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 2003 
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 (9/2003)
PNNL-14337

Model Documentation for the 

MiniCAM 

AL Brenkert SH Kim 

AJ Smith HM Pitcher 

July 2003 

Prepared for the United States Environmental 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 99352 
3

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 Protection 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, methane 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 determining 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 countries; (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 consisting 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 using 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 climate 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 
5

• regional patterns of climate change using 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 supply 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), hydrogen 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 production, and synthetic fuel production). Biomass supply includes 

“waste” biomass streams and commercial biomass produced 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, synthetic 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 efficiency 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 change 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-coefficient (Leontief) production function requiring 

three parameters: fuel input, efficiency, and non-fuel costs. During the transformation processes 
6

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 means 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 fuel 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 supply 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, levels 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 refined 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 gas emissions) determine regional energy prices, 

which affect, in turn, regional energy demands. Regional energy resources and prices determine 

regional energy supplies, which impact global supply 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 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. 

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 that are intended to alter the baseline emissions 

trajectory. In the present version of the MiniCAM, 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 function 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 are generally allowed to freely respond to any 

changes in energy prices. The model can then be used 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. AN OVERVIEW OF THE MINICAM MODEL ............................................................................ 12

1.1 MODEL COMPONENTS .......................................................................................................... 12

1.2 A PARTIAL EQUILIBRIUM MODEL AS ECONOMIC PARADIGM ............................................... 15

1.3 STATIC VERSUS DYNAMIC MODELING ................................................................................. 19

1.4 REGIONS .............................................................................................................................. 19

1.5 MARKETS ............................................................................................................................. 20

1.6. MINICAM’S FOCUS AND NICHE.......................................................................................... 20

PART II ........................................................................................................................................ 22

2. THE ERB MODULE ................................................................................................................. 22

2.1 DEMOGRAPHICS................................................................................................................... 22

2.2 ECONOMICS AND ENERGY ................................................................................................... 23

2.2.1 Carbon Prices .............................................................................................................. 27

2.2.2 Energy supply .............................................................................................................. 28

Supply (resources) of crude oil, natural 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 fuel 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 the form of fuel mode prices .......................................... 49

Total cost of energy services to an end-sector .................................................................. 50

The energy service price index ......................................................................................... 51

2.2.4 GDP ............................................................................................................................. 52

2.2.5 Energy Demand ........................................................................................................... 53

Demand for energy services ............................................................................................. 53

Elasticities ........................................................................................................................ 54

Demand for each fuel mode ............................................................................................. 55

Demand for each secondary fuel ...................................................................................... 57

Electricity and hydrogen interaction ............................................................................ 57

Primary fuel demand ........................................................................................................ 58

2.2.6 The energy balance and other markets ........................................................................ 60

2.2.7 Imports, Exports .......................................................................................................... 63
8

2.2.8 Calibration procedures ................................................................................................ 64

2.3 CALCULATING GREENHOUSE AND NON-GREENHOUSE GAS EMISSION .............................. 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-CO2 Greenhouse Gas and Reactive Gas Emissions from the ERB module ......... 70

2.3.4 Emissions from the AgLU module ............................................................................... 71

2.3.5 Non-CO2 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. AGLU: THE AGRICULTURE LAND USE MODULE ................................................................... 76

3.1 DATA THAT ARE REQUIRED ................................................................................................. 79

3.2 THE PRICE OF BIOMASS IN AGLU IN STAND-ALONE MODE ................................................. 79

3.3 AGLU 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: MODEL FOR THE ASSESSMENT OF GREENHOUSE-GAS INDUCED CLIMATE 

CHANGE .................................................................................................................................... 90

4.1 ATMOSPHERIC CONCENTRATIONS ...................................................................................... 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 RADIATIVE FORCING ........................................................................................................... 94

4.3 TEMPERATURE CHANGE: TERRESTRIAL, ATMOSPHERIC AND IN THE OCEAN ...................... 95

Terrestrial and atmospheric compartments .......................................................................... 95

The ocean .............................................................................................................................. 95

4.4 SEA-LEVEL RISE ................................................................................................................... 97

PART V ...................................................................................................................................... 100

5. SCENGEN: REGIONAL CLIMATE CHANGE SCENARIO GENERATOR .................................. 100

PART VI ..................................................................................................................................... 102

7. RESULTS .............................................................................................................................. 102

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

Regional outputs ................................................................................................................. 110

Policy cases ........................................................................................................................ 113

REFERENCES .......................................................................................................................... 116
9

TABLE OF FIGURES 

Figure 1 MiniCAM’s modules ..................................................................................................................... 12

Figure 2 The flow of services in MiniCAM ................................................................................................. 16

Figure 3 An energy-economics-emissions model (based 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 1985:245) .................................................................................................................................. 24

Figure 5 Schematic cost distributions for three different energy options (Adapted from ............................. 26

Figure 6 Cumulative Energy Supply Curve .................................................................................................. 29

Figure 7 Nesting of cost calculations of hydrogen generation ..................................................................... 45

Figure 8 Nesting of cost calculations of electricity generation ..................................................................... 46

Figure 9 Cost curve example relating carbon prices to emission reductions ................................................ 71

Figure 10 Nested approach 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 and technological change. ..........104

Figure 15 Average diets in the four SRES scenarios with divergence in the A1 scenario. .........................105

Figure 16 Global anthropogenic carbon-equivalent emissions in the four SRES scenarios ........................106

Figure 17 Carbon dioxide concentrations in the four SRES scenarios ........................................................106

Figure 18 Sulfur emissions in the 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 scenarios with divergence in the A1 scenarios. ...............108

Figure 21 Projected global temperatures in the SRES scenarios .................................................................109

Figure 22 Projected sea-level rise in the SRES scenarios ............................................................................109

Figure 23 Regional differences in income over time in IPCC’s B2 scenario ..............................................110

Figure 24 Regional differences in caloric intake in IPCC’s B2 scenario ....................................................111

Figure 25 Regional differences in electricity consumption per capita in IPCC’s B2 scenario ....................112

Figure 26 Regional differences in anthropogenic emissions in IPCC’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 scenarios ..........................................114

Figure 29 Sulfur emissions in the USA in IPCC’s B2 carbon policy scenarios ..........................................115

Figure 30 Carbon prices in the USA in IPCC’s B2 carbon policy scenarios ...............................................115
10

TABLE OF TABLES 

Table 1 MiniCAM Modules ......................................................................................................................... 14

Table 2 MiniCAM’s twelve markets ............................................................................................................ 17

Table 3 Regions in MiniCAM ...................................................................................................................... 19

Table 4 ERB non-CO2 emissions ................................................................................................................. 70

Table 5 AgLU non-CO2 emissions ............................................................................................................... 73

Table 6 FAO production and demand example (from Sands and Leimbach 2001) ...................................... 83
11

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 carbon 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 calculates energy supply and demand and resulting 

emissions. Part III describes the processes simulated in agriculture and land-use using the 

Agriculture and Land Use model (AgLU). In the 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 detail 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 Regional 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 atmospheric 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 processes described in Parts 

II and III. Part VII shows some results of model runs. 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 Battelle. 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 Assessment Model, is a highly aggregated integrated 

assessment model that focuses on the world’s energy and agriculture systems, atmospheric 

concentrations of greenhouse gases (CO2 and non-CO2) 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 technology 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 model 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 markets for labor and capital, and there are no 

constraints such as balance of payments. It is therefore 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 Appendix 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 modules 
13

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 2001; Gillingham et al. 2002; Sands and Edmonds 2002); 

• atmospheric composition and global-mean climate 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 MiniCAM 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 the 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 been sought” (Edmonds and Reilly 1985:242). Since 

then the model has been modified but the essential premise and fundamental structure has been 

retained. The ERB module includes energy-producing 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 model1

. 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 mechanism to balance supply and demand, which includes 

international trade. This becomes the basis for determining (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; biomass 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 Greenhouse-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 atmospheric concentrations, to radiative forcing, to 

global-mean climate change. The ERB and AgLU MiniCAM modules supply projections of 

emissions for greenhouse gases, sulfur dioxide, and reactive gases which MAGICC uses to 

produce atmospheric concentrations and global-mean temperature and sea-level rise projections 

by using a combined set of gas-cycle, climate, and ice-melt models. 

Climate impact analysis generally requires regional climate changes, not global-mean values. 

Regional temperature and precipitation changes 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 Modules Model Institutional Affiliation 

Description Inputs and Outputs References 

ERB PNNL 

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 (CO2, CH4, N2O, SO2, 

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) 

AgLU PNNL 

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 2002 

MAGICC NCAR 

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) 

SCENGEN NCAR 

SCENGEN models the 

regional pattern 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 module. Both these modules were developed by 

researchers at Pacific Northwest National Laboratory (PNNL). In Parts IV and V we will describe 
15

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 model as economic paradigm 

MiniCAM’s ERB and AgLU modules form a partial 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 supply and demand of food and fiber products using 

the same market mechanism, which 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 additional 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 evaluation 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 demand & supplies

Figure 2 The flow of services in MiniCAM 

At the onset of the model development it was recognized that “at the very least, an assessment 

tool must provide a global energy balance to enable consistent CO2 release scenarios to be 

generated” (Edmonds and Reilly1985:244). This requirement has been expanded to account for 

other radiatively important gases. Secondly, it was 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 energy services. Conceptually, energy services are 

provided to the demand or end-use sectors. Energy 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 (conventional and unconventional fossil oil, natural 

gas, coal, and waste and commercial biomass), 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, food 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 user 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 Crops 

5 = 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 commodity decreases, supply decreases and demand 

increases. The different regions produce the demanded fuels and agricultural products when their 

production costs are competitive. Trade is therefore implicitly simulated. Animal product supply 

is balanced with demand at the regional level. Trade 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 response to demand can be determined from supply 

curves but no explicit market is established. Electricity 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 modeling 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 regional economic activity and energy demands. 

Technological change impacts energy demand, while regional taxes and tariffs (and climate 

policies which influence the price of greenhouse gas emissions) determine regional energy prices, 

which affect, in turn, regional energy demands. Regional energy resources and prices determine 

regional energy supplies, which impact global supply 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 model (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 algorithm affect technology costs, demand for inputs and 

sector outputs. 

It has been our experience that the use of multiple solution algorithms ensures that a solution (all 

the markets are cleared) is found quickly and that the solution is robust. Routines that are 

commonly used for economic modeling are the 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 time 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 through the energy-price feedback will carry 

through to subsequent periods. 

1.4 Regions 

MiniCAM’s global coverage is comprised of fourteen 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 MiniCAM2

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 differ 
20

Australia & New Zealand Latin America 

Former Soviet Union Africa 

Eastern Europe (rest of) S&E Asia 

1.5 Markets 

The energy markets are the core of the MiniCAM model. Markets are defined for oil 

(conventional and unconventional are traded together), gas, coal, biomass, carbon, and 

agricultural products (see Table 2). Through a market 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 regions 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 such as balance of payments. The MiniCAM does 

balance supply and demand of energy commodities 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 mechanism 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. Alternatively, emissions constraints can be in the form of 

total greenhouse gas emissions, which are the sum of the carbon-equivalent emissions for all 

greenhouse gases. Note that carbon fees are not applied 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 content. If the user has specified that non-CO2

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-specified Global Warming Potential (GWP) weighting 

factor (see Table 5). For non-CO2 greenhouse gases a marginal abatement curve approach is used 

to determine the amount of emissions reductions obtained for a given carbon price (see section 

2.3). Under a configuration with one global carbon market, there is implicit global trading of 

carbon permits. Alternatively, regional carbon markets 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 and global context. Secondly, it provides for the 

ability to quickly evaluate technologies including carbon sequestration. Thirdly, it provides for an 
21

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 change 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 participant in the Intergovernmental Panel of Climate 

Change (IPCC) SRES scenario development (Nakicenovic et al. (2000). Part VI of this 

documentation provides an overview of some of the results. 

Outputs of the MiniCAM have allowed for evaluations 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 driving 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, and 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 inputs such as land, transformation costs, technology 

options, technological change parameters, population levels, and labor productivity rates. 

The three major exogenous inputs determining energy demands over time are 

• Regional population changes 

• Regional economic activity changes, which are determined primarily by the rate of labor 

productivity increase and 

• Regional 

o technological change in energy transformation3

, and 

o autonomous end-use energy intensity improvements4

, 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 specified in a number of ways, as described in the 

demographics section below (Section 2.1). The simulated 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 specifying demographic variables. There are two 

primary demographic inputs that are needed 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 population 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 parameter), 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 participation 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 survival rates, fertility rates, and migration rates 

(Appendix 4 provides the equations). 

2.2 Economics and Energy 

The MiniCAM model has three general equation structures that recur. These are the Leontief or 

constant input-output coefficient 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 markets) and region-specific taxes, tariffs and 

subsidies. Primary energy is transformed at a certain efficiency and cost to secondary energy and 

is then converted, again at a certain efficiency and cost, such that end-use sector-specific energy 

services 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 particular 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 resources; carbon prices can be levied on production, 

and/or consumption. Implicit trade of raw fuels 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

CO2 & CH4 & NO2 & 

SO2 6

Not 

traded

CH4 & N2O &

net CO2

CH4 &

N2O

N2O

from

Adiphic

acids

Oil: 

unconvention

al (oil shale, 

tar sands)

Coal ds

cs

Uranium

Coal

Electricity

Aggregate Energy Services

Fiber demand

* = sequestration technologies

SO2

ds = desulfurization option; cs = carbon scrubbing option or share

Logit fuel

sharing

logit

6= emissions from unconventional oil and synfuels calculated separately

Synfuel gas 

conversion *

Logit

fuel

sharing

Logit

energy

service

sharing

Gas 

processing

S

e

c

o

n

d

ary

E

n

erg

y

Coal processing

Biomass/waste 

processing

Logit fuel

demands

by sector

Logit

sectoral

demands

Hydrogen 

*

logit

logit

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 costs are captured by the Leontief equation 

+•= hgPicePr ($/energy unit) Eq. 1 

where 

Price is the cost of energy (or an energy service) which is determined by 

P the costs of energy input, 

g a conversion coefficient representing the relationship between the input of one unit of 

energy to one unit of transformed fuel, and 

h, which represents the levelized non-energy costs associated with one unit of transformed 

fuel. 

Some of the secondary fuels (electricity, hydrogen, synfuels) can be provided in a number of 

different ways (see Figure 4). Electricity as a secondary 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 compete 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 competing 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 transformed 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 calculated 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 competing fuels and are dependent on the elasticities 

of their prices. Thus, the share Sj of a fuel j allocated to a demand or market where the fuels 

compete is given by 

∑( ) •

• =

j

r

fuelj j

r

fuelj j

j p

p

Pb

Pb

Share (unitless) Eq. 2 

where 

 Pfuelj is the cost of fuel j (or the cost of providing an energy service), 

rp is the price exponent, that is the parameter that determines the variance of the price 

distribution; rp 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, 

bj is the base share or weight of fuel j, sometimes called scale parameter, and 

the denominator is the sum over all possible shares. 

 
26

Probability

Cost 

Option 1 Option 2 Option 3

Price 1 Price 2 Price 3

Figure 5 Schematic cost distributions for three 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 equation 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 determined 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 elasticities. 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 fuels, 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, the demand for fuel j in sector k is given 

by

rpk rxk ••= 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, 

rpk 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 

rxk 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 options have been explored and they will be 

discussed next (Section 2.2.1). Then we will discuss how energy supplies are simulated (Section 

2.2.2). This will be followed by a detailed description 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 operates using the same mechanism 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. GHG 

fees can be added to 

1) the raw fuel extraction processes (as Pfisis,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 Pfii,l,m) (see Equation 24), 

3) the consumption of fossil fuels (as Pfuui,l,,m)

6

; by raising the prices of the to be consumed 

refined oil, processed gas and coal7

 when meeting the liquids and gas energy service 

demands (see Equations 31, 32, 33, and 35), the fractions (or shares) of the total demand 

of each of the secondary (processed/refined) fuels will change resulting in a change in 

emissions, 

4) the consumption of fossil fuels (as Pfuui,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 

Pfjkj,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 Pfuui,l,m and the Pfjkj,k,l,m fees are 

applied, while the Pfisis,l,m fees are set to zero; (case 2) the Pfuui,l,m, Pfjkj,k,l,m, and Pfisis,l,m fees are 

all applied but halved; or (case 3) only the Pfisis,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 Pfuui,l,m carbon fee option, in practice, carbon fees are imposed during the 

tranformation of secondary fuels to fuel modes for energy services, Pfjkj,k,l,m 7

 in the determination of the SynShares 
28

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 (Pfisis,l,m) may be applied when extraction 

costs are determined. This fee is an exogenous 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 depending on the type of constraints assumed in a simulation. 

(2) The regional price increases (Pfii,l,m) on oil, gas, coal, and biomass production costs are 

regional and time-period specific (through 2050) input parameters. These multipliers can also be 

interpreted as trade barriers or as scale factors 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 (Pfuui,l,m) fees can be fixed (exogenously set and changing over 

time) or may function as constraints such that, for example, exogenously set greenhouse gas 

emissions standards can be met. 

3⁄4 If the Pfuui,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 and synfuels may be exogenously determined 

input. 

3⁄4 If the Pfuui,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 (COi: tons C/Joule energy combusted) is recalculated by means of a conversion 

factor (CVRT908

) and the resulting parameter is called Pf0ui,l,m. This parameter (Pf0ui,l,m) 

has units of tons C/J*dollar conversion ratio (COi divided by CVRT) such that when it is 

multiplied with the 1990$ carbon price-costs (PRCl,m in $/million tons C) the resulting 

Pfuui,l,m price increases are in units of $/GJ. Thus, Pf0ui,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, Pfjkj,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 for 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 Pfuui,l,m values. 

Note that a global or regional carbon price (PRCl,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=2.212 
29

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 production schedule which depends on the previous 

period’s annual production rate. 

Biomass comes, first of all, from waste, which 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 competition with food crops and other land uses. 

Hydroelectric power is a resource constrained renewable technology. Geothermal power is not 

modeled separately, but is (assumed) included 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 energy 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 crude oil, gas, coal, and uranium are governed by cumulative supply curves. Energy 

resources with similar extraction costs are grouped into grades where each grade has a range of 

extraction costs. A representative cumulative supply curve is shown in Figure 6 with extraction 

costs (Cig,is) on the vertical axis and cumulative supply (Rig,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 Curve 
30

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 may simply be breakpoints needed to define a 

cumulative supply curve. In the MiniCAM unconventional oil is a separate category because of 

its greater carbon content. Unconventional natural 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 tend to be cheaper than more limited, highergrade resources. Regional resource prices determine how much energy needs to be supplied by 

other regions; moreover, the regional resources determine the final balance of global supply and 

demand. Regional resource costs9

 are simulated by the following sets of parameters and 

processes: 

Extraction costs (Cig,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 

(Rigis,l in Joules) and prices ($/EJ). 

Each regional supply (Rig,is,l RIGISL: EJ) of conventional oil, unconventional oil, natural gas, 

coal, and uranium is determined by combinations 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 (Vis,l,m: VISLM: $/GJ) are exogenous regional time- and primary fuelspecific input parameter. The environmental costs are added to the production (extraction) cost 

for each fuel. Like other parameters in the MiniCAM, 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 reference 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 (Techm unitless) is calculated from 

the exogenous unitless time-dependent technological change parameter STis,m (STISM). The rate of 

technological change determines the rate at which 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 1m m,is Tech +•= )ST1(Tech − (unitless) Eq. 4 

where 

Techm 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

STis,m is the technology change parameter used in calculating the rate of technological change 

over time (unitless: exogenous global time- and fuel-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 (Pfisis,l,m; TXISLM: $/GJ) may be applied when 

extraction costs are determined. 

Thus, over time, global primary fuel prices (extraction 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 Cig,is is the exogenous global raw fuel-specific minimum cost of a next 

grade in a supply curve (CIGIS: $/EJ), 

the environmental costs Vis,l,m is a regional, exogenous time-specific input parameter (VISLM: 

$/EJ), 

Techm is calculated from input STis,m which represents a global, exogenous fuel-specific 

technological change coefficient (STISM: unitless), and 

Pfisis,l,m, which is a regional time-dependent severance fee that can be imposed when 

extraction costs are calculated (TXISLM: $/GJ); this fee is an exogenous or endogenous regional 

time-period specific (input) parameter. The parameter 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: 

i conventionaloil

i unconventionaloil

m,l,is is convention m,l,aloil CO

CO Pfis Pfis =

= = = • 

 for unconventional oil ($/GJ) Eq. 6 

Once the regional extraction costs are determined, the amount of fuel (ESILMi,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 regional extraction costs on the vertical axis of the 

regional supply curves by interpolation between grades from the Cig,is data and calculating the 

related energy from the Rig,is,l data. We are concerned in these calculations about the amounts of 

energy available for a certain price; the demand equations will ultimately determine, in an 

iterative process with prices, how much fuel needs to be extracted when markets need to be 

cleared.10 

 

10 We therefore do not calculate specific fuel prices at this stage, but only set up equation 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 demands are determined, the primary fuel supply can be 

calculated when markets need to be cleared. 
32

Determining the location of the calculated regional 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 the 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 (Qis,l,m) would be 

∑=

=

n

1ig

Q m,l,is R l,is,ig (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 (ExtrCostis,l,m: see Equation 5, 

which is modified for unconventional oil based on Equation 6) become larger than this market 

price (Pi,l,m), extraction costs have to be scaled back and the exact allowable fuel-specific 

extraction costs have to be determined that meet 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 curve. Next, the supply required for production is 

calculated: 

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

1n

1ig

m,l,is l,is,ig = ∑ −+ •

−

=

 (EJ) Eq. 9 

where the calculated potential supply (EJ) is reduced by one grade level and added to by the 

difference between the market price and the extraction 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 (ESILMil,m: Energy Supply of primary fuel i in region l

is set equal to ESFILis,l: EJ/year) 

ESILM =1m,l,i = ESFIL l,is for oil, gas, coal and unconventional 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 ESILM 2 −

− − − •= 

 for oil, gas, coal and unconventional oil in projections (EJ/year) Eq. 11 
33

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 crudely, 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 expansion 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

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

GDP

GDP

ESILM ESILM •• ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = •

−

− (EJ/year) Eq. 12 

where 

ESILMi,l,m is the regional annual energy production from the previous period; this production 

rate is exogenously set in the base year (ESFIL: EJ/year) and calculated thereafter, 

Techm is the rate of technological change defined above, 

GDPl,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 parameter of that ratio. The fuel prices are adjusted to 

be the extraction costs only, so that the environmental costs are not included. Thus, 

l,ir

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 

 Pi,l,m is the global (market) primary fuel price ($/GJ)11 at time t (m), and 

ril is a regional, exogenous primary time period- and fuel-specific extraction cost elasticity 

parameter12 (RIL: unitless). 

Note that the GDP factor in the above equation is only applied if GDP is expanding 

(GDP m,l Tech m >• GDP −1m,l ) so that regions with contracting GDPs do not suffer a production 

penalty. 

 

11 Pi,l,m gets updated in the solution routines 12 Representing that a one percent change in the Pfac 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 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 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 minimum 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 production, 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 equal 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, determined by a cost curve calculation, adjusted 

downward if the resulting production exceeds the short-term capacity limit. 

Gas lost in gas production (which implicitly includes non-commercial gas use) due to flaring is 

calculated from flaring coefficients. The equation that determines gas flaring (FLRl,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 Flr3

Nstep*1m

2 Flr

Nstep*1m1

FlrFLR 1m,l Flr −− −= • (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 

ESILM ESILM )FLR1( m,l,gasi m,l,gasi − m,l = • = = (EJ/year) Eq. 15 

If regional production rates are larger than the production capacity limit, the amount of fuel that is 

regionally produced (ESILMi,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

QQ Nstep m,l,i 1m,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 (Qis=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 

Q = Q −1m,l,ism,l,nuclearis Nstep ESU −1m,l,ui •+= (EJ/year) Eq. 17 

where 

 ESUui,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

QQ m,l,is (EJ/year) Eq. 18 

∑ ∑= =

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

n

1ig

nreg

1l

W R l,is,ig (EJ/year) Eq. 19 

where 

Rig,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 

m,l,uraniumis is,ig C is,1ig W

)QR( 1C

W

)QR( tcosExtr = − ⎟ •

⎠

⎞ ⎜

⎝

⎛ − −+• − = ($/GJ) Eq. 20 

and uranium costs are calculated based on environmental costs (Vis,l,m), raw fuel costs (Cig,is) and 

technological change which is calculated as time period dependent as 

( )Nstep Tech m −1m +•= ST1Tech m,is starting with the second period’s technological change as 

unity: Techm=2=1 

The price of uranium is then 

m

m,l,isis,ig

m,l,uraniumi Tech

VC

P

+

= = ($/GJ) Eq. 21

where 

Cig,is is the exogenous global raw fuel-specific minimum extraction cost of a grade in a supply 

curve (CIGIS: J:$/GJ), 

Vis,l,m is a regional, exogenous time-specific the environmental costs input parameter (VISLM: 

$/GJ), 
36

Techm is calculated from input STis,m a global, exogenous fuel-specific technological change 

coefficient (STISM: unitless). 

Biomass supply 

Biomass supply 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 the 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 Rigisl/Cigis 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

m,l,i 1990m,l GDP

GDP

ESILM BIO ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = •

=

= (EJ/year) Eq. 22 

where 

the waste resource supply rate in the base year (BIOl,m=1990: BIOLM in EJ/yr) is an exogenous 

regional input for the base year (not time-specific), 

GDPl,m is as described in Section 2.2.4, and 

rysht is the elasticity coefficient13 (RYSHT: unitless) which is set to 0.1 for all regions, such 

that the total amount of waste biomass available increases only slowly with increases in GDP. 

The cost of much of the available waste biomass 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 (ESILMi,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 synthetic gas, or can be used for hydrogen production 

or electricity generation (see Figure 4). 

Hydroelectric power 

Hydroelectric power is a resource constrained renewable technology. Thus, electricity generation 

by hydropower is assumed to approach an exogenously specified limit within each region. 

Regional production of hydropower is simulated 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 calculated 
37

Hydro NstepmHydro

Hydro NstepmHydro

m,l,hydroi 3 1 2

1 2

e1

e ESILM Hydro ••+

••+

= + •= (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 production 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 regional electricity demand that can be supplied by 

each of these forms (see below). 

Other Renewables 

Geothermal 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 and 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 prices 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 for 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 primary fuel prices (Pi,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 solution mechanism when global 

supplies and demands are balanced. 

Base year regional fuel supply prices 

Base year regional fuel prices function only as initial conditions (Pinin,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 year (1990) by the market prices resulting from the 

solution algorithm. Thus, Pi,l,m, as Pinin,l,m equal initial-condition fuel prices that only have a role 

for model initiation. 

Regional fuel prices 

Market prices (Pi,l,m), obtained when supply and demand are balanced are transformed to regional 

fuel supply prices by adding fuel-specific transportation costs and a regional fee multiplier which 

represents any regional tax, tariff or subsidy such that reasonable differentiation between regions 

can be represented: 

( ) PfiTrPP m,l,iim,l,im,l,i •+= ($/GJ) Eq. 24 

where 

Pi,l,m, is the global primary fuel price described above. 

Tri is the transportation cost which is an exogenous input parameter for oil, gas, coal, or 

biomass (TRI: $/GJ), and

Pfii,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 scale 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 regional fuel prices or cost of a secondary fuel (Pjj,l,m) is calculated by means of a 

Leontief production equation (Edmonds and Reilly 1985:248): 

+•= hijgijPPj iim,l,im,l,j for oil, gas, coal, and biomass/waste ($/GJ) Eq. 25 

where 

Pjj,l,m is the regional processed/refined fuel-specific price ($/GJ), 

Pi,l,m is the regionalized primary fuel-specific price ($/GJ),

giji is an exogenous input parameter representing a conversion coefficient that is not time 

dependent nor region-specific and has values close to or equal to one; giji represents the 

relationship of the unrefined input producing one unit of secondary fuel; giji is also called 

conversion intensity of oil, gas, coal, and biomass (GIJ: unitless or GJ of primary energy/GJ 

refined fuel), and 

hiji 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 coefficients representing conversion efficiency and 
39

additional non-fuel cost. The refinery coefficients, giji, have been set to one in recent versions. 

The non-fuel costs, hiji, are small for biomass and coal, moderate for gas, and much more 

significant for oil. 

The regional refined (secondary) fuel-specific costs (Pjj,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 shares 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 domestic 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 produced from natural gas (one technology); no 

syngas is produced from natural gas. Either liquids or gas can be produced from biomass (two 

technologies). The final price of syncrude (synliquid) 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 HCLT3

Nstep1m

2 HCIL

Nstep1m1

hc i,j HCILT1 HCLT •−− •−= • ($/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 (PCj,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 PCj,i,l,m is 

used): 

( ) m,l,im,l,i,j + hcgctscossynPPC i,ji,j += • 

 synliquid from coal, gas, or biomass; syngas from coal or biomass ($/GJ) Eq. 27 

where 

j denotes the feedstock: gas, coal, or biomass, 

i denotes the produced crude or gas,

Pi,l,m, is the market price for the input fuel feedstock (before transportation costs and taxes are 

added), 

gcj,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, 

hcj,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 to 
40

which carbon disposal costs (calculated below) are added when scrub technology is added (see 

hci=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 synfuel is produced from coal. If scrubbing is 

implemented, carbon sequestration is calculated for the difference in carbon content between coal 

and the final synfuel type: liquid or gas. The fractional difference of carbon content in emissions 

from coal, compared to liquids or gas is for example: 

coali

coali oili

CO

CO CO SeqFractMax

=

= − = = (fraction) Eq. 28 

where 

COi 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 are based on capital costs of sequestration equipment 

for electricity generating plants {(huscrubbed-huunscrubbed)/gu}, adjusted for synfuel production 

through multiplication with synfuel-specific conversion rates that are specific for the fuels to be 

processed (gc,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,m,l,ui non,m,l,ui scrubbed

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, 

huui,l,m are the non-energy costs in 1975 dollars per GJ, which does not include technology and 

development (HUILM: exogenous regional time- and fuel specific parameters), 

guui,l,m is a conversion or energy intensity coefficient, which is unitless (GUILM: units GJ/GJ 

and values larger than one); an exogenous regional time- and fuel specific parameter representing 

the ratio of Joules energy input to Joules electricity generated; these conversion factors tend to be 

larger than one, and 

gcj,i is the intensity rate coefficient of synfuel production (GCI: input GJ/output GJ with values 

of 1.5), and 

COi is the fuel-specific emission rate in ton C/EJ before refining. 

To obtain the total additional cost for carbon sequestration, 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 the 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 (Pf0ui,l,m) that is calculated from the carbon 

emission rates COi and a conversion factor (CVRT90: GDP deflator from 1975$ to 1990$ 

hardwired: CVRT90=2.212). The carbon disposal costs (Cstdisp) are then correctly expressed in 

$/GJ: 
41

( ) disp 0PfCst m,l,ui Carbdisp m,l SeqFractMax + Cpenaltyj •= • ($/GJ) Eq. 30 

where 

Pf0j,l,m is explained above (ton C/GJ), 

Carbdisplm 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 

Cpenalyj 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: 

seq disp m,l,ui ( ) 1PfuCstC −•+= SeqFractMa + 0001.0x ($/GJ) Eq. 31 

where 

Cstdisp is the carbon sequestration cost described above (units are $/GJ Equation 33), 

SeqFractMax is described above (unitless), and 

Pfuui,l,m (in $/GJ) is the carbon fee based on the fuel-specific carbon contents, which in this 

case are the Pf0j,l,m values (tons C/GJ) and PCRl,m in $/tons C) such that the resulting Pfuui,l,m fees 

are in units of $/GJ. This type of carbon pricing is set to zero for biomass as energy source. 

The variables determining the shares of scrub and non-scrub technology (Sscrub and Sno-scrub) 

participating in determining the syncost (PCi,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 Pfuui,l,m *(1-Sscrub*RemFraci,l) where 

Pfuui,l,m is the carbon fee, RemFraci,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 Sscrub) are not levied, 

o from coal without scrub technology the syncost equals the carbon fee Pfuui,l,m ($/GJ: see 

the description of Equation 31), 

o from gas the syncost equals the carbon fee Pfuui,l,m, and 

o from biomass the syncost is zero. 

The non-fuel transformation costs, hcj,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

coali,j scrubbed i,j scrub CstShc disp hc += •+= ($/GJ) Eq. 34 

where 

hcj,i is the updated for scrub technology non-fuel transformation costs (units are $/GJ), and

Cstdisp 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 cases15. 

To simulate the participation of the synliquid technologies 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 the following share equation was developed: 

∑ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ =

−−

−−

ns

RCI

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

m,l,i,j

RCI

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

m,l,i,j

m,l,i,j ji

ji

Pj Pfu

PC

Pj Pfu

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, 

PCj,i,l,m is the cost of each technology producing synfuels: synliquid from coal, gas, or 

biomass; syngas from coal or biomass, which includes sequestration costs as described above, 

 Pjj,l,m is the cost of producing refined oil or processed natural gas ($/GJ), 

 Pfuui,l,m is the consumption or carbon price (added to the refined oil or processed gas) ($/GJ), 

RCIji is the exponent in the logit share equation; these elasticity coefficient values represent 

the relationship between syncrude produced from coal, gas and biomass, and syngas produced 

from coal and biomass, and 

ns is 4 for synliquids (when produced from coal, 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 produced from natural gas). Each of the technology 

costs are normalized against the refined oil costs (the fourth technology in refined oil production) 

 

15 Synfuel generation’s cost from coal depends on the Sscub fraction which results in a weighted cost 

between scrubber and non-scrub technologies: 

PCjilm =(Pinlm+ Pfuuilm*(1-Sscrub*RemFracil))*gcji + Pf0uilm * Sscrub {Carbdisplm* SeqFractMax +(huuilm,scrubbedhuuilm,non-scrubbed)/guuilm *gcji *1/COi)} +hcji 

Hydrogen and electricity generation costs from scrub technologies are formulated as 

( ) m,l,issh m,l,ui l,i 0Pf)mFracRe1(PfuPPssh m,l,ui Carbdisplm m,l,hi +• hhgh m,l,hi −•+= •+
43

resulting in an endogenous weighting scheme that is represented by exogenous weight parameters 

in share equations described in the next paragraphs (e.g., bsui,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 fuels to synfuel conversions is omitted given that 

the final share equations are implemented only when 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, Pjj=liquids,l,m, is the summation of the products of the SynShares and the 

technology-specific prices of synliquids generated from gas, biomass and coal, with the latter 

generated with or without scrub technology, plus the product of the calculated SynShare and the 

price of conventional (fossil) refined oil. Similarly, the final price of gas, Pjj=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 of 

the SynShare of processed natural gas and the price of processed natural gas. Note that the sectorspecific consumption taxes are added to the refined oil and processed natural gas prices. Note also 

that carbon fees were not applied in the production of secondary fuels (Equation 25). 

Pj SynShare PC SynShare Pj( )Pfjk m,l,gasorliquidsjm,l,i,j m,l,k,j

ns

−−= m,l,gasorliquidsj = ∑ m,l,i,jm,l,i,j +• • −−= +

 ($/GJ) Eq. 36 

Note that Pfjkj,k,l,m is added here while in the SynShare calculation Pfuui,l,m was added to Pjj,l,m of 

oil and gas; this can be considered alright given that only unitless shares are calculated in the 

SynShare equation while secondary prices are calculated in Equation 36. 

Synfuels are not used for electricity or hydrogen generation; they are only in end-use sectors. 

Hydrogen generation 

Hydrogen 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: 

( ) ssh m,l,i m,l,ui m,l,hi m,l,hi PfuPPssh •+= + hhgh ($/GJ) Eq. 37 

where 

 Pi,l,m is the price of a regional primary fossil fuel (in units of $/GJ), 

 gii,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 going up during the transformation process, 

hhi,l,m are non-fuel costs associated with the conversion process (HHILM: $/GJ) (an exogenous 

technology-, regional- and time-period specific input parameter), 

Pfuui,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 the competing technology costs, when oil, gas 

or solids are transformed, are calculated as follows: 
44

( ) m,l,issh m,l,ui l,i 0Pf)mFracRe1(PfuPPssh m,l,ui Carbdisplm m,l,hi + hhgh m,l,hi −•+= + • •

 ($/GJ) Eq. 38 

where 

RemFraci,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, 

Pf0i,l,m is a conversion factor that accounts for the carbon content of the fuel used and is 

calculated from carbon content factors COi (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 

Carbdispl,m, the carbon disposal cost (CARBDISPlm an exogenous regional time dependent 

disposal cost in units of $/Mton C), the correct result is expressed in $/GJ. 

Sshhi,,l are the shares of the scrubbed and non-scrubbed oil, or scrubbed and non-scrubbed gas, or 

scrubbed and unscrubbed coal: 

∑( ) •

• =

nc

ruiss

m,l,hi ssh

ruiss

m,l,hi ssh

l,hi

bssh Pssh

bssh Pssh

Ssh (unitless) Eq. 39 

where 

nc equals two (the competingscrub and non-scrub technologies), 

bsshhi,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), 

Psshssh is the cost of each technology participating (competing) in producing hydrogen, and

ruiss is the logit exponent for the technology cost (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: 

= ∑( ) • ncPH m,l,hi l,hi PsshSsh ssh 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,im,l,hi m,l,hi m,l,hi +•= hhghPPH generated from biomass ($/GJ) Eq. 41 

Hydrogen can also be generated through electrolysis. The cost calculation is the same as the 

equation above, except that the price (Pi,l,m) is not the price of biomass but is the price of 

electricity (PUui,l,: see Equation 47). Several options exist for specifying the electricity price used 

for H2 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

NonScrubbingNonScrubbing

Scrubbing

Hydrogen Generation

Electrolysis

Figure 7 Nesting of cost calculations of hydrogen generation 

The final price of hydrogen, PjJ=hydrogen,l,m, is calculated by summing the weighted hydrogen 

costs. Figure 7 illustrates the nesting of the weights. 

= ∑ • =

nhprices

Pj m,l,hydrogenj l,hi PHSh m,l,hi ($/GJ) Eq. 42 

where 

 PHhi,l,m is the technology-specific and/or resulting from competing technologies hydrogen 

generation cost, 

Shhi,l are the shares of the competing sources (in the 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

bsh PH

bsh PH

Sh (unitless) Eq. 43 

where 

nhprices equals four for hydrogen generation, 

bshhi,l,m are the fuel-specific time-dependent global base share coefficients or weights of 

hydrogen technologies, presently set to one, 

rhi is a global technology specific logit exponent 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 and carbon sequestration, (11) hydrogen fuel cells, 

(12) fusion, (13) wind power, (14) solar-wind storage, and (15) space satellite PV solar. 

Oil

Gas

Coal

Electricity Generation

Biomass

Scrubbing

NonScrubbing

Scrubbing Scrubbing

NonScrubbingNonScrubbing

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 hydrogen 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 these fuels. Additional electricity generation 

coefficients (or price adjusters: pai,ls) adjust the regionalized fossil fuel prices (Pi,l,ms for oil, gas 

and solids), however, to account for fuel use in utilities given the fact that electric generators, in 

general, get lower rates than other sectors. Thus, Pssu, the cost of each fossil-fuel combusting 

technology participating (competing) in producing electricity is calculated for non-scrub 

technologies as: 

( ) m,l,issu l,ui PfupaPPssu m,l,ui m,l,ui + hugu m,l,ui +•= • 

 from oil, gas, and solids ($/GJ) Eq. 44 

and for scrub technologies as: 

[ ( ) ] ssu m,l,uil,uim,l,i mFracRe1PfupaPPssu l,j 0Pf m,l,ui Carbdisp m.l m,l,ui +• hugu m,l,ui •+•= − + •

 from oil, gas, or solids ($/GJ) Eq. 45 

where 

paui,l is the electricity generation coefficient (or price adjuster), which adjusts the regionalized 

fossil fuel price (oil, gas, solids) to account for fuel use in utilities (unitless: PAUIL exogenous 
47

regional fossil fuel-specific parameter), and all other parameters are as described for hydrogen 

production, 

Pfuui,l,m raises the cost of the regional primary fuel consumption in producing electricity 

representing a carbon fee (TXUILM: $/GJ), 

RemFraci,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, 

Pf0ui,l,m is a conversion factor that accounts for the carbon content of the fuel used and is 

calculated from carbon content factors COi (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 

Carbdispl,m, the carbon disposal cost (CARBDISPlm an exogenous regional time dependent 

disposal cost in units of $/Mton C), the correct result is expressed in $/GJ. 

 guui,l,m is the inverse of conversion efficiency specific to the technology, which is unitless 

(GUILM: GJ/GJ; an exogenous technology-, regional- 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 

huui,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 Pfuui,l,m carbon fees are set to zero16: 

( ) m,l,issu PfuPPssu m,l,ui m,l,uil,ui + hugupa m,l,ui •+= • for biomass ($/GJ) Eq. 46 

The costs of electricity generation for oil or gas 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). 

= ∑ • ncPU m,l,ui Ssu l,ui Pssu ssu ($/GJ) Eq. 47 

where 

Ssuui,l are the electricity generation shares of the scrub and non-scrub technologies using the 

logit share equation: 

∑( ) •

• =

nc

ruiss

m,l,ui uus

ruiss

m,l,ui uus

l,ui

bssu Pssu

bssu Pssu

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’ represented byscrub and non-scrub technologies of 

electricity generation from coal and an additional technology from biomass, 

bssuui,l,m are the base shares or weights (sometimes called scale parameters) of each of the 

electricity generating scrub and non-scrub fuel technologies (BSSUILM: unitless exogenous 

regional time-period fuel technology-specific input 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 (pauil) and carbon prices (Pfuuilm) are potentially interacting differently: 

Pfuuilm *pauil
48

scrubbing in 1990) while values for other fuels for the base year are calculated by the model 

during the base year calibration, 

ruiss 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; rui determines the rates that shares change in response 

to a change in generation cost17 (an exogenous technology and 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 fraction of the non-scrub technology based on 

“grandfathering” of existing plants. This means that a fraction of the old plants remains active 

until the plants’ lifetimes have been reached. This concept can be applied to hydrogen production 

as well. 

Note that when prices are calculated for non-fossil fuels, as shown below, the Pfuui,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 uranium fuel is only used for nuclear power: 

( ) PPU m,l,uraniumim,l,ui Pfu m,l,ui m,l,ui + hugu m,l,ui = + • = from nuclear energy ($/GJ) Eq. 49 

Electricity generation from hydropower, fusion, solar PV, space-solar power, or wind differs 

from the above in that Pi,l,m equals zero: 

 

( ) m,l,ui Pfu0PU m,l,ui m,l,ui + hugu m,l,ui •+= 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

3 solar

solar,uus

3

wind,uus

3

wind,uus

m,l,ui m,l,ui wind PP

P

P

PP

P

PU Phu − −

−

− −

−

+

•+

+

•+= 

 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: 

= PjPU = m,l,hydrogenjm,l,ui m,l,ui +• hugu m.,l,ui 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=XB

, 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, Pjj=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

Pj m,l,yelectricitj l,ui PUSU m,l,ui ($/GJ) Eq. 53 

where 

PUui,l,m is the technology-specific electricity generation cost, 

SUui,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

bsu PU

bsu PU

SU (unitless) Eq. 54 

where 

neprices are the number of participating electricity generating technologies, 

bsuui,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 parameter 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 use 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 technology 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 maximum 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 renewable technologies such as solar photovoltaics and 

wind. The technology-specific capacity limit capacity limit is implemented by rescaling the fuel 

shares (Suui,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 H2. 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 in 
50

buildings will be met by different fuel transformation 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 Pjkj,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 which combines the secondary fuel price (Pjj=liquidss,l,m, 

Pjj=gases,l,m, Pjj=coal,l,m, Pjj=electricity,l,m, Pjj=hydrogen,l,m or Pjj=biomass,l,m), the energy service-specific 

conversion coefficients or input-output coefficients (gjkj,k) and the non-energy costs of the 

transformation process (hjkj,k): 

)hjkgjkPj(Pjk m,l,k,j m,l,j k,j +•= k,j ($/energy service) Eq. 55 

where 

gjkj,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, hydrogen, and biomass) for use in end-sector k (GJK: GJ/energy 

service; an exogenous sector-specific input parameter); these coefficients are further 

disaggregated for the transportation sector as sectoral-, regional- and time-specific (as gjklj,k,l,m), 

and for the hydrogen fuel cell technology unique and sector- and time-specific (as gjkj,k,m), 

hjkj,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 hjklj,k,l,m) and hydrogen fuel cells (as hjkj,k,m), and 

Pjj,l,m is the price of a secondary fuel j in region l at time m ($/GJ), where 

o Pjj=liquids,l,m and Pjj=gases,l,m were discussed under the synfuel 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: 

Pj = = Pj = m,l,coaljm,l,coalj + Pfjk m,l,k,j ($/GJ) Eq. 56 

o The cost of biomass production, Pjj=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: 

Pjj=electricity,l,m= Pj = m,l,electicityj + PUTD m,k ($/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: 

Pj = = Pj = m,l,hydrogenjm,l,hydrogenj + TD2PH m,k ($/GJ) Eq. 58 

Total cost of energy services to an end-sector 

The total cost of energy services to an end-sector k (Pkk,l,m in $/energy services) can now be 

calculated from the fuel mode-specific prices Pjkj,k,l,m and the shares SPjkj,k,l of the fuels in an endsector k: 
51

= ∑( ) • jPk m,l,k SPjk Pjk m,l,k,jl,k,j ($/energy service) Eq. 59 

where 

Pjkj,k,l,m is the energy service price of fuel mode j to end-sector k ($/energy service), and 

SPjkj,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 sector shares that are specific 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) Sjkj,k,l demand shares as calculated for the 

previous period. These demand shares are calculated as follows: 

∑( ) • •

• • =

j

rpjk ryjk

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

rpjk ryjk

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

l,k,j

jk jklm

jk jklm

bsjk Pjk X

bsjk Pjk X

SPjk (unitless) Eq. 60 

where 

bsjkj,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 may be used in the calibration process, 

Pjkj,k,l,m is the price of the service as provided by a given fuel mode j in sector k ($/energy 

service), 

rpjkj,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 electricity’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, 

ryjkjklm 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 the 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 index 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 ryklm: 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 (ryklm) of X represents the relationship between energy services demands and the change in 

income (represented by GDP per capita) from the base year 
52

∑

∑

=

− − k 1m,l,k1m,l,k

k m,l,kl,k

ratio

Pkbsk

Pkbsk

PS (unitless ratio) Eq. 61 

wh ere 

Pkk,l,m is the cost of energy services to end-sector k ($/energy service), and 

bskk,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, PSratio, 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 levels 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 GDPindex m,l = GDPindex 1m,l +• m,l )oPr1( • LBFindex − (unitless) Eq. 62 

where 

GDPindexl,m is the normalized GDP value (normalized against the base year GDP value, 

which makes the GDPindex for the base year equal to one), 

Prol,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, 

LBFindexl,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 GDPindex m,l GDPindex m,l PSratio = • (unitless) Eq. 63 

where 

GDPindexl,m is the normalized regional GDP at time t (m), 

PSratio is the ratio of the aggregate price for all energy services at time t (m) divided by the 

calculated aggregate price for all energy services at the previous point in time, and 

rGDPadj is the elasticity coefficient representing the percentage change in GDP resulting from a 

one percent change in the PS ratio20 (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 driver 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 calculate. 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, adjusted 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 and 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 exogenous 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=XB

, 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=AXB

YC where the dependent variable Z (e.g., aggregate service 

demand) is a function of X (e.g., the price of the aggregate 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 Y
54

Energy service demand by the transportation and building sectors is simulated as follows: 

index

ryk

rpk

2m,l,k

m,l,k

k transporta ortion m,l,buildings l,k X Pop Pk

Pk

Fk bsk m,l,k

l,k

•• ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•=

=

= −− (EJ/year) Eq. 64 

where 

bskk,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), 

Pkk,l,m/ Pkk,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 Pkk,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 Pkk,l,m/Pkk,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 the 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 

Popindex 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

m,l,industryk l,k Y

Pk

Pk

Fk bsk • ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•=

=

= (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 service shares as described below. 

Elasticities 

The energy service price 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 elasticies 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,ls are held at the 

2035 value. The update is calculated by means of the following equation: 

m,l,k

m,l,k

l,k 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), 

Pkk,l,m is the regional time-dependent total energy services cost ($/energy services) to a 

regional end sector k (the value of Pkk,l,m is part of the iterative process); Pkk,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; Pfkk,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, ryjkj,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 demand 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 

Determining 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 energy service demand to energy use. Each fuel 

has a coefficient that represents the efficiency at which that fuel is transformed into an energy 

service. In addition, the overall transformation between 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 changes over time. In practice, this parameter 
56

embodies both efficiency improvements and changes such 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 (Fjkj,k,l,m in energy units, EJ) by each end-use sector k

is equal to the product of total service demand (Fkk,l,m in energy services units), the fuel service 

share (Sjkj,k,l unitless) and the fuel requirement per unit service (gjkj,k), divided by the level of 

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

jk

m,l,k

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

Fk

Fjk Sjkgjk ••= (EJ/year) Eq. 67 

where 

gjkj,k is an energy service-specific conversion coefficient 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 transformation process) (an exogenous sector-specific input 

parameter); note that gjkj,k,l,m is a regional and time-specific parameter for the transportation 

sector, and gjkj,k,m is an exogenous sector- and time-specific input parameter for hydrogen fuel 

cells, 

Fkk,l,m is the energy service demand of sector k (in energy services units), and 

Techjk is the level of technological progress (calculated 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 considered” (Edmonds and Reilly 1985:260); this 

technology parameter can be set by region and end-use sector for future points in time: 

Nstep

m,k,j 1m,k,j m,l,k Tech = + )T1(*Tech − (unitless) Eq. 68

where 

Nstep is the time step of 15 years, and 

Tk,l,m is the sector dependent regional technology dependent technological rate change 

(TKLM: unitless). This technological change parameter, 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 independent of such other factors as energy 

prices and real incomes. The inclusion of an exogenous 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,

Sjkj,k,l is described in Equation 60 as SPjkj,k,l, which represent the shares of the fuel modes j

competing in obtaining the lowest total cost of energy services, Pkk,l at time m, to an end-sector k,. 

Calculation of these shares is part of the iterative 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 energy demand shares. The share value Sjkj,k,l depends on (1) 

bsjkj,k,l,m, the share or weight of a given fuel mode j in sector k, on (2) Pjkj,k,l,m the price of the 

service as provided by a given fuel mode j in sector k, on (3) rpjkj,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) ryjkj,k,l,m, the sector’s economic activity elasticity: 
57

∑( ) ••

• • =

j

rpjk ryjk

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

rpjk ryjk

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

l,k,j

k,j m,l,k,j

jk, m,l,k,j

bsjk XPjk

bsjk Pjk X

Sjk (unitless) Eq. 69 

The shares of the fuel modes (Sjkj,k,l) that, initially for the base year, are calculated from input 

parameters for weights (bsjkj,k,l,m), are re-calculated during the calibration process by adjusting 

these weights (bsjkj,k,l,m for j=liquids, gas, solids and electricity). In addition, adjustments have to 

be made through the calibration process for the correct 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 (Fjj,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

Fj m,l,j Fjk m,l,k,j (EJ/year) Eq. 70 

where 

 Fjkj,k,l,m are the fuel mode demands by the end-use sectors. 

 

Secondary fuel demands, Fjj,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 MiniCAM framework, each electricity and hydrogen production technology is described by 

a share, which represents the fraction of the total generation that is provided by that technology 

(Suui,l and Shhi,l, respectively; Equations 54 and 43, respectively). 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 (guui,l,m and ghhi,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 amount 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 equal to that needed for end-uses plus the hydrogen needed to 

generate electricity via fuel cells. 

This interaction requires a set of linear equations that 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 (Suui,l) for electricity generation by fuel cells and the fuel shares (Shhi,l) for 

hydrogen production through electrolysis and the transformation coefficients (guui,l,m and ghhi,l,m). 

The consistency coefficient for the amount of electricity that is needed to generate hydrogen by 

electrolysis (hcoeff) is calculated as the product of the share (Shhi,l) of the hydrogen in generating 

hydrogen as secondary fuel from electricity and the transformation coefficient or energy intensity 

(ghhi,l,m) of that process. Similarly, the consistency coefficient for the amount of hydrogen that is 

needed to generate electricity from fuel cell technology (ecoeff), is the product of the share (Suui,l) 

of the electricity in generating electricity as secondary fuel from fuel cells and the transformation 

coefficient or energy intensity (guui,l,m) of that process. As long as the product of the two 
58

coefficients is less than one the total demands for hydrogen and electricity can be adjusted as 

follows: 

coeff coeff

m,l,yelectricitjm,l,hydrogenj coeff

m,l,hydrogenj h*e1

Fj Fj e

Fj −

+ • = = =

= (EJ/year) Eq. 71 

coeff coeff

m,l,hydrogenjm,l,yelectricitj coeff

m,l,electrictyj h*e1

Fj Fj h

Fj −

+ • = = =

= (EJ/year) Eq. 72 

where 

coeff ghShh m,l,hil,hi •= (unitless) Eq. 73 

and 

coeff guSue m,l,uil,ui •= (unitless) Eq. 74 

where 

Shhi,l is the share of hydrogen that is generated by electrolysis and ghhi,l,m is the inverse of the 

transformation efficiency, that is the energy intensity, of that process. Similarly, Suui,l is the share 

of electricity that is generated from fuel cell technology and guui,l,m is the inverse of the efficiency 

of that process. 

The potential for an inconsistency exists if either of the denominators in Equations 71 or 72 is 

negative, that is, if either of the share coefficients (Shhi,l or Suui,l) is too large. This would be the 

case if, for example, most of the electricity would be generated by hydrogen and insufficient 

electricity would be generated by non-fuel cell sources to meet the demand for electrolytic 

hydrogen. The product of the two consistency coefficients (ecoeff and hcoeff) is therefore checked 

and if that product is greater than one, the shares (Suui,l and Shhi,l) are automatically rescaled and 

only then the process outlined is executed. 

In addition, the solution described above interacts 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 electricity shares are re-balanced while keeping the 

hydropower share constant. 

Primary fuel demand 

Primary 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 plus fuel needed as inputs to the transformation 

sectors (electricity, hydrogen, and synfuels). 

Primary fuel demand (EDRIKLi,k,l Energy Demand of Regional primary fuels I by end-use sector 

K in regions L) to meet the direct demands of fuel modes by the end-use sectors (Fjkj,k,l,m ; see 

Equation 67) (see also Figure 4) is calculated by end-use sector for oil, gas, coal and biomass, 

respectively, as: 

EDRIKL l,k,i Fjk gijim,l,k,j •= i = oil, gas, coal or biomass (EJ/year) Eq. 75 

where 

 Fjkj,k,l,m are the fuel mode demands by end-use sectors k (EJ; Equation 67), 
59

giji represents the relationship between the unrefined 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 EDRIKLikl stands for regional primary fuel energy demand calculated from the regional l

secondary fuel mode demand for each sector k. 

Regional direct primary fuel demands for oil, gas, coal and biomass (EDRILi,l: Energy 

Demand of Regional primary fuels I in regions L) are found by summing over the end-use 

sectors: 

= ∑

k

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

Primary sectoral end-use fuel demand (EDRIKLi,k,l) to meet synfuel generation 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). These 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 processed 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

SFuel m,l,i,j = ∑EDRIKL l,k,i •SynShare (EJ/year) Eq. 77 

where 

j is the feedstock: gas, coal, or biomass, 

i is the produced crude or gas, 

 EDRIKLi,k,l stands for regional sectoral end-use primary fuel energy demand (see Equation 

75), and 

 SynSharej,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 calculated direct primary fuel demands (Equation 76): 

ji

j

m,l,i m,l,i m,l,i,j EDRIL = EDRIL +∑SFuel • gc i = oil, gas, coal or biomass (EJ/year) Eq. 78 

where 

 Sfuelj,i,l,m are the primary fuel demands for synfuel generation (Equation 77), and 

gcj,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 change 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): 

EDRIL m,l,i EDRIL Fj m,l,hydrogenjm,l,i gijghSh im,l,hil,hii = + • • • = 

 i = oil, gas, coal or biomass (EJ/year) Eq. 79 

where 
60

Fjj,l,m is the total secondary fuel demand (Equation 68) that needs to be shared out with the 

Shhi,l share coefficient by fossil fuel type: oil, coal, gas, biomass, etc. and (re)transformed to 

primary fuel, 

Shhi,,l are the shares of the competing fuels in generating hydrogen, 

ghhi,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 

giji is the conversion intensity coefficient representing the ratio of Joules primary energy as 

input and Joules of secondary energy generated (GIJ: unitless or GJ of primary energy/GJ refined 

fuel); giji 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 calculated primary fuel demand (Equation 79): 

EDRIL m,l,i EDRIL Fj gijguiSu im,l,uil,uim,l,yelectricitjm,l,i = + • • • = 

 i=oil, gas, coal or biomass (EJ/year) Eq. 80 

with the same methodology as described for hydrogen. 

The regional primary fuel demands (EDRILi,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 (∑EDRILi,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 balance and other markets 

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

primary fuels22. 

The global primary energy demands are the summations of the regional primary energy 

demands (EDRIL) as described above: 

= ∑

l

EDRI m,i EDRIL m,l,i 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 (ESRILMi,l,m) (Energy Supply of 

Regional primary fuels I of regions L at time period M) are set equal to the calculated supply 

(ESILMi,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 (Sfuelj,i,l,m) as 

calculated in Equation 77 are added to the (raw) oil and gas supplies. Thus, 

= +∑

i

ESRILM m,l,i ESILM m,l,i Sfuel m,l,i,j for oil and gas (EJ/year) Eq. 82 

 

22 With regard to emissions these are the markets of importance. 
61

where for Sfuelj,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, ESILMi,l,,m and ESRILMi,l,m. 

To determine the global supplies, the regional primary fossil fuel supplies are summed over the 

regions: 

= ∑

l

ESRI m,i ESRILM m,l,i oil, gas, coal, and biomass (EJ/year) Eq. 83 

The balance between the supply (ESRIi,m) and demand (EDRIi,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 vector23 that is comprised of the primary fossl fuels is determined 

by the ESRIi,m elements: 

MrkPRDmk = ESRI m,i oil, gas, coal Eq. 84 

The part of the market-demand vector that is comprised of the primary fossl fuels is determined 

by the EDRIi elements: 

MrkDEMmk = EDRI m,i 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:

MrkPrdmk=4=ESRIi=4 +∑Agsupi=biomass,l where ESRIi=4 refers to the ERB related biomass and 

Agsupi=biomass,l refers to the AgLU generated biomass CDRi=biomass,l,m after converting calories to 

EJ, and 

MrkDemmk=4=EDRIi=4+∑Agdemi=4=biomass,l where EDRIi=4 refers to the ERB related biomass and 

Agdemi=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 Products 
62

The part of the market-supply vector representing GHG emissions can be determined by carbon 

emissions produced (CemTot: Equation 114): 

MrkPRD CemTot =5mk = Eq. 86 

Analogously, the part of the market-demand vector representing GHG emissions can be 

determined by carbon emission targets (Emiss: exogenous): 

MrkDEM =5mk = Emiss m,l Eq. 87 

The part of the market-supply vector comprised of the agricultural products is determined 

by agricultural supplies (AgSupi,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

MrkPRD 12:6mk AgSup l,i Eq. 88 

where 

MrkPrdmk=6=∑Agsupi=wood,l refers to wood produced; 

MrkPrdmk=7=∑Agsupi=fwood,l refers to forward wood; 

MrkPrdmk=8=∑Agsupi=beef_mutton,l refers to beef and mutton produced; 

MrkPrdmk=9=∑Agsupi=foodgrains,l refers to food grains produced; 

MrkPrdmk=10=∑Agsupi=coarsegrains,l refers to coarse grains produced; 

MrkPrdmk=11=∑Agsupi=oilcrops,l refers to oilcrops produced; and 

MrkPrdmk=12=∑Agsupi=misccorps,l referes to miscellaneous crops produced. 

The part of the market-demand vector comprised of agricultural products is determined by 

agricultural demands (AgDemi,l= CDRi,l,m,for crops, processed crops, and animal products: see 

Equation 120; AgDemi,l= WDRi,l,m,for wood products: see Equation 121). Agricultural demands 

are expressed as constant elasticity demand equations where for the agricultural demands the total 

amount of calories demanded for each of the agricultural demands, CDRi,l,m, are further described 

in Part III, Equation 120, and demands for cubic meters industrial wood and fuel wood are further 

described in Part III, Equation 121) Thus, 

∑=

= =

nr

1l

MrkDEM 12:6mk AgDem l,i Eq. 89 

where 

MrkDemmk=6=∑Agdemi=wood,l refers to the over the regions summed wood production for 

wood products and wood fuels WDRi=present,l,m; 

MrkDemmk=7=∑Agdemi=fwood,l refers to the over the regions summed forward wood production 

for wood products and wood fuels WDRi=forward,l,m; 

MrkDemmk=8=∑Agdemi=beef&mutton,l refers to the total amount of calories demanded from beef 

and mutton, CDRi=beef_mutton,l,m multiplied by PastOut which is the ratio of pasture-based feed 

calories needed per calorie of animal product, which is based on land demand for pasture. The 
63

total amount of calories demanded from beef and mutton is first corrected for self consumption 

and fixed trade, however; 

MrkDemmk=9=∑Agdemi=foodgrains,l refers to the sum of two types of foodgrain demands, 

CDRi=food grains,l,m; 

MrkDemmk=10=∑Agdemi=coarsegrains,l refers to the sum of two types of coarse grain demands, 

CDRi=coarse grains,l,m; 

MrkDemmk=11=∑Agdemi=oilcrops,l refers to the sum of two types of oil crop demands, 

CDRi=oilcrops,l,m; and 

MrkDemmk=12=∑Agdemi=misccorps,l refers to the summed two types of miscellaneous crop 

demands, CDRi=misccrops,l,m. 

Processed crop demand fractions are calculated analogously to all other agricultural demands as 

CDRi=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 

CDRi=poultry,l,m and CDRi=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: 

ExDemmk = MrkDEMmk − MrkPRD mk Eq. 90 

where 

mk refers to the markets as described above. 

Global market prices are retained in the market price array, Pi,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 needs 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. Prices adjusted by the 

solution algorithm affect technology costs, demand for inputs and sector outputs. 

Note that calibration is achieved through the iterative process of recalculating the shares of the 

different technologies such that ultimately the energy 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-combusting fuel amounts and after accounting for scrub 

technologies. 

2.2.7 Imports, Exports 
64

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 export (or import) of that fuel to other regions. 

Global demand is met, but the specific amount traded from one region to another is not defined. 

Only global and regional total net export (or import) volumes are defined. 

2.2.8 Calibration procedures 

There are two parts to the calibration process: calibration 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 CO2 or carbon-equivalent emissions: 

GDP calibration is achieved by adjusting regional labor productivity. 

Calibrating the participation of oil, gas, coal, biomass, nuclear and hydro energy in the generation 

of electricity is achieved in a number of steps: First the weights of coal and biomass are reevaluated (the bssuui,l,m parameters are re-scaled based on the input end-use energy shares for each 

fuel); then, the weights of the input fuel shares, the bsuui,l,m parameters for oil, gas, coal, biomass 

and nuclear energy are rescaled and the hydro weight, bsuui,l,m is set equal to its fixed fuel share 

(needed by the electricity price routine). 

To calibrate the total and fuel-specific sectoral distributions 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 transportation and industry sectoral shares are readjusted. Then, on the basis of input sector and secondary fuel-specific final demand data, the 

weights for oil, gas, coal, and electricity, bsjkjklm, 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 for the first period). Given that hydrogen fuels 

are not a factor in the base year, the fuel share weight readjustments are limited to the fuels listed. 

The sectoral total energy use is calibrated by adjusting the sectoral technological efficiency 

parameters, Tk,l,m , which determine levels of technological change and innovation. These end-use 

efficiency parameters represent the level of sectoral technology (e.g., transportation, buildings, 

industry). The sectoral technological efficiency parameters, Tk,l,ms, are rescaled based on the ratio 

of the summed energy services demands simulated and the summed energy service demands from 

the input data. 

CO2 emissions in the base year are calibrated by adjusting the carbon emission coefficients (COi: 

tons C/EJ/year), which are based on the carbon content of the fuels. Since CO2 emissions 

coefficients can be based on different assumptions for energy units (higher versus lower heating 

values for example), this calibration assures that 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 for final (or primary) energy consumption follows 
65

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 integrated 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 are 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 procedures 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 emissions 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 equal to the carbon emission coefficient times the 

amount of fuel used. Emissions associated with energy transformations (synthetic fuels, 

electricity generation, and hydrogen production) are allocated to the region where the 

transformation occurs. 

Global average carbon coefficients for oil, gas, and coal combustion, unconventional oil and 

biomass (COi: fuel-specific emission coefficients) represent 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 represents 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 with 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 added to primary fuel demands 

ji

j

EDRIL m,l,i = EDRIL m,l,i +∑SFuel m,l,i,j • gc (see Equations 76 through 80). The 

raw fuel requirements (gas, coal and biomass) for synfuel production are referred to in 

the next set of equations as 

ji

j

SynInput m,l,i = ∑SFuel m,l,i,j • gc (EJ/year) Eq. 91 

where 

Sfuelj,i,l,m are the primary fuel demands for synfuel generation (Equation 77), and 

gcj,i is an intensity conversion coefficient 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 SBl,m. 

Burning of shales is determined by shale burning parameters (Shale1, Shale2, and Shale3) as 

SHALl,m. The equation that determines gas flaring (FLRl,m), gas burning (SBl,m) and shale burning 

(SHALl,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 Flr3

Nstep1m

2 Flr

Nstep1m1

FlrFLR 1m,l Flr •−− •−= • (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 substitute the regional gas burn parameters Sbr1, 

Sbr2 and Sbr3 to calculate gas venting and burning, SBl,m used in Equation 93, or the regional 

shale burn parameters Shale1, Shale2 and Shale3 to calculate shale burning, SHALl,m used in 

Equation 104. 

Emissions due to gas venting and flaring are calculated as follows: 

m,l,gasi

m,l

m,l

gasil,gasflarei m,l ESILM

)FLR1(

FLR

Cemissions = = SBCO = • − ••= (MMTC) Eq. 93 

(b) Carbon dioxide is not released from fossil fuels 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 technologies and non-scrub technologies is calculated 

from the total electricity demanded (Fjj,l,m) and the shares of the fuel-specific (Suui,l) scrub and 

non-scrub technologies (Ssuui,l) where ui is the technology. Thus the demanded electricity supply 

through fuel-specific scrub and non-scrub technologies, ESUui,l,m, is calculated as follows where 

ESUui,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 guui,l,m or ghhi,l,m and gij I; see Equation 99). 

ESU m,l,ui l,ui FjSsuSu m,l,jl,ui ••= (EJ/year) Eq. 94 

where 

ui is an indicator of any of the electricity generating technologies, 

Fjj,l,m is the total electricity (j) demand for region l at time m, 

Suui,l is the share coefficient of the competing fuels (in the form of prices) in generating 

electricity, and 

Ssuui,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, ESHhi,l,m, is calculated in an analogous fashion: 

ESH m,l,hi l,hi FjSshSh m,l,jl,hi ••= (EJ/year) Eq. 95 
67

where 

hi is an indicator of any of the hydrogen generating technologies, 

Fjj,l,m is the total hydrogen (j) demand for region l at time m, 

Shhi,l is the share coefficient of the competing fuels (in the form of prices) in generating 

hydrogen, and 

Sshhi,,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 the 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: 

m,l,liqj,gasi l,oili coali

gas_synfueli gasi coali

SFuel CO)SedFil1(

Cemissions SynInput CO

== = =

= = =

−• •

= −•

 (MMTC) Eq. 96 

Emissions from synliquids derived from coal and syngas derived from coal are calculated as 

follows, which includes carbon removed in the transformation process due to scrub technology if 

RemFrac1,l is not equal to one: 

)mFracRe1(

SFuel CO)SedFil1()

SFuel CO)SedFil1(

SynInput CO

Cemissions l,1

m,l,gasj,coali l,gasi gasi

m,l,liqj,coali l,oili coali

coali coali

coal_synfueli −•

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

−• •

−• −•

−•

=

== = =

== = =

= =

=

(MMTC) Eq. 97 

where 

 RemFrac1,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: 

SFuel )CO)SedFil1()

SFuel CO)SedFil1(

Cemissions SynInput( CO

m,l,gasj,biomassi l,gasi gasi

m,l,liquidj,biomassi l,oili biomassi

b_synfueli biomassi biomassi

= = = =

= = = =

= = =

−• •

−• • −

= • −

 (MMTC) Eq. 98 

(e) For conventional oil, gas, coal, and biomass emissions are calculated as follows, which 

includes, if the RemFrac2,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

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

••

+•••

−−•

•=

ESH )gijgh

ESU(mFracRe gijgu

)SedFil1(FFcons

Cemissions CO

im,him,l,hi

l,2 im,l,uim,l,ui

l,i

ii (MMTC) Eq. 99 

 where 

COi is the emission coefficient of oil, gas, coal or biomass, 

SedFili,l is the fraction of the feedstock that is not combusted, 

RemFrac2,l is the fraction of the emissions that can be scrubbed during electricity and/or 

hydrogen generation, 

ESUui,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 guui,l,m and giji. 

ESHhi,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 ghhi,l,m and giji, 

guui,l,m is the transformation efficiency when electricity is produced,

ghhi,l,m is the transformation efficiency when hydrogen is produced, 

giji is the transformation efficiency from primary to secondary fuel conversion, and 

FFcons equals the primary fuel demanded for transformation into secondary fuel supply, but 

for the primary fuels demanded for synfuel production, which implies that 

for conventional oil, fossil fuel consumption is represented by conventional plus 

unconventional oil; thus 

FFcons = l,oili = EDRIL= l,oili + ESILi=unconventionaloil (EJ/year) Eq. 100 

refined gas fossil fuel consumption refers to refined gas consumption (EDRILi=gas,l) without the 

additional syngas (Syninputi=gas,l,m) that can be consumed; thus 

FFcons = l,gasi = EDRIL l,i −SynInput = m,l,gasi (EJ/year) Eq. 101 

for conventional coal, fossil fuel consumption refers to EDRILi=coal,l while subtracting for the coal 

that is used for gasification and/or liquefaction; thus 

FFcons = l,coali = EDRIL l,i − SynInput = m,l,coali (EJ/year) Eq. 102 

and for biomass fuel, consumption refers to EDRILi=biomass,l while subtracting for the biomass that 

is used for gasification and/or liquefaction; thus 

FFcons = l,biomassi = EDRIL l,i − SynInput = m,l,biomassi (EJ/year) Eq. 103 

Emissions from shale oils are calculated based on shale oil burning (SHAL,l,m) as follows: 

Cemissions =shaleoili COi •= ESILM m,l,i •SHAL m,l + i • − l,i )SedFil1(CO (MMTC) Eq. 104 

where 

SHALl,m is the shale burning fraction. 

For each of the end-use sectors emissions are based on fuel mode demands, attributing shale oil 

production emissions and flared emissions to the industrial sector. Thus, for transportation, 

buildings and industry 

l,j )SedFil1(FjkCO2CO

j

k ∑ m,l,k,jj −••= (MMTC) Eq. 105 
69

For hydrogen production carbon emissions are calculated from the primary fuel demands meeting 

hydrogen demand (EDRIKLj,l,m) from which the amounts potentially sequestered have to be 

subtracted: 

hydrogen_scrub

j

2CO hydrogen ∑COj •= EDRIKL m,l,j −• l,j − C)SedFil1( (MMTC) Eq. 106 

Electric utilities carbon emissions are calculated from the primary fuel demands meeting 

electricity demand (EDRIKLj,l,m) from which the amounts potentially sequestered have to be 

subtracted: 

electricty_scrub

j

2CO electricty ∑COj •= EDRIKL m,l,j −• l,j − C)SedFil1( (MMTC) Eq. 107 

Emissions from the processing of limestone during cement production are input exogenously and 

are added to fossil emissions before emissions 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

m,l,gasj,coali l,gasi gasi

coali coali m,l,liqj,coali l,oili coali

seq mFracRe

SFuel CO)SedFil1()

SynInput CO SFuel CO)SedFil1( 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 calculated from the total electricity demanded (Fjjlm) and the 

shares of the fuel-specific (Suui,l) scrub technologies (Ssuui,l) where i is the scrub technology. The 

demanded electricity supply from fuel-specific scrub technologies, is based on ESUui,l,m, when ui

represents a scrub technology. 

The amount that is scrubbed and then sequestered is: 

scrub i ESUCOC m,l,ui im,l,ui mFracRegijgu l,2 ••••= (tons C) Eq. 109 

where 

COi is the carbon emission coefficient based on the carbon content of the fuel combusted 

(COI: tons C/EJ for oil, gas, or coal), 

ESUui,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 guui,l,m and giji. 

 

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: 

scrub i ESHCOC m,l,hi im,l,hi mFracRegijgh l,2 ••= • • (tons C) Eq. 110 
70

where 

 ESHhi,l,m and ghii,l,m are equivalents to the utility variables (ESUui,l,m and guui,l,m), but specific to 

hydrogen generation. 

2.3.3 Non-CO2 Greenhouse Gas and Reactive Gas Emissions from the 

ERB module

Emissions of radiatively important substances other than CO2 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 depend, 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-CO2 greenhouse gases. When the 

calculations incorporate GWP (Global Warming Potentials: see Table 4; or alternative indices) 

unit conversions are therefore not required. 

Radiatively important substances are often controlled for reasons other than climate concerns and 

these reductions, are not modeled at the same level 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 implemented using marginal abatement cost curves. 

Mathematically, non-CO2 greenhouse gas emissions are modeled as follows 

( ) ( ) t t t t = factor_EmEm −•• • − • − )icePr_C(MAC1USER1))Cap/GDP(Control1(Driver

 (variable units) Eq. 111 

where 

Em_factor is an emission factor, which is either input by technology, or derived from base 

year emissions. All CH4 and N2O emissions factors are currently derived by the model directly 

from base year emissions data, 

Control(GDP/Capt) is an emission control due to non-climate policy (e.g., SO2 or NOx

specific), 

MAC(C_Price)t is a Marginal Abatement Curve (MAC) that represents emissions reductions 

due to climate policy as a function of the price of carbon (or carbon-equivalents). The MAC’s 

used are adapted from EPA studies, and 

USERt is an user-defined reduction in emissions intensity over time that represents efficiency 

improvements or adjustments for other factors not directly modeled. 

Drivers and controls for each source are listed in Appendix 6 and summarized in Table 4. 

Table 4 ERB non-CO2 emissions 

Methane: CH4

Industrial Sources 

Transportation (Mobile Sources) 

Coal Mining 

Electric Utilities (Stationary) 

Natural Gas Systems 

Petroleum Systems 

Wastewater Treatment 

Biofuel Combustion 
71

 

Nitrous oxide: N2O 

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 cost 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 price

percent reduction in emissions

Figure 9 Cost curve example relating carbon prices to emission reductions 

Each cost curve is, for a particular emissions source, defined by two indices; the first specifies the 

gas (e.g., 1= ERB CH4; 2= ERB N2O; 3= Ag CH4; 4= Ag N2O), 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 carbon 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-in 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 module 
72

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 applied 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 change 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 

(CSdensl,i=landuse: TgC/000ha) and above ground plant material (CLdensl,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 (ha/000) multiplied by carbon densities (Tg/000ha) for 

each land-use class. 

Historical land use changes are used when vegetation 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 unmanaged land the carbon emissions from above 

ground are calculated as follows: 

∑=

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − = •

nr

1l

m,l,i 1m,l,i

m,l,i i,l Nstep

Landuse Landuse

EmLC CLdens (MMTC) Eq. 112 

where 

 i is an index for land use: crops, biomass, pasture, 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 PercDecaym=0.6); 30% of 

the soil carbon is assumed to only decay in the next time period PercDecaym-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 (PercDecaym-2=0.1): 

∑ ∑ = − =

−

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − = • •

nr

1l

m

2mm

m 1m

m,i i,l m Nstep

Landuse Landuse EmSC CSdens PercDecay 

 (MMTC) Eq. 113 

2.3.5 Non-CO2 greenhouse gas emissions from the AgLU module 

Variables and drivers for the calculation of non-CO2 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 emissions from agricultural processes result from 
73

fertilizer use (scaled to overall crop production), and managed and unmanaged manure (scaled to 

livestock production). 

Drivers and controls for each source are listed in Appendix 6 and summarized in Table 5. 

Table 5 AgLU non-CO2 emissions 

Methane: CH4

Land Use/Burning 

Enteric Fermentation 

Manure Management 

Rice Cultivation 

Agricultural Residue Burning 

Temperate Forest Fires 

 

Nitrous oxide: N2O 

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 exogenously 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

CemTot Cemissionsi 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 which 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 particles 
74

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 implemented as shown in Equation 115 (Smith et al. 

2002). Sulfur emissions from fossil fuel combustion are modeled using region and fuel-specific 

sulfur contents (see Table 72 in Appendix 6), ash retention percentages (for coal) (see Table 71 in 

Appendix 6), and appropriate control percentages (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 efficiency 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 fmax, the maximum control 

percentage in Equation 115. This allows the future 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 simulated 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 there 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 purchasing power parity, which is, in this case a better 

measure of relative wealth than simply exchange-rate-based GDP. 

SulfurCont ( ) )f1(f1ent EnergyContent

FuelUse EmSulfurt ash −•−• control = • (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, 

 fash is the ash-retention fraction, and 

fcontrol is determined as follows ( )

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

=

τ

− t GDPpercap intmidpo c GDPpercap /

max

e1

f fcontrol Eq. 116 

 where 

 fmax is the ultimate reduction percentage, 

GDPpercapmidpoint is the midpoint of the GDP control curve at which point emissions are 

reduced by 0.5*GDPpercap, and 
75

Τ is the per GDP per capita range over which the control percentage goes from 10% to 

90% of fmax. 

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 content, 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 potential future increases in radiative forcing and 

climate change. Greenhouse gas emissions associated with agriculture 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 through 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 initially developed to simulate global land use 

change and carbon emissions as responding to a carbon policy. Edmonds et al. (1996) constructed 

the first version of the AgLU model as an addition 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 that 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 one century, that is, over the same time period 

as the ERB model. AgLU adds markets for composite 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 energy 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 response 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 Products 
77

in a carbon-constrained world, and to (3) provide estimates of methane and nitrous oxide 

emissions from the agricultural sector. 

AgLU is a dynamic25 partial equilibrium economic model; it has 1990 as base year and performs 

its calculations in 15-year time steps as does ERB. The three primary drivers of land use change 

are population growth, income growth, and autonomous 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, expressed as calories in the AgLU model. Changes in 

the regional composition of consumption in response to higher incomes can also be important, 

especially if people in developing countries increase per-capita consumption of animal products 

to the level seen today in the United States 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 additional information on prices and non-land cost of 

production, landowners are assumed to select the land use with the greatest economic return 

calculated as revenue less non-land cost of production. 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

crops biomass

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. Methane emissions resulting from agricultural 

processes are due to enteric fermentation and animal 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 production), and managed and 

unmanaged manure (scaled to livestock production). 

 

25 The dynamic aspect results from the fact that changes 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 adapted 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 region. 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 from MAGICC and/or SCENGEN outputs, however) 

through climate parameters. These climate parameters are multipliers representing climate, 

implemented to simulate changes in yield. Technological change is simulated as an autonomous 

process as in the ERB module. Commercial biomass 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 energy production. Given a high enough biomass 

feedstock price, regions are capable of growing commercial biomass. Production and markets for 

biomass are separate from forest products; commercial 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 produced at lower costs than commercial biomass. 

Commercial biomass is only produced if the global biomass 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 kilograms to calories using weights with units of 

kilocalories per kilogram. Individual crops are then aggregated to composite crops (markets are 

active for food grains; coarse grains; oil crops; and other crops) using units of calories. A similar 

procedure is used for animal products. The three animal composite products (beef and mutton; 

pork; and poultry) are built from FAO data on meat, animal fats, milk, and eggs (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 cubic meters (markets are for wood and for future 

wood). 

Productivity of field crops is calibrated in the model 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 increasing 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 production in a region contracts. The net of the 

modeled agricultural productivity is the 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 use 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, emissions partake in the calculations of the fuel 

price by linking emissions with a carbon price. 

In the AgLU market equilibrium, in the stand-alone mode26, 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 Leontief 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 (Pcarbon): 

 

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

Pbiofuelfromoil Poil += + PtOilTranCos carbon • OilCarb ($/GJ) Eq. 117 

where 

Poil is the price of crude oil $/GJ, 

OilTranCost is the cost of refining oil to a transportation fuel ($/GJ) which is an equivalent to 

a combination of the non-fuel cost parameters in the ERB module, 

Pcarbon 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 oil 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: 

BioTranCost

EtoBio

P

P biomass

biofuelfrombiomass += ($/GJ) Eq. 118 

where 

Pbiomass is the price of the biomass feedstock ($/cubic meter biomass feedstock), 

EtoBio is the energy efficiency of converting solid 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 biomass 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 (Pbiomass in $/m3

C) using Equations 117 and 118 

(in a market equilibrium, the price paid for biomass liquids will equal the price of refined 

petroleum-based liquids), we obtain the price received for biomass as a function of the crude oil 

price and the carbon price: 

P ( ) PPEtoBio OilCarb tOilTranCos BioTranCost biomass oil carbon •+•= + − 

 ($/m3

C ) Eq. 119 

To convert this biomass feedstock price from $/m3

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 the forest products, future forest products and 

biomass (after commercial biomass supply from 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 imported to produce more animal products. 

International trade is an important mechanism in AgLU allowing regions with a growing 

population to maintain adequate diets even when limited amounts of unmanaged land can be 

converted to agriculture. 
81

The composite crops in AgLU are traded freely among regions so that increases in global demand 

are supplied wherever it is least expensive to grow 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 remaining food crops, such as fruits, vegetables, 

and starchy roots. Even though trade in animal products 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 trade 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 are 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 measured 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 the 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 vintage of trees that was planted three time steps 

previously is cut to provide current supply of forest products. Supply of current forest products is 

therefore fixed, and AgLU searches for a price that 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 demanded to be dedicated to producing biomass. 

If the AgLU module is linked with the ERB module, determination of the biomass price is 

dependent on the linked model solution process. 

Consumer demand for food (calories) creates direct 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 consists primarily of cereals, but also includes 

starchy roots, fruits and vegetables. Processed crops include vegetable oils from oil crops, 

sweeteners from sugar crops, and alcoholic beverages. 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, processed crops, and animal products is expressed 

similarly to the (constant elasticity) demand equations 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

CDR A jl

jl

••• ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•= β

α

=

 

 (total calories demanded per year) Eq. 120 

where

 CDRi,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, 

Ai,l is a scaling coefficient (unitless) to calibrate the price and income feedback terms in the 

base year, 

Pi,l,m is the market price of the commodity ($/calories consumed per person per day), 

α

i,l is the price elasticity, 

Yi,l,m is per-capita income index {$ GDP/population/($ GDP/population in base year)}, 

βi,l is the income elasticity for the calories demanded which implies it may differ from income 

elasticity in the demand equation for transportation, industry, or buildings (ryklm), 

Nl,m is the total population by region (which differs 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 

Ci,l,m is calories consumed per person per day (multiplied by 365 to get yearly consumption). 

Demand for agricultural products may vary over time in two ways. The first is through directly 

varying Ci,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 and 
83

income elasticities, α

i,l and βi,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 processed crops are set to be small and positive, or 

zero. Similarly, price elasticities for these two food categories are set to be small and negative, or 

zero. Data from Figure 11 suggest that consumption 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 consumption 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 inputs to these activities. For example, the first 

row 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 example (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 average efficiency of converting crops into animal 

products is roughly 37%. The efficiency would be even 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

WDR A jl

jl

•• ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•= β

α

=

 

 (total m3

 wood demanded per year) Eq. 121 

where 

WDRi,l,m is industrial wood and fuel wood 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, 

 Ai,l is used to calibrate base year demands ($/m3

 wood) to historical data by region 
84

Pi,l,m/Pi,l,m=baseyear is the price ratio of the commodity ($/m3

 wood/ same in base year), 

α

I,l is the price elasticity, 

Yi,l,m is per-capita income index {$ GDP/population/($ GDP/population in base year)}, 

βI,l is the income elasticity for the wood demanded which implies it differs from income 

elasticity in the demand equation for transportation, industry, or buildings (ryklm), 

Nl,m is the total population by region (which differs 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 industrial wood and negative for fuel wood. With rising income, demand 

for industrial wood increases and demand for fuel wood decreases. 

Consumer demand for food grains and miscellaneous 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, sweeteners, and alcoholic beverages. Demand for animal 

products creates an indirect demand for crop land and pasture land used as animal feed but with a 

net loss of calories through the conversion from crops to animal products. Demand for biomass 

fuels also requires cropland especially in scenarios with high prices of fossil fuels or scenarios 

that place a high value on limiting carbon dioxide emissions. 

Prices of agricultural products are adjusted when solutions are sought in balancing demand and 

supply while supply is determined by a land allocation 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, pasture, and newly planted trees. Crops and 

commercial biomass are grouped in a nest because 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 model 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 price 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. 

( ) −•=π GPyr m,l,im,l,ip,m,l,ip,m,l,i i = crops, biomass, pasture (annual $/ha) Eq. 122 

where 

πri,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, 

yi,l,m,p is yield per hectare for land use i in region j at location p (calories/ha), 

Pi,l,m is the market price for the product produced by land use i (units $/yield units: calories or 

m3

); prices of biomass are obtained from the ERB module; market prices of animal products 

(Pi=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 

Gi,l,m is the non-land cost per unit of output in land use (units are $/yield units: calories or m3

). 

The profit rate (πr) calculation for forest products is somewhat different because of the time lag 

between planting and harvest. The profit rate expression for forest products includes a term that 

discounts future earnings into the present and levelizes those earnings over 45 years; this forward 

price is denoted by P m,l,i

~ . 

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

~ 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 sunlight, 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 patterns. 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 land use type, land use shares would, in general, 

be calculated numerically, by summing over the land distributions implied in Equations 122 and 

123. In the usual integrated modeling context, however, 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 Gumbel distribution is again Gumbel. This is 

described in more detail in Appendix 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 those 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 consider this an intrinsic parameter of the yield 

distribution, i y , because it is invariant with respect to prices or land use shares, and is an average 

across all locations that a particular crop could possibly be grown. This parameter is allowed to 
86

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 alternative 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 description of the logit share equation exponent), 

the denominator is summed over all possible uses for land, and 

p,m,l,i πr 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 ( ) − GPyr m,l,im,l,ip,m,l,ip,m,l,i π = • is the average 

profit rate for crops, biomass, and pasture; and ( ) ( ) p,m,l,i 45 GP m,l,im,l,ip,m,l,i

~ 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 

Landuse S m,l,im,l,i Totallandl •= Eq. 125 

This allocation mechanism is convenient because greater 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 (general) or 123 (new forests). The profit rate 

calculation for pasture requires a price for pasture-based feed, Pi=pasture. AgLU calculates the 

price of pasture indirectly from the market prices of animal products (Pi=animal) and crops (Pi=crops), 

both of which are solved for within the model. Given these two prices, Pi=pasture is found by 

solving: 

P = P = m,l,cropsim,l,animali FeedOut P = m,l,pasturei + GPastOut = m,l,animali +•= • ($/cal) Eq. 126 

where 

FeedOut is the ratio of crop-based feed calories needed per calorie of animal product; PastOut 

is the ratio of pasture-based feed calories needed per calorie of animal product, and 

Ganimal,l,m is the non-land cost per unit of output (an exogenous region and time-specific input 

parameter in units of $/cal or $/m3

). 
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. Intrinsic 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 intrinsic yield does not vary with prices or land 

shares. However, the average yield of land for 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 year prices are used as calibration parameters to 

match base year data on observed average yield 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 greater than any of the individual (unobserved) 

profit rates. 

λ

λ

⎥

⎦

⎤ ⎢

⎣

⎡

∑π=π

p

1

m,l,i m,l,p,i ˆr r ($/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 πˆr ) are equal across land use types as 

indicated in Equation 127. This result is not derived 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. 

ˆr ˆr i π=π i = crops, biomass, pasture, forest ($/cal or $/m3) Eq. 128 

 

We exploit this result to calculate an observed average yield ( i yˆ ) 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 yˆ −

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

where 

Pi,l,m is the market price for the product produced by land use i (units $/yield units: calories or 

m3

), and 

Gi,l,m is the non-land cost per unit of output (an exogenous region and time-specific input 

parameter in units of $/cal or $/m3

. 

Therefore, the observed average yield ( i yˆ ) is defined to be the yield at which the profit rate is 

equal to the observed profit rate i πˆr . 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 (yi,l,p; m3

/ha/yr) are projected by 

multiplying the intrinsic yields with a climate 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, Techi,m, are functions of time m according to 

Nstep

m,i m,i1m,i Tech = + )S1(Tech − (unitless) Eq. 130 

where 

Techi,m is the rate of technological change, set to one in the base year, 

Si,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 the 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 for 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

crops biomass

crops

rr

r

ss

s

λ λ

λ

π+π

π = +

 (unitless) Eq. 131 

where 

λ2 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 1 2

biomass

1

biomass/crops crops r rr

λ λ λ π π+π= ($/cal) Eq. 132 
89

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 λ2 from the lower nest, then the land share equations 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 Assessment of Greenhouse-gas Induced 

Climate Change 

MAGICC is a ‘Simple Climate Model’ as defined 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) (Wigley 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 (sulfur 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. The MINICAM currently incorporates 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. Through 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 greenhouse 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 forcing moves the earth system toward a (new) 

equilibrium temperature where incoming and outgoing 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 chosen for the climate sensitivity is one of the 

principle determinants of the level of future climate 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 changes 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 atmospheric chemical processes, sinks, and other sources. 

Atmospheric concentrations in MAGICC are annually 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 terrestrial 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 

by29

n ocean FFDE fert 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, 

Dn is the carbon flux due to land-use changes. These can be either provided by the AgLU 

module or set as an exogenous input,

Focean is the carbon flux into the oceans (see below), and 

Ffert is carbon storage changes due to terrestrial feedbacks, considered by MiniCAM to be due 

to carbon dioxide fertilization; a positive value for Ffert 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 dioxide 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 onto 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 used in MAGICC are 330, 80, 20, and 1.6 years.30 A 

fraction of any emissions simply stays in the atmosphere, 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 for 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 (1987) 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 dioxide stays in the ocean/atmosphere system. 
92

oceanic sink is specified by setting, as an input parameter, the total oceanic carbon sink (Focean 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 deforestation 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 into 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: fast 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 remains either as living plants (perennials, 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 atmosphere 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 category can be altered by land-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 also 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 carbon 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 included 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 (Dn) and mean ocean flux (Focean) 

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 simpler. The atmospheric concentrations of 

methane, nitrous oxide, and the halocarbons are modeled as: 

τ − β = Δ CEdt

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 lifetime, 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 appear 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 concentration 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 lifetime will increase. Thus methane has a positive 

feedback on its own lifetime. The formula for methane 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 exogenously. The amount of stratospheric ozone 

depletion due to these gases is estimated through 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 initial (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 ozone will affect the amount of UV light that 

penetrates to lower levels, which 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 = 2.75TgCH4/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 for 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. The forcing due to remaining gases not explicitly 

covered can be added as an exogenous input. Alternatively, emissions 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 the 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 logarithmic in emissions. Forcing is split into three 

regions (North Atlantic, Eurasia, and Southern Hemisphere) in order 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 version 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 greenhouse 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 concentration 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 that spectral overlap between methane and nitrous 

oxide is taken into account in the forcing formulas. 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 increase36

largely because of the heat capacity of the oceans. 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 using the global radiative energy balance and an 

upwelling-diffusion model of ocean heat transport. 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 absorbed solar radiation 

and by any heat that is transported from any other climate “box”. This assumption is justified 

because the time scale over which the land surface 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: the 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 the deep ocean by two processes. 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 large-scale circulation known as upwelling. Cold, 

salty water near the poles sinks down where it spreads over most of the ocean floor (known as 

ocean “deep water”). The return flow is a general 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 diffusion result in downward heat transport over the bulk of the oceans, the 

two processes have different mathematical dependencies and both 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 the 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 centuries. 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 heat 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 specified 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 developed 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 including diffusive/convective heat transport, 

latent heat transport, and for the mixed-layer ocean 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 equation for global average energy balance is:38

⎥

⎦

⎤ ⎢

⎣

⎡ θ •⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+•⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

τ

τ − τ

− = dt

d

h

h

dt

TaT dT

dt

dT d

m

m d

a

m

a

a eq 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 proportional to the temperature gradient (dT/dz) while diffusive transport 

is proportional to the second derivative (d 2T/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 that, in the absence of the ocean, the atmospheric 

temperature would approach an equilibrium value (T eq) over an atmospheric equilibrium time 

scale, τa, 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 few years and the deep ocean would take a couple 

centuries to come into equilibrium. 

The equilibrium temperature (Teq) is determined by the amount of incoming solar radiation, the 

planetary albedo and the climate sensitivity39. 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 sensitivity 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 construct 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 “best 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 known, it will be useful to examine some of the 

other simplifying assumptions that are used in such models. At present, however, the global-mean 

results produced by almost any of the more complex 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 change, global mean sea-level rise40 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 scales, 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 forcing is stabilized. Greenland runoff and Antarctic 

accumulation (see below) will follow the atmospheric 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 precipitation, 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 properties 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 calculate 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 highly 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 latitudinal 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 higher latitudes. The global-mean expansion is found 

by averaging the zonal values, weighted by the ocean area of each zone. 

As global temperatures have increased over the last century glaciers have been melting and this 

trend is expected to continue under the influence 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, ΔT. 

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 zo (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 were 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 scales44 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 Oerlemans et al. (1992). 44 Total ice mass divided by the accumulation rate. 
99

The Greenland ice sheet is assumed to have a sensitivity 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, increases 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 discharging into the ocean through runoff and calving 

of icebergs will have an impact on sea-level rise. The West Antarctic ice sheet is an area of 

particular concern since this ice sheet is grounded below sea level. Some think that the West 

Antarctic ice sheet might therefore be particularly 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 sheets 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 temperature. 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 climate change are required. A global energy balance 

model such as MAGICC cannot supply regional 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 results 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 gases 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 global change into still more spatially explicit 

information the climate change generator SCENGEN (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 pattern-scaling method developed by Hulme et al. 

(2000). For example, temperature change is expressed 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 greenhouse 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 change as determined by MAGICC resulting in 

spatially explicit ERB-scenario related climate change. 

The climate change produced by each GCM is different, in both magnitude and pattern. This is 

due to the different, and necessarily limited, representations of the relevant physical processes in 

each GCM and also indicates our uncertain knowledge of the climate system. Therefore, no one 

model can be considered definitive and this uncertainty must be included in assessments. 

SCENGEN allows two methods of indicating this uncertainty. The first, and most widely used, is 

to use different GCM patterns for the impacts assessment (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 models can also be averaged together to form a 

composite climate change pattern. In the composite 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 procedure 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 assessment 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 some 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, with 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 may 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 other types of simplified 

climate models, are useful for their speed and flexibility. 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 provide some results to give an overview of 

MiniCAM’s types of output. 

Global outputs 

The initial long-term scenarios that the Intergovernmental 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 evaluation 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 called for the use of multiple models, an “open 

process” and a better understanding of the driving forces, such as demographic development, 

socio-economic development, and technical change. 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 participation 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 development 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 increases 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; A1G 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 sustainable” world with the same population peak 

around 2065 as in the A1 scenario, but with rapid 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. People, 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 results in low global income per capita. Some 
103

attention is given to potential local and regional environmental damage (sulfur and particulate 

emissions are reduced in Asia) but this is not uniform (SO2 emissions increase in Africa as a 

result of the intensified exploitation of coal). 

In the “heterogeneous world with local sustainability” 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 fertility. Environmental protection is a priority, 

although strategies to address global environmental challenges are less successful than in other 

scenarios. There is a gradual reduction in the current reliance on fossil resources, but the energy 

supply is still predominately hydrocarbon-based even in 2100. Another way of capturing this 

scenario would be by calling it the “coal-use” scenario. 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 MiniCAM2001 model documented in this manuscript. 

Average incomes are highest for the A1 scenario, followed, in order, 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

A1

B1

B2

A2

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 “balanced” approach had more coal technologies 
104

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 per 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 the 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. The 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 scenarios 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 agricultural GHG emissions like methane and nitrous oxides 

(Figures 19-20). 

Figure 16 shows total carbon-equivalent emissions. From this graph it can be observed that in the 

A2 scenario, the “delayed development” scenario emissions emissions surpass those of the A1B 

and A1G scenarios as is the case for electricity generation (Figure 14). The A1T and A1G 

scenarios are reversed in order however (anthropogenic carbon-equivalent emissions versus 

electricity), given that the A1T scenario focused non-fossil energy resources. 

Projected carbon dioxide concentrations, calculated in the MAGICC module are shown in Figure 

17. The carbon dioxide concentrations patterns are analogous to the total anthropogenic GHG 

emissions. 
106

Global Carbon-Equivalent Emissions (GtCE 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 scenarios 
107

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 investments 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 intensity 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 scenario with largest declines over time, while 

following the same path as the other A1 and the B1 and B2 scenarios through 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 scenarios 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 Emissions (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 scenarios with divergence in the A1 scenarios. 
109

Temperature changes and sea-level rise are calculated in the MAGICC module and are illustrated 

in the next two graphs for the SRES scenarios. 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 scenarios 
110

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, however, although both the Former Soviet Union and 

Korea show the largest differences. 

Regional Differences over Time in Income (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 USA

02 Canada

03 WEUR

04 Japan

05 A&NZ

06 FSU

07 AcenP

08 MidEast

09 Africa

10 LatAmerica

11 SEAsia

12 EEU

13 Korea

14 India

1990

2005

2020

2035

2050

2065

2080

2095

Figure 23 Regional differences in income 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 developing economies. Developed 

economies still show, however, large increases in expected electricity consumption (Figure 25). 
111

Regional Differences over Time in Caloric Intake (Kcal per year per person) in 

IPCC's B2 Scenario

1900

2100

2300

2500

2700

2900

3100

3300

3500

00 Global

01 USA

02 Canada

03 WEUR

04 Japan

05 A&NZ

06 FSU

07 AcenP

08 MidEast

09 Africa

10 LatAmerica

11 SEAsia

12 EEU

13 Korea

14 India

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 only 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 expected 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 Electricity Consumption per Capita (GJ per 

year per capita)

0

10

20

30

40

50

60

70

80

90

01 USA

02 Canada

03 WEUR

04 Japan

05 A&NZ

06 FSU

07 AcenP

08 MidEast

09 Africa

10 LatAmerica

11 SEAsia

12 EEU

13 Korea

14 India

1990

2005

2020

2035

2050

2065

2080

2095

Figure 25 Regional differences in electricity consumption 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 Global

01 USA

02 Canada

03 WEUR

04 Japan

05 A&NZ

06 FSU

07 AcenP

08 MidEast

09 Africa

10 LatAmerica

11 SEAsia

12 EEU

13 Korea

14 India

1990

2005

2020

2035

2050

2065

2080

2095

Figure 26 Regional differences in anthropogenic emissions in IPCC’s B2 scenario 
113

Policy cases 

Results of carbon policy implantation are illustrated in the next set of graphs. Carbon policies 

can be implemented by determining a carbon fee 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, through scrub technology and 

sequestration some relaxation of carbon constraints 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 dioxide 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 per year) in IPCC's B2 Scenario with 

Policy Implemetations of Emission Constraints 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 scenario 
114

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 illustrates 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 implementations 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

B2

B2seq450

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 2095

Carbon 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 scenarios 
116

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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 Energy 
2

TABLE OF CONTENTS 

TABLE OF TABLES ...................................................................................................................................................... 3

APPENDIX 1: INDICES AND NOMENCLATURE; DEFINITIONS; UNITS ........................................................ 5

Indices and nomenclature ............................................................................................................................................. 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 AGLU MODULE ......................................................................... 11

Land allocation ........................................................................................................................................................... 11

APPENDIX 6: LIST OF TABLES .............................................................................................................................. 13

Demographics and GDP parameters .......................................................................................................................... 13

Energy supply and extraction parameters ................................................................................................................... 15

Primary energy price parameters ................................................................................................................................ 23

Parameters to calculate prices of secondary fuels ...................................................................................................... 25

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

Hydrogen production B2 Scenario ............................................................................................................................. 28

Electricity generation B2 Scenario ............................................................................................................................. 30

Fuel sharing and energy services ............................................................................................................................... 36

Elasticities .................................................................................................................................................................. 39

1990 Input data for calibration ................................................................................................................................... 45

Resulting, for example, for the USA for the B2 scenario in Final Energy Demand: .................................................. 46

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

Parameters for emission calculations ......................................................................................................................... 47

Non-CO2 emissions ................................................................................................................................................... 49

Sulfur emissions ......................................................................................................................................................... 51

Parameters related to the AgLU module .................................................................................................................... 56

APPENDIX 7: LIST OF EQUATIONS ...................................................................................................................... 62
3

TABLE OF TABLES

Table 1 Regional population projections for the B2 story line ..................................................................... 13

Table 2 GDP projections for the B2 story line [90$GDP(90mer)] ............................................................... 13

Table 3 Market-based GDP to PPP conversion factors ................................................................................ 14

Table 4 Regional GDP elasticities ................................................................................................................ 14

Table 5 Examples of projections of regional labor productivity increases and regional labor force 

participation rates ................................................................................................................................. 14

Table 6 Examples of projections of regional labor force participation ......................................................... 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 estimates of energy supplies ............................................................................... 20

Table 12 Regional minimum production rates for fuel production .............................................................. 20

Table 13 Regional initial estimates of available biomass waste ................................................................... 21

Table 14 Regional supply price elasticities ................................................................................................. 21

Table 15 Initial prices and base share weights for biomass supply shares ................................................... 21

Table 16 Aggregate income elasticity of biomass supply ............................................................................ 22

Table 17 Hydropower generation parameters ............................................................................................... 22

Table 18 Regional energy from hydropower obtained in the base year in the B2 scenario and the fixed 

hydro shares for producing electricity ................................................................................................. 22

Table 19 Regional initial market prices for all goods ................................................................................... 23

Table 20 Transportation costs for traded fuels ............................................................................................. 23

Table 21 Trade barrier scale factors such that fuel prices can be region specific ......................................... 23

Table 22 Energy conversion factors from primary energy to secondary energy and markup costs ............. 25

Table 23 Synfuel parameters to calculate non-energy costs of synliquid production 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-energy costs of synfuel production from biomass ............... 26

Table 26 Synfuel efficiency coefficients ...................................................................................................... 26

Table 27 Non-energy costs in synfuel and electricity generation (values 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 regional carbon disposal costs .................................................................................... 27

Table 30 Synfuel logit share exponent ......................................................................................................... 28

Table 31 Conversion factors to calculate carbon fees towards final consumption ....................................... 28

Table 32 Total System Efficiency of Hydrogen Production GHILM ........................................................... 28

Table 33 Non-energy costs in hydrogen generation (values are 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 subsector share weights ................................................................................................ 29

Table 36 Hydrogen and electricity generation logit exponent ..................................................................... 30

Table 37 Hydrogen production share coefficients ........................................................................................ 30

Table 38 Logit share exponent for hydrogen production .............................................................................. 30

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

electricity ............................................................................................................................................. 30

Table 40 Regional electricity price coefficients used to account for end-sector differences and distribution 

costs ..................................................................................................................................................... 32

Table 41 Electricity generating subsector-specific base-share weights ....................................................... 32

Table 42 Logit function scale parameters for electricity .............................................................................. 33

Table 43 Energy services input-output coefficients GJK ............................................................................. 36

Table 44 Energy services non-fuel costs HJK .............................................................................................. 36

Table 45 Hydrogen energy service fuel-related efficiency coefficient (Gjk: j=hydrogen) ........................... 36

Table 46 Hydrogen energy service related non-fuel costs (Hjk: j=hydrogen) .............................................. 36

Table 47 Transportation sector fuel-related efficiency coefficients ............................................................. 37
4

Table 48 Transportation sector non-energy costs ......................................................................................... 37

Table 49 Aggregate price elasticity .............................................................................................................. 37

Table 50 End-use sector-specific price elasticities for oil, gas, coal and electricity ..................................... 37

Table 51 Transmission and Distribution Costs for Hydrogen ...................................................................... 38

Table 52 Transmission and Distribution Cost of Electricity ........................................................................ 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, electricity) for end-use sectors .... 39

Table 55 Regional income elasticities for end-use sectors ........................................................................... 43

Table 56 End-use sector-specific price elasticities ....................................................................................... 44

Table 57 Regional end-use sector efficiency coefficients for 1990 .............................................................. 44

Table 58 End-use sector efficiency improvement coefficients for 2005 through 2095 ................................ 44

Table 59 Fuel demand (EJ) Industry sector .................................................................................................. 45

Table 60 Fuel demand, Transportation sector .............................................................................................. 45

Table 61 Fuel demand, Buildings ................................................................................................................. 45

Table 62 Fuel demand, Electricity generation 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-CO2

Greenhouse Gases ................................................................................................................................ 47

Table 68 Gas flare, flared gas burn, and shale burn parameters ................................................................... 48

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

Table 70 Overview of variables and considerations of non-CO2 emission calculations .............................. 49

Table 71 Regional end-use sector specific 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 control fraction .................................................................. 53

Table 75 Additional sulfur emission control 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-energy related industrial sulfur emissions ...................... 56

Table 79 Regional coefficients determining changes in industrial sulfur emissions over time .................... 56

Table 80 Example of historical land use data collected ................................................................................ 56

Table 81 Regional land areas in 1990 ........................................................................................................... 57

Table 82 Land Carbon Density Parameters, by Region (TgC/000ha) .......................................................... 57

Table 83 Harvested (1990 data in 000 ha) .................................................................................................... 58

Table 84 Example of regional technical improvements in food production in two time periods ................. 58

Table 85 Example of regional food demand data ......................................................................................... 59

Table 86 Although not directly used, an example of data collected for the AgLU module.......................... 61

Table 87 1990 Base Year CH4 and N2O emissions (in TgCH4 or TgN) ..................................................... 61
5

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, except 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 text
6

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 determined 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-African-Republic Belize 

Australia Kyrgyzstan Chad Virgin-Islands-(British) 

New-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 

Netherlands Cambodia Malawi Jamaica 

Norway China Mali Martinique 

Portugal North-Korea Mauritania Aruba 

San-Marino Laos Mauritius Nicaragua 

Spain Macau Morocco Niue 

Svalbard Mongolia Mozambique Marshall-Islands 

Sweden Vietnam Namibia Panama 

Switzerland Korea Niger Paraguay 
7

Turkey South-Korea Nigeria 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-Africa 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 

Nepal Zambia 

New-Caledonia 

Vanuatu 

Northern-Mariana-Islands 

Micronesia 

Palau-Islands 

Pakistan 

Papua-New-Guinea 

Philippines 

Seychelles 

Singapore 

Thailand 
8

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 bracketed. Bracketing is achieved when the price of a 

good is adjusted up or down until the excess demand (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 the 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 εn, then after the next iteration it 

will be bracketed by an interval of size 

εn+1 = εn/2 Eq. A3.1 

From the initial bracketed interval, εo, to the desired tolerance, ε, the number of iterations to 

achieve the tolerance is given by 

n = log2 (εo/ε) Eq. A3.2 

Because there are multiple markets, however, the 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 bracketing intervals. New bracketing intervals must be 

determined in such a case. In other situations, bracketing may not be possible at all. For instance, 

when resources are exhausted and there are no longer 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 Newton-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 quickly 
9

(Ref. Numerical Recipes). In the vicinity of the solution, each iteration of the routine 

approximately doubles the number of significant digits in the trial solution. The Newton-Raphson 

routine requires the evaluation of the function and its derivative at arbitrary points. The NewtonRaphson formula is given by 

xi+1 = xi + f(xi)/f’(xi) Eq. A3.3 

where xi is the trial solution, xi+1 is the next trial solution, and f’(xi) is the derivative of the 

function evaluated at xi. 

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 routine is that it is unstable where there are 

discontinuities and therefore, the routine’s global 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-Raphson methods. This hybrid algorithm relies on 

bisection 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 all markets. The Newton-Raphson routine is then 

applied to quickly come to the solution. If the 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 repeated 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

POP m,tot POP m,males,age POP m,females,age Eq. A4.1 

where 

 POPage,,males is the number of males in age group age, 

 POPage, 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

POP m,gender,1age gender,age m,age POPfg m,females,age Eq. A4.2 

where 

 gender is male or female 

 POPage=1,gender,m is population in the youngest age group, age=1, by gender, in period t, 

 fage,m is the fertility rate for females in age group, age, in period t, 

 gage,gender is the fraction of births by gender, with gage,fr+gage,m=1, and 

 POPage,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 m,gender,age POP 1m,gender,1age POPmig m,gender,age POP = sv • − − + Eq. A4.3 

where 

 age is 2,...NAGE, 

 svage,gender,m is the survival rate from age group age to age+1, and 

 POPmigage,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− −− σμ− − σ

=σμ

x

exp

x

exp

1 ),;x(f σ > 0 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 ith distribution is given by 

( )

∑ ( ) μσρ

μσρ = −−

−−

p

p

11

i

11

i

exp

exp prob ρ< ≤ 10 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, μi, 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 response 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. 

−=ρ r1 Eq. A5.3 

If we consider only the random samples that survive this selection process, they also are 

distributed Gumbel and the average (mode) of this distribution is μˆ , 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 closed form expressions because we started with a 

Gumbel distribution. Equations A5.2 and A5.4 are only approximate for other distributions. Note 

that if we substitute the following 
12

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 use 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 i i −+=π ii Eq. A5.8 

Assume that ln yi is distributed Gumbel with mode ηi and scale parameter σ. Then ln πri is 

distributed Gumbel with mode 

)GPln( ii −+η=μ ii 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 μi. Next define 

)exp(yi η= i Eq. A5.10 

This just tells us where γi must lie on the distribution of crop yields. Equation A6.10 can be 

substituted into A5.9 to obtain 

)GPln(yln i i −+=μ ii Eq. A5.11 

using Equation 122 for the intrinsic profit rate, we can write 

i i π=μ rln Eq. A5.12 

which is the same as A5.5. 

We have covered only the non-nested case. See Amemiya (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 1929.923 251.861 
14

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 labor productivity increases and regional labor force 

participation rates 
15

 Labor productivity growth rate: Prodl,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 ratio of working persons over total population 

LFPerc(L,M); UN_98 Med Pop for the 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 NUCLEAR 
16

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; Recent values for total fossil 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 69271 
17

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 20 
18

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 ACENP 
19

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 2050 
20

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 0.03 
21

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: Biol,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 0.213 
23

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 market prices for all goods 

P(in,l,1) Initial starting market prices for 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 analysis 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); Pxii,l,m a regional fee towards oil, gas, coal, and biomass prices; see Equation 24 
24

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 BIOMASS 
25

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 prices 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-energy 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 25 
26

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-energy 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 & 91 
27

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 electricity 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 turned 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 5000 
28

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 

Pfjkj,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 0.128 
29

Table 33 Non-energy costs in hydrogen generation (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 Scrub 
30

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 coefficients 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 1 
33

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 0.125 
34

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 0.0949 
35

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 0.125 
36

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 Cost 
37

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 elasticities 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 TRANSPORT 
38

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 0.5171 
39

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 -0.1 
40

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 0 
41

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 0.3 
42

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 0.5 
43

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 AFRICA 
44

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 2095 
45

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 IEA 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 IndCoal 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 sector 
46

fdemand(L,K,J) 

Region# sec# BldgOil BldgGas BldgCoal BldgElec BldgBio 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 the B2 scenario in Electric Power Generation by 

Technologies 

Electric Power Generation 

 EJ/yr 

 Oil Gas Coal Nuclear Solar Hydro Biomass H2Fcell Fusion Wind SWStor SatSolar Tota

1990 0.3696 0.8341 4.926 2.1541 0 1.0128 0.1877 0 0 0 0 0 9.48

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 18.0
47

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 Pt3 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-CO2 Greenhouse Gases 

Greenhouse Gas GWP Approximate removal times 

that is half-lives in the 

atmosphere 

Climate forcing (W/m2) up to 

the year 2000 

Carbon dioxide (CO2) 1 >100 years 1.3 to 1.5 

Methane (CH4) 23 10 years 0.5 to 0.7 

Nitrous oxide (N2O) 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 aerosols 
48

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 NUMBER OF YEARS TO REACH "FLRL2." 

THE MODEL EXPONENTIALLY INTERPOLATES BETWEEN THE RATES; see 

Equation 93 

See Equation 

92 & 93 

Region FLRL1 FLRL2 FLRL3 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 INDIA 
49

Non-CO2 emissions 

Table 70 Overview of variables and considerations 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 set 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 use 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 grain 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 forest 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 Forest 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: (Fuel 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 INDUSTRY 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 1.75 
52

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 INDUSTRY 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 42.02 
53

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 0.24415 
54

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 Percentage 
55

SO2MAXCTRL (JKL) For oil, can use alternative formulation based on 

S% below 

Reg FuelName RESCOM INDUSTRY 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 90 
56

Table 78 Regional maximum percentages of non-energy related industrial sulfur emissions 

Max 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 collected 
57

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 Other 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 Forest 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 Parameters, by Region (TgC/000ha) 

CDensity Vegetation C Density (TgC/000ha) Soil C Density (TgC/000ha) 

Region crops biomass pasture trees UnMan crops biomass pasture trees UnMan 

USA 0.0050 0.0300 0.0070 0.0920 0.0920 0.1420 0.1890 0.1890 0.1392 0.1392 
58

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 improvements 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 0.01 
59

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 technical 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 per day per person 

Region FoodGr CoarseGr OilCrops MiscCrop ProcCrop 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 
60

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 per day per person 

Region FoodGr CoarseGr OilCrops MiscCrop ProcCrop 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 ProcCrop 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 0.1005 
61

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 0 
62

Appendix 7: List of equations 

+•= hgPicePr ($/energy unit) Eq. 1

∑( ) •

• =

j

r

fuelj j

r

fuelj j

j p

p

Pb

Pb

Share (unitless) Eq. 2

rpk rxk ••= XPbDemand (energy/year) Eq. 3

Nstep

m 1m m,is Tech +•= )ST1(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

i conventionaloil

i unconventionaloil

m,l,is is convention m,l,aloil CO

CO Pfis Pfis =

= = = • for 

unconventional oil ($/GJ) Eq. 6

∑=

=

n

1ig

Q m,l,is R l,is,ig (EJ) Eq. 7

m

is,1igis,ig

l,is,1ig Tech

)CC(

R

slope

−

−

− = Eq. 8

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

1n

1ig

m,l,is l,is,ig = ∑ −+ •

−

=

 (EJ) Eq. 9

ESILM =1m,l,i = ESFIL l,is 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 ESILM 2 −

− − − •= for oil, gas, coal and 

unconventional oil in projections (EJ/year) Eq. 11

m

anexpfos_r

1m,l

m,l

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

GDP

GDP

ESILM ESILM •• ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = •

−

− (EJ/year) Eq. 12

l,ir

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 Flr3

Nstep*1m

2 Flr

Nstep*1m1

FlrFLR 1m,l Flr −− −= • (unitless) Eq. 14

ESILM ESILM )FLR1( m,l,gasi m,l,gasi − m,l = • = = (EJ/year) Eq. 15

2

ESILM ESILM

QQ Nstep m,l,i 1m,l.i

1m,l,ism,l,is

−

−

+

•+= (EJ/year) Eq. 16

Q = Q −1m,l,ism,l,nuclearis Nstep ESU −1m,l,ui •+= (EJ/year) Eq. 17
63

∑=

=

nreg

1l

QQ m,l,is (EJ/year) Eq. 18

∑ ∑= =

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ =

n

1ig

nreg

1l

W R l,is,ig (EJ/year) Eq. 19

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

m,l,i 1990m,l GDP

GDP

ESILM BIO ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = •

=

= (EJ/year) Eq. 22

Hydro NstepmHydro

Hydro NstepmHydro

m,l,hydroi 3 1 2

1 2

e1

e ESILM Hydro ••+

••+

= + •= (EJ/year) Eq. 23

( ) PfiTrPP m,l,iim,l,im,l,i •+= ($/GJ) Eq. 24

+•= hijgijPPj iim,l,im,l,j for oil, gas, coal, and biomass/waste ($/GJ) Eq. 25

( ) ( ) ( )

3 HCLT3

Nstep1m

2 HCIL

Nstep1m1

hc i,j HCILT1 HCLT •−− •−= • ($/GJ) Eq. 26

( ) m,l,im,l,i,j + hcgctscossynPPC i,ji,j += • synliquid from coal, gas, or biomass; 

syngas from coal or biomass ($/GJ) Eq. 27

coali

coali oili

CO

CO CO SeqFractMax

=

= − = = (fraction) Eq. 28

( )

coali

i,j

m,l,ui

scrubbed,m,l,ui non,m,l,ui scrubbed

j CO

1

gc

gu

hu hu

Cpenalty

=

− •• − = ($/ton C) Eq. 29

( ) disp 0PfCst m,l,ui Carbdisp m,l SeqFractMax + Cpenaltyj •= • ($/GJ) Eq. 30

seq disp m,l,ui ( ) 1PfuCstC −•+= SeqFractMa + 0001.0x ($/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

coali,j scrubbed i,j scrub CstShc disp hc += •+= ($/GJ) Eq. 34
64

∑ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ =

−−

−−

ns

RCI

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

m,l,i,j

RCI

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

m,l,i,j

m,l,i,j ji

ji

Pj Pfu

PC

Pj Pfu

PC

SynShare for each of the technologies 

(unitless) Eq. 35

Pj SynShare PC SynShare Pj( )Pfjk m,l,gasorliquidsjm,l,i,j m,l,k,j

ns

−−= m,l,gasorliquidsj = ∑ m,l,i,jm,l,i,j +• • −−= + 

($/GJ) Eq. 36

( ) ssh m,l,i m,l,ui m,l,hi m,l,hi PfuPPssh •+= + hhgh ($/GJ) Eq. 37

( ) m,l,issh m,l,ui l,i 0Pf)mFracRe1(PfuPPssh m,l,ui Carbdisplm m,l,hi + hhgh m,l,hi −•+= + • • ... 

($/GJ) Eq. 38

∑( ) •

• =

nc

ruiss

m,l,hi ssh

ruiss

m,l,hi ssh

l,hi

bssh Pssh

bssh Pssh

Ssh (unitless) Eq. 39

= ∑( ) • ncPH m,l,hi l,hi PsshSsh ssh generated from oil, gas, or solids ($/GJ) Eq. 40

m,l,im,l,hi m,l,hi m,l,hi +•= hhghPPH generated from biomass ($/GJ) Eq. 41

= ∑ • =

nhprices

Pj m,l,hydrogenj l,hi PHSh m,l,hi ($/GJ) Eq. 42

∑( ) •

• =

nhprices

rhi

m,l,hi m,l,hi

rhi

m,l,hi m,l,hi

l,hi

bsh PH

bsh PH

Sh (unitless) Eq. 43

( ) m,l,issu l,ui PfupaPPssu m,l,ui m,l,ui + hugu m,l,ui +•= • from oil, gas, and 

solids ($/GJ) Eq. 44

[ ( ) ] ssu m,l,uil,uim,l,i mFracRe1PfupaPPssu l,j 0Pf m,l,ui Carbdisp m.l m,l,ui + hugu m,l,ui +•= • − + • •

 ..................................................................... from oil, gas, or solids ($/GJ) Eq. 45

( ) m,l,issu PfuPPssu m,l,ui m,l,uil,ui + hugupa m,l,ui •+= • for biomass ($/GJ) Eq. 46

= ∑ • ncPU m,l,ui Ssu l,ui Pssu ssu ($/GJ) Eq. 47

∑( ) •

• =

nc

ruiss

m,l,ui uus

ruiss

m,l,ui uus

l,ui

bssu Pssu

bssu Pssu

Ssu (unitless) Eq. 48

( ) PPU m,l,uraniumim,l,ui Pfu m,l,ui m,l,ui + hugu m,l,ui = + • = from nuclear energy ($/GJ) Eq. 49

( ) m,l,ui Pfu0PU m,l,ui m,l,ui + hugu m,l,ui •+= from solar PV or wind ($/GJ) Eq. 50
65

3

solar,uus

3

wind,uus

3

solar,uus

3 solar

solar,uus

3

wind,uus

3

wind,uus

m,l,ui m,l,ui wind PP

P

P

PP

P

PU Phu − −

−

− −

−

+

•+

+

•+= from 

wind-solar storage ($/GJ) Eq. 51

= PjPU = m,l,hydrogenjm,l,ui m,l,ui +• hugu m.,l,ui from hydrogen fuel cells ($/GJ) Eq. 52

= ∑ • =

neprices

Pj m,l,yelectricitj l,ui PUSU m,l,ui ($/GJ) Eq. 53

∑( ) •

• =

neprices

rui

m,l,ui m,l,ui

rui

m,l,ui m,l,ui

l,ui

bsu PU

bsu PU

SU (unitless) Eq. 54

)hjkgjkPj(Pjk m,l,k,j m,l,j k,j +•= k,j ($/energy service) Eq. 55

Pj = = Pj = m,l,coaljm,l,coalj + Pfjk m,l,k,j ($/GJ) Eq. 56

Pjj=electricity,l,m= Pj = m,l,electicityj + PUTD m,k ($/GJ) Eq. 57

Pj = = Pj = m,l,hydrogenjm,l,hydrogenj + TD2PH m,k ($/GJ) Eq. 58

= ∑( ) • jPk m,l,k SPjk Pjk m,l,k,jl,k,j ($/energy service) Eq. 59

∑( ) • •

• • =

j

rpjk ryjk

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

rpjk ryjk

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

l,k,j

jk jklm

jk jklm

bsjk Pjk X

bsjk Pjk X

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 GDPindex m,l = GDPindex 1m,l +• m,l )oPr1( • LBFindex − (unitless) Eq. 62

adj rGDP GDPindex m,l GDPindex m,l PSratio = • (unitless) Eq. 63

index

ryk

rpk

2m,l,k

m,l,k

k transporta ortion m,l,buildings l,k X Pop Pk

Pk

Fk bsk m,l,k

l,k

•• ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•=

=

= −− (EJ/year) Eq. 64

m,l,k

l,k

ryk

rpk

2m,l,k

m,l,k

m,l,industryk l,k Y

Pk

Pk

Fk bsk • ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•=

=

= (EJ/year) Eq. 65

m,l,k

m,l,k

l,k k Pfk

Pk

Rpkrpk •= (unitless) Eq. 66

jk

m,l,k

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

Fk

Fjk Sjkgjk ••= (EJ/year) Eq. 67

Nstep

m,k,j 1m,k,j m,l,k Tech = + )T1(*Tech − (unitless) Eq. 68
66

∑( ) ••

• • =

j

rpjk ryjk

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

rpjk ryjk

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

l,k,j

k,j m,l,k,j

jk, m,l,k,j

bsjk XPjk

bsjk Pjk X

Sjk (unitless) Eq. 69

=∑

k

Fj m,l,j Fjk m,l,k,j (EJ/year) Eq. 70

coeff coeff

m,l,yelectricitjm,l,hydrogenj coeff

m,l,hydrogenj h*e1

Fj Fj e

Fj −

+ • = = =

= (EJ/year) Eq. 71

coeff coeff

m,l,hydrogenjm,l,yelectricitj coeff

m,l,electrictyj h*e1

Fj Fj h

Fj −

+ • = = =

= (EJ/year) Eq. 72

coeff ghShh m,l,hil,hi •= (unitless) Eq. 73

coeff guSue m,l,uil,ui •= (unitless) Eq. 74

EDRIKL l,k,i Fjk gijim,l,k,j •= i = oil, gas, coal or biomass (EJ/year) Eq. 75

= ∑

k

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

m,l,i,j

k

SFuel m,l,i,j = ∑EDRIKL l,k,i •SynShare (EJ/year) Eq. 77

ji

j

m,l,i m,l,i m,l,i,j EDRIL = EDRIL +∑SFuel • gc i = oil, gas, coal or biomass (EJ/year) Eq. 78

EDRIL m,l,i EDRIL Fj m,l,hydrogenjm,l,i gijghSh im,l,hil,hii = + • • • = i = oil, gas, coal 

or biomass (EJ/year) Eq. 79

EDRIL m,l,i EDRIL Fj gijguiSu im,l,uil,uim,l,yelectricitjm,l,i = + • • • = i=oil, gas, coal 

or biomass (EJ/year) Eq. 80

= ∑

l

EDRI m,i EDRIL m,l,i for oil, gas, coal, and biomass (EJ/year) Eq. 81

= +∑

i

ESRILM m,l,i ESILM m,l,i Sfuel m,l,i,j for oil and gas (EJ/year) Eq. 82

= ∑

l

ESRI m,i ESRILM m,l,i oil, gas, coal, and biomass (EJ/year) Eq. 83

MrkPRDmk = ESRI m,i oil, gas, coal Eq. 84

MrkDEMmk = EDRI m,i oil, gas, coal Eq. 85

MrkPRD CemTot =5mk = Eq. 86

MrkDEM =5mk = Emiss m,l Eq. 87

∑=

= =

nr

1l

MrkPRD 12:6mk AgSup l,i Eq. 88
67

∑=

= =

nr

1l

MrkDEM 12:6mk AgDem l,i Eq. 89

ExDemmk = MrkDEMmk − MrkPRD mk Eq. 90

ji

j

m,l,i m,l,i,j SynInput = ∑SFuel • gc (EJ/year) Eq. 91

( ) ( ) ( )

3 Flr3

Nstep1m

2 Flr

Nstep1m1

FlrFLR 1m,l Flr •−− •−= • (unitless) Eq. 92

m,l,gasi

m,l

m,l

gasil,gasflarei m,l ESILM

)FLR1(

FLR

Cemissions = = SBCO = • − ••= (MMTC) Eq. 93

ESU m,l,ui l,ui FjSsuSu m,l,jl,ui ••= (EJ/year) Eq. 94

ESH m,l,hi l,hi FjSshSh m,l,jl,hi ••= (EJ/year) Eq. 95

m,l,liqj,gasi l,oili coali

gas_synfueli gasi coali

SFuel CO)SedFil1(

Cemissions SynInput CO

== = =

= = =

−• •

= −• (MMTC) Eq. 96

)mFracRe1(

SFuel CO)SedFil1()

SFuel CO)SedFil1(

SynInput CO

Cemissions l,1

m,l,gasj,coali l,gasi gasi

m,l,liqj,coali l,oili coali

coali coali

coal_synfueli −•

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

−• •

−• −•

−•

=

== = =

== = =

= =

=

(MMTC) ................................................................................................................. Eq. 97

SFuel )CO)SedFil1()

SFuel CO)SedFil1(

Cemissions SynInput( CO

m,l,gasj,biomassi l,gasi gasi

m,l,liquidj,biomassi l,oili biomassi

b_synfueli biomassi biomassi

= = = =

= = = =

= = =

−• •

−• • −

= • −

 (MMTC) Eq. 98

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

••

+•••

−−•

•=

ESH )gijgh

ESU(mFracRe gijgu

)SedFil1(FFcons

Cemissions CO

im,him,l,hi

l,2 im,l,uim,l,ui

l,i

ii (MMTC) Eq. 99

FFcons = l,oili = EDRIL= l,oili + ESILi=unconventionaloil (EJ/year) Eq. 100

FFcons = l,gasi = EDRIL l,i −SynInput = m,l,gasi (EJ/year) Eq. 101

FFcons = l,coali = EDRIL l,i − SynInput = m,l,coali (EJ/year) Eq. 102

FFcons = l,biomassi = EDRIL l,i − SynInput = m,l,biomassi (EJ/year) Eq. 103

Cemissions =shaleoili COi •= ESILM m,l,i •SHAL m,l + i • − l,i )SedFil1(CO (MMTC) Eq. 104

l,j )SedFil1(FjkCO2CO

j

k ∑ m,l,k,jj −••= (MMTC) Eq. 105

hydrogen_scrub

j

2CO hydrogen ∑COj •= EDRIKL m,l,j −• l,j − C)SedFil1( (MMTC) Eq. 106

electricty_scrub

j

2CO electricty ∑COj •= EDRIKL m,l,j −• l,j − C)SedFil1( (MMTC) Eq. 107
68

l,1

m,l,gasj,coali l,gasi gasi

coali coali m,l,liqj,coali l,oili coali

seq mFracRe

SFuel CO)SedFil1()

SynInput CO SFuel CO)SedFil1( C •

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−• •

−• −• −• =

== = =

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

scrub i ESUCOC m,l,ui im,l,ui mFracRegijgu l,2 ••••= (tons C) Eq. 109

scrub i ESHCOC m,l,hi im,l,hi mFracRegijgh l,2 ••= • • (tons C) Eq. 110

( ) ( ) t t t t = factor_EmEm −•• • − • − )icePr_C(MAC1USER1))Cap/GDP(Control1(Driver .. 

(variable units) Eq. 111

∑=

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − = •

nr

1l

m,l,i 1m,l,i

m,l,i i,l Nstep

Landuse Landuse

EmLC CLdens (MMTC) Eq. 112

∑ ∑ = − =

−

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − = • •

nr

1l

m

2mm

m 1m

m,i i,l m Nstep

Landuse Landuse EmSC CSdens PercDecay 

(MMTC) Eq. 113

∑=

=

4

coal,gas,oili

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

SulfurCont ( ) )f1(f1ent EnergyContent

FuelUse EmSulfurt ash −•−• control = • (TgS) Eq. 115

fcontrol is determined as follows ( )

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

=

τ

− t GDPpercap intmidpo c GDPpercap /

max

e1

f fcontrol Eq. 116

Pbiofuelfromoil Poil += + PtOilTranCos carbon • OilCarb ($/GJ) Eq. 117

BioTranCost

EtoBio

P

P biomass

biofuelfrombiomass += ($/GJ) Eq. 118

P ( ) PPEtoBio OilCarb tOilTranCos BioTranCost biomass oil carbon •+•= + − 

($/m3

C ) Eq. 119

m,l,im,lm,l,i

baseyearm,l,i

m,l,i

l,im,l,i CNY

P

P

CDR A 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

WDR A jl

jl

•• ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

•= β

α

=

 (total m3 wood 

demanded per year) Eq. 121

( ) −•=π GPyr m,l,im,l,ip,m,l,ip,m,l,i i = crops, biomass, pasture (annual $/ha) Eq. 122

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

~ 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

Landuse S m,l,im,l,i Totallandl •= Eq. 125
69

P = P = m,l,cropsim,l,animali FeedOut P = m,l,pasturei + GPastOut = m,l,animali +•= • ($/cal) Eq. 126

λ

λ

⎥

⎦

⎤ ⎢

⎣

⎡

∑π=π

p

1

m,l,i m,l,p,i ˆr r ($/cal or $/m3) Eq. 127

ˆr ˆr i π=π i = crops, biomass, pasture, forest ($/cal or $/m3) Eq. 128

m,l,im,l,i

i

i GP

ˆ yˆ −

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

Nstep

m,i m,i1m,i Tech = + )S1(Tech − (unitless) Eq. 130

2 2

2

1

biomass

1

crops

1

crops

crops biomass

crops

rr

r

ss

s

λ λ

λ

π+π

π = +

 (unitless) Eq. 131

[ ] 2 2 1 2

biomass

1

biomass/crops crops r rr

λ λ λ π π+π= ($/cal) Eq. 132

n ocean FFDE fert dt

Cd

−−+=

Δ

 Eq. 133

τ − β = Δ CEdt

Cd

 Eq. 134

HFS

dt

dT

−−∝ Eq. 135

⎥

⎦

⎤ ⎢

⎣

⎡ θ •⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+•⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

τ

τ − τ

− = dt

d

h

h

dt

TaT dT

dt

dT d

m

m d

a

m

a

a eq Eq. 136

τ

−+− • ΔΤ•β = )zz(z

dt

dz 0 Eq. 137