Modelling of climate indicators - WITCH

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Model Documentation - WITCH
Corresponding documentation
Model information
Institution Fondazione Eni Enrico Mattei (FEEM), Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC)
Concept 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)
Anticipation Perfect foresight

World GHG emissions

The regional emissions are collected into the world emission and converted into CO2 equivalent using the the global warming potentials over a time horizon of 100 years (AR4 IPCC report,2007).


The carbon-cycle model is a 3-layer linear model calibrated to MAGICC. The carbon dioxide emissions go into the atmosphere box and alter the atmospheric carbon concentration, then the carbon is exchanged through the ocean-biosphere-atmosphere carbon fluxes. The ocean carbon sink is divided in two layers: the upper layer u (shallow oceans) and the lower layer l (deep oceans). In this representation, the upper layer also includes the biosphere. The CO2 atmospheric concentrations are computed by the carbon-cycle equations.

Accumulation of non-CO2 GHG in the atmosphere

The non-CO2 greenhouse gases are accumulated in the atmosphere using a decay function given a yearly retention factor, and a constant one-period retention factor. These function are calibrated on a stock of the greenhouse gas at equilibrium, which is not subject to decay.

Radiative forcing

The CO2 radiative forcing is calculated according to the TAR expression, proportional to the natural logarithm of the ratio of the current concentration to preindustrial level. While the radiative forcing of the greenhouse gases CH4 and N2O are interdependent and have a complex formulation, WITCH uses an approximation as in the MERGE model v5. The radiative forcing of short-lived and long-lived F-gases are proportional to the concentration levels. Exogenous radiative forcing from aerosols is coming from the RCP3D scenario, and the exogenous radiative forcing from ozone depletion substances (ODS) is also coming from the RCPs scenarios. The radiative forcing of all greenhouse gases are summed up to compute the total radiative forcing.

Global temperature increase from pre-industrial levels

The global temperature increase from pre-industrial level is obtained from an energy balance 2-layer model with two major coefficients: the atmosphere ocean exchange coefficient and the climate sensitivity.