing-stock sources. 

Timberland -- Forest land that is producing or is capable of producing crops of industrial wood 

and not withdrawn from timber use by statute or administrative regulation. Areas 

qualifying as timberland have the capability of producing in excess of 20 cubic feet per 

acre per year of industrial wood in natural stands. Currently inaccessible and inoperable 

areas are included. 

Tops -- The wood of a tree above the merchantable height (or above the point on the stem 4.0-

inches diameter outside bark [dob]). It includes the usable material in the uppermost stem 

and branches. 

Unreserved forest land -- Forest land (timberland and woodland) that is not withdrawn from 

use by statute or administrative regulation. Includes forest lands that are not capable of 

producing in excess of 20 cubic feet per year of industrial wood in natural stands. 

Urban and other areas -- Areas within the legal boundaries of cities and towns; suburban areas 

developed for residential, industrial, or recreational purposes; school yards; cemeteries; 

roads and railroads; airports; beaches, power lines, and other rights-of-way; or other 

nonforest land not included in any other specified land use class. 
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22 APPENDIX NATIONAL FOREST YIELDS 

Existing and regenerated timber yield projections for National Forest aggregates were 

estimated using strata similar to those used in the private existing yield tables. Forest types were 

aggregated into softwood and hardwood groups, while all inventory with timber 90 years or 

older aggregated into an uppermost FASOMGHG age cohort. Yield projections are based on 

ATLAS modeling by Mills and Zhou (2003). Based on data limitations, each stand in the 

inventory was assigned a medium site class. 

In the Southern regions, ATLAS was unable to project yields of older stands for the 

entire 100-year time horizon. In the older stands the total volume within the strata was used to 

extrapolate yield curves throughout the period. Fire management, along with other natural 

disturbances and forest management activities, and wildfire occurrence are implicit in the 

ATLAS yield curves. 

Timber yield estimation for regenerated stands was also based on the ATLAS approach 

described by Mills and Zhou (2003). Mills and Zhou (2003) calculated regeneration failures by 

region, and used lagged yields to reflect failed cases. They had acres remain in the youngest 

timber age class for an extra five or ten-years. Lacking data on pre- and post-disturbance forest 

types, all regenerated stands returned to the same forest type from which they originated.