Snapshot of - REMIND-MAgPIE

Archive of REMIND-MAgPIE, version: 2.0-4.1

Reference card - REMIND-MAgPIE

The reference card is a clearly defined description of model features. The numerous options have been organized into a limited amount of default and model specific (non default) options. In addition some features are described by a short clarifying text.

Legend:

• not implemented
• implemented
• implemented (not default option)

About

Name and version

REMIND-MAgPIE 2.0-4.1

Model link

https://www.pik-potsdam.de/research/sustainable-solutions/models/remind; https://rse.pik-potsdam.de/doc/remind/2.1.3; https://github.com/remindmodel/remind/releases/tag/v2.1.3; https://github.com/magpiemodel/magpie/releases/tag/v4.2.1; https://rse.pik-potsdam.de/doc/magpie/4.2.1/

Institution

Potsdam Institut für Klimafolgenforschung (PIK), Germany, https://www.pik-potsdam.de.

Documentation

REMIND-MAgPIE documentation consists of a referencecard and detailed model documentation

Process state

published

Model scope and methods

Model documentation: Model scope and methods - REMIND-MAgPIE

Model type

• Integrated assessment model
• Energy system model
• CGE
• CBA-integrated assessment model

Geographical scope

• Global
• Regional

Objective

REMIND-MAgPIE is a global multi-regional model incorporating the economy, the climate system and a detailed representation of the energy sector. REMIND-MAgPIE allows for a sophisticated analysis of technology options and policy proposals for climate mitigation. It accounts for economic and energy investments in the model regions, and interregional trade in goods, energy carriers and emissions allowances.

Solution concept

• Partial equilibrium (price elastic demand)
• Partial equilibrium (fixed demand)
• General equilibrium (closed economy)
• MAgPIE: partial equilibrium model of the agricultural sector

Solution horizon

• Recursive dynamic (myopic)
• Intertemporal optimization (foresight)
• MAgPIE: recursive-dynamic
• REMIND-MAgPIE: Inter-temporal (foresight)

Solution method

• Simulation
• Optimization
• MAgPIE: cost minimization

Temporal dimension

Base year:2005, time steps:5, horizon: 2005-2100

Spatial dimension

Number of regions:12

Time discounting type

• Discount rate exogenous
• Discount rate endogenous

Policies

• Emission tax
• Emission pricing
• Cap and trade
• Fuel taxes
• Fuel subsidies
• Feed-in-tariff
• Portfolio standard
• Capacity targets
• Emission standards
• Energy efficiency standards
• Agricultural producer subsidies
• Agricultural consumer subsidies
• Land protection
• Pricing carbon stocks

Socio-economic drivers

Model documentation: Socio-economic drivers - REMIND-MAgPIE

Population

• Yes (exogenous)
• Yes (endogenous)

Population age structure

• Yes (exogenous)
• Yes (endogenous)

Education level

• Yes (exogenous)
• Yes (endogenous)

Urbanization rate

• Yes (exogenous)
• Yes (endogenous)

GDP

• Yes (exogenous)
• Yes (endogenous)

Income distribution

• Yes (exogenous)
• Yes (endogenous)

Employment rate

• Yes (exogenous)
• Yes (endogenous)

Labor productivity

• Yes (exogenous)
• Yes (endogenous)

Total factor productivity

• Yes (exogenous)
• Yes (endogenous)

Autonomous energy efficiency improvements

• Yes (exogenous)
• Yes (endogenous)

Macro-economy

Model documentation: Macro-economy - REMIND-MAgPIE

Economic sector

Industry

• Yes (physical)
• Yes (economic)
• Yes (physical & economic)

Energy

• Yes (physical)
• Yes (economic)
• Yes (physical & economic)

Transportation

• Yes (physical)
• Yes (economic)
• Yes (physical & economic)

Residential and commercial

• Yes (physical)
• Yes (economic)
• Yes (physical & economic)

Agriculture

• Yes (physical)
• Yes (economic)
• Yes (physical & economic)

Forestry

• Yes (physical)
• Yes (economic)
• Yes (physical & economic)

Other economic sector

Note: The macro-economic part contains a single sector representation of the entire economy. A generic final good is produced from capital, labor, and different final energy types.

Macro-economy

Trade

• Coal
• Oil
• Gas
• Uranium
• Electricity
• Bioenergy crops
• Food crops
• Capital
• Emissions permits
• Non-energy goods
• Energy goods

Cost measures

• GDP loss
• Welfare loss
• Consumption loss
• Area under MAC
• Energy system cost mark-up

Categorization by group

• Income
• Urban - rural
• Technology adoption
• Age
• Gender
• Education level
• Household size

Institutional and political factors

• Early retirement of capital allowed
• Interest rates differentiated by country/region
• Regional risk factors included
• Technology costs differentiated by country/region
• Technological change differentiated by country/region
• Behavioural change differentiated by country/region
• Constraints on cross country financial transfers

Resource use

Coal

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Conventional Oil

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Unconventional Oil

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Conventional Gas

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Unconventional Gas

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Uranium

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Bioenergy

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Water

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Raw Materials

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Land

• Yes (fixed)
• Yes (supply curve)
• Yes (process model)

Technological change

Energy conversion technologies

• No technological change
• Exogenous technological change
• Endogenous technological change

Energy End-use

• No technological change
• Exogenous technological change
• Endogenous technological change

Material Use

• No technological change
• Exogenous technological change
• Endogenous technological change

Agriculture (tc)

• No technological change
• Exogenous technological change
• Endogenous technological change

Energy

Model documentation: Energy - REMIND-MAgPIE

Energy technology substitution

Energy technology choice

• No discrete technology choices
• Logit choice model
• Production function
• Linear choice (lowest cost)
• Lowest cost with adjustment penalties

Energy technology substitutability

• Mostly high substitutability
• Mostly low substitutability
• Mixed high and low substitutability

Energy technology deployment

• Expansion and decline constraints
• System integration constraints

Energy

Electricity technologies

• Coal w/o CCS
• Coal w/ CCS
• Gas w/o CCS
• Gas w/ CCS
• Oil w/o CCS
• Oil w/ CCS
• Bioenergy w/o CCS
• Bioenergy w/ CCS
• Geothermal power
• Nuclear power
• Solar power
• Solar power-central PV
• Solar power-distributed PV
• Solar power-CSP
• Wind power
• Wind power-onshore
• Wind power-offshore
• Hydroelectric power
• Ocean power

Hydrogen production

• Coal to hydrogen w/o CCS
• Coal to hydrogen w/ CCS
• Natural gas to hydrogen w/o CCS
• Natural gas to hydrogen w/ CCS
• Oil to hydrogen w/o CCS
• Oil to hydrogen w/ CCS
• Biomass to hydrogen w/o CCS
• Biomass to hydrogen w/ CCS
• Nuclear thermochemical hydrogen
• Solar thermochemical hydrogen
• Electrolysis

Refined liquids

• Coal to liquids w/o CCS
• Coal to liquids w/ CCS
• Gas to liquids w/o CCS
• Gas to liquids w/ CCS
• Bioliquids w/o CCS
• Bioliquids w/ CCS
• Oil refining

Refined gases

• Coal to gas w/o CCS
• Coal to gas w/ CCS
• Oil to gas w/o CCS
• Oil to gas w/ CCS
• Biomass to gas w/o CCS
• Biomass to gas w/ CCS

Heat generation

• Coal heat
• Natural gas heat
• Oil heat
• Biomass heat
• Geothermal heat
• Solarthermal heat
• CHP (coupled heat and power)

Grid Infra Structure

Electricity

• Yes (aggregate)
• Yes (spatially explicit)

Gas

• Yes (aggregate)
• Yes (spatially explicit)

Heat

• Yes (aggregate)
• Yes (spatially explicit)

CO2

• Yes (aggregate)
• Yes (spatially explicit)

Hydrogen

• Yes (aggregate)
• Yes (spatially explicit)

Other grid and infrastructure

Note: Generalized transmission and distribution costs are included, but not modeled on an explicit spatial level. Regionalized additional grid and storage costs for renewable integration are included.

Energy end-use technologies

Passenger transportation

• Passenger trains
• Buses
• Light Duty Vehicles (LDVs)
• Electric LDVs
• Hydrogen LDVs
• Hybrid LDVs
• Gasoline LDVs
• Diesel LDVs
• Passenger aircrafts

Freight transportation

• Freight trains
• Heavy duty vehicles
• Freight aircrafts
• Freight ships

Industry

• Steel production
• Aluminium production
• Cement production
• Petrochemical production
• Paper production
• Plastics production
• Pulp production

Residential and commercial

• Space heating
• Space cooling
• Cooking
• Refrigeration
• Washing
• Lighting

Land-use

Model documentation: Land-use - REMIND-MAgPIE

Land cover

• Cropland
• Cropland irrigated
• Cropland food crops
• Cropland feed crops
• Cropland energy crops
• Forest
• Managed forest
• Natural forest
• Pasture
• Shrubland
• Built-up area

Agriculture and forestry demands

• Agriculture food
• Agriculture food crops
• Agriculture food livestock
• Agriculture feed
• Agriculture feed crops
• Agriculture feed livestock
• Agriculture non-food
• Agriculture non-food crops
• Agriculture non-food livestock
• Agriculture bioenergy
• Agriculture residues
• Forest industrial roundwood
• Forest fuelwood
• Forest residues

Agricultural commodities

• Wheat
• Rice
• Other coarse grains
• Oilseeds
• Sugar crops
• Ruminant meat
• Non-ruminant meat and eggs
• Dairy products

Emission, climate and impacts

Model documentation: Emissions - REMIND-MAgPIE, Climate - REMIND-MAgPIE, Non-climate sustainability dimension - REMIND-MAgPIE

Greenhouse gases

• CO2 fossil fuels
• CO2 cement
• CO2 land use
• CH4 energy
• CH4 land use
• CH4 other
• N2O energy
• N2O land use
• N2O other
• CFCs
• HFCs
• SF6
• PFCs

Pollutants

• CO energy
• CO land use
• CO other
• NOx energy
• NOx land use
• NOx other
• VOC energy
• VOC land use
• VOC other
• SO2 energy
• SO2 land use
• SO2 other
• BC energy
• BC land use
• BC other
• OC energy
• OC land use
• OC other
• NH3 energy
• NH3 land use
• NH3 other

Note: Ozone is not modeled as emission, but is an endogenous result of atmospheric chemistry.

Climate indicators

• Concentration: CO2
• Concentration: CH4
• Concentration: N2O
• Concentration: Kyoto gases
• Radiative forcing: CO2
• Radiative forcing: CH4
• Radiative forcing: N2O
• Radiative forcing: F-gases
• Radiative forcing: Kyoto gases
• Radiative forcing: aerosols
• Radiative forcing: land albedo
• Radiative forcing: AN3A
• Radiative forcing: total
• Temperature change
• Sea level rise
• Ocean acidification
• Radiative Forcing (Land Albedo) - Yes (exogenous)

Carbon dioxide removal

• Bioenergy with CCS
• Reforestation
• Afforestation
• Soil carbon enhancement
• Direct air capture
• Enhanced weathering

Climate change impacts

• Agriculture
• Energy supply
• Energy demand
• Economic output
• Built capital
• Inequality

Co-Linkages

• Energy security: Fossil fuel imports & exports (region)
• Energy access: Household energy consumption
• Air pollution & health: Source-based aerosol emissions
• Air pollution & health: Health impacts of air Pollution
• Food access
• Water availability
• Biodiversity

Model Documentation - REMIND-MAgPIE

This documentation describes the REMIND-MAgPIE framework coupling the energy-economy model REMIND and the agricultural production model MAgPIE.

REMIND

The Integrated Assessment Model REMIND (REgional Model of Investment and Development) represents the future evolution of the world economies with a special focus on the development of the energy sector and the implications for our world climate. Given a set of population, technology, policy and climate constraints, the goal of REMIND is to find the welfare-optimal mix of investments in the economy and the energy sectors of each model region. It also accounts for regional trade characteristics on goods, energy fuels, and emissions allowances. All greenhouse gas emissions due to human activities are represented in the model.

REMIND is an energy-economy general equilibrium model linking a macro-economic growth model with a bottom-up engineering-based energy system model. It covers twelve world regions, differentiates various energy carriers and technologies and represents the dynamics of economic growth and international trade.

A Ramsey-type growth model with perfect foresight serves as a macro-economic core projecting growth, savings and investments, factor incomes, energy and material demand. The macro-economic production factors are capital, labor, and final energy. A nested production function with constant elasticity of substitution determines the final energy demand. REMIND uses economic output for investments in the macro-economic capital stock as well as for consumption, trade, and energy system expenditures.

The energy system representation differentiates between a variety of fossil, biogenic, nuclear and renewable energy resources. More than 50 technologies are available for the conversion of primary energy into secondary energy carriers as well as for the distribution of secondary energy carriers into final energy. The macro-economic core and the energy system part are hard-linked via the final energy demand and the costs incurred by the energy system. Economic activity results in demand for final energy in different sectors (transport, industry, buildings..) and of different type (electric and non-electric).

The model accounts for crucial drivers of energy system inertia and path dependencies by representing full capacity vintage structure, technological learning of emergent new technologies, as well as adjustment costs for rapid upscaling of new technologies. The emissions of greenhouse gases (GHGs) and air pollutants are largely represented by source and linked to activities in the energy-economic system. Several energy sector policies are represented explicitly, including energy-sector fuel taxes and consumer subsidies.

Further reading:

• REMIND code on GitHub: https://github.com/remindmodel/remind
• REMIND documentation (version 2.1.3): https://rse.pik-potsdam.de/doc/remind/2.1.3
• REMIND2.1 paper: https://doi.org/10.5194/gmd-14-6571-2021

MAgPIE

The Model of Agricultural Production and its Impact on the Environment (MAgPIE) is a global land use allocation model, which is connected to the grid-based dynamic vegetation model LPJmL, with a spatial resolution of 0.5°x0.5°. It takes regional economic conditions such as demand for agricultural commodities, technological development and production costs as well as spatially explicit data on potential crop yields, land and water constraints (from LPJmL) into account. Based on these, the model derives specific land use patterns, yields and total costs of agricultural production for each grid cell. The objective function of the land use model is to minimize total cost of production for a given amount of regional food and bioenergy demand. Regional food energy demand is defined for an exogenously given population in 10 food energy categories, based on regional diets. Future trends in food demand are derived from a cross-country regression analysis, based on future scenarios on GDP and population growth.

Food and feed energy for the demand categories can be produced by 20 cropping activities and 3 livestock activities. Feed for livestock is produced as a mixture of crops, crop residuals, processing byproducts, green fodder produced on crop land, and pasture. Variable inputs of production are labour, chemicals, and other capital (all measured in US$). Costs of production are derived from the Global Trade Analysis Project (GTAP) Database. The model can endogenously decide to acquire yield-increasing technological change at additional costs. The costs for technological change for each economic region are based on its level of agricultural development, measured as agricultural land-use intensity. These costs grow with further investment in technological change. The use of technological change is either triggered by a better cost-effectiveness compared to other investments or as a response to resource constraints, such as land scarcity.

For future projections the model works on 5-10 year a time steps of 10 years in a recursive dynamic mode. The link between two consecutive periods is established through the land-use pattern. The optimized land-use pattern from one period is taken as the initial land constraint in the next. If necessary, additional land from non-agricultural areas can be converted into cropland at additional costs. Potential crop yields for MAgPIE are originally computed with LPJmL at a 0.5° resolution, as weighted average of irrigated and non-irrigated production, if part of the grid cell is equipped for irrigation according to the global map of irrigated areas. In case of purely rain-fed production, no additional water is required, but yields are generally lower than under irrigation. If a certain area share is irrigated, additional water for agriculture is taken from available water discharge in the grid cell. Each cell of the geographic grid is assigned to 1 of 120 economic world regions: CAZ (Canada, Australia and New Zealand; CHA (China); EUR (European Union); IND (India); JPN (Japan); LAM (Latin America); MEA (Middle East and north Africa); NEU (non-EU member states); OAS (other Asia); REF (reforming countries); SSA (Sub-Saharan Africa); USA (United States) The regions are initially characterized by data for the year 1995 on population, gross domestic product (GDP), food energy demand, average production costs for different production activities, and current self-sufficiency ratios for food. Land-conversion activities provide for potential expansion and shifts of agricultural land in specific locations. For the base year 1995, total agricultural land is constrained to the area currently used within each grid cell, according to the dataset of as extended by. Cropland can be converted into rangeland, and vice versa. If additional land is required for fulfilling demand, this can be taken from the pool of non-agricultural land at additional costs. These land-conversion costs force the model to utilize available cropland and rangeland first, and land conversion will become relevant only if land becomes scarce in a certain location or if the marginal cost reductions by producing crops on converted land outweigh the costs of conversion.

Further reading:

• MAgPIE code on GitHub: https://github.com/magpiemodel/magpie
• MAgPIE documentation (Version 4.3.0): https://rse.pik-potsdam.de/doc/magpie/4.3/
• MAgPIE 4 paper: https://doi.org/10.5194/gmd-12-1299-2019

REMIND-MAgPIE

For some questions, REMIND and MAgPIE are soft coupled to provide a detailed answer. From a climate protection perspective, two aspects of the land-use sector are of particular interest: the supply of biomass that can be used for energy production (possibly with carbon capture and storage – CCS) and the total emissions of the land-use sector. Changing crucial parameters in REMIND (such as the climate target or the availability of technologies or resources) can have significant impact on GHG prices and bioenergy demand. Thus, REMIND and MAgPIE can be run in an iterative soft-coupled mode, where REMIND updates MAgPIE's assumptions regarding bioenergy demand and GHG prices, and MAgPIE, in turn, updates REMIND's assumptions regarding bioenergy prices and land-use emissions and agricultural production costs. The iteration is continued until changes between iterations become negligible. The resulting scenarios are consistent regarding the price and quantity of bioenergy and GHG emissions.

1) Model scope and methods - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

REMIND-MAgPIE (Regional Model of Investments and Development)is a global multi-regional model incorporating the economy, the climate system, and a detailed representation of the energy sector.

1.1) XML-test Model concept, solver and details

REMIND-MAgPIE solves for an inter-temporal Pareto optimum in economic and energy investments in each model region, fully accounting for inter-regional trade in goods, energy carriers and emissions allowances. The model allows for the analysis of technology options and policy proposals for climate change mitigation as well as related energy-economic transformation pathways.

The macro-economic core of REMIND-MAgPIE in each region is a Ramsey-type optimal growth model, where the inter-temporal welfare of each region is maximized. Macro-economic production factors are capital, labor, and final energy. Economic output is used for investments in the macro-economic capital stock as well as consumption, trade, and energy system expenditures. It is possible to compute the co-operative Pareto-optimal global equilibrium including inter-regional trade as the global social optimum using the Negishi method , or the non-cooperative market solution among regions using the Nash concept ,. In the absence of non-internalized externalities between regions, these two solutions coincide. The inclusion of inter-regional externalities (in particular technology spillovers) causes a difference between the market and the socially optimal solution.

The macro-economic core and the energy system module are hard-linked via the final energy demand and costs incurred by the energy system see for further details. Economic activity results in demand for final energy such as transport energy, electricity, and non-electric energy for stationary end uses. A production function with constant elasticity of substitution (nested CES production function) determines final energy demand. The energy system module accounts for regional endowments of exhaustible primary energy resources as well as renewable energy potentials. More than 50 technologies are available for the conversion of primary energy into secondary energy carriers as well as for the distribution of secondary energy carriers into final energy.

The model accounts for CO2 emissions from fossil fuel combustion and land use as well as emissions from other greenhouse gases (GHGs). REMIND-MAgPIE determines non-CO2 GHG emissions by applying marginal abatement costs curves relative to baseline emission levels that depend on activity variables or by assuming exogenous scenarios. For numerical reasons, we use a reduced-form climate module, which is calibrated to the MAGICC-6 model , to translate emissions into changes in atmospheric GHG concentrations, radiative forcing, and global mean temperature. For a more detailed evaluation, the model can be linked to the full MAGICC-6 climate model in an ex-post mode. REMIND-MAgPIE is solved as a non-linear programming model. It is programmed in GAMS and uses the CONOPT solver by default.

1.3) Temporal dimension - REMIND-MAgPIE

REMIND-MAgPIE is an inter-temporal optimization model, solving for the perfect-foresight equilibrium of the world economy between the years 2005-2150. The spacing of time steps is flexible. In the default case, there are five-year time steps until 2060, ten-year time steps until 2100 and twenty-year time steps after that. We typically focus analysis on the time span 2005-2100, but run the model until 2150 to avoid distortions due to end effects.

2) Socio-economic drivers - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

Population and GDP are main drivers of future energy demand and, thus, GHG emissions in REMIND-MAgPIE. We base population and GDP inputs on the Shared Socio-economic Pathway (SSP) scenarios. REMIND-MAgPIE’s default population projections (both total population as well as working age population) are based on IIASA (and the GDP scenarios from the OECD . Both Population and GDP scenario data are available at https://secure.iiasa.ac.at/web-apps/ene/SspDb/dsd?Action=htmlpage&page=about. These projections are available for all five different SSP scenarios . For default scenarios, we use SSP2 scenario data as they represent a middle-of-the road scenario. To calibrate GDP, which is an endogenous result of the growth engine in REMIND-MAgPIE, we calibrate labor productivity parameters in an iterative procedure so as to reproduce the OECD's GDP reference scenarios. Within REMIND-MAgPIE GDP is measured in market exchange rates (MER).

<figure id="fig:REMIND-MAgPIE_3"> </figure>

Figure 1. Projections of (a) population and (b) GDP used in the REMIND-MAgPIE SSP2 (“Middle-of-the-Road”) scenario.

2.1) Population - REMIND-MAgPIE

Population is an exogenous input for REMIND-MAgPIE (see description under Socio-economic drivers). It enters the model in just two forms: total population and working age population. While the welfare measuring is based on total population, the working age population is used as labor input in the macroeconomic production function. The exogenous labor input affects the dynamics of other macroeconomic production factors (capital, energy) since the model seeks an optimal allocation of production factors.

Total population is also used for generating energy demand scenarios that are mainly based on assumptions about the development of per capita demand on different energy types (see description under Energy demand)

3) Macro-economy - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

Objective function

REMIND-MAgPIE models each region r as a representative household with a utility function Ur that depends upon per-capita consumption

<figure id="fig:REMIND-MAgPIE_3.2.1 1."> </figure>

where C(r,t) is the consumption of region r at time t, and P(r,t) is the population in region r at time t. The calculation of utility is subject to discounting; 3% is assumed for the pure rate of time preference rho. The logarithmic relationship between per-capita consumption and regional utility implies an elasticity of marginal consumption of 1. Thus, in line with the Keynes-Ramsey rule, REMIND-MAgPIE yields an endogenous interest rate in real terms of 5–6% for an economic growth rate of 2–3%. This is in line with the interest rates typically observed on capital markets.

REMIND-MAgPIE can compute maximum regional utility (welfare) by two different solution concepts – the Negishi approach and the Nash approach . In the Negishi approach, which computes a cooperative solution, the objective of the Joint Maximization Problem is the weighted sum of regional utilities, maximized subject to all other constraints:

<figure id="fig:REMIND-MAgPIE_3.2.1 2."> </figure>

An iterative algorithm adjusts the weights so as to equalize the intertemporal balance of payments of each region over the entire time horizon. This convergence criterion ensures that the Pareto-optimal solution of the model corresponds with the market equilibrium in the absence of non-internalized externalities. The algorithm is an inter-temporal extension of the original Negishi approach ; see also for a discussion of the extension. Other models such as MERGE and RICE50+ use this algorithm in a similar way.

The Nash solution concept, by contrast, arrives at the Pareto solution not by Joint Maximization, but by maximizing the regional welfare subject to regional constraints and international prices that are taken as exogenous data for each region. The intertemporal balance of payments of each region has to equal zero and is one particular constraint imposed on each region. The equilibrium solution is found by iteratively adjusting the international prices until global demand and supply are balanced on each market. The choice of the solution concept is also important for the representation of trade, as discussed in Section the section on Trade.

In contrast to the Negishi approach, which solves for a co-operative Pareto solution, the Nash approach solves for a non-cooperative Pareto solution. The cooperative solution internalizes interregional spillovers between regions by optimizing the global welfare by using Joint Maximization. The non-cooperative solution considers spillovers as well, but they are not internalized. The relevant externalities are the technology learning effects in the energy sector.

3.1) Production system and representation of economic sectors - REMIND-MAgPIE

REMIND-MAgPIE uses a nested production function with constant elasticity of substitution (CES) to determine a region’s gross domestic product (GDP) (see <xr id="fig:REMIND-MAgPIE_4"/> bleow). Inputs at the upper level of the production function include labor, capital, and final energy. We use the population at working age to determine labor. Final energy input to the upper production level forms a CES nest, which comprises energy for transportation and stationary energy coupled with a substitution elasticity of 0.3. In turn, these two energy types are determined by the nested CES functions of more specific final energy carriers. REMIND-MAgPIE assumes substitution elasticities between 1.5 and 3 for the lower levels of the CES nest. It assigns an efficiency parameter to each production factor in the various macroeconomic CES functions. The changes of efficiency parameters over time are tuned such that baseline economic growth and energy intensity improvements match exogenous scenario specifications, such as the shared socio-economic pathways SSP .

<figure id="fig:REMIND-MAgPIE_4"> </figure>

Figure 1. Production structure of REMIND-MAgPIE. Linear production functions describe the conversion of primary energy (lowest level) to final energy carriers. Nested CES structures describe the aggregation of final energy carriers for end-use.

The macro-economic budget constraint for each region ensures that, in each region and for every time step, the sum of GDP Y(r,t) and imports of composite goods M_G(r,t) can be spent on consumption C(r,t), investments into the macroeconomic capital stock I(r,t), energy system expenditures E(r,t) and the export of composite goods X_G(r,t). Energy system expenditures consist of investment costs, fuel costs, and operation and maintenance costs.

The balance of demand from the macro-economy and supply from the energy system delivers equilibrium prices at the final energy level. Macroeconomic capital depreciates at 5% per year, and investments are subject to adjustment costs that scale with the square of the rate of change in investments relative to the capital stock.

3.4) Trade - REMIND-MAgPIE

REMIND-MAgPIE considers the trade of coal, gas, oil, biomass, uranium, the composite good (aggregated output of the macro-economic system), and emissions permits (in the case of climate policy). It assumes that renewable energy sources (other than biomass) and secondary energy carriers are non-tradable across regions. As an exception, REMIND-MAgPIE can consider bilateral trade in electricity between specific region pairs (e.g., Europe and North Africa / Middle East), but this is not part of the default scenario. To be consistent with trade statistics, trade in petroleum products is subsumed under crude oil trade.

For each good i a global trade balance equation ensures that markets are cleared:

<figure id="fig:REMIND-MAgPIE_3.2.1 3"> </figure>

REMIND-MAgPIE models regional trade via a common pool, with the exception of the bilateral electricity trade mentioned above. While each region is an open system - meaning that it can import more than it exports - the global system is closed. The combination of regional budget constraints and international trade balances ensures that the sum of regional consumption, investments, and energy-system expenditures cannot be greater than the global total output in each period. In line with the classical Heckscher-Ohlin and Ricardian models , trade between regions is induced by differences in factor endowments and technologies. REMIND-MAgPIE also represents the additional possibility of inter-temporal trade. This can be interpreted as capital trade or borrowing and lending. For each region, the value of exports must balance the value of imports within the time horizon of the model. This is ensured by the inter-temporal budget constraint, where πir is the present value price of good i.

<figure id="fig:REMIND-MAgPIE_3.2.1 4"> File:REMIND-MAgPIE trade 2.JPG </figure>

In this equation discounting is implicit by using present value prices. Inter-temporal trade and the capital mobility implied by trade in the composite good, cause prices of mobile factors to equalize, thus providing the basis for an inter-temporal and inter-regional equilibrium. Since no capital market distortions are considered, the interest rates equalize across regions. Similarly, permit prices equalize across regions, unless their trade is restricted. By contrast, final energy prices and wages can differ across regions because these factors are immobile. Prices for traded primary energy carriers differ according to the transportation costs.

<figure id="fig:REMIND-MAgPIE_3.2.1 5"> </figure>

Trade balances imply that the regional current accounts (and their counterparts - capital accounts) have a sum of zero at each point in time. In other words, regions with a current account surplus balance regions with a current account deficit. The inter-temporal budget constraints clear debts and assets that accrue through trade over time. This means that an export surplus qualifies the exporting region for an import surplus (of the same present value) in the future, thus also implying a loss of consumption for the current period. REMIND-MAgPIE models trading of emissions permits in a similar way. In the presence of a global carbon market, the initial allocation of emissions rights is determined by a burden-sharing rule wherein permits can be freely traded among world regions. A permit-constraint equation ensures that an emissions certificate covers each unit of GHG emissions. Trade of resources is subject to trade costs. In terms of consumable generic goods, the representative households in REMIND-MAgPIE are indifferent to domestic and foreign goods as well as foreign goods from different origins. This can potentially lead to a strong specialization pattern.

Two solution concepts for the treatment of trade exist, called Nash and Negishi approach. The Negishi approach includes trade balances of all goods explicitly and adjusts the welfare weights in order to guarantee that the intertemporal balance of payments of each region is settled. Prices are derived from the shadow prices of the trade balances in each iteration. In contrast, the Nash approach adjusts goods prices until demand and supply of traded goods are equalized. There are no explicit market clearning conditions, and regions optimize separately, facing their individual intertemporal balance of payments. In each iteration, the international prices are exogenous parameters for all regions. In the absence of inter-regional externalities, both solution approaches converge to the same solution.

Table 1. Characterization of the treatment of trade in the two alternative Negishi and Nash solution concepts.

<figtable id="tab:REMIND-MAgPIEtable_2"> </figtable>

4) Energy - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

Energy is a factor input demanded by the economy, as different final energy types are inputs to GDP generation in the nested CES production function as described in Figure 1: Production structure of REMIND-MAgPIE. Linear production functions describe the conversion of primary energy (lowest level) to final energy carriers. Nested CES structures describe the aggregation of final energy carriers for end-use. . This chapter explains the different primary energy resources modelled and their potentials (Section Energy resource endowments). REMIND-MAgPIE considers more than 40 technologies for the conversion of these resources into different secondary energy types (Sections Electricity, Heat, Other conversion) and the conversion of secondary to final energy (Section Grid and infrastructure). The subsequent subsections explain the use of those final energy types in the different demand sectors (Sections Transport and Stationary sector).

4.1) Energy resource endowments - REMIND-MAgPIE

The primary energy carriers in REMIND-MAgPIE include both exhaustible and renewable resources. Exhaustible resources comprise uranium as well as three fossil resources, namely coal, oil, and gas. Renewable resources include hydro, wind, solar, geothermal, and biomass. It is possible to trade coal, oil, gas, uranium, and biomass across regions, but the trading of resources is subject to regional and resource-specific trade costs.

4.1.1) Fossil energy resources - REMIND-MAgPIE

Exhaustible resources

REMIND-MAgPIE characterizes exhaustible resources such as coal, oil, gas, and uranium in terms of extraction cost curves. Fossil resources (e.g., oil, coal, and gas) are further defined by decline rates and adjustment costs . Extraction costs increase over time as low-cost deposits become exhausted , ; ; ; . In REMIND-MAgPIE, we use region-specific extraction cost curves that relate production cost increases to cumulative extraction ; .

<xr id="fig:REMIND-MAgPIE_5"/> shows extraction cost curves at the global level as implemented for various SSPs. More details on the underlying data and method will be presented in a separate pape . The default scenario used in REMIND-MAgPIE is SSP2 (“Middle-of-the-Road”). In the model, these fossil extraction cost input data are approximated by piecewise linear functions that are employed for fossil resource extraction curves. Additionally, as a scenario choice, it is possible to make oil and gas extraction cost curves time dependent. This means that resources and costs may increase or decrease over time depending on expected future conditions such as technological and geopolitical changes.

For uranium, extraction costs follow a third-order polynomial parameterization. The amount of available uranium is limited to 23 Mt. This resource potential includes reserves, conventional resources, and a conservative estimate of unconventional resources .

REMIND-MAgPIE prescribes decline rates for the extraction of coal, oil, and gas. In the case of oil and gas, these are dynamic extraction constraints based on data published by the International Energy Agency ; . An additional dynamic constraint limits the extraction growth of coal, oil, and gas to 10% per year. In addition, we use adjustment costs to represent short-term price markups resulting from rapid expansion of resource production ; ; .

<figure id="fig:REMIND-MAgPIE_5"> </figure>

Figure 1: Global aggregate Cumulative Availability Curves of coal, oil and gas for the different SSPs. The bars at the top indicate the minimum, median and maximum extraction in baseline scenarios in the EMF-27 study; the shaded area covers the range of extraction cost functions given in the EMF-27 and AMPERE studies.

Trade costs in REMIND-MAgPIE are both region-and resource-specific. Oil trade costs range between 0.22 USD/GJ in AFR and 0.63 USD/GJ in EUR. Gas trade costs are lowest in EUR and JPN with a value of 1.52 USD/GJ and reach a maximum in CHN with a value of 2.16 USD/GJ. Coal trade costs range between 0.54 USD/GJ in JPN and 0.95 USD/GJ in IND.

4.1.2) Uranium and other fissile resources - REMIND-MAgPIE

A comparison of regularly up-dated assessments of global uranium availability is given in <xr id="fig:REMIND-MAgPIE_1"/>. Conventional identified resources of uranium are differentiated into recovery cost categories. The assessment by the Nuclear Energy Agency comprises 6.3Mt of uranium, which equals approximately one hundred times current reactor requirements. The estimates of World Energy Council and German Geological Survey mainly rely on the numbers of NEA but apply different interpretations for identified uranium resources. The more uncertain category of conventional undiscovered uranium resources are also assessed differently by the three institutions.

For the default version the assumption is that 23MtUr are ultimately available with increasing extraction costs up to 260$US per tUr. The implementation uses a quadratic extraction cost function for each region that starts at 25US$ per kg uranium and cuts off at the same marginal costs (300$US per kg uranium), if - at the global level - 23MtUr are reached. The shape parameter of the regional extraction cost functions depend on the regional availability of uranium resources. The default version does not represent reprocessing and fast breeding reactors integrated into the nuclear fuel cycle. Given the optimistic assessment of uranium resources this assumption is economically reasonable in the near-term.

Figure 1. Overview of assessments on global uranium in Mt uranium. Identified resources are differentiated by cost categories; undiscovered resources are differentiated by geological certainty.

<figure id="fig:REMIND-MAgPIE_1"> </figure>

4.1.3) Bioenergy - REMIND-MAgPIE

REMIND-MAgPIE models three types of bioenergy feedstocks:

1. First-generation biomass produced from sugar, starch, and oilseeds (typically small in quantity, based on an exogenous scenario);
2. Ligno-cellulosic residues from agriculture and forest; and
3. Second-generation purpose-grown biomass from specialized ligno-cellulosic grassy and woody bioenergy crops, such as miscanthus, poplar, and eucalyptus.

To represent supply of purpose-grown bioenergy from the land-use sector, REMIND-MAgPIE can either be run in standalone mode or soft-coupled to the land-use model MAgPIE (Model of Agricultural Production and its Impact on the Environment) ; ; , see also Section “Land Use” . In standalone mode, REMIND-MAgPIE draws on an emulator of MAgPIE, which describes bioenergy supply costs and total agricultural emissions as a function of bioenergy demand, as described in detail in Klein . The supply curves capture the time, scale and region dependent change of bioenergy production costs, as well as path dependencies resulting from past land conversions and induced technological changes in the land-use sector, as represented in MAgPIE. Ligno-cellulosic agricultural and forest residues are based on low-cost bioenergy supply options. Their potential is assumed to increase from 20 EJ/yr in 2005 to 70 EJ/yr in 2100 , based on Haberl .

In REMIND-MAgPIE, we assume that the use of traditional biomass (supplied by residues) is phased out, as modern and less harmful fuels are increasingly used with rising incomes . We also assume that first generation modern biofuels are phased out, reflecting their high costs and accounting for concerns about land-use impacts, co-emissions, and competition with food production from first-generation biofuels ; . As a consequence, the main sources of bioenergy in REMIND-MAgPIE scenarios are second-generation purpose-grown biomass and ligno-cellulosic agricultural and forestry residues.

To further reflect concerns about the sustainability of large-scale deployment of lingo-cellulosic bioenergy, REMIND-MAgPIE assumes an ad valorem tax on bioenergy. The tax increases linearly from 0 to 100% between 2030 and 2100 and is applied to the bioenergy price given by the emulator (see above). Based on the current public debate, we consider this tax to be a reflection of the potential institutional limitations on the widespread-use of bioenergy.

4.1.4) Non-biomass renewables - REMIND-MAgPIE

REMIND-MAgPIE models resource potentials for non-biomass renewables (hydro, solar, wind, and geothermal) using region-specific potentials. For each renewable energy type, we classify the potentials into different grades, specified by capacity factors (<xr id="fig:REMIND-MAgPIE_6"/>). Superior grades have higher capacity factors, which correspond to more full-load hours per year. This implies higher energy production for a given installed capacity. Therefore, the grade structure leads to a gradual expansion of renewable energy deployment over time as a result of optimization.

REMIND-MAgPIE’s renewable energy potentials often appear higher than the potentials used in other models . However, these models typically limit potentials to specific locations that are currently competitive or close to becoming competitive. REMIND-MAgPIE’s grade structure allows for the inclusion of sites that are less attractive, but may become competitive in the long-term as the costs of other power-generation technologies increase. This choice is dependent on the model. The regionally aggregated potentials for solar PV and CSP used in REMIND-MAgPIE were developed in Pietzcker in cooperation with the German Aerospace Center DLR. In total, the solar potential is almost unlimited, with a total amount of 6500 EJ/year for PV and 2000EJ/year for CSP. However, the resource quality differs strongly across regions, so that some regions have mostly sites with low full-load hours. To account for the competition between PV and CSP for the same sites with good irradiation, an additional constraint for the combined deployment of PV and CSP was introduced in REMIND-MAgPIE . This implies that the sum of the area used by both technologies is smaller than the total available area.

The regionally aggregated wind potentials were developed based on a number of studies ; ; ; . The technical potentials for combined on- and off-shore wind power amount to 370EJ/year (half of this amount is at sites with less than 1400 full-load hours). The total value is twice as large as the potential estimated by WGBU , but is less than one fifth of the potential in Lu .

<figure id="fig:REMIND-MAgPIE_6"> </figure>

Figure 1. Regionalized resource potentials for solar PV, CSP, wind and hydro power as a function of resource quality expressed in terms of attainable capacity factors.

The global potentials of hydropower amount to 50 EJ/year. These estimates are based on the technological potentials provided in WGBU (2003). The regional disaggregation is based on information from a background paper produced for this report (Horlacher 2003).

4.2) Energy conversion - REMIND-MAgPIE

The core part of the energy system is the conversion of primary energy into secondary energy carriers via specific energy conversion technologies. Around fifty different energy conversion technologies are represented in REMIND-MAgPIE. In general, technologies providing a certain secondary energy type compete linearly against each other, i.e. technology choice follows cost optimization based on investment costs, fixed and variable operation and maintenance costs, fuel costs, emission costs, efficiencies, lifetimes, and learning rates. REMIND-MAgPIE assumes full substitutability between different technologies producing one energy type. The various secondary energy carriers included in REMIND-MAgPIE are:

• Electricity
• Gases
• Liquids
• Hydrogen
• Solid fuels
• District heat and local renewable heat

<xr id="tab:REMIND-MAgPIEtable_3"/> gives an overview over which energy carriers are used in which end use sector.

Table 1. Overview of energy carriers used in end-use sectors

<figtable id="tab:REMIND-MAgPIEtable_3"> </figtable>

REMIND-MAgPIE specifies each technology through a number of characteristic parameters

• Specific overnight investment costs that are constant for most technologies and decrease due to learning-by-doing for some relatively new technologies (see below).
• Cost markups due to financing costs over the construction time.
• Fixed yearly operating and maintenance costs in percent of investment costs.
• Variable operating costs (per unit of output, excluding fuel costs).
• Conversion efficiency from input to output.
• Capacity factor (maximum utilization time per year). This parameter also reflects maintenance periods and other technological limitations that prevent the continuous operation of the technology.
• Technical lifetime of the conversion technology in years.
• If the technology experiences learning-by-doing: initial learn rate, initial cumulative capacity, as well as floor costs that can only be approached asymptotically.

REMIND-MAgPIE represents all technologies as capacity stocks with full vintage tracking. Since there are no hard constraints on the rate of change in investments, the possibility of investing in different capital stocks provides high flexibility for technological evolution. However, the model includes cost mark-ups for the fast up-scaling of investments into individual technologies; therefore, a more realistic phasing in and out of technologies is achieved. The model allows for pre-mature retirement of capacities before the end of their technological life-time (at a maximum rate of 4 %/year), and the lifetimes of capacities differ between various types of technologies. Furthermore, depreciation rates are relatively low in the first half of the lifetime and increase thereafter.

Each region is initialized with a vintage capital stock and conversion efficiencies are calibrated to reflect the input-output relations provided by IEA energy statistics ; . The conversion efficiencies for new vintages converge across the regions from the 2005 values to a global constant value in 2050. Furthermore, for some fossil power plants, transformation efficiencies improve exogenously over time. Finally, REMIND-MAgPIE adjusts by-production coefficients of combined power-heat technologies (CHP) by region to meet the empirical conditions of the base year.

Only two technologies convert secondary energy into secondary energy, namely the production of hydrogen from electricity via electrolysis and the opposite route, the production of electricity from a hydrogen turbine.

Technology choice for energy supply follows cost optimization based on investment costs, fixed and variable operation and maintenance costs, fuel costs, emission costs, efficiencies, lifetimes, and learning rates. Endogenous technological change (learning-by-doing) influences wind and solar investment costs. For fossil fuel power plants, some exogenous time-dependent improvement of efficiency parameters until 2050 and convergence of efficiencies that are regionally calibrated to observed 2005 values are implemented. REMIND-MAgPIE assumes full substitutability between different technologies producing one final energy type.

4.2.1) Electricity - REMIND-MAgPIE

Around twenty electricity generation technologies are represented in REMIND-MAgPIE, see <xr id="tab:REMIND-MAgPIE_electricity_technologies"/>, with several low-carbon (CCS) and zero carbon options (nuclear and renewables).

Table 1. Energy Conversion Technologies for Electricity (Note: † indicates that technologies can be combined with CCS). <figtable id="tab:REMIND-MAgPIE_electricity_technologies">

Energy Conversion Technologies for Electricity

Energy Carrier	Technology
Primary exhaustible resource
Coal	Conventional coal power plant Integrated coal gasification combined cycle† Coal combined heat and power plant
Oil	Diesel oil turbine
Gas	Gas turbine Natural gas combined cycle† Gas combined heat and power plant
Uranium	Light water reactor
Primary renewable resource
Solar	Solar photovoltaic Concentrating solar power
Wind	Wind turbine
Hydropower	Hydropower
Biomass	Integrated biomass gasification combined cycle† Biomass combined heat and power plant
Geothermal	Hot dry rock
Secondary energy type
Hydrogen	Hydrogen turbine

</figtable>

<figure id="fig:REMIND-MAgPIEtable_4"> </figure>

Table 2. Techno-economic characteristics of technologies based on exhaustible energy sources and biomass ; ; ; ; ; ; ; ; ; ; ; ; .

<figtable id="tab:REMIND-MAgPIEtable_5"> </figtable>

Abbreviations: PC - pulverized coal, IGCC - integrated coal gasification combined cycle, CHP - coal combined heat and power plant, C2H2 - coal to hydrogen, C2L - coal to liquids, C2G - coal gasification, NGT - natural gas turbine, NGCC - natural gas combined cycle, SMR - steam methane reforming, BIGCC – Biomass IGCC, BioCHP – biomass combined heat and power, B2H2 – biomass to hydrogen, B2L – biomass to liquids, B2G – biogas, TNR - thermo-nuclear reactor; * for joint production processes; ^§ nuclear reactors with thermal efficiency of 33%; ^# technologies with exogenously improving efficiencies. 2005 values are represented by the lower end of the range. Long-term efficiencies (reached after 2045) are represented by high-end ranges.

For variable renewable energies, we implemented two parameterized cost markup functions for storage and long-distance transmission grids - see Section Grid and Infrastructure. To represent the general need for flexibility even in a thermal power system, we included a further flexibility constraint based on Sullivan .

The techno-economic parameters of power technologies used in the model are given in <xr id="tab:REMIND-MAgPIEtable_5"/> for fuel-based technologies and <xr id="tab:REMIND-MAgPIEtable_6"/> for non-biomass renewables. For wind, solar and hydro, capacity factors depend on grades, see Section Non-biomass renewables.

Table 3. Techno-economic characteristics of technologies based on non-biomass renewable energy sources ; ; ; ; .

<figtable id="tab:REMIND-MAgPIEtable_6"> </figtable>

4.2.2) Heat - REMIND-MAgPIE

REMIND-MAgPIE also features a broad range of technologies for the supply of non-electric secondary energy carriers, such solids, liquids, gases, heat and hydrogen, as listed in <xr id="tab:REMIND-MAgPIEtable_7"/>. Note that biomass is the main non-fossil feedstock for the supply of non-electric energy.

Table 1. Conversion Technologies for non-electric energy carriers (Note: * indicates that technologies can be combined with CCS)

<figtable id="tab:REMIND-MAgPIEtable_7">

</figtable>

4.2.6) Grid, pipelines and other infrastructure - REMIND-MAgPIE

General distribution costs

REMIND-MAgPIE represents electricity/gas/hydrogen grids as well as distribution costs for solids and liquids in terms of a linear cost-markups on final energy use.

Variable renewable energy sources

Variable renewable electricity (VRE) sources such as wind and solar PV require storage to guarantee a stable supply of electricity . Since the techno-economic parameters applied to CSP include the cost of thermal storage to continue electricity production at nighttime, REMIND-MAgPIE assumes that CSP requires only limited additional storage for balancing fluctuations.

The approach used in REMIND-MAgPIE follows the idea that storage demands for each VRE type rise with increasing market share. This is because balancing fluctuations becomes ever more challenging with higher penetration.

<figure id="fig:REMIND-MAgPIE_3.2.1 6"> </figure>

For modeling reasons, there is a 'generalized storage unit', tailor-made for each VRE. This construct consists of a VRE-specific mix of short- and medium-term storage as well as curtailment. Examples are redox-flow batteries for short-term storage, electrolysis and hydrogen storage for medium-term storage, as well as curtailment to balance seasonal fluctuations. A specific combination of these three real-world storage options is determined in order to match the VRE-specific fluctuation pattern. From this combination of actual storage technologies, we calculate aggregated capital costs and efficiency parameters for the 'generalized storage unit' of a specific VRE.

To calculate the total storage costs and losses at each point in time, the calculated 'generalized storage unit' of a VRE is scaled with this VRE's scale-factor _VRE. The capital costs of the generalized storage units decrease through learning-by-doing with a 10% learning rate.

Costs for long-term HVDC transmission are included following a similar logic as storage costs. REMIND-MAgPIE assumes that grid requirements increase with market share. Furthermore, since resource potentials for PV (suitable for decentralized installation) are not as localized as those for wind and CSP, REMIND-MAgPIE assumes that grid costs for PV are comparatively smaller.

Both storage and grid requirements are partly regionalized: in regions where high demand coincides with high wind (EUR) or solar (USA, ROW, AFR, IND, MEA) incidence, storage requirements are slightly reduced. If a region is small or has homogeneously distributed VRE potentials (EUR, USA, IND, JPN), grid requirements are lower.

For a market share of 20%, marginal integration costs (including storage, curtailment and grid costs) are in a range of 19-25 USD/MWh for wind, 20-35 USD/MWh for PV, and 8-15 USD/MWh for CSP. For more details on the modeling of VRE integration in REMIND-MAgPIE, see Pietzcker .

Carbon capture and Storage

REMIND-MAgPIE represents several carbon capture and storage (CCS) applications. First, CCS can curb emissions from fossil fuel combustion. In REMIND-MAgPIE, CCS technologies exist for generating electricity as well as for the production of liquid fuels, gases, and hydrogen from coal and gas. Secondly, it is possible to combine biomass with CCS to generate net negative emissions. Such bioenergy CCS (BECCS) technologies are available for electricity generation (e.g., biomass integrated gasification combined cycle power plant), biofuels (e.g., biomass liquefaction), hydrogen, and syngas production. Thirdly, CCS can be used to reduce atmospheric CO2 emissions from the industry sector.

The sequestration of captured CO2 is explicitly represented in the model by accounting for transportation and storage costs . There are regional constraints on CO2 storage potentials which are largely based on IEA . In total, the global storage potential amounts to around 1000 GtC . It is smaller for EUR with 50 GtC, Japan with 20 GtC, and India with 50 GtC. The yearly injection rate of CO2 is assumed not to exceed 0.5% of total storage capacity due to technical and geological constraints. This creates an upper limit of 5 GtC per year for global CO2 injection.

4.3) Energy end-use - REMIND-MAgPIE

Since version 1.7, REMIND-MAgPIE represents the transport, industry and residential/commercial end use sectors. In former REMIND-MAgPIE versions, residential/commercial and industry were represented as an aggregate stationary sector.

Table 1. Overview of energy carriers used in the various end-use sectors

<figtable id="tab:REMIND-MAgPIEtable_8"> </figtable>

4.3.1) Transport - REMIND-MAgPIE

REMIND-MAgPIE models the transport sector by using a hybrid approach combining top-down and bottom-up elements (see Figure 1. Production structure of REMIND-MAgPIE. Linear production functions describe the conversion of primary energy (lowest level) to final energy carriers. Nested CES structures describe the aggregation of final energy carriers for end-use.). Specifically, mobility demands for the 4 modeled transport sub-sectors (Passenger-light duty vehicles (LDV), Freight, Electric Rail, Passenger-Aviation and Buses) are derived in a top-down fashion, since they are input to a nested CES production function that ultimately produces GDP. For the LDV mode, three different technology options (internal combustion engine, battery electric vehicle, and fuel cell vehicle) compete against each other in a linear bottom-up technology model.

The transport sector requires input of final energy in different forms (liquids, electricity and hydrogen) and requires investments and operation and maintenance payments into the distribution infrastructure (infrastructure capacity grows linearly with distributed final energy) as well as into the vehicle stock. It generates emissions that go into the climate model and, depending on the scenario, can be taxed or limited by a budget. Furthermore, it is possible to consider taxes and subsidies on fuels. Material needs and embodied energy are not considered.

The main drivers/determinants of transport demand are GDP growth, the autonomous efficiency improvements (efficiency parameters of CES production function), and the elasticities of substitution between capital and energy and between stationary and transport energy forms. In more detail, mobility from the different modes comes as an input to a CES function, the output of which is combined with stationary energy to generate a generalized energy good, which is combined with labor and capital in the main production function for GDP. Finally, inside a model run, different final energy prices (due to climate policy, different resource assumptions, etc.) can lead to substitution of different transport modes inside the CES function, or a total reduction of travel demand (see Pietzcker for a comparison of the different contributions to transport mitigation). For passenger transport, we consider LDV (powered by liquids, electricity or hydrogen), Aviation and Bus (aggregated, only powered by liquids) and Electric Trains (only powered by electricity). For freight transport, there is only one generic mode based on liquid fuels. For the conversion technologies of primary energy sources into these secondary energy carriers, see Section Energy Conversion.

The distribution of vehicles inside the LDV mode follows cost optimization (perfect linear substitutability), although with different non-linear constraints (learning curve, upper limits of 70% on share of battery-electric vehicles and 90% on Fuel Cell vehicles) that in most realizations lead to a technology mix.

Efficiency, lifetime, investment costs, and fixed O&M costs parameters characterize all vehicle technologies. All these parameters, except investment costs for battery electric and fuel cell vehicles, are constant over time. Battery electric vehicles and fuel cell vehicles undergo learning-by-doing through a one-factor learning curve with floor costs that are asymptotically approached as cumulated capacity increases. Fuel prices are fully endogenous, as determined by the supply sector (intertemporal optimization with resource and capacity constraints as well as prices/constraints on emissions in policy scenarios).

Table 1. Overview of LDV technologies <figtable id="tab:REMIND-MAgPIEtable_9"> </figtable>

4.3.2) Residential and commercial sectors - REMIND-MAgPIE

In REMIND-MAgPIE, the residential and commercial sectors are modeled together within the buildings sector. The demand and the supply of energy for buildings follow different modelling approaches:

Demand for energy types used in the buildings sector (electricity, solids, liquids, gas, district heat, and hydrogen) is modeled in a top-down fashion: they are input to a nested CES production function that produces GDP.

Supply of these final energies is modeled in a bottom-up energy model, where detailed capital stocks of conversion technologies convert primary energies to secondary and final energies, with full substitutability between technologies. The bottom-up energy model is described in full detail in Section “Energy conversion”.

The buildings sector differentiates between two explicit energy functions: electricity, and all energy inputs used for heating purposes (gas, solids, district heat, liquids, and hydrogen). It is easier to substitute one energy carrier for another in the latter group, than it is to substitute electricity for another energy carrier (see Figure 3 for the full CES production function with all substitution elasticity values).

The main energy demand drivers are GDP growth, the autonomous efficiency improvements (efficiency parameters of CES production function), the elasticities of substitution between capital and energy and between the buildings, industry, and transport energy sectors. These drivers influence demand in a similar manner as described for the transport sector, i.e. final energy types are inputs to a CES function, the output of which is combined with transport energy in another CES function to generate a generalized energy good, which in turn is combined with labor and capital in the main production function for GDP.

The indirect energy use and material needs for production of appliances or houses is not explicitly represented, only implicitly accounted for by the main CES production function, which is calibrated to the total historical energy demand of a region.

Inside a model run, different FE prices (due to climate policy, different resource assumptions, etc.) can lead to substitution of different buildings energy types inside the CES function, or a total reduction of buildings energy demand. There is no single direct price elasticity of demand in the model, the nested CES function results in different price elasticities at different points in time/system configurations.

The buildings sector generates direct emissions – from fuel combustion in buildings and is responsible for indirect emissions (emissions from the energy supply sector) that go into the climate model and, depending on the scenario, are taxed or limited by a budget.

4.3.3) Industrial sector - REMIND-MAgPIE

Demand for final energy carriers used in the industry sector (solids, liquids, gases, hydrogen, district heat and electricity) is modeled in a top-down fashion: they are input to a nested CES production function that produces GDP. Supply of these final energies is modeled in a bottom-up energy model, where detailed capital stocks of conversion technologies convert primary energies to secondary and final energies, with full substitutability between technologies. The bottom-up energy model supplying the energy carriers is described in full detail in Section “Energy conversion”.

The industry sector differentiates between two types of energy functions supplied by the final energy carriers: electricity, and energy inputs used for heating purposes (solids, liquids, gas, hydrogen, and district heat).

The industry sector requires investments and operation and maintenance payments into the distribution infrastructure (generic capacity constraint). It generates emissions that go into the climate model and, depending on the scenario, are taxed or limited by a budget.

The indirect energy use and material needs for construction of factories and machinery is not explicitly represented, only implicitly accounted for by the main CES production function, which is calibrated to the total historical energy demand of a region.

The main determinants of final energy demand in the industry sector are GDP growth, the autonomous efficiency improvements (efficiency parameters of CES production function), the elasticities of substitution between capital and energy and between industry, residential/commercial and transport energy use. These factors influence demand in a similar manner as described for the residential/commercial and transport sectors, i.e., final energy types are inputs to a CES function, the output of which is combined with energy from other sectors in another CES function to generate a generalized energy good, which in turn is combined with labor and capital in the main production function for GDP.

Emissions of the three largest industry sub-sectors (cement, chemicals and steel production) can partially be abated by the use of CCS. To that end, emissions of the sub-sectors are calculated based on region-specific sub-sector shares in the use of CO2-emitting final energy carriers (solids, liquids and gases). The share of emissions abated by CCS is determined via sub-sector specific marginal abatement cost (MAC) curves; according to the explicit or implicit CO2 price total emissions are reduced and sequestered CO2 is increased accordingly, while additional abatement costs are incurred and accounted for in the budget.

Process emissions from cement production are calculated based either on per capita GDP or on per capita investments, based on the level of economic development of a region. REMIND-MAgPIE reduces cement emissions when CO2 prices increase and thereby drive up clinker/cement prices. This reduction of cement emissions represents both a reduction in demand through improved molds and structural redesign and a reduction of emissions from changing the composition of cement. These options are represented by a MAC curve (exemplary points: 10% reduction at 30$/tCO2, 40% reduction at 200$/tCO2, 60% reduction at 600$/tCO2), and the costs for reducing cement emissions are fully accounted for in the budget equation. Additionally, process emissions from cement production can be further reduced by using CCS – the model employs the same MAC curve as for energy-use emissions in the cement sub-sector.

4.4) Energy demand - REMIND-MAgPIE

Baseline final energy in REMIND-MAgPIE is calibrated to projections from theEDGE2 model (Energy Demand Generator, version 2). EDGE2 integrates econometric projections based on historical trends with scenario assumptions about long-term developments. The econometric projections play an important role in the short term while scenario assumptions rather influence the long-term behavior. The EDGE2 model covers six energy carriers— biomass, coal, electricity, liquids, gas, district heat —and six sectors —residential, commercial, industry, non-energy use, agriculture and fisheries, others.

The econometric regressions draw on the historical relationship between the per capita energy carrier demand in each sector and the GDP or sectoral value added per capita. The specification of the econometric model differs from one energy carrier to the other depending upon the observed relationship in historical data between the explained and the explanatory variables, or upon the regional heterogeneity. Each sectoral energy carrier is treated individually, which allows for a better control of the econometric fit, but has the disadvantage of ignoring the interdependencies between them. However, these interdependencies are partly reflected in the historical data.

The scenario assumptions follow the SSP framework and narratives . In the SSP2 middle-of-the road scenario, EDGE 2 assumes a continuation of historical per-capita energy demand trends, and a regional partial convergence towards a global trend line over time. This global trend line relates globally averaged per capita demand for an energy carrier with per capita GDP. The convergence assumption differs across energy carriers and sectors. Typically, demand for electricity will assume greater convergence than demand for gas, liquids or district heat, which reflects the diverse regional heating requirements. The resulting demands were then user-adjusted to ensure that aggregated demand for energy carriers used to provide heat lies within a band of expected per-capita heat demand at a given per capita income.

To derive SSP1 and SSP5 demand trajectories, three types of modifications were performed relative to SSP2 to reflect the respective scenario narratives: (1) a change in the energy intensity in the end-use sectors transportation, industry, residential and commercial buildings, (2) a change in the energy carrier intensities (most importantly, electric vs. non-electric), and (3) a change in the regional convergence of trajectories.

The projections show agreement with several energy stylized facts . In line with the energy-ladder concept , the share of solids decreases widely. Most notably, they exhibit a phase-out of traditional biomass in developing countries. By contrast, the share of grid-based energy carriers, in particular electricity, is projected to increase across all regions over the century. Following GDP per capita and population projections, developing regions’ demands grow fast, while developed regions experience a slower increase. In line with other studies, we find that currently least-developed countries will account for the bulk of global energy demand in the long-term.

Once these projections are calculated, they are aggregated to the sectoral and energy carrier levels present in REMIND-MAgPIE. Then, the macro-economic production function of REMIND-MAgPIE is calibrated to meet these energy demand pathways in the baseline scenario .

In policy cases, REMIND-MAgPIE can reduce energy intensity energy service input per unit of economic output through two mechanisms. First, the CES production function allows for price-dependent substitutions between aggregated energy and capital (substitution elasticity of 0.5). The introduction of additional constraints on the supply side (e.g., carbon taxes, resource, or emission constraints) results in higher energy prices and thus lower final energy consumption compared to the reference trajectories. As a consequence, the share of macro-economic capital input in the production function increases. In absence of distortions, a reduction in final energy results in a lower GDP and, subsequently, lower consumption and welfare values. Second, the model can endogenously improve end-use efficiency by investing in more efficient technologies for the conversion of final energies into energy services. For example, three vehicle technologies with different efficiencies are implemented in the light duty vehicle (LDV) mode of the transport sector, including internal combustion engine vehicles, battery-electric vehicles, and fuel cell vehicles.

4.5) Technological change in energy - REMIND-MAgPIE

REMIND-MAgPIE assumes endogenous technological change through learning-by-doing for wind and solar power, electric (BEV) and fuel cell vehicle (FCV) technologies, as well as variable renewable energy (VRE) storage, through global learning curves and internalized spillovers. The specific investment costs for wind, solar PV, and solar CSP decrease by 12, 20, and 9%, respectively, for each doubling of cumulated capacity. The capital costs of the generalized storage units for VRE, as well as of advanced vehicle technologies (BEV, FCV), decrease with a 10% learning rate. REMIND-MAgPIE reduces learning rates as capacities increase such that the investment costs asymptotically approach endogenously prescribed floor costs.

For variable renewable energies, we implemented two parameterized cost markup functions for storage and long-distance transmission grids - see Section "Electricity". To represent the general need for flexibility even in a thermal power system, we included a further flexibility constraint based on Sullivan .

The techno-economic parameters of power technologies used in the model are given in Table 2 Techno-economic characteristics of technologies based on exhaustible energy sources and biomass. for fuel-based technologies and in Table 3 echno-economic characteristics of technologies based on non-biomass renewable energy sources. for non-biomass renewables. For wind, solar and hydro, capacity factors depend on grades, see Section "Non-biomass renewables"

As discussed in Section "Macro-economy", REMIND-MAgPIE represents energy efficiency improvements via an exogenously prescribed increase in the efficiency parameters of the CES production function, as well as price induced reductions in energy demand and changes in technology choice. REMIND-MAgPIE represents investment dynamics in terms of capital motion equations, vintages for energy supply technologies and adjustment costs related to the acceleration of capacity expansion (for further details see Section "Energy conversion").

5) Land-use - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

There are a number of important interactions of the energy, economy and climate systems represented in REMIND-MAgPIE with the land system, such as emissions from land use changes and agriculture, or bioenergy supply. In the default standalone mode, REMIND-MAgPIE relies on reduced-form approaches to account for these inter-linkages between the energy and the agricultural and land-use sectors (stand-alone mode). These are derived based on the state-of-the-art land use model MAgPIE ; ; . For a detailed and fully consistent analysis of the integrated energy-economy-land use system, REMIND-MAgPIE can also be soft-linked and run iteratively with MAgPIE as depicted in Figure 7 (coupled mode). The soft-link between REMIND-MAgPIE and MAgPIE focuses on two crucial interactions: (i) bioenergy demand and supply, (ii) land use/land use change emissions and GHG prices. At the end-point of the iterative solution process, the markets for bioenergy and emission mitigation across the energy and land-use sector are in equilibrium.

<figure id="fig:REMIND-MAgPIE_7"> </figure>

Figure 1. In the coupled mode REMIND-MAgPIE is soft-linked to the land-use model MAgPIE. The models are run iteratively and exchange information about bioenergy demand and supply and about emission mitigation in the land-use system.

5.1) Agriculture - REMIND-MAgPIE

REMIND-MAgPIE derives non-CO2 emissions in the absence of climate policies from various agricultural activities for given assumptions on socio-economic pathways from corresponding MAgPIE scenarios. An important nexus between the energy system and agriculture is bioenergy demand. In standalone mode, REMIND-MAgPIE uses bioenergy supply costs derived from MAgPIE, see section “Bioenergy”. To account for the sensitivity of resource potentials to carbon pricing, REMIND-MAgPIE uses different supply curve parameterizations in baseline and climate policy scenarios. Bioenergy-induced emissions of N2O (fertilizer use) and CO2 (land-use change) are accounted for using specific per-unit emission coefficients.

In standalone mode, REMIND-MAgPIE derives the economic mitigation potential of agricultural CH4 and N2O emissions is calculated using marginal abatement cost curves (MACCs) from Lucas . For land-use related CO2, similar MACCs derived from MAgPIE are employed.

As described in Figure 1, if run in coupled mode REMIND-MAgPIE adopts consistent GHG emission projections and bioenergy supply curves from MAgPIE.

5.2) Forestry - REMIND-MAgPIE

If run in stand-alone mode, REMIND-MAgPIE relies on results from MAgPIE to account for CO₂ emissions from land use, land use change and forestry. Reduced emissions from deforestation and forest degradation (REDD) as a mitigation option is represented via a climate policy dependent marginal abatement cost curve

The coupled REMIND-MAgPIE system allows for a detailed analysis of forestry-based mitigation options in the context of an integrated climate change mitigation scenario.

6) Emissions - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

6.1) GHGs - REMIND-MAgPIE

REMIND-MAgPIE simulates emissions from long-lived GHGs (CO2, CH4, N2O), short-lived GHGs (CO, NOx, VOC) and aerosols (SO2, BC, OC). REMIND-MAgPIE accounts for these emissions with different levels of detail depending on the types and sources of emissions (see <xr id="tab:REMIND-MAgPIEtable_10"/>). It calculates CO2 emissions from fuel combustion, CH4 emissions from fossil fuel extraction and residential energy use and N2O emissions from energy supply based on sources. The energy system provides information on the regional consumption of fossil fuels and biomass for each time step and technology. For each fuel, region and technology, REMIND-MAgPIE applies specific emissions factors, which are calibrated to match base year GHG inventories .

CH4, N2O, and CO2 from land-use change have mitigation options that are independent of energy consumption. However, costs are associated with these emissions. Therefore, REMIND-MAgPIE derives the mitigation options from marginal abatement cost (MAC) curves, which describe the percentage of abated emissions as a function of the costs (see <xr id="fig:REMIND-MAgPIE_8"/>). It is possible to obtain baseline emissions - to which the MAC curves are applied - by three different methods: by source (as described above), by an econometric estimate, or exogenously. REMIND-MAgPIE uses the econometric estimate for CO2 emissions from cement production as well as CH4 and N2O emissions from waste handling. In both cases, the driver of emissions depends on the development of the GDP (as a proxy for waste production) or capital investment (as a proxy for cement production in infrastructure). REMIND-MAgPIE uses exogenous baselines for N2O emissions from transport and industry.

Emissions of other GHGs (e.g. F-gases, Montreal gases) are exogenous and are taken from the SSP scenario data set from the IMAGE model (Van Vuuren et al. under review). REMIND-MAgPIE does not represent abatement options for these gases; therefore, emissions from the corresponding SSP/RCP scenario best matching the target of the specific model simulation are used.

<figure id="fig:REMIND-MAgPIE_8"> </figure>

Figure 1. Globally and sectorally aggregated abatement costs and potentials for CH4 (left panel) and N2O (right panel) for different points in time. Marginal abatement cost curves are shifted over time such that more abatement is possible and the same level of abatement is available for a lower price. Adapted from Strefler, et al. (2014).

Table 1. Overview of the treatment of GHG and air pollutant emissions.

<figtable id="tab:REMIND-MAgPIEtable_10"> </figtable>

6.2) Pollutants and non-GHG forcing agents - REMIND-MAgPIE

REMIND-MAgPIE calculates emissions of aerosols and ozone precursors (SO2, BC, OC, NOx, CO, VOC, NH3). It accounts for these emissions with different levels of detail depending on sources and species.

For pollutant emissions of SO2, BC, OC, NOx, CO, VOC and NH3 related to the combustion of fossil fuels, REMIND-MAgPIE considers time- and region-specific emissions factors coupled to model-endogenous activity data. BC and OC emissions in 2005 are calibrated to the GAINS model (Klimont et al. in prep.a; Amann et al. 2011). All other emissions from fuel combustion in 2005 are calibrated to EDGAR . Emission factors for SO2, BC, and OC are assumed to decline over time according to air pollution policies based on Klimont et al. (in prep.b). Current near-term policies are enforced in high-income countries, with gradual strengthening of goals over time and gradual technology RDD&D. Low-income countries do not fully implement near-term policies, but gradually improve over the century.

Emissions from international shipping and aviation and waste of all species are exogenous and taken from Fujino . Further, REMIND-MAgPIE uses landuse emissions from the MAgPIE model, which in turn are based on emission factors from van der Werf . Other emissions are exogenous and are taken from the RCP scenarios .

7) Climate - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

By default, REMIND-MAgPIE is coupled with the MAGICC 6 climate model to translate emissions into changes in atmospheric composition, radiative forcing and temperature increase. Due to numerical complexity, after running REMIND-MAgPIE we perform the evaluation of climate change using MAGICC. Iterative adjustment of emission constraints or carbon taxes allows meeting specific temperature or radiative forcing limits in case of mitigation scenarios (see Section “Policy”).

In addition, REMIND-MAgPIE includes a reduced-form climate model similar to the one used in DICE (Nordhaus and Boyer 2000) which can be used within the REMIND-MAgPIE optimization to enable direct formulation of temperature or radiative forcing targets in climate mitigation scenarios. It comprises (1) an impulse-response function with three time scales for the carbon cycle, (2) an energy balance temperature model with a fast mixed layer, and (3) a slow deep ocean temperature box. Equations in the carbon-cycle temperature model describe concentration and radiative forcing that result from CH4, N2O, sulfate aerosols, black carbon, and organic carbon . The climate module determines the atmospheric concentrations of CO2, CH4, and N2O and computes the resulting radiative forcing and mean temperature at the global level. Its key parameters are calibrated to reproduce MAGICC, with a climate sensitivity of around 3.0°C.

REMIND-MAgPIE does not account for climate damages.

8) Non-climate sustainability dimension - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

Air pollution

Emissions of air pollutants are derived as described in section "GHGs".

Water

The water module of REMIND-MAgPIE represents water demand for electricity production and is extensively described in Mouratiadou ; . The description that follows is based on excerpts from these two papers. More extensive details on the methodology can be found in their Supplementary Online Materials, while a summary is provided below.

In REMIND-MAgPIE, water demand for electricity production represents requirements associated to cleaning, cooling, and other process related needs (e.g. flue gas desulfurization). Both the water withdrawal and water consumption indicators are quantified. All four principal cooling systems are considered, those being once-through open systems (with freshwater or sea water), recirculating wet towers, pond cooling, and dry towers.

Based on these indicators and cooling systems, REMIND-MAgPIE carries out an ex-post estimation of operational water demand for the electricity sector, by combining exogenous information on the water requirements per electricity and cooling technology with endogenous information on the electricity mix and technology vintages. Thermoelectric power plant cooling requirements are estimated as a function of excess heat, as opposed to a function of electricity output. Therefore, differences in water intensities in time or across regions due to differences in power plant thermal efficiencies and the age structure of thermal power plants are taken explicitly into account.

In sum, our estimate of water demand for electricity is based on the mix of electricity production technologies, the shares of cooling technologies, the water withdrawal and water consumption intensities, the vintage structures and the power plant thermal efficiencies. Global water withdrawal and consumption for thermal power technologies (WTt) are calculated by multiplying the excess heat from thermal power plants with the share of technology vintages (Vin), the vintage-specific share (csh) of different cooling technologies (cl), and the cooling technology specific water withdrawal or consumption coefficient for excess heat (cheat) and summing over regions, technologies and vintages.

<figure id="fig:REMIND-MAgPIE_3.2.1 6"> </figure>

Global water withdrawal and consumption for non-biomass renewable technologies elr (WRt) are estimated in a similar manner, only that they are based on electricity output (El) and electricity output-based coefficients instead of excess heat.

<figure id="fig:REMIND-MAgPIE_3.2.1 7"> </figure>

Water withdrawal and consumption coefficients per electricity output are based on Macknick ; , and have been converted into the coefficients for excess heat for the thermal power plant technologies (cheat) by back calculating the respective value for the US for 2005. The shares of cooling technologies per electricity technology are deduced from Kyle .

Currently, the electricity water demand estimates do not include water demand for fossil fuel extraction or for the irrigation of bioenergy crops. Additionally, water quantity and quality constraints, or the costs and technical characteristics of various cooling technologies, are not taken explicitly into account.

9) Appendices - REMIND-MAgPIE

Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

<figure id="fig:REMIND-MAgPIEtable_11"> </figure>

<figure id="fig:REMIND-MAgPIEtable_12"> </figure>

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Note: This pages describes the REMIND 1.7 model. It will be updated shortly to describe the most recent version of REMIND-MAgPIE.

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