# **2. Modeling framework**

The analysis provided throughout this paper relies on an integrated assessment framework designed for analyzing the chain of climate change impact, and climate change mitigation. The global partial equilibrium agriculture and forest sector model GLOBIOM (Havlík _et al._ , 2011; Havlík _et al._ , 2014) constitutes the central component of this framework. GLOBIOM is combined with the EPIC crop model (Williams, 1995) to calculate the impact of climate change on the agricultural sector, according to a framework described in Leclère _et al._ (2014) and Havlík _et al._ (2015). For a comprehensive accounting of greenhouse gas emissions from afforestation, deforestation and forest management and the effect of mitigation, GLOBIOM is coupled with the Global Forest Model (G4M, Kindermann _et al._ , 2008a).<sup>2</sup> GLOBIOM is a partial equilibrium model covering the agricultural, forestry and bioenergy sectors. It represents the world partitioned into 30 economic regions, in which a representative consumer tries to optimize his consumption, depending on his income, preferences and product prices. On the production side, producers maximize their margins and the model solves the market equilibrium corresponding to the overall welfare maximization based on the spatial equilibrium modeling approach (Takayama and Judge, 1971; McCarl and Spreen, 1980). More extensive information on the model structure and parameterization can be found in (Havlík _et al._ , 2011; Havlík _et al._ , 2014).

The supply side of the model relies on a detailed spatial resolution based on the concept of Simulation Units, which are aggregates of 5 pixels belonging to the same altitude, slope, and soil class, within the same 30 arcmin pixel, and in the same country. For crops, livestock, and forest activities, different production systems are parameterized using sectoral biophysical models, such as EPIC for crops, RUMINANT for livestock (Herrero _et al._ , 2013), and G4M for forestry. For this study, the supply side spatial resolution is aggregated to 120 arcmin (about 200 x 200 km at the Equator). The model is calibrated to the year 2000 FAOSTAT activities levels and prices, and is then recursively solved in 10 year time‐steps until 2100.

Production in the model reacts to economic incentives with activities and land use allocation as important aspects of the model responses. Six land cover types are distinguished: cropland, grassland, short rotation tree plantations, managed forest, unmanaged forest and other natural vegetation. Depending on the relative profitability of the individual activities and on the recursivity constraints, the model can switch from one land cover type to another. Comprehensive greenhouse gas accounting for agriculture forestry and other land use is implemented in the model. Detailed description of these accounts and additional background information are provided in Valin _et al._ (2013) and Havlík _et al._ (2014).

EPIC is an important component of the framework for the estimation of climate change impacts. This crop model is used in GLOBIOM to simulate yield associated to each location, management practice and climatic conditions. The model estimates the biophysical and environmental parameters of 18 crops for three different types of management systems (low input rain‐fed, high input rain‐fed and irrigated systems). To predict impacts of climate change, daily climate input data of solar radiation, min and max temperature, precipitation, relative humidity and wind speed are taken as inputs from

> 2 G4M is a spatially explicit global forest dynamics model used to project patterns of deforestation and afforestation based on relative profitability of forestry compared to other land based activities. It can be used as a GLOBIOM module in order to refine estimates of carbon stock losses and carbon sequestration under different land use and carbon pricing policies.

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