Reference card - WITCH

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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.


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


Name and version


Institution and users

Fondazione Eni Enrico Mattei (FEEM), Italy,
Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC), Italy,


WITCH documentation consists of a referencecard and detailed model documentation

Model scope and methods

Model documentation: Model scope and methods - WITCH


WITCH evaluates the impacts of climate policies on global and regional economic systems and provides information on the optimal responses of these economies to climate change. The model considers the positive externalities from leaning-by-doing and learning-by-researching in the technological change.


Hybrid: Economic optimal growth model, including a bottom-up energy sector and a simple climate model, embedded in a `game theory` framework.

Solution method

Regional growth models solved by non-linear optimization and game theoretic setup solved by tatonnement algorithm (cooperative solution: Negishi welfare aggregation, non-cooperative solution: Nash equilibrium)


Perfect foresight

Temporal dimension

Base year:2005, time steps:5, horizon: 2150

Spatial dimension

Number of regions:14

  1. cajaz: Canada, Japan, New Zeland
  2. china: China, including Taiwan
  3. easia: South East Asia
  4. india: India
  5. kosau: South Korea, South Africa, Australia
  6. laca: Latin America, Mexico and Caribbean
  7. indo: Indonesia
  8. mena: Middle East and North Africa
  9. neweuro: EU new countries + Switzerland + Norway
  10. oldeuro: EU old countries (EU-15)
  11. sasia: South Asia
  12. ssa: Sub Saharan Africa
  13. te: Non-EU Eastern European countries, including Russia
  14. usa: United States of America

Note: The number of regions is not fixed, as they can be aggregated or downscaled until country level.

Policy implementation

Quantitative climate targets (temperature, radiative forcing, concentration), carbon budgets, emissions profiles as optimization constraints. Carbon taxes. Allocation and trading of emission permits, banking and borrowing. Subsidies, taxes and penalty on energies sources.

Socio economic drivers

Model documentation: Socio-economic drivers - WITCH

Exogenous drivers

  • Exogenous GDP
  • Total Factor Productivity
  • Labour Productivity
  • Capital Technical progress
  • Energy Technical progress
  • Materials Technical progress
  • GDP per capita


  • GDP per capita
  • Income distribution in a region
  • Urbanisation rate
  • Education level
  • Labour participation rate

Macro economy

Model documentation: Macro-economy - WITCH

Economic sectors

  • Agriculture
  • Industry
  • Energy
  • Transport
  • Services
  • other

Note: A single economy sector is represented. Production inputs are capital, labor and energy services, accounting for the Energy sector split into 8 energy technologies sectors (coal, oil, gas, wind&solar, nuclear, electricity and biofuels).

Cost measures

  • GDP loss
  • Welfare loss
  • Consumption loss
  • Area under MAC
  • Energy system costs


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


Model documentation: Energy - WITCH

Resource use

  • Coal
  • Oil
  • Gas
  • Uranium
  • Biomass

Electricity technologies

  • Coal
  • Gas
  • Oil
  • Nuclear
  • Biomass
  • Wind
  • Solar PV
  • CCS

Conversion technologies

  • CHP
  • Heat pumps
  • Hydrogen
  • Fuel to gas
  • Fuel to liquid

Grid and infrastructure

  • Electricity
  • Gas
  • Heat
  • CO2
  • H2

Energy technology substitution

  • Discrete technology choices
  • Expansion and decline constraints
  • System integration constraints

Energy service sectors

  • Industry
  • Residential and commercial
  • Transportation


Model documentation: Land-use - WITCH; Non-climate sustainability dimension - WITCH


  • Cropland
  • Forest

Note: Bioenergy related cost and emissions are obtained by an soft linking with the GLOBIOM model.

Other resources

Model documentation: Non-climate sustainability dimension - WITCH

Other resources

  • Water
  • Metals
  • Cement

Emissions and climate

Model documentation: Emissions - WITCH; Climate - WITCH

Green house gasses

  • CO2
  • CH4
  • N2O
  • HFCs
  • CFCs
  • SF6


  • NOx
  • SOx
  • BC
  • OC
  • Ozone

Climate indicators

  • CO2e concentration (ppm)
  • Climate damages $ or equivalent
  • Radiative Forcing (W/m2 )
  • Temperature change (°C)