### PNNL-14337

Prepared for the U.S. Department of Energy Under Contract DE-AC05-76RL01830



# Model Documentation for the MiniCAM

AL Brenkert SH Kim AJ Smith HM Pitcher

July 2003DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor Battelle Memorial Institute, nor any of their employees, makes any warranty , express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights . Referen ce herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency there of, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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### PNNL-14337



# Model Documentation for the MiniCAM

AL Brenkert SH Kim AJ Smith HM Pitcher

July 2003

Prepared for the United States En vironmental Protection Agency under Contracts AGRDW89939464- 01 and AGRDW89939645-01 for the U.S. Department of Energy under Contract DE-AC05-76RL01830

Pacific Northwest National Laboratory Richland, Washington 993523 

# Acknowledgments

We want to thank Elizabeth L. Malone for steadfast support. We want to thank Marshall Wise for his review. We want to thank the Environmental Prot ection Agency’s Clean Air Markets Division (Office of Atmospheric Programs) for making this documentation become reality.4 

# Summary

The MiniCAM, short for the Mini-Climate Assessment Model, is an integrated assessment model of moderate complexity focused on energy and agriculture sectors. The model produces emissions of greenhouse gases (carbon dioxide, meth ane and nitrous oxide) and other radiatively important substances such as sulfur dioxide. Through incorporation of the simple climate model MAGICC, the consequences of these emissions for climate change and sea-level rise can be examined. The MiniCAM is designed to be fast and flexible.The MiniCAM is a long-term, partial-equilibrium model designed to examine long-term, largescale changes in global and regional energy system where the characteristics of existing capital stocks are not the dominant factor in determini ng the dynamics of the energy system. Markets are defined for oil (conventional and unconventional), gas, coal, biomass, carbon, and agricultural products. The MiniCAM has no markets for labor and capital. It is specifically designed to address issues associated with global change, including (1) projecting baseline carbon dioxide emissions over time for a country or group of c ountries; (2) projecting various other radiatively important gases ( e.g. , methane, nitrous oxide, sulfur dioxide, reactive gases); (3) evaluating the energy-system, emissions, and other consequences of various technological options; (4) evaluating some aspects of potential climate change, e.g. , temperature change, sea-level rise; (5) providing a measure of the carbon price, in dollars per metric ton for an emissions target; and (6) providing a measure of the overall cost of meeting an emissions target. The MiniCAM model can be conceptualized as c onsisting of four modules (see Figure below).

Human activities ERB

Atmospheric Composition, Climate & Sea Level Rise MAGICC Land Use AgLU

Regional Climate Patterns SCENGEN

These modules can be described as simulating

• energy supply and demand us ing an updated version of the Edmonds-Reilly-Barnes model ( ERB) (Edmonds and Reilly 1985; Edmonds, Reilly, Gardner and Brenkert 1986; Edmonds, Wise, Pitcher, Wigley and MacCracken 1997);

• agriculture and land-use using the Agriculture and Land Use model ( AgLU) (Edmonds et al. 1996; Sands and Leimbach 2001; Gillingham et al. 2002; Sands and Edmonds 2002);

• atmospheric composition and global-mean cl imate changes using the Model for the Assessment of Greenhouse-gas Induced Climate Change ( MAGICC) (Hulme and Raper 1993; Wigley 1994a,b; Wigley and Raper 1987, 1992, 1993, 2001); and5 • regional patterns of climate change usin g the Regional Climate Change Scenario Generator ( SCENGEN) (Hulme, Jiang, and Wigley 1995). The MiniCAM projects economic activity, energy consumption, and emissions in 15-year time steps from 1990 through 2095. The MiniCAM has global coverage in the form of 14 distinct regions (United States, Canada, Western Europe, Japan, Australia & New Zealand, Former Soviet Union, Eastern Europe, Latin America, Africa, Middle East, China [& Asian Reforming Economies], India, South Korea, Rest of South & East Asia). The MiniCAM has a strong focus on energy supply technologies. A wide range of technologies, fuels, and energy carriers can be used to s upply end-use energy demands. Transformation losses are accounted for throughout the supply system. Technologies include electricity generation (from coal, oil, gas, biomass, hydro power, fuel cells, nuclear energy, wind energy, solar PV, solar-wind storage, and space solar PV), hydroge n production (from coal, oil, gas, biomass, and electrolysis), synthetic fuel production (synthetic liquids from coal, gas, and biomass; synthetic gas from coal, and biomass), geologic carbon sequestration from fossil fuels (during electricity generation, hydrogen pr oduction, and synthetic fuel production). Biomass supply includes “waste” biomass streams and commercial biomass pr oduced regionally by the AgLU module. End-use fuels include those currently in widespread use (coal, oil, gas, biomass, electricity), and future options such as synthetic liquids, synthe tic gases and hydrogen. Carbon sequestration is an option for all conversion technologies, particularly electric generation and hydrogen production. The MiniCAM contains a large set of parameters to simulate technical change over time. These parameters include the rate of change in efficien cy of inputs to any particular production sector in the model ( e.g. , primary energy transformation to secondary energy; secondary energy transformation to tertiary energy). These rates of ch ange in input efficiency can be varied at each 15-year time step.



### Production Sectors Energy primary energy

fuel conversion secondary energy

energy conversion tertiary energy Agriculture biomass 

### Demand Sectors Transportation Buildings Industry

Agricultural demand & supplies

The conceptual framework of the ERB and AgLU modules is shown in the figure above. Each production process is represented by a fixed-co efficient (Leontief) pr oduction function requiring three parameters: fuel input, efficiency, and n on-fuel costs. During the transformation processes6 from raw fuel to refined fuels and to fuels to be consumed by end-users, fuels compete based on their prices. This competition is simulated by mean s of a share equation (the logit share equation) which is based on fuel prices and their elasticities. The price of each of the fuels is assumed to fall within a fuel-price range based on the cost of fu el and various costs like transportation costs, taxes, non-fuel costs, and structural factors. This variance of each fuel price is captured in an energy price exponent or elasticity coefficient. Through the logit methodology all fuels that compete can contribute in the generation of the su pply of a secondary fuel or an energy service, with shares changing in a smooth manner as prices or policies change with time. The demand for energy is determined by regional population levels, leve ls of economic activity and the price of energy services. The demand by the end-use sectors for energy services is simulated as a demand for the least costly energy service fuel mode through a combination of the constant elasticity and logit share equations. The constant elasticity equation includes price elasticities and income elasticities. End-use energy services can be supplied by refi ned fossil-fuels, biomass (traditional and from dedicated biomass farms), electricity, hydrogen, and synthetic fuels. The three end-use sectors are buildings, industry, and transportation. Regional populations determine regional economic activity and end-use demands. Technological change impacts energy demand, while regional taxes and tariffs (and climate policies which influence the price of greenhouse g as emissions) determine regional energy prices, which affect, in turn, regional energy demands . Regional energy resources and prices determine regional energy supplies, which impact global su pply and demand, which in turn affect world prices that feed back to the regional energy prices, which then impact regional supply and demands. Through this iterative process, global su pply and demand of the primary fuels are balanced. Emissions are calculated simultaneously with the balancing process, so as to efficiently solve for any carbon constraint. When equilibrium occurs, the markets are said to “clear.” The mechanism for clearing the markets is through the solution algorithm, which adjusts market prices ( e.g. , primary fuel prices) until the excess demand

─ the difference between demand and supply

─ is less than the solution criteria, typically a small number (less than one but greater than zero). The MiniCAM is most often used to examine one or more baseline (no climate policy) scenarios in combination with possible climate policies th at are intended to alter the baseline emissions trajectory. In the present version of the Mini CAM, the SRES scenarios are generally used for analysis. In order to facilitate this analysis and make comparisons with other models, the MiniCAM is able to exactly calibrate to any specified scenario in terms of population, GDP, and/or final energy use. It is these parameters that are the primary determinants of energy demands in each region. When a baseline scenario is generated, the f unction of the model in non-policy cases is to determine the least-cost method of supplying the energy services demanded. In a policy ( i.e., GHG emissions control) case, GDP and energy ar e generally allowed to freely respond to any changes in energy prices. The model can then be u sed to determine the cost of meeting a specified policy goal. The change in the shares of energy technologies that occurs as a result of meeting some policy goal is also an important output of the model.7 TABLE OF CONTENTS ACKNOWLEDGMENTS ............................................................................................................. 3
SUMMARY .......................................................................................................................
............. 4
INTRODUCTION ..................................................................................................................
..... 11
PART I.......................................................................................................................................... 12 1. A N O VERVIEW OF THE M INI CAM M ODEL

............................................................................ 12 1.1 M ODEL COMPONENTS

.......................................................................................................... 12 1.2 A PARTIAL EQUILIBRIUM MODEL AS ECONOMIC PARADIGM

............................................... 15 1.3 S TATIC VERSUS DYNAMIC MODELING

................................................................................. 19 1.4 R EGIONS

.............................................................................................................................. 19 1.5 M ARKETS

............................................................................................................................. 20 1.6. M INI CAM’ S FOCUS AND NICHE

.......................................................................................... 20 PART II ........................................................................................................................................ 22 2. T HE ERB MODULE

................................................................................................................. 22 2.1 D EMOGRAPHICS

................................................................................................................... 22 2.2 E CONOMICS AND E NERGY

................................................................................................... 23 2.2.1 Carbon Prices ...........................................................................................................

... 27 2.2.2 Energy supply ...........................................................................................................

... 28 Supply (resources) of crude oil, natu ral gas, and coal and uranium ................................. 29 Uranium supply and its price ............................................................................................ 35 Biomass supply................................................................................................................. 36 Hydroelectric power ......................................................................................................... 36 Solar PV and Wind ........................................................................................................... 37 Other Renewables ............................................................................................................. 37 2.2.3 Energy prices ...........................................................................................................

.... 37 Global primary fuel prices ................................................................................................ 38 Base year regional fu el supply prices ............................................................................... 38 Regional fuel prices .......................................................................................................... 38 Refined regional fuel price ............................................................................................... 38 Production and production costs of synfuels .................................................................... 39 Hydrogen generation ........................................................................................................ 43 Electricity generation ....................................................................................................... 46 The costs of energy services in th e form of fuel mode prices .......................................... 49 Total cost of energy ser vices to an end-sector .................................................................. 50 The energy service price index ......................................................................................... 51 2.2.4 GDP .....................................................................................................................

........ 52 2.2.5 Energy Demand ........................................................................................................... 53 Demand for ener gy services ............................................................................................. 53 Elasticities ..................................................................................................................

...... 54 Demand for each fuel mode ............................................................................................. 55 Demand for each secondary fuel ...................................................................................... 57 Electricity and hydr ogen interaction ............................................................................ 57 Primary fuel demand ........................................................................................................ 58 2.2.6 The energy balan ce and other markets ........................................................................ 60 2.2.7 Imports, Exports ........................................................................................................

.. 638 2.2.8 Calibration procedures ................................................................................................ 64 2.3 C ALCULATING G REENHOUSE AND N ON -G REENHOUSE G AS E MISSION

.............................. 65 2.3.1 Carbon dioxide emissions from the ERB module ........................................................ 65 2.3.2 Carbon sequestered in the ERB module ...................................................................... 69 2.3.3 Non-CO 2 Greenhouse Gas and Reactive Gas Emissions from the ERB module ......... 70 2.3.4 Emissions from the AgLU module ............................................................................... 71 2.3.5 Non-CO 2 greenhouse gas emissions from the AgLU module ...................................... 72 2.3.6 Total carbon emissions ................................................................................................ 73 2.3.7 Sulfur Dioxide Emissions ............................................................................................. 73 PART III ...................................................................................................................................... 76 3. A G LU: THE A GRICULTURE L AND U SE MODULE

................................................................... 76 3.1 D ATA THAT ARE REQUIRED

................................................................................................. 79 3.2 T HE PRICE OF BIOMASS IN A G LU IN STAND

- ALONE MODE

................................................. 79 3.3 A G LU MARKETS

.................................................................................................................. 80 3.2.1 Demand ..................................................................................................................

...... 81 3.2.2 Land allocation .........................................................................................................

... 84 Profit rates ..................................................................................................................

...... 84 Land shares and yields ..................................................................................................... 85 Observed Yield ................................................................................................................. 87 3.2.3 Supply ..................................................................................................................

........ 88 Technical change .............................................................................................................. 88 3.2.4 Nested Model ............................................................................................................... 88 PART IV ....................................................................................................................................... 90 4. MAGICC: M ODEL FOR THE A SSESSMENT OF G REENHOUSE

- GAS I NDUCED C LIMATE C HANGE

.............................................................................................................................. ...... 90 4.1 A TMOSPHERIC C ONCENTRATIONS

...................................................................................... 90 4.1.1 Carbon Dioxide ..........................................................................................................

. 91 The ocean and carbon dioxide .......................................................................................... 91 The terrestrial system and carbon dioxide ........................................................................ 92 Carbon balance ................................................................................................................. 92 4.1.2 Methane and other gases ............................................................................................ 93 4.1.3 Tropospheric ozone and aerosols ................................................................................ 94 4.2 R ADIATIVE FORCING

........................................................................................................... 94 4.3 T EMPERATURE CHANGE : TERRESTRIAL , ATMOSPHERIC AND IN THE OCEAN

...................... 95 Terrestrial and atmospheric compartments .......................................................................... 95 The ocean .............................................................................................................................. 95 4.4 S EA

- LEVEL RISE

................................................................................................................... 97 PART V ...................................................................................................................................... 100 5. SCENGEN: R EGIONAL C LIMATE C HANGE S CENARIO G ENERATOR

.................................. 100 PART VI ..................................................................................................................................... 102 7. R ESULTS

.............................................................................................................................. 102 Global outputs ................................................................................................................

.... 102 Regional outputs ..............................................................................................................

... 110 Policy cases ..................................................................................................................

...... 113 REFERENCES ....................................................................................................................
...... 1169 TABLE OF FIGURES Figure 1 MiniCA M’s modules ....................................................................................................

................. 12 Figure 2 The flow of services in MiniCAM ......................................................................................

........... 16 Figure 3 An energy-economics-emissions model (b ased on Edmonds and Reilly, 1985 p17 & p247) ........ 18 Figure 4 Energy flow processes in the ERB and AgLU modules of MiniCAM (Adapted from Edmonds and Reilly 198 5:245 ) ..............................................................................................................

.................... 24 Figure 5 Schematic cost distri butions for three different ener gy options (Adapted from ............................. 26 Figure 6 Cumulative En ergy Supply Curve .......................................................................................

........... 29 Figure 7 Nesting of cost calcula tions of hydrogen generation ..................................................................

... 45 Figure 8 Nesting of cost calculati ons of electricity generation ...............................................................

...... 46 Figure 9 Cost curve example relating carbon prices to em ission reductions ................................................ 71 Figure 10 Nested ap proach to land use .........................................................................................

................ 77 Figure 11 AgLU schemata .......................................................................................................

..................... 78 Figure 12 Food consumption in 11 regions in 1990 (from Sands and Leimbach 2001) ............................... 82 Figure 13 Average incomes, globally , in the four SRES scenarios ............................................................. 103 Figure 14 Total global electricity generation in the four SRES scenarios showing divergence in the A1 scenario due to various assumptions with regard to fossil fuel use an d technological change. .......... 104 Figure 15 Average diets in the four SRES sc enarios with divergence in the A1 scenario. ......................... 105 Figure 16 Global anthropogenic carbon-equivalent emissions in the four SRES scenarios ........................ 106 Figure 17 Carbon dioxide concentra tions in the four SRES scenarios ........................................................ 106 Figure 18 Sulfur emissions in th e four SRES scenarios with divergence in the A1 scenarios. ................... 107 Figure 19 Nitrous oxide emissions in the four SRES scenarios with divergence in the A1 scenarios. ....... 108 Figure 20 Methane emissions in the four SRES sc enarios with divergence in the A1 scenarios. ............... 108 Figure 21 Projected global temper atures in the SR ES scenarios ................................................................. 109 Figure 22 Projected sea-level rise in the SR ES scenarios ......................................................................

...... 109 Figure 23 Regional differences in income over time in IP CC’s B2 scenario .............................................. 110 Figure 24 Regional differences in calor ic intake in IPCC’ s B2 scenario .................................................... 111 Figure 25 Regional differences in electricity co nsumption per capita in IPCC’s B2 scenario .................... 112 Figure 26 Regional differences in anthropogenic emissions in IP CC’s B2 scenario ................................... 112 Figure 27 An example of anthropogenic carbon-equivalent emissions under carbon policy implementations in the USA IPCC’s B2 scenario .................................................................................................

......... 113 Figure 28 Carbon sequestered in the USA IPCC’s B2 carbon policy scen arios .......................................... 114 Figure 29 Sulfur emissions in the US A in IPCC’s B2 carbo n policy scenarios .......................................... 115 Figure 30 Carbon prices in the USA in IPCC’s B2 carbon policy s cenarios ............................................... 11510 TABLE OF TABLES

Table 1 MiniCA M Modu les .......................................................................................................

.................. 14 Table 2 MiniCAM’s twelve markets ..............................................................................................

.............. 17 Table 3 Regions in MiniCAM ....................................................................................................

.................. 19 Table 4 ERB non-CO 2 emissions ................................................................................................................. 70 Table 5 AgLU non-CO 2 emissions ............................................................................................................... 73 Table 6 FAO production and demand exampl e (from Sands and Leimbach 2001) ...................................... 8311 

# Introduction

This documentation consists of six parts. Part I provides for an overview of the MiniCAM model (the Mini-Climate Assessment Model), its model components, how the model solves for market prices of fossil fuels, biomass and carbon or car bon equivalents, its regional divisions and its niche in the energy and economics modeling context. Part II describes the detailed processes of the energy and economics module, an updated Edmonds-Reilly-Barnes module (ERB) that calcula tes energy supply and demand and resulting emissions. Part III describes the processes simu lated in agriculture and land-use using the Agriculture and Land Use model (AgLU). In th e AgLU module the amount of land used for crops, animal grazing, forest products, and energy crops and the emissions associated with the production of food and fiber and with land-use changes is determined. Part IV describes MAGICC (the Model for the Assessment of Greenhouse-gas induced climate change). This description contains less deta il than the ERB and AgLU modules given that MAGICC was not developed at JGCRI and that its component parts are documented in numerous journal articles. Similarly, SCENGEN (the Re gional Climate Change Scenario Generator) is described only in general terms in Part V for the same reasons. MAGICC calculates global aspects of climate change such as of atmospheri c concentrations of greenhouse gases, radiative forcing, temperature, and sea-level rise, while SCENGEN simulates the regional pattern of climate change. Part VI provides for data tables that support and illustrate the model pr ocesses described in Parts II and III. Part VII shows some results of model r uns. Part VIII attempts to put both model results and modeling approach in perspective.
Part VI shows some results of model runs to illustrate the model processes described. The Appendices provide for data tables and a table of the equations Much of the MiniCAM, including updates to the ERB, and the AgLU module, and all non-CO2 emissions code is based on original work by the modeling team at the Joint Global Change Research Institute (JGCRI), a collaboration between Pacific Northwest National Laboratory and the University of Maryland, operated by Batte lle. The MiniCAM is maintained and further developed at JGCRI. Verification of the 

### MiniCAM’s modules ERB and AgLU has been achieved through this documentation process.12 

# PART I

1. An Overview of the MiniCAM Model 1.1 Model components
The MiniCAM, short for the Mini-Climate Assessmen t Model, is a highly aggregated integrated assessment model that focuses on the world’s en ergy and agriculture systems, atmospheric concentrations of greenhouse gases (CO 2 and non-CO 2 ) and sulfur dioxide, and consequences regarding climate change and sea-level rise. It has been updated many times since the early Eighties to include additional t echnology options. The MiniCAM is capable of incorporating a shadow price for carbon and carbon constraints in conjunction with numerous technology options including carbon capture and sequestration. The mode l has been exercised extensively to explore how the technology gap can be filled between a business-as-usual emissions future and an atmospheric stabilization scenario. The MiniCAM model is designed to assess various climate change policies and technology strategies for the globe over long time scales. It is configured as a partial equilibrium model that balances supply and demand for commodities such as oil, gas, coal, biomass and agricultural products. The MiniCAM does not contain explicit ma rkets for labor and capital, and there are no constraints such as balance of payments. It is th erefore considered a partial equilibrium model of the economy. The model runs in 15-year time steps from 1990 to 2095 and includes (presently) 14 geographic regions (see Appendi x 3) and is composed of four modules (see Figure 1) that can be run separately or linked.



## Human activities ERB

Atmospheric Composition, Climate & Sea Level Rise MAGICC Land Use AgLU

Regional Climate Patterns SCENGEN

Figure 1 MiniCAM’s modules13 The MiniCAM model (Figure 1) includes modules simulating:

• energy supply and demand using an updated Edmonds-Reilly-Barnes module ( ERB) (Edmonds and Reilly 1985; Edmonds, Reilly, Gardner and Brenkert 1986; Edmonds, Wise, Pitcher, Wigley and MacCracken 1997);

• agriculture and land-use using the Agriculture and Land Use model ( AgLU) (Edmonds et al. 1996; Sands and Leimbach 20 01; Gillingham et al. 2002; Sa nds and Edmonds 2002);

• atmospheric composition and global-mean cl imate changes using the Model for the Assessment of Greenhouse-gas Induced Climate Change ( MAGICC) (Hulme and Raper 1993; Wigley 1994a,b; Wigley and Raper 1987, 1992, 1993, 2001); and

• regional patterns of climate change using the Regional Climate Change Scenario Generator ( SCENGEN) (Hulme, Jiang, and Wigley 1995). The precursor of one of the modules of the Mi niCAM model, the Edmonds-Reilly-Barns (ERB) module, was documented by Edmonds and Reilly (1985). ERB was based on a long history of energy-economic research at th e Institute for Energy Analysis (IEA). ERB was developed such that “at every decision juncture the simplest possible representation of policy interactions of energy, economics, and demographics have b een sought” (Edmonds and Reilly 1985:242). Since then the model has been modified but the essen tial premise and fundamental structure has been retained. The ERB module includes energy-pro ducing activities, and industrial and waste management processes and their associated emissions. The demand for energy services, as well as the efficiency of fuel conversion to energy are the major factors determining total emissions. Demographics characteristics can be included as a set of exogenous parameters or modeled by an age-cohort method. In this documentation, we will describe the MiniCAM model and refer, when comparisons are relevant, to the Second Generation Model (SGM), which is a process-level version of the ERB formulated as a general-equilibrium energy-economy model 1 . The MiniCAM is concerned with the supply and demand of energy, of agricultural production and land use, interactions between emissions of various greenhouse gases and other substances ( e.g., sulfur dioxide, reactive gases), and links with climate change and sea-level rise. In contrast, the SGM tracks many more aspects of the economy but does not extend its calculations to atmospheric greenhouse gas concentrations, climate change and sea-level rise. The MiniCAM results represent long-term scenario projections based on various views on how economics and energy use may develop in the future. The SGM results can be evaluated for short(er) term mitigation and cost alternatives. The Agriculture and Land-Use module (AgLU) of the MiniCAM simulates land use based upon available land and competing demands for that land. AgLU simulates the supply and demand for food and fiber products using a market mechanis m to balance supply and demand, which includes international trade. This becomes the basis for de termining (1) the amount of land used for crops, animal grazing, forest products, and energy crops and (2) the emissions associated with the production of food and fiber and with land-use changes. The production of biomass energy crops is, however, assumed to be carbon-neutral; biomas s production sequesters and releases the same carbon when used for energy.

1 Brenkert et al. 2003. SGM model documentation.14 MAGICC (Model for the Assessment of Gr eenhouse-gas Induced Climate Change; http://sedac.ciesin.org/mva/magicc/MAGICC.html) is a reduced form climate model that simulates the causal chain from emissions to atmos pheric concentrations, to radiative forcing, to global-mean climate change. The ERB and Ag LU MiniCAM modules supply projections of emissions for greenhouse gases, sulfur dioxide , and reactive gases which MAGICC uses to produce atmospheric concentrations and global-me an temperature and sea-level rise projections by using a combined set of gas-cycle, climate, and ice-melt models. Climate impact analysis generally requires regi onal climate changes, not global-mean values. Regional temperature and precipitation chang es can be provided using SCENGEN (SCENario GENerator). SCENGEN produces regional patterns of future climate change by scaling General Circulation Model (GCM) simulation outputs to match the output of MAGICC.

Table 1 MiniCAM ModulesModelInstitutionalAffiliation Description Inputs and Outputs ReferencesERBPNNL The Edmonds-ReillyBarnes (ERB) model is a market equilibrium model of the energy and economic systems. Inputs : labor productivity growth; population, fossil and non-fossil fuel resources, energy technologies (69) and productivity growth rates; Outputs : Energy supplies and demands by fuel (4 primary + renewables, 6 final) and region (14), emissions (CO 2 , CH 4 , N 2 O, SO 2 , others), and economic activity. Temporal Resolution : 15-year time step. Edmonds and Reilly (1985); Edmonds, Reilly, Gardner and Brenkert (1986); Edmonds, Wise, Pitcher, Wigley and MacCracken (1997)AgLUPNNL The Agriculture-Land-use Model (AgLU) is a market equilibrium model of the land use. Inputs : Income, population, regional climate, initial land-use allocation, productivity growth rates, and biomass energy price. Outputs : Agriculture and forestry production; greenhouse emissions; land-use and land-use emissions, and agricultural prices Temporal Resolution : 15-year time step. Edmonds, Wise, Sands, Brown, and Kheshgi (1996); Sands and Leimbach (2001); Sands and Edmonds 2002MAGICCNCAR MAGICC is an integrated model of the carbon cycle, atmospheric chemistry,radiative forcing, sealevel, and global mean climate change. Inputs : Emissions of greenhouse gases; historic atmospheric composition, climate feedback parameters, ocean inertia; Outputs : Concentration of greenhouse gases; radiative forcing; global mean temperature; sea-level Temporal Resolution : 1-year time step. Hulme and Raper (1993); Wigley (1994a,b); Wigley and Raper (1987, 1992, 1993, 2001)SCENGENNCAR SCENGEN models the regional patter n of climate change. Inputs : Global mean temperature; sulfurdioxide emissions; Outputs : Geographic patterns of temperature and precipitation change. Temporal Resolution : NA (steady-state) Hulme, Jiang, and Wigley (1995)

Table 1 provides summaries of the modules. Part II of this documentation describes MiniCAM’s ERB module; Part III decribes the AgLU modul e. Both these modules were developed by researchers at Pacific Northwest National Laborator y (PNNL). In Parts IV and V we will describe15 MAGICC and SCENGEN, respectively, but in much less detail. Part VI shows reference case results. The Appendix 6 deals with input data and Appendix 7 provides a list of the equations described.


## 1.2 A partial equilibrium mode l as economic paradigm
MiniCAM’s ERB and AgLU modules form a partia l equilibrium model that balances supply and demand of energy commodities and agricultural products. The ERB module handles the energy balancing; the AgLU module simulates the suppl y and demand of food and fiber products using the same market mechanism, whic h includes international trade. The objectives of the ERB and AgLU modules are to determine greenhouse gas emissions based on supply of and demand for energy services, food and fiber products, and the efficiency of converting fossil fuels into energy. The efficiency of fuels conversion to energy is based upon the fuels themselves and the technologies used to combust them. An important additional objective is the evaluation and quantification of how much the level of emissions can be affected by policies aimed at reducing emissions.
The version of the ERB used in the MiniCAM has three major components not present in the original version:

• links to agricultural and land-use activities through the AgLU, which includes biomass production,

• quantification of emissions of sulfur dioxide and additiona l greenhouse gases, e.g. , methane and nitrous oxide, and

• additional technologies such as carbon capture and sequestration, hydrogen-fuel production and consumption ( e.g. , fuel cells), and energy production from biomass. Numerous other enhancements to the original ERB have been implemented such as calibration, and a multi-gas emissions market for the evalua tion of generalized emission reduction policies.16 

### Production Sectors Energy primary energy

fuel conversion secondary energy

energy conversion tertiary energy Agriculture biomass 

### Demand Sectors Transportation Buildings Industry

Agricultural dema nd & supplies

Figure 2 The flow of services in MiniCAM

At the onset of the model development it was re cognized that “at the very least, an assessment tool must provide a global energy balance to enable consistent CO 2 release scenarios to be generated” (Edmonds and Reilly1 985:244). This requirement has been expanded to account for other radiatively important gases. Secondly, it w as deemed important to differentiate between primary or raw fuels, and secondary forms of energy (see Figure 2 and the more detailed Figure 4) – secondary fuels being usable energy – and to be able to distinguish between fuels that are combusted and fuels for non-combustion uses ( e.g. , petrochemical feedstock, asphalt). Primary energy is comprised of the raw fuels, graded based on extraction costs, traded and ultimately balanced, based on prices. These raw fuels are:

• Conventional oil

• Unconventional oil

• Coal

• Biomass & waste

• Natural gas

• Uranium. The six secondary fuel and energy carriers are:

• Liquids (which include refined liquids, and synthetic liquids from coal, natural gas or biomass)

• Coal

• Biomass (from commercial biomass and/or waste)

• Gases (which include natural gas and synthetic gas from coal or biomass)

• Electricity (from oil, coal, biomass, natural gas, hydrogen, nuclear power, fusion hydro power or renewables like solar PV, wind, and space satellite solar)

• Hydrogen (from oil, coal, biomass, gas or electrolysis).17 The secondary fuels are consumed to produce ener gy services. Conceptually, energy services are provided to the demand or end-use sectors. En ergy services include heating, cooling, transportation, etc. The energy used to supply these services is sometimes called tertiary energy. The demand, or end-use, sectors in the MiniCAM are:

• Transportation

• Buildings (residential/commercial)

• Industry Balancing the energy, carbon, and agricultural products at each time step ensures global equilibrium in each of the global primary energy fuel markets, the greenhouse gas (GHG) market, and each of the agricultural product markets. This balancing is achieved by pooling the regional demands for and supplies of each of the fuels (c onventional and unconventio nal fossil oil, natural gas, coal, and waste and commercial biomas s), total carbon or greenhouse gas emissions (accounting for any carbon sequestration), and each of the agricultural products, which are current and forward market wood products, f ood grains, oil crops, miscellaneous crops, and pasture products. The pooling results in12 markets to be cleared, as shown in Table 2. Note that the global markets can be re-configured by the u ser into regional blocks as needed — the markets shown in Table 2 are most commonly used in the global context.
Table 2 MiniCAM’s twelve markets

Fuel markets Agricultural product markets 1 = Oil 6 = Wood 2 = Gas 7 = Forward Wood 3 = Coal 8 = Food Grains which includes wheat and rice, 4 = Biomass 9 = Coarse Grains which includes all other cereals GHG market 10 = Oil Crops5 = Carbon Dioxide or CarbonEquivalents 11 = Miscellaneous Crops which includes fruits, vegetables, starchy roots and pulses 12 = Pasture Products which includes beef and mutton Supply and demand is made to balance in each time period by adjusting the prices of the traded (pooled) commodities. As the price of a commodity increases, supply increases and demand decreases. Similarly, as the price of a co mmodity decreases, supply decreases and demand increases. The different regions produce the demanded fuels and agricultural products when their production costs are competitive. Trade is therefor e implicitly simulated. Animal product supply is balanced with demand at the regional level. Tr ade in animal products between regions is fixed at 1990 levels given the relatively small amount of trade between regions. Uranium is implicitly traded by pooling regional supplies. Price r esponse to demand can be determined from supply curves but no explicit market is established. Elect ricity and hydrogen are not traded, since they are not primary energy fuels. Moreover, sufficient electricity and hydrogen is assumed to be generated, regionally, to meet demand. The MiniCAM does not contain an explicit backstop technology, which is often included in mode ling as a generic unlimited electricity source available at a fixed price. While nuclear and some other non-fossil-fuel technologies can, in principle, provide unlimited amounts of electricity, the cost of these sources are not necessarily constant in the MiniCAM.18 Figure 3 illustrates the conceptual framework of the ERB module in a different way from Figure 2. Regional populations determine regiona l economic activity and energy demands. Technological change impacts energy demand, while regional taxes and tariffs (and climate policies which influence the price of greenhouse g as emissions) determine regional energy prices, which affect, in turn, regional energy demands . Regional energy resources and prices determine regional energy supplies, which impact global su pply and demand, which in turn affect world prices that feed back to the regional energy prices, which then impact regional supply and demands. Through an iterative process, global supply and demand of the primary fuels are balanced. Emissions are calculated simultaneously with the balancing process, so as to efficiently solve for any carbon constraint.

Regional Populations Regional Labor Forces Regional GDP

Regional Labor Productivities Technological Change Regional Energy Demands

Regional Taxes and Tariffs

Regional Resources Constraints Regional Energy Supplies Regional Prices World Prices Global Supplies and Demands Emissions

Figure 3 An energy-economics-emissions mode l (based on Edmonds and Reilly, 1985 p17 & p247) When equilibrium occurs, the markets are said to “clear.” The mechanism for clearing the markets is through the solution algorithm, which adjusts market prices ( e.g. , primary fuel prices) until excess demand

─ the difference between demand and supply

─ is less than a specified solution criteria, typically a small number (less than one but greater than zero). The solution algorithm needs only to access information on the price, supply, and demand to operate. The solution algorithm adjusts prices until supplies and demands are balanced to within the solution criteria. Prices adjusted by the solution algorith m affect technology costs, demand for inputs and sector outputs. It has been our experience that the use of multip le solution algorithms ensures that a solution (all the markets are cleared) is found quickly and th at the solution is robust. Routines that are commonly used for economic modeling are th e bisection and Newton-Raphson routines. These routines are used in the MiniCAM (and the SGM). The bisection and Newton-Raphson routines are called independently. (See Appendix 3 for a further description of the routines.)19 

## 1.3 Static versus dynamic modeling
Dynamic modeling means that a solution in one tim e step has impacts on the next time step. The ERB and AgLU are dynamic in some aspects but not in others. The ways in which the ERB and AgLU are static rather than dynamic are as follows:

• The solution in each time period is largely separate from those of the prior periods because ERB (unlike the SGM) does not take into account capital stock lifetimes. The assumption is that over one to two of the 15-year periods considered by the model, relatively large changes in the energy system are possible.

• In the AgLU module the primary drivers of land use are population and GDP-levels over time. Both parameter sets are identical for the ERB and AgLU modules and are exogenous.

• Technical change and changes in labor productivity are dependent on values in the previous time-period, but these are all specified exogenously. The limited effects of a solution in a previous time period on a subsequent time period in the MiniCAM are:

• Physical stocks of depletable resources, such as fossil fuels, are modeled explicitly. Therefore, production rates and resulting prices of depletable fuels are dependent on production occurring in the previous time-periods. When easily accessible (or processable) fossil resources are extracted, remaining resources will be more difficult to exploit and require higher extraction costs. The same applies to uranium, if a limited supply is assumed.

• In cases where the GDP is not exogenous but allowed to vary ( i.e. , not calibrated to exogenously set data) changes in GDP thr ough the energy-price feedback will carry through to subsequent periods.


## 1.4 Regions
MiniCAM’s global coverage is comprised of f ourteen regions. The regions are determined by economic criteria and do not necessarily follow political divisions. Seven of the regions represent countries listed in Annex I of the Framework Convention on Climate Change (FCCC). Models of these regions are especially useful for simulating international trade in carbon emissions rights.

Table 3 Regions in MiniCAM 2

Annex I Non-Annex I United States China/Asia Reforming Canada India Western Europe (OECD90) South Korea Japan Middle East

2 See Appendix 2 for the list of countries in the regions. Annex I regions are the same in the MiniCAM and SGM; Non-Annex I regions differ20 Australia & New Zeal and Latin America Former Soviet Union Africa Eastern Europe (rest of) S&E Asia



## 1.5 Markets
The energy markets are the core of the Mi niCAM model. Markets are defined for oil (conventional and unconventional are traded together), gas, coal, biomass, carbon, and agricultural products (see Table 2). Through a ma rket definition procedure the MiniCAM regions can be fully integrated and trade is implicit for all commodities brought to market. Alternatively, through the market definition procedure some regi ons may trade while others remain independent representing a partial market clearing. A third alternative is that regions are completely independent. Note that the MiniCAM is a partial equilibrium model: the MiniCAM has no explicit markets for labor and capital and there are no constraints su ch as balance of payments. The MiniCAM does balance supply and demand of energy commod ities and agricultural products, while the GHG market is used through the implementation of a carbon fee to either limit carbon dioxide or all greenhouse gas emissions. Carbon revenue is not recycled. The GHG market operates using the same mechan ism as each of the energy and agricultural markets. Implementation of a carbon market can be achieved by (1) imposing an emission limit or target or 2) imposing a global or regional carbon price. In either case the impacts on energy production, consumption and sector-specific emission levels can be analyzed. In its simplest form, a carbon dioxide constraint is specified as a global carbon emissions target for each time period. The global carbon price is adjusted until global carbon dioxide emissions are below the specified target value. Alternativel y, emissions constraints can be in the form of total greenhouse gas emissions, which are the su m of the carbon-equivalent emissions for all greenhouse gases. Note that carbon fees are not a pplied to biomass production or consumption. If a carbon price is specified, fees can be added to all fossil fuels within the specified market region at a value proportional to their carbon co ntent. If the user has specified that non-CO 2 greenhouse gases are part of the market, then a carbon fee is translated to a carbon-equivalent value appropriate for that gas using a user-sp ecified Global Warming Potential (GWP) weighting factor (see Table 5). For non-CO 2 greenhouse gases a marginal abat ement curve approach is used to determine the amount of emissions reducti ons obtained for a given carbon price (see section 2.3). Under a configuration with one global car bon market, there is implicit global trading of carbon permits. Alternatively, regional carbon mark ets remain independent and there is no trading of carbon permits.



## 1.6. MiniCAM’s focus and niche
Implementing the MiniCAM provides for the ability to understand the impact of technologies and policies related to GHG emissions in a national a nd global context. Secondly, it provides for the ability to quickly evaluate technologies including carbon sequestration. Thirdly, it provides for an21 evaluation of land use given that biomass land competes with food and fiber uses in the agriculture/land-use model. And finally, MAGICC allows for the calculation of GHG concentrations, radiative forcing, and climate cha nge in the form of changes in temperature and sea level rise which can be regionalized through the use of SCENGEN. PNNL’s modeling team has been an active particip ant in the Intergovernmental Panel of Climate Change (IPCC) SRES scenario development (Nak icenovic et al. (2000). Part VI of this documentation provides an overview of some of the results. Outputs of the MiniCAM have allowed for ev aluations of sustainability (Pitcher 1993) and country-based vulnerabilities (Moss, Brenkert, and Malone, 2001).22 

# PART II

2. The ERB module
MiniCAM’s ERB and AgLU modules are run as mutually dependent modules. AgLU can be run separately. We describe the ERB module in PART II and the AgLU module in PART III. Commercial biomass, along with the shared driv ing forces of GDP and population, provide the link between the energy structure of ERB and land use in AgLU. The AgLU module adds markets for composite crops, animal products, a nd forest products to the ERB world markets for oil, gas, coal, and biomass (see Table 2 for a list of the final 12 markets). The fundamental problem the ERB model must address is finding global energy supply consistent with demand for each market. If supply and demand of the primary fuels is equal, the market clears. If not, then, within each time period, prices are re-iterated until supply and demands for each fuel are equal. A given model scenario requires, for each region, primary fuel resource supply curves, the prices of fuels and other input s such as land, transformation costs, technology options, technological change parameters, popula tion levels, and labor productivity rates. The three major exogenous inputs determ ining energy demands over time are

• Regional population changes

• Regional economic activity changes, which are de termined primarily by the rate of labor productivity increase and

• Regional
o technological change in energy transformation 3 , and
o autonomous end-use energy intensity improvements 4 , which are improvements in the amount of energy needed to provide a given level of service. Changes in regional energy prices, based on global prices, also impact energy demands over time. Three end-use sectors for energy services are simulated (see Figures 2 and 4), which are

• Transportation

• Buildings (residential/commercial)

• Industry. Changes over time in the population affect economic activity and energy demands. The population and labor force parameters can be speci fied in a number of ways, as described in the demographics section below (Section 2.1). The simula ted interactions of energy supply, energy prices, energy demand and technological change is described in sections thereafter.


## 2.1 Demographics

3 Autonomous, given that technological changes are input parameters which are independent of price

. 4 Autonomous energy intensity improvement (AEII): the AEII specifies how the amount of energy required to produce a given level of output would decline over time as a result of technical change, independent of energy prices (Edmonds, Roop and Scott 2000)23 The MiniCAM can use a number of methods for sp ecifying demographic variables. There are two primary demographic inputs that are ne eded in MiniCAM: total population ( ZLM , where L stands for region and M for time-period) and the fraction of the population in the labor force ( RLFP : unitless; a regional time-dependent input). Total po pulation levels are used to drive energy and agricultural demands. The size of the labor force, together with labor productivity ( PROLM : unitless rate; a regional time-dependent input parame ter), determines the level of economic output (for data examples see Appendix 6). The simplest demographic method is to obtain the regional total populations (population data may be read in, using the projections from either the World Bank or United Nations) and regional labor force fractions (representing the number of people between the ages of 15 and 65) for each region at each point in time. Note that the labor force fraction tends to be relatively stable over time, given that a decrease in mortality rates and increases in female partic ipation in the formal work force tends to be offset by increased time spent in school.As an alternative, the MiniCAM contains an internal demographics module that uses an agecohort method of calculating population by age and gender for each region. The required input variables are fertility, migration, and mortality rates. The demographics module keeps track of population within each region by gender and five -year age cohort. Base year populations may evolve by applying assumptions with regard to surv ival rates, fertility rates, and migration rates (Appendix 4 provides the equations).


## 2.2 Economics and Energy
The MiniCAM model has three general equation st ructures that recur. These are the Leontief or constant input-output coeffici ent equation for the description of energy transformation technologies, the logit structure determining fuel sharing and the constant elasticity equation determining demand. Figure 4 illustrates fully the energy transformation processes. Details of the transformation processes are described in the sections below. MiniCAM can be described as follows: each region has a unique set of primary energy prices, which are derived from world prices (market prices, determined when solving the model for supply and demand in the energy and other mark ets) and region-specific taxes, tariffs and subsidies. Primary energy is transformed at a cer tain efficiency and cost to secondary energy and is then converted, again at a certain efficiency and cost, such that end- use sector-specific energyservices can be met in the form of tertiary fuels or energy carriers, that is, of end-use sectorspecific fuel modes. The demand for secondary energy depends not only on the overall demand for energy and the relative cost of that partic ular energy modality, but also on the non-energy costs of transforming that modality into a useful energy service (see also Edmonds and Reilly1985:244). Supply prices are, however, not only determined by demand, but also by the fact that easily obtained abundant resources tend to be cheaper than more limited, higher grade resources. Raw fuel supplies are cost based res ources; carbon prices can be levied on production, and/or consumption. Implicit trade of raw fuel s takes place when regional supplies do not meet demand.24 Electric utilities

* Natural Gas cs

Commercial Biomass

Hydro Nuclear

Solar, Wind, Geo, Oil : Conventional ds cs 

### Primary Energy: graded based on quality and extraction costs; traded and balanced based on prices 

### Conversions to secondary fuels through fuelspecific efficiency factors (that are set to one); through the Leontief equation when actual conversion takes place plus the logit when fuel modes are generated from multiple primary sources; the logit is based on fuel prices Liquids refining Liquids

Gas

Biomass

Hydrogen 

### Conversions to tertiary energy ( to energy services by means of fuel modes)

Land use, Agriculture, Animal husbandry Biomass & Waste

Agricultural products 

### End-Use or Demand Sectors : energy is available by fuel mode: liquids, coal, biomass, gas, hydrogen, and electricity for various prices; fuel shares by demand sector through the logit share function which includes fuel price and income dependency

Transport ation energy services

Building energy services (residential, commercial)

Industry energy services Synfuel liquid conversion *

Caloric demand Land demand Exogenous: population, economic activity (GNP), technological change, regionspecific energy taxes and tariffs, and initial primary fuel world prices. Endogenous: energy prices while balancing fuel supply and demand

CO 2 & CH 4 & NO 2 & SO 2 6

Not traded

CH 4 & N 2 O & n e t CO 2 CH 4 & N 2 O

N 2 O f r o m A d i p h i c a c i d s Oil: unconvention al (oil shale, tar sands)

Coal ds cs

Uranium Coal

ElectricityAggregate Energy Services

Fiber demand

* = sequestration technologies SO 2

ds = desulfurization option; cs = carbon scrubbing option or share L o g i t f u e l

s h

a r i n g

l o g i t

6 = emissions from unconventional oi l and synfuels calculated separately Synfuel gas conversion * L o g i t
f u e l s h

a r i n g

L o g i t
e n e r g y

s e r v i c e

s h

a r i n g Gas processing S e c o n d a r y E n e r g y

Coal processing

Biomass/waste processing

L o g i t f u e l

d

e m

a n d

s

b y

s e ct

o r L o g i t
s e c t o r a l
d

e m

a n d

s

Hydrogen

* l o g i t l o g i t

Figure 4 Energy flow processes in the ERB and AgLU modules of MiniCAM (Adapted from Edmonds and Reilly 1985:245)25 The basic energy transformation process cost s are captured by the Leontief equation 

### hgPicePr +•= ($/energy unit) Eq. 1 where Price is the cost of energy (or an en ergy service) which is determined by P the costs of energy input, g a conversion coefficient representing the rela tionship between the input of one unit of energy to one unit of transformed fuel, and h

, which represents the levelized non-energy cost s associated with one unit of transformed fuel. Some of the secondary fuels (electricity, hydrog en, synfuels) can be provided in a number of different ways (see Figure 4). Electricity as a sec ondary fuel, can, for example, be generated by coal-fired power plants and by nuclear energy. Analogously, different fuel modes can provide an energy service, e.g. , residential energy services such as heating can be generated by electricity, gas, and/or fuel oil. The different primary fuels or fuel modes will co mpete for generating a secondary fuel or energy service. The price of each of the fuels is assumed to fall within a fuel-price range which is based on the cost of fuel and various other costs such as transportation costs, taxes, non-fuel costs, and structural factors. This variance of each fuel price is captured in an energy price exponent (Edmonds and Reilly 1985:259). The share each co mpeting fuel will capture will depend on both its price and its variance and how those compare with competing fuels. Figure 5 illustrates the basic premise that in the case of providing a tr ansformed energy, the cost distributions show alternative costs of providing this energy (Edmonds and Reilly 1985:250, 259). Shares of the fuels providing the transformed energy are calcu lated by means of the McFadden’s (1981) logit share equation. In that formulation the shares of the competing fuels add to one, are dependent on an assumed base share value for each of the compe ting fuels and are dependent on the elasticities of their prices. Thus, the share S j of a fuel j allocated to a demand or market where the fuels compete is given by 

# ( ) ∑ • •

=

j r j fuelj r j fuelj j p p 

### Pb Pb Share (unitless) Eq. 2

where P fuelj is the cost of fuel j (or the cost of providing an energy service),
r p is the price exponent, that is the paramete r that determines the variance of the price distribution; r p is the parameter that determines the rate that the use of this fuel will change in response to a change in the cost of this fuel (mode); this exponent has also been called the elasticity, b

j is the base share or weight of fuel j , sometimes called scale parameter, and the denominator is the sum over all possible shares.26Probability

Cost Option 1 Option 3 Option 2 Price 1 Price 2 Pr i ce 3

Figure 5 Schematic cost distributions for th ree different energy options (Adapted from Edmonds and Reilly 1985:251). Options 1 and 2 will compete for market share. The price distribution for option three does not overlap and will not have a significant share for the market shown. For a further theoretical discussion of the logit sharing mechanism see Clarke and Edmonds (1993). Synfuel generation is based on the share equa tion as is the competition between scrub and nonscrub technologies in the production of electricity and hydrogen (see Figure 4 for various other share equation implementations). The aggregate demand for energy services is dete rmined for each region by a constant elasticity equation where the aggregate demand is a function of population, income, the aggregate price of the energy services and the income and price elas ticities. The aggregate price for energy services is based on the average price of energy services in that demand sector. This prices is derived, ultimately, from the market prices of primary energy, adjusted step-wise from market prices of primary fuels, to regional prices for secondary fuel s, and, finally, to prices or costs of energy services. An energy price elasticity measures the relationship between energy service price and energy demand for the given sector. An economic activity elasticity represents the elasticity of economic activity either based on GDP or income. Thus, t he demand for fuel j in sector k is given by

rxk rpk 

### XPbDemand ••= (energy/year) Eq. 3

where P is the energy service price, X may be income or a GDP index, b is a base scale parameter or weight,
r pk is the energy price elasticity of demand which equals d

ln Demand/ d ln P representing the percentage change in demand resulting from a one percent change in price and
r xk is the income elasticity of demand which equals d

ln Demand/ d ln X representing the percentage change in demand resulting from a one percent change in X.27 In the MiniCAM a variety of climate policy op tions have been explored and they will be discussed next (Section 2.2.1). Then we will di scuss how energy supplies are simulated (Section 2.2.2). This will be followed by a detailed descripti on of energy prices (Section 2.2.3) and energy demands (Section 2.2.5) and how they interrelate (Section 2.2.6).



### 2.2.1 Carbon Prices
As was described before, the GHG market opera tes using the same mechanism as each of the energy and agricultural markets. Implementati on of a carbon market can be achieved by (1) imposing an emission limit or target or (2) impos ing a global or regional carbon price. In either case the impacts on energy production, consumption and sector-specific emission levels. GHG fees can be added to 1) the raw fuel extraction processes (as Pfis is,l,m 5 ); these fees are regional time-dependent severance costs that can be imposed when prices of resource supplies of regional primary fuels are determined (see Equation 5), 2) the production of regional primary fuels (as Pfi i,l,m ) (see Equation 24), 3) the consumption of fossil fuels (as Pfu ui,l,,m ) 6 ; by raising the prices of the to be consumed refined oil, processed gas and coal 7 when meeting the liquids and gas energy service demands (see Equations 31, 32, 33, and 35), th e fractions (or shares) of the total demand of each of the secondary (processed/refined) fu els will change resulting in a change in emissions, 4) the consumption of fossil fuels (as Pfu ui,l,m ) by electricity and hydrogen production (see Equations 37, 38, 44 and 45), and/or 5) the transformation of secondary to sector-specific tertiary energy (fuel modes) (as Pfjk j,k,l,m ), that is on the consumption of liquids, gas, and coal; not on biomass (see Equations 36 and 56). The implementation of fees may vary; e.g. , (case 1) both the Pfu ui,l,m and the Pfjk j,k,l,m fees are applied, while the Pfis is,l,m fees are set to zero; (case 2) the Pfu ui,l,m , Pfjk j,k,l,m , and Pfis is,l,m fees are all applied but halved; or (case 3) only the Pfis is,l,m fees are levied. Numerous variations can be

5 To aid the reading of the parameter names in this document (see also Appendix 1) one has to keep in mind that ‘is’ stands for raw fuel, ‘ig’ stands for grades of primary fuel, ‘i’ stands for primary fuel, except in the synfuel calculations where i refers to synliquid and syngas produced ‘ui’ stands for electric utilities, ‘hi’ indicates hydrogen fuel production ‘j’ indicates secondary fuel, except in the synfuel calculations where j refers to the feedstocks ‘k’ indicates end-use sector, ‘l’ indicates region, ‘m’ indicates time period, ‘es’ indicates energy supply, ‘ed’ indicates energy demand.

6 Although the MiniCAM has this Pfu ui,l,m carbon fee option, in practice, ca rbon fees are imposed during the tranformation of secondary fuels to fuel modes for energy services, Pfjk j,k,l,m 7 in the determination of the SynShares28 envisioned with some regions not applying fees to some fuels, some regions applying fees only when emissions exceed a certain amount, etc. (1) The severance fee of regional extraction processes ( Pfis is,l,m ) may be applied when extraction costs are determined. This fee is an exoge nous or endogenous regional time-period specific (input) parameter for conventional and unconventional oil, conventional gas, and coal and set to zero for biomass and uranium (units: $/EJ). The parameter has an exogenously set or endogenously determined value de pending on the type of constraints assumed in a simulation. (2) The regional price increases ( Pfi i,l,m ) on oil, gas, coal, and biomass production costs are regional and time-period specific (through 2050) in put parameters. These multipliers can also be interpreted as trade barriers or as scale factor s to regionalize the global fuel prices; the coefficients range from 1.8 to 0.75; for biomass they equal one. (3 & 4) The energy consumption ( Pfu ui,l,m ) fees can be fixed (exogenous ly set and changing over time) or may function as constraints such th at, for example, exogenously set greenhouse gas emissions standards can be met. 3⁄4 If the Pfu ui,l,m fees are not directly related to carbon emissions, the fees on the consumption of energy sources generating electricity (which includes nuclear, hydro, solar and other renewables), hydrogen fuels a nd synfuels may be e xogenously determined input. 3⁄4 If the Pfu ui,l,m fees are intended to impact carbon emission levels then the fossil fuelspecific fees are based on the fuel-specific carbon content. The fuel-specific carbon content ( CO i : tons C/Joule energy combusted) is recalculated by means of a conversion factor ( CVRT90 8 ) and the resulting parameter is called Pf0 ui,l,m . This parameter ( Pf0 ui,l,m ) has units of tons C/J*dollar conversion ratio ( CO i divided by CVRT ) such that when it is multiplied with the 1990$ carbon price-costs ( PRC l,m in $/million tons C) the resulting Pfu ui,l,m price increases are in units of $/GJ. Thus, Pf0 ui,l,m is a conversion factor that accounts for the carbon content of the fuel and incorporates a conversion of 1975 to 1990$. (5) The carbon fees, Pfjk j,k,l,m , are added to the costs of the transformation of secondary fuels to fuel modes (see Equation 56 where this fee is implemented for coal and Equation 36 where it is implemented for liquids and gas when synfuel liquids and syngas are shared with oil and gas, respectively); they are global; they are the same fo r each of the three end-use sectors and they are the same for refined oil, processed gas and coal and can be obtained from exogenously set input or can be set identical to the Pfu ui,l,m values. Note that a global or regional carbon price ( PRC l,m ) can be exogenously set; emissions are then dependent on this price; or, when emission limits are set exogenously the carbon price is determined in the GHG market.


### 2.2.2 Energy supply

8 The GDP deflator from 1975$ to 1990$ is hardwired in the code and its use is for accounting purposes only: CVRT90=2.21229 Energy supplies in the MiniCAM fall in a number of categories. Oil, gas, coal and uranium supplies of raw resources are determined by cumulative supply curves. These supply curves reflect that easily obtained resources tend to be cheaper than more difficult to extract resources. Uranium production is based on a long-term produc tion schedule which depends on the previous period’s annual production rate. Biomass comes, first of all, from waste, whic h for most regions supplies all of the present biomass demands. Secondly, biomass may be obtained from dedicated biomass farms which produce biomass on an economic basis under competit ion with food crops and other land uses. Hydroelectric power is a resource constrained re newable technology. Geothermal power is not modeled separately, but is (assumed) in cluded in the hydropower category. Generation of electricity by solar PV ( photovoltaic) and wind turbines are considered unrestrained renewable resources (apart from capacity limits, see below). Space solar power (SSP) is implemented as a source of electricity with no capacity constraints. Solar-wind storage is implemented as a means of storing and then delivering solar PV or wind energy. With this technology, solar PV and wind en ergy is generated and then stored for delivery into the electric grid as needed. Details of the different aspects of the different supplies of energy are described below. Supply (resources) of crude oil, natural gas, and coal and uranium Supplies of cr ude oil, gas, coal, and uranium are governed by cumulative supply curves. Energy resources with similar extraction costs are groupe d into grades where each grade has a range of extraction costs. A representative cumulative supply curve is shown in Figure 6 with extraction costs (C ig,is ) on the vertical axis and cumulative supply (R ig,is,l ) on the horizontal axis. Note that the model does not use a static resource curve as shown, however, since technological change is included (see below).

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

0 200 400 600 800 1000 1200 1400 1600 EJ $ per EJ

Figure 6 Cumulative Energy Supply Curve30 Note also that resource grade definitions are somewhat arbitrary and grades may be defined in any way convenient to the modeler. Grades may represent different types of oil, say proven reserves compared to speculative resources, or ma y simply be breakpoints needed to define a cumulative supply curve. In the MiniCAM unconvent ional oil is a separate category because of its greater carbon content. Unconventional natura l gas resources are treated as more expensive grades of natural gas. Nuclear fission is resource limited if light-water reactors are the dominant technology. Use of breeder reactors results in an essentially unlimited source of energy at a higher cost. Figure 6 illustrates that easily obtained resources te nd to be cheaper than more limited, highergrade resources. Regional resource prices determin e how much energy needs to be supplied by other regions; moreover, the regional resources de termine the final balance of global supply and demand. Regional resource costs 9 are simulated by the following sets of parameters and processes:
Extraction costs ( C ig,is CIGIS : $/GJ) determine the minimum cost of a global primary fuel by grade; they are global grade- and fuel-specific sets of input parameters relating energy resources ( R igis,l in Joules) and prices ($/EJ)

. Each regional supply ( R ig,is,l RIGIS L: EJ) of conventional oil, unc onventional oil, natural gas, coal, and uranium is determined by combinati ons of (6) grade levels and amounts of energy (Joules) assumed available at that grade level-specific extraction costs. The by-grade determined extraction costs relate to the regional primary fuel supply curves through regional environmental costs and taxes, and global time-dependent technological change in production costs:
Environmental costs ( V is,l,m : VISLM : $/GJ) are exogenous regional time- and primary fuelspecific input parameter. The environmental cost s are added to the production (extraction) cost for each fuel. Like other parameters in the Mini CAM, environmental costs can be considered a parameter that is scenario-dependent. Dependent on the analysis to be made impacts of environmental costs can be evaluated. For the re ference case the environmental costs are low for gas extraction and highest for coal extraction. Note , that if environmental costs are kept constant the effective cost may, in effect, decrease significantly in the future.

A global primary fuel-specific rate of technological change ( Tech m unitless) is calculated from the exogenous unitless time-dependent technological change parameter ST is,m ( STISM ). The rate of technological change determines the rate at whic h the sum of the extraction and environmental costs decline with time. This is a key variable that affects the future price of fossil fuels. The cumulative supply curve shifts downward over time as technical change causes extraction costs to decline. Technical change is calculated as follows: Nstep m,is 1m m 

### )ST1(Tech Tech +•=

− (unitless) Eq. 4 where Tech m is the global primary fuel-specific rate of technological change, set to one in the base year,

9 Prices and costs of energy are calculated in $/GJ, while physical energy quatities are calculated in EJ.31 ST is,m is the technology change parameter used in calculating the rate of technological change over time (unitless: exogenous global time- and fu el-specific for conventional and unconventional oil, coal, gas, and uranium), and Nstep is the time span from one time period to the next (15 years in MiniCAM)

A severance fee of regional extraction processes ( Pfis is,l,m ; TXISLM : $/GJ) may be applied when extraction costs are determined. Thus, over time, global primary fuel prices (extra ction costs of conventional oil, unconventional oil, coal, gas, and uranium) in units of $/GJ are in part determined by the regional fuel-specific supply curves, environmental and other costs as follows: 

# ( )

m,l,is

m m,l,isis,ig m,l,is 

### Pfis Tech VC ExtrCost + +

= for oil, gas, coal and unconventional oil ($/GJ) Eq. 5 where the extraction cost C ig,is is the exogenous global raw fuel-specific minimum cost of a next grade in a supply curve (CIGIS: $/EJ), the environmental costs V is,l,m is a regional, exogenous time- specific input parameter (VISLM: $/EJ), Tech m is calculated from input ST is,m which represents a global, exogenous fuel-specific technological change coefficient (STISM: unitless), and Pfis is,l,m , which is a regional time-dependent severance fee that can be imposed when extraction costs are calculated (TXISLM: $/GJ); th is fee is an exogenous or endogenous regional time-period specific (input) parameter. The parame ter has an exogenously set or endogenously determined value depending on the type of constraints assumed in a simulation. The parameter may have values for conventional and unconventional oil, conventional gas, and coal extraction but is set to zero for uranium and biomass. If this fee is considered a carbon severance fee, the fee for unconventional oil is a modified conventional oil fee through multiplication with a carbon emission coefficient ratio:

aloil convention i onaloil unconventi i m,l,aloil convention is m,l,is 

### CO CO Pfis Pfis

= =

= 

### • = for unconventional oil ($/GJ) Eq. 6 Once the regional extraction costs are determined, the amount of fuel ( ESILM i,l.m : Energy Supply of primary fuel i in region l : EJ/year) that can be produced for that price is determined by determining the location of the calculated regiona l extraction costs on the vertical axis of the regional supply curves by interpolation between grades from the C ig,is data and calculating the related energy from the R ig,is,l data. We are concerned in these calculations about the amounts of energy available for a certain price; the dema nd equations will ultimately determine, in an iterative process with prices, how much fuel need s to be extracted when markets need to be cleared. 10

10 We therefore do not calculate specific fuel prices at this stag e, but only set up equa tion structures that can be activated when prices of energy have been determined through its transformation processes from global primary fuels to energy services, such that when de mands are determined, the primary fuel supply can be calculated when markets need to be cleared.32 Determining the location of the calculated regiona l extraction costs on the vertical axis of the regional supply curves and determining from that point the amount of each of the fossil fuel supplies available is calculated in steps. The annual production rate is calculated from th e cumulative production, which is based on the resource amounts and short-term capacity limits . Thus, the cumulative production over time is calculated first.
Total resource available at time t ( Q is,l,m ) would be 

# ∑

= 

### = n

1ig l,is,ig m,l,is 

### R Q (EJ) Eq. 7
where n is the grade level below which extraction has to take place for demands to be met at the market price. Thus, when the extraction costs for a grade level ( ExtrCost is,l,m : see Equation 5, which is modified for unconventional oil based on Equation 6) become larger than this market price ( P i,l,m ), extraction costs have to be scaled back and the exact allowable fuel-specific extraction costs have to be determined that m eet the fuel-specific market price. The final extraction costs will be located somewhere between grade level n-1 and grade level n . To determine that price point the following calculation is made

m is,1igis,ig l,is,1ig 

### Tech )CC( R slope

− −



### − = Eq. 8

which determines the location on the resource curv e. Next, the supply required for production is calculated:


### slope) ExtrCost P(R Q m,l,is m,l,i 1n

1ig l,is,ig m,l,is 

### • −+ = 

# ∑ −

= (EJ) Eq. 9

where the calculated potential supply (EJ) is redu ced by one grade level and added to by the difference between the market price and the extr action costs of the next grade (Equation 5) multiplied by the ‘slope’ location. For the base year, the amount of fossil fuel available at the onset of the simulation is set exogenously, based on annual production ( ESILM il,m : Energy Supply of primary fuel i in region l is set equal to ESFIL is,l : EJ/year)

l,is 1m,l,i 

### ESFIL ESILM =
= for oil, gas, coal and unconventiona l oil in base year (EJ/year) Eq. 10
For the projections, annual supply equals double the annualized difference between the supply required for the production at the present and previous point in time divided by the time step minus the previous time period’s annual supply:

1m,l,i 1m,l,ism,l,is m,l,i 

### ESILM Nstep QQ 2 ESILM

− −



### − − •= for oil, gas, coal and unconventional oil in projections (EJ/year) Eq. 1133 This calculation of supply is subject to a short term capacity constraint. This constraint represents the notion that production can only increase by so much from one period to the next. This maximum rate, in EJ/year, is called the short-term supply limit. The short-term supply limit is assumed to be a function of GDP , fuel price, and technological change. The GDP and technological change factors represent, albeit cr udely, potential increases in expansion capability due to technological change and the ability of an expanding economy to foster new investment. The price dependence represents a further expans ion drive by price increases. Thus, supply can always expand, but this expansion may need to be driven by price increases. The short-term capacity limit is determined by the production in the previous period time (in EJ/yr) multiplied by the change in GDP and a price factor as

m anexpfos_r

1m,l m,l 1m,l,i m,l,i 

### TechPfac GDP GDP ESILM ESILM •• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

• =

− − (EJ/year) Eq. 12

where ESILM i,l,m is the regional annual energy production fr om the previous period; this production rate is exogenously set in the base year (ESFIL: EJ/year) and calculated thereafter, Tech m is the rate of technologi cal change defined above, GDP l,m is either an exogenously set parameter or calculated and re-iterated in the model (see Section 2.3), r_fosexpan is an input parameter that controls how fast the short term capacity limit can expand as GDP grows, and Pfac is a regional primary fuel-specific multiplier (price factor) determined by the ratio of the current to previous price and an elasticity paramete r of that ratio. The fuel prices are adjusted to be the extraction costs only, so that the environmental costs are not included. Thus,

l,i r

m 1m 1m,l,is1m,l,i m m,l,is m,l,i


### Tech Tech VP Tech V P Pfac ⎟ ⎟ ⎟ ⎟
⎠ ⎞
⎜ ⎜ ⎜ ⎜
⎝ ⎛

•− −

=

−

− − (unitless) Eq. 13

where P i,l,m is the global (market) primary fuel price ($/GJ) 11 at time t (m), and
r il is a regional, exogenous primary time period- and fuel-specific extraction cost elasticity parameter 12 (RIL: unitless).
Note that the GDP factor in the above equation is only applied if GDP is expanding ( 1m,l m m,l 

### GDP Tech GDP

− 

### >• ) so that regions with contracting GDPs do not suffer a production penalty.

11 P i,l,m gets updated in the solution routines 12 Representing that a one percent change in the P fac at time t results from a one percent 1 % change in the PS ratio; the PS ratio represents the change in the sum of the cost of en ergy services in each service sector weighted by that sector’s share of all energy services at time t divi ded by the weighted sum calculated during the previous point in time.34 The short-term capacity limit thus calculated is compared to an exogenous value (by fuel and region) for a minimum short-term capacity limit. If the capacity limit is smaller than this value, the short-term capacity limit is set to this minimu m value. This feature allows production of a fuel to be “re-started” in case production falls to very low levels in any period. Given the dependence of the short-term supply rate on previous productio n, production of a fuel could be quite small if minimum short-term supply is insufficient. The minimum short-term supplies for conventional oil and gas equal one EJ; for coal they are set e qual to the production of coal in 1990; and for unconventional oil they are set to regional-specific values to enable that fuel to always play a role. The supply of depletable resources is, therefore, de termined by a cost curv e calculation, adjusted downward if the resulting production exceed s the short-term capacity limit. Gas lost in gas production (which implicitly incl udes non-commercial gas use) due to flaring is calculated from flaring coefficients. The equation that determines gas flaring ( FLR l,m ) is illustrated in Equation 14 where Flr1 is the initial proportion of flared gas lost, FLr2 is the ultimate fraction that is lost at time m and Flr3 is the number of years losing FLr2

. ( ) ( ) ( )

3 3 Flr Nstep*1m
2 Flr Nstep*1m1 1m,l 

### Flr FlrFLR − −− 

### • = (unitless) Eq. 14

where Nstep equals 15 and m is the number of time periods since the base year, and Flrl1, Flrl2, and Flrl3 are regional gas flare parameters. Gas supply correction is simply 

### )FLR1( ESILM ESILM m,l m,l,gasi m,l,gasi 

### − • =
= = (EJ/year) Eq. 15
If regional production rates are larger than the production capacity limit, the amount of fuel that is regionally produced ( ESILM i,l,m ) is reduced accordingly (Equations 11 and 12) as are the resources that are left (as starting points for a new period)



### 2 ESILM ESILM Nstep QQ 1m,l.i m,l,i 1m,l,ism,l,is −

− 

### + •+= (EJ/year) Eq. 16

If regional supply is less than regional demand, additional demands are met through trade. The concept of trade in the MinCAM thus involves finding regions where production of fuels can meet global demand. This is achieved by (1) pooling all regional demands and pooling all regional supplies, and (2) balancing the global supplies and demands of the primary fuels. Trade in primary fuels includes not only crude oil, natural gas, and coal, but also biomass. In practice this is done globally, although regional trading blocks can be constructed for any fuel. No electricity generation sources (nuclear, hydropower, wind, etc.) are traded. Appendix 6 lists values for parameters described above. Note that market prices for fuels are ultimately determined by the market solution algorithms.35 Uranium supply and its price There are no explicit markets for uranium . Therefore the price of uranium is not market dependent and can be determined directly from extraction costs, regional supplies and environmental costs. Uranium supply is based on a long-term supply schedule defined in the same manner as for the other depletable resources. For the first period ( m=1 ) the regional cumulative production ( Q is=uranium,l,m ) is zero. At and after the second period, ( m ≥ 2 ) the regional cumulative production is updated by means of the last period’s annual production rate

1m,l,ui 1m,l,ism,l,nuclearis 

### ESU Nstep Q Q

− − = 

### •+= (EJ/year) Eq. 17

where ESU ui,l,m-1 is the demanded (yearly) electricity supply (secondary energy in Joules) generated by nuclear energy in the previous time period. Global production and the global resource of uranium are used in determining the nuclear fuel price 

# ∑

= 

### = nreg

1l m,l,is 

### QQ (EJ/year) Eq. 18


# ∑ ∑

= = 

### ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

= n

1ig nreg

1l l,is,ig 

### R W (EJ/year) Eq. 19

where R ig,is,l are the regional supplies (RIGISL: EJ) of uranium (see Figure 5), and n is the grade level below which extraction can take place for the global production demands (Q) to be met (Q ≤ W).
Extraction costs are then calculated based on regional supply and global production demands

is,1ig is,ig m,l,uraniumis 

### C W )QR( 1C W )QR( tcosExtr

− = 

### • ⎟ ⎠ ⎞ ⎜ ⎝ ⎛

− −+• − = ($/GJ) Eq. 20

and uranium costs are calculated based on environmental costs ( V is,l,m ), raw fuel costs ( C ig,is ) and technological change which is calcu lated as time period dependent as 

# ( ) Nstep m,is 1m m 

### ST1Tech Tech +•=

− starting with the second period’s technological change as unity: Tech m=2 =1 The price of uranium is then

m m,l,isis,ig m,l,uraniumi 

### Tech VC P +

=
= ($/GJ) Eq. 21
where C ig,is is the exogenous global raw fuel-specific minimum extraction cost of a grade in a supply curve (CIGIS: J:$/GJ), V is,l,m is a regional, exogenous time-specific the environmental costs input parameter (VISLM: $/GJ),36 Tech m is calculated from input ST is,m a global, exogenous fuel-specific technological change coefficient (STISM: unitless).

Biomass supply Biomass suppl y has two components. The first is biomass from waste which includes landfills, agricultural waste, wood wastes, etc. For most regions this supplies almost all of the present biomass demands. The second component of th e biomass resource base is biomass from dedicated biomass farms. A global supply function, analogous to the regional supply curves for coal, gas, oil, and uranium is described by an exogenous parameter set ( BIOPSM ) relating the costs of waste biomass (1975 $/GJ) to the fraction of total waste biomass supply available at a given biomass price. This supply function differs from the R igis l/C igis resource curve in that it has cumulative shares on the horizontal axis and cost on the vertical axis. Future biomass supply in each region is calculated relative to the current supply and depends on the level of economic activity as follows: rysht

1990m,l

m,l 1990m,l m,l,i 

### GDP GDP BIO ESILM ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

• =

= = (EJ/year) Eq. 22

where the waste resource supply rate in the base year (BIO l,m=1990 : BIOLM in EJ/yr) is an exogenous regional input for the base year (not time-specific), GDP l,m is as described in Section 2.2.4, and rysht is the elasticity coefficient 13 (RYSHT: unitless) which is set to 0.1 for all regions, such that the total amount of waste biomass availa ble increases only slowly with increases in GDP.
The cost of much of the available waste bioma ss is lower than the cost for biomass produced as a crop; this type of biomass resource is therefore used first. If the price paid for biomass increases enough to exceed the fixed costs of production of agricultural biomass, additional biomass can be supplied by output from the AgLU module. This (second) component of the biomass resource base is biomass from dedicated biomass farms. A biomass price (calculated according to the methodology described in Section 2.2.3) is passed to the AgLU model, which returns the amount of biomass in each region that can be produced at that price. That amount of biomass in EJ per year is added to the biomass supply ( ESILM i,l,m ) available at that point in time. 14
The AgLU module is described in Part III. Note that biomass can be used directly in the end-use sectors, or converted to a synthetic liquid, a synt hetic gas, or can be used for hydrogen production or electricity generation (see Figure 4). Hydroelectric power Hy droelectric power is a resource constrained re newable technology. Thus, electricity generation by hydropower is assumed to approach an exogenously specified limit within each region. Regional production of hydropower is simulate d by three parameters that determine its production expectations into the future:

13 Representing that a one percent change in the biomass resource base at time t results from a one percent 1 % change in the GDP ratio; the GDP ratio represents the change in economic activity at time t over the base year. 14 This addition is done when synfuel production is calculated37 NstepmHydro Hydro NstepmHydro Hydro

3 m,l,hydroi 2 1 2 1 

### e1

e Hydro ESILM ••+ ••+

= 

### + •= (EJ/year) Eq. 23
where Hydro3 is the resource amount in (E)J, Hydro1 determines the production path over time, which is modified by Hydro2 which determines the shape of that pr oduction path over time after being multiplied by Nstep which is MiniCAM’s time step of 15 years, and m which is the number of timesteps
. The price of hydropower is determined by non-fuel costs only. If, for some reason, total electricity demand in a region falls below the specified hydropower production level, then all electricity demand is assumed to be supplied by hydropower and total hydropower production is scaled back to meet this demand.
Solar PV and Wind Generation of electricity by solar PV ( photovoltaic) and wind turbines are considered unconstrained renewable resources. The cost of solar PV and wind are each input as exogenous parameters by region and time period. The amount of electricity that can be usefully delivered by solar PV and wind are limited by the intermittence of these sources. This effect is represented by an exogenously specified capacity limit in the form of the maximum share of regi onal electricity demand that can be supplied by each of these forms (see below).
Other Renewables Geotherm al power is not modeled separately, but is assumed included in the hydropower category. Space solar power (SSP) is implemented as a source of electricity with no capacity constraints. The cost of SSP is specified as a fixed cost for each time period. Solar-wind (SW) storage is also implemented as a means of storing and then delivering solar PV or wind energy. With this technology, solar PV a nd wind energy is generated and then stored for delivery into the electric grid as needed. The additional cost of operating the SW-Storage technology is specified. The cost of generating solar and/or wind energy is added to the cost of the SW Storage technology.


### 2.2.3 Energy prices
The MiniCAM calculates a sequence of energy pri ces that are internally consistent and that ultimately determine supply and demand. Prices are per unit energy ($/GJ) for primary and secondary energy, and per unit energy services fo r tertiary energy. The energy service units are technology dependent and can be transformed to energy units (Joules) by technology-specific coefficients (energy services/GJ) (see Figure 4).38 Global primary fuel prices The global pri mary fuel prices ( P i,l,m ) are the market prices of each of the primary fuels. They will be identical for each region l . They are determined by the so lution mechanism when global supplies and demands are balanced. Base year regional fuel supply prices Base y ear regional fuel prices function only as initial conditions ( Pin in,l,m ). These initial starting market prices for goods are in (1975) $/GJ for oil, gas, coal, and biomass and are replaced during the model solution’s first iteration in the base y ear (1990) by the market prices resulting from the solution algorithm. Thus, P i,l,m , as Pin in,l,m equal initial-condition fuel prices that only have a role for model initiation. Regional fuel prices Market prices ( P i,l,m ), obtained when supply and demand ar e balanced are transformed to regional fuel supply prices by adding fuel-specific tran sportation costs and a regional fee multiplier which represents any regional tax, tariff or subsidy such that reasonable differe ntiation between regions can be represented: 

# ( ) m,l,iim,l,im,l,i 

### PfiTrPP •+= ($/GJ) Eq. 24 where P i,l,m , is the global primary fuel price described above. Tr i is the transportation cost which is an exogenous input parameter for oil, gas, coal, or biomass (TRI: $/GJ), and Pfi i,l,m represents regional taxes or subsidies for oil, gas, coal, and biomass (TXILM: unitless) (an exogenous regional and time-period specific through 2050 input parameter). These multipliers can also be interpreted as trade barriers or as a sc ale factors to regionalize the global fuel prices; the coefficients range from 1.8 to 0.75; for biomass they equal one. Refined regional fuel price The refined r egional fuel prices or cost of a secondary fuel ( Pj

j,l,m ) is calculated by means of a Leontief production equation (E dmonds and Reilly 1985:248):

iim,l,im,l,j 

### hijgijPPj +•= for oil, gas, coal, and biomass/waste ($/GJ) Eq. 25 where Pj j,l,m is the regional processed/refin ed fuel-specific price ($/GJ), P i,l,m is the regionalized primary fuel-specific price ($/GJ), gij i is an exogenous input parameter representi ng a conversion coefficient that is not time dependent nor region-specific and has values close to or equal to one; gij i represents the relationship of the unrefined input pr oducing one unit of secondary fuel; gij i is also called conversion intensity of oil, gas, coal, and bi omass (GIJ: unitless or GJ of primary energy/GJ refined fuel), and hij i is the non-energy refining costs associated with a unit of secondary fuel (HIJ: $/GJ), which is an exogenous input parameter that is not time dependent nor region-specific; these costs are also described as mark-up costs or accounting costs of refining and distributing energy in the form of oil, gas, coal, and biomass. Thus, the production costs or transformation costs from primary fuels to secondary fuels are calculated with fuel-specific input-output coe fficients representing conversion efficiency and39 additional non-fuel cost. The refinery coefficients, gij i , have been set to one in recent versions. The non-fuel costs, hij i , are small for biomass and coal, moderate for gas, and much more significant for oil. The regional refined (secondary) fuel-specific costs ( Pj j,l,m ) resulting from oil refining and gas processing compete with the costs of synliquid and syngas technology costs, respectively, in determining the final secondary fuel prices for the end-use sectors (see Equation 36). This cost determination in the form of synfuel sh ares is described in the next section. Production and production costs of synfuels Synfuels are produced from the “raw” fuels. The process is simulated analogously to the refining process described above with the Leontief equation. There are, however, a number of additional considerations. Synfuels are produced for dom estic end-use consumption only. They are produced from coal, gas, and biomass with seven potential technologies. When synliquids or syngas are produced from coal, both scrub and non-scrub technologies can be active (four technologies total). Only synthetic liquid is pr oduced from natural gas (one technology); no syngas is produced from natural gas. Either li quids or gas can be produced from biomass (two technologies). The final price of syncrude (s ynliquid) and syngas production is captured in Equation 36 below. The variables leading up to that equation are described next. The non-energy costs of syncrude and syngas production from coal, gas and biomass are calculated as follows:
( ) ( ) ( )

3 3 HCLT Nstep1m
2 HCIL Nstep1m1
1 i,j 

### HCLT HCILT hc •− •−− 

### • = ($/GJ) Eq. 26 where j is the feedstock: gas, coal, or biomass, i is the produced crude or gas, HCILT1, 2, and 3 are the initial non-energy costs, final costs, and the time when final costs are reached, respectively (HCLT parameters are region- and crude and gas specific), Nstep is 15 (years), and m is the number of time periods since the base year. The basic calculation for the cost of each technology ( PC j,i,l,m where i =synliquid from j =coal, gas, or biomass; and i =syngas from j =coal or biomass) is as follows (see Equation 36 how PC j,i,l,m is used): 

# ( ) i,ji,j m,l,im,l,i,j 

### hcgctscossynPPC + • += synliquid from coal, gas, or biomass; sy ngas from coal or biomass ($/GJ) Eq. 27 where j denotes the feedstock: gas, coal, or biomass, i denotes the produced crude or gas, P i,l,m , is the market price for the input fuel feedstock (before transportation costs and taxes are added), gc

j,i is an intensity conversion coefficient of synfuel production (GCI: input GJ/output GJ; a fuel source-specific (coal, gas, biomass) and synfuel-specific (liquid, gas) exogenous conversion coefficient that is the same for each region, does not change over time and has values of 1.5, hc

j,i is the non-energy costs of synfuel production from coal, gas and biomass, as calculated above (Equation 26) for syncrude and syngas when no scrub technology is implemented, but to40 which carbon disposal costs (calculated below) are added when scrub technology is added (see h ci=coal-scrubbed ), and syncosts are the additional costs due to any carbon fee and are calculated in a number of steps that are explained below

. Scrub technologies can be simulated when s ynfuel is produced from coal. If scrubbing is implemented, carbon sequestration is calculated fo r the difference in carbon content between coal and the final synfuel type: liquid or gas. The fr actional difference of carbon content in emissions from coal, compared to liquids or gas is for example:

coali oili coali



### CO CO CO x SeqFractMa

= = = 

### − = (fraction) Eq. 28
where CO i are the fuel-specific carbon contents of fuels, directly related to carbon emission coefficients, in ton C/EJ. To calculate the disposal costs of the carbon potentially scrubbed and sequestered, the “carbon penalty” is determined first. Disposal costs ar e based on capital costs of sequestration equipment for electricity generating plants {( hu scrubbed -hu unscrubbed )/gu }, adjusted for synfuel production through multiplication with synfuel-specific conversi on rates that are specifi c for the fuels to be processed ( g

c,j,i ). When this levelized capital cost ($/GJ) is divided by the carbon emission rates, an estimate of the levelized capital costs per unit carbon sequestered is obtained ($/tonC). 

# ( )

coali i,j m,l,ui scrubbed non,m,l,ui scrubbed,m,l,ui j 

### CO 1 gc gu hu hu Cpenalty

= − 

### •• −
= ($/ton C) Eq. 29

where j is the feedstock: gas, coal, or biomass, i refers to the crude fuel sources, ui refers to the utilities, hu ui,l,m are the non-energy costs in 1975 dollars pe r GJ, which does not include technology and development (HUILM: exogenous regional time- and fuel specific parameters), gu ui,l,m is a conversion or energy intensity coefficient, which is unitless (GUILM: units GJ/GJ and values larger than one); an exogenous regi onal time- and fuel specific parameter representing the ratio of Joules energy input to Joules electric ity generated; these conversion factors tend to be larger than one, and gc

j,i is the intensity rate coefficient of synfuel production (GCI: input GJ/output GJ with values of 1.5), and CO i is the fuel-specific emission rate in ton C/EJ before refining. To obtain the total additional cost for carbon sequest ration, we must add the cost for disposal of the sequestered carbon, which are assumed to be proportional to the amount sequestered. The cost of disposal is calculated by (1) multiplying th e carbon disposal rate (input parameter) by the maximum fraction a plant can sequester, (2) adding the calculated carbon penalty, and (3) multiplying with a converted carbon emission rate ( Pf0 ui,l,m ) that is calculated from the carbon emission rates CO i and a conversion factor ( CVRT90 : GDP deflator from 1975$ to 1990$ hardwired: CVRT90 =2.212). The carbon disposal costs ( Cst disp ) are then correctly expressed in $/GJ :41 

# ( ) j m,l m,l,ui disp 

### Cpenalty x SeqFractMa Carbdisp 0PfCst + • •= ($/GJ) Eq. 30 where Pf0 j,l,m is explained above (ton C/GJ), Carbdisp lm are the exogenous regional time-specific carbon disposal or sequestration costs in units of (1990) $/mtC, SeqFractMax is explained above (a fraction: Equation 28), and Cpenaly j is explained above ($/ton C: Equation 29). Under a carbon policy the carbon disposal costs plus the price penalty for the carbon that is not sequestered play a role in the final cost determination: 

## ( ) 0001.0x SeqFractMa 1PfuCstC m,l,ui disp seq 

### + −•+= ($/GJ) Eq. 31 where Cst disp is the carbon sequestration cost described above (units are $/GJ Equation 33), SeqFractMax is described above (unitless), and Pfu ui,l,m (in $/GJ) is the carbon fee based on the fuel-specific carbon contents, which in this case are the Pf0 j,l,m values (tons C/GJ) and PCR l,m in $/tons C) such that the resulting Pfu ui,l,m fees are in units of $/GJ. This type of carbon pric ing is set to zero for biomass as energy source. The variables determining the shar es of scrub and non-scrub technology ( S scrub and S no-scrub ) participating in determining the syncost ( PC i,j,l,m : Equation 27) are the carbon sequestration costs and the penalties for carbon emissions based on carbon prices levied on non-scrub technology. The exponents required in the logit share function are set to –4. Thus,

4 seq 4 m,l,ui 4 m,l,ui scrubno 

### CPfu Pfu S

− − −

− 

### + = (unitless) Eq. 32

and

4 seq 4 m,l,ui 4 seq scrub 

### CPfu C S

− − −


### + = (unitless) Eq. 33

The syncost parameter (as part of Equation 27) that represents additional costs due to carbon fees are feedstock-dependent:
o from coal with scrub technology the syncost equals Pfu ui,l,m *(1-S scrub *RemFrac i,l ) where Pfu ui,l,m is the carbon fee, RemFrac i,l is an exogenous regional input for the base year, which for coal is 0.9 implying that 90% of the carbon prices on plants with scrub technology (as determined by S scrub ) are not levied,
o from coal without scrub technology the syncost equals the carbon fee Pfu ui,l,m ($/GJ: see the description of Equation 31),
o from gas the syncost equals the carbon fee Pfu ui,l,m , and
o from biomass the syncost is zero. The non-fuel transformation costs, hc j,i

, (see Equation 26 for calculation of the base non-fuel costs of synfuel production) in the case of coal combustion are increased by the carbon disposal costs; these carbon disposal costs are weighted by the Scrub fraction, which represents the fraction of plants using scrub technology:42 disp scrub i,j scrubbed coali,j 

### CstShc hc •+= += ($/GJ) Eq. 34 where hc

j,i is the updated for scrub technology non-fuel transformation costs (units are $/GJ), and Cst disp is the cost of carbon sequestration described above in Equation 33 {units are $/GJ). Note that when electricity and hydrogen are produced from scrub and non-scrub technologies the shares and averaged fuel-specific prices of the two competing technologies (scrub and non-scrub) are determined; when synfuel generation is simulated the share calculations are performed among all secondary fuel liquid technologies and all secondary fuel gas technologies (see Figure 4 and below). Secondly, accounting for the carbon disposal costs is done slightly differently in the electricity and hydrogen generation cases 15

. To simulate the participation of the synliquid t echnologies and refined oil in the secondary energy supply called “liquids” and the participation of the syngas technologies and processed natural gas in “gas” as secondary energy supply th e following share equation was developed:



# ∑ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+

=

−− −−

ns RCI

m,l,ui gas,or,oilform,l,j m,l,i,j RCI

m,l,ui gas,or,oilform,l,j m,l,i,j

m,l,i,j ji ji



### Pfu Pj PC Pfu Pj PC SynShare for each of the technologies

(unitless) Eq. 35 where j is the feedstock: gas, coal, or oil, i is the produced crude or gas, PC j,i,l,m is the cost of each technology producing synfuels: synliquid from coal, gas, or biomass; syngas from coal or biomass, which in cludes sequestration costs as described above, Pj j,l,m is the cost of producing refined oil or processed natural gas ($/GJ), Pfu ui,l,m is the consumption or carbon price (added to the refined oil or processed gas) ($/GJ), RCI ji is the exponent in the logit share equation; these elasticity coefficient values represent the relationship between syncrude produced fro m coal, gas and biomass, and syngas produced from coal and biomass, and ns is 4 for synliquids (when produced from co al, gas, or biomass and competing with refined oil) and ns=3 for syngas (when produced from coal or biomass and competing with processed gas).
Note that this SynShare equation calculates the shares first for four liquid technologies and then for three gas technologies (there is no syngas produc ed from natural gas). Each of the technology costs are normalized against the refined oil costs (t he fourth technology in refined oil production)

15 Synfuel generation’s cost from coal depends on the S scub fraction which results in a weighted cost between scrubber and non-scrub technologies: PC jilm =(P inlm + Pfu uilm *(1-S scrub *RemFrac il ))*g cji + Pf0 uilm * S scrub {Carbdisp lm* SeqFractMax +(hu uilm,scrubbed hu uilm,non-scrubbed )/gu uilm *g cji *1/CO i )} +h cji Hydrogen and electricity generation costs from scrub technologies are formulated as 

### ( ) m,l,hi m,l,hi lm m,l,ui l,i m,l,ui m,l,issh hhgh Carbdisp 0Pf)mFracRe1(PfuPPssh +• •+ −•+=43 resulting in an endogenous weighting scheme that is represented by exogenous weight parameters in share equations described in the next paragraphs ( e.g. , bsu i,l,m parameters). Similarly, each of the liquid producing technology costs is normalized against the processed natural gas costs. In Figure 4 sharing is depicted by diagonal boxes. In the case of tracing the synfuel calculations the word “logit” in the diagonal boxes from the raw fu els to synfuel conversions is omitted given that the final share equations are implemented only wh en the four technologies for liquid production and the three technologies for gas production participate in the cost determination of the secondary fuels.
The final price of liquids, Pj j=liquids,l,m , is the summation of the products of the SynShares and the technology-specific prices of synliquids genera ted from gas, biomass and coal, with the latter generated with or without scrub technology, plus the produc t of the calculated SynShare and the price of conventional (fossil) refined oil. Similarly, the final price of gas , Pj j=gas,l,m , as secondary fuel is the summation of the products of the SynShares and prices of syngas generated from biomass and coal, with the latter generated with or without scrub technology, plus the product ofthe SynShare of processed natural gas and the price of processed natural gas. Note that the sectorspecific consumption taxes are added to the refine d oil and processed natural gas prices. Note also that carbon fees were not applied in the production of secondary fuels (Equation 25). 

### )Pfjk Pj( SynShare PC SynShare Pj m,l,k,j m,l,gasorliquidsjm,l,i,j
ns m,l,i,jm,l,i,j m,l,gasorliquidsj 

### + • +• =
−−= −−= 

# ∑ ($/GJ) Eq. 36
Note that Pfjk j,k,l,m is added here while in the SynShare calculation Pfu ui,l,m was added to Pj j,l,m of oil and gas; this can be considered alright gi ven that only unitless shares are calculated in the SynShare equation while secondary pri ces are calculated in Equation 36. Synfuels are not used for electricity or hydroge n generation; they are only in end-use sectors. Hydrogen generation Hy drogen fuel can be generated from oil, gas, coal, biomass, and through electrolysis. When oil, gas or solids (comprised of coal and biomass) are converted to hydrogen, technologies with carbon scrubbing and without carbon scrubbing compete if a carbon-policy is in effect. Without carbon scrubbing the hydrogen generation costs are calculated as follows: 

# ( ) m,l,hi m,l,hi m,l,ui m,l,i ssh 

### hhgh PfuPPssh + •+= ($/GJ) Eq. 37 where P i,l,m is the price of a regional primary fossil fuel (in units of $/GJ), gi i,l,m is the inverse of conversion efficiency, which is unitless (GHILM: GJ/GJ; an exogenous technology-, regional- and time-period specific input parameter); these conversion factors tend to be larger than one, resulting in prices go ing up during the transformation process, hh i,l,m are non-fuel costs associat ed with the conversion process (HHILM: $/GJ) (an exogenous technology-, regional- and time-pe riod specific input parameter), Pfu ui,l,m raises the cost of the regional primary fuel consumption in producing hydrogen representing a carbon fee (TXUILM: $/GJ). If scrubbing and sequestration are simulated, then th e competing technology costs, when oil, gas or solids are transformed, are calculated as follows:44 

# ( ) m,l,hi m,l,hi lm m,l,ui l,i m,l,ui m,l,issh 

### hhgh Carbdisp 0Pf)mFracRe1(PfuPPssh + • • + −•+= ($/GJ) Eq. 38 where RemFrac i,l is the carbon removal rate (REMFRAC: a regional fuel-specific input for the base year); as with synfuels, any carbon not sequestered is subject to a carbon price, Pf0 i,l,m is a conversion factor that accounts for the carbon content of the fuel used and is calculated from carbon content factors CO i (COI: tons C/J) and a conversion factor (CVRT90: GDP deflator from 1975$ to 1990$) for accounting purposes, such that when these carbon emission rates (tons C/EJ divided by CVRT90) are multiplied with Carbdisp l,m , the carbon disposal cost (CARBDISP lm an exogenous regional time dependent disposal cost in units of $/Mton C), the correct result is expressed in $/GJ.
Ssh hi,,l are the shares of the scrubbed and non-scrubbed oil, or scrubbed and non-scrubbed gas, or scrubbed and unscrubbed coal: 

# ( ) ∑ • •

=

nc ruiss ssh m,l,hi ruiss ssh m,l,hi l,hi 

### Pssh bssh Pssh bssh Ssh (unitless) Eq. 39

where nc equals two (the competingscrub and non-scrub technologies), bssh hi,l,m is the base share or weight of a scrub or non-scrub technology (BSSHILM: unitless) (an exogenous regional time- period fuel/technology-specific input parameter), Pssh ssh is the cost of each technology participa ting (competing) in producing hydrogen, and
r uiss is the logit exponent for the technology co st (RUISS: unitless; an exogenous technology specific input parameter set to –6 for all technologies). When a scrub and non-scrub technologies compete, the costs of the fuel-specific hydrogen generation are the weighted sums of the technology-specific costs: 

# ( ) ∑ • =

nc ssh l,hi m,l,hi 

### PsshSsh PH generated from oil, gas, or solids ($/GJ) Eq. 40

The cost of hydrogen generation from biomass is calculated as follows, given that no taxes are levied when produced and no scrub technology is deployed:

m,l,hi m,l,hi m,l,im,l,hi 

### hhghPPH +•= generated from biomass ($/GJ) Eq. 41
Hydrogen can also be generated through electroly sis. The cost calculation is the same as the equation above, except that the price ( P i,l,m ) is not the price of biomass but is the price of electricity ( PU ui,l, : see Equation 47). Several options exist fo r specifying the electricity price used for H 2 production. It can be the average price of electricity before capacity limitations are implemented (see next section) or the weighted price of wind and solar.45 Oil Gas Solids Biomass

NonScrubbing Scrubbing Scrubbing

NonScrubbing NonScrubbing Scrubbing Hydrogen Generation

Electrolysis

Figure 7 Nesting of cost calculations of hydrogen generation

The final price of hydrogen , Pj J=hydrogen,l,m , is calculated by summing the weighted hydrogen costs. Figure 7 illustrates the nesting of the weights. 

# ∑ • =
= nhprices m,l,hi l,hi m,l,hydrogenj 

### PHSh Pj ($/GJ) Eq. 42
where PH hi,l,m is the technology-specific and/or resulting from competing technologies hydrogen generation cost, Sh hi,l are the shares of the competing sources (in th e form of prices) in generating hydrogen; the shares are calculated with the share equation as follows: 

# ( ) ∑ • •

=

nhprices rhi m,l,hi m,l,hi rhi m,l,hi m,l,hi l,hi 

### PH bsh PH bsh Sh (unitless) Eq. 43

where nhprices equals four fo r hydrogen generation, bsh hi,l,m are the fuel-specific time-dependent glob al base share coefficients or weights of hydrogen technologies, presently set to one, rhi is a global technology specific logit expone nt reflecting the responses of hydrogen prices to changes in technology costs (RHI: unitless). When scrub technology competes with non-scrub technologies, an option exists to allow the scrub share of the technology to be set as a fraction of the non-scrub technology based on “grandfathering” existing plants. This means that a fraction of the old plants remains active until the plants’ lifetimes have been reached. The fraction of plants with scrub technology is determined by the number of time periods past the policy start date (maximally three) divided by three, given that the maximum lifetime of a non-scrub technology is set to three time periods. The share parameters are consequently adjusted accordingly.46 Electricity generation Electricity can be generated directly by any one of the following sources and technologies: (1) oil, (2) gas, (3) coal, (4) nuclear power, (5) solar PV , (6) hydro power, (7) biomass, (8) coal with scrub technology and carbon sequestration, (9) oil with scrub technology and carbon sequestration, (10) gas with scrub technology an d carbon sequestration, (11) hydrogen fuel cells, (12) fusion, (13) wind power, (14) solar-wind st orage, and (15) space satellite PV solar.

Oil Gas Coal Electricity Generation

Biomass Scrubbing

NonScrubbing Scrubbing Scrubbing

NonScrubbing NonScrubbing Hydro power
Nuclear

Solar PV Hydrogen fuel cells Fusion

Wind
Solar-wind storage

Space satellite PV solar

Figure 8 Nesting of cost calculations of electricity generation
Electricity generation cost is computed, as for hy drogen generation with two levels of nesting using the logit approach (Figure 8). The costs of electricity generated through scrub and non-scrub technologies using oil, gas or solids (which are comprised of coal and biomass) as feedstock are calculated similarly to hydrogen production cost calculations from th ese fuels. Additional electricity generation coefficients (or price adjusters: pa i,l s ) adjust the regionalized fossil fuel prices ( P i,l,m s for oil, gas and solids), however, to account for fuel use in u tilities given the fact that electric generators, in general, get lower rates than other sectors. Thus, P ssu , the cost of each fossil-fuel combusting technology participating (competing) in produc ing electricity is calculated for non-scrub technologies as: 

# ( ) m,l,ui m,l,ui m,l,ui l,ui m,l,issu 

### hugu PfupaPPssu + • +•= from oil, gas, and solids ($/GJ) Eq. 44 and for scrub technologies as: 

# ( ) 

# [ ] m,l,ui m,l,ui m.l m,l,ui l,j m,l,uil,uim,l,i ssu 

### hugu Carbdisp 0Pf mFracRe1PfupaPPssu +• • +

− •+•= from oil, gas, or solids ($/GJ) Eq. 45 where pa ui,l is the electricity generation coefficient (or price adjuster), which adjusts the regionalized fossil fuel price (oil, gas, solids) to account fo r fuel use in utilities (unitless: PAUIL exogenous47 regional fossil fuel-specific parameter), and all other parameters are as described for hydrogen production, Pfu ui,l,m raises the cost of the regional primary fuel consumption in producing electricity representing a carbon fee (TXUILM: $/GJ), RemFrac i,l is the carbon removal rate (REMFRAC: a regional fuel-specific input for the base year); as with synfuels, any carbon not sequestered is subject to a carbon price, Pf0 ui,l,m is a conversion factor that accounts for th e carbon content of the fuel used and is calculated from carbon content factors CO i (COI: tons C/J) and a conversion factor (CVRT90: GDP deflator from 1975$ to 1990$) for accounting purposes, such that when these carbon emission rates (tons C/EJ divided by CVRT90) are multiplied with Carbdisp l,m , the carbon disposal cost (CARBDISP lm an exogenous regional time dependent disposal cost in units of $/Mton C), the correct result is expressed in $/GJ. gu ui,l,m is the inverse of conversion efficiency specific to the technology, which is unitless (GUILM: GJ/GJ; an exogenous technology-, region al- and time-period specific input parameter); these conversion factors tend to be larger than one, resulting in prices going up during the transformation process, and hu ui,l,m are non-fuel costs specific to the technology associated with the conversion process (HUILM: $/GJ) (an exogenous technology-, regional- and time-period specific input parameter representing operation and maintenance costs and plant costs levelized over its lifetime). When (pure) biomass is used as feedstock the Pfu ui,l,m carbon fees are set to zero 16 : 

# ( ) m,l,ui m,l,uil,ui m,l,ui m,l,issu 

### hugupa PfuPPssu + • •+= for biomass ($/GJ) Eq. 46
The costs of electricity generation for oil or g as are the weighted sums of the scrub and non-scrub technology costs ( nc=2 ). The cost of electricity generated from ‘solids’ is the weighted sum of thescrub and non-scrub technologies of coal and the biomass technology ( nc=3 ). 

# ∑ • =

nc ssu l,ui m,l,ui 

### Pssu Ssu PU ($/GJ) Eq. 47
where Ssu ui,l are the electricity generation shares of the scrub and non-scrub technologies using the logit share equation: 

# ( ) ∑ • •

=

nc ruiss
uus m,l,ui ruiss
uus m,l,ui l,ui 

### Pssu bssu Pssu bssu Ssu (unitless) Eq. 48

where nc is the number of competing technologies; nc=2 for oil and gas representingscrub and nonscrub technologies; nc=3 for ‘solids’ repr esented byscrub and non-scrub technologies of electricity generation from coal and an additional technology from biomass, bssu ui,l,m are the base shares or weights (sometimes called scale parameters) of each of the electricity generating scrub and non-scrub fu el technologies (BSSUILM: unitless exogenous regional time-period fuel technology-specific i nput parameters as initial values); these share parameters are zero in the base year for the carbon sequestration technologies (there is no carbon

16 the fuel-price adjuster (pa uil ) and carbon prices (Pfu uilm ) are potentially interacting differently: Pfu uilm *pa uil48 scrubbing in 1990) while values for other fuels fo r the base year are calculated by the model during the base year calibration,
r uiss is the elasticity of the fuel price (RUI(SS): unitless), that is, a parameter that is related to the variance of the fuel price distribution; r ui determines the rates that shares change in response to a change in generation cost 17 (an exogenous technology a nd time-period specific input parameter). When scrub technologies competes with non-scrub technologies, the scrub share of the technology can simply be set to be a fr action of the non-scrub technology based on “grandfathering” of existing plants. This means th at a fraction of the old plants remains active until the plants’ lifetimes have been reached. Th is concept can be applie d to hydrogen production as well. Note that when prices are calculated fo r non-fossil fuels, as shown below, the Pfu ui,l,m parameters do not represent the so-called “carbon fees”; they are separate input parameters ( e.g. , utility consumption fees) or set to zero.

The cost calculation of electricity generated by nuclear energy is similar to those above, although with no price adjustment since uran ium fuel is only used for nuclear power: 

# ( ) m,l,ui m,l,ui m,l,ui m,l,uraniumim,l,ui 

### hugu Pfu PPU + • + =
= from nuclear energy ($/GJ) Eq. 49

Electricity generation from hydropower , fusion, solar PV , space-solar power , or wind differs from the above in that P i,l,m equals zero: 

# ( ) m,l,ui m,l,ui m,l,ui m,l,ui 

### hugu Pfu0PU + •+= from solar PV or wind ($/GJ) Eq. 50

When wind-solar storage is calculated a simple weighted price is calculated with price elasticities of –3 plus an additional non-fuel storage cost:

3 solar,uus 3 wind,uus 3 solar,uus solar 3 solar,uus 3 wind,uus 3 wind,uus wind m,l,ui m,l,ui 

### PP P P PP P Phu PU

− − −

− − −


### + •+ + •+= from wind-solar storage ($/GJ) Eq. 51 When electricity is generated by means of hydrogen fuel cells , the fuel price is from hydrogen, as calculated above. No carbon fees are applied in this case:

m.,l,ui m,l,ui m,l,hydrogenjm,l,ui 

### hugu PjPU +• =
= from hydrogen fuel cells ($/GJ) Eq. 52

17 Elasticities are parameters representing the relationship between the percentage change in output resulting from a one percentage change in the value of the base parameter. Thus, when Z=X B , B= d lnZ/d ln X , or, the percentage change in Z results from a one percentage change in X (Edmonds and Reilly 1985:248-249).49 The final price of electricity , Pj j=electricity,l,m , is the simple summation of the cost of each of the generation processes (technologies) weighted by that generation process’ share of all processes (technologies): 

# ∑ • =
= neprices m,l,ui l,ui m,l,yelectricitj 

### PUSU Pj ($/GJ) Eq. 53
where PU ui,l,m is the technology-specific electricity generation cost, SU ui,l are the shares of a the competing fuels (technologies) (in the form of prices) in generating electricity as secondary fuel; these shares are calculated with the logit share equation: 

# ( ) ∑ • •

=

neprices rui m,l,ui m,l,ui rui m,l,ui m,l,ui l,ui 

### PU bsu PU bsu SU (unitless) Eq. 54

where neprices are the number of participati ng electricity generating technologies, bsu ui,l,m are the regional fuel-specific and time dependent base shares or weights of the fuels/technologies participating in electricity generation. These parameters are overridden during the calibration process; most shares are assumed to have equal values by 2050; Coal is an exception -- deviates from price-derived shares are found in many regions, so extrapolation is extended to 2065 and is non-linear (BSUILM: unitless), and rui is a global technology specific elasticity pa rameter reflecting the responses of electricity prices to changes in technology costs (RUI: unitless). The MiniCAM does not explicitly model dispatch for electricity generation. One of the more important implications of this is that direct u se of intermittent sources such as wind or solar PV is limited unless some storage mechanism is provided. Therefore, each electricity generation technology is assigned a capacity limit ( EcapLim ; an exogenous technology-specific fraction representing the maximum contribution of that techno logy to the generation of electricity). This can also be used to represent technologies that are generally used for base-load generation such as coal-fired plants or nuclear generation that cannot be rapidly shifted to follow changing loads. The technology-specific capacity limit is the maximu m share that any of the electricity generation technology can supply which feeds back into the fossil fuel balance of supply and demand. This is particularly important for intermittent rene wable technologies such as solar photovoltaics and wind. The technology-specific capacity limit capacity limit is implemented by rescaling the fuel shares ( Su ui,l ) that partake in the generation of electricity if any of the technologies exceeds the limit (see Equation 54). Hydropower contribution remains fixed. Note that the capacity limits set in variable ECapLim apply to end-use electricity only, not to the total electricity generated, which includes electricity used to make H 2 . The capacity limit does not apply to electrolytic hydrogen production. Solar PV, for example, may be limited to supplying 10% of the total end-use electricity demand but can supply an unlimited amount of electrolytic hydrogen. The costs of energy services in the form of fuel mode prices Energy services are envisioned as energy available for a specific end-use demand in the end-use or demand sectors. Energy services are generated by processes transforming the secondary energy into meeting sector-specific demands, e.g. , meeting heating and cooling demands for liquids in50 buildings will be met by different fuel transf ormation processes than meeting liquid demands for the transportation sector. Since the MiniCAM operates on a very aggregate level, the transformation parameters do not represent specific technologies, but broad classes of technologies aggregated by sector (transportation, buildings, industry) and secondary fuel-type (liquids, gas, coal, biomass, electricity, hydrogen) . For example, we aggregate all energy services provided by liquid fuels in the building sector. The fuel mode price Pjk j,k,l,m is the cost of an energy service to an end-use sector k , for region l at time m. This is (again) a Leontief equation wh ich combines the secondary fuel price ( Pj

j=liquidss,l,m, Pj

j=gases,l,m, Pj j=coal,l,m , Pj j=electricity,l,m , Pj j=hydrogen,l,m or Pj j=biomass,l,m ), the energy service-specific conversion coefficients or input-output coefficients ( gjk j,k

) and the non-energy costs of the transformation process ( hjk j,k

): 

### )hjkgjkPj(Pjk k,j k,j m,l,j m,l,k,j 

### +•= ($/energy service) Eq. 55 where gjk j,k

s an energy service-specific conversion coefficient or input-output coefficient, representing the relative amount of energy that is needed to provide energy services by fuel j (liquids, gas, coal, electricity, hydroge n, and biomass) for use in end-sector k (GJK: GJ/energy service; an exogenous sector-specific input pa rameter); these coefficients are further disaggregated for the transportation sector as se ctoral-, regional- and time-specific (as gjkl j,k,l,m ), and for the hydrogen fuel cell technology uni que and sector- and time-specific (as gjk j,k,m ), hjk j,k

is the non-energy cost of the end-use technology that uses fuel j (liquids, gas, coal, electricity, hydrogen, or biomass) in end-sector k (HJK: $/energy service; an exogenous sector specific input parameter): these coefficients are also more disaggregated for the transportation sector (as hjkl j,k,l,m ) and hydrogen fuel cells (as hjk j,k,m ), and Pj j,l,m is the price of a secondary fuel j in region l at time m ($/GJ), where
o Pj j=liquids,l,m and Pj j=gases,l,m were discussed under the synf uel generation section (see final liquids and gas calculation in Equation 36), which contain any carbon fees for these fuels;
o Carbon fees ( Pfjk ; $/GJ) are added to the price of coal (see Equation 25 and Equation 56 below) before Equation 55 is calculated:
m,l,k,j m,l,coaljm,l,coalj 

### Pfjk Pj Pj + =
= = ($/GJ) Eq. 56

o The cost of biomass production, Pj j=biomass,l,m , does not incur carbon fees and is determined with Equation 25;
o Sector- and time-specific transmission and distribution costs ( PUTD ; $/GJ) are added to the cost of electricity (see Equation 53 and Equation 57 below) before Equation 55 is calculated: Pj j=electricity,l,m = m,k m,l,electicityj 

### PUTD Pj +

= ($/GJ) Eq. 57

o Sector- and time-specific distribution costs ( PH2TD ; $/GJ) are added to the cost of hydrogen fuel (see Equation 42 and Equation 58 below) before Equation 55 is calculated:

m,k m,l,hydrogenjm,l,hydrogenj 

### TD2PH Pj Pj + =
= = ($/GJ) Eq. 58

Total cost of energy services to an end-sector The total cost of energy services to an end-sector k

(

Pk k,l,m in $/energy services) can now be calculated from the fuel mode-specific prices Pjk j,k,l,m and the shares SPjk j,k,lof the fuels in an endsector k :51 

# ( ) ∑ • = j m,l,k,jl,k,j m,l,k 

### Pjk SPjk Pk ($/energy service) Eq. 59
where Pjk j,k,l,m is the energy service price of fuel mode j to end-sector k ($/energy service), and SPjk j,k,l are the shares of the fuel modes j in end-sector k (unitless); these share coefficients are read in for the base year (SJKLP: unitless regional sec tor shares that are specifi c for oil, gas, coal, biomass, electricity, and hydrogen); they are overridden after future demands for energy services are calculated by the ( lagged for one time period) Sjk j,k,l demand shares as calculated for the previous period. These demand shares are calculated as follows: 

# ( ) ∑ • • • •

=

j ryjk rpjk m,l,k,j m,l,k,j ryjk rpjk m,l,k,j m,l,k,j l,k,j jklm jk jklm jk


### X Pjk bsjk X Pjk bsjk SPjk (unitless) Eq. 60

where bsjk j,k,l,m is the base share or weight of a given fuel mode j in end-use sector k and is unitless (BSJK); BSSJKLM separates out coal and biomass and is also an exogenous regional sector- and time period-specific parameter used in calibration in the base year; these weights are recalculated during the model’s re-iteration process and ma y be used in the calibration process, Pjk j,k,l,m is the price of the service as provided by a given fuel mode j in sector k ($/energy service), rpjk j,k

is the price elasticity of that service in sector k (RPJK: unitless; exogenously sector- and secondary fuel-specific parameter for liquids, gas, solids (coal+biomass), electricity, and hydrogen (hydrogen ‘s rpjk value is that of el ectricity’s); RSSPJK is the price elasticity when separating out coal and biomass, X represents economic activity by the ratio (unitless) of GDP per capita at time t ( m ) and GDP per capita in the base year, ryjk jklm is the economic activity elasticity (RYJKLM: unitless) (regional sector- and fuel mode-specific time-dependent input parameter). This elasticity exponent of X represents the relationship between the fuel mode demand and th e economic activity (represented by the change in GDP at time m from the base year). 18 19

The energy service price index The energy service price i ndex or aggregate service price index represents the change in aggregate energy prices between two model periods. This is computed as the ratio of the sum of the cost of energy services in each service sector weighted by that sector’s share of all energy services at time t divided by the weighted sum calculated during the previous model period. Thus, the weighted sum of the individual energy service prices, PS (unitless), is

18 r yklm : hydrogen’s economic elasticity value equals that for electricity; in the case of biomass it equals that for coal. 19 In the demand equation for energy services by the transportation and building sectors the elasticity coefficient ( ry klm ) of X represents the relationship between energy services demands and the change in income (represented by GDP per capita ) from the base year52 

### ∑ ∑

=

− − k 1m,l,k1m,l,k k m,l,kl,k
ratio 

### Pkbsk Pkbsk PS (unitless ratio) Eq. 61

wh ere Pk k,l,m is the cost of energy services to end-sector k ($/energy service), and bsk k,l is the regional base year energy consumption (BSKL: in EJ) of sector k of the aggregate energy service demand (an exogenous regional sector-specific input parameter). The weighted sum of the individual energy service prices, PS ratio , is used in the iterative GDP adjustment (see Section 2.2.4).



### 2.2.4 GDP

GDP is a major determinant of energy demands. It functions as a proxy for both the overall level of economic activity and as an index of income (Edmonds and Reilly, 1985:15). GDP is primarily a function of labor force leve ls and exogenously set rates of labor productivity increases. GDP as a determinant of energy demands is normalized against the base year. The impact of labor productivity and the labor force on GDP is simulated as follows:

m,l Nstep m,l 1m,l m,l 

### LBFindex )oPr1( GDPindex GDPindex • +• =

− (unitless) Eq. 62 where GDPindex l,m is the normalized GDP value (normalized against the base year GDP value, which makes the GDPindex for the base year equal to one), Pro l , m is the labor productivity increase (labor productivity growth) from one point in time to the next (PROLM: unitless rate; a regional time-dependent input parameter), Nstep is the time span from one time period to the next (15 years in MiniCAM) and, LBFindex l,m is the ratio of the size of the labor force in the current period to that in the previous period. The size of the labor force is calculated by one of two methods:
o The product of the population and the fraction of the population in the labor force (both exogenously set parameters at time t , ZLM : regional time-dependent population; LFPerc : unitless fraction; a regional time-dependent input ) (see Tables 1 and 6 in Appendix 6 for data examples), or
o the working age population as calculated using an internal demographics module. The first method is used in most current work

. Base year GDP and GDP values in baseline scenarios are calibrated to base year data and exogenous GDP scenario specifications by adjusting labor productivities. When MiniCAM is used for alternative scenario analyses ( i.e. , policy cases), GDP values are allowed to vary as energy prices influence GDP

. To reflect the impact energy prices can have on GDP , the normalized GDP value ( GDPindex ) is adjusted for the overall energy service price ( PS ) (Edmonds and Reilly 1985: 260). This feedback is part of the iterative process of finding the energy balances. A first order approximation of this effect is represented with the following elasticity relationship:53 adj rGDP ratio m,l m,l 

### PS GDPindex GDPindex • = (unitless) Eq. 63 where GDPindex l,m is the normalized regional GDP at time t ( m ), PS ratio is the ratio of the aggregate pr ice for all energy services at time t ( m ) divided by the calculated aggregate price for all energy ser vices at the previous point in time, and
r GDPadj is the elasticity coefficient representing the percentage change in GDP resulting from a one percent change in the PS ratio 20 (see Table 4 in Appendix 6 for example values). This GDP feedback is intended to provide a simple long term feedback from changing energy prices to GDP when used as the dr iver of energy and non-energy emissions. This formulation is not intended to provide a measure of the change in GDP due to changes in energy prices or policy. Such changes are far more complex to cal culate. Note that the change in GDP due to changes in energy prices is small.


### 2.2.5 Energy Demand
The demand for energy is determined by the population level, the level of economic activity ( GDP ) and the market prices of primary energy, adju sted step-wise from market prices of primary fuels, to regional prices for secondary fuels, to prices or costs of energy services as described in the previous section. The three end-use sectors for energy services are (see Figure 4):

• Transportation

• Buildings (residential/commercial)

• Industry

Demand for energy services The demand by the end-use sectors for energy services is modeled as a demand for the least costly energy service fuel mode (Edmonds a nd Reilly 1985:248). “The constant elasticity equation structure offers a first-order approximation to an arbitrary energy service demand function at a point. That is, it can replicate not only the total demand for service, given an arbitrary set of exogenous variables, but also provides a log-linear estimate of the effect on total demand of a change in these independent variables. It does not provide a second-order approximation of an arbitrary demand function at a point. That is, it does not provide an estimate of the rate at which elasticities change as e xogenous variables change for an arbitrary demand function” (Edmonds and Reilly 1985:249) 21

.

20 Elasticities are parameters representing the relationship between the percentage change in output resulting from a one percentage change in the value of the base parameter. Thus, when Z=X B , B= d lnZ/d ln X , or, the percentage change in Z results from a one percentage change in X (Edmonds and Reilly 1985:248-249).

21 Edmonds and Reilly 1985:248-249: “The demand for total energy services is derived from a constant elasticity equation, generally written as Z=AX B Y C where the dependent variable Z ( e.g. , aggregate service demand) is a function of X ( e.g ., the price of the aggreg ate energy services) and Y ( e.g. , income) and where A is a scale term and B and C are elasticities (parameters), where B=d lnZ/d ln X and C= d lnZ/d ln Y (percentage change in Z (energy service demand) resulting from a percent change in either X (price) or Y54 Energy service demand by the transportation and building sectors is simulated as follows:

index ryk rpk

2m,l,k

m,l,k l,k m,l,buildings ortion transporta k 

### Pop X Pk

Pk bsk Fk m,l,k l,k


### •• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•=

= −− = (EJ/year) Eq. 64

where bsk k,l is the regional base year energy consumption (BSKL: in EJ) of sector k of the aggregate energy service demand (an exogenous regional sector-specific input parameter), Pk k,l,m / Pk k,l,m= base year is the ratio (unitless ratio) of the total cost of energy services to an endsector k at a point in time (in $/GJ calculated in the price-processing) and the total cost of energy services to an end-sector k in the base year (1990). The value of Pk k,l.m is part of the iterative process, r p k,,l is the regional sector-specific energy service price elasticity of the energy services price ratio Pk k,l,m /Pk k,l, m=baseyear (unitless); this elasticity parameter is recalculated as part of the iterative process (see Equation 66 below), X represents the economic activity in the form of the regional GDP per capita (income) at time t ( m ) divided by the regional GDP per capita in th e base year (a unitless ratio) (The value of the GDP is part of the iterative process in policy impact scenario analyses: after the calculation of energy prices the GDP is adjusted (see Section 2.3); the adjusted GDP impacts income, which impacts the demand for services, etc.), ryk k,l,m is the sector-specific economic activity elasticity (RYKLM: unitless) (an exogenous regional sector- and time period-specific input parameter), and Pop index is the ratio of the population at time t divided by the population in the base year (unitless). Demand for energy services by the industrial sector is determined similarly except that, instead of population size index, demand is indexed to the change in GDP over the base year:

m,l,k l,k ryk rpk

2m,l,k

m,l,k l,k m,l,industryk 

### Y Pk

Pk bsk Fk • ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•=

= = (EJ/year) Eq. 65

where Y as economic activity is represented by the regional GDP at time m divided by the regional GDP in the base year (unitless )

. Demands for a particular energy service, such as transportation, may be assumed to grow even if population stabilizes, because income continues to increase. However, the amount of energy needed to meet those demands may not grow at the same rate due to technological improvements as well as to shifts in fuel serv ice shares as described below.
Elasticities The energy service pri ce elasticities, r p k,l , in the equations above (Equation 65), measure the relationship between energy service price and energy service demand for the given sector. This elasticity is negative because demand decreases as prices increase. The (regional) energy service price elasticities r p k,l are iteratively updated for four time periods (1990, 2005, 2020, 2035). This

(income). ( B and C are the price and income elasticities, respectively). See also Equation 23 in Edmonds and Reilly 1985:260.55 update is performed because energy service el asticies in developing economies can change significantly as their energy systems evolve into ones that use modern energy forms. After 2035, that is, from the year 2050 on, the energy service price elasticity coefficients r p k,l s are held at the 2035 value. The update is calculated by means of the following equation:

m,l,k m,l,k k l,k 

### Pfk Pk Rpkrpk •= (unitless) Eq. 66

where Rpk k is the energy price elasticity – with one value for each end-use sector (an exogenous service sector specific input parameter; RPKK: unitless), Pk k,l,m is the regional time-dependent total energy services cost ($/energy services) to a regional end sector k (the value of Pk k,l,m is part of the iterative process); Pk k,l,m represents the costs of all secondary fuels that partake in the sector-specific energy services (liquids, gases, coal, biomass, electricity, and hydrogen) according to their shares in that energy service, Pfk k,l,m represents the fuel costs only, of the regional total energy services cost ($/energy services) to a regional end-sector k at a point in time; Pfk k,l,m represents the costs of all secondary fuels minus their non-energy cost of transformation of fuel j for end-sector k , that partake in the sector-specific energy services (liquids, gases, coal, biomass, electricity, and hydrogen) according to their shares in that energy service.
The economic activity elasticity, ryjk j,k,l,m , represents the elasticity of economic activity in the form of the change in GDP at time m from the base year when determining the shares of the fuelmode demands (see Equation 60).
The economic activity elasticity, ryk k,l,m , represents the elasticity of economic activity in the form of changes in income ( GDP per capita ) at time m from the base year when determining the transportation and building sectors’ energy services demand (see Equation 64).
For the industry sector , the economic activity elasticity, ryk k,l,m , represents the elasticity of economic activity in the form of the change in GDP at time m from the base year when determining the energy services dema nd by industry (see Equation 65).
Note that the economic activity elasticities of demand as used here relate to the demand for energy services, not the demand for energy itself.
The values of these elasticities , particularly over long time periods, are not certain and there are large variations in estimated values.
Demand for each fuel mode Deter mining fuel demand from the total demand for energy services for an end-use sector has two parts. The first part is a transformation from energy service demand to energy use. The second is a logit share equation that splits the service demand between the individual fuel modes. Two parameters embody the transformation from ener gy service demand to energy use. Each fuel has a coefficient that represents th e efficiency at which that fuel is transformed into an energy service. In addition, the overall transformation be tween energy service and fuel use is adjusted by the amount of cumulative technological change as represented by an annual rate of end-use energy intensity improvement (AEII). This latter parameter is the way by which the relationship between energy service demand and fuel use cha nges over time. In practice, this parameter56 embodies both efficiency improvements and changes su ch as the shift to a more service oriented economy, which results in a lower rate of energy demand for a given increase in income. In more detail, demand for each fuel mode ( Fjk j,k,l,m in energy units, EJ) by each end-use sector k is equal to the product of total service demand ( Fk k,l,m in energy services units), the fuel service share ( Sjk j,k,l unitless) and the fuel requirement per unit service ( gjk j,k

), divided by the level of technological improvement ( Tech jk

unitless) (Edmonds and Reilly 1985:260 eq 24).

jk m,l,k l,k,jk,j m,l,k,j 

### Tech Fk Sjkgjk Fjk ••= (EJ/year) Eq. 67

where gjk j,k

is an energy service-specific conversion coe fficient or input-output coefficient, which represents the energy intensity of transformation of secondary fuel j (liquids, gas, coal, biomass, electricity, or hydrogen) for use in end-sector k (GJK: GJ/energy service; the energy service unit depends on the technology-specific transformati on process) (an exogenous sector-specific input parameter); note that gjk j,k,l,m is a regional and time-specific parameter for the transportation sector, and gjk j,k,m is an exogenous sector- and time-specific input parameter for hydrogen fuel cells, Fk k,l,m is the energy service demand of sector k (in energy services units), and Tech jk

is the level of technological progress (cal culated from TKLM, which is unitless), which may act to conserve energy even when prices fall. “This specification allows for both continued progress and stagnation to be explicitly cons idered” (Edmonds and Reilly 1985:260); this technology parameter can be set by region and end-use sector for future points in time:

Nstep m,l,k 1m,k,j m,k,j 

### )T1(*Tech Tech + =

− (unitless) Eq. 68 where Nstep is the time step of 15 years, and T k,l,m is the sector dependent regional technol ogy dependent technological rate change (TKLM: unitless). This technological change para meter, also called efficiency parameter or autonomous end-use energy intensity improvement parameter (the AEII), is a time-dependent index. It represents the annual rate of change in the relationship between the demand for energy services and actual energy use that would go on i ndependent of such other factors as energy prices and real incomes. The inclusion of an e xogenous end-use energy efficiency improvement parameter allows scenarios to be developed that incorporate different levels of improvement in end-use energy intensity. This parameter is used in the final calibration step in sectoral energy consumption for scenarios with specified final energy demand pathways (see Tables 57 and 58 for example values), and, Sjk j,k,l is described in Equation 60 as SPjk j,k,l , which represent the shares of the fuel modes j competing in obtaining the lowest total cost of energy services, Pk k,l at time m , to an end-sector k ,. Calculation of these shares is part of the ite rative process of the model solution of balancing supply and demand. In the final solution, the share values (Equation 60) used in determining the total costs of energy services to an end-sector k (Equation 59) are the lagged (by one time period) share values of the fuel-specific ener gy demand shares. The share value Sjk j,k,l depends on (1) bsjk j,k,l,m , the share or weight of a given fuel mode j in sector k , on (2) Pjk j,k,l,m the price of the service as provided by a given fuel mode j in sector k , on (3) rpjk j,k , the price elasticity of that service in sector k , on (4) X, which represents economic activity as a ratio income at time t and income in the base year, and on (5) ryjk j,k,l,m , the sector’s economic activity elasticity:57 

# ( ) ∑ •• • •

=

j ryjk rpjk m,l,k,j m,l,k,j ryjk rpjk m,l,k,j m,l,k,j l,k,j m,l,k,j k,j m,l,k,j

jk, 

### XPjk bsjk X Pjk bsjk Sjk (unitless) Eq. 69

The shares of the fuel modes ( Sjk j,k,l ) that, initially for the base year, are calculated from input parameters for weights ( bsjk j,k,l,m ), are re-calculated during the calibration process by adjusting these weights ( bsjk j,k,l,m for j =liquids, gas, solids and electricity). In addition, adjustments have to be made through the calibration process for the co rrect split between coal and biomass which fall both under “solids”. Demand for each secondary fuel A region’ s total demands for each of the secondary fuels j ( Fj

j,l,m where j are liquids, gas, coal and biomass; see Figure 4) are calculated as summations of the sectoral end-use fuel demands: 

# ∑ = k m,l,k,j m,l,j 

### Fjk Fj (EJ/year) Eq. 70
where Fjk j,k,l,m are the fuel mode demands by the end-use sectors. Secondary fuel demands, Fj j,l,m , of electricity and hydrogen are calculated in a more complex way, given that they are interdependent. This is described in the next section. Electricity and hydrogen interaction In the MiniC AM framework, each electricity and hydrogen production technology is described by a share, which represents the fraction of the tota l generation that is provided by that technology ( Su ui,l and Sh hi,l , respectively; Equations 54 and 43, respec tively). If electricity and hydrogen were used only by end-use sectors, then the shares could be multiplied by the total secondary fuelspecific end-use demand and their transformation coefficients ( gu ui,l,m and gh hi,l,m , respectively) and the fuel demand by each technology would be known as would electricity and hydrogen production after solving for the energy balance. Total electricity and hydrogen production are, however, mutually interdependent. The total generation of electricity is equal to the total am ount of electricity needed for end-uses plus the total amount needed for generation of hydrogen. The same is true for hydrogen production where the total hydrogen demand is e qual to that needed for end-u ses plus the hydrogen needed to generate electricity via fuel cells. This interaction requires a set of linear equations th at can be solved algebraically. They are solved for the total demand for hydrogen and electricity as a function of the end-use demands by means of the fuel shares ( Su ui,l ) for electricity generation by fuel cells and the fuel shares ( Sh hi,l ) for hydrogen production through electrolysis and the transformation coefficients ( gu ui,l,m and gh hi,l,m ). The consistency coefficient for the amount of elect ricity that is needed to generate hydrogen by electrolysis ( h coeff ) is calculated as the product of the share ( Sh hi,l ) of the hydrogen in generating hydrogen as secondary fuel from electricity and the transformation coefficient or energy intensity ( gh hi,l,m ) of that process. Similarly, the consistency co efficient for the amount of hydrogen that is needed to generate electrici ty from fuel cell technology ( e coeff ), is the product of the share ( Su ui,l ) of the electricity in generating electricity as sec ondary fuel from fuel cells and the transformation coefficient or energy intensity ( gu ui,l,m ) of that process. As long as the product of the two58 coefficients is less than one the total demands for hydrogen and electricity can be adjusted as follows:

coeff coeff coeff m,l,yelectricitjm,l,hydrogenj m,l,hydrogenj 

### h*e1 e Fj Fj Fj

− • +

= = =

= (EJ/year) Eq. 71

coeff coeff coeff m,l,hydrogenjm,l,yelectricitj m,l,electrictyj 

### h*e1 h Fj Fj Fj

− • +

= = =

= (EJ/year) Eq. 72
where

m,l,hil,hi coeff 

### ghShh •= (unitless) Eq. 73 and

m,l,uil,ui coeff 

### guSue •= (unitless) Eq. 74 where Sh hi,l is the share of hydrogen that is generated by electrolysis and gh hi,l,m is the inverse of the transformation efficiency, that is the energy intensity, of that process. Similarly, Su ui,l is the share of electricity that is generated from fuel cell technology and gu ui,l,m is the inverse of the efficiency of that process. The potential for an inconsistency exists if eith er of the denominators in Equations 71 or 72 is negative, that is, if either of the share coefficients ( Sh hi,l or Su ui,l ) is too large. This would be the case if, for example, most of the electricity w ould be generated by hydrogen and insufficient electricity would be generated by non-fuel ce ll sources to meet the demand for electrolytic hydrogen. The product of the two consistency coefficients ( e coeff and h coeff ) is therefore checked and if that product is greater than one, the shares ( Su ui,l and Sh hi,l ) are automatically rescaled and only then the process ou tlined is executed. In addition, the solution described above interact s with capacity limits in a complex manner since intermittent renewable technologies have no capacity limits for electricity generation, the amount of which is not known before these equations are solved. An iterative solution is implemented which converges within a few iterations. The electri city shares are re-balanced while keeping the hydropower share constant. Primary fuel demand Pri mary fuel demands are the total amounts of each fuel that are needed to meet the requirements for direct use of fuels in the end-use sectors pl us fuel needed as inputs to the transformation sectors (electricity, hydrogen, and synfuels). Primary fuel demand ( EDRIKL i,k,l E nergy D emand of R egional primary fuels I by end-use sector K

in regions L ) to meet the direct demands of fuel modes by the end-use sectors ( Fjk j,k,l,m ; see Equation 67) (see also Figure 4) is calculated by end-use sector for oil, gas, coal and biomass, respectively, as:

im,l,k,j l,k,i 

### gij Fjk EDRIKL •= i = oil, gas, coal or biomass (EJ/year) Eq. 75 where Fjk j,k,l,m are the fuel mode demands by end-use sectors k (EJ; Equation 67),59 gij i represents the relationship between the unref ined input producing one unit of secondary fuel; also called conversion intensity of oil, gas, coal, and biomass (GIJ: unitless or j of primary energy/J refined fuel), and i in EDRIKL ikl stands for regional primary fuel en ergy demand calculated from the regional l secondary fuel mode demand for each sector k

. Regional direct primary fuel demand s for oil, gas, coal and biomass ( EDRIL i,l : E nergy D emand of R egional primary fuels I in regions L ) are found by summing over the end-use sectors: 

# ∑ = k l,k,i m,l,i 

### EDRIKL EDRIL i = oil, gas, coal or biomass (EJ/year) Eq. 76

Primary sectoral end-use fuel demand ( EDRIKL i,k,l ) to meet synfuel genera tion demand is equal to the end-use demand for each synthetic fuel times the conversion ratio for the appropriate feedstock. The end-use demand for each synthetic fuel is, however, a shared demand as described under synfuel production (Equations 35 and 36). Th ese shares determine the demands of primary energy and need to be summed in a number of steps. The generated synliquids compete with refined oil; the generated syngas compete with pr ocessed gas. The primary fuel demands to meet synfuel generation demands are summed over the end-use sectors k after multiplication with the share values for each of the synfuels:

m,l,i,j k l,k,i m,l,i,j 

### SynShare EDRIKL SFuel • = 

# ∑ (EJ/year) Eq. 77
where j is the feedstock: gas, coal, or biomass, i is the produced crude or gas, EDRIKL i,k,l stands for regional sectoral end-use primary fuel energy demand (see Equation 75), and SynShare j,i,l,m are the shares (see Equation 35) of feedstocks j when producing liquids or gas i

. The primary fuel demands for synfuel production are then transformed to their primary fuel equivalents by multiplying with the appropriate conversion factor and summing over the synfuels ( i ); next they are added to the previously calcu lated direct primary fuel demands (Equation 76):

ji j m,l,i,j m,l,i m,l,i 

### gc SFuel EDRIL EDRIL • + = 

# ∑ i = oil, gas, coal or biomass (EJ/year) Eq. 78
where Sfuel j,i,l,m are the primary fuel demands for synfuel generation (Equation 77), and gc

j,i is an intensity conversion coefficient of synfuel production (GCI: input J/output J; a fuel source-specific (coal, gas, biomass) and synfuel-specific (liquid, gas) conversion coefficient that is the same for each region, does not ch ange over time and has values of 1.5. Primary fuel demand to meet hydrogen demand for fossil fuels is calculated as follows and added to the previously calculated primary fuel demands (Equation 78):

im,l,hil,hii m,l,hydrogenjm,l,i m,l,i 

### gijghSh Fj EDRIL EDRIL • • • + =
= i = oil, gas, coal or biomass (EJ/year) Eq. 79 where60 Fj j,l,m is the total secondary fuel demand (Equation 68) that needs to be shared out with the Sh hi,l share coefficient by fossil fuel type: oil, co al, gas, biomass, etc. and (re)transformed to primary fuel, Sh hi,,l are the shares of the competing fuels in generating hydrogen, gh hi,l,m is a conversion coefficient which is unitless (GHILM: units GJ/GJ); an exogenous regional time- and fuel specific parameter representing the ratio of Joules energy input to Joules hydrogen fuel generated, and gij i is the conversion intensity coefficient repr esenting the ratio of Joules primary energy as input and Joules of secondary energy generated (GIJ: unitless or GJ of primary energy/GJ refined fuel); gij i is an exogenous input parameter that is not time dependent nor region-specific. Primary fuel demand to meet electricity demand for fossil fuels is calculated as follows and added to the previously calculate d primary fuel demand (Equation 79):

im,l,uil,uim,l,yelectricitjm,l,i m,l,i 

### gijguiSu Fj EDRIL EDRIL • • • + =
= i=oil, gas, coal or biomass (EJ/year) Eq. 80 with the same methodology as described for hydrogen. The regional primary fuel demands ( EDRIL i,l,m ), thus determined, are the summed over the transformation sectors regional primary fuel demands for oil, gas, coal and biomass. In cases where the fuel market is global (as set by the user), the regional demands are summed to obtain a global fuel demand ( ∑ EDRIL i,l,m , summed over the regions l ). This demand must be met by an equivalent supply, which is described in the next section.


### 2.2.6 The energy bala nce and other markets

The variables for which the markets are solved are the global supplies and global demands of the primary fuels 22

. The global primary energy demands are the summations of the regional primary energy demands ( EDRIL ) as described above: 

# ∑ = l m,l,i m,i 

### EDRIL EDRI for oil, gas, coal, and biomass (EJ/year) Eq. 81
The global primary fossil fuel supplies required to meet the demands are based on the calculated potential regional supplies, which are based on the prices of the demanded fuels and the regional supply curves (see Section 2.2.2). Regional supplies ( ESRILM i,l, m ) ( E nergy S upply of R egional primary fuels I of regions L at time period M ) are set equal to the calculated supply ( ESILM i,l,,m ), that is, equal to the number of Joules that can be supplied regionally. In addition, to meet regional synfuel generation demand, the synfuel primary fuel demands ( Sfuel j,i,l,m ) as calculated in Equation 77 are added to the (raw) oil and gas supplies. Thus, 

# ∑ + = i m,l,i,j m,l,i m,l,i 

### Sfuel ESILM ESRILM for oil and gas (EJ/year) Eq. 82

22 With regard to emissions these are the markets of importance.61 where for Sfuel j,i,l,m , i denotes the produced liquid or gas and j denotes the feedstock of gas, coal, or biomass corresponding to the i indicators in the supply notations, ESILM i,l,,m and ESRILM i,l, m . To determine the global supplies, the regional primary fossil fuel supplies are summed over the regions: 

# ∑ = l m,l,i m,i 

### ESRILM ESRI oil, gas, coal, and biomass (EJ/year) Eq. 83 The balance between the supply ( ESRI i,m ) and demand ( EDRI i,m ) of the primary fuels is reached when the model is solved for an excess demand of zero – the difference between demand and supply. Thus, for any period, an equilibrium will exist when a set of prices are found for which all excess demands are zero. To reach an excess demand of zero, both demand and supply has to be determined iteratively. The part of the market-supply vector 23 that is comprised of the primary fossl fuels is determined by the ESRI i,m elements:

m,i mk 

### ESRI MrkPRD = oil, gas, coal Eq. 84
The part of the market-demand vector that is co mprised of the primary fossl fuels is determined by the EDRI i elements:

m,i mk 

### EDRI MrkDEM = oil, gas, coal Eq. 85

For the biomass market the market vector elements are comprised of AgLU biomass from dedicated biomass farms and ERB biomass:

MrkPrd mk=4 =ESRI i=4 + ∑ Agsup i=biomass,l where ESRI i=4 refers to the ERB related biomass and Agsup i=biomass,l refers to the AgLU generated biomass CDR i=biomass,l,m after converting calories to EJ, and

MrkDem mk=4 =EDRI i=4 + ∑ Agdem i=4=biomass,l where EDRI i=4 refers to the ERB related biomass and Agdem i=4=biomass,l refers to the AGLU demanded biomass after converting calories to EJ

For the greenhouse gas emission market the market vector elements are the emissions produced and the emission targets or constraints:

23 Fuel markets Agricultural product markets 1 = Oil 6 = Wood 2 = Gas 7 = Forward Wood 3 = Coal 8 = Food Grains 4 = Biomass 9 = Coarse Grains 10 = Oil Crops GHG market 11 = Miscellaneous Crops 5 = Carbon, Methane, etc. 12 = Pasture Products62 The part of the market-supply vector representing GHG emissions can be determined by carbon emissions produced (CemTot: Equation 114):


### CemTot MrkPRD 5mk 

### =
= Eq. 86
Analogously, the part of the market-demand vector representing GHG emissions can be determined by carbon emission targets (Emiss : exogenous):

m,l 5mk 

### Emiss MrkDEM =
= Eq. 87
The part of the market-supply vector comprised of the agricultural products is determined by agricultural supplies (AgSup i,l ) (see Part III) where supplies depend on yield. The supply, in brief, of crops, biomass, pasture, and forest products is calculated as the product of amount of land allocated to each land use (Equation 125) and that land’s use average yield (Equation 129). Agricultural supplies are expressed in calories for crops and animal products and in cubic meters wood for forest products. 

# ∑

= = 

### = nr

1l l,i 12:6mk 

### AgSup MrkPRD Eq. 88
where MrkPrd mk=6 = ∑ Agsup i=wood,l refers to wood produced; MrkPrd mk=7 = ∑ Agsup i=fwood,l refers to forward wood; MrkPrd mk=8 = ∑ Agsup i=beef_mutton,l refers to beef and mutton produced; MrkPrd mk=9 = ∑ Agsup i=foodgrains,l refers to food grains produced; MrkPrd mk=10 = ∑ Agsup i=coarsegrains,l refers to coarse grains produced; MrkPrd mk=11 = ∑ Agsup i=oilcrops,l refers to oilcrops produced; and MrkPrd mk=12 = ∑ Agsup i=misccorps,l referes to miscellaneous crops produced.

The part of the market-demand vector comprised of agricultural products is determined by agricultural demands ( AgDem i,l= CDR i,l,m , for crops, processed crops, and animal products: see Equation 120; AgDem i,l= WDR i,l,m , for wood products: see Equation 121). Agricultural demands are expressed as constant elasticity demand equatio ns where for the agricu ltural demands the total amount of calories demanded for each of the agricultural demands, CDR i,l,m , are further described in Part III, Equation 120, and de mands for cubic meters industria l wood and fuel wood are further described in Part III, Equation 121) Thus, 

# ∑

= = 

### = nr

1l l,i 12:6mk 

### AgDem MrkDEM Eq. 89
where MrkDem mk=6 = ∑ Agdem i=wood,l refers to the over the regions summed wood production for wood products and wood fuels WDR i=present,l,m ; MrkDem mk=7 = ∑ Agdem i=fwood,l refers to the over the regions summed forward wood production for wood products and wood fuels WDR i=forward,l,m ; MrkDem mk=8 = ∑ Agdem i=beef&mutton,l refers to the total amount of calories demanded from beef and mutton, CDR i=beef_mutton,l,m multiplied by PastOut which is th e ratio of pasture-based feed calories needed per calorie of animal product, which is based on land demand for pasture. The63 total amount of calories demanded from beef and mutton is first corrected for self consumption and fixed trade, however; MrkDem mk=9 = ∑ Agdem i=foodgrains,l refers to the sum of two types of foodgrain demands, CDR i=food grains,l,m ; MrkDem mk=10 = ∑ Agdem i=coarsegrains,l refers to the sum of two types of coarse grain demands, CDR i=coarse grains,l,m ; MrkDem mk=11 = ∑ Agdem i=oilcrops,l refers to the sum of two types of oil crop demands, CDR i=oilcrops,l,m ; and MrkDem mk=12 = ∑ Agdem i=misccorps,l refers to the summed two types of miscellaneous crop demands, CDR i=misccrops,l,m . Processed crop demand fractions are calculated an alogously to all other agricultural demands as CDR i=processedcrops,l,m , and corrected for net exports. These fractions are then multiplied by the overall demands for food grain, coarse grain, oil crop and miscellaneous crop and the results are added to the food grain, coarse grain, oil crop and miscellaneous crop demands, respectively. Pork and poultry demand fractions are calculated similarly to other agricultural demands as CDR i=poultry,l,m and CDR i=pork,l,m ,, multiplied by exogenous input of animal products and added to the food grain, coarse grain, oil crop and miscellaneous crop demands.
Excess demand is then calculated as:

mk mk mk 

### MrkPRD MrkDEM ExDem

− = Eq. 90 where mk refers to the markets as described above. Global market prices are retained in the market price array, P i,l=1,m . with the region indicator l set to one. When equilibrium occurs, the markets are said to “clear.” The mechanism for clearing the markets is through the solution algorithm, which adjusts market prices ( e.g. , primary fuel prices) until the excess demand is less than the solution criteria, typically a small number (less than one but greater than zero). The solution algorithm n eeds only to access the price, supply, demand, and excess demand information to operate. The solution algorithm adjusts prices until supplies and demands are balanced or the excess demand meets the solution criteria. Pr ices adjusted by the solution algorithm affect technology cost s, demand for inputs and sector outputs. Note that calibration is achieved through the ite rative process of recalculating the shares of the different technologies such that ultimately the en ergy service demands of the end-use sectors are met. Calibration is part of the iterative process of clearing the markets (see Section 2.2.8). After balancing the total demand and supply of each of the primary fuels in energy units (GJ) emissions can be calculated by multiplying the consumed energy with the appropriate emission coefficients, after subtracting the non-combus ting fuel amounts and after accounting for scrub technologies.


### 2.2.7 Imports, Exports64 The crux of MiniCAM’s treatment of trade is that any surplus (or deficit) in regional production relative to regional supply results in an implicit e xport (or import) of that fuel to other regions. Global demand is met, but the specific amount trad ed from one region to another is not defined. Only global and regional total net e xport (or import) volumes are defined.


### 2.2.8 Calibration procedures
There are two parts to the calibration process: ca libration to base year data and calibration to future scenario assumptions.
The base year calibration procedure adjusts parameters such that the following quantities match base year values for each region: (a) GDP , (b) electricity generation by fuel, (c) total energy use, (d) fuel-specific energy use by end-use sector, and (e) total CO 2 or carbon-equivalent emissions: GDP calibration is achieved by adjus ting regional labor productivity. Calibrating the participation of oil, gas, coal, bi omass, nuclear and hydro energy in the generationof electricity is achieved in a number of steps: First the weights of coal and biomass are reevaluated (the bssu ui,l,m parameters are re-scaled based on th e input end-use ener gy shares for each fuel); then, the weights of the input fuel shares, the bsu ui,l,m parameters for oil, gas, coal, biomass and nuclear energy are rescaled and the hydro weight, bsu ui,l,m is set equal to its fixed fuel share (needed by the electricity price routine). To calibrate the total and fuel-specific sectoral di stributions of the end-use sectors, the first check is on the transportation sector: if the new module for US transportation is activated and if there are discrepancies with external data (the tran sportation and industry sectoral shares are readjusted. Then, on the basis of input sector a nd secondary fuel-specific final demand data, the weights for oil, gas, coal, and electricity, bsjk jklm , are adjusted and the correct split between coal and biomass confirmed. Biomass supplies are adjusted if biomass supply in each region is not sufficient to meet demand (no biomass is assumed fo r the first period). Given that hydrogen fuels are not a factor in the base year, the fuel share we ight readjustments are limited to the fuels listed. The sectoral total energy use is calibrated by adjusting the sectoral technological efficiency parameters, T k,l,m , which determine levels of technologi cal change and innovation. These end-use efficiency parameters represent the level of sectoral technology ( e.g. , transportation, buildings, industry). The sectoral technological efficiency parameters, T k,l,m s, are rescaled based on the ratio of the summed energy services demands simulated and the summed energy service demands from the input data.

CO 2 emissions in the base year are calibrated by adjusting the carbon emission coefficients ( CO i : tons C/EJ/year), which are based on the carbon content of the fuels. Since CO 2 emissions coefficients can be based on different assumptions for energy units (higher versus lower heating values for example), this calibration assures th at accurate base year emissions values are obtained. Calibration to future paths for GDP and final energy use can be done when simulations are intended to meet certain criteria with regard to changes in economic activity and/or certain assumed developments in energy use, as in prescribed scenarios. For a prescribed GDP path step (a) is followed. Calibration to a regional path fo r final (or primary) energy consumption follows65 step (d). Note that exact regional calibrations to primary energy consumption cannot always be achieved due to different regional assumptions on conversion losses and primary-energy equivalents for non-fossil energy sources. Therefore, primary energy calibration is only assured for global calibration.


## 2.3 Calculating Greenhouse and Non-Greenhouse Gas Emission
One of the main focus points of MiniCAM’s inte grated assessment modeling is the calculation of the greenhouse gas emissions. In the MiniCAM, carbon dioxide, nitrous oxide, methane, sulfur dioxide, reactive gas, and halocarbon emissions ar e calculated once global fuel use has been determined. Reactive gas and halocarbon emissions are recent additions to the model and are not documented here, although the mathematical pr ocedures followed are identical to those for methane and nitrous oxide with the substitution of appropriate driver values and emissions coefficients.



### 2.3.1 Carbon dioxide emis sions from the ERB module In the ERB module carbon dioxide emissions from fossil fuel use are calculated after global fuel demands have been determined. Emissions are e qual to the carbon emission coefficient times the amount of fuel used. Emissions associated with energy transformations (synthetic fuels, electricity generation, and hydrogen produc tion) are allocated to the region where the transformation occurs. Global average carbon coefficients for oil, gas, and coal combustion, unconventional oil and biomass ( CO i : fuel-specific emission coefficients) re present carbon release, based on the carbon content of the fuel, during combustion or processing in teragrams carbon per EJ energy. The emissions coefficient for unconventional oil repr esents combustion’s carbon release related to oils from heavy oil deposits, tar sands, or oil shales. Emissions are calculated after a) gas flaring losses have been accounted for in the case of gas production (see Equation 92), b) the non-fuel use fraction has been subtracted, c) the amount of secondary fuel combusted w ith and without scrub technologies is determined, d) after synfuel production is accounted for; note that previously the raw fuels required for synfuel production had been a dded to primary fuel demands

ji j m,l,i,j m,l,i m,l,i 

### gc SFuel EDRIL EDRIL • + = 

# ∑ (see Equations 76 through 80). The raw fuel requirements (gas, coal and biomas s) for synfuel production are referred to in the next set of equations as

ji j m,l,i,j m,l,i 

### gc SFuel SynInput • = 

# ∑ (EJ/year) Eq. 91
where

Sfuel j,i,l,m are the primary fuel demands for s ynfuel generation (Equation 77), and gc

j,i is an intensity conversion co efficient of synfuel production.66 e) emissions from primary fuels can now be calculated. (a) Gas lost in gas production (which implicitly includes non-commercial gas use) due to flaring is calculated from flaring coefficients ( Flr1 , Flr2 , and Flr3 ) as FLR. Emissions due to burning of gas flaring are determined by flared gas burning parameters (Sbr1 , Sbr2 , and Sbr3 ) as SB l,m . Burning of shales is determined by shale burning parameters (Shale1, Shale2, and Shale3 ) as SHAL l,m . The equation that determines gas flaring ( FLR l,m ), gas burning ( SB l,m ) and shale burning ( SHAL l,m ) is illustrated in Equation 92 for gas flaring, where Flr1 is the initial proportion of flared gas lost, FLr2 is the ultimate fraction that is lost at time m and Flr3 is the number of years losing FLr2 ; ( ) ( ) ( )

3 3 Flr Nstep1m
2 Flr Nstep1m1 1m,l 

### Flr FlrFLR •− •−− 

### • = (unitless) Eq. 92 where Nstep equals 15 and m is the number of time periods since the base year, and Flrl1, Flrl2, and Flrl3 are regional gas flare parameters; we may s ubstitute the regional gas burn parameters Sbr1, Sbr2 and Sbr3 to calculate gas venting and burning, SB l,m used in Equation 93, or the regional shale burn parameters Shale1, Shale2 and Shale3 to calculate shale burning, SHAL l,m used in Equation 104. Emissions due to gas venting and flaring are calculated as follows:

m,l,gasi m,l m,l m,l gasil,gasflarei 

### ESILM )FLR1( FLR SBCO Cemissions

= = = 

### •

− ••= (MMTC) Eq. 93

(b) Carbon dioxide is not released from fossil fuel s due to fossil fuel used as asphalt, lubricants, and waxes; “1-SFEDIL” represents regional feed stock shares for oil, gas, coal, and biomass (unitless fractions). (c) The amount of secondary fuel combusted with and without scrub technologies needs to be determined. The fuel demanded for scrub tec hnologies and non-scrub technologies is calculated from the total electricity demanded ( Fj

j,l,m ) and the shares of the fuel-specific ( Su ui,l ) scrub and non-scrub technologies ( Ssu ui,l ) where u i is the technology. Thus the demanded electricity supply through fuel-specific scrub and non-scrub technologies, ESU ui,l,m , is calculated as follows where ESU ui,l,m is the energy in Joules that needs to be combusted as secondary energy to meet demand (and that needs to be converted to primary ener gy for emission calculations by multiplying with the conversion coefficients gu ui,l,m or gh hi,l,m and gij I ; see Equation 99).

m,l,jl,ui l,ui m,l,ui 

### FjSsuSu ESU ••= (EJ/year) Eq. 94 where ui is an indicator of any of the electricity generating technologies, Fj j,l,m is the total electricity ( j ) demand for region l at time m , Su ui,l is the share coefficient of the competing fu els (in the form of prices) in generating electricity, and Ssu ui,l are the electricity generation shares of the scrub- and non-scrub technologies.

For hydrogen production the demanded fuel supplies through fuel-specific scrub and non-scrub technologies, ESH hi,l,m , is calculated in an analogous fashion:

m,l,jl,hi l,hi m,l,hi 

### FjSshSh ESH ••= (EJ/year) Eq. 9567 where hi is an indicator of any of the hydrogen generating technologies, Fj j,l,m is the total hydrogen ( j ) demand for region l at time m , Sh hi,l is the share coefficient of the competing fu els (in the form of prices) in generating hydrogen, and Ssh hi,,l are the shares of the scrubbed and unscrubbed oil, or scrubbed and unscrubbed gas, or scrubbed and unscrubbed coal in generating hydrogen. (d) Synfuels are assumed to emit carbon via the appropriate product coefficient, that is, syngas is assumed to emit carbon by means of th e gas coefficient; and synoil by means of the oil carbon coefficient. The difference in emissions between the emissions of the product and that of the feedstock is assigned to the production sector. If carbon is sequestered during the synfuel production processes, that carbon is subtracted from the emissions of the production sector. Emissions from liquified gas are calculated as follows:

coali l,oili m,l,liqj,gasi coali gasi gas_synfueli 

### CO)SedFil1( SFuel CO SynInput Cemissions

= = == = = =


### • −• −• = (MMTC) Eq. 96

Emissions from synliquids derived from coal and syngas derived from coal are calculated as follows, which includes carbon removed in the tr ansformation process due to scrub technology if RemFrac 1,l is not equal to one:


### )mFracRe1( CO)SedFil1() SFuel CO)SedFil1( SFuel CO SynInput Cemissions l,1
gasi l,gasi m,l,gasj,coali coali l,oili m,l,liqj,coali coali coali
coal_synfueli 

### −• ⎥ ⎥ ⎥ ⎦ ⎤
⎢ ⎢ ⎢ ⎣ ⎡

• −• −• −• −•

=

= = == = = == = =

=
(MMTC) Eq. 97 where RemFrac 1,l is the fraction of the emissions that can be scrubbed during synfuel generation checked for maximum sequestration criteria, SeqFractMax (Equation 28). Emissions from synliquids derived from biomass and syngas derived from biomass are calculated as follows:



### )CO)SedFil1() SFuel CO)SedFil1( SFuel CO SynInput( Cemissions

gasi l,gasi m,l,gasj,biomassi biomassi l,oili m,l,liquidj,biomassi biomassi biomassi b_synfueli

= = = = = = = = = = =



### • −• − • −• − • = (MMTC) Eq. 98

(e) For conventional oil, gas, coal, and bi omass emissions are calculated as follows, which includes, if the RemFrac 2,j parameter is not equal to zero, carbon removal through scrubbing by utility scrub technology and hydrogen production scrub technology. Emissions from direct biomass burning are set to zero in most scenarios, however.68 

## ⎥ ⎥ ⎥ ⎦ ⎤
⎢ ⎢ ⎢ ⎣ ⎡

•• +••• −−•

•= )gijgh ESH gijgu ESU(mFracRe )SedFil1(FFcons CO Cemissions

im,him,l,hi im,l,uim,l,ui l,2 l,i

ii (MMTC) Eq. 99

where CO i is the emission coefficient of oil, gas, coal or biomass, SedFil i,l is the fraction of the feedstock that is not combusted, RemFrac 2,l is the fraction of the emissions that can be scrubbed during electricity and/or hydrogen generation, ESU ui,l,m is the energy in Joules (Equation 94) that needs to be combusted as secondary energy, electricity, to meet demand and that needs to be converted to primary energy for emission calculations by multiplying with the conversion coefficients gu ui,l,m and gij i . ESH hi,l,m is the energy in Joules (see Equation 94) that needs to be combusted as secondary energy, hydrogen, to meet demand and that needs to be converted to primary energy for emission calculations by multiplying with the conversion coefficients gh hi,l,m and gij i , gu ui,l,m is the transformation efficiency when electricity is produced, gh hi,l,m is the transformation efficiency when hydrogen is produced, gij i is the transformation efficiency from pr imary to secondary fuel conversion, and FFcons equals the primary fuel demanded for tr ansformation into secondary fuel supply, but for the primary fuels demanded for synfuel production, which implies that f or conventional oil, fossil fuel consump tion is represented by conventional plus unconventional oil; thus

onaloil unconventi i l,oili l,oili 

### ESIL EDRIL FFcons

= = = 

### + = (EJ/year) Eq. 100 refined gas fossil fuel consumption refe rs to refined gas consumption (EDRIL i=gas,l ) without the additional syngas (Syninput i=gas,l,m ) that can be consumed; thus
m,l,gasi l,i l,gasi 

### SynInput EDRIL FFcons

= = 

### − = (EJ/year) Eq. 101 f or conventional coal, fossil fuel consumption refers to EDRIL i=coal,l while subtracting for the coal that is used for gasification and/or liquefaction; thus

m,l,coali l,i l,coali 

### SynInput EDRIL FFcons

= = 

### − = (EJ/year) Eq. 102 and for biomass fuel, consumption refers to EDRIL i=biomass,l while subtracting for the biomass that is used for gasification and/or liquefaction; thus

m,l,biomassi l,i l,biomassi 

### SynInput EDRIL FFcons

= = 

### − = (EJ/year) Eq. 103
Emissions from shale oils are calculated based on shale oil burning ( SHAL ,l,m ) as follows: 

### )SedFil1(CO SHAL ESILM CO Cemissions l,i i m,l m,l,i i shaleoili 

### − • + • •=

= (MMTC) Eq. 104 where SHAL l,m is the shale burning fraction.
For each of the end-use sectors emissions are ba sed on fuel mode demands, attributing shale oil production emissions and flared emissions to th e industrial sector. Thus, for transportation, buildings and industry 

### )SedFil1(FjkCO2CO l,j j m,l,k,jj k 

### −••= 

# ∑ (MMTC) Eq. 10569 For hydrogen production carbon emissions are calcu lated from the primary fuel demands meeting hydrogen demand ( EDRIKL j,l,m ) from which the amounts potentially sequestered have to be subtracted:

hydrogen_scrub j l,j m,l,j j hydrogen 

### C)SedFil1( EDRIKL CO 2CO

− −• •=



# ∑ (MMTC) Eq. 106

Electric utilities carbon emissions are calculate d from the primary fuel demands meeting electricity demand ( EDRIKL j,l,m ) from which the amounts potentially sequestered have to be subtracted:

electricty_scrub j l,j m,l,j j electricty 

### C)SedFil1( EDRIKL CO 2CO

− −• •=



# ∑ (MMTC) Eq. 107

Emissions from the processing of limestone during cement production are input exogenously and are added to fossil emissions before emissi ons are passed to the climate module.


### 2.3.2 Carbon sequestered in the ERB module

If carbon is removed in synfuel generation processes, the removed carbon is kept track of as “carbon sequestered”.

l,1 gasi l,gasi m,l,gasj,coali coali l,oili m,l,liqj,coali coali coali seq mFracRe CO)SedFil1() SFuel CO)SedFil1( SFuel CO SynInput C • ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡

• −• −• −• −•

=

= = == = = == = = (tons C) Eq. 108

When emissions are removed by electric utilities ’ scrub technologies when oil, gas, or coal are combusted, the scrubbed carbon is calculate d from the total electricity demanded ( Fj

jlm ) and the shares of the fuel-specific ( Su ui,l ) scrub technologies ( Ssu ui,l ) where i is the scrub technology. The demanded electricity supply from fuel-specific scrub technologies, is based on ESU ui,l,m , when ui represents a scrub technology. The amount that is scrubbed and then sequestered is:

l,2 im,l,ui m,l,ui i scrub 

### mFracRegijgu ESUCOC ••••= (tons C) Eq. 109 where CO i is the carbon emission coefficient based on the carbon content of the fuel combusted (COI: tons C/EJ for oil, gas, or coal), ESU ui,l,m is the energy in Joules that needs to be combusted as secondary energy to meet demand and that needs to be converted to primary energy for emission calculations by multiplying with the conversion coefficients gu ui,l,m and gij i . During hydrogen production carbon can be removed through scrub technology when oil, gas, or coal is combusted and hi denotes a scrub technology in quantities calculated as above:

l,2 im,l,hi m,l,hi i scrub 

### mFracRegijgh ESHCOC • • ••= (tons C) Eq. 11070 where ESH hi,l,m and ghi i,l,m are equivalents to the utility variables (ESU ui,l,m and gu ui,l,m ), but specific to hydrogen generation.



### 2.3.3 Non-CO 2 

### Greenhouse Gas and Reactive Gas Emissions from the ERB module
Emissions of radiatively important substances other than CO 2 are more difficult to model since these emissions are not simply proportional to fuel use or other activity factors. These emissions are often by-products of some activity and de pend, in general, on the technology used. The “activity factor” can be any quantity calculated by the model. Units vary with the gases. The model works internally in terms of gas weights for the non-CO 2 greenhouse gases. When the calculations incorporate GWP (Global Warming Po tentials: see Table 4; or alternative indices) unit conversions are therefore not required. Radiatively important substances are often controlle d for reasons other than climate concerns and these reductions, are not modeled at the same leve l of detail as are changes within the energy system. Instead, an aggregate formulation based on income-driven controls is used. Reductions in these gases due to a climate policy are implemen ted using marginal abatement cost curves. Mathematically, non-CO 2 greenhouse gas emissions are modeled as follows 

## ( ) ( ) t t t t )icePr_C(MAC1USER1))Cap/GDP(Control1(Driver factor_EmEm

− •

− • −•• = (variable units) Eq. 111 where Em_factor is an emission factor, which is eith er input by technology, or derived from base year emissions. All CH 4 and N 2 O emissions factors are currently derived by the model directly from base year emissions data, Control(GDP/Cap t ) is an emission control due to non-climate policy ( e.g. , SO 2 or NO x specific), MAC(C_Price) t is a Marginal Abatement Curve (MAC) that represents emissions reductions due to climate policy as a function of the pr ice of carbon (or carbon-equivalents). The MAC’s used are adapted from EPA studies, and USER t is an user-defined reduction in emissions in tensity over time that represents efficiency improvements or adjustments for other factors not directly modeled.
Drivers and controls for each source are liste d in Appendix 6 and summarized in Table 4.
Table 4 ERB non-CO 2 emissions

Methane: CH 4 Industrial Sources Transportation (Mobile Sources) Coal Mining Electric Utilities (Stationary) Natural Gas Systems Petroleum Systems Wastewater Treatment Biofuel Combustion71 Nitrous oxide: N 2 O Elec Utilities (Stationary) Transportation (Mobile) Adiphic Acid Nitric Acid Most cost curves for non-CO2 greenhouse gases are estimated using bottom-up methodologies. Such curves often include reductions that are co st effective even without carbon cost pricing. Such “below zero” options can be dealt with in a number of ways. The MiniCAM contains an option to phase in any “below zero” options over a number time steps as specified by the user.

A cost curve example

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 50 100 150 200 Carbon pricepercent reduction in emissions

Figure 9 Cost curve example relating carbon prices to emission reductions

Each cost curve is, for a particular emissions sour ce, defined by two indices; the first specifies the gas ( e.g ., 1= ERB CH 4 ; 2= ERB N 2 O; 3= Ag CH 4 ; 4= Ag N 2 O), and a second index that defines the source. The cost curves can be defined for a variable number of points in each curve. An example cost curve is shown above. The x-axis is the carbon price, the y-axis is the percentage reduction in emissions that corresponds to the car bon fee. The model finds a percentage reduction in emissions through linear interpolations based on the carbon fee.
The model works in one of two modes. In one mode , as depicted in Equation 111, the base year emissions level for each of source is read in for every region. The model then calculates an emissions coefficient using the base year activity factor so that emissions are calibrated to base year emissions data. Alternatively, an emissions factor can be read-i n directly for each source sector and region. These methods can be applied separately by source and region as needed by the nature of the available data.


### 2.3.4 Emissions from the AgLU module72 While net land-use emissions are small relative to fossil fuel carbon emissions, their treatment can have a major impact on the initial cost of achieving any emissions mitigation objective ( e.g. , PNNL12021) In the AgLU calculations, carbon densities are app lied to each land-use category to provide an estimate of the carbon stock during each 15-year time step (see Table 81 in Appendix 6 for data estimates). Carbon emissions from land-use cha nge are calculated as the difference in carbon stock between periods. The land allocated to crops, pasture, forests, commercial biomass, and unmanaged land changes over time in response to changing demands, income, agricultural technologies, and prices of agricultural products. Each regional land-use category is assigned a carbon density for soils ( CSdens l,i=landuse : TgC/000ha) and above ground plant material ( CLdens l,i=landuse : TgC/000ha). Changes in land use are translated directly to changes in carbon stocks with net carbon emissions equal to the product of land use changes (h a/000) multiplied by carbon densities (Tg/000ha) for each land-use class. Historical land use changes are used when vege tation change and soil emissions are calculated for the first time period and for soils when the more refractory carbon decays (slower) in subsequent time periods. For crops, biomass, pasture, forests, and unm anaged land the carbon emissions from above ground are calculated as follows: 

# ∑

= − 

### ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

− • = nr

1l 1m,l,i m,l,i i,l m,l,i 

### Nstep Landuse Landuse CLdens EmLC (MMTC) Eq. 112
where i is an index for land use: crops, biomass, past ure, forests, and unmanaged land (see also Part III) For soils the carbon emissions are not only based on changes in land use, but also on a fractionation of the carbon according to decay rates. Thus, 60% of the soil carbon is assumed to decay when land use change occurs during the simulated time period PercDecay m =0.6); 30% of the soil carbon is assumed to only decay in the next time period PercDecay m-1 =0.3), and 10% of the soil carbon is assumed to decay during the second time period

− 30 years

− after the land use change occurs ( PercDecay m-2 =0.1): 

# ∑ ∑

= − = − 

### ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

− • • = nr

1l m

2mm 1m m m i,l m,i 

### Nstep Landuse Landuse PercDecay CSdens EmSC
(MMTC) Eq. 113



### 2.3.5 Non-CO 2 

### greenhouse gas emissions from the AgLU module

Variables and drivers for the calculation of non-CO 2 greenhouse gas emissions from the AgLU module are listed in Table 5. Methane emissions resulting from agricultural processes are due to enteric fermentation and animal waste (scaled to livestock production) and rice cultivation (scaled to overall crop production). Nitrous oxide em issions from agricultural processes result from73 fertilizer use (scaled to overall crop production) , and managed and unmanaged manure (scaled to livestock production).
Drivers and controls for each source are liste d in Appendix 6 and summarized in Table 5. Table 5 AgLU non-CO 2 emissions

Methane: CH 4 Land Use/Burning Enteric Fermentation Manure Management Rice Cultivation Agricultural Residue Burning Temperate Forest Fires

Nitrous oxide: N 2 O Human Sewage Agricultural Soils Manure Management Biomass Combustion Agricultural Residue Burning Land Use/Burning Unmanaged Manure Temperate Forest Fires



### 2.3.6 Total carbon emissions
Carbon emissions are accounted for in two separate categories, those from industry and fossil fuel use and those as net land-use emissions. This is necessary because land-use emissions have different implications for the carbon-cycle than industrial emissions.
Industrial emissions are the sum of emissions from fossil-fuel production and from cement production. Cement emissions are currently ex ogenously specified and are added to fossil emissions before they are passed to MAGICC.
Total net land-use emissions are calculated by the AgLU module as indicated above. Emissions from energy use can be reported for each point in time by fuel, end-use or transformation sector, and region. 

# ∑

= 

### = 4

coal,gas,oili i 

### Cemissions CemTot from oil, gas, and oil (MMTC) Eq. 114



### 2.3.7 Sulfur Dioxide Emissions
Sulfur dioxide is thought to be an important climate forcing agent. Once emitted into the atmosphere, sulfur dioxide forms sulfate aerosols wh ich are light in color, reflect sunlight, and act as a cooling agent. Aerosol particles tend to make clouds more dense and reflective. The magnitude of both these effects are very uncertain. The radiative effects of aerosol particles74 depends on the mix of particles, particularly the presence or absence of absorbing black carbon or soot particles. Emissions of sulfur dioxide depend primarily on the amount of coal and oil combusted and any emission controls in place. Emission controls in this context include de-sulfurization of fuels, using a lower sulfur source for the same fuel , and end-of-pipe sulfur removal. Additional anthropogenic sulfur sources include industrial process emissions, natural gas processing, use of traditional biomass fuels, and biomass burning (savanna burning and deforestation). Sulfur dioxide emission calculations are implem ented as shown in Equation 115 (Smith et al. 2002). Sulfur emissions from fossil fuel combusti on are modeled using region and fuel-specific sulfur contents (see Table 72 in Appendix 6), as h retention percentages (for coal) (see Table 71 in Appendix 6), and appropriate control percen tages (see Tables 73-79 in Appendix 6). The effect of advanced energy transformation technologies has a significant impact on sulfur emissions. Fuels used in advanced electric combustion technologies like combined-cycle gasification systems, hydrogen production, or the production of synthetic fuels are assumed to emit no, or almost no sulfur dioxide. Given that the MiniCAM is an aggregated model the average electricity generation efficiency for each region and time step for these technologies is specified as follows: if electric generation effici ency is 55% or greater, 99% of the sulfur is removed while zero removal is assumed for an average efficiency of 40% or less. A linear interpolation between these two efficiency values determines actual sulfur removal (Smith et al. 2002). For liquid fuels a final sulfur content is used to calculate f max , the maximum control percentage in Equation 115. This allows the futu re sulfur content of end-use petroleum products to be directly set as an input parameter. The degree (percentage) to which regional emissions will be controlled is si mulated as a logistic function of income based on the assumptions that attention to local and regional air pollution will increase with increased affluence (for which ther e is historical evidence) and that increasing affluence allows for an increase in resources that can be devoted to pollution controls (Smith et al. 2002). Income is measured in terms of purchasi ng power parity, which is, in this case a better measure of relative wealth than simply exchange-rate-based GDP

. 

## ( ) )f1(f1ent SulfurCont ent EnergyCont FuelUse EmSulfur control ash t −•−• • = (TgS) Eq. 115
where FuelUse is the regional and sectoral-specific fuel consumption in EJ, EnergyContent of each fuel is measured in GJ/kg, SulfureContent is a constant percentage over time, f ash

is the ash-retention fraction, and
fcontrol is determined as follows 

### ( ) 

### ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + =

τ − intmidpo t GDPpercap / GDPpercap c max 

### e1 f fcontrol Eq. 116

where f max is the ultimate reduction percentage, GDPpercap midpoint is the midpoint of the GDP control curve at which point emissions are reduced by 0.5*GDPpercap, and75 Τ is the per GDP per capita range over whic h the control percentage goes from 10% to 90% of f max . The regional, sectoral, and fuel-specific emissions can be summed to obtain and estimate of the global sulfur emissions. Only regional fuel consumption ( FuelUse ) and control percentages change in the future. The regional energy conten t, sulfur content, and ash retention are held constant at the 1990 base year emissions in the projections. How these regional base year emissions are obtained is described in Smith et al . (2001). In brief, 56% of 1990 world emissions were estimated as being derived from coal, 24% from oil, 15% from industrial processes and 3% from biomass burning.76 

# PART III
3. AgLU: the Agriculture Land Use module
Projections of global greenhouse gas emissions over the next century show that the agricultural sector will likely play a significant role in pot ential future increases in radiative forcing and climate change. Greenhouse gas emi ssions associated with agricultu re include methane, nitrous oxide and carbon dioxide (Sands and Leimbach 2001; Sands and Edmonds 2002; Edmonds et al. 1996) .

. The agricultural sector can reduce net emissions of carbon dioxide through the production of carbon-neutral biomass fuels to substitute for some portion of fossil fuels that would otherwise be used. Conversely, carbon dioxide emissions may result from deforestation

. Carbon, methane and nitrous oxide emissions may be reducible thr ough improved agriculture management techniques and/or technological innovation. Conversely, increasing demand of agriculture products may cause increasing emissions. The Agriculture and Land Use (AgLU) model was in itially developed to simu late global land use change and carbon emissions as responding to a car bon policy. Edmonds et al. (1996) constructed the first version of the AgLU model as an additi on to the ERB model. The current version (Sands and Leimbach 2001; Gillingham et al. 2002; Sands and Edmonds 2002) expands on the original version with a revised demand structure; a supply structure derived in analogy with the ERB logit sharing mechanism; and a future forests market th at eliminates instabilities in forest production. The AgLU model is a top-down economic model with sufficient structure to simulate regional land use change and the resulting emissions over on e century, that is, over the same time period as the ERB model. AgLU adds markets for compos ite crops, animal products, and forest products to the original ERB world markets for oil, gas, coal, and biomass (see Table 2 for a list of the final 12 markets) 24 . Commercial biomass, along with the shared (with ERB) driving forces of GDP and population provide the link between the en ergy structure of ERB and land use in AgLU. The AgLU model contains enough complexity to (1) provide estimates of carbon emissions from land-use change over the next century in re sponse to changing population, income, and agricultural technologies, (2) evaluate the role of commercial biomass and its impact on land use

24 ERB’s and AgLU’s markets (Table 2) Fuel markets Agricultural product markets 1 = Oil 6 = Wood 2 = Gas 7 = Forward Wood 3 = Coal 8 = Food Grains 4 = Biomass 9 = Coarse Grains 10 = Oil Crops Carbon market 11 = Miscellaneous Crops 5 = Carbon 12 = Pasture Products77 in a carbon-constrained world, and to (3) provi de estimates of methane and nitrous oxide emissions from the agricultural sector. AgLU is a dynamic 25 partial equilibrium economic model; it has 1990 as base year and performs its calculations in 15-year time steps as does E RB. The three primary drivers of land use change are population growth, income growth, and autonom ous increases in future crop yields. Even small changes in the rate of increase in future yields can have a large impact on the amount of cropland needed to maintain adequate diets, expr essed as calories in the AgLU model. Changes in the regional composition of consumption in respons e to higher incomes can also be important, especially if people in developing countries incr ease per-capita consumption of animal products to the level seen today in the United Stat es and Europe (Sands and Edmonds 2002). At the core of the AgLU model is a mechanism that allocates land among crops, pasture, forests, and unmanaged land such that economic return from each land use type in each region is maximized (see Figure 10). A joint probability distribution is defined over yield in each alternative land use. Yield is measured in units of calories per hectare for crops and pasture, and in cubic meter wood for forests. With additi onal information on prices and non-land cost of production, landowners are assumed to select th e land use with the greatest economic return calculated as revenue less non-land cost of pr oduction. With simplifying assumptions on the geographic distribution of yield, a reduced form solution can be obtained for the share of total land in each region allocated to each land use as a function of prices and non-land costs of production.

unmanaged pasture

biomass crops forest

Figure 10 Nested approach to land use Carbon densities appropriate for each land-use category provide an estimate of the carbon stock during each 15-year time step. Carbon emissions from land-use change are calculated as the difference in carbon stock between periods. Me thane emissions resulting from agricultural processes are due to enteric fermentation and an imal waste (scaled to livestock production) and rice cultivation (scaled to rice production area) . Nitrous oxide emissions from agricultural processes result from fertilizer use (scaled to overall crop producti on), and managed and unmanaged manure (scaled to livestock production).

25 The dynamic aspect results from the fact that change s that have occurred up to one point in time form the initial conditions for the calculations for the next point in time, analogous to the ERB module. Land allocation is, however, input as an initial condition at each point in time and then, for that point in time, recalculated as explained in the text below.78 The land allocation methodology used is adap ted from Clarke and Edmonds (1993) which considers the related problem of selecting a set of energy technologies to produce a given energy service at minimum cost.

World Market stand-alone or ERB Demand for Crops, Livestock, & Forest Products Supply of Crops, Livestock, Biomass Energy, &

Forest Products Local Price Local Taxes & Subsidies Climate

Technology Population

Income

Land Use

Emissions Biomass

Price 

### Supply Solution Mechanism Demand

Figure 11 AgLU schemata
Figure 11 shows how AgLU can be run as a stand- alone model once time paths of gross domestic product and population are specified for each regi on. Note that two other arrows impacting AgLU’s production are climate and technology. Climate impact as such can be simulated explicitly (with no input or feedback fro m MAGICC and/or SCENGEN outputs, however) through climate parameters. These climate para meters are multipliers representing climate, implemented to simulate changes in yield. Technological change is simulated as an autonomous process as in the ERB module. Commercial biom ass is simulated through regional-specific input parameters. The price of biomass calculation in the stand-alone AgLU is described in Section 3.2. When the AGLU module is linked with the ERB module, the price of biomass as feedstock (in $/GJ) is determined through a global market by adding biomass supply and demand to waste biomass supply and demand in the ERB module. The AgLU land use allocation responds to the demand for biomass as competitive fuel for en ergy production. Given a high enough biomass feedstock price, regions are capable of growi ng commercial biomass. Production and markets for biomass are separate from forest products; comme rcial biomass is envisioned as short-rotation trees, switch grass, etc. Biomass production is, in general, not competitive with the ERB biomass waste given that ERB’s biomass waste is produ ced at lower costs than commercial biomass. Commercial biomass is only produced if the global bi omass price is greater than the fixed cost of biomass production, which is an input parameter to the AgLU.79 

## 3.1 Data that are required
Agricultural data for base year calibration were obtained from the Food and Agricultural Organization (FAO 2000) of the United Nations. The four composite crops are built from FAO data on cereals, starchy roots, sugar crops, oil crops , fruit, and vegetables. Each individual crop is first converted from the original FAO units of k ilograms to calories using weights with units of kilocalories per kilogram. Individual crops are th en aggregated to composite crops (markets are active for food grains; coarse grains; oil crops; a nd other crops) using units of calories. A similar procedure is used for animal products. The thr ee animal composite products (beef and mutton; pork; and poultry) are built from FAO data on meat, animal fats, milk, and eg gs (trade in animal products between regions is fixed at 1990 levels; crops and forest products have global markets). Forest products use the original FAO units of c ubic meters (markets are for wood and for future wood). Productivity of field crops is calibrated in the m odel base year to match historical FAO data. However, these crop yields do not necessarily remain constant over the simulation time frame. Historical crop yields have been steadily incr easing over time and AgLU allows crop yields to increase in the future at a rate specified by the model user. Average productivity tends to fall, however, as agricultural production expands into more marginal lands. Conversely, average productivity will tend to increase if agricultural pr oduction in a region contracts. The net of the modeled agricultural productivity is th e combination of these two forces.


## 3.2 The price of biomass in AgLU in stand-alone mode
When the AgLU is executed in stand-alone mode or linked with ERB the role the carbon price plays in the model solution is analogous to the market prices for wood, crops and animal products. Once (regional) population and income over time are specified the remaining key inputs are the price of biomass and the carbon price. Increases in the carbon price create incentives for production of commercial biomass, given that the carbon price in part determines the price received by growers of commercial biomass. As a consequence, carbon price affects land allocation and, therefore, (carbon) emissions from land use change. Carbon prices can be provided exogenously or set to zero for land us e simulations without a carbon policy. Carbon prices are assumed to have units of $/metric ton C. When a carbon policy is implemented, it is represented by a positive carbon price; that is, emi ssions partake in the calculations of the fuel price by linking emissions with a carbon price. In the AgLU market equilibrium, in the stand-alone mode 26 , the price paid for biomass liquids will equal the price of refined petroleum-based liquids. Therefore, the price received for a biomass-based fuel is calculated with the Le ontief equation, similar to cost and price determinations of fuels described in the ERB module. The Leontief cost calculation needs the price of crude oil, the cost of refining oil to a transportation fuel ( OilTranCost ), and the nonenergy costs in the form of carbon content of oil ( OilCarb ) valued at the price of carbon ( P carbon ):

26 When the AgLU module is linked with the other MiniCAM modules the biomass price is part of the iterative supply and demand equilibrium solution with the AgLU land use allocation responding to the demand of biomass as competitive fuel for energy production and carbon price is not simulated

.80 

### OilCarb PtOilTranCos P P carbon oil moil biofuelfro 

### • + += ($/GJ) Eq. 117 where P oil is the price of crude oil $/GJ, OilTranCost is the cost of refining oil to a trans portation fuel ($/GJ) which is an equivalent to a combination of the non-fuel cost parameters in the ERB module, P carbon is the market price of carbon ($/metric ton or Kg C) which in principle does not differ from a carbon penalty as described in the ERB module when scrub technology in synfuel generation was described, and OilCarb is the carbon content of oil (kg C/GJ). Biomass-based liquid fuels are competitive with o il when the price of biomass feedstock adjusted by its net energy content after conversion plus the cost of transformation to liquid fuel, is equal to the price received for biomass-based fuels:


### t BioTranCos EtoBio P P biomass mbiomass biofuelfro 

### += ($/GJ) Eq. 118
where P biomass is the price of the biomass feedst ock ($/cubic meter biomass feedstock), EtoBio is the energy efficiency of converting so lid biomass to a liquid fuel (GJ of biofuel per metric ton of biomass) (is as the fuel cost ( g ) parameter in the traditional Leontief; see Section 2.2), and BioTranCost is the cost of transformation biom ass feedstock to liquid fuel ($/GJ) (is a nonfuel cost ( h ) parameter in the traditional Leontief; see Section 2.2).
If we solve for the price of biomass feedstock ( P biomass in $/m 3 C) using Equations 117 and 118 (in a market equilibrium, the price paid for bi omass liquids will equal the price of refined petroleum-based liquids), we obtain the price recei ved for biomass as a function of the crude oil price and the carbon price: 

## ( ) t BioTranCos tOilTranCos OilCarb PPEtoBio P carbon oil biomass 

### − + •+•= ($/m 3 C ) Eq. 119 To convert this biomass feedstock price from $/m 3 C to $/J it is multiplied by a conversion factor ( GJperGCAL which is an input parameter ).


## 3.3 AgLU markets
In the AgLU module, in the stand alone mode or linked with the ERB module, markets are modeled globally for each composite crop, for th e forest products, future forest products and biomass (after commercial biomass supply fro m the AgLU module is added to the biomass supply of waste if AgLU is linked to the ERB module). The markets are modeled regionally for composite animal and pasture products – if production of animal products is not sufficient to meet regional demand then grain must be impor ted to produce more animal products. International trade is an important mechanis m in AgLU allowing regions with a growing population to maintain adequate diets even wh en limited amounts of unmanaged land can be converted to agriculture.81 The composite crops in AgLU are traded freely am ong regions so that increases in global demand are supplied wherever it is least expensive to gr ow them. The four composite crop types are food grains, coarse grains, oil crops, and other crops. The food grains composite is a combination of wheat and rice, and is actually the total number of calories of wheat and rice produced within a region. The coarse grains composite crop in AgLU includes corn and all other cereals. Oil crops consist primarily of soybeans in the United States, but other oil crops are included. The “other crops” category includes the total calories of all re maining food crops, such as fruits, vegetables, and starchy roots. Even though trade in animal produ cts is limited, trade in coarse grains used for animal feed provides a mechanism for indirect trade in animal products. Animal products are limited to regional markets. Regional supply must equal regional demand, adjusted for trade in animal products between regions at fixed 1990 levels. This assumption is reasonable given the relatively small amount of tr ade between regions in animal products, due mostly to high transport costs for these products. Animal products are treated separately from grains because people in developing countries ar e assumed to consume a greater share of calories from animal products as per capita incomes rise. A composite forest product is used to meet demand for both industrial wood and fuel wood. Unlike the other products, forest products are meas ured in units of cubic meters. The forest product markets are also cleared globally with one world price. Two markets for forest products are brought into equilibrium within each AgLU time step. One market is for trees cut today and another market is for trees planted today but harvested in the future. The current market determines today’s price of forest products and th e forward market determines a future price of forest products. Current supply of forest products depends on the number of trees planted in the past. AgLU operates in 15-year time steps and assumes that tree lifetime is 45 years, or three model time steps. During any given AgLU time step, the vintag e of trees that was planted three time steps previously is cut to provide current supply of fore st products. Supply of current forest products is therefore fixed, and AgLU searches for a price th at brings global demand for industrial wood and fuelwood into equilibrium with this fixed global supply.



### 3.2.1 Demand
Demand for biomass is not computed directly. Instead, a price for biomass is exogenously supplied, which determines the amount of land dema nded to be dedicated to producing biomass. If the AgLU module is linked with the ERB modul e, determination of the biomass price is dependent on the linked model solution process. Consumer demand for food (calories) creates di rect demands for crops as well as indirect demands through animal products. FAO food balance data for 1990 were aggregated into three broad food categories: crops consumed directly, crops consumed indirectly as processed crops, and animal products. Direct crop consumption cons ists primarily of cereals, but also includes starchy roots, fruits and vegetables. Processe d crops include vegetable oils from oil crops, sweeteners from sugar crops, and alcoholic be verages. Animal products include meat, milk, butter, eggs, and animal fats. As shown in Figure 12, consumption of processed crops and animal products varies greatly across regions.82 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

NAM LAM WEU EEU FSU MEA AFR CPA SAS PAS PAO kcal per person

per day

Crops Processed Crops Animal Products

Figure 12 Food consumption in 11 regions in 1990 (from Sands and Leimbach 2001)
The demand equation for each of the crops, pro cessed crops, and animal products is expressed similarly to the (constant elasticity) demand equati ons for transportation, buildings and industry in the ERB module:

m,l,im,lm,l,i baseyearm,l,i m,l,i l,im,l,i 

### CNY P P A CDR jl jl


### ••• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•= β α

= (total calories demanded per year) Eq. 120 where CDR i,l,m is the demand for calories (total calories demanded per year in a region at time t ), i can be crops, processed crops, animal products, l is a region index, m is the point in time of the calculation, A i,l is a scaling coefficient (unitless) to calibrate the price and income feedback terms in the base year, P i,l,m is the market price of the commodity ($/calories consumed per person per day),
α

 i,l is the price elasticity, Y i,l,m is per-capita income index {$ GDP/population/($ GDP/population in base year) }, β i,l is the income elasticity for the calories de manded which implies it may differ from income elasticity in the demand equation for tran sportation, industry, or buildings (r yklm ), N l,m is the total population by region (which diffe rs from the population index, the ratio of the regional population at time t divided by the regional population in the base year, in the demand equation for energy services in the transportation and building sector), and C i,l,m is calories consumed per pe rson per day (multiplied by 365 to get yearly consumption). Demand for agricultural products may vary over tim e in two ways. The first is through directly varying C i,l,m (calories consumed) as an exogenous input by region and food category, providing a simple way to create scenarios of alternative future diets. The second way is through the price and83 income elasticities, α

 i,l and β i,l , respectively. Care must be taken in setting price and income elasticities so that simulated consumption stays within a plausible range in each region and food category. Income elasticities for crops and pro cessed crops are set to be small and positive, or zero. Similarly, price elasticities for these two food categories are se t to be small and negative, or zero. Data from Figure 11 suggest that consumpti on of animal products is more responsive to income and price than is consumption of crops and processed crops. Price elasticities for animal products are negative and greater (in absolute value) than price elasticities for crops and processed crops. This price feedback on consumpti on of animal products is necessary to find an AgLU market solution for scenarios with slow rates of improvement in crop yield over time. A broader view of global food supply and demand is shown in Table 6, which is a simplified food use table in units of kilocalories per person per day derived from FAO food balances. Total production of crops, including crops used in the production of animal products, is much larger than final demand for crops. Table 6 is structured with each column representing a production or consumption activity, and each row containing input s to these activities. For example, the firstrow of Table 6 shows all uses for crops. The first entry in the row for crops represents selfconsumption as seed and waste; the third entry is the amount of crops used as feed in the production of animal products.

Table 6 FAO production and demand exam ple (from Sands and Leimbach 2001) Production Activity Final Demand Crops Processed Crops Animal Products Food Other Uses Stock Change Total Production Crops 344 748 1,041 1,726 51 49 3,959 Processed Crops 0 0 2 532 80 -4 609 Animal Products 0 0 37 382 38 0 457

By comparing the number of calories of crops fed to animals with calories of animal products consumed as food, we see that the global averag e efficiency of converting crops into animal products is roughly 37%. The efficiency would be ev en lower if we considered the caloric content of pasture used as feed. This illustrates the importance of preferences for consumption of animal products as a driver of future land use changes. We could also compare the number of calories of crops used to make vegetable oils, sweeteners, and alcoholic beverages to the calories of these processed crops consumed as food. This conversion process has a much higher efficiency than converting crops into animal products. AgLU computes demand for two types of forest products: industrial wood and fuel wood.

m,lm,l,i baseyearm,l,i m,l,i l,im,l,i 

### NY P P A WDR jl jl


### •• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•= β α

= (total m 3 wood demanded per year) Eq. 121 where WDR i,l,m is industrial wood and fuel wo od in cubic meters demanded, i is industrial wood, or fuel wood, l is a region index, m is the point in time of the calculations, A i,l is used to calibrate base year demands ($/m 3 wood) to historical data by region84 P i,l,m /P i,l,m=baseyear is the price ratio of the commodity ($/m 3 wood/ same in base year),
α

 I,l is the price elasticity, Y i,l,m is per-capita income index {$ GDP/population/($ GDP/population in base year) }, β I,l is the income elasticity for the wood demanded which implies it differs from income elasticity in the demand equation for tran sportation, industry, or buildings (r yklm ), N l,m is the total population by region (which diffe rs from the population index, the ratio of the regional population at time t divided by the regional population in the base year, in the demand equation for energy services in the transportation and building sector). The price per cubic meter is assumed the same for industrial wood and fuel wood. Income elasticity is positive for industria l wood and negative for fuel w ood. With rising income, demand for industrial wood increases and demand for fuel wood decreases. Consumer demand for food grains and misce llaneous crops creates a demand for cropland directly. Demand for processed crops creates an indirect demand for cropland through the conversion of crops to vegetable oils, sweetener s, and alcoholic beverages. Demand for animal products creates an indirect demand for crop land an d pasture land used as animal feed but with a net loss of calories through the conversion from cr ops to animal products. Demand for biomass fuels also requires cropland especially in scenario s with high prices of fossil fuels or scenarios that place a high value on lim iting carbon dioxide emissions. Prices of agricultural products are adjusted wh en solutions are sought in balancing demand and supply while supply is determined by a land a llocation mechanism and assumptions on yield.



### 3.2.2 Land allocation
The land allocation diagram (Figure 10) shows how land is allocated among alternative land uses. During any model time step, some land is already committed to trees previously planted. Other land will be allocated among crops/biomass, pa sture, and newly planted trees. Crops and commercial biomass are grouped in a nest becau se we assume that land for growing crops competes directly with land for growing commercial biomass, e.g. , the case of a biomass crop such as switchgrass that could be used for energy. The land allocation scheme used in the AgLU mode l is based on profit; this is described next.
Profit rates Selection of land use is based on maximizing economic return at each location. Profit per hectare is equal to revenue (yield per hectare times pric e received) less production cost (yield per hectare times non-land cost per unit of output). This relationship is shown in Equation 122 where i is an index for land use type, l is the region index, and p is an index for geographical location within a region. 

# ( ) m,l,im,l,ip,m,l,ip,m,l,i 

### GPyr −•=π i = crops, biomass, pasture (annual $/ha) Eq. 122 where
π r i,l,m,p is the economic return of the land as a profit rate ($/ha-yr), i is

 an index for land use: crops, biomass, pasture, forests and unmanaged land l is the region index,85 p is an index for geographical location within a region, y i,l,m,p is yield per hectare for land use i in region j at location p (calories/ha), P i,l,m is the market price for the product produced by land use i (units $/yield units: calories or
m 3 ); prices of biomass are obtained from the ER B module; market prices of animal products (P i=animal ) and crops (P i=crops ) are solved for within the model; prices of pasture are obtained as shown in Equation 126 as dependent on crop-feed and pasture-feed calories, non-land costs per unit output, and the prices of crops and pasture; and G i,l,m is the non-land cost per unit of output in land use (units are $/yield units: calories or m 3 ). The profit rate ( π r) calculation for forest products is somewhat different because of the time lag between planting and harvest. The profit rate expre ssion for forest products includes a term that discounts future earnings into the present and leve lizes those earnings over 45 years; this forward price is denoted by m,l,i 

### P ~

. 

## ( ) 

# ( ) m,l,im,l,ip,m,l,i 45 p,m,l,i 

### GP ~ y 1r1 r r −•• −+ =π i = forests (annual $/ha) Eq. 123
where r is the interest rate ($/$ that is unitless). Land shares and yields Implicit in the equations below are the assumptions that a yield distribution exists for each land use where yield varies by geographic location, and that geographic location captures variation across temperature, precipitation, available sun light, soil quality, and slope of land. A joint probability distribution of yield is defined over each alternative land use within a region. Some locations may offer a high crop and pasture yield, but low forest yields. Other locations may show the opposite pattern, or other patte rns. Given a joint probability distribution of yield, information on prices received, and non-land costs of production, it is possible to determine the share of land allocated to each use and the average yield within each land use (Sands and Edmonds 2002).
To determine the share of land allocated to each la nd use type, land use shares would, in general, be calculated numerically, by summing over the la nd distributions implied in Equations 122 and 123. In the usual integrated modeling context, howev er, we wish to work on large regional scales. We use instead a reduced-form expression for land shares that effectively sums over the index p in Equations 122 and 123 based on maximizing profit rates which is at the core of finding land shares that provide the yields leading to maximum profits. This suggests using a Gumbel distribution because the maximum extreme of a Gu mbel distribution is again Gumbel. This is described in more detail in Appe ndix 5. An interesting feature of this land allocation mechanism is that for any given land use, average yield may fall as the amount of land allocated to that use increases. For example, if the most productive land is first allocated to crops, cropland can only expand into land less suitable for crops (Sands and Edmonds 2002). If all land within a region were allocated to a single use, say crops, then we could construct a distribution of crop yields, even though most of t hose yields would never be observed in practice. This distribution is characterized by a scale parameter and variance, and covers all potential yields for a crop, whether observed or not. The scale parameter can be thought of as a type of average, such as the mean or mode. We consid er this an intrinsic parameter of the yield distribution, i 

### y , because it is invariant with respect to pr ices or land use shares, and is an average across all locations that a particular crop could po ssibly be grown. This pa rameter is allowed to86 vary between time steps to represent autonomous increases in yield over time, represented by technological change (as described in Section 2.2 and below.) Yield distributions may be correlated. For example, land that produces high yields for crops is likely to also provide high yields for commercial biomass. Land use i will be selected only at locations where its profit rate is greater than that of all alternative land uses. Given a joint probability distribution for yield across alternativ e land uses, the set of potential yields at any particular location can be considered a random sample from that joint probability distribution. Since yield is a random variable, profit rate as defined by Equations 122 and 123 is also a random variable. With specific assumptions on the functional form of the yield distribution, the share of land allocated to use i is given by a logit share equation: 

# ∑ λ λ



### π π
=

p 1 p,m,l,i 1 m,l,i m,l,i 

### r r S (unitless) Eq. 124

where λ is a positive parameter that determines the rate that land shares change in response to a change in profit rate (see Section 2.2 for a desc ription of the logit share equation exponent), the denominator is summed over all possible uses for land, and
p,m,l,i 

### r π is the average profit rate using land i , which is the profit rate evaluated at an average or intrinsic yield, i 

### y , for land use i , where 

# ( ) m,l,im,l,ip,m,l,ip,m,l,i 

### GPyr

− • = π is the average profit rate for crops, biomass, and pasture; and 

## ( ) 

# ( ) m,l,im,l,ip,m,l,i 45 p,m,l,i 

### GP ~ y 1r1 r r −•• −+ =π is the average profit rate for new forests (see Equations 122 and 123). Land use for a specific purpose (see Figure 10) is calculated based on this logit-based share of total land

l m,l,im,l,i 

### Totalland S Landuse •= Eq. 125
This allocation mechanism is convenient because gr eater profit rates imply greater shares of land, it can be calculated quickly, and the shares sum to one. The profit rate calculations required for Equation 124 are given by Equations 122 (gen eral) or 123 (new forests). The profit rate calculation for pasture requires a price for pasture-based feed, P i=pasture . AgLU calculates the price of pasture indirectly from the market prices of animal products ( P i=animal ) and crops ( P i=crops ), both of which are solved for within the model. Given these two prices, P i=pasture is found by solving:

m,l,animali m,l,pasturei m,l,cropsim,l,animali 

### GPastOut P FeedOut P P

= = = = 

### + • +•= ($/cal) Eq. 126 where FeedOut is the ratio of crop-based feed calorie s needed per calorie of animal product; PastOut is the ratio of pasture-based feed calories n eeded per calorie of animal product, and G animal,l,m is the non-land cost per unit of output (an exogenous region and time-specific input parameter in units of $/cal or $/m 3 ).87 Observed Yield In the previous section, we showed how land use shares were calculated using profit rates evaluated at an intrinsic yield for each land use. In trinsic yield should be thought of as an average yield across all possible locations where a crop could be grown, regardless of the actual land use selected by profit-maximizing land owners. This intr insic yield does not vary with prices or land shares. However, the average yield of land fo r any given land type that survives the land allocation process is always greater than the corresponding intrinsic yield. We call this the observed average yield. In modeling practice, intrinsic yields and base y ear prices are used as calibration parameters to match base year data on observed average yiel d and land allocated to each use. The following equations show how the observed average yield is calculated for each land use type. An observed average profit rate for all land within a region is written as a function of the profit rates evaluated at intrinsic yields. This is shown in Equation 127 where p is an index across land use types. The observed average profit rate is gr eater than any of the individual (unobserved) profit rates. λ λ 

### ⎥

⎦ ⎤ ⎢ ⎣ ⎡ π=π 

# ∑

p 1 m,l,p,i m,l,i 

### r r ˆ ($/cal or $/m3) Eq. 127

where λ is a positive parameter that determines the rate that land shares change in response to a change in profit rate (unitless). An interesting result is that observed average profit rates ( i 

### r ˆ π ) are equal across land use types as indicated in Equation 127. This result is not de rived here, but is a consequence of assuming economic optimization. Clarke and Edmonds (1993) derive a similar result in the context of selecting a set of cost-minimizing energy technologies.



### r ˆ r ˆ i 

### π=π i = crops, biomass, pasture, forest ($/cal or $/m3) Eq. 128
We exploit this result to calculate an observed average yield ( i 

### y ˆ ) for each land use analogous to Equation 122. The observed average yield for crops, biomass, and pasture is given by

m,l,im,l,i i i 

### GP ˆ y ˆ

− π
= i = crops, biomass, pasture ($/cal) Eq. 129

where P i,l,m is the market price for the product produced by land use i (units $/yield units: calories or
m 3 ), and G i,l,m is the non-land cost per unit of output (an exogenous region and time-specific input parameter in units of $/cal or $/m 3

. Therefore, the observed average yield ( i 

### y ˆ ) is defined to be the yield at which the profit rate is equal to the observed profit rate i 

### r ˆ π . Average yield is multiplied by the amount of land, given by the land share from Equation 125, to determine supply
.88 

### 3.2.3 Supply
Supplies of crops, biomass, pasture, and forest products are calculated as average yields, multiplied by the amount of land allocated to each land use. Yield per hectare for land use i in region j at location p ( y i,l,p ; m 3 /ha/yr) are projected by multiplying the intrinsic yields with a climat e factor and a technological change factor. Animal products are produced with a combination of crop-based feed and pasture-based feed.

Technical change All of the technical change parameters, Tech i,m , are functions of time m according to

Nstep m,i1m,i m,i 

### )S1(Tech Tech + =

− (unitless) Eq. 130

where Tech i,m is the rate of technological change, set to one in the base year, S i,m is the technology change parameter used in calculating the rate of technological change over time (unitless: exogenous time- and purpose-specific), and Nstep is the time span from one time period to the next (15 years in MiniCAM) Equation 130 provides a way to simulate exogenous increases in yield, especially for crops. Crop yields will likely increase in the future, but th e rate of increase is uncertain. We simulate increases in AgLU crop yield in a range of 0.0% to 1.5% per year, with the amount of land needed for crops varying widely in later years depending on this assumption. 

### 3.2.4 Nested Model Previous equations cover the non-nested case fo r allocating land. However, Figure 10 shows a nested structure for land allocation. The top nest allocates land to a crops/biomass aggregate, but does not allocate land between them. The lower nest allocates land between crops and biomass depending on their relative profit rates. The share of land allocated to crops within the crops/biomass nest is given by Equation 131.

2 2 2
1 biomass 1 crops 1 crops

biomass crops crops 

### rr r
ss s λ λ λ



### π+π π

= + (unitless) Eq. 131

where λ 2 is a positive parameter that determines the rate that land shares change in response to a change in profit rate. If we calculate the following profit rate for the crops/biomass composite, 

# [ ] 2 2 2 1 biomass 1 crops biomass/crops 

### rr r λ λ λ 

### π+π= π ($/cal) Eq. 13289 then it can be used in Equation 124, the land share equation for the top nest, and in Equation 127, the observed average profit rate for all land uses. If the exponent term λ from the top nest is equal to λ 2 from the lower nest, then the land share equati ons collapse to a single nest. A single nest is used for the case where the correlation coefficient is the same between all yield distributions. If not, a nested model is used.90 

# Part IV

4. MAGICC: Model for the Asse ssment of Greenhouse-gas Induced Climate Change
MAGICC is a ‘Simple Climate Model’ as define d by the IPCC (1997) that uses a series of reduced-form models to emulate the behavior of fully three-dimensional, dynamic General Circulation Models (GCMs) (Wig ley and Raper 1992, 1987, 2002). MAGICC is coupled with the MiniCAM’s emission outputs for greenhouse gases ( carbon dioxide, nitrous oxide and methane) and aerosol or ozone precursor compounds (sul fur dioxide, nitrogen oxides, carbon monoxide, and volatile organic hydrocarbons). From these emissions MAGICC calculates greenhouse gas concentrations, radiative forcings, global mean temperature changes and sea level rise. MAGICC makes its calculations with annual time steps. Th e MINICAM currently inco rporates the version of MAGICC used to calculate the temperature and sea-level projections for the Intergovernmental Panel on Climate Change (IPCC) assessment reports. 27
MAGICC is a global energy balance model. Throug h its simple hierarchy the climate system is conceptualized as consisting of atmosphere, land, and ocean that absorb incoming solar radiation. Changes in the atmospheric concentrations of gr eenhouse gases and other forcing agents such as ozone and aerosols change the radiative balance of the earth system. This change is termed radiative forcing. A change in radiative fo rcing moves the earth system toward a (new) equilibrium temperature where incoming and outgoi ng radiation will be in balance. The ocean acts as a large heat reservoir slowing the approach to this temperature equilibrium. The net response to a change in radiative forcing is determined by the climate sensitivity, which is an input parameter for MAGICC. The value c hosen for the climate sensitivity is one of the principle determinants of the level of future cl imate change. Estimates of the climate sensitivity are generated by general circulation models, with each model having a characteristic climate sensitivity as well as historical reconstructions.
The version of MAGICC described here is the one used in the second assessment report (SAR; Kattenberg et al. 1996). A more recent version of MAGICC, as used in the third assessment report (TAR) can also be used with the MiniCAM. The TAR version of MAGICC is very similar in overall structure and operation, with some ch anges and additional feedbacks included (Wigley and Raper 2002).


## 4.1 Atmospheric Concentrations
Determining future atmospheric concentrations of greenhouse gases requires an emissions scenario and a specification of relevant atmosphe ric chemical processes, sinks, and other sources. Atmospheric concentrations in MAGICC are annua lly calculated from linearly interpolated larger time-step input emission, which are then converted into radiative forcing.

27 Kattenberg et al. (1996)91 MAGICC uses the historical record of greenhouse gas emissions and concentrations to assure consistency with specified emissions from 1990. In order to avoid an unrealistic jump in concentrations at the beginning of a model run, model parameters are adjusted so that the input emissions are consistent with the historical record. Emissions of methane and nitrous oxide are adjusted to conform with the historical record by changing the assumed (constant) natural source and not the gas-cycle parameters. An adjustment to net land-use change emissions is also applied over the first portion of the simulated period in order to match the land-use history assumed in MAGICC. 

### 4.1.1 Carbon Dioxide The atmospheric concentration of carbon dioxide is determined using a reduced form model of the carbon cycle. 28 The carbon dioxide sources considered are fossil fuel use and land-use changes and the sinks are the ocean and the terrest rial biosphere including enhanced biotic uptake due to carbon dioxide fertilization. The change in the amount of atmospheric carbon dioxide ( ∆ C in units of carbon weight.) is given by 29

fert ocean n 

### FFDE dt Cd −−+=

Δ Eq. 133

where in units of GtC/yr, E is total carbon emissions, which are the sum of fossil fuels and cement emissions. The latter are not calculated by this version of MiniCAM but are an exogenous input, D n is the carbon flux due to land-use changes. These can be either provided by the AgLU module or set as an exogenous input, F ocean is the carbon flux into the oceans (see below), and F fert is carbon storage changes due to terrestrial feedbacks, considered by MiniCAM to be due to carbon dioxide fertilization; a positive value for F fert indicates a transfer from the atmosphere to the terrestrial biosphere. Through this equation, the carbon cycle is balanced at each time step.
The ocean and carbon dioxide An increase in atmospheric levels of carbon dioxi de causes carbon dioxide to dissolve in ocean surface waters. This excess carbon is transported through the oceans by turbulent mixing and ocean currents until equilibrium is reached. This transport is represented by a set of oceanic “sinks” with different time scales that map ont o set fractions of the atmospheric carbon increase going into each sink. The parameter values are obtained from the results of a three-dimensional ocean circulation model. The time scales us ed in MAGICC are 330, 80, 20, and 1.6 years. 30 A fraction of any emissions simply stays in the at mosphere, representing the long-term equilibrium of the system. 31 A first-order approximation to account for ocean carbon-cycle non-linearity is obtained by using a second response function fo r large changes. The overall strength of the

28 Wigley (1983). Some notations have been changed. 29 In units of carbon weight. 30 Wigley (1991). See Maier-Reimer and Hasselmann (198 7) for the initial development of this formalism. 31 Dissolved carbon will eventually be removed by the system as biotic remains form sediments. However, over time scales of interest here, carbon di oxide stays in the ocean/atmosphere system.92 oceanic sink is specified by setting, as an input parameter, the total oceanic carbon sink ( F ocean in Eq. 133) over the decade of the 1980s. The terrestrial system and carbon dioxide The modeled change in atmospheric carbon dioxide concentrations due to the terrestrial biosphere will depend on the net deforesta tion and the amount of carbon dioxide fertilization. These depend on the amount of terrestrial biomass and how it is distributed. These are modeled by the terrestrial component of the model, which represents on a global level how carbon cycles through living plants into dead plant material, soils and back in to the atmosphere. In this version of the model, these calculations are independent of those in the AgLU module except for the possible input of global net-deforestation from AgLU to MAGICC. The model divides carbon stocks into four parts: fa st turnover, living biomass, detritus, and soil carbon. A fraction of the carbon contained in the biological material produced each year returns to the atmosphere immediately, that is, on time scales shorter than the yearly time step of the model. The remaining material rema ins either as living plants (per ennials, trees, etc.) or becomes detritus or part of the soil. A similar partition is applied at each time step to living plants and detritus. Some fraction of the carbon in living plants either returns to the atmosphe re or becomes part of either detritus or soil. Detritus either remains in place, returns to the atmosphere or is incorporated into soils. In addition, the amount of carbon in each categor y can be altered by la nd-use changes, which return carbon to the atmosphere. This is measured by the net deforestation, which is the gross deforestation minus forest regrowth, which is input to the model along with anthropogenic emissions. The time scale for litter production is al so the time scale for forest regrowth. This is the time scale over which the system will return to its initial state after a land-use change.
There are thus three time scales in the terrestrial carbon model: litter production (the transfer of carbon from living plant material to either detritus or soil), biological decay of detritus (transfer to either atmosphere or soil), and oxidation resulting in transfer to the atmosphere. These time scales are determined by the initial size of the four car bon reservoirs and the partitioning between them. For the parameters used, the regrowth (litter) time scale is ~ 60 years, the detritus decay time scale is ~ 1.4 years, and the oxidation time scale is ~ 209 years.
The effect of carbon dioxide fertilization is also in cluded as a hyperbolic formula that tends to go to zero as carbon dioxide concentrations reduce to a limiting value (31 ppmv) and to a constant value as concentrations tend to infinity.
Carbon balance In principle, all the parameters on the right side of Equation 133, above, could be specified. This would not, however, assure constancy between the specified parameters and the historical change in carbon dioxide concentrations. MAGICC is set up so that the primary input parameters for the carbon cycle model are the net deforestation over the 1980’s ( D n ) and mean ocean flux ( F

ocean ) over the 1980’s. The strength of the carbon dioxide feedback is adjusted to assure consistency between the two specified fluxes and the historical atmospheric concentrations over this period. There is no “missing sink” since the carbon cycle is balanced at all times.93 

### 4.1.2 Methane and other gases Modeling the other greenhouse gases is much si mpler. The atmospheric concentrations of methane, nitrous oxide, and the halocarbons are modeled as:



### τ − β = Δ CE dt Cd Eq. 134

where C is the atmospheric concentration of each gas, E is emissions, β is a numerical conversion factor, 32 and 

## τ is an atmospheric lifetime. Nitrous oxide is modeled with a single lifet ime, taken to be constant (~ 120 years). Methane has two primary sinks, oxidation by the hydroxyl radical and a small sink due to oxidation within soils. Therefore two sink terms a ppear in the equation for methane, one with a constant lifetime for the soil sink and another with a variable lifetime for atmospheric oxidation. The oxidation time scale depends on the con centration of various precursor gases ( CO , NO , and non-methane hydrocarbons), 33 however the most important effect is the dependence on methane concentration. As atmospheric methane concentrations increase, OH concentrations will decrease due to methane oxidation and therefore the methane lifet ime will increase. Thus methane has a positive feedback on its own lifetime. The formula for me thane lifetime was derived by fitting analytic forms to the results of a number of atmospheric chemistry models (Osborne and Wigley 1994). Methane in the troposphere eventually oxidizes to carbon dioxide and this small source of carbon dioxide is added to the direct emissions. There are a large number of halocarbons and, for simplicity, MAGICC treats theses in a limited number of specified groups. 34 The first group is composed of those substances that cause stratospheric ozone depletion. Emissions of these gases are controlled under the Montreal protocol and its amendments and are set e xogenously. The amount of stratospheric ozone depletion due to these gases is estimated thro ugh an equivalent chlorine loading concept. 34, 35
Stratospheric ozone depletion also results in cooling of the troposphere, thus offsetting some of the direct warming caused by these gases. The in itial (1990) strength of this warming effect is specified as an input parameter and is scaled in the future by the estimated level of stratospheric ozone depletion. Changes in stratospheric oz one will affect the amount of UV light that penetrates to lower levels, whic h may alter tropospheric chemistry, but this effect is not included in the model. Any such changes are likely to be small in comparison to the present uncertainties in tropospheric chemistry modeling results.

32 For methane β = 2.75TgCH 4 /ppbv, and for nitrous oxide β = 4.81TgN/ppbv. 33 The model includes the production of CO from methane oxidation (Osborn and Wigley 1994). 34 Wigley and Raper (1992). 35 Ramaswamy et al. (1992)94 Emissions for eight species of halocarbons that do not deplete ozone can be input into MAGICC. These are: HFC125, HFC134a, HFC143, HFC227, HFC245, CF4, C2F6, and SF6 . MAGICC can provide radiative forcing and concentrations fo r each of theses gases. Included are changes in the lifetimes of HFC ’s due to changes in the oxidation state of the atmosphere from methane and (in the “TAR version”) reactive gas emissions. Th e forcing due to remaining gases not explicitly covered can be added as an e xogenous input. Alternatively, emi ssions not explicitly covered can be “mapped” to the gas with the closest lifetime. 

### 4.1.3 Tropospheric ozone and aerosols Tropospheric ozone and aerosols are also considered by the model. The model does not calculate an explicit concentrations for these substances but, instead, uses relationships between emissions of precursor substances and th e resulting radiative forcing. The effect of tropospheric ozone is taken to be proportional to fossil fuel use for historical periods. In the “SAR version” of MAGICC used in MiniCAM 2001, future changes in ozone concentrations are due to methane oxidation only. The updated “TAR version” of MAGICC includes the effect of reactive gas emissions ( NOx , VOC , and CO ) on global ozone forcing. Sulfate aerosol forcing is split into a direct effect, taken to be proportional to sulfur dioxide emissions, and an indirect effect that is logar ithmic in emissions. Forcing is split into three regions (North Atlantic, Eurasia, and Southern Hemisphere) in or der to provide regional sulfur forcing data to SCENGEN (see below). Emissions of sulfur dioxide are passed to MAGICC from the rest of the MiniCAM. In the present vers ion of MAGICC, forcing from black and organic carbon is assumed to be proportional to sulfur dioxide emissions. The net aerosol forcing from biomass burning is also included and is taken to be proportional to gross deforestation, an output of the MAGICC carbon-cycle model. The base-year (1990) values of all aerosol forcings are specified as input parameters.


## 4.2 Radiative forcing
Given the atmospheric concentrations of gr eenhouse gases, MAGICC then calculates the resulting radiative forcing. This gives the amount of extra solar energy trapped by solar radiation. The direct radiative forcing caused by changing concentrations of carbon dioxide, methane, nitrous oxide, and CFC ’s are calculated using standard analytic approximations for the relationship between concentrati on and forcing for each gas. Forcing from ozone and aerosols is calculated as described above. No explicit concentration values are calculated for these substances. There are also a number of indirect effects. Tropospheric oxidization of methane produces ozone, which contributes a positive forcing proportional to methane concentrations. In the stratosphere, the oxidation of methane produces water vapor, which also contributes a positive forcing. The total radiative forcing is the sum of all the above: well mixed greenhouse gases, tropospheric ozone, aerosols, and indirect effects. Note th at spectral overlap between methane and nitrous oxide is taken into account in the forcing formul as. Other forcings, such as changes in solar irradiance or those due to volcanic activity can be included as external inputs.95 

## 4.3 Temperature change: terrestrial, atmospheric and in the ocean
A positive radiative forcing does not immediately translate into a global temperature increase 36 largely because of the heat capacity of the ocean s. The temperature change is found by modeling the global energy balance, that is, by considering how the extra energy added due to a change in radiative forcing is redistributed within the earth system. Four components of the climate system are considered: the atmosphere, the land surface, the ocean’s mixed layer, and the ocean’s deep water. The ocean energy balance over time is calculated us ing the global radiative energy balance and an upwelling-diffusion model of ocean heat transpor t. In the upwelling-diffusion model the average vertical temperature structure of the ocean is explicitly calculated. This estimates the thermal “lag” effects of the ocean along with an estimate of the thermal expansion of the ocean. Melting from small glaciers and estimated net changes in Antarctic and Greenland ice masses are added to this value to obtain total sea-level rise. 

### Terrestrial and atmospheric compartments The land surface and atmosphere are assumed to be instantly heated by ab sorbed solar radiation and by any heat that is transported from any ot her climate “box”. This assumption is justified because the time scale over which the land su rface and atmosphere will come into (rough) equilibrium with an addition heat source is much less than the yearly time steps used by the model. 

### The ocean Solar radiation not only heats the land surface and the atmosphere, it also heats the surface of the ocean. The oceans are divided into two parts: th e mixed layer which is the top layer of ~ 100 meters depth, and the deep ocean. The internal heat mixing time of the top layer is less than a year with mixing driven primarily by wind stress. Any heat input into the mixed layer is assumed to heat the entire mixed layer at once. Since water has a higher heat capacity than air or land, the heat storage effects of the mixed layer are important. Heat is transported from the mixed layer into th e deep ocean by two pr ocesses. One is heat diffusion, where heat from the warmer mixed layer diffuses downward into the colder deep ocean. The second process is associated with a la rge-scale circulation known as upwelling. Cold, salty water near the poles sinks down where it sp reads over most of the ocean floor (known as ocean “deep water”). The return flow is a genera l rising or upwelling over the rest of the ocean. In this framework, global average temperatures do not respond instantly to forcing changes because of thermal inertia of the mixed layer and heat transport into the deep ocean. Even though both upwelling and diffusio n result in downward heat transpor t over the bulk of the oceans, the two processes have different ma thematical dependencies and bot h are needed for a realistic

36 See Hoffert, Callegari, and Hsieh (1980) for a detailed description of this type of energy balance model. The specific model used here is described in Wigley and Raper (1987, 1991, 1992). Some notation has been changed.96 approximation of oceanic heat transport. 37 The primary parameters that characterize the strength of upwelling and diffusion components are th e upwelling velocity and vertical thermal diffusivity, respectively. If the deep ocean were neglected, the climate system would come into equilibrium with a radiative forcing change within a few years. When the deep ocean is included the time scale for equilibrium increases to one to several centu ries. Since the ocean carbon sink has a very long time scale response, the inclusion of the ocean is critical for modeling long-term climate effects. Results are sensitive to the upwelling rate, the ocean diffusivity rate ( κ ), and the deep-water temperature. Results are not very sensitive to the assumed depth of the mixed layer

− again highlighting the importance of the deep ocean. The model will produce a temperature change time series when given a time series of future greenhouse gas emissions, parameters describing h eat transport into the deep ocean, a climate sensitivity parameter, and a number of secondary parameters. Note that the climate model actually runs from 1795 onward, using the user speci fied parameters, instead of simply starting from the present day. This avoids the “cold start” problem that occurs when past radiative forcing changes are ignored.
The mathematical realization of this model is deve loped by considering the energy that flows into and out of each of the “boxes”. Each atmosphere , land, and mixed layer “box” can be described by an energy balance equation as follows:



### HFS dt dT −−∝ Eq. 135

where T is the average temperature, S is the amount of solar radiation absorbed, F is the net flux of radiation from the given box, and H represents other heat transport from the box in cluding diffusive/convective heat transport, latent heat transport, and for the mixed-layer o cean box, heat transport into the deep ocean. The equation describing the deep ocean is slightly more complicated since the vertical structure of the deep ocean must also be described. However when the equations for each “box” are added together many terms cancel. The final equa tion for global average energy balance is: 38


### ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ θ • ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

τ

τ

− τ −
= dt d h h dt dT TaT dt dT d

m d m

a m

a eq a Eq. 136

where the subscripts refer to the atmosphere (a), ocean mixed layer (m), and deep ocean (d), 

## τ is the radiative relaxation time scale,

37 Heat transport by upwelling is propo rtional to the temperature gradient (dT/dz) while diffusive transport is proportional to the second derivative (d 2 T/dz 2 ). Note that, since heat transport depends on the vertical (global average) ocean temperature profile this must be included in the model. The evolution of this profile is explicitly calculated in MAGICC. 38 From Hoffert, et al (1980)97 h is the height of the ocean mixed layer and deep ocean, and 

### θ is the mean potential temperature of the deep sea. The first term on the right hand side indicates th at, in the absence of the ocean, the atmospheric temperature would approach an equilibrium value ( T eq ) over an atmospheric equilibrium time scale, τ a , of about a month. Storage of heat in the mixed layer and deep ocean slows the approach to equilibrium. The mixed layer time scale is a fe w years and the deep ocean would take a couple centuries to come into equilibrium. The equilibrium temperature ( T eq ) is determined by the amount of incoming solar radiation, the planetary albedo and the climate sensitivity 39 . Much of the complexity of the climate system is folded into this last parameter, the climate sensitivity, which is the global mean temperature change that results from doubling of carbon dioxide concentrations. In MAGICC, as in all other current models of this type, the climate sensitivit y is assumed to be the same for all radiative forcings regardless of source. The energy balance equation for MAGICC is slightly more complex than this simple depiction. Each hemisphere contains land and ocean “boxes” with inter-box heat transfer coefficients tuned to match the mean seasonal temperature cycle over each hemisphere. Different temperature sensitivities for land and ocean areas are included. For the same increase in solar radiation, the land will heat up more than the ocean since the ocean is more reflective. The land/ocean and hemispheric split also allows regionally -differentiated aerosol forcing. The assumptions that are made in order to constr uct a model such as this are not only necessary so that calculations can be performed in a reasonable amount of time but are also prudent since further detail is not warranted given the level of uncertainty as to the magnitude and nature of anthropogenic climate change. For example the “b est estimate” values of the climate sensitivity vary by a factor of two, while some argue for an even larger range. If, in the future, the basic response of the climate system becomes better know n, it will be useful to examine some of the other simplifying assumptions that are used in su ch models. At present, however, the global-mean results produced by almost any of the more comp lex models can be reproduced by varying model parameters in MAGICC, the two most important of which are the climate sensitivity and the ocean thermal diffusivity.



## 4.4 Sea-level rise
In addition to temperature cha nge, global mean sea-level rise 40 is also calculated by MAGICC. As temperatures increase, sea-level will rise due to thermal expansion of the ocean, melting of small glaciers, and possible changes in Antarctic and Greenland ice sheets. Such projections, particularly at large time scal es, are quite uncertain. The relative magnitude of each component varies. Ocean thermal expansion will increase as long as temperatures are increasing, and even long after radiative forc ing is stabilized. Greenland runoff and Antarctic accumulation (see below) will follow the atmospheri c temperature trend closely, but will depend

39 The climate sensitivity is the global mean temperature change that results from the forcing equivalent to a doubling of carbon dioxide concentrations 40 Further details can be found in Wigley and Raper (1993).98 on the net balance of a changing melt rate and pr ecipitation, which are very uncertain. If warming becomes significant enough, practically all the mass in small terrestrial glaciers will disappear. Thermal expansion of the ocean is a complex phenomenon, which will depend on the temperature distribution within the ocean and the expansion pr operties of sea-water. The expansion rate of sea-water depends on pressure, temperature and salinity, and is well quantified. The results of the model, as with any model of sea-level rise, are sensitive to the choice of the initial temperature profile. The vertical distribution of ocean temperature is calculated as part of the upwelling-diffusion model described above. This can be used to calcu late thermal expansion of the ocean. However, use of the global-mean ocean temperature profile directly would lead to errors since the coefficient of thermal expansion is highl y non-linear with respect to temperature. 41 To reduce this problem, the ocean is divided into six regions by latitude. The mean ocean temperature profile for each hemisphere is scaled for each latitudina l region by the “doubling of carbon dioxide concentration” equilibrium results from a coupled atmospheric/ocean general circulation model. As a result, thermal expansion is greater at hi gher latitudes. The global-mean expansion is found by averaging the zonal values, weight ed by the ocean area of each zone. As global temperatures have increased over the la st century glaciers have been melting and this trend is expected to continue under the influe nce of greenhouse warming. The contribution of small glaciers to sea level change, z , is modeled with a simple mass balance equation.



### τ ΔΤ•β • −+−

= )zz(z dt dz 0 Eq. 137

where z is sea-level change
τ is the characteristic time scale of melting, β denotes a melting rate response parameter to a temperature increase, Δ T. Glaciers have a sensitivity β to melting in response to a global temperature increase ΔΤ . They melt in a characteristic time scale, 

## τ , starting with an initial ice mass z o (in units of sea level rise). These parameters are calibrated using 0.46 ± 0.2 mm /yr as the estimate of the historical glacial melt. 42 A set of low, medium, and high estimates we re derived for these parameters (Wigley and Raper, 1993). All but one percent of the land ice on earth is contained in the Antarctic and Greenland ice sheets. 43 Overall, these ice masses change very slowly — the turnover time scales 44 are about 13,000 and 6,000 years respectively. However the total equivalent sea-level rise of the ice contained in the large ice sheets is approximately 70 meters — so even a relatively small change can be significant. Note that only melting or calving of ice that is grounded

− resting on continental or sea-floor rock

− can contribute to sea-level rise.

41 In other words, the amount that sea water will expand under a, say, one degree increase in temperature depends very strongly on the pre-existing temperature of the water. 42 Meier (1993), for the period 1900-1961. 43 For a detailed discussion of the Greenland and Antartic ice sheets see Oe rlemans et al. (1992). 44 Total ice mass divided by the accumulation rate.99 The Greenland ice sheet is assumed to have a se nsitivity to warming of 0.3 ± 0.2 mm/yr/°C, with the positive value indicating a net increase in sea- level with warming. Accumulation changes in Antarctica are assumed to be -0.3 ± 0.1 mm/yr/°C, a decrease in sea-level with temperature. The West Antarctic ice sheet sensitivity is assumed to be 0.1 ± 0.1 mm/yr/°C. Large scale ice changes are assumed to be 0.0± 0.1 mm/yr, that is, zero for the middle case. The level of uncertainty about the state of the Antarctic and Greenland is greater than that for small glaciers because of increased measurement difficulties. There are three main effects that control the net contribution of the ice sheets to sea-level: (1) accumulation of snow, (2) ablation, and (3) ice sheet dynamics. Ablation

− the process that removes snow and ice

− increases as temperature increases. Accumulation, however, in creases up to 0° centigrade, and then decreases rapidly. The net direct effect of temperature is the sum of these two processes. Ice sheet dynamics in the form of ice sheets di scharging into the ocean through runoff and calving of icebergs will have an impact on sea-level ri se. The West Antarctic ice sheet is an area of particular concern since this ice sheet is groun ded below sea level. Some think that the West Antarctic ice sheet might therefore be particular ly sensitive to changes in sea level or melting rates. Neither the Antarctic nor Greenland ice sheets are likely to be in an equilibrium state. The assumptions used in MAGICC are that both ice sh eets were in balance some time before the historical (since 1880) warming trend. Contributions to sea-level rise are split into four sources: (1) Greenland, (2) possible instability in the West Antarctic ice sheet, (3) changes in Antarctic accumulation, and (4) other large-scale changes in Antarctic ice sheet dynamics. All but the last are assumed to be linearly proportional to temper ature. Since ice-sheet dynamic time-scales are large, the latter factor (4) is assumed to be constant for the time horizons of interest. For many applications, regional details of climat e change are required. A global energy balance model such as MAGICC cannot supply regiona l temperature changes and cannot produce any meaningful results for precipitation. Therefore, global average temperature change, calculated as described above (Equation 136), is used to scale re sults from general circulation models in order to obtain regional climate change scenarios. This procedure is described in the next section.100 

# Part V 5. SCENGEN: Regional Climate Change Scenario Generator
MAGICC, described above, calculates global average temperature changes due to changes in radiative forcing from emissions of greenhouse gase s and other forcing agents as simulated by the MiniCAM. As was noted, regionally-differentiated aerosol forcings for hemisphere-specific land and ocean can be calculated. To transform globa l change into still more spatially explicit information the climate change generator SCE NGEN (Hulme, Jiang, and Wigley 1995) can be linked to MAGICC’s modules. SCENGEN generates global and regional climate- change scenarios based on one or more GCM experiments. SCENGEN results are based on a library of data generated from a number of general circulation models. For each GCM, the spatial pattern of results for variables such as mean, minimum, and maximum temperatures; wind speed; and precipitation are stored. Surface level results are needed for most climate impacts assessments and therefore a latitude-longitude grid of results is stored with all variables interpolated onto the same 5° by 5° grid. GCM results are then normalized through the pa ttern-scaling method developed by Hulme et al. (2000). For example, temperature change is expr essed as the difference between the value found in the GCM projection and the climatological (1961-1990) average, divided by the global temperature change. For temperature and most other variables the difference between a control (no greenhouse forcing) model run and the greenhous e run is scaled by the climate sensitivity of the model. 45 After normalization the resulting spatially explicit data are multiplied by a factor representing the global-mean temperature cha nge as determined by MAGICC resulting in spatially explicit ERB-scenario related climate change. The climate change produced by each GCM is di fferent, in both magnitude and pattern. This is due to the different, and necessarily limited, repres entations of the relevant physical processes in each GCM and also indicates our uncertain knowle dge of the climate system. Therefore, no one model can be considered definitive and this un certainty must be included in assessments. SCENGEN allows two methods of indicating this un certainty. The first, and most widely used, is to use different GCM patterns for the impacts as sessment (see below) and compare results. Using normalized patterns is particularly useful since this allows the effect of the different GCM patterns to be seen without the additional effect of the different climate change magnitudes. However, the normalized patterns from a set of mode ls can also be averaged together to form a composite climate change pattern. In the compos ite pattern, differences between models tend to cancel out, and the resulting pattern will tend to reflect where the models agree. High and low scenarios can also be generated by assuming that the models in the database are drawn from a normal distribution and generating scenarios that reflect the 90% limits of the distribution. While this assumption is open to question, this procedur e does allow derivation of a reasonable range of scenarios based on a set of GCM results.

45 For some variables, such as precipitation and wind speed, changes are expressed as percentages.101 The use of composite scenarios in an impact asse ssment gives, in a rough sense, the location, and magnitude at that location, of the most likely impacts. The high and low scenarios give rough limits on impacts. However composite scenarios may not have the same level of spatial variability as individual GCM results. Using the SCENGEN approach results in losing so me degree of consistency between assumptions used to generate global average temperature and sea-level changes and regional patterns emerging the assumptions underlying the GCMs. Moreover, w ith composite scenarios, the assumptions of the individual GCMs do not relate to the averaged outputs. A GCM, or as sometimes referred to now as ‘earth systems models’ can take a month or more to run for just one scenario; and even then it ma y not include all the relevant greenhouse gases, carbon cycle aspects, and atmospheric chemistry, ocean, and other relevant feedbacks. Moreover, this does not guarantee that the relationship between , say, temperature and precipitation in a given model run is fully representative of the relationships in the ‘real world’. Therefore it is prudent to explore multiple scenarios. Approaches such as described here and ot her types of simplified climate models, are useful for their speed and fl exibility. With SCENGEN, multiple scenarios can be explored quickly.102 

# PART VI

7. Results
When using an integrated assessment model like MiniCAM, model output will be directed to the specific questions asked. Here we will only pr ovide some results to give an overview of MiniCAM’s types of output. 

### Global outputs The initial long-term scenarios that the Inter governmental Panel of Climate Change (IPCC) developed between 1990 and 1992 were widely used in the analysis of possible climate change, its impacts, and options for mitigation. After ev aluation of the scenarios in 1995, a new set of scenarios were developed, the so-called SRES scenarios, based on the Special Report on Emissions Scenarios Terms of Reference which ca lled for the use of multiple models, an “open process” and a better understanding of the drivi ng forces, such as demographic development, socio-economic development, and technical cha nge. Scenarios were defined as “alternative images of how the future might unfold” (Nakicenovic et al. (2000). The results shown below are based on MiniCAM’s pa rticipation in the SRES scenario analyses.
The scenarios are based on “business as usual” ; that is, the scenarios incorporate neither additional climate mitigation options nor adaptation to projected climate change. The descriptions that follow are from Nakicenovic et al. (2000), Moss et al. (2001), and Smith et al. (2002). In the “convergent and rapid growth” scenario (A1) economic devel opment is robust and population growth moderate. Population peaks around the year 2065. Over time, current distinctions between “poor” and “rich” countries decrease. There is great improvement in the health and social conditions of most. With incr eases in income, dietary patterns shift towards increased consumption of meat and dairy products . Land use shifts to sprawling urbanization and intensification of agriculture. In the analyses shown, the A1B represents a balance across all energy sources with high energy demands through which coal becomes a particularly important energy source by the end of the century; A1 G represents a scenario where technological developments focus on fossil fuels, particularly unconventional natural gas; the A1T represents a focus on energy efficiency and non-fossil energy sources. The B1 scenario describes a “convergent and su stainable” world with the same population peak around 2065 as in the A1 scenario, but with ra pid changes in economic structures toward a service and information economy with reductions in material intensity, and the introduction of clean and resource-efficient technologies. Global solutions are sought to economic, social, and environmental sustainability, including improved equity. The A2 scenario may be called the “heterogeneous with delayed development” scenario. In this scenario, economic development in Africa and parts of Asia and Latin America is less vigorous because of continuing institutional setbacks. Peopl e, ideas, and capital are less mobile so that technology diffuses slowly with the result that international disparities in productivity, and hence income per capita, are maintained or increased. Fertility rates decline only slowly, although they vary among regions, and high population growth re sults in low global income per capita. Some103 attention is given to potential local and regiona l environmental damage (sulfur and particulate emissions are reduced in Asia) but this is not uniform (SO 2 emissions increase in Africa as a result of the intensified exploitation of coal). In the “heterogeneous world with local sustainab ility” scenario (B2) there is increased concern for environmental and social sustainability. Global average income per capita grows at a moderate rate. International income differences are reduced considerably . Education and welfare programs lead to reductions in mortality and fe rtility. Environmental protection is a priority, although strategies to address global environmenta l challenges are less successful than in other scenarios. There is a gradual reduction in the cu rrent reliance on fossil resources, but the energy supply is still predominately h ydrocarbon-based even in 2100. Another way of capturing this scenario would be by calling it the “coal-use” sc enario. Scenario results show relatively high sulfur emissions offsetting the high carbon emissions. In this world, there is less wealth for adaptation, but social networks would be presumed to be more effective. Ecosystems would also be under less stress than in the rapid growth scenario. Figure 13 illustrates results with regard to economic strength in the four SRES scenarios analyzed by PNNL’s modelling group using the MiniCAM2 001 model documented in this manuscript. Average incomes are highest for th e A1 scenario, followed, in orde r, by the B1 scenario, the B2 scenario and the A2 scenario.

Global Averaged Incomes (GDP(mer) (1990 US$ per year per capita)) for the IPCC SRES Scenarios

$0 $10 $20 $30 $40 $50 $60 $70 $80

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2 A 1

B1

B2

A 2

Figure 13 Average incomes, globally, in the four SRES scenarios

Electricity generation in the four scenarios reflect the SRES storylines as follows: The A1 scenario, as a “rapid growth” scenario shows through 2085 by far the highest generation capacity. The A1G scenario lags behind the A1B and A1T scenarios, having focused on unconventional natural gas, while A1B’s “balan ced” approach had more coal technologies104 available and A1T focused on energy efficiency. Electricity generation is low in the B1 scenario, the scenario with high population growth (as the A1 scenario) and reductions in material intensity. The A2 pathway of electricity generation shows clearly its “delayed development”, while the B2 scenario can be best considered as the most “average” and “to be expected” pathway.

Global Electricity Generation (EJ pe r year) in the IPCC SRES Scenarios

0 100 200 300 400 500 600 700

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 14 Total global electricity generation in th e four SRES scenarios showing divergence in the A1 scenario due to various assumptions with regard to fossil fuel use and technological change.

Diets in the scenarios show much the same pattern as income with the A1 scenario allowing for the highest caloric intake, followed by the B1, B2 , and A2 scenarios. Th e B2 and A2 scenarios diverge more for caloric intake compared to income, however.105 Average Diets (kcal per person per year) in the IPCC SRES Scenarios

2200 2300 2400 2500 2600 2700 2800 2900

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 15 Average diets in the four SRES scen arios with divergence in the A1 scenario. Given that the MiniCAM model is not just an “energy and economics” model but that it includes the agriculture module AgLU, not only differences in diets can be determined based on different driver-related assumptions, but also agricultura l GHG emissions like methane and nitrous oxides (Figures 19-20). Figure 16 shows total carbon-equivalent emissions. Fr om this graph it can be observed that in the A2 scenario, the “delayed devel opment” scenario emissions emissions surpass those of the A1B and A1G scenarios as is the case for electr icity generation (Figure 14). The A1T and A1G scenarios are reversed in order however (ant hropogenic carbon-equivale nt emissions versus electricity), given that the A1T scenario focused non-fossil energy resources. Projected carbon dioxide concentrations, calculate d in the MAGICC module are shown in Figure 17. The carbon dioxide concentrations pattern s are analogous to the total anthropogenic GHG emissions.106 Global Carbon-Equivalent Emissions (G tCE per year) in the IPCC SRES Scenarios

0 5 10 15 20 25 30 35 40 45 50

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 16 Global anthropogenic carbon-equivalent emissions in the four SRES scenarios

MAGICC's Global Carbon Dioxide Concentrations (ppm) in the IPCC SRES Scenarios

300 400 500 600 700 800 900 1000 1100

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 17 Carbon dioxide concentrations in the four SRES scenarios107 Total sulfur, nitrous oxide and methane emissions are shown in the next set of figures. Sulfur emissions are assumed to decline over time but for the A2 scenario, with the B1 scenario showing the largest decline. These patterns can be explained by the assumptions that in the A2 scenario with its delayed development invest ments are less in sulfur removal while very dependent on coal in, for example, Africa. The B1 scenario is based on assumptions of clean and efficient technologies pared with low material inte nsity which results in a decline of global sulfur emissions. Nitrous oxide emissions show a similar scenario differentiation as sulfur emissions. Methane emission, however, show the A1B scenar io with largest declines over time, while following the same path as the other A1 and the B1 and B2 scenarios throug h 2065. Only the A2 scenario stands out with increasing methane emissions over time, illustrating its “delayed development’ aspects.

Total Global Sulfur Emissions (TgS per year) in the IPCC SRES Scenarios

0 10 20 30 40 50 60 70 80 90 100

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 18 Sulfur emissions in the four SRES s cenarios with divergence in the A1 scenarios.108 Total Agricultural Nitrous Oxide Emissions (TgN per year) in the IPCC SRES Scenarios

3 4 5 6 7 8 9 10

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 19 Nitrous oxide emissions in the four SRES scenarios with divergence in the A1 scenarios.

Total Global Agricultural Methane Em issions (Tg CH4 per year) in the IPCC SRES Scenarios

120 130 140 150 160 170 180

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 20 Methane emissions in the four SRES s cenarios with divergence in the A1 scenarios.109 Temperature changes and sea-level rise are cal culated in the MAGICC module and are illustrated in the next two graphs for the SRES scenario s. Differences between the scenarios remain considerably smaller than the changes over time from 1990 through the end of the twenty-first century. Global Temeperature Rise (degrees C) in the IPCC SRES Scenarios

0 0.5

1 1.5

2 2.5

3 3.5

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 21 Projected global temperatures in the SRES scenarios

Global Sealevel Rise (cm) in the IPCC SRES Scenarios

0 10 20 30 40 50 60 70

1990 2005 2020 2035 2050 2065 2080 2095 A1B A1G A1T A2 B1 B2

Figure 22 Projected sea-level rise in the SRES scenarios110 

### Regional outputs Regional differences are illustrated in the next set of graphs. Most regions show a steady increase in personal income in the projections of the B2 scenario. Exceptions are the Former Soviet Union and Korea. These gradual patterns do not translate into similar regional patterns of caloric intake, howev er, although both the Former Soviet Union and Korea show the largest differences.

Regional Differences over Time in In come (GDP (mer) (1990 US$ per year per capita)) for IPCC's B2 Scenario

$0.00 $10.00 $20.00 $30.00 $40.00 $50.00 $60.00 $70.00

01 US A 02 C an

ada

03 W E UR

04 Ja p an

05 A&NZ 06 FS U

0 7 Ace

n P 08

Mid

E a s t
0

9 Africa

10 LatAmerica 11 S E A

s i a 12 E E U 13 K o rea 14 I ndia 1990 2005 2020 2035 2050 2065 2080 2095

Figure 23 Regional differences in inco me over time in IPCC’s B2 scenario

Changes in caloric intake (Figure 24) are partly due to assumed changes in diet from cereals to animal proteins related to increased income, especially in developi ng economies. Developed economies still show, however, large increases in expected electricity consumption (Figure 25).111 Regional Differences over Time in Calo ric Intake (Kcal per year per person) in IPCC's B2 Scenario

1900 2100 2300 2500 2700 2900 3100 3300 3500

0 0 Glo b a l 01 US A

0 2

Can

a d a
0 3 WE

UR

04 Ja p an

0 5 A&N Z 0 6

F SU

0 7 Ace

n P 08

MidEast 09 Africa

10

Lat

A

m e rica

1 1 S E A

s i a 12 E E U

1 3

Kore a
1

4

In dia 1990 2005 2020 2035 2050 2065 2080 2095

Figure 24 Regional differences in caloric intake in IPCC’s B2 scenario

Figure 26 shows the regional changes over time in total anthropogenic emissions, showing still different patterns, which can be explained not on ly by electricity consumption (Figure 24), but also by differences in industrialization, energy efficiencies and changes in land use. Note that Canada’s average carbon equivalent emissions are ex pected to change significantly more that the USA’s; also note that Korea’s emissions increased significantly between 1990 and 2005 but then increased only minimally afterwards in this B2 scenario.112 Regional Differences over Time in Elect ricity Consumption per Capita (GJ per year per capita)

0 10 20 30 40 50 60 70 80 90

0 1 USA

0 2 Canada
0 3 W

EUR 04 Ja

p a n 05 A&NZ 06 F S U

0 7 Ac

en

P

0 8 Mid

E

a s t
0

9 Afr

i ca

1 0 L

a tA

me

r i ca

11

SEAsia
1 2 EE

U 13 Korea

1 4 I nd

ia 1990 2005 2020 2035 2050 2065 2080 2095

Figure 25 Regional differences in electricity co nsumption per capita in IPCC’s B2 scenario

Regional Differences in Base Year Values and Projections in Antrhropogenic Emissions per Capita (metric tons CE per year per capita) in IPCC's B2 Scenario

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

00

G

lo b a l 01 U S A

0 2

C

an

a d a
0 3 WEUR
0 4

Japan 05 A & NZ 06 F SU

0 7 A

c enP

0 8 MidEa s t
0 9 A

f r ica

1 0

LatAmer i ca 11 SEAsia
1 2

E E U

13 K o rea
1 4

In di

a 1990 2005 2020 2035 2050 2065 2080 2095

Figure 26 Regional differences in anthropoge nic emissions in IPCC’s B2 scenario113 

### Policy cases Results of carbon policy implantation are illustrated in the next set of graphs. Carbon policies can be implemented by determining a carbon f ee upfront and having the model solve for the emissions that are then constraint by an increase in fuel prices. Alternatively emission limits can be set upfront as targets to be met at a certain point in time and have the model solve for the necessary carbon fees to be imposed to reach the targets. Thirdly, thr ough scrub technology and sequestration some relaxation of carbon constraint s can be implemented by actively sequestering carbon such that atmospheric emissions remain constraint. Figure 27 illustrates for the USA, for the B2 scenario results of implementing emission constraints such that by the year 2050 carbon dioxi de atmospheric concentrations either reach 450 or 550 MM ppm, with and without the sequestration option. Those results are compared with the unconstrained B2 scenario emissions. Figure 28 illustrates the amounts of carbon captured in the USA (MMtC).

USA's Anthropogenic Emissions (MMtCE pe r year) in IPCC's B2 Scenario with Policy Implemetations of Emission C onstraints with and without Carbon Sequestration

0 500 1000 1500 2000 2500 3000 3500

1990 2005 2020 2035 2050 2065 2080 2095 B2 B2-550 B2-450 B2seq-550 B2seq-450

Figure 27 An example of anthropogenic carbon-equivalent emissions under carbon policy implementations in the USA IPCC’s B2 scenario114 Carbon Sequestered (MMtC) in the USA's IPCC's B2 Scenario with a Sequestration Policy

-600 -500 -400 -300 -200 -100

0

1990 2005 2020 2035 2050 2065 2080 2095 B2 B2-550 B2-450 B2seq-550 B2seq-450

Figure 28 Carbon sequestered in the USA IPCC’s B2 carbon policy scenarios

Carbon policies do not only impact carbon emissions but also impact emissions from industrial processes such as sulfur dioxide. Figure 29 illustr ates the beneficial effects on sulfur emissions. When emissions are sequestered the beneficial effect is reduced given that the emission constraints are relaxed due to the sequestration offset. Figure 30 shows examples of the carbon prices required to constrain the emissions at the 450 and 550 ppm levels with and without the sequestration options. Carbon prices will be scenario and policy dependent. Timing of policy implementati ons is an important factor in this case.115 Sulfur emissions over time (TgS) in the USA's IPCC B2 Scenario with and without Carbon Policies

0 2 4 6 8 10 12

1990 2005 2020 2035 2050 2065 2080 B2 B2-550 B2-450 B2seq-550 B2seq-450

B2B2seq450

B2-450

Figure 29 Sulfur emissions in the USA in IPCC’s B2 carbon policy scenarios

Carbon prices in the IPCC SRES B2 Senarios with carbon pollcies imposed in the form of emission with and without sequestration

$0 $200 $400 $600 $800 $1,000 $1,200 $1,400 $1,600

1990 2005 2020 2035 2050 2065 2080 2095Carbon prices ($90 per ton C)

B2-450 B2seq-450 B2-550 B2seq-550

Figure 30 Carbon prices in the USA in IPCC’s B2 carbon policy scenarios116 

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Sands 1996. “Agriculture, Land Use, and Commercial Biomass Energy.” Report No. PNNL-SA-27726, Pacific Northwest National Laboratories, Washington, DC. 25 pp. Fisher-Vanden, K.A., R. Baron, J.A. Edmonds, H. M. Pitcher, R.D. Sands and M.A. Wise. 1993. Calibration of the Second Generation Model, draft report. Pacific Northwest National Laboratory, Washington, D.C. Fisher-Vanden, K.A., P.R. Shukla, J.A. Edmonds , S.H. Kim, and H.M. Pitcher. 1997. “Carbon Taxes and India,” Energy Economics 19, 289-325. Food and Agriculture Organization of the United Nations: FAOSTAT data base available at http://apps.fao.org , 2000. Gillingham et al. 2002 In preparation Hulme, M., T. Jiang, and T.M.L. Wigley. 1995. "SCENGEN, a climate change scenario generator, a user manual." (Norwich, U.K.: Clima tic Research Unit, University of East Anglia). Hoffert, M.I., A.J. Callegari, and C.-T. Hsieh. 1980 . "The role of deep sea heat storage in the secular response to climate forcing." 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Sands. 1999. “The Economics of the Kyoto Protocol,” in The Costs of the Kyoto Protocol: A Multi-Model Eval uation, John Weyant (ed.), special issue of The Energy Journal. Maier-Reimer, E., and K. Hasselmann. 1987. Transport and storage of CO 2in the ocean -- an inorganic ocean-circulation carbon cycle model, Climate Dynamics, 2 , 63-90. Meier, M.F., 1993: Ice, climate and sea level; do we know what is happening? (In) Ice in the Climate System , NATO ASI Series Vol. I 12 (ed. W.R. Peltier), Springer-Verlag, Berlin, Germany, 141-160. Miller, Ronald E., and Peter D. Blair. 1985. Input-Output Analysis: F oundations and Extensions. Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Moss, Richard H., Antoinette L. Brenkert, and Elizabeth L. Malone 2001. Vulnerability to Climate Change: A Quantitative Approach . 2001. PNNL-SA-33642, Pacific Northwest National Laboratory, Washington, DC. http://www.pnl .gov/globalchange/projects/vul/index.htm Oerlemans, J. and Fortuin, J.P.F., 1992: Sens itivity of glaciers and small ice caps to greenhouse warming. Science 258 , 115-117. Ramaswamy, V., Schwarzkopf, M.D. and Shine, K.P. 1992. Radiative forcing of climate from halocarbon-induced global stratospheric ozone loss. Nature 355 , 810-812. Rogner, H. 1997. An Assessment of World H ydrocarbon Resources. Annual Review of Energy and the Environment 22: 217-262. Sands, R.D. and J.A. Edmonds, 2002 Climate Change Impacts for the Conterminous USA: An Integrated Assessment; In preparation Sands, R.D., J.A. Edmonds, S.H. Kim, C.N. MacC racken, and M.A. Wise. 1998. “The Cost of Mitigating United States Carbon Emissions in th e Post-2000 Period,” in Economic Modelling of Climate Change: OECD Workshop Report, 17-18 Se ptember, 1998. Organization for Economic Cooperation and Development, Paris, France. Sands, R. and Leimbach, M.: Modeling Agriculture and Land Use in an Integrated Assessment Framework. Climatic Change 56(1) (2003), pp.185-210. Smith, Steven. J., Hugh Pitcher and T.M.L. Wigl ey. 2001. “Global and regional anthropogenic sulfur dioxide emissions”. Global and Planetary Change 29:99-119 Smith, Steven. J., Hugh Pitcher and T.M.L. Wigley. 2002. “Future Sulfur Dioxide Emissions”, submitted to Climatic Change Wigley, T.M.L. and S.C.B. Raper. 2002. "Reasons for larger warming projections in the IPCC Third Assessment Report " J Climate 15 (20), 2945-2952; and http://sedac.ciesin.org/mva/magicc/MAGICC.html118 Wigley, T.M.L., 1991. A simple inverse carbon cycle model. Global Biogeochemical Cycles 5: 373-382. Wigley, T.M.L., 1993. Balancing the carbon budget. Implications for projections of future carbon dioxide concentration changes. Tellus 45B, 409-425. Wigley, T.M.L. and Raper, S.C.B., 1987. Thermal expansion of sea water associated with global warming. Nature 330, 127-131. Wigley, T.M.L. and Raper, S.C.B., 1992. Implica tions for climate and sea level of revised IPCC emissions scenarios. Nature 357, 293-300. Wigley, T.M.L. and Raper, S.C.B., 1993. Future changes in global-mean temperature and sea level. (In) Climate and Sea Level Change: Observa tions, Projections and Implications (eds. R.A. Warrick, E.M. Barrow and T.M.L. Wigley), Cambridge University Press, Cambridge, U.K., 111-133. Wigley, T.M.L. and Raper, S.C.B., 1995. An heur istic model for sea level rise due to the melting of small glaciers. Geophysical Research Letters (submitted).

# Appendices to the Model Documentation for the MiniCAM

Antoinette L. Brenkert Steven J. Smith Son H. Kim Hugh M. Pitcher

July 2003

Prepared for the United States Environmental Protection Agency under Contracts AGRDW89939464-01 and AGRDW89939645-01

Joint Global Change Research Institute, College Park, MD Pacific Northwest National Laboratory Operated by Battelle for the U.S. Department of Energy2 TABLE OF CONTENTS

TABLE OF TA BLES ...............................................................................................................
....................................... 3 APPENDIX 1: INDICES AND NOMENCLATURE; DEFINITIONS; UNITS ........................................................ 5 Indices and nom enclature ......................................................................................................

....................................... 5 Units .........................................................................................................................

.................................................... 5 APPENDIX 2: MINICAM REGIONS ...................................................................................................
....................... 6 APPENDIX 3: DESCRIPTION OF THE SOLUTION ALGORITHMS ................................................................... 8 Bisection Routine .............................................................................................................

............................................ 8 Newton-Raphson Routine ........................................................................................................

.................................... 8 APPENDIX 4: DEMOGRAPHICS ......................................................................................................
....................... 10 APPENDIX 5: LAND ALLOCATION IN THE AG LU MO DULE ......................................................................... 11 Land allo cation ...............................................................................................................

............................................ 11 APPENDIX 6: LIST OF TABLES ....................................................................................................
.......................... 13 Demographics and GDP parameters ...............................................................................................

........................... 13 Energy supply and extr action parameters .......................................................................................

............................ 15 Primary energy pr ice parameters ...............................................................................................

................................. 23 Parameters to calculate pr ices of sec ondary fu els .............................................................................

......................... 25 Synfuel production parameters .................................................................................................

.................................. 25 Hydrogen production B2 Scenario ...............................................................................................

.............................. 28 Electricity generation B2 Scenario ............................................................................................

................................. 30 Fuel sharing and en ergy services ..............................................................................................

................................. 36 Elasticities ..................................................................................................................

................................................ 39 1990 Input data fo r calibration ...............................................................................................

.................................... 45 Resulting, for example, for the USA for the B2 scenario in Fina l Energy Demand: ...............................................

... 46 Resulting, for example, for the USA for the B2 scenario in elect ricty generation: .............................................

....... 46 Parameters for emi ssion calculations ..........................................................................................

............................... 47 Non-CO2 em issions .............................................................................................................

...................................... 49 Sulfur em issions ..............................................................................................................

........................................... 51 Parameters related to the AgLU module .........................................................................................

........................... 56 APPENDIX 7: LIST OF EQUATIONS .................................................................................................
..................... 623 

### TABLE OF TABLES
Table 1 Regional population proj ections for the B2 story line .................................................................

.... 13 Table 2 GDP projections for the B2 story line [9 0$GDP(90mer)] ............................................................... 13 Table 3 Market-based GDP to PPP conversion factors ............................................................................

.... 14 Table 4 Regional GDP elas ticities .............................................................................................

................... 14 Table 5 Examples of projections of regional labor productivity increases and regional labor force participatio n rates ...........................................................................................................

...................... 14 Table 6 Examples of projections of regional labor for ce particip ation ......................................................... 15 Table 7 Minimum extraction costs by grade and fuel (1975$/GJ) ............................................................... 15 Table 8 Energy resources by grade and region (EJ) ..................................................................................... 16 Table 9 Regional environmental costs (1975 $/GJ) for the B2 scenario ...................................................... 18 Table 10 Technological change in generating energy supplies ...................................................................

. 19 Table 11 Regional initial es timates of en ergy supp lies .......................................................................

........ 20 Table 12 Regional minimum produc tion rates for fu el prod uction .............................................................. 20 Table 13 Regional initial estimate s of available biomass waste ................................................................

... 21 Table 14 Regional supp ly price el asticitie s ..................................................................................

............... 21 Table 15 Initial prices and base share weights for biomass supply shares ................................................... 21 Table 16 Aggregate income el asticity of biom ass supply ........................................................................

.... 22 Table 17 Hydropower ge neration parameters .....................................................................................

.......... 22 Table 18 Regional energy from hydropower obtained in the base year in the B2 scenario and the fixed hydro shares for produ cing elect ricity ........................................................................................

......... 22 Table 19 Regional initial mark et prices fo r all goods .........................................................................

.......... 23 Table 20 Transportation co sts for traded fuels ................................................................................

............. 23 Table 21 Trade barrier scale factors such th at fuel prices can be region specific ......................................... 23 Table 22 Energy conversion factors from primary energy to secondary ener gy and markup costs ............. 25 Table 23 Synfuel parameters to calculate non-energy costs of synliquid prod uction from natural gas ........ 25 Table 24 Synfuel parameters to calculate non-energy costs of synfuel production from coal in 75 $/GJ .... 26 Table 25 Synfuel parameters to calculate non-en ergy costs of synfuel production from biomass ............... 26 Table 26 Synfuel effici ency coeffi cients ......................................................................................

................ 26 Table 27 Non-energy costs in synfuel and electricity generation (v alues are the same for each region) ..... 27 Table 28 Example of carbon coefficients: carbon release by source (in Teragrams C per ExaJoule) .......... 27 Table 29 Example of regiona l carbon dispos al costs ............................................................................

........ 27 Table 30 Synfuel lo git share exponent .........................................................................................

................ 28 Table 31 Conversion factors to calculate carbon fees towards final cons umption ....................................... 28 Table 32 Total System Efficiency of Hydrogen Pr oduction GHILM ........................................................... 28 Table 33 Non-energy costs in hydrogen generation (values ar e the same for each region).......................... 29 Table 34 Examples of carbon fractions to be removed when synfuels are produced or in coal-electric plants

.............................................................................................................................. ............................... 29 Table 35 Hydrogen subs ector share weights .....................................................................................

........... 29 Table 36 Hydrogen and electric ity generation lo git expo nent ..................................................................

... 30 Table 37 Hydrogen productio n share coefficients ...............................................................................

......... 30 Table 38 Logit share exponen t for hydrogen produc tion

.............................................................................. 30 Table 39 Regional electricity generation efficiency coefficients for oil-, gas-, coal-, and biomass-generated electric ity ...................................................................................................................

.......................... 30 Table 40 Regional electricity price coefficients used to account for en d-sector differences and distribution costs .........................................................................................................................

............................ 32 Table 41 Electricity generating subs ector-specific base -share we ights ....................................................... 32 Table 42 Logit function scale parameters for electric ity ......................................................................

........ 33 Table 43 Energy services in put-output coefficients GJK ........................................................................

..... 36 Table 44 Energy servi ces non-fuel costs HJK ...................................................................................

........... 36 Table 45 Hydrogen energy service fuel-related efficiency coefficien t (Gjk: j=hydrogen) ........................... 36 Table 46 Hydrogen energy service relate d non-fuel costs (Hjk: j=hydrogen) .............................................. 36 Table 47 Transportation sector fuel-r elated efficiency coefficients ...........................................................

.. 374 Table 48 Transportation s ector non-energy costs ...............................................................................

.......... 37 Table 49 Aggregate price elas ticity ...........................................................................................

................... 37 Table 50 End-use sector-specific price elastic ities for oil, gas, co al and elec tricity ..................................... 37 Table 51 Transmission and Dist ribution Costs for Hydrogen .....................................................................

. 38 Table 52 Transmission and Distribution Cost of Elect ricity ....................................................................

.... 38 Table 53 Regional weights of fuel share coefficients and initial shares of energy services consumptions .. 38 Table 54 Regional income elasticities by secondary fuel (oil, gas, coal, electric ity) for end-use sectors .... 39 Table 55 Regional income elas ticities for end- use sectors .....................................................................

...... 43 Table 56 End-use sector-s pecific price elastic ities ...........................................................................

............ 44 Table 57 Regional end-use sector e fficiency coeffici ents for 1990 .............................................................

. 44 Table 58 End-use sector efficiency improv ement coefficients fo r 2005 thr ough 209 5 ................................ 44 Table 59 Fuel demand (E J) Industry sector .....................................................................................

............. 45 Table 60 Fuel demand, Transportatio n sect or ...................................................................................

........... 45 Table 61 Fuel de mand, Buildings ...............................................................................................

.................. 45 Table 62 Fuel demand, Elect ricity genera tion sector ...........................................................................

........ 46 Table 63 Final energy demand, for example, for the USA for the B2 scenario (MiniCAM output) ............ 46 Table 64 Results, for example, for the USA for the B2 scenario in Electric Power Generation by Technologies ..................................................................................................................

...................... 46 Table 65 An example of a cost curve ...........................................................................................

................ 47 Table 66 Global carbon emissions from oil, natural gas and coal combustion to calibrate against for 1990 47 Table 67 Global Warming Potential, Atmospheric Half-Lives and Climate Forcing Information of Non-CO 2 Greenhouse Gases ..............................................................................................................

.................. 47 Table 68 Gas flare, flared gas bu rn, and shale burn parameters ................................................................

... 48 Table 69 Regional non-feedstock use of oil, gas, and coal (Sfedl) .............................................................

.. 48 Table 70 Overview of variables and consid erations of non-CO2 emission calculations .............................. 49 Table 71 Regional end-use sector specifi c ash retention parameters for coal .............................................. 51 Table 72 Sulfur content (percentage by weight) ................................................................................

........... 51 Table 73 Regional end-use specific and fuel-specific heat content values .................................................. 52 Table 74 An example of the non- climate sulfur co ntrol fraction ................................................................

.. 53 Table 75 Additional sulfur emission contro l factors ...........................................................................

......... 54 Table 76 Sulfur Emissions Control Mid-point GDP_0 (PPP-based GDPcap) S Emissions Control "timescale" Tau (PPP -based GDPcap) ............................................................................................

..... 54 Table 77 Regional end-use and fuel -specific maximum control values ...................................................... 54 Table 78 Regional maximum percentages of non-en ergy related industrial sulfur emissions ...................... 56 Table 79 Regional coefficients de termining changes in industrial sulfur emissions over time .................... 56 Table 80 Example of histori cal land use data collect ed ........................................................................

........ 56 Table 81 Regional la nd areas in 1 990 ..........................................................................................

................. 57 Table 82 Land Carbon Density Para meters, by Region (TgC/000ha) .......................................................... 57 Table 83 Harvested (199 0 data in 000 ha) ......................................................................................

.............. 58 Table 84 Example of regional t echnical improvements in food pr oduction in two time periods ................. 58 Table 85 Example of regi onal food demand data .................................................................................

........ 59 Table 86 Although not directly used, an exam ple of data collected for the AgLU module.......................... 61 Table 87 1990 Base Year CH4 and N2 O emissions (in TgCH4 or TgN) ..................................................... 615 

# Appendix 1: Indices and nomenclature; Definitions; Units

Indices and nomenclature

ERB is = raw fuel ig = grade of raw fuel in = raw fuel index i = primary energy type index, excep t in the synfuel calculations where i refers to synliquid and syngas produced j = secondary energy type index, except in the synfuel calculations where j refers to the feedstocks ui = electric utility index hi = hydrogen fuel production k = end-use or demand sector index l = regional index m = time period index es indicates energy supply, ed indicates energy demand. Ntech = number of technologies Nstep = the 15 year time step
Synfuel shares j = feedstocks: coal, gas, biomass i = synfuel types: crude, gas
AgLU p=represent a geographic location in a region when AgLU handles land use allocation i=products with markets l=region m=time



## Units
Fossil/Primary Energy in terms of Net Energy (lower heating value); Energy units: Joules [exa (1.e18), peta (1.e15), tera (1.e12), giga (1.e9)]; dimensions are omitted at times in text6 

# Appendix 2: MiniCAM regions

The 14 regions in the current MiniCAM are: USA, Canada, Japan, Western Europe, Australia & New Zealand, Former Soviet Union, Eastern Europe, Centrally Planned Asia, India, Korea, (rest of) South & East Asia, Middle East, Africa, and Latin America. The countries within regions are listed below. Note that these regions are dete rmined by economic criteria and do not necessarily follow political divisions.
14-region version

USA FSU Africa Latin America United-States Azerbaijan Algeria Antigua-and-Barbuda Canada Armenia Angola Bahamas Canada Belarus Botswana Barbados Japan Estonia Burundi Bermuda Japan Georgia Cameroon Bolivia Aus & NZ Kazakhstan Central-A frican-Republic Belize Australia Kyrgyzstan Chad Virgin-Islands-(British) N ew-Zealand Latvia Comoros Cayman-Islands OECD90 Europe Lithuania Congo Chile Austria Russia Zaire Colombia Belgium Tadzhikistan Benin Costa-Rica Cyprus Turkmenistan Equatorial-Guinea Cuba Denmark Ukraine Ethiopia Dominica Faroe-Islands Uzbekistan Djibouti Dominican-Republic Finland Eastern Europe Gabon Ecuador France Albania Gambia El-Salvador Germany Bulgaria Ghana Falkland-Islands Greece Czechoslovakia Guinea French-Guiana Greenland Hungary Ivory-Coast Grenada Iceland Moldova Kenya Guadeloupe Ireland Poland Lesotho Guatemala Italy Romania Liberia Guyana Luxembourg Yugoslavia Libya Haiti Malta China/CPA Madagascar Honduras N etherlands Cambodi a Malawi Jamaica N orway China Mali Martinique Portugal N orth-Korea Mauritania Aruba San-Marino Laos Mauritius N icaragua Spain Macau Morocco N iue Svalbard Mongolia Mozam bique Marshall-Islands Sweden Vietnam N amibia Panama Switzerland Korea N ige r Paraguay7 Turkey South-Korea N igeria Peru United-Kingdom India Guinea-Bissau Puerto-Rico Jan-Mayen India Reunion Anguilla S&E Asia Middle East Rwanda St.-Lucia Afghanistan Bahrain Senegal St.-Vincent Bangladesh Iran Sierra -Leone Suriname Bhutan Iraq Somalia Trinidad Solomon-Islands Israel South-A frica Turks-And-Caicos-Islands Brunei Jordan Zimbabwe Virgin-Islands-(USA) Myanmar Kuwait Western-Sahara Uruguay Sri-Lanka Lebanon Sudan Venezuela Taiwan Oman Swaziland Canary-Islands Cook-Islands Iraq-Saudi-Arabia-Neutral-Zone Togo St.-Martin Fiji Qatar Tunisia Hong-Kong Saudi-Arabia Uganda Indonesia Syria Egypt Malaysia United-Arab-Emirates Tanzania Maldives Yemen Burkina N epal Zambia N ew-Caledonia Vanuatu N orthern-Mariana-Islands Micronesia Palau-Islands Pakistan Papua-New-Guinea Philippines Seychelles Singapore Thailand8 

# Appendix 3: Description of the Solution Algorithms
Bisection Routine
The bisection routine is a simple but robust approach to finding roots. To begin the bisection routine, the solution or the root must be bracket ed. Bracketing is achieved when the price of a good is adjusted up or down until the excess de mand (demand minus supply) changes sign. The two prices at which the sign change occurs represent the initial bracketing interval. Bracketing price intervals are found for all markets. Then, the midpoints of the price intervals are used to determine the sign of the new excess demands. The midpoint price is used to replace th e initial bracketing price that has the same sign in excess demand. Each successive iteration reduces the bracketed price intervals by a factor of 2. After n iterations, if the solution is bound by an interval of size ε n , then after the next iteration it will be bracketed by an interval of size

ε n+1 = ε n /2 Eq. A3.1
From the initial bracketed interval, ε o , to the desired tolerance, ε , the number of iterations to achieve the tolerance is given by n = log 2 ( ε o / ε ) Eq. A3.2

Because there are multiple markets, however, th e actual number of iterations to achieve the tolerance for all the markets is determined by the largest initial bracketed interval. In certain situations, a market must be bracketed again and the bisection routine reapplied. Supply and demand for one market is dependent on the market prices of other goods. Thus, the solution may shift and no longer lie in the initial bracketi ng intervals. New bracketing intervals must be determined in such a case. In other situations, br acketing may not be possible at all. For instance, when resources are exhausted and there are no l onger any supplies. In this case, the bisection routine cannot be applied. Although the advantages of the bisection routine is its robustness and sureness in finding the solution price, it disadvantage is that it is slow. To improve the speed of finding solution prices, the bisection routine is combined with the Ne wton-Raphson routine, which relies on the use of derivative. 

## Newton-Raphson Routine
The Newton-Raphson routine is a numerical derivative approach to finding the solution. The advantage of this routine over the bracketing and bisection routine is that it converges quadratically near a solution as opposed to linearly and approaches the solution very quickly9 (Ref. Numerical Recipes). In the vicinity of the solution, each iteration of the routine approximately doubles the number of significant di gits in the trial solution. The Newton-Raphsonroutine requires the evaluation of the function and its derivative at arbitrary points. The NewtonRaphson formula is given by

x i+1 = x i + f(x i )/f’(x i ) Eq. A3.3
where x i is the trial solution, x i+1 is the next trial solution, and f’(x i ) is the derivative of the function evaluated at x i . Graphically, the routine extends the tangent line of the function at a point until it crosses zero and sets the next trial solution to the abscissa of that zero-crossing. This is repeated until the solution is found. The disadvantage of the Newton-Raphson routin e is that it is unstable where there are discontinuities and therefore, the routine’s globa l convergence properties are poor. For instance, at local discontinuities or extreme values, the tangent line of the trial point can move the next trial point hopelessly far away from the real solution. An effective strategy for creating a solution algorithm that is both fast and robust it to utilize both the bracketing and bisection and the Newton-Raphs on methods. This hybrid algorithm relies onbisection whenever Newton-Raphson takes the solution out of bounds, or whenever NewtonRaphson is not reducing the size of the brackets rapidly enough. The bracketing and bisection routine is applied first to find the initial bracketing intervals and to come near the vicinity of the solution for a ll markets. The Newton-Raphson routine is then applied to quickly come to the solution. If th e Newton-Raphson routine takes the solution out of bounds or does not find the solution within a set number of iterations, the bisection routine is called. This procedure is rep eated until the solution is found.10 

# Appendix 4: Demographics

Using the age-cohort method, the total population (of a region) for any time period, is given by 

# ∑

= 

### + = NAGE

1age m,females,age m,males,age m,tot 

### POP POP POP Eq. A4.1
where POP age,,males is the number of males in age group age, POP age, females is the number of females in age group age, and NAGE is the number of age groups defined. For the youngest age group age=1: 

# ∑

= = 

### •• = NAGE

2age m,females,age m,age gender,age m,gender,1age 

### POPfg POP Eq. A4.2
where gender is male or female POP age=1,gender,m is population in the youngest age group, age=1, by gender, in period t, f age,m is the fertility rate for females in age group, age, in period t, g age,gender is the fraction of births by gender, with g age,fr+ g age,m =1, and POP age,female,m is population of females in age group age in period t. For all other age groups, population is determined by survival:

m,gender,age 1m,gender,1age m,gender,age m,gender,age 

### POPmig POP sv POP + • =

− − Eq. A4.3

where age is 2,...NAGE,
sv age,gender,m is the survival rate from age group age to age+1, and POPmig age,gender,m is net immigration of population by gender into the region in age group, age.11 

# Appendix 5: Land allocation in the AgLU module

Land allocation

The text below is from Sands and Leimbach 2001. Using the notation from Bury (1999), the univarite Gumbel distribution is defined as



### ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎭ ⎬ ⎫ ⎩ ⎨ ⎧

σ μ−

−− σ μ−

− σ =σμ 

### x exp x exp 1 ),;x(f 

### 0 > σ Eq. A5.1
where x is the variable of interest, in our case profit rate, μ is the mode of the distribution, and
σ is a scale parameter. If a random sample is drawn from each of several distributions with identical scale parameters but different modes, then the probability of selecting the i th distribution is given by 

# ( )

( ) ∑ μσρ μσρ
=

−− −−

p p 11 i 11
i 

### exp exp prob 

### 10 ≤ ρ< Eq. A5.2

where p is the location index, ρ is a function of the correlation coefficient r if certain land-uses are correlated (see Equation A5.3 below),
σ is a scale parameter, and μ is the mode of the distribution i, where i is the index for land use. This implies that the distribution with the greatest average value, μ i

 , has the highest probability of being selected. Notation here is similar to that of Amemiya (1985). See Amemiya for a discussion of these types of distributions in qualitative res ponse models, often referred to as logit models. Equation A5.2 considers the possibility that the distributions are correlated, where ρ is a function of the correlation coefficient r.



### r1 −=ρ Eq. A5.3
If we consider only the random samples that su rvive this selection process, they also are distributed Gumbel and the average (mode) of this distribution is 

### μ ˆ , which is calculated using

ρσ

−− 

### ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ μσρ=μ 

# ∑

i i 11 

### ) exp() ˆ exp( Eq. A5.4

It is possible to write A5.2 and A5.4 as clo sed form expressions because we started with a Gumbel distribution. Equations A5.2 and A5.4 ar e only approximate for other distributions. Note that if we substitute the following12 i i 

### ln π=μ Eq. A5.5

into A5.2 we obtain


# ∑ ρσ ρσ



### π π
=

p 1 p 1 i i 

### s Eq. A5.6

which becomes Equation A5.5 if we let 

### ρσ=λ Eq. A5.7
Similarly, we obtain Equation A5.9 when we substitute A5.5 into A5.4) Here, we are trying to describe the implicit assumptions that justify the u se of share equations A5.6 or A5.5. So far we have shown that share equation A5.6 can be derived if we accept substitution A5.5. Next, we describe the assumptions needed to derive A5.5. If we write the profit rate calculation (Equation 122) in logarithmic form, then 

### )GPln(ylnrln ii i i 

### −+=π Eq. A5.8
Assume that ln y i is distributed Gumbel with mode η i and scale parameter σ . Then ln π r i is distributed Gumbel with mode 

### )GPln( ii ii 

### −+η=μ Eq. A5.9
The share equation operates as if the logarithm of profit rate has a Gumbel distribution and the mode of this distribution is μ i . Next define 

### )exp(y i i 

### η= Eq. A5.10
This just tells us where γ i must lie on the distribution of crop yields. Equation A6.10 can be substituted into A5.9 to obtain 

### )GPln(yln ii i i 

### −+=μ Eq. A5.11
using Equation 122 for the intrinsic profit rate, we can write

i i 

### rln π=μ Eq. A5.12

which is the same as A5.5. We have covered only the non-nested case. See Am emiya (1985) for examples of nested logit models. The advantage of using these share equations is that, given somewhat restrictive assumptions on the distribution of crop yields, we can calculate land shares immediately using Equation A5.5. Otherwise, an exact solution of the land share problem requires numeric integration.13 

# Appendix 6: List of Tables Demographics and GDP parameters

Table 1 Regional population projections for the B2 story line

POPPOPULATION (ZLM) UNITS=THOUSANDS OF PERSONS MiniCAM B2 storyline Region 1990 2005 2020 2035 2050 2065 2080 2095 USA 249,012 291,604 327,682 361,786 384,810 406,002 432,120 457,962 Canada 29,003 32,551 36,641 39, 957 42,311 42,353 42,372 42,321 OECD90 Europe 409,134 461,601 469,347 463,994 445,148 416,434 387,266 373,396 Japan 128,901 127,457 123,893 114,987 104,921 96,127 88,023 80,469 Aus & NZ 21,256 23,797 26,861 29, 311 31,009 31,758 31,775 31,739 FSU 286,923 292,095 295,368 293,066 283,685 275,473 266,303 261,273 China/CPA 1,210,204 1,458,890 1,613,709 1,685,243 1,674,223 1,623,512 1,571,503 1,542,891 MiddleEast 128,789 191,146 259,713 320,266 370,830 397,255 423,382 435,292 Africa 653,996 875,614 1,187,119 1,504,410 1,765,661 1,942,835 2,120,274 2,207,827 Latin America 439,633 556,548 663,663 749,413 806,986 836,324 865,418 879,127 S&E Asia 653,975 861,736 1,061,895 1,225,959 1,345,722 1,402,474 1,458,874 1,480,712 EEU 122,164 120,928 118,739 112,953 104,599 97,852 90,999 87,739 Korea 42,869 48,548 51,893 52,979 51,275 49,608 47,774 45,932 India 850,785 1,087,459 1,272, 166 1,428,018 1,528,853 1, 566,324 1,603,203 1,612,875 Global 5,226,644 6,429,974 7, 508,689 8,382,342 8,940,033 9, 184,331 9,429,286 9,539,555
Table 2 GDP projections for the B2 story line [90$GDP(90mer)] GDP Data in Billions $1990 Region 1990 2005 2020 2035 2050 2065 2080 2095 USA 5520.983 8554.664 11737.339 14454.176 17187.665 20281.864 24110.795 5520.983 Canada 547.423 771.262 1060.940 1302. 592 1576.518 1815.001 2094.299 547.423 OECD90 Europe 7036.162 10369.438 12914.397 14341.557 15521.928 16391.864 17235.901 7036.162 Japan 2952.073 3379.307 3876.940 4026.639 4201.292 4473.005 4791.285 2952.073 Aus & NZ 323.320 485.527 678.994 840. 315 1006.205 1167.175 1320.868 323.320 FSU 944.363 626.271 973.510 2030.690 3908.101 5911.471 7450.930 944.363 China/CPA 358.220 1366.404 4676.583 10941. 509 19637.697 25967.952 31043.131 358.220 Middle East 444.610 720.942 1202.268 2348.568 4173.202 5921.313 7246.299 444.610 Africa 379.202 533.858 934.185 2293. 770 5565.397 11082.333 17966.650 379.202 Latin America 1085.387 1860.465 3061.945 5969.454 10614.602 15466.871 18958.356 1085.387

S&E Asia 416.740 818.041 2200.596 4974. 567 9308.257 13274.558 17477.341 416.740 EEU 212.252 308.553 647.203 1372.211 2370.169 3143.213 3496.310 212.252 Korea 251.861 608.991 1277.191 1795.794 2078.325 2026.957 1929.923 251.86114 India 294.588 666.853 1954.793 4808.818 9643.295 14610.354 20155.099 294.588 Global 20767.185 31070.572 47196.885 71500.660 106792.652 141533.931 175277.188 20767.185

Table 3 Market-based GDP to PPP conversion factors
Market-based GDP to PPP conversion factors Region PPPCONV(L) USA 1 Canada 1.12 WEUR 0.88 Japan 0.81 Aus&NZ 1 FSU 1.86 ACENP 4.4 MidEast 1.51 Africa 2.8 LatAmer 1.76 SEAsia 2.34 EEUR 2 Korea 1.23 India 4.17

Table 4 Regional GDP elasticities
Y -0.15 USA -0.15 Canada -0.15 WEUR -0.15 Japan -0.15 Aus&NZ -0.15 FSU -0.20 ACENP 0.05 MidEast -0.20 Africa -0.20 LatAmer -0.20 SEAsia -0.15 EEUR -0.15 Korea -0.20 India

Table 5 Examples of projections of regional la bor productivity increases and regional labor force participation rates15 Labor productivity growth rate: Prod l,m (Equation 62) Region 1975 1990 2005 2020 2035 2050 2065 2080 2095 USA 0.0170 0.0118 0.0162 0. 0132 0.0114 0.0076 0.0090 0.0093 0.0116 Canada 0.0170 0.0046 0.0193 0.0089 0.0241 0.0028 0.0125 0.0041 0.0110 WEUR 0.0170 0.0127 0.0241 0. 0058 0.0107 0.0052 0.0112 0.0119 0.0096 Japan 0.0170 0.0103 0.0126 0.0226 0.0044 0.0091 0.0044 0.0126 0.0154 Aus&NZ 0.0170 0.0290 0.0121 0.0207 0.0185 0.0132 0.0068 -0.0028 0.0096 FSU 0.0170 0.0659 -0.0344 0. 0353 0.0540 0.0535 0.0242 0.0158 0.0131 ACENP 0.0250 0.0901 0.0813 0.0718 0.0649 0.0446 0.0324 0.0184 0.0122 MidEast 0.0250 0.1232 -0.0044 0.0082 0.0211 0.0259 0.0146 0.0091 0.0012 Africa 0.0250 0.0647 0.0034 0.0158 0.0385 0.0486 0.0393 0.0326 0.0221 LatAmer 0.0250 0.0137 0.0108 0.0188 0.0358 0.0342 0.0231 0.0135 0.0068 SEAsia 0.0250 0.0252 0.0225 0.0507 0.0446 0.0379 0.0213 0.0180 0.0152 EEUR 0.0170 0.0500 0.0194 0.0586 0.0582 0.0490 0.0177 0.0100 0.0086 Korea 0.0170 0.1290 0.0474 0.0431 0.0203 0.0135 0.0007 0.0012 0.0013 India 0.0200 0.0737 0.0343 0.0604 0.0524 0.0445 0.0266 0.0223 0.0188

Table 6 Examples of projections of regional labor force participation Labor force Percentage This is the rati o of working persons over total population LFPerc(L,M); UN_98 Med Pop for th e B2 scenario; see Equation 62 REGION 1975 1990 2005 2020 2035 2050 2065 2080 2095 1 0.45 0.5 0.52 0.52 0.49 0.49 0.48 0.47 0.45 2 0.44 0.52 0.49 0.52 0.41 0.45 0.43 0.47 0.47 3 0.43 0.46 0.42 0.47 0.45 0.47 0.45 0.43 0.43 4 0.49 0.52 0.5 0.42 0.44 0.44 0.48 0.47 0.45 5 0.43 0.5 0.56 0.51 0. 44 0.41 0.42 0.5 0.5 6 0.51 0.49 0.54 0.49 0.47 0.43 0.47 0.49 0.49 7 0.53 0.59 0.58 0.64 0.57 0.54 0.46 0.44 0.44 8 0.29 0.3 0.35 0.38 0.44 0.46 0.49 0.49 0.51 9 0.47 0.48 0.48 0.49 0. 54 0.55 0.56 0.52 0.5 10 0.34 0.39 0.45 0.47 0. 48 0.48 0.48 0.47 0.47 11 0.35 0.44 0.47 0.49 0. 5 0.49 0.49 0.48 0.47 12 0.51 0.49 0.54 0.49 0. 47 0.43 0.47 0.49 0.49 13 0.35 0.44 0.47 0.49 0. 5 0.49 0.49 0.48 0.47 14 0.35 0.44 0.47 0.49 0. 5 0.49 0.49 0.48 0.47



## Energy supply and extraction parameters

Table 7 Minimum extraction costs by grade and fuel (1975$/GJ) Extraction costs CIGIS(IG,IS); see Equation 5 & 21
Grade CONV OIL CONV GAS COAL UNCON OIL NUCLEAR16 1 0.50 0.62 0.34 3.80 1.07 2 0.55 0.68 0.37 4.10 2.00 3 0.92 1.10 1.20 5.60 2.10 4 1.30 1.70 1.70 6.70 2.50 5 2.10 3.10 2.00 8.00 3.00 6 2.70 3.70 2.30 9.00 4.00 100 3.50 6.50 2.60 10.00 8.00

Table 8 Energy resources by grade and region (EJ) Regional supply RIGISL(IG,IS,L); see Equation 7, 8, & 9; Re cent values for total foss il resources were taken from Rogner (1997) Grade REGION CONV OIL CONV GAS COAL UNCON OIL NUCLEAR 1 US 247 207 284 4397 105 2 US 312 778 6851 8594 562 3 US 356 575 9469 82637 87084 4 US 226 1431 13456 247909 87084 5 US 236 716 18440 0 0 6 US 343 1339 18440 0 0 1 CANADA 55 44 20 803 77 2 CANADA 115 279 293 1570 411 3 CANADA 199 119 293 15095 34833 4 CANADA 208 279 415 45285 34833 5 CANADA 216 478 569 0 0 6 CANADA 314 893 569 0 0 1 WEUR 121 78 117 1204 116 2 WEUR 49 496 2633 2355 617 3 WEUR 85 278 2632 22643 52250 4 WEUR 89 647 3740 67928 52250 5 WEUR 92 382 5125 0 0 6 WEUR 134 714 5125 0 0 1 JAPAN 0 1 2 146 10 2 JAPAN 0 6 336 287 50 3 JAPAN 0 23 496 2754 8708 4 JAPAN 0 51 704 8263 8708 5 JAPAN 0 239 965 0 0 6 JAPAN 0 446 965 0 0 1 AUS&NZ 18 10 57 1320 84 2 AUS&NZ 5 67 1186 2578 449 3 AUS&NZ 6 46 1753 24791 78375 4 AUS&NZ 7 99 2491 74374 78375 5 AUS&NZ 9 478 3414 0 0 6 AUS&NZ 12 893 3414 0 0 1 FSU 333 325 158 3874 205 2 FSU 305 2074 8728 7575 1092 3 FSU 569 1409 15404 72804 6927117 4 FSU 551 1389 21890 218412 69271 5 FSU 572 478 29997 0 0 6 FSU 556 893 29997 0 0 1 ACENP 83 6 295 2012 123 2 ACENP 102 40 7032 3933 657 3 ACENP 98 171 4820 37820 87084 4 ACENP 137 379 6849 113461 87084 5 ACENP 136 239 9387 0 0 6 ACENP 187 446 9387 0 0 1 MIDEAST 501 41 0 503 2 2 MIDEAST 657 810 2 983 12 3 MIDEAST 485 735 2 9455 87084 4 MIDEAST 452 2252 3 28366 87084 5 MIDEAST 1380 239 4 0 0 6 MIDEAST 1820 446 4 0 0 1 AFR 188 30 56 6009 426 2 AFR 296 194 1059 11745 2269 3 AFR 56 335 723 112937 87084 4 AFR 397 739 1026 338813 87084 5 AFR 393 716 1406 0 0 6 AFR 1298 1339 1406 0 0 1 LA 222 37 11 3004 973 2 LA 261 236 116 5873 5188 3 LA 119 372 144 56469 87084 4 LA 348 783 205 169406 87084 5 LA 346 716 280 0 0 6 LA 475 1339 280 0 0 1 SEASIA 73 45 6 1509 20 2 SEASIA 48 287 1018 2950 109 3 SEASIA 110 301 434 28366 87084 4 SEASIA 63 339 616 85096 87084 5 SEASIA 63 478 845 0 0 6 SEASIA 314 893 845 0 0 1 EEUR 8 16 86 151 53 2 EEUR 7 101 390 295 281 3 EEUR 13 25 689 2837 17813 4 EEUR 12 24 979 8510 17813 5 EEUR 13 48 1341 0 0 6 EEUR 12 89 1341 0 0 1 KOREA 0 0 4 0 10 2 KOREA 0 0 17 0 50 3 KOREA 0 0 0 0 8708 4 KOREA 0 0 0 0 8708 5 KOREA 0 191 0 0 0 6 KOREA 0 357 0 0 0 1 INDIA 21 5 55 1509 2018 2 INDIA 48 32 1018 2950 109 3 INDIA 110 301 434 28366 87084 4 INDIA 63 339 616 85096 87084 5 INDIA 63 382 845 0 0 6 INDIA 314 714 845 0 0

Table 9 Regional environmental costs (1975 $/GJ) for the B2 scenario Environmental costs VISLM(IS,L ,M)); see Equation 5, 13 & 21
fuel 1975 1990 2005 2020 2035 2050 2065 2080 REGION Oil 0 0 0 0.07 0.12 0.19 0.24 0.32 USA Oil 0 0 0 0.07 0.12 0.19 0.24 0.32 CANADA Oil 0 0 0 0.07 0.12 0.19 0.24 0.32 WEUR Oil 0 0 0 0.07 0.12 0.19 0.24 0.32 JAPAN Oil 0 0 0 0.07 0.12 0.19 0.24 0.32 AUS&NZ Oil 0 0 0 0.05 0.07 0.12 0.17 0.19 FSU Oil 0 0 0 0.05 0.07 0.12 0.17 0.19 ACENP Oil 0 0 0 0.02 0.07 0.1 0.12 0.17 MIDEAST Oil 0 0 0 0.02 0.05 0.07 0.07 0.1 AFR Oil 0 0 0 0.05 0.07 0.12 0.17 0.19 LA Oil 0 0 0 0.02 0.07 0.1 0.12 0.17 S&E ASIA Oil 0 0 0 0.07 0.12 0.19 0.24 0.32 EEUR Oil 0 0 0 0.07 0.12 0.19 0.24 0.32 KOR Oil 0 0 0 0.02 0.07 0.1 0.12 0.17 INDIA Gas 0 0 0 0 0 0 0 0 USA Gas 0 0 0 0 0 0 0 0 CANADA Gas 0 0 0 0 0 0 0 0 WEUR Gas 0 0 0 0 0 0 0 0 JAPAN Gas 0 0 0 0 0 0 0 0 AUS&NZ Gas 0 0 0 0 0 0 0 0 FSU Gas 0 0 0 0 0 0 0 0 ACENP Gas 0 0 0 0 0 0 0 0 MIDEAST Gas 0 0 0 0 0 0 0 0 AFR Gas 0 0 0 0 0 0 0 0 LA Gas 0 0 0 0 0 0 0 0 S&E ASIA Gas 0 0 0 0 0 0 0 0 EEUR Gas 0 0 0 0 0 0 0 0 KOR Gas 0 0 0 0 0 0 0 0 INDIA Coal 0 0 0.02 0.15 0.27 0.39 0.48 0.6 USA Coal 0 0 0.02 0.15 0.27 0.39 0.48 0.6 CANADA Coal 0 0 0.02 0.15 0.27 0.39 0.48 0.6 WEUR Coal 0 0 0.02 0.15 0.27 0.39 0.48 0.6 JAPAN Coal 0 0 0.02 0.15 0.27 0.39 0.48 0.6 AUS&NZ Coal 0 0 0.02 0.1 0.17 0.27 0.34 0.41 FSU Coal 0 0 0.02 0.1 0.17 0.27 0.34 0.41 ACENP19 Coal 0 0 0.02 0.1 0.15 0.22 0.27 0.34 MIDEAST Coal 0 0 0.02 0.07 0.1 0.15 0.17 0.22 AFR Coal 0 0 0.02 0.1 0.17 0.27 0.34 0.41 LA Coal 0 0 0.02 0.1 0.15 0.22 0.27 0.34 S&E ASIA Coal 0 0 0.02 0.15 0.27 0.39 0.48 0.6 EEUR Coal 0 0 0.02 0.15 0.27 0.39 0.48 0.6 KOR Coal 0 0 0.02 0.1 0.15 0.22 0.27 0.34 INDIA Unconventional Oil 0 0.1 0.15 0. 32 0.46 0.63 0.77 0.94 USA Unconventional Oil 0 0.1 0.15 0.32 0.46 0.63 0.77 0.94 CANADA Unconventional Oil 0 0.1 0.15 0.32 0.46 0.63 0.77 0.94 WEUR Unconventional Oil 0 0.1 0.15 0.32 0.46 0.63 0.77 0.94 JAPAN Unconventional Oil 0 0.1 0.15 0.32 0.46 0.63 0.77 0.94 AUS&NZ Unconventional Oil 0 0.02 0.05 0.17 0.27 0.39 0.51 0.6 FSU Unconventional Oil 0 0.02 0.05 0. 17 0.27 0.39 0.51 0.6 ACENP Unconventional Oil 0 0.02 0.05 0.15 0.22 0.32 0.41 0.48 MIDEAST Unconventional Oil 0 0.02 0.05 0.1 0.15 0.22 0.27 0.32 AFR Unconventional Oil 0 0.02 0.05 0.17 0.27 0.39 0.51 0.6 LA Unconventional Oil 0 0.02 0.05 0.15 0.22 0.32 0.41 0.48 S&E ASIA Unconventional Oil 0 0.02 0.05 0. 22 0.39 0.58 0.75 0.92 EEUR Unconventional Oil 0 0.1 0.15 0. 32 0.46 0.63 0.77 0.94 KOR Unconventional Oil 0 0.02 0.05 0. 15 0.22 0.32 0.41 0.48 INDIA Nuclear Fuel 0 0 0 0 0 0 0 0 USA Nuclear Fuel 0 0 0 0 0 0 0 0 CANADA Nuclear Fuel 0 0 0 0 0 0 0 0 WEUR Nuclear Fuel 0 0 0 0 0 0 0 0 JAPAN Nuclear Fuel 0 0 0 0 0 0 0 0 AUS&NZ Nuclear Fuel 0 0 0 0 0 0 0 0 FSU Nuclear Fuel 0 0 0 0 0 0 0 0 ACENP Nuclear Fuel 0 0 0 0 0 0 0 0 MIDEAST Nuclear Fuel 0 0 0 0 0 0 0 0 AFR Nuclear Fuel 0 0 0 0 0 0 0 0 LA Nuclear Fuel 0 0 0 0 0 0 0 0 S&E ASIA Nuclear Fuel 0 0 0 0 0 0 0 0 EEUR Nuclear Fuel 0 0 0 0 0 0 0 0 KOR Nuclear Fuel 0 0 0 0 0 0 0 0 INDIA
Table 10 Technological change in generating energy supplies STISM(IS,M); see Equation 4 PERIOD CONV OIL CONV GAS COAL UNCON OIL NUCLEAR FUEL

1 0.005 0.005 0.005 0.01 0.005 1975 2 0.005 0.005 0.005 0.01 0.005 1990 3 0.0075 0.0075 0.0075 0.01 0.005 2005 4 0.0075 0.0075 0.0075 0.01 0.005 2020 5 0.0075 0.0075 0.0075 0.01 0.005 2035 6 0.0075 0.0075 0.0075 0.01 0.005 205020 7 0.0075 0.0075 0.0075 0.01 0.005 2065 8 0.0075 0.0075 0.0075 0.01 0.005 2080 9 0.0075 0.0075 0.0075 0.01 0.005 2095

Table 11 Regional initial estimates of energy supplies
ESFIL--INITIAL ESTIMATE OF ENERGY SUPPLY BY FUEL, REGION, AND PERIOD (UNITS=EXAJOULES/YR): ESFIL(IS,L ) - YEAR 1975; see Equation 10 REGION CONV OIL CONV GAS COAL UNCON OIL NUCLEAR US 19.9 18.5 12.8 0 0.62 CAN 3.6 2.5 0.5 0 0.06 WEUR 1.2 5.7 9 0 0.52 JAPAN 0 0.1 0.5 0 0.09 AUS&NZ 0.9 0.2 1.6 0 0 FSU 20.6 10 12.1 0 0.06 ACENP 3.3 0.3 9.3 0 0 MIDEAST 41.8 1.3 0 0 0 AFR 10.4 0.4 1.5 0 0 LA 9.7 1.5 0.2 0 0.01 SEASIA 2.9 0.3 7.2 0 0.01 EEUR 1 1.6 6.1 0 0.01 KOR 0 0 0.3 0 0.09 INDIA 0.4 0 1.8 0 0.01

Table 12 Regional minimum production rates for fuel production BESIL(IS,L); see description of Equation 11 REGION CONV OIL CONV GAS COAL UNCON OIL NUCLEAR

USA 9 9 22 5 0.03 Canada 2 2 2 1 0.03 WEUR 5 3 9 3 0.03 Japan 1 1 1 1 0.03 Aus&NZ 1 1 4 1 0.03 FSU 12 14 12 3 0.03 ACENP 3 1 23 2 0.03 MidEast 18 2 1 1 0.03 Africa 7 2 4 1 0.03 LatAmer 8 2 1 1 0.03 SEAsia 3 2 1 1 0.03 EEUR 1 1 7 1 0.03 Korea 1 1 1 1 0.03 India 1 1 4 1 0.0321 Table 13 Regional initial estimates of available biomass waste WASTE ENERGY: BIOLM(L,IM); see Equation 22
Value (EJ) Region 5.48 US 1 CANADA 6.95 WEUR 2.21 JAPAN 0.5 AUS&NZ 5 FSU 5 ACENP 0.35 MIDEAST 6 AFRICA 8.21 L AMER 2.5 S&E ASIA 0.55 EEUR 1 KOR 5 INDIA

Table 14 Regional supply price elasticities
RIL--PRICE ELASTICITY OF SUPPLY, EVALUATED PREVIOUS PRICE (BY SUPPLY TYPE AND REGION) RIL(IS,L); see Equation 13 REGION CONV OIL CONV GAS COAL UNCON OIL US 1.5 2 2 2 CANADA 1.5 2 2 2 WEUR 1.5 2 2 2 JAPAN 1.5 2 2 2 AUS&NZ 1.5 2 2 2 FSU 1.5 2 2 2 ACENP 1.5 2 2 2 MIDEAST 1.5 2 2 2 AFR 1.5 2 2 2 LA 1.5 2 2 2 SEASIA 1.5 2 2 2 EEUR 1.5 2 2 2 KOR 1.5 2 2 2 INDIA 1.5 2 2 2

Table 15 Initial prices and base share weights for biomass supply shares
BIOMASS COEFFICIENTS:22 BIOPSM: Bio l,m ; Equation 22 PRICE SHARE 0.1 0 0.56 0.3 0.74 0.7 0.93 1 2.22 1.5

Table 16 Aggregate income elasticity of biomass supply
INCOME ELASTICITY OF BIOMASS SUPPLY RYSHT; see Equation 22 0.1

Table 17 Hydropower generation parameters Hydro parameters; see Equation 23 REGION HYDRO1L HYDRO2L HYDRO3L HYDRO4L HYDRO5L USA 0.4080 0.0158 1.5441 4.03 0.107 Canada -0.1570 0.0655 1.3281 4.03 0.616 WEUR 0.2975 0.0274 2.0599 4.03 0.19 Japan 1.4034 0.0352 0.3338 4.03 0.107 Aus&NZ 0.7305 0.0490 0.1485 4.03 0.213 FSU -0.4164 0.0452 0.9901 4.03 0.124 ACENP -2.0631 0.0641 1.9259 4.03 0.235 MidEast -2.4897 0.0725 0.2207 4.03 0.063 Africa -2.9014 0.0393 1.4400 4.03 0.14 LatAmer -1.9800 0.0952 3.2674 4.03 0.667 SEAsia -2.0491 0.0880 0.5860 4.03 0.205 EEUR -0.0371 0.0180 0.2732 4.03 0.119 Korea -1.2333 0.2357 0.0218 4.03 0.059 India -1.6957 0.0663 0.5900 4.03 0.252

Table 18 Regional energy from hydropower obtained in the base year in the B2 scenario and the fixed hydro shares for producing electricity EJ of electricity generated by hydropower by hydro Hydro share 1990 US 1.01 0.107 CANADA 0.92 0.616 WEUR 1.38 0.19 JAPAN 0.29 0.107 AUS&NZ 0.12 0.21323 FSU 0.56 0.124 ACENP 0.48 0.235 MIDEAST 0.04 0.063 AFR 0.13 0.14 LA 1.19 0.667 SEASIA 0.19 0.205 EEUR 0.15 0.119 KOR 0.02 0.059 INDIA 0.2 0.252 6.69



## Primary energy price parameters

Table 19 Regional initial mark et prices for all goods

P(in,l,1) Initial starting market prices fo r all goods in 1975 $/GJ; see Equation 24 region OIL(1) GAS(2) COAL(3) BIOMASS(4) USA 1.8398 0.6256 0.5121 2.5 CANADA 1.8398 0.6256 0.5121 2.5 WEUR 1.8398 0.6256 0.5121 2.5 JAPAN 1.8398 0.6256 0.5121 2.5 AUS&NZ 1.8398 0.6256 0.5121 2.5 FSU 1.8398 0.6256 0.5121 2.5 ACENP 1.8398 0.6256 0.5121 2.5 MIDEAST 1.8398 0.6256 0.5121 2.5 AFR 1.8398 0.6256 0.5121 2.5 LA 1.8398 0.6256 0.5121 2.5 S&E ASIA 1.8398 0.6256 0.5121 2.5

EEUR 1.8398 0.6256 0.5121 2.5 KOR 1.8398 0.6256 0.5121 2.5 INDIA 1.8398 0.6256 0.5121 2.5

Table 20 Transportation costs for traded fuels
TRI--TRANSPORTATION COSTS FOR TRADED FUELS (UNITS=1975 DOLLARS PER GJ (GIGAJOULE)): Costs for coal & gas taken from an alysis of US cost figures; see Equation 24 TRI(I) OIL GAS COAL BIOMASS 0.1397 0.4 0.25 0.681

Table 21 Trade barrier scale factors such that fuel prices can be region specific TXILM(I,L,M); Pxi i,l,m a regional fee towards oil, gas, coal , and biomass prices; see Equation 2424 REGION 1975 1990 2005 2020 2035 2050 USA 1 1 1 1 1 1 OIL CANADA 1 1 1 1 1 1 OIL WEUR 1.8 1.5 1.3 1.1 1 1 OIL JAPAN 1 1 1 1 1 1 OIL AUS&NZ 1 1 1 1 1 1 OIL FSU 1 1 1 1 1 1 OIL ACENP 1 1 1 1 1 1 OIL MIDEAST 1 1 1 1 1 1 OIL AFR 1 1 1 1 1 1 OIL LA 1 1 1 1 1 1 OIL S&E ASIA 1 1 1 1 1 1 OIL EEUR 1 1 1 1 1 1 OIL KOR 1 1 1 1 1 1 OIL INDIA 1 1 1 1 1 1 OIL USA 1 1 1 1 1 1 GAS CANADA 1 1 1 1 1 1 GAS WEUR 1.8 1.5 1.3 1.1 1 1 GAS JAPAN 1 1 1 1 1 1 GAS AUS&NZ 1 1 1 1 1 1 GAS FSU 1 1 1 1 1 1 GAS ACENP 1 1 1 1 1 1 GAS MIDEAST 1 1 1 1 1 1 GAS AFR 1 1 1 1 1 1 GAS LA 1 1 1 1 1 1 GAS S&E ASIA 1 1 1 1 1 1 GAS EEUR 1 1 1 1 1 1 GAS KOR 1 1 1 1 1 1 GAS INDIA 1 1 1 1 1 1 GAS USA 1 1 1 1 1 1 COAL CANADA 1 1 1 1 1 1 COAL WEUR 1.8 1.5 1.3 1.1 1 1 COAL JAPAN 1 1 1 1 1 1 COAL AUS&NZ 0.75 0.75 0.75 0.75 0.75 0.75 COAL FSU 1 1 1 1 1 1 COAL ACENP 0.75 0.75 0.75 0.75 0.75 0.75 COAL MIDEAST 1 1 1 1 1 1 COAL AFR 1 1 1 1 1 1 COAL LA 1 1 1 1 1 1 COAL S&E ASIA 1 1 1 1 1 1 COAL EEUR 1 1 1 1 1 1 COAL KOR 1 1 1 1 1 1 COAL INDIA 1 1 1 1 1 1 COAL USA 1 1 1 1 1 1 BIOMASS CANADA 1 1 1 1 1 1 BIOMASS WEUR 1 1 1 1 1 1 BIOMASS25 JAPAN 1 1 1 1 1 1 BIOMASS AUS&NZ 1 1 1 1 1 1 BIOMASS FSU 1 1 1 1 1 1 BIOMASS ACENP 1 1 1 1 1 1 BIOMASS MIDEAST 1 1 1 1 1 1 BIOMASS AFR 1 1 1 1 1 1 BIOMASS LA 1 1 1 1 1 1 BIOMASS S&E ASIA 1 1 1 1 1 1 BIOMASS EEUR 1 1 1 1 1 1 BIOMASS KOR 1 1 1 1 1 1 BIOMASS INDIA 1 1 1 1 1 1 BIOMASS



## Parameters to calculate pr ices of secondary fuels

Table 22 Energy conversion factors from primary energy to secondary energy and markup costs See Equation 25 OIL GAS COAL BIOMASS GIJ(I); see also Equation 75, 109, 110 1 1 1 1

HIJ(I) 1.425 0.3487 0.14 0.14



## Synfuel production parameters

Table 23 Synfuel parameters to calculate non-en ergy costs of synliquid production from natural gas SYNCRUDE from Natural Gas; see Equation 26 REGION HCILT1 HCILT2 HCILT3 US 100 5 25 CAN 100 5 25 WEUR 100 5 25 JAPAN 100 5 25 AUS&NZ 100 5 25 FSU 100 5 25 ACENP 100 5 25 MIDEAST 100 5 25 AFR 100 5 25 LA 100 5 25 SEASIA 100 5 25 EEUR 100 5 25 KOR 100 5 2526 INDIA 100 5 25

Table 24 Synfuel parameters to calculate non-energy costs of synfuel production from coal in 75 $/GJ SYNCRUDE from Coal; see Equation 26 SYNGAS from Coal; see Equation 26 REGION HCILT1 HCILT2 HCILT3 HCILT1 HCILT2 HCILT3 US 100 5 25 100 3.63 25 CAN 100 5 25 100 3.63 25 WEUR 100 5 25 100 3.63 25 JAPAN 100 5 25 100 3.63 25 AUS&NZ 100 5 25 100 3.63 25 FSU 100 5 25 100 3.63 25 ACENP 100 5 50 100 3.63 50 MIDEAST 100 5 100 100 3.63 100 AFR 12.54 5 25 100 3.63 25 LA 12.54 5 25 100 3.63 25 SEASIA 100 5 50 100 3.63 50 EEUR 100 50 25 100 3.63 25 KOR 100 5 25 100 3.63 25 INDIA 100 5 50 100 3.63 50

Table 25 Synfuel parameters to calculate non-ener gy costs of synfuel production from biomass SYNCRUDE from Biomass; see Equation 26 SYNGAS from Biomass; see Equation 26 REGION HCILT1 HCILT2 HCILT3 HCILT1 HCILT2 HCILT3 US 100 5 25 100 3.63 25 CAN 100 5 25 100 3.63 25 WEUR 100 5 25 100 3.63 25 JAPAN 100 5 25 100 3.63 25 AUS&NZ 100 5 25 100 3.63 25 FSU 100 5 25 100 3.63 25 ACENP 100 5 50 100 3.63 50 MIDEAST 100 5 100 100 3.63 100 AFR 12.54 5 25 100 3.63 25 LA 12.54 5 25 100 3.63 25 SEASIA 100 5 50 100 3.63 50 EEUR 100 5 25 100 3.63 25 KOR 100 5 25 100 3.63 25 INDIA 100 5 50 100 3.63 50

Table 26 Synfuel efficiency coefficients GCI; see Equation 27 & 78 & 9127 SYNFUEL N.Gas Coal Biomass 1 1.5 1.5 1.5 SYNCRUDE GCI 2 1.5 1.5 1.5 SYNGAS GCI
Table 27 Non-energy costs in synfuel and electri city generation (values are the same for each region) HUILM(I,L,M); see Equation 29, 47, 49, 50 & 52 FuelName 1975 1990 2005 2020 2035 2050 2065 2080 2095 OIL 2.8 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 GAS 2 2 2 2 2 2 2 2 2 COAL 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 NUCLEAR 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 SOLAR 201.7 92.4 53.3 30. 8 17.7 10.2 8 7.7 7.5 HYDRO 4.03 4.03 4.03 4.03 4.03 4.03 4.03 4.03 4.03 BIOMASS 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 COAL W/ CO2 CAPT 5.193 5.193 5.193 5.193 5.099 5.012 4.932 4.857 4.788 OIL W/ CO2 CAPT 3.728 3.595 3.595 3.595 3.530 3.470 3.414 3.363 3.315 GAS W/ CO2 CAPT 2.915 2.915 2.915 2.915 2.849 2.787 2.730 2.677 2.628 H2 FUEL CELL 4.533 4.533 4.0797 4.0797 4.0797 4.0797 4.0797 4.0797 4.0797 FUSION 100 100 100 100 100 18.2 8.8 8.4 8 WIND 10 10 7 6.1 5.75 5. 65 5.44 5.24 5.05 SWSTOR 1000 500 350 200 150 100 75 50 25 SatSolar 1000 100 79 63 50 40 32 32 32

Table 28 Example of carbon coefficients: carbon release by source (in Teragrams C per ExaJoule) See Equation 28 GAS BURNUP COAL BURNUP COAL LIQUIFICAT ION GASIFICATI ON OIL BURNUP SHALE OIL PRODUCTIO N BIOMASS

14.2 27.3 18.9 26.9 18.9 27.9 0

Table 29 Example of regional carbon disposal costs Carbon Disposal Costs; see Equation 30 Example where carbon sequestration is tu rned off by setting disposal costs to a high value CARBDISP(L,M) REGION 2005 2020 2035 2050 2065 2080 2095 US 5000 5000 5000 5000 5000 5000 5000 CAN 5000 5000 5000 5000 5000 5000 5000 WEUR 5000 5000 5000 5000 5000 5000 5000 JAPAN 5000 5000 5000 5000 5000 5000 5000 AUS&NZ 5000 5000 5000 5000 5000 5000 5000 FSU 5000 5000 5000 5000 5000 5000 500028 ACENP 5000 5000 5000 5000 5000 5000 5000 MIDEAST 5000 5000 5000 5000 5000 5000 5000 AFRICA 5000 5000 5000 5000 5000 5000 5000 L AMER 5000 5000 5000 5000 5000 5000 5000 S&E ASIA 5000 5000 5000 5000 5000 5000 5000

EEUR 5000 5000 5000 5000 5000 5000 5000 KOR 5000 5000 5000 5000 5000 5000 5000 INDIA 5000 5000 5000 5000 5000 5000 5000

Table 30 Synfuel logit share exponent RCI; see Equation 35 SYNFUEL N.Gas Coal Biomass 1 -6 -6 -8 SYNCRUDE RCI 2 -6 -6 -8 SYNGAS RCI

Table 31 Conversion factors to calculate carbon fees towards final consumption Pfjk j,k,l,m ; see Equation 36 REGION 1975 1990 2005 2020 2035 2050 ALL 0 0 0.896 0.896 0.896 0.896 OIL ALL 0 0 0.617 0.617 0.617 0.617 GAS ALL 0 0 1.084 1.084 1.084 1.084 COAL ALL 0 0 0 0 0 0 ELECTRIC



## Hydrogen production B2 Scenario

Table 32 Total System Efficiency of Hydrogen Production GHILM GHILM: see Equation 37, 38 & 41 & 73 & 110 (efficiency improves at 0.5%/yr after 2005) FUEL 1975 1990 2005 2020 2035 2050 2065 2080 2095 OIL 10 10 1.67 1.547 1.435 1.333 1.333 1.333 1.333 GAS 10 10 1.43 1.326 1.25 1.25 1.25 1.25 1.25 COAL 10 10 1.61 1.515 1.515 1.515 1.515 1.515 1.515 BIOMASS 10 10 1.663 1.543 1.432 1.329 1.25 1.25 1.25 ELECTRO 10 10 1.15 1.067 1.064 1.064 1.064 1.064 1.064 OIL CO2 Cap 10 10 2 1.83 1.68 1.55 1.53 1.52 1.5 GAS CO2 Cap 10 10 1.71 1.57 1. 47 1.45 1.44 1.42 1.41 COAL CO2 Cap 10 10 1.94 1.8 1. 78 1.76 1.74 1.72 1.71
Penalty 0.2 0.2 0.2 0.186 0. 172 0.16 0.148 0.138 0.12829 Table 33 Non-energy costs in hydrogen genera tion (values are the same for each region) "HHILM" is the non-energy cost in 1975$ for hydrogen production; see Equation 37, 38 & 41 HHILM 0.005 (efficiency improves at 0.5%/yr after 2005) FUEL 1975 1990 2005 2020 2035 2050 2065 2080 2095 OIL 10 10 6.7 6.217 5.769 5.353 4.967 4.609 4.277 GAS 10 10 1.1 1.021 0.947 0.879 0.816 0.757 0.702 COAL 10 10 3.1 2.877 2.669 2.477 2.298 2.133 1.979 BIOMASS 10 10 2.5 2.32 2.153 1.997 1.853 1.72 1.596 ELECTRO 10 10 2.523 2.341 2.172 2.016 1.87 1.736 1.611 OIL CO2 Cap 13 13 8.71 7.95 7.26 6.64 6.07 5.56 5.1 GAS CO2 Cap 13 13 1.43 1.3 1.19 1.09 1 0.91 0.84 COAL CO2 Cap 13 13 4.03 3.68 3.36 3.07 2.81 2.57 2.36
Penalty 0.3 0.3 0.3 0.278 0. 258 0.24 0.222 0.206 0.192

Table 34 Examples of carbon fractions to be removed when synfuels are produced or in coalelectric plants Carbon removal fraction,by mode: REMFRAC(1,L); see Equation 38 Region 1 for synfuel 2 for coal electric US 0.9 0.9 CAN 0.9 0.9 WEUR 0.9 0.9 JAPAN 0.9 0.9 AUS&NZ 0.9 0.9 FSU 0.9 0.9 ACENP 0.9 0.9 MIDEAST 0.9 0.9 AFRICA 0.9 0.9 L AMER 0.9 0.9 S&E ASIA 0.9 0.9

EEUR 0.9 0.9 KOR 0.9 0.9 INDIA 0.9 0.9

Table 35 Hydrogen subsector share weights BSSHILM(I,ISS,L,M) For ISS=1, 0 = off 1 = on ; see Equation 39 ISS 1975 1990 2005 2020 2035 2050 2065 2080 2095 FUEL 1 1 1 1 1 1 1 1 1 1 OIL 2 1 1 1 1 1 1 1 1 1 OIL Scrub 1 1 1 1 1 1 1 1 1 1 GAS 2 1 1 1 1 1 1 1 1 1 GAS Scrub30 1 1 1 1 1 1 1 1 1 1 COAL 2 1 1 1 1 1 1 1 1 1 Coal Scrub

Table 36 Hydrogen and electricity generation logit exponent RUISS is the logit exponent for the electric subsector competition; see Equation 39 and 48 NO SCRUB SCRUB BIOMASS -6 -6 Oil -6 -6 Gas -6 -6 -6 Coal

Table 37 Hydrogen production share coefficients "BSHILM" iare scale or base weigh share coef ficients for hydrogen production; see Equation 43 Give electrolysis equal weight FUEL 1975 1990 2005 2020 2035 2050 2065 2080 2095 OIL 1 1 1 1 1 1 1 1 1 GAS 1 1 1 1 1 1 1 1 1 COAL 1 1 1 1 1 1 1 1 1 BIOMASS 1 1 1 1 1 1 1 1 1 ELECTRO 1 1 1 1 1 1 1 1 1

Table 38 Logit share exponent for hydrogen production
"RHI" is the SHARE EXPONENT FOR PRODUCING HYDROGEN; see Equation 43 FUELNum RHI OIL -3 GAS -3 COAL -3 BIOMASS -3 ELECTRO -3



## Electricity generation B2 Scenario

Table 39 Regional electricity generation efficiency coefficients for oil-, gas-, coal-, and biomassgenerated electricity GUILM(I,L,M); see Equation 44, 45, 46, 49, 50, 52 & 74 & 109 Max REG# 1975 1990 2005 2020 2035 2050 2065 2080 2095 Efficiency USA 3.277 3.1051 2.8788 2.6526 2.4263 2.2 2 1.91 1.82 OIL 55% Canada 3.569 2.8964 2.7223 2.5482 2.3741 2.2 2 1.91 1.82 OIL 55%31 WEUR 2.987 3.0214 2.8161 2.6107 2.4054 2.2 2 1.91 1.82 OIL 55% Japan 2.738 2.4672 2.4004 2.3336 2.2668 2.2 2 1.91 1.82 OIL 55% Aus&NZ 3.034 2.8553 2.6915 2.5277 2.3638 2.2 2 1.91 1.82 OIL 55% FSU 3.604 2.7867 2.64 2.4934 2.3467 2.2 2 1.91 1.82 OIL 55% ACENP 4.394 4.1417 3.6563 3.1709 2.6854 2.2 2 1.91 1.82 OIL 55% MidEast 3.504 3.5531 3.2148 2.8766 2.5383 2.2 2 1.91 1.82 OIL 55% Africa 3.873 2.761 2.6958 2.6305 2.5653 2.5 2.2045 1.9 1.82 OIL 55% LatAmer 4.143 3.8734 3.4551 3.0367 2.6184 2.2 2 1.91 1.82 OIL 55% SEAsia 3.505 3.6277 3.3458 3.0639 2.7819 2.5 2.2045 1.9 1.82 OIL 55% EEUR 3.207 3.2816 3.0253 2.769 2.5126 2.2 2 1.91 1.82 OIL 55% Korea 3.564 3.0398 2.83184 2.62388 2.41592 2.2 2 1.91 1.82 OIL 55% India 4.807 3.2212 3.0409 2.8606 2.6803 2.5 2.2045 1.9 1.82 OIL 55%
GUILM(I,L,M) Max REG# 1975 1990 2005 2020 2035 2050 2065 2080 2095 Efficiency USA 3.143 3.2972 2.9229 2.5486 2.1743 1.9 1.8 1.73 1.67 GAS 60% Canada 3.608 2.2936 2.1702 2.0468 1.9234 1.9 1.8 1.73 1.67 GAS 60% WEUR 2.934 2.9988 2.6991 2.3994 2.0997 1.9 1.8 1.73 1.67 GAS 60% Japan 2.852 2.5173 2.338 2.1587 1.9793 1.9 1.8 1.73 1.67 GAS 60% Aus&NZ 3.234 2.9331 2.6498 2.3666 2.0833 1.9 1.8 1.73 1.67 GAS 60% FSU 3.283 3.9704 3.4528 2.9352 2.4176 1.9 1.8 1.73 1.67 GAS 60% ACENP 3.03 2.7671 2.5503 2.3336 2.1168 1.9 1.8 1.73 1.67 GAS 60% MidEast 5.055 3.2493 2.912 2.5747 2.2373 1.9 1.8 1.73 1.67 GAS 60% Africa 3.837 4.1246 3.7685 3.4123 3. 0562 2.7 2.2167 1.73 1.67 GAS 60% LatAmer 5.181 4.307 3.7053 3.1035 2.5018 1.9 1.8 1.73 1.67 GAS 60% SEAsia 4.136 4.3048 3.8536 3.4024 2.9512 2.5 2.1167 1.73 1.67 GAS 60% EEUR 3.571 3.7954 3.3963 2.9972 2.5982 1.9 1.8 1.73 1.67 GAS 60% Korea 3.03 3.0874 2.82992 2.57244 2.31496 1.9 1.8 1.73 1.67 GAS 60% India 4.136 5.2882 4.5912 3.8941 3.1971 2.5 2.1167 1.73 1.67 GAS 60%
GUILM(I,L,M) Max REG# 1975 1990 2005 2020 2035 2050 2065 2080 2095 Efficiency USA 3.502 3.3131 2.9741 2.6351 2.296 2.2 2 1.9 1.82 COAL 55% Canada 3.247 3.2359 2.9162 2.5965 2.2767 2.2 2 1.91 1.82 COAL 55% WEUR 3.217 2.9877 2.73 2.4724 2.2147 2.2 2 1.91 1.82 COAL 55% Japan 3.478 2.6414 2.4703 2.2992 2.1281 2.2 2 1.91 1.82 COAL 55% Aus&NZ 4.293 3.3252 2.9832 2.6411 2.2991 2.2 2 1.91 1.82 COAL 55% FSU 3.654 3.5998 3.2499 2.8999 2.55 2.2 2 1.91 1.82 COAL 55% ACENP 4.317 3.8966 3.4725 3.0483 2.6242 2.2 2 1.91 1.82 COAL 55% MidEast 3.03 3.288 3.016 2.744 2.472 2.2 2 1.91 1.82 COAL 55% Africa 3.875 3.2894 3.0921 2.8947 2. 6974 2.5 2.2045 1.91 1.82 COAL 55% LatAmer 4.877 3.9332 3.4999 3.0666 2. 6333 2.2 1.791 1.8 1.82 COAL 55% SEAsia 4.903 2.8471 2.7603 2.6736 2.5868 2.5 2.1523 1.8 1.82 COAL 55% EEUR 3.654 3.7921 3.4337 3.0753 2.7168 2.2 2 1.91 1.82 COAL 55% Korea 4.903 3.0553 2.84424 2.63318 2.42212 2.2 2 1.91 1.82 COAL 55% India 4.903 4.7243 4.1682 3.6122 3. 0561 2.5 2.2045 1.91 1.82 COAL 55%32 GUILM(I,L,M) Max REG# 1975 1990 2005 2020 2035 2050 2065 2080 2095 Efficiency USA 3.325 3.325 2.553 2.336 2.138 2.2 2 1.9 1.82 BIOMASS 55% Canada 3.325 3.325 2.553 2.336 2.138 2.2 2 1.91 1.82 BIOMASS 55% WEUR 3.325 3.325 2.553 2.336 2.138 2.2 2 1.91 1.82 BIOMASS 55% Japan 3.325 3.325 2.553 2.336 2.138 2.2 2 1.91 1.82 BIOMASS 55% Aus&NZ 3.325 3.325 2.553 2.336 2.138 2.2 2 1.91 1.82 BIOMASS 55% FSU 3.325 3.325 3.0438 2.7625 2.4813 2.2 2 1.91 1.82 BIOMASS 55% ACENP 3.325 3.325 3.0438 2.7625 2.4813 2.2 2 1.91 1.82 BIOMASS 55% MidEast 3.325 3.325 3.0438 2.7625 2. 4813 2.2 2 1.91 1.82 BIOMASS 55% Africa 3.325 3.325 3.1188 2.9125 2.7063 2.5 2.2045 1.91 1.82 BIOMASS 55% LatAmer 3.325 3.325 3.0438 2.7625 2. 4813 2.2 1.791 1.8 1.82 BIOMASS 55% SEAsia 3.325 3.325 3.1188 2.9125 2. 7063 2.5 2.1523 1.8 1.82 BIOMASS 55% EEUR 3.325 3.325 3.06 2.795 2.53 2.2 2 1.91 1.82 BIOMASS 55% Korea 3.325 3.325 3.06 2.795 2.53 2.2 2 1.91 1.82 BIOMASS 55% India 3.325 3.325 3.1188 2.9125 2. 7063 2.5 2.2045 1.91 1.82 BIOMASS 55%

Table 40 Regional electricity price coefficients used to account for end-sector differences and distribution costs PAUIL(I,L); see Equation 44, 45 & 46 REGION OIL GAS COAL BIOMASS US 1 0.8 0.5 0.8 CANADA 1 0.8 0.5 0.8 WEUR 1 0.8 0.5 0.8 JAPAN 1 0.8 1.5 0.8 AUS&NZ 1 0.8 0.5 0.8 FSU 1 0.8 0.5 0.8 ACENP 1 0.8 0.5 0.8 MIDEAST 1 0.8 0.8 0.8 AFRICA 1 0.8 0.8 0.8 L AMER 1 0.8 0.8 0.8 S&E ASIA 1 0.8 0.8 0.8 EEUR 1 0.8 0.5 0.8 KOR 1 0.8 0.8 0.8 INDIA 1 0.8 0.8 0.8

Table 41 Electricity generating subsector-specific base-share weights BSSUILM: ELECTRIC SUBSECTOR SHARE WEIGHTS, BY PERIOD, FUEL; see Equation 48 ISS- Fuel 1975 1990 2005 2020 2035 2050 2065 2080 2095 OIL 1 1 1 1 1 1 1 1 1 OIL SCRUB 0 0 1 1 1 1 1 1 133 GAS 1 1 1 1 1 1 1 1 1 GAS SCRUB 0 0 1 1 1 1 1 1 1

COAL 1 1 1 1 1 1 1 1 1 COAL SCRUB 0 0 1 1 1 1 1 1 1

BIOMASS 0 0 0.25 0.33 0.66 1 1 1 1

Table 42 Logit function scale parameters for electricity

NOTE: shares between 1990 and 2050 are automatically overwritten Most techs have equal base shares in 2050 Extrapolate between 1990 and 2050 Coal is an exception -- deviates from price-derivied shares in many regions, so extrapolation is extended to 2065 and is non-linear BSUILM; see Equation 54 Fuel 1975 1990 2005 2020 2035 2050 2065 2080 2095 USA OIL 0.0915 0.0244 0.0495 0.0747 0.0998 0.125 0.125 0.125 0.125 Canada OIL 0.168 0.0386 0.0602 0. 0818 0.1034 0.125 0.125 0.125 0.125 WEUR OIL 0.168 0.073 0.086 0.099 0.112 0.125 0.125 0.125 0.125 Japan OIL 0.1937 0.1419 0.1377 0. 1335 0.1292 0.125 0.125 0.125 0.125 Aus&NZ OIL 0.1937 0.0276 0.052 0. 0763 0.1007 0.125 0.125 0.125 0.125 FSU OIL 0.1157 0.0968 0.1039 0.1109 0.118 0.125 0.125 0.125 0.125 ACENP OIL 0.0547 0.104 0.1092 0. 1145 0.1197 0.125 0.125 0.125 0.125 MidEast OIL 0.2 0.5405 0.4366 0.3327 0.2289 0.125 0.125 0.125 0.125 Africa OIL 0.1851 0.1345 0.1321 0. 1297 0.1274 0.125 0.125 0.125 0.125 LatAmer OIL 0.2 0.4316 0.355 0.2783 0.2017 0.125 0.125 0.125 0.125 SEAsia OIL 0.1158 0.2918 0.2501 0. 2084 0.1667 0.125 0.125 0.125 0.125 EEUR OIL 0.1157 0.0444 0.0645 0. 0847 0.1048 0.125 0.125 0.125 0.125 Korea OIL 1 0.0731 0.086 0.099 0.112 0.125 0.125 0.125 0.125 India OIL 1 0.0287 0.0528 0.0769 0.1009 0.125 0.125 0.125 0.125 USA GAS 0.0274 0.0551 0.0726 0.0901 0.1075 0.125 0.125 0.125 0.125 Canada GAS 0.0694 0.0157 0.0431 0. 0704 0.0977 0.125 0.125 0.125 0.125 WEUR GAS 0.0694 0.0604 0.0766 0.0927 0.1089 0.125 0.125 0.125 0.125 Japan GAS 0.2 0.0776 0.0895 0. 1013 0.1132 0.125 0.125 0.125 0.125 Aus&NZ GAS 0.2 0.1319 0.1302 0. 1284 0.1267 0.125 0.125 0.125 0.125 FSU GAS 0.0565 0.3678 0.3071 0.2464 0.1857 0.125 0.125 0.125 0.125 ACENP GAS 0.0074 0.0045 0.0347 0. 0648 0.0949 0.125 0.125 0.125 0.125 MidEast GAS 0.0408 0.395 0.3275 0. 26 0.1925 0.125 0.125 0.125 0.125 Africa GAS 0.0128 0.1341 0.1318 0. 1295 0.1273 0.125 0.125 0.125 0.125 LatAmer GAS 0.0453 0.2674 0.2318 0. 1962 0.1606 0.125 0.125 0.125 0.125 SEAsia GAS 0.0007 0.1764 0.1636 0. 1507 0.1379 0.125 0.125 0.125 0.125 EEUR GAS 0.0565 0.0728 0.0859 0. 0989 0.112 0.125 0.125 0.125 0.125 Korea GAS 0.5005 0.0343 0.057 0. 0796 0.1023 0.125 0.125 0.125 0.125 India GAS 1 0.0514 0.0698 0.0882 0.1066 0.125 0.125 0.125 0.125 USA COAL 0.2 0.3967 0.336 0.2753 0.2147 0.154 0.125 0.125 0.125 Canada COAL 0.2 0.2522 0.2219 0. 1916 0.1613 0.131 0.125 0.125 0.12534 WEUR COAL 0.2 0.249 0.2215 0.194 0.1665 0.139 0.125 0.125 0.125 Japan COAL 0.0458 0.2359 0.2117 0.1875 0.1632 0.139 0.125 0.125 0.125 Aus&NZ COAL 0.0458 0.8405 0.6744 0.5082 0.3421 0.176 0.125 0.125 0.125 FSU COAL 0.2 0.2259 0.2036 0.1814 0.1592 0.137 0.125 0.125 0.125 ACENP COAL 0.2 0.8915 0.7128 0. 5342 0.3556 0.177 0.125 0.125 0.125 MidEast COAL 0 0.0645 0.0753 0.0862 0.0971 0.108 0.125 0.125 0.125 Africa COAL 0.2 0.6662 0.5422 0. 4181 0.2941 0.17 0.125 0.125 0.125 LatAmer COAL 0.0319 0.1285 0.1246 0. 1207 0.1169 0.113 0.125 0.125 0.125 SEAsia COAL 0.2 0.2723 0.2395 0. 2067 0.1738 0.141 0.125 0.125 0.125 EEUR COAL 0.2 0.4743 0.3958 0. 3172 0.2386 0.16 0.125 0.125 0.125 Korea COAL 4.0012 0.1156 0.1172 0.1188 0.1204 0.122 0.125 0.125 0.125 India COAL 4.0012 0.8722 0.6981 0.5241 0.35 0.176 0.125 0.125 0.125 USA NUCLEAR 0.0346 0.5238 0.4241 0.3244 0.2247 0.125 0.125 0.125 0.125 Canada NUCLEAR 0.0192 0.6935 0.5514 0.4092 0.2671 0.125 0.125 0.125 0.125 WEUR NUCLEAR 0.0192 0.6176 0.4944 0.3713 0.2481 0.125 0.125 0.125 0.125 Japan NUCLEAR 0.0082 0.5446 0.4397 0.3348 0.2299 0.125 0.125 0.125 0.125 Aus&NZ NUCLEAR 0.0082 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 FSU NUCLEAR 0.006 0.3095 0.2634 0.2172 0.1711 0.125 0.125 0.125 0.125 ACENP NUCLEAR 0 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 MidEast NUCLEAR 0.0001 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Africa NUCLEAR 0 0.0652 0.0802 0.0951 0.1101 0.125 0.125 0.125 0.125 LatAmer NUCLEAR 0.008 0.1726 0.1607 0. 1488 0.1369 0.125 0.125 0.125 0.125 SEAsia NUCLEAR 0.0039 0.2594 0.2258 0.1922 0.1586 0.125 0.125 0.125 0.125 EEUR NUCLEAR 0.006 0.4085 0.3376 0.2668 0.1959 0.125 0.125 0.125 0.125 Korea NUCLEAR 31.335 0.777 0.614 0.451 0.288 0.125 0.125 0.125 0.125 India NUCLEAR 31.335 0.0477 0.067 0.0863 0.1057 0.125 0.125 0.125 0.125 USA SOLAR PV 0.0253 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Canada SOLAR PV 0.0172 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 WEUR SOLAR PV 0.0172 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Japan SOLAR PV 0.0056 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Aus&NZ SOLAR PV 0.0056 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 FSU SOLAR PV 0.006 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 ACENP SOLAR PV 0.0011 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 MidEast SOLAR PV 0 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Africa SOLAR PV 0.0009 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 LatAmer SOLAR PV 0.0061 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 SEAsia SOLAR PV 0.0036 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 EEUR SOLAR PV 0.006 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Korea SOLAR PV 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 India SOLAR PV 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 USA HYDRO 0.1 0.1073 0.2957 0. 3641 0.3268 0.2995 0.2065 0.1488 0.0985 Canada HYDRO 0.63 0.6154 0. 9 0.9 0.9 0.9 0.9 0.9 0.8447 WEUR HYDRO 0.21 0.1897 0.426 0.9693 0.9051 0.8939 0.5987 0.4658 0.356 Japan HYDRO 0.13 0.1074 0.2435 0. 3256 0.5686 0.5984 0.4748 0.3429 0.2464 Aus&NZ HYDRO 0.23 0.2129 0.5841 0. 5329 0.5373 0.557 0.4275 0.3957 0.2457 FSU HYDRO 0.14 0.1242 0.9 0. 7756 0.326 0.1999 0.1947 0.158 0.094935 ACENP HYDRO 0.22 0.2362 0.2675 0. 8649 0.2568 0.125 0.0817 0.0759 0.0411 MidEast HYDRO 0.06 0.0624 0.2764 0. 2078 0.1376 0.1106 0.0727 0.0718 0.0543 Africa HYDRO 0.17 0.1398 0.554 0. 4931 0.3633 0.3232 0.2028 0.1024 0.058 LatAmer HYDRO 0.63 0.6701 0.9 0.9 0.9 0.9 0.7741 0.5338 0.4229 SEAsia HYDRO 0.19 0.205 0.864 0. 3952 0.3294 0.2019 0.1549 0.0626 0.038 EEUR HYDRO 0.16 0.119 0.3877 0. 5733 0.3956 0.1711 0.2246 0.1934 0.1297 Korea HYDRO 0.08 0.0591 0.0285 0. 0336 0.0519 0.0247 0.0184 0.0193 0.0144 India HYDRO 0.19 0.2523 0.5818 0. 303 0.225 0.1123 0.0635 0.041 0.0242 USA H2 FUEL CELL 0 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Canada H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 WEUR H2 FUEL CELL 0 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Japan H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 Aus&NZ H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 FSU H2 FUEL CELL 0 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 ACENP H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 MidEast H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 Africa H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 LatAmer H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 SEAsia H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 EEUR H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 Korea H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 India H2 FUEL CELL 0 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 USA FUSION 0 0 0 0 0 0 0 0 0 Canada FUSION 0 0 0 0 0 0 0 0 0 WEUR FUSION 0 0 0 0 0 0 0 0 0 Japan FUSION 0 0 0 0 0 0 0 0 0 Aus&NZ FUSION 0 0 0 0 0 0 0 0 0 FSU FUSION 0 0 0 0 0 0 0 0 0 ACENP FUSION 0 0 0 0 0 0 0 0 0 MidEast FUSION 0 0 0 0 0 0 0 0 0 Africa FUSION 0 0 0 0 0 0 0 0 0 LatAmer FUSION 0 0 0 0 0 0 0 0 0 SEAsia FUSION 0 0 0 0 0 0 0 0 0 EEUR FUSION 0 0 0 0 0 0 0 0 0 Korea FUSION 0 0 0 0 0 0 0 0 0 India FUSION 0 0 0 0 0 0 0 0 0 USA WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 Canada WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 WEUR WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 Japan WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 Aus&NZ WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 FSU WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 ACENP WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 MidEast WIND 0.001 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 Africa WIND 0.001 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.125 LatAmer WIND 0.001 0 0.0313 0.0625 0.0938 0.125 0.125 0.125 0.12536 SEAsia WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 EEUR WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 Korea WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125 India WIND 0.001 0 0.0313 0. 0625 0.0938 0.125 0.125 0.125 0.125



## Fuel sharing and energy services

Table 43 Energy services input-output coefficients GJK
ENERGY SERVICE INPUT-OUTPUT COEFFICIENTS GJK; see Equation 55 SECTOR OIL GAS COAL ELECTRIC BIOMASS 1 1.67 1.54 2.5 0.86 2.5 RES/COM 2 1.92 1.9 2 1.05 2 INDUSTRY 3 3 3 3.33 1.05 3.33 TRANSPORT

Table 44 Energy services non-fuel costs HJK
NON-ENERGY Costs BY SECTOR HJK; see equation 55 SECTOR OIL GAS COAL ELECTRIC BIOMASS 1 4.98 3.24 2.87 3.41 2.87 RES/COM 2 0.41 0.32 0.8 1.16 0.8 INDUSTRY 3 98.88 200 200 153.17 200 TRANSPORT

Table 45 Hydrogen energy service fuel-related efficiency coefficient (Gjk: j=hydrogen) GJ Hydrogen per generic energy service GJK(JSH2,K,M); see Equation 55 & 67 SECTOR 1975 1990 2005 2020 2035 2050 2065 2080 2095 RES/COM 5 5 3 1.483 1.246 1.075 1.075 1.075 1.075 INDUSTRY 5 5 5 1.727 1.727 1.727 1.727 1.727 1.727 TRANSPORT 5 5 2.22 1. 2 1.2 1.2 1.2 1.2 1.2

energy service increase 0 0 0 0 0 0 0 0 0 0 0 0 1.5 1.5 1.5 1.5 1.5 1.5

Table 46 Hydrogen energy service related non-fuel costs (Hjk: j=hydrogen) ENERGY SERVICE non-energy Cost37 ENERGY TRANSFORMATION BY SECTOR, Hydrogen fuel cells $/GJ energy service capital and O&M for hydrogen fuel cell HJK(JSH2,K,M); see Equation 55 SECTOR 1975 1990 2005 2020 2035 2050 2065 2080 2095 RES/COM 5 5 5 5 5 5 5 5 5 INDUSTRY 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 TRANSPORT 120 120 120 120 120 120 120 120 120 Note: Transport non-energy cost is significantly higher than that for oil

Table 47 Transportation sector fuel-related efficiency coefficients GJKLM for transport sector GJKLM(J,K,L,M) 1975 1990 2005 2020 2035 2050 2065 2080 2095 OIL 3 3 3 3 3 3 3 3 3 GAS 3 3 3 3 3 3 3 3 3 COAL 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33 ELECTRIC 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 1.05 BIOMASS 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33 3.33

Table 48 Transportation sector non-energy costs HJKLM More detailed transportation coefficients HJKLM(J,K,L,M) 1975 1990 2005 2020 2035 2050 2065 2080 2095 OIL 98.88 98.88 98.88 98.88 98.88 98.88 98.88 98.88 98.88 GAS 200 200 200 200 200 200 200 200 200 COAL 105 105 110 120 130 150 200 200 200 ELECTRIC 153.17 153.17 153.17 153.17 153.17 153.17 153.17 153.17 153.17 BIOMASS 200 200 200 200 200 200 200 200 200

Table 49 Aggregate price elasticity RPK See Equation 66 -0.7 AGGREGATE

Table 50 End-use sector-specific price elastic ities for oil, gas, coal and electricity RPJK; see Equation 69 OIL GAS COAL ELECTRIC SECTOR -3 -3 -3 -3 RES/COM -3 -3 -3 -3 INDUSTRY -13 -13 -13 -13 TRANSPORT38 Table 51 Transmission and Distribution Costs for Hydrogen PH2TDKM(K,M); see Equation 56 SECTOR 1975 1990 2005 2020 2035 2050 2065 2080 2095 SecName 1 1.5 1.5 1.2 0.94 0.75 0. 7 0.65 0.6 0.56 RES/COM 2 0.75 0.75 0.6 0.47 0.375 0.35 0.32 0.3 0.28 INDUSTRY 3 1.5 1.5 1.2 0.94 0.75 0. 7 0.65 0.6 0.56 TRANSPORT
Table 52 Transmission and Distribution Cost of Electricity PUTDKM(K,M): 1975 $/GJ see Equation 57 SECTOR 1975 1990 2005 2020 2035 2050 2065 2080 2095 SecName 1 3.03 3.03 2.81 2.61 2.42 2.25 2.08 1.93 1.79 RES/COM 2 0.75 0.75 0.7 0.65 0.6 0. 56 0.52 0.48 0.44 INDUSTRY 3 3.03 3.03 2.81 2.61 2.42 2. 25 2.08 1.93 1.79 TRANSPORT

Table 53 Regional weights of fuel share coefficients and initial shares of energy services consumptions
BASE ENERGY SERVICE CONSUMPTION WEIGHTS BY FUEL BY SECTOR BY REGION SJKLP(J,K,L) (UNITS=UNDIMENTIONED); see Equation 60 & 69 BASE ENERGY SERVICE CONSUMPTION WEIGHTS BY FUEL BY SECTOR BY REGION BSKL(K,L) (UNITS=EXAJOULES); see Equation 60, 61, 64, 65 & 69 OIL GAS COAL ELECTRIC SECTOR BSKL USA 0.185 0.683 0.011 0.379 RES/COM 15.238 USA 0.091 0.345 0.129 0.145 INDUSTRY 9.7881 USA 1.369 0 0 0.001 TRANSPORT 6.6411 CANADA 0.359 0.122 0.112 0.372 RES/COM 2.2295 CANADA 0.26 0.065 0.131 0.212 INDUSTRY 1.8809 CANADA 1.962 0 0.003 0.028 TRANSPORT 0.6795 WEUR 0.359 0.122 0.112 0.372 RES/COM 10.256 WEUR 0.26 0.065 0.131 0.212 INDUSTRY 8.6523 WEUR 1.962 0 0.003 0. 028 TRANSPORT 3.1256 JAPAN 0.443 0.088 0.207 0.462 RES/COM 1.6701 JAPAN 0.224 0.032 0.267 0.263 INDUSTRY 3.1513 JAPAN 2.672 0 0.001 0.05 TRANSPORT 0.7153 AUS&NZ 0.443 0.088 0.207 0.462 RES/COM 0.6263 AUS&NZ 0.224 0.032 0.267 0.263 INDUSTRY 1.1817 AUS&NZ 2.672 0 0.001 0.05 TRANSPORT 0.2682 FSU 0.359 0.122 0.112 0.372 RES/COM 5.4703 FSU 0.26 0.065 0.131 0.212 INDUSTRY 14.525 FSU 1.962 0 0.003 0. 028 TRANSPORT 2.1262 CHINA 0.443 0.088 0.207 0.462 RES/COM 1.7254 CHINA 0.224 0.032 0.267 0.263 INDUSTRY 7.0613 CHINA 2.672 0 0.001 0.05 TRANSPORT 0.3344 MIDEAST 0.443 0.088 0.207 0.462 RES/COM 0.517139 MIDEAST 0.224 0.032 0.267 0.263 INDUSTRY 0.9323 MIDEAST 2.672 0 0.001 0.05 TRANSPORT 0.3659 AFRICA 0.443 0.088 0.207 0.462 RES/COM 0.4621 AFRICA 0.224 0.032 0.267 0.263 INDUSTRY 1.4083 AFRICA 2.672 0 0.001 0.05 TRANSPORT 0.413 L.AMERICA 0.443 0.088 0. 207 0.462 RES/COM 1.2285 L.AMERICA 0.224 0.032 0.267 0.263 INDUSTRY 2.7492 L.AMERICA 2.672 0 0.001 0.05 TRANSPORT 1.0636 S&E ASIA 0.443 0.088 0. 207 0.462 RES/COM 0.5077 S&E ASIA 0.224 0.032 0.267 0.263 INDUSTRY 1.2696 S&E ASIA 2.672 0 0.001 0.05 TRANSPORT 0.3854 EEUR 0.359 0.122 0.112 0.372 RES/COM 1.5735 EEUR 0.26 0.065 0.131 0.212 INDUSTRY 4.0853 EEUR 1.962 0 0.003 0.028 TRANSPORT 0.4494 KOR 0.443 0.088 0.207 0.462 RES/COM 0.6953 KOR 0.224 0.032 0.267 0.263 INDUSTRY 0.7109 KOR 2.672 0 0.001 0.05 TRANSPORT 0.2515 INDIA 0.443 0.088 0.207 0.462 RES/COM 0.5077 INDIA 0.224 0.032 0.267 0.263 INDUSTRY 1.2696 INDIA 2.672 0 0.001 0.05 TRANSPORT 0.31



## Elasticities

Note: Developing country parameters have more effect since income change is greater Increased preference away from building use of coal Increased preference for building use of electricity

Table 54 Regional income elasticities by secondary fuel (oil, gas, coal, electricity) for end-use sectors RYJKLM(J,K,L,M); see Equation 60 & 69 REGION SECTOR FUEL 197 5 1990 2005 2020 2035 2050 2065 2080 2095

USA RES/COM OIL -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 USA INDUSTRY OIL 0 0 0 0 0 0 0 0 0 USA TRANSPORT OIL 0 0 0 0 0 0 0 0 0 USA RES/COM GAS 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 USA INDUSTRY GAS 0.1 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 USA TRANSPORT GAS 0 0 0 0 0 0 0 0 0 USA RES/COM COAL -1 -1 -1 -1 -1 -1 -1 -1 -1 USA INDUSTRY COAL -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0 .3 -0.3 -0.3 USA TRANSPORT COAL 0 0 0 0 0 0 0 0 0 USA RES/COM ELECTRIC 1 1 1 1 1 1 1 1 1 USA INDUSTRY ELECTRIC 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 USA TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 CANADA RES/COM OIL -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0 .1 -0.1 -0.140 CANADA INDUSTRY OIL 0 0 0 0 0 0 0 0 0 CANADA TRANSPORT OIL 0 0 0 0 0 0 0 0 0 CANADA RES/COM GAS 0.3 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 CANADA INDUSTRY GAS 0.1 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 CANADA TRANSPORT GAS 0 0 0 0 0 0 0 0 0 CANADA RES/COM COAL -1 -1 -1 -1 -1 -1 -1 -1 -1 CANADA INDUSTRY COAL -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0 .3 -0.3 -0.3 CANADA TRANSPORT COAL 0 0 0 0 0 0 0 0 0 CANADA RES/COM ELECTRIC 1 1 1 1 1 1 1 1 1 CANADA INDUSTRY ELECTRIC 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 CANADA TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 WEUR RES/COM OIL -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 WEUR INDUSTRY OIL 0 0 0 0 0 0 0 0 0 WEUR TRANSPORT OIL 0 0 0 0 0 0 0 0 0 WEUR RES/COM GAS 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 WEUR INDUSTRY GAS 0.1 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 WEUR TRANSPORT GAS 0 0 0 0 0 0 0 0 0 WEUR RES/COM COAL -1 -1 -1 -1 -1 -1 -1 -1 -1 WEUR INDUSTRY COAL -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0 .3 -0.3 -0.3 WEUR TRANSPORT COAL 0 0 0 0 0 0 0 0 0 WEUR RES/COM ELECTRIC 1 1 1 1 1 1 1 1 1 WEUR INDUSTRY ELECTRIC 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 WEUR TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 JAPAN RES/COM OIL -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 JAPAN INDUSTRY OIL 0 0 0 0 0 0 0 0 0 JAPAN TRANSPORT OIL 0 0 0 0 0 0 0 0 0 JAPAN RES/COM GAS 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 JAPAN INDUSTRY GAS 0.1 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 JAPAN TRANSPORT GAS 0 0 0 0 0 0 0 0 0 JAPAN RES/COM COAL -1 -1 -1 -1 -1 -1 -1 -1 -1 JAPAN INDUSTRY COAL -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0 .3 -0.3 -0.3 JAPAN TRANSPORT COAL 0 0 0 0 0 0 0 0 0 JAPAN RES/COM ELECTRIC 1 1 1 1 1 1 1 1 1 JAPAN INDUSTRY ELECTRIC 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 JAPAN TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 AUS&NZ RES/COM OIL -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 AUS&NZ INDUSTRY OIL 0 0 0 0 0 0 0 0 0 AUS&NZ TRANSPORT OIL 0 0 0 0 0 0 0 0 0 AUS&NZ RES/COM GAS 0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 AUS&NZ INDUSTRY GAS 0.1 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 AUS&NZ TRANSPORT GAS 0 0 0 0 0 0 0 0 0 AUS&NZ RES/COM COAL -1 -1 -1 -1 -1 -1 -1 -1 -1 AUS&NZ INDUSTRY COAL -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0 .3 -0.3 -0.3 AUS&NZ TRANSPORT COAL 0 0 0 0 0 0 0 0 0 AUS&NZ RES/COM ELECTRIC 1 1 1 1 1 1 1 1 1 AUS&NZ INDUSTRY ELECTRIC 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 AUS&NZ TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 041 FSU RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 FSU INDUSTRY OIL 0 0 0 0 0 0 0 0 0 FSU TRANSPORT OIL 0 0 0 0 0 0 0 0 0 FSU RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 FSU INDUSTRY GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 FSU TRANSPORT GAS 0 0 0 0 0 0 0 0 0 FSU RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.75 -0.75 -0.75 -0.75 -0.75 FSU INDUSTRY COAL 0 -0.3 -0.3 -0 .3 -0.3 -0.3 -0 .3 -0.3 -0.3 FSU TRANSPORT COAL 0 0 0 0 0 0 0 0 0 FSU RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.75 0.75 0.75 0.75 0.75 FSU INDUSTRY ELECTRIC 0.1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 FSU TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 CHINA RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 CHINA INDUSTRY OIL 0 0 0 0 0 0 0 0 0 CHINA TRANSPORT OIL 0 0 0 0 0 0 0 0 0 CHINA RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 CHINA INDUSTRY GAS 0 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 CHINA TRANSPORT GAS 0 0 0 0 0 0 0 0 0 CHINA RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 CHINA INDUSTRY COAL 0 -0.3 -0.3 -0 .3 -0.3 -0.3 -0 .3 -0.3 -0.3 CHINA TRANSPORT COAL 0 0 0 0 0 0 0 0 0 CHINA RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 CHINA INDUSTRY ELECTRIC 0.1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 CHINA TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 MIDEAST RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 MIDEAST INDUSTRY OIL 0 0 0 0 0 0 0 0 0 MIDEAST TRANSPORT OIL 0 0 0 0 0 0 0 0 0 MIDEAST RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 MIDEAST INDUSTRY GAS 0 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 MIDEAST TRANSPORT GAS 0 0 0 0 0 0 0 0 0 MIDEAST RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 MIDEAST INDUSTRY COAL 0 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 MIDEAST TRANSPORT COAL 0 0 0 0 0 0 0 0 0 MIDEAST RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 MIDEAST INDUSTRY ELECTRIC 0.1 0. 3 0.3 0.3 0.3 0. 3 0.3 0.3 0.3 MIDEAST TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 AFRICA RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 AFRICA INDUSTRY OIL 0 0 0 0 0 0 0 0 0 AFRICA TRANSPORT OIL 0 0 0 0 0 0 0 0 0 AFRICA RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 AFRICA INDUSTRY GAS 0 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 AFRICA TRANSPORT GAS 0 0 0 0 0 0 0 0 0 AFRICA RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 AFRICA INDUSTRY COAL 0 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 AFRICA TRANSPORT COAL 0 0 0 0 0 0 0 0 0 AFRICA RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 AFRICA INDUSTRY ELECTRIC 0.1 0. 3 0.3 0.3 0.3 0. 3 0.3 0.3 0.342 AFRICA TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 L.AMERICA RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 L.AMERICA INDUSTRY OIL 0 0 0 0 0 0 0 0 0 L.AMERICA TRANSPORT OIL 0 0 0 0 0 0 0 0 0 L.AMERICA RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 L.AMERICA INDUSTRY GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 L.AMERICA TRANSPORT GAS 0 0 0 0 0 0 0 0 0 L.AMERICA RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 L.AMERICA INDUSTRY COAL 0 -0.3 -0.3 -0.3 -0.3 -0.3 -0 .3 -0.3 -0.3 L.AMERICA TRANSPORT COAL 0 0 0 0 0 0 0 0 0 L.AMERICA RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 L.AMERICA INDUSTRY ELECTRIC 0.1 0. 3 0.3 0.3 0.3 0. 3 0.3 0.3 0.3 L.AMERICA TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 S&E ASIA RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 S&E ASIA INDUSTRY OIL 0 0 0 0 0 0 0 0 0 S&E ASIA TRANSPORT OIL 0 0 0 0 0 0 0 0 0 S&E ASIA RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 S&E ASIA INDUSTRY GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 S&E ASIA TRANSPORT GAS 0 0 0 0 0 0 0 0 0 S&E ASIA RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 S&E ASIA INDUSTRY COAL 0 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 S&E ASIA TRANSPORT COAL 0 0 0 0 0 0 0 0 0 S&E ASIA RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 S&E ASIA INDUSTRY ELECTRIC 0.1 0. 3 0.3 0.3 0.3 0. 3 0.3 0.3 0.3 S&E ASIA TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 EEUR RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 EEUR INDUSTRY OIL 0 0 0 0 0 0 0 0 0 EEUR TRANSPORT OIL 0 0 0 0 0 0 0 0 0 EEUR RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 EEUR INDUSTRY GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 EEUR TRANSPORT GAS 0 0 0 0 0 0 0 0 0 EEUR RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 EEUR INDUSTRY COAL 0 -0.3 -0.3 -0 .3 -0.3 -0.3 -0 .3 -0.3 -0.3 EEUR TRANSPORT COAL 0 0 0 0 0 0 0 0 0 EEUR RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 EEUR INDUSTRY ELECTRIC 0.1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 EEUR TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 KOR RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 KOR INDUSTRY OIL 0 0 0 0 0 0 0 0 0 KOR TRANSPORT OIL 0 0 0 0 0 0 0 0 0 KOR RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 KOR INDUSTRY GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 KOR TRANSPORT GAS 0 0 0 0 0 0 0 0 0 KOR RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 KOR INDUSTRY COAL 0 -0.3 -0.3 -0 .3 -0.3 -0.3 -0 .3 -0.3 -0.3 KOR TRANSPORT COAL 0 0 0 0 0 0 0 0 0 KOR RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.543 KOR INDUSTRY ELECTRIC 0.1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 KOR TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0 INDIA RES/COM OIL 0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 INDIA INDUSTRY OIL 0 0 0 0 0 0 0 0 0 INDIA TRANSPORT OIL 0 0 0 0 0 0 0 0 0 INDIA RES/COM GAS 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 INDIA INDUSTRY GAS 0 0.1 0. 1 0.1 0.1 0.1 0.1 0.1 0.1 INDIA TRANSPORT GAS 0 0 0 0 0 0 0 0 0 INDIA RES/COM COAL -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 INDIA INDUSTRY COAL 0 -0.3 -0.3 -0 .3 -0.3 -0.3 -0 .3 -0.3 -0.3 INDIA TRANSPORT COAL 0 0 0 0 0 0 0 0 0 INDIA RES/COM ELECTRIC 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 INDIA INDUSTRY ELECTRIC 0.1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 INDIA TRANSPORT ELECTRIC 0 0 0 0 0 0 0 0 0

Table 55 Regional income elasticities for end-use sectors RYKLM(K,L,M); see Equation 64 & 65 SECTOR 1975 1990 2005 2020 2035 2050 2065 2080 2095 REGION RES/COM 1 1 1 1 1 1 1 1 1 USA INDUSTRY 1 1.1 1 1 1 1 1 1 1 USA TRANSPORT 1 1 1 1 1 1 1 1 1 USA RES/COM 1 1 1 1 1 1 1 1 1 CANADA INDUSTRY 1 1 1 1 1 1 1 1 1 CANADA TRANSPORT 1 1 1 1 1 1 1 1 1 CANADA RES/COM 1 1 1 1 1 1 1 1 1 WEUR INDUSTRY 1 1 1 1 1 1 1 1 1 WEUR TRANSPORT 1 1 1 1 1 1 1 1 1 WEUR RES/COM 1 1 1 1 1 1 1 1 1 JAPAN INDUSTRY 1 1 1 1 1 1 1 1 1 JAPAN TRANSPORT 1 1 1 1 1 1 1 1 1 JAPAN RES/COM 1 1 1 1 1 1 1 1 1 AUS&NZ INDUSTRY 1 1 1 1 1 1 1 1 1 AUS&NZ TRANSPORT 1 1 1 1 1 1 1 1 1 AUS&NZ RES/COM 1.25 1.209 1.169 1.131 1.11 1.05 1.05 1.05 1 FSU INDUSTRY 1.25 1.209 1. 169 1.131 1.11 1.05 1.05 1.05 1 FSU TRANSPORT 1.25 1.209 1.169 1.131 1.11 1.05 1.05 1.05 1 FSU RES/COM 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 CHINA INDUSTRY 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 CHINA TRANSPORT 1.4 1.331 1.265 1.203 1. 144 1.087 1.087 1.0653 1.0435 CHINA RES/COM 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 MIDEAST INDUSTRY 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 MIDEAST TRANSPORT 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 MIDEAST RES/COM 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 AFRICA INDUSTRY 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 AFRICA TRANSPORT 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 AFRICA44 RES/COM 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 L.AMERICA INDUSTRY 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 L.AMERICA TRANSPORT 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0653 1.0435 L.AMERICA RES/COM 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0816 1.0761 S&E ASIA INDUSTRY 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0816 1.0761 S&E ASIA TRANSPORT 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0816 1.0761 S&E ASIA RES/COM 1.25 1.209 1.169 1. 25 1.09 1.02 1 1 1 EEUR INDUSTRY 1.25 1.209 1.169 1. 25 1.09 1.02 1 1 1 EEUR TRANSPORT 1.25 1.209 1.169 1.25 1.09 1.02 1 1 1 EEUR RES/COM 1.35 1.205 1.265 1.2 1.1 1 1 1 1 KOR INDUSTRY 1.35 1.205 1.265 1.2 1.1 1 1 1 1 KOR TRANSPORT 1.35 1.205 1. 265 1.2 1.1 1 1 1 1 KOR RES/COM 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0816 1.0761 INDIA INDUSTRY 1.4 1.331 1.265 1.203 1.144 1.087 1.087 1.0816 1.0761 INDIA TRANSPORT 1.4 1.331 1.265 1.203 1. 144 1.087 1.087 1.0816 1.0761 INDIA

Table 56 End-use sector-specific price elasticities RPKK(K); see Equation 64, 65 & 66 AGG SECTOR -0.5 RES/COM RPKK,JK,K=1 -0.8 INDUSTRY RPKK,JK,K=2 -0.07 TRANSPORT RPKK,JK,K=3

Table 57 Regional end-use sector efficiency coefficients for 1990 TKLM- see Equation 68 Region Buildings Industry Transport US 0.019565 -0.00056 0.013115 CAN 0.039315 0.033156 0.021391 WEUR 0.025902 0.007587 -0.01245 Japan 0.020001 0.029208 0.010587 AUS&NZ 0.074481 0.082479 0.022877 FSU -0.00492 0.00876 0.006304 ACENP 0.002941 0.014158 -0.02308 MIDEAST 0.027642 -0.01459 -0.00216 AFRICA 0.003204 0.018172 0.010918 L AMER -0.01118 0.002468 -0.01948 S&E ASIA -0.0148 -0.00167 -0.02505 EEUR -0.00492 0.00876 0.006304 KOR 0.066001 0.040868 0.071239 INDIA -0.0148 -0.00167 -0.02505

Table 58 End-use sector efficiency improvement coefficients for 2005 through 209545 TKLM(K,L,M); see Equation 68 Region 2005 2020 2035 2050 2065 2080 2095 US 0.005 0.005 0.005 0. 005 0.005 0.005 0.005 CAN 0.005 0.005 0.005 0.005 0.005 0.005 0.005 WEUR 0.015 0.005 0.005 0.005 0.005 0.005 0.005 Japan 0.025 0.005 0.005 0.005 0.005 0.005 0.005 AUS&NZ 0.005 0.005 0.005 0.005 0.005 0.005 0.005 FSU 0.02 0.025 0.02 0. 015 0.0075 0.0075 0.005 ACENP 0.05 0.035 0.025 0.015 0.01 0.005 0.005 MIDEAST 0.005 0.005 0.015 0.015 0.02 0.01 0.01 AFRICA 0.015 0.015 0.01 0.01 0.02 0.02 0.015 L AMER 0.01 0.01 0.01 0.02 0.02 0.02 0.01 S&E ASIA 0.015 0.02 0.01 0.01 0.01 0.01 0.01 EEUR 0.02 0.025 0.02 0.015 0.0075 0.0075 0.005 KOR 0.025 0.02 0.01 0.01 0.01 0.01 0.01 INDIA 0.015 0.02 0.01 0.01 0.01 0.01 0.01



## 1990 Input data for calibration

The next 4 tables are 1990 input data for calibration for the US

Data from IE A database Units: EJ Net energy (HHV) Non-fossil electricity inputs evaluated at average fossil generation efficiency for that region

*** Oil consumption figures for industry INCLUDE non-energy use

Table 59 Fuel demand (EJ) Industry sector fdemand(L,K,J) Region# sec# IndOil IndGas IndC oal IndElec IndBio IndTotal USA 2 7.356 7.0887 2.7183 3.1207 1.1701 21.5

Table 60 Fuel demand, Transportation sector fdemand -- Fuel demand, Transportation sector fdemand(L,K,J) Region# sec# TranOil TranGas TranCoal TranElec TranBio TranTotal USA 3 22.5011 0.7371 0 0.0149 0 23.3
Table 61 Fuel demand, Buildings fdemand -- Fuel demand, Buildings sector46 fdemand(L,K,J) Region# sec# BldgOil BldgGas Bl dgCoal BldgElec Bl dgBio BldgTotal USA 1 2.0986 7.836 0.1725 6.3488 0.6209 17.1

Table 62 Fuel demand, Electricity generation sector fdemand -- Fuel demand, Electric Gen sector fdemand(L,K,J) Region# sec# ElecOil ElecGas ElecCoal ElecNuc ElecSol ElecHydr
o ElecBio ElecTot

USA 4 1.1414 2.7354 16.2322 7.0663 0 3.341 0.6209 31.1


## Resulting, for example, for the USA for the B2 scenario in Final Energy Demand:

Table 63 Final energy demand, for example, for the USA for the B2 scenario (MiniCAM output) Final Energy Total-By Fuel EJ/yr Oil Gas Coal Elec Biom H2 Total 1990 31.95551 15.66202 2.89031 9.48416 1.79046 0 61.78246 2005 37.76573 24.58468 2.66865 10.98545 1.41134 0 77.41586 2020 39.77497 32.67494 2.22209 11.0709 1.19786 0 86.94076 2035 42.12493 39.07377 2.41247 11.02969 1.25828 0 95.89915 2050 46.10209 40.7299 2.87739 10.80512 1.44334 0 101.9579 2065 51.43048 37.19612 3.89162 13.47239 1.49725 0 107.4879 2080 53.06372 35.71502 4.9359 17.97672 1.61982 0 113.3112 2095 56.9303 32.48741 6.07086 22.79717 1.7928 0 120.0785 

## Resulting, for example, for the USA for the B2 scenario in electricty generation:

Table 64 Results, for example, for the USA for th e B2 scenario in Electric Power Generation by Technologies
Electric Power Generation EJ/yr Oil Gas Coal Nuclear Solar Hydro Biomas s H2Fcell Fusion Wind SWStor SatSolar Tot a 1990 0.3696 0.8341 4.926 2.1541 0 1.0128 0.1877 0 0 0 0 0 9.4 8 2005 0.6707 1.4479 5.0687 2.1362 0.0004 1. 0922 0.3522 0.0416 0 0.1766 0 0.0001 10. 9 2020 0.7513 2.1479 4.1 1.7371 0.0043 1.1644 0.4734 0.1375 0 0.5583 1E-05 0.0005 11. 0 2035 0.7342 2.7299 3.2278 1.2523 0.0351 1.2285 0.5253 0.2794 0 1.0228 5E-05 0.0016 11. 0 2050 0.9367 3.0457 2.4818 0.7853 0.2709 1.2846 0.4499 0.465 0 1.0919 0.0002 0.0045 10. 8 2065 1.4595 3.5024 2.784 1.0825 0.7651 1.3324 0.5731 0.6135 0 1.3649 0.0007 0.012 13. 4 2080 1.0266 4.4432 4.4743 1.723 1.3612 1.3732 0.8283 0.9268 0 1.8315 0.0036 0.019 18. 047 2095 1.0364 5.0218 6.2393 2.349 2.0284 1.4073 1.1117 1.2677 0 2.3341 0.0298 0.0261 22. 8



## Parameters for emission calculations

Table 65 An example of a cost curve
1 4 from US METHANE REPORT Region NumPts Pt1 Pt2 Pt 3 Pt4 Pt5 Pt6 Pt7 Pt8 Pt9 1 9 0 1 5 10 30.6 57.1 79.4 108 160.8 1 0 0.0662 0.1325 0.1656 0.2318 0.3113 0.3689 0.4258 0.4536 (and so on for all regions, for each cost curve)

Table 66 Global carbon emissions from oil, natural gas and coal combustion to calibrate against for 1990

1990 Carbon Emissions CO2Calib(I) Source 1 2372 Oil 2 1005 Nat Gas 3 2495 Coal

Table 67 Global Warming Potential, Atmospheric Half-Lives and Climate Forcing Information of Non-CO 2 Greenhouse Gases Greenhouse Gas GWP Appr oximate removal times that is half-lives in the atmosphere Climate forcing (W/m2) up to the year 2000 Carbon dioxide (CO 2 ) 1 >100 years 1.3 to 1.5 Methane (CH 4 ) 23 10 years 0.5 to 0.7 Nitrous oxide (N 2 O) 296 100 years 0.1 to 0.2 HFC-23 12,000 HFC-125 3,400 HFC-134a 1,300 HFC-143a 4,300 HFC-152a 120 HFC-227ea 3,500 HFC-236fa 9,400 Perfluoromethane (CF4) 5,700 >1000 years approximately 0.01

Perfluoroethane (C2F6) 11,900

Sulfur Hexafluoride (SF6) 22,200

Tropospheric Ozone 10-100 days 0.25 to 0.75

Fine aerosols48 Sulfate 10 days minus 0.3 to -1.0 Black carbon 10 days 0.1 to 0.8

Table 68 Gas flare, flared gas burn, and shale burn parameters "FLRL1" IS THE FLARING RATE IN 1975, "FLRL2" IS THE ULTIMATE FLARING RATE, AND "FLRL3" IS THE NUM BER OF YEARS TO REACH "FLRL2." THE MODEL EXPONENTIALLY INTER POLATES BETWEEN THE RATES; see Equation 93 See Equation 92 & 93 Region FLRL1 FLRL2 FLRL 3 SBRL1 SBRL2 SBRL3 SHAL E1 SHAL E2 SHAL E3 US 1 0.08 0.025 25 0.11 0.20 25 0.01 0.99 70 CANADA 2 0.07 0.025 25 0.25 0.20 25 0.01 0.45 70 WEUR 3 0.07 0.025 25 0.25 0.20 25 0.01 0.45 70 JAPAN 4 0.03 0.025 25 0.80 0.20 25 0.01 0.99 70 AUS&NZ 5 0.03 0.025 25 0.80 0.20 25 0.01 0.99 70 FSU 6 0.02 0.015 25 0.80 0.28 25 0.01 0.9 70 ACENP 7 0.107 0.035 50 0.80 0.59 50 0.01 0.25 70 MIDEAST 8 0.687 0.023 50 0. 75 0.44 50 0.01 0.25 70 AFRICA 9 0.753 0.08 50 0. 60 0.28 50 0.01 0.25 70 L AMER 10 0.499 0.08 50 0.29 0.28 50 0.01 0.25 70 S&E ASIA 11 0.38 0.045 50 0.71 0.47 50 0.01 0.25 70 EEUR 12 0.02 0.015 50 0.80 0.20 25 0.01 0.9 70 KOREA 13 0.0001 0.0001 50 0. 80 0.20 25 0.01 0.9 70 INDIA 14 0.38 0.045 50 0.71 0.47 50 0.01 0.25 70

Table 69 Regional non-feedstock use of oil, gas, and coal (Sfedl) FEEDSTOCK USES OF FOSSIL FUELS (SFEDIL) -- SHARE OF EACH FOSSIL FUEL USED AS A FEEDSTOCK; equation 97, 98, 99, 105, 106, 107, 108 OIL GAS COAL Region 0.078 0.029 0.007 US 0.06 0.029 0.007 CANADA 0.05 0.029 0.007 WEUR 0.045 0.029 0.007 JAPAN 0.074 0.029 0.007 AUS&NZ 0.097 0.029 0.007 FSU 0.069 0.029 0.007 ACENP 0.042 0.029 0.007 MIDEAST 0.041 0.029 0.007 AFRICA 0.043 0.029 0.007 L AMER 0.025 0.029 0.007 S&E ASIA 0.093 0.029 0.007 EEUR 0.018 0.029 0.007 KOR 0.063 0.029 0.007 INDIA49 

## Non-CO2 emissions

Table 70 Overview of variables and consid erations of non-CO2 emission calculations
Source Index Driver Activity Base Year Data % of Total (base year) Cost Curve (max)

Methane (Gas 1) Industrial Sources 1 GDP (exponent se t to 0.25) EDGAR I10:Metals + I30:Chemicals 0.3%
Transportation (Mobile Sources) 2 Oil for transportation Fuel Stat & Mobile (split using ICF/EPA models 2/03) 0.4%

Coal Mining 3 Average of coal production and consumption (to smooth for regional swings in coal production) Coal 10.0% Coal (20-98%)

Elec Utilities (Stationary) 4 Tier 1 Coefficients on stationary fossil use (except buildings biomass which is in source 9) Fuel Stat & Mobile (split) 0.7%

Natural Gas Systems 5 0.66*gas consumption + 0.33*gas production Natural Gas 15.6% Natural Gas (35-45%)

Petroleum Systems 6 Oil production Oil 1.0% Oil (0-40%) Landfills 7 Population with an exponential logistic to approximate waste per capita based on income Solid Waste 13.1% Solid Waste (60-90%)

Wastewater Treatment 8 Population Wastewater 8.6%

Biofuel Combustion 9 Biomass in buildings sector Biofuel Combustion 3.3%
Land Use/Burning 10 Land us e emissions (restricted to positive values) EDGAR: LU Change and Burning 4.1%

Enteric Fermentation 11 Beef/mutton production Enteric Fermentation 28.0%

Manure Management 12 Managed beef (fraction beef grain-fed), plus 5 x pork and 5 x poultry production Manure 3.4% Manure Management (0-20%)50 Rice Cultivation 13 Food gr ain production / cumul. technological change in food grain production Rice 10.6%

Agricultural Residue Burning 14 Total crop area EDGAR Ag Residue 0.3%

Temperate Forest Fires 15 Forest land EDGAR fo rest fires 0.4%

N2O (Gas 2) Elec Utilities (Stationary) 1 IPCC Tier 1 coefs for Coal (end-use) and Fuel Oil (stationary oil) Fossil Fuel (Split using spreadsheet models 2- 03) 6.8%

Transportation (Mobile) 2 Oil for transportation Fossil Fuel (Split using spreadsheet models 2- 03) 1.0%

Human Sewage 3 Population * percap calories from meat (protein proxy) HumanSewage 2.6%
Adipic Acid 4 GDP (exponent set to 0.25) ICF/EPA 2-03 Spreadsheet model 2.7% Adipic Acid (96%) Nitric Acid 5 GDP (exponent set to 0.25) ICF/EPA 2-03 Spreadsheet model 5.1% Nitric Acid (89%) Agricultural Soils 6 Oil crops and part of misc. crops (proxy for N fixing crops), and total crops (proxy for fert use) weighted by estimated emissions factors Ag Soil Values (split using EDGAR) 41.0%

Manure Management 7 Managed beef (fraction beef grain-fed), plus pork and poultry production Manure 7.4%

Biomass Combustion 8 Biomass (total energy consumption) Biomass Fuel 1.2%

Agricultural Residue Burning 9 Total crop area EDGAR Ag Residue Burning 0.3%
Land Use/Burning 10 Same as methane from land use / burning EDGAR: LU change and burning 5.5%
Unmanaged Manure 11 Beef production from pasture land Ag Soil Values (split using EDGAR) 26.3%

Temperate Forest Fires 12 Forest land EDGAR Fo rest fires 0.1%51 

## Sulfur emissions

Table 71 Regional end-use sector specific ash retention parameters for coal Ash Retention percentage for Coal SO2ASHR (KL) Reg RESCOM INDUSTRY TRANSPORT E Power G USA 10 7.3 5 5 CANADA 18 7.3 5 20 WEUR 15 11.3 5 13.3 JAPAN 10 58.1 5 5 AUSNZ 10 5 5 13.3 FSUEE 30 30 30 30 ACENP 29.7 19.5 30 8 MIDEAST 10 5 5 5 AFR 10 5 5 5 LA 10 10 5 13.3 SEASIA 11 10.3 5 8.5 EEuro 15 30 15 5 Korea 10 5 5 5 India 10 5 5 5.5

Table 72 Sulfur content (percentage by weight)

For emissions in TgS, use: (Fue l Use in EJ) / (GJ/Tonne) * (S %/100) * 1000 * (1 - f_control%) Biomass has fixed emission coefficient For nat gas, the factor below is really the emissions rate, not S% Generally identical for coal (adjusted in some instances to match sectoral inventories) SO2SCT Sulfur content (percentage by weight) Note that in dev countries , the S% of pet products is the S% before controls (which include, reducing S%!) SO2SCT Sulfur content (percentage by weight) Reg FuelName RESCOM I NDUSTRY TRANSPORT E Power G USA OIL 0.67 0.26 0.17 1.34 CANADA OIL 0.28 0.57 0.17 1 WEUR OIL 0.3 0.32 0.19 0.5 JAPAN OIL 0.43 0.33 0.49 1.2 AUSNZ OIL 0.4 1 0.2 1.4 FSU OIL 0.4 1.3 0.4 1.3 ACENP OIL 0.23 0.45 0.21 0.56 MIDEAST OIL 0.2 1 0.25 1.4 AFR OIL 0.32 1.05 0.27 1.7552 LA OIL 0.4 2.43 0.55 2.7 SEASIA OIL 0.3 1.73 0.54 1.66 EEuro OIL 0.3 0.75 0.55 0.9 Korea OIL 0.78 1.74 0.45 2.85 India OIL 0.5 3.17 0.56 1.6 USA GAS 0.0063 0.4389 0.0063 0.0063 CANADA GAS 0.0063 1.254 0.0063 0.0063 WEUR GAS 0.0063 0.1568 0.0063 0.0063 JAPAN GAS 0.0063 0.1568 0.0063 0.0063 AUSNZ GAS 0.0063 0.1568 0.0063 0.0063 FSU GAS 0.0063 0.35 0.0063 0.0627 ACENP GAS 0.0063 0.5 0.0063 0.0063 MIDEAST GAS 0.0063 0.5 0.0063 0.0063 AFR GAS 0.0063 0.5 0.0063 0.0063 LA GAS 0.0063 0.5 0.0063 0.0063 SEASIA GAS 0.0063 0.5 0.0063 0.0063 EEuro GAS 0.0063 0.5 0.0063 0.0627 Korea GAS 0.0063 0.5 0.0063 0.0063 India GAS 0.0063 0.5 0.0063 0.0063 USA COAL 1.84 1.18 1.38 1.38 CANADA COAL 1.05 1.05 1.05 1.05 WEUR COAL 1.14 1.23 1.23 1.23 JAPAN COAL 0.55 0.75 0.55 0.55 AUSNZ COAL 0.34 0.34 0.34 0.34 FSU COAL 1.04 1.15 1.04 1.04 ACENP COAL 1.25 1.25 1.25 1.25 MIDEAST COAL 1.25 1.25 1.25 1.25 AFR COAL 0.59 0.59 0.59 0.59 LA COAL 1.23 1.23 1.23 1.23 SEASIA COAL 1.23 1.23 1.23 1.23 EEuro COAL 1.07 1.33 1.33 1.4 Korea COAL 0.99 0.99 0.99 0.99 India COAL 0.55 0.55 0.55 0.55

Table 73 Regional end-use specific and fuel-specific heat content values Heat Content (GJTonne) SO2ENDN (JKL) Reg FuelName RESCOM I NDUSTRY TRANSPORT E Power G USA OIL 42.98 42 44.68 42 CANADA OIL 42.98 42 44.68 42 WEUR OIL 42.98 42 44.68 42 JAPAN OIL 42.87 42.91 43.87 42.0253 AUSNZ OIL 42.01 42.56 44.46 43.03 FSUEE OIL 42.98 42 44.68 42 ACENP OIL 40.49 39.41 40.61 39.41 MIDEAST OIL 41.17 43.13 44.61 42.49 AFR OIL 42.4 42.72 44.48 42.35 LA OIL 40.86 42.89 40.86 42.17 SEASIA OIL 43.28 40.1 41.89 39.58 EEuro OIL 42.98 42 44.68 42 Korea OIL 41.17 39.87 41.42 38.36 India OIL 41.52 40.01 40.96 39.83 USA GAS 100 100 100 100 CANADA GAS 100 100 100 100 WEUR GAS 100 100 100 100 JAPAN GAS 100 100 100 100 AUSNZ GAS 100 100 100 100 FSU GAS 100 100 100 100 ACENP GAS 100 100 100 100 MIDEAST GAS 100 100 100 100 AFR GAS 100 100 100 100 LA GAS 100 100 100 100 SEASIA GAS 100 100 100 100 EEuro GAS 100 100 100 100 Korea GAS 100 100 100 100 India GAS 100 100 100 100 USA COAL 23.53 23.53 23.53 23.53 CANADA COAL 20.56 20.56 20.56 20.56 WEUR COAL 15.34 15.34 15.34 15.34 JAPAN COAL 27.34 27.34 27.34 27.34 AUSNZ COAL 15.46 15.46 15.46 15.46 FSU COAL 18.54 18.54 18.54 18.54 ACENP COAL 20.97 20.97 20.97 20.97 MIDEAST COAL 26.53 26.53 26.53 26.53 AFR COAL 22.71 22.71 22.71 22.71 LA COAL 25.86 25.86 25.86 25.86 SEASIA COAL 21.46 21.46 21.46 21.46 EEuro COAL 13.99 13.99 13.99 13.99 Korea COAL 26.79 26.79 26.79 26.79 India COAL 20.22 20.22 20.22 20.22

Table 74 An example of the non-climate sulfur control fraction
Oth Emiss SO2 Cntl Frac % Bld Oil Bld Gas Bld Coal Bld Biom Ind Oil Ind Gas Ind Coal Ind Biom 1990 0.23181 0.12261 0.12261 0 0. 06288 0.2722 0.2207 0.11035 2005 0.51286 0.27128 0.27128 0 0. 13912 0.60223 0.4883 0.2441554 2020 0.71749 0.37951 0.37951 0 0. 19462 0.84252 0.68312 0.34156 2035 0.78565 0.41557 0.41557 0 0. 21311 0.92256 0.74802 0.37401 2050 0.82357 0.43562 0.43562 0 0. 2234 0.96708 0.78412 0.39206 2065 0.84087 0.44478 0.44478 0 0. 22809 0.9874 0.8006 0.4003 2080 0.84757 0.44832 0.44832 0 0. 22991 0.99526 0.80697 0.40349 2095 0.85001 0.44961 0.44961 0 0. 23057 0.99813 0.8093 0.40465

Table 75 Additional sulfur emission control factors
Oth Emiss SO2 Cntl Frac % Tran Oil Tran Gas Tran Coal Tran Biom Elec Oil Elec Gas Elec Coal Elec Biom

1990 0.19233 0.12261 0.2207 0.2207 0.1708 0.24523 0.24523 0.12261 2005 0.42553 0.27128 0.4883 0.4883 0.3779 0.54255 0.54255 0.27128 2020 0.59531 0.37951 0.68312 0.68312 0.52867 0.75902 0.75902 0.37951 2035 0.65187 0.41557 0.74802 0.74802 0.5789 0.83114 0.83114 0.41557 2050 0.68333 0.43562 0.78412 0.78412 0.60684 0.87125 0.87125 0.43562 2065 0.69769 0.44478 0.8006 0.8006 0.61959 0.88955 0.88955 0.44478 2080 0.70324 0.44832 0.80697 0.80697 0.62452 0.89663 0.89663 0.44832 2095 0.70527 0.44961 0.8093 0.8093 0.62632 0.89922 0.89922 0.44961
Table 76 Sulfur Emissions Control Mid-point GDP_0 (PPP-based GDPcap) S Emissions Control "timescale" Tau (PPP-based GDPcap) Sulfur Emissions Control Mid-point GDP_0 (ppp-based GDPcap) SO2GDP0 Reg Value USA 27.2 CANADA 32.3 WEUR 16.8 JAPAN 8 AUSNZ 16.9 FSUEE 12 ACENP 8 MIDEAST 8 AFR 8 LA 8 SEASIA 8 EEuro 10.3 Korea 8 India 8

Table 77 Regional end-use and fuel-specific maximum control values Maximum Control Percentage55 SO2MAXCTRL (JKL) For oil, can us e alternative formulation based on S% below Reg FuelName RESCOM INDUS TRY TRANSPORT E Power G USA OIL 45 81 45 81 CANADA OIL 45 81 45 81 WEUR OIL 45 81 45 81 JAPAN OIL 45 81 45 81 AUSNZ OIL 45 81 45 81 FSUEE OIL 45 81 45 81 ACENP OIL 90 81 72 90 MIDEAST OIL 90 81 72 90 AFR OIL 90 81 72 90 LA OIL 90 81 72 90 SEASIA OIL 90 81 79.2 90 EEuro OIL 45 81 45 81 Korea OIL 90 81 79.2 90 India OIL 90 81 79.2 90 USA GAS 45 99.9 45 90 CANADA GAS 45 99.9 45 90 WEUR GAS 45 99.9 45 90 JAPAN GAS 45 99.9 45 90 AUSNZ GAS 45 99.9 45 90 FSU GAS 45 99.9 45 90 ACENP GAS 45 99.9 45 90 MIDEAST GAS 45 99.9 45 90 AFR GAS 45 99.9 45 90 LA GAS 45 99.9 45 90 SEASIA GAS 45 99.9 45 90 EEuro GAS 45 99.9 45 90 Korea GAS 45 99.9 45 90 India GAS 45 99.9 45 90 USA COAL 45 81 81 90 CANADA COAL 45 81 81 90 WEUR COAL 45 81 81 90 JAPAN COAL 45 81 81 90 AUSNZ COAL 45 81 81 90 FSU COAL 45 81 81 90 ACENP COAL 45 81 81 90 MIDEAST COAL 45 81 81 90 AFR COAL 45 81 81 90 LA COAL 45 81 81 90 SEASIA COAL 45 81 81 90 EEuro COAL 45 81 81 90 Korea COAL 45 81 81 90 India COAL 45 81 81 9056 Table 78 Regional maximum percentages of non-en ergy related industrial sulfur emissionsMax Reduction % for Industrial (nonEnergy) Emissions SO2IPMR Reg Value USA 45 CANADA 45 WEUR 45 JAPAN 45 AUSNZ 45 FSUEE 80 ACENP 90 MIDEAST 90 AFR 90 LA 90 SEASIA 90 EEuro 45 Korea 90 India 90

Table 79 Regional coefficients determining changes in industrial sulfur emissions over time Power-law growth in industrial emissions (as yr^r) SO2PLG Region Value USA 0 CANADA 0 WEUR 0 JAPAN 0 AUSNZ 0 FSUEE 0 ACENP 0.25 MIDEAST 0.25 AFR 0.25 LA 0.25 SEASIA 0.25 EEuro 0 Korea 0.25 India 0.25


## Parameters related to the AgLU module

Table 80 Example of historical land use data collected57 Historical Land Use (000ha) Based on FAO numbers and converted to AgLU land allocation methodology HistLand 1961 (due to lack of FAO data for 1960) 1975 Region CropLand Pasture Forest Unmgd Ot her CropLand Pasture Forest Unmgd Other USA 90582 276067 200025 165410 183828 93416 252044 195019 191605 183828 Canada 21158 22041 59430 425252 394217 21599 27159 59430 419693 394217 OECD90 Europe 81520 89259 112775 52173 100505 78110 85775 121645 50207 100505 Japan 4849 254 11310 14797 6443 4182 1119 11076 14832 6443 Aus & NZ 9475 34436 12022 608228 130868 12846 35521 12022 603772 130868 FSU 133332 309929 140509 954933 651367 129218 326184 140509 942791 651367 China/CPA 173712 341012 142086 211950 305855 166364 398302 130977 173117 305855 MiddleEast 16462 20487 3437 201205 272611 17357 20484 3433 200316 272611 Africa 84711 51247 188865 1460883 1148280 93777 50956 187652 1453237 1148280 Latin America 46595 125369 146625 1424004 263752 57721 138624 139124 1407138 263752

S&E Asia 49821 50291 176468 151149 162703 56011 50735 166079 154884 162703 EEU 35245 24205 26551 17110 11523 34071 24119 27425 17481 11523 Korea 2598 41 1239 5231 764 2778 73 1227 5031 764 India 153229 21173 51601 37023 34294 159914 19541 59648 23922 34294

Table 81 Regional land areas in 1990 Land Area (1990 data in 000 ha) Region ArableLand Pasture Fo rest Other TotalLand NonWild USA 139099 249161 295990 183828 915912 732084 Canada 32150 33731 453300 394217 922097 527880 OECD90 Europe 96320 81749 142822 100505 436214 335709 Japan 4611 1493 25105 6443 37652 31209 Aus & NZ 47649 33342 153280 130868 795029 664161 FSU 195820 335893 941530 651367 2190070 1538703 China/CPA 160243 421777 181791 305855 1174615 868760 MiddleEast 26572 24905 16187 272611 514201 241590 Africa 144177 51523 715388 1148280 2934225 1785945 Latin America 106132 147691 1011154 263752 2005002 1741250 S&E Asia 106717 52245 257910 162703 590410 427707 EEU 39219 24605 35158 11523 114581 103058 Korea 2415 200 6476 764 9873 9109 India 175297 17646 67762 34294 297319 263025

Table 82 Land Carbon Density Para meters, by Region (TgC/000ha) CDensity Vegetation C Density (TgC /000ha) Soil C Density (TgC/000ha) Region crops biomass pasture trees Un Man crops biomass pasture trees UnMan USA 0.0050 0.0300 0.0070 0.0920 0.0920 0.1420 0.1890 0.1890 0.1392 0.139258 Canada 0.0050 0.0300 0.0070 0.0920 0. 0920 0.1420 0.1890 0.1890 0.1392 0.1392 OECD90 Europe 0.0050 0.0300 0.0070 0.1388 0.1388 0.1420 0.1890 0.1890 0.1465 0.1465 Japan 0.0050 0.0300 0.0070 0.1161 0.1161 0.1420 0.1890 0.1890 0.0947 0.0947 Aus & NZ 0.0050 0.0300 0.0070 0.1161 0. 1161 0.1420 0.1890 0.1890 0.0947 0.0947 FSU 0.0050 0.0300 0.0100 0.0936 0.0936 0.1510 0.1890 0.1890 0.2002 0.2002 China/CPA 0.0050 0.0300 0.0070 0.1565 0. 1565 0.1420 0.1890 0.1890 0.1332 0.1332 MiddleEast 0.0050 0.0300 0.0032 0.1800 0. 0032 0.0972 0.0649 0.0649 0.1309 0.0649 Africa 0.0150 0.0300 0.0150 0.1191 0. 1191 0.0736 0.0736 0.0736 0.0920 0.0920 Latin America 0.0050 0.0300 0.0100 0.1543 0.1543 0.0801 0.0420 0.0420 0.1066 0.1066

S&E Asia 0.0050 0.0300 0.0600 0.2159 0. 2159 0.0644 0.0500 0.0500 0.0915 0.0915 EEU 0.0050 0.0300 0.0070 0.1388 0.1388 0.1420 0.1890 0.1890 0.1465 0.1465 Korea 0.0050 0.0300 0.0070 0.1161 0.1161 0.1420 0.1890 0.1890 0.0947 0.0947 India 0.0050 0.0300 0.0600 0.2159 0.2159 0.0644 0.0500 0.0500 0.0915 0.0915

Table 83 Harvested (1990 data in 000 ha) Area Harvested (1990 data in 000 ha) USA FoodGr CoarseGr OilCrops OthCrops Biomass Hay/Grass Canada 29107.40 36530.60 29337.76 4059.20 0 31274.53 OECD90 Europe 14097.50 7480.80 4002.10 621.71 0 5903.90 Japan 27360.19 26644.81 12647.97 16729.04 0 10224.03 Aus & NZ 2334.40 137.09 165.78 1127.62 0 846.20 FSU 9361.14 4242.61 468.79 1781.48 0 30998.49 China/CPA 48792.00 55114.80 10329.00 16435.84 0 56000.00 MiddleEast 73964.20 30837.77 24949.28 28512.02 0 1979.84 Africa 10448.00 8499.65 1283.80 4124.17 0 1169.37 Latin America 14575.58 64823.14 19352.34 37077.16 0 4438.26 S&E Asia 16923.29 30559.93 27621.39 20717.49 0 5098.87 EEU 53814.89 12632.93 18539.89 14892.62 0 340.93 Korea 9926.81 16050.49 2717.42 6757.19 0 3644.94 India 1244.64 196.35 263.73 579.79 0 130.00 14 66188.51 36347.39 32330.60 32066.87 0 8364.00

Table 84 Example of regional technical improveme nts in food production in two time periods Annual percent technical improvement (start) KJIMP(J,L,M) period region UnMgd MgdFore st Pasture AnimPrds Biomass FoodGr CoarseGr OilCrops

3 USA 0 0.005 0 0 0.01 0.01 0.01 0.01 3 Canada 0 0.005 0 0 0.01 0.01 0.01 0.01 3 OECD90 Europe 0 0.005 0 0 0.01 0.01 0.01 0.01 3 Japan 0 0.005 0 0 0.01 0.01 0.01 0.01 3 Aus & NZ 0 0.005 0 0 0.01 0.01 0.01 0.0159 3 FSU 0 0.005 0 0 0.01 0.01 0.01 0.01 3 China/CPA 0 0.005 0 0 0.01 0.01 0.01 0.01 3 MiddleEast 0 0.005 0 0 0.01 0.01 0.01 0.01 3 Africa 0 0.005 0 0 0.01 0.01 0.01 0.01 3 Latin America 0 0.005 0 0 0.01 0.01 0.01 0.01

3 S&E Asia 0 0.005 0 0 0.01 0.01 0.01 0.01 3 EEU 0 0.005 0 0 0.01 0.01 0.01 0.01 3 Korea 0 0.005 0 0 0.01 0.01 0.01 0.01 3 India 0 0.005 0 0 0.01 0.01 0.01 0.01 Annual percent tec hnical improvement (for later period) KJIMP(J,L,M) period region UnMgd MgdFore st Pasture AnimPrds Biomass FoodGr CoarseGr OilCrops

6 USA 0 0.005 0 0 0.005 0.005 0.005 0.005 6 Canada 0 0.005 0 0 0.005 0.005 0.005 0.005 6 OECD90 Europe 0 0.005 0 0 0.005 0.005 0.005 0.005 6 Japan 0 0.005 0 0 0.005 0.005 0.005 0.005 6 Aus & NZ 0 0.005 0 0 0.005 0.005 0.005 0.005 6 FSU 0 0.005 0 0 0.005 0.005 0.005 0.005 6 China/CPA 0 0.005 0 0 0.005 0.005 0.005 0.005 6 MiddleEast 0 0.005 0 0 0.005 0.005 0.005 0.005 6 Africa 0 0.005 0 0 0.005 0.005 0.005 0.005 6 Latin America 0 0.005 0 0 0.005 0.005 0.005 0.005

6 S&E Asia 0 0.005 0 0 0.005 0.005 0.005 0.005 6 EEU 0 0.005 0 0 0.005 0.005 0.005 0.005 6 Korea 0 0.005 0 0 0.005 0.005 0.005 0.005 6 India 0 0.005 0 0 0.005 0.005 0.005 0.005

Table 85 Example of regional food demand data Base year demand for food kcal1(L,J,2) Units are kcal pe r day per person Region FoodGr CoarseGr OilCrops MiscCrop ProcCr op BeefPrds PorkPrds Poultry AnimFats Fish USA 675.20 147.78 54.03 318.54 1339.64 554.00 128.21 212.01 97.66 29.09 Canada 590.40 41.89 74.37 303.10 907. 98 476.39 116.26 142.23 276.99 31.10 OECD90 Europe 864.77 107.55 44.91 394.66 978.81 537.30 165.08 120.72 240.45 31.60 Japan 971.52 167.08 105.05 198.46 669.89 131.27 64.45 120.01 43.94 92.04 Aus & NZ 553.80 63.93 53.32 290.33 971. 04 711.39 74.06 125.39 171.14 24.80 FSU 1103.11 120.13 20.43 279.18 761.96 533.89 104.18 107.94 280.48 33.21 China/CPA 1651.55 249.13 57.93 207.84 221. 77 20.15 89.10 37.30 23.21 16.71 MiddleEast 1352.73 80.29 31.83 295.44 557. 13 196.32 0.56 68.53 38.89 6.25 Africa 476.48 585.77 46.21 345.37 350. 50 93.97 4.13 24.26 17.64 11.45 Latin America 635.40 349.16 31.70 296.10 755.59 217.66 29.36 73.21 53.64 12.6960 S&E Asia 1462.46 116.31 168.16 157.54 332. 66 73.52 15.18 25.04 19.87 19.22 EEU 1034.51 217.80 7.83 282.91 747.39 415.97 197.72 102.13 309.43 9.09 Korea 1461.07 191.62 137.38 208.22 600.41 66.00 55.13 56.58 35.32 63.65 India 1159.75 278.30 73.34 228.05 359.65 111.41 2.16 6.55 23.19 5.14

End-year demand for food kcal1(L,J,9) Units are kcal pe r day per person Region FoodGr CoarseGr OilCrops MiscCrop ProcCr op BeefPrds PorkPrds Poultry AnimFats Fish USA 675.20 147.78 54.03 318.54 1339.64 554.00 128.21 212.01 97.66 29.09 Canada 590.40 41.89 74.37 303.10 907. 98 476.39 116.26 142.23 276.99 31.10 OECD90 Europe 864.77 107.55 44.91 394.66 978.81 537.30 165.08 120.72 240.45 31.60 Japan 971.52 167.08 105.05 198.46 669.89 131.27 64.45 120.01 43.94 92.04 Aus & NZ 553.80 63.93 53.32 290.33 971. 04 711.39 74.06 125.39 171.14 24.80 FSU 1103.11 120.13 20.43 279.18 761.96 533.89 104.18 107.94 280.48 33.21 China/CPA 1651.55 249.13 57.93 207.84 221. 77 20.15 89.10 37.30 23.21 16.71 MiddleEast 1352.73 80.29 31.83 295.44 557. 13 196.32 0.56 68.53 38.89 6.25 Africa 476.48 585.77 46.21 345.37 350. 50 93.97 4.13 24.26 17.64 11.45 Latin America 635.40 349.16 31.70 296.10 755.59 217.66 29.36 73.21 53.64 12.69

S&E Asia 1462.46 116.31 168.16 157.54 332. 66 73.52 15.18 25.04 19.87 19.22 EEU 1034.51 217.80 7.83 282.91 747.39 415.97 197.72 102.13 309.43 9.09 Korea 1461.07 191.62 137.38 208.22 600.41 66.00 55.13 56.58 35.32 63.65 India 1159.75 278.30 73.34 228.05 359.65 111.41 2.16 6.55 23.19 5.14

Base year demand - other uses of food products kcal2(L,J) Units are kcal per person per day Region FoodGr CoarseGr OilCrops MiscCrop ProcCr op BeefPrds PorkPrds Poultry AnimFats Fish USA 6.1414 153.0042 2.9264 9.1475 219.4345 22.2849 0.9099 1.2802 133.3342 0.0445 Canada 44.2317 47.9629 22.3945 0.7130 173. 7042 50.6715 0.0000 0.0000 20.4128 2.5020 OECD90 Europe 54.4028 67.0509 4.1315 20.2397 252.2770 16.7601 0.5859 0.2032 99.4131 1.5630 Japan 0.0328 5.1103 0.2425 0.8880 145.9263 6.0484 0.0000 0.0000 79.8360 0.0458 Aus & NZ 179.2458 4.0296 0.2252 2.7263 177. 5072 110.3789 0.0000 0.0000 139.9965 1.1543 FSU 10.9669 207.9060 11.7750 9.4401 109.8181 8.0609 0.0000 0.0000 141.1541 0.0000 China/CPA 2.0549 6.8088 8.6101 1.9255 30. 0525 0.0143 0.0078 0.4006 6.8217 1.0940 MiddleEast 19.4974 20.5331 8.4541 6.9333 81. 1233 6.0253 0.0000 2.1661 17.1720 0.4904 Africa 3.4359 3.1369 6.4576 1.8920 40. 0746 0.9458 0.0020 0.0557 11.8259 0.1675 Latin America 3.4860 13.9732 5.3332 15.7309 125.0216 1.1377 0.0359 0.0900 55.8780 0.0122

S&E Asia 1.6782 14.1605 7.5486 3.9164 40. 5451 0.1872 0.0692 0.1579 5.4917 0.2849 EEU 51.9228 75.1785 2.9829 16.3179 107.5803 10.2540 2.5745 4.3775 50.0716 0.0464 Korea 0.2090 11.1464 0.0000 0.3538 111.1167 1.7294 1.7070 0.0000 35.3954 1.9608 India 0.3235 0.6388 0.0314 0.0000 18.3877 0.0000 0.0000 0.0000 3.2986 0.100561 Table 86 Although not directly used, an example of data collected for the AgLU module 1990 Land Use Carbon Emissions (TgC) Based on numbers from: R. Houghton, ORNL Region USA 7.45 Canada 4.97 OECD90 Europe -9.04 Japan 1.96 Aus & NZ 1.96 FSU 20.11 China/CPA 48.69 MiddleEast 16.27 Africa 348.47 Latin America 577.16 S&E Asia 766.07 EEU -9.04 Korea 0.00 India 328.32
Table 87 1990 Base Year CH4 and N2O emissions (in TgCH4 or TgN) Region CH4 enteric CH4 manure CH4 other/rice N2O soils N2O managed manure N2O empty USA 6.1700 1.2600 0.4400 0.5524 0.0328 0 Canada 0.7620 0.2190 0.0000 0.0738 0.0089 0 OECD90 Europe 8.1841 2.4560 0.1342 0.4039 0.0654 0 Japan 0.3460 0.1190 0.3780 0.0024 0.0031 0 Aus & NZ 4.5400 0.0927 0.2780 0.0534 0.0006 0 FSU 8.7896 1.0420 0.1152 0.1577 0.0848 0 China/CPA 5.3891 0.8208 17.1679 0.7557 0.1093 0 MiddleEast 1.1060 0.1088 0.2374 0.0521 0.0007 0 Africa 8.6117 0.5301 1.2381 0.1365 0.0086 0 Latin America 17.4797 0.6455 1.0386 0.2898 0.0176 0 S&E Asia 5.0582 0.6026 15.8724 0.1801 0.0338 0 EEU 2.3557 0.4654 0.0431 0.1037 0.0266 0 Korea 0.1440 0.0400 0.4777 0.0196 0.0016 0 India 7.5630 0.9050 14.4735 0.1990 0.0106 062 

# Appendix 7: List of equations
hgPicePr +•= ($/energy unit) Eq. 1 

# ( ) ∑ • •

=

j r j fuelj r j fuelj j p p 

### Pb Pb Share (unitless) Eq. 2

rxk rpk 

### XPbDemand ••= (energy/year) Eq. 3 Nstep m,is 1m m 

### )ST1(Tech Tech +•=

− (unitless) Eq. 4 

# ( )

m,l,is

m m,l,isis,ig m,l,is 

### Pfis Tech VC ExtrCost + +

= for oil, gas, coal and unconventional oil ($/GJ) Eq. 5

aloil convention i onaloil unconventi i m,l,aloil convention is m,l,is 

### CO CO Pfis Pfis

= =

= 

### • = for unconventional oil ($/GJ) Eq. 6 

# ∑

= 

### = n

1ig l,is,ig m,l,is 

### R Q (EJ) Eq. 7

m is,1igis,ig l,is,1ig 

### Tech )CC( R slope

− −



### − = Eq. 8


### slope) ExtrCost P(R Q m,l,is m,l,i 1n

1ig l,is,ig m,l,is 

### • −+ = 

# ∑ −

= (EJ) Eq. 9

l,is 1m,l,i 

### ESFIL ESILM =
= for oil, gas, coal and unconventional oil in base year (EJ/year) 

### .... Eq. 10

1m,l,i 1m,l,ism,l,is m,l,i 

### ESILM Nstep QQ 2 ESILM

− −



### − − •= for oil, gas, coal and unconventional oil in projections (EJ/year) Eq. 11

m anexpfos_r

1m,l m,l 1m,l,i m,l,i 

### TechPfac GDP GDP ESILM ESILM •• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

• =

− − (EJ/year) Eq. 12

l,i r

m 1m 1m,l,is1m,l,i m m,l,is m,l,i


### Tech Tech VP Tech V P Pfac ⎟ ⎟ ⎟ ⎟
⎠ ⎞
⎜ ⎜ ⎜ ⎜
⎝ ⎛

•− −

=

−

− − (unitless) Eq. 13

( ) ( ) ( )

3 3 Flr Nstep*1m
2 Flr Nstep*1m1 1m,l 

### Flr FlrFLR − −− 

### • = (unitless) Eq. 14 

### )FLR1( ESILM ESILM m,l m,l,gasi m,l,gasi 

### − • =
= = (EJ/year) Eq. 15



### 2 ESILM ESILM Nstep QQ 1m,l.i m,l,i 1m,l,ism,l,is −

− 

### + •+= (EJ/year) Eq. 16

1m,l,ui 1m,l,ism,l,nuclearis 

### ESU Nstep Q Q

− − = 

### •+= (EJ/year) Eq. 1763 

# ∑

= 

### = nreg

1l m,l,is 

### QQ (EJ/year) Eq. 18 

# ∑ ∑

= = 

### ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

= n

1ig nreg

1l l,is,ig 

### R W (EJ/year) Eq. 19

is,1ig is,ig m,l,uraniumis 

### C W )QR( 1C W )QR( tcosExtr

− = 

### • ⎟ ⎠ ⎞ ⎜ ⎝ ⎛

− −+• − = ($/GJ) Eq. 20

m m,l,isis,ig m,l,uraniumi 

### Tech VC P +

=
= ($/GJ) Eq. 21

rysht

1990m,l

m,l 1990m,l m,l,i 

### GDP GDP BIO ESILM ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

• =

= = (EJ/year) Eq. 22

NstepmHydro Hydro NstepmHydro Hydro

3 m,l,hydroi 2 1 2 1 

### e1

e Hydro ESILM ••+ ••+

= 

### + •= (EJ/year) Eq. 23 

# ( ) m,l,iim,l,im,l,i 

### PfiTrPP •+= ($/GJ) Eq. 24

iim,l,im,l,j 

### hijgijPPj +•= for oil, gas, coal, and biomass/waste ($/GJ) Eq. 25 ( ) ( ) ( )

3 3 HCLT Nstep1m
2 HCIL Nstep1m1
1 i,j 

### HCLT HCILT hc •− •−− 

### • = ($/GJ) Eq. 26 

# ( ) i,ji,j m,l,im,l,i,j 

### hcgctscossynPPC + • += synliquid from coal, gas, or biomass; syngas from coal or biomass ($/GJ) Eq. 27

coali oili coali



### CO CO CO x SeqFractMa

= = = 

### − = (fraction) Eq. 28 

# ( )

coali i,j m,l,ui scrubbed non,m,l,ui scrubbed,m,l,ui j 

### CO 1 gc gu hu hu Cpenalty

= − 

### •• −
= ($/ton C) Eq. 29 

# ( ) j m,l m,l,ui disp 

### Cpenalty x SeqFractMa Carbdisp 0PfCst + • •= ($/GJ) Eq. 30 

## ( ) 0001.0x SeqFractMa 1PfuCstC m,l,ui disp seq 

### + −•+= ($/GJ) Eq. 31

4 seq 4 m,l,ui 4 m,l,ui scrubno 

### CPfu Pfu S

− − −

− 

### + = (unitless) Eq. 32

4 seq 4 m,l,ui 4 seq scrub 

### CPfu C S

− − −


### + = (unitless) Eq. 33

disp scrub i,j scrubbed coali,j 

### CstShc hc •+= += ($/GJ) Eq. 3464 

# ∑ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

+

=

−− −−

ns RCI

m,l,ui gas,or,oilform,l,j m,l,i,j RCI

m,l,ui gas,or,oilform,l,j m,l,i,j

m,l,i,j ji ji



### Pfu Pj PC Pfu Pj PC SynShare for each of the technologies

(unitless) Eq. 35 

### )Pfjk Pj( SynShare PC SynShare Pj m,l,k,j m,l,gasorliquidsjm,l,i,j
ns m,l,i,jm,l,i,j m,l,gasorliquidsj 

### + • +• =
−−= −−= 

# ∑

($/GJ) Eq. 36 

# ( ) m,l,hi m,l,hi m,l,ui m,l,i ssh 

### hhgh PfuPPssh + •+= ($/GJ) Eq. 37 

# ( ) m,l,hi m,l,hi lm m,l,ui l,i m,l,ui m,l,issh 

### hhgh Carbdisp 0Pf)mFracRe1(PfuPPssh + • • + −•+= ... ($/GJ) Eq. 38 

# ( ) ∑ • •

=

nc ruiss ssh m,l,hi ruiss ssh m,l,hi l,hi 

### Pssh bssh Pssh bssh Ssh (unitless) Eq. 39 

# ( ) ∑ • =

nc ssh l,hi m,l,hi 

### PsshSsh PH generated from oil, gas, or solids ($/GJ) Eq. 40

m,l,hi m,l,hi m,l,im,l,hi 

### hhghPPH +•= generated from biomass ($/GJ) Eq. 41 

# ∑ • =
= nhprices m,l,hi l,hi m,l,hydrogenj 

### PHSh Pj ($/GJ) Eq. 42 

# ( ) ∑ • •

=

nhprices rhi m,l,hi m,l,hi rhi m,l,hi m,l,hi l,hi 

### PH bsh PH bsh Sh (unitless) Eq. 43 

# ( ) m,l,ui m,l,ui m,l,ui l,ui m,l,issu 

### hugu PfupaPPssu + • +•= from oil, gas, and solids ($/GJ) Eq. 44 

# ( ) 

# [ ] m,l,ui m,l,ui m.l m,l,ui l,j m,l,uil,uim,l,i ssu 

### hugu Carbdisp 0Pf mFracRe1PfupaPPssu + • • +

− • +•=

..................................................................... from oil, gas, or solids ($/GJ) Eq. 45 

# ( ) m,l,ui m,l,uil,ui m,l,ui m,l,issu 

### hugupa PfuPPssu + • •+= for biomass ($/GJ) Eq. 46 

# ∑ • =

nc ssu l,ui m,l,ui 

### Pssu Ssu PU ($/GJ) Eq. 47 

# ( ) ∑ • •

=

nc ruiss
uus m,l,ui ruiss
uus m,l,ui l,ui 

### Pssu bssu Pssu bssu Ssu (unitless) Eq. 48 

# ( ) m,l,ui m,l,ui m,l,ui m,l,uraniumim,l,ui 

### hugu Pfu PPU + • + =
= from nuclear energy ($/GJ) Eq. 49 

# ( ) m,l,ui m,l,ui m,l,ui m,l,ui 

### hugu Pfu0PU + •+= from solar PV or wind ($/GJ) Eq. 5065 3 solar,uus 3 wind,uus 3 solar,uus solar 3 solar,uus 3 wind,uus 3 wind,uus wind m,l,ui m,l,ui 

### PP P P PP P Phu PU

− − −

− − −


### + •+ + •+= from wind-solar storage ($/GJ) Eq. 51
m.,l,ui m,l,ui m,l,hydrogenjm,l,ui 

### hugu PjPU +• =
= from hydrogen fuel cells ($/GJ) Eq. 52 

# ∑ • =
= neprices m,l,ui l,ui m,l,yelectricitj 

### PUSU Pj ($/GJ) Eq. 53 

# ( ) ∑ • •

=

neprices rui m,l,ui m,l,ui rui m,l,ui m,l,ui l,ui 

### PU bsu PU bsu SU (unitless) Eq. 54



### )hjkgjkPj(Pjk k,j k,j m,l,j m,l,k,j 

### +•= ($/energy service) Eq. 55

m,l,k,j m,l,coaljm,l,coalj 

### Pfjk Pj Pj + =
= = ($/GJ) Eq. 56 Pj j=electricity,l,m = m,k m,l,electicityj 

### PUTD Pj +

= ($/GJ) Eq. 57

m,k m,l,hydrogenjm,l,hydrogenj 

### TD2PH Pj Pj + =
= = ($/GJ) Eq. 58 

# ( ) ∑ • = j m,l,k,jl,k,j m,l,k 

### Pjk SPjk Pk ($/energy service) Eq. 59 

# ( ) ∑ • • • •

=

j ryjk rpjk m,l,k,j m,l,k,j ryjk rpjk m,l,k,j m,l,k,j l,k,j jklm jk jklm jk


### X Pjk bsjk X Pjk bsjk SPjk (unitless) Eq. 60



### ∑ ∑

=

− − k 1m,l,k1m,l,k k m,l,kl,k
ratio 

### Pkbsk Pkbsk PS (unitless ratio) Eq. 61

m,l Nstep m,l 1m,l m,l 

### LBFindex )oPr1( GDPindex GDPindex • +• =

− (unitless) Eq. 62

adj rGDP ratio m,l m,l 

### PS GDPindex GDPindex • = (unitless) Eq. 63

index ryk rpk

2m,l,k

m,l,k l,k m,l,buildings ortion transporta k 

### Pop X Pk

Pk bsk Fk m,l,k l,k


### •• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•=

= −− = (EJ/year) Eq. 64

m,l,k l,k ryk rpk

2m,l,k

m,l,k l,k m,l,industryk 

### Y Pk

Pk bsk Fk • ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•=

= = (EJ/year) Eq. 65

m,l,k m,l,k k l,k 

### Pfk Pk Rpkrpk •= (unitless) Eq. 66

jk m,l,k l,k,jk,j m,l,k,j 

### Tech Fk Sjkgjk Fjk ••= (EJ/year) Eq. 67

Nstep m,l,k 1m,k,j m,k,j 

### )T1(*Tech Tech + =

− (unitless) Eq. 6866 

# ( ) ∑ •• • •

=

j ryjk rpjk m,l,k,j m,l,k,j ryjk rpjk m,l,k,j m,l,k,j l,k,j m,l,k,j k,j m,l,k,j

jk, 

### XPjk bsjk X Pjk bsjk Sjk (unitless) Eq. 69


# ∑ = k m,l,k,j m,l,j 

### Fjk Fj (EJ/year) Eq. 70

coeff coeff coeff m,l,yelectricitjm,l,hydrogenj m,l,hydrogenj 

### h*e1 e Fj Fj Fj

− • +

= = =

= (EJ/year) Eq. 71

coeff coeff coeff m,l,hydrogenjm,l,yelectricitj m,l,electrictyj 

### h*e1 h Fj Fj Fj

− • +

= = =

= (EJ/year) Eq. 72

m,l,hil,hi coeff 

### ghShh •= (unitless) Eq. 73

m,l,uil,ui coeff 

### guSue •= (unitless) Eq. 74

im,l,k,j l,k,i 

### gij Fjk EDRIKL •= i = oil, gas, coal or biomass (EJ/year) Eq. 75 

# ∑ = k l,k,i m,l,i 

### EDRIKL EDRIL i = oil, gas, coal or biomass (EJ/year) Eq. 76

m,l,i,j k l,k,i m,l,i,j 

### SynShare EDRIKL SFuel • = 

# ∑ (EJ/year) Eq. 77

ji j m,l,i,j m,l,i m,l,i 

### gc SFuel EDRIL EDRIL • + = 

# ∑ i = oil, gas, coal or biomass (EJ/year) Eq. 78

im,l,hil,hii m,l,hydrogenjm,l,i m,l,i 

### gijghSh Fj EDRIL EDRIL • • • + =
= i = oil, gas, coal or biomass (EJ/year) Eq. 79
im,l,uil,uim,l,yelectricitjm,l,i m,l,i 

### gijguiSu Fj EDRIL EDRIL • • • + =
= i=oil, gas, coal or biomass (EJ/year) Eq. 80 

# ∑ = l m,l,i m,i 

### EDRIL EDRI for oil, gas, coal, and biomass (EJ/year) Eq. 81 

# ∑ + = i m,l,i,j m,l,i m,l,i 

### Sfuel ESILM ESRILM for oil and gas (EJ/year) Eq. 82 

# ∑ = l m,l,i m,i 

### ESRILM ESRI oil, gas, coal, and biomass (EJ/year) Eq. 83

m,i mk 

### ESRI MrkPRD = oil, gas, coal Eq. 84

m,i mk 

### EDRI MrkDEM = oil, gas, coal Eq. 85 

### CemTot MrkPRD 5mk 

### =
= Eq. 86

m,l 5mk 

### Emiss MrkDEM =
= Eq. 87 

# ∑

= = 

### = nr

1l l,i 12:6mk 

### AgSup MrkPRD Eq. 8867 

# ∑

= = 

### = nr

1l l,i 12:6mk 

### AgDem MrkDEM Eq. 89

mk mk mk 

### MrkPRD MrkDEM ExDem

− = Eq. 90

ji j m,l,i,j m,l,i 

### gc SFuel SynInput • = 

# ∑ (EJ/year) Eq. 91

( ) ( ) ( )

3 3 Flr Nstep1m
2 Flr Nstep1m1 1m,l 

### Flr FlrFLR •− •−− 

### • = (unitless) Eq. 92

m,l,gasi m,l m,l m,l gasil,gasflarei 

### ESILM )FLR1( FLR SBCO Cemissions

= = = 

### •

− ••= (MMTC) Eq. 93

m,l,jl,ui l,ui m,l,ui 

### FjSsuSu ESU ••= (EJ/year) Eq. 94

m,l,jl,hi l,hi m,l,hi 

### FjSshSh ESH ••= (EJ/year) Eq. 95

coali l,oili m,l,liqj,gasi coali gasi gas_synfueli 

### CO)SedFil1( SFuel CO SynInput Cemissions

= = == = = =


### • −• −• = (MMTC) Eq. 96



### )mFracRe1( CO)SedFil1() SFuel CO)SedFil1( SFuel CO SynInput Cemissions l,1
gasi l,gasi m,l,gasj,coali coali l,oili m,l,liqj,coali coali coali
coal_synfueli 

### −• ⎥ ⎥ ⎥ ⎦ ⎤
⎢ ⎢ ⎢ ⎣ ⎡

• −• −• −• −•

=

= = == = = == = =

=

(MMTC) 

### ................................................................................................................. Eq. 97



### )CO)SedFil1() SFuel CO)SedFil1( SFuel CO SynInput( Cemissions

gasi l,gasi m,l,gasj,biomassi biomassi l,oili m,l,liquidj,biomassi biomassi biomassi b_synfueli

= = = = = = = = = = =



### • −• − • −• − • = (MMTC) Eq. 98



### ⎥ ⎥ ⎥ ⎦ ⎤
⎢ ⎢ ⎢ ⎣ ⎡

•• +••• −−•

•= )gijgh ESH gijgu ESU(mFracRe )SedFil1(FFcons CO Cemissions

im,him,l,hi im,l,uim,l,ui l,2 l,i

ii (MMTC) Eq. 99

onaloil unconventi i l,oili l,oili 

### ESIL EDRIL FFcons

= = = 

### + = (EJ/year) Eq. 100

m,l,gasi l,i l,gasi 

### SynInput EDRIL FFcons

= = 

### − = (EJ/year) Eq. 101

m,l,coali l,i l,coali 

### SynInput EDRIL FFcons

= = 

### − = (EJ/year) Eq. 102

m,l,biomassi l,i l,biomassi 

### SynInput EDRIL FFcons

= = 

### − = (EJ/year) Eq. 103 

### )SedFil1(CO SHAL ESILM CO Cemissions l,i i m,l m,l,i i shaleoili 

### − • + • •=

= (MMTC) Eq. 104 

### )SedFil1(FjkCO2CO l,j j m,l,k,jj k 

### −••= 

# ∑ (MMTC) Eq. 105

hydrogen_scrub j l,j m,l,j j hydrogen 

### C)SedFil1( EDRIKL CO 2CO

− −• •=



# ∑ (MMTC) Eq. 106

electricty_scrub j l,j m,l,j j electricty 

### C)SedFil1( EDRIKL CO 2CO

− −• •=



# ∑ (MMTC) Eq. 10768 l,1 gasi l,gasi m,l,gasj,coali coali l,oili m,l,liqj,coali coali coali seq mFracRe CO)SedFil1() SFuel CO)SedFil1( SFuel CO SynInput C • ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡

• −• −• −• −•

=

= = == = = == = = (tons C) Eq. 108

l,2 im,l,ui m,l,ui i scrub 

### mFracRegijgu ESUCOC ••••= (tons C) Eq. 109

l,2 im,l,hi m,l,hi i scrub 

### mFracRegijgh ESHCOC • • ••= (tons C) Eq. 110 

## ( ) ( ) t t t t )icePr_C(MAC1USER1))Cap/GDP(Control1(Driver factor_EmEm

− •

− • −•• = 

### .. (variable units) Eq. 111 

# ∑

= − 

### ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

− • = nr

1l 1m,l,i m,l,i i,l m,l,i 

### Nstep Landuse Landuse CLdens EmLC (MMTC) Eq. 112 

# ∑ ∑

= − = − 

### ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

− • • = nr

1l m

2mm 1m m m i,l m,i 

### Nstep Landuse Landuse PercDecay CSdens EmSC
(MMTC) Eq. 113 

# ∑

= 

### = 4

coal,gas,oili i 

### Cemissions CemTot from oil, gas, and oil (MMTC) Eq. 114 

## ( ) )f1(f1ent SulfurCont ent EnergyCont FuelUse EmSulfur control ash t −•−• • = (TgS) Eq. 115

fcontrol is determined as follows 

### ( ) 

### ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + =

τ − intmidpo t GDPpercap / GDPpercap c max 

### e1 f fcontrol Eq. 116



### OilCarb PtOilTranCos P P carbon oil moil biofuelfro 

### • + += ($/GJ) Eq. 117



### t BioTranCos EtoBio P P biomass mbiomass biofuelfro 

### += ($/GJ) Eq. 118 

## ( ) t BioTranCos tOilTranCos OilCarb PPEtoBio P carbon oil biomass 

### − + •+•= ($/m 3 C ) Eq. 119

m,l,im,lm,l,i baseyearm,l,i m,l,i l,im,l,i 

### CNY P P A CDR jl jl


### ••• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•= β α

= (total calories
demanded per year) Eq. 120

m,lm,l,i baseyearm,l,i m,l,i l,im,l,i 

### NY P P A WDR jl jl


### •• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

•= β α

= (total m 3 wood
demanded per year) Eq. 121 

# ( ) m,l,im,l,ip,m,l,ip,m,l,i 

### GPyr −•=π i = crops, biomass, pasture (annual $/ha) Eq. 122 

## ( ) 

# ( ) m,l,im,l,ip,m,l,i 45 p,m,l,i 

### GP ~ y 1r1 r r −•• −+ =π i = forests (annual $/ha) Eq. 123


# ∑ λ λ



### π π
=

p 1 p,m,l,i 1 m,l,i m,l,i 

### r r S (unitless) Eq. 124

l m,l,im,l,i 

### Totalland S Landuse •= Eq. 12569 m,l,animali m,l,pasturei m,l,cropsim,l,animali 

### GPastOut P FeedOut P P

= = = = 

### + • +•= ($/cal) Eq. 126

λ λ 

### ⎥

⎦ ⎤ ⎢ ⎣ ⎡ π=π 

# ∑

p 1 m,l,p,i m,l,i 

### r r ˆ ($/cal or $/m3) Eq. 127



### r ˆ r ˆ i 

### π=π i = crops, biomass, pasture, forest ($/cal or $/m3) Eq. 128

m,l,im,l,i i i 

### GP ˆ y ˆ

− π
= i = crops, biomass, pasture ($/cal) Eq. 129

Nstep m,i1m,i m,i 

### )S1(Tech Tech + =

− (unitless) Eq. 130

2 2 2
1 biomass 1 crops 1 crops

biomass crops crops 

### rr r
ss s λ λ λ



### π+π π

= + (unitless) Eq. 131 

# [ ] 2 2 2 1 biomass 1 crops biomass/crops 

### rr r λ λ λ 

### π+π= π ($/cal) Eq. 132

fert ocean n 

### FFDE dt Cd −−+=

Δ Eq. 133



### τ − β = Δ CE dt Cd Eq. 134



### HFS dt dT −−∝ Eq. 135 

### ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ θ • ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +• ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

τ

τ

− τ −
= dt d h h dt dT TaT dt dT d

m d m

a m

a eq a Eq. 136



### τ ΔΤ•β • −+−

= )zz(z dt dz 0 Eq. 137