## 2 Materials and Methods  
### SURFEX Model and ISBA-A-gs Scheme  
In the SURFEX system, each surface grid point is separated into 4 different tiles: nature, sea, lake, and town. The model handles each tile independently. In our work, only the nature tile was treated, and was further divided into 12 patches according to the vegetation or surface type: bare soil, rock, permanent snow, deciduous tree, coniferous trees, broadleaf evergreen tree, C3 crops, C4 crops, irrigated crops, grassland, parks, and gardens. The model solves the prognostic equations for soil moisture and temperature and calculates the surface fluxes separately for the different patches. Each patch uses the same atmospheric forcing (air temperature, humidity, wind speed, downward long- and shortwave radiation, pressure, precipitation), but the parameter settings are different and independent of each other. The resulting surface fluxes (momentum, sensible- and latent heat) are averaged according to the area fraction of the patches and returned to the atmosphere. Surface parameters are defined by physiographic databases: GTOPO30 for orography, ECOCLIMAP-II for surface covers [23], and FAO for soil texture. The dominant ecosystems in our domain are C3 crops (27%), grassland (21%), deciduous trees (19%), C4 crops (15%), bare soil (8%), and a coniferous tree (6%).  
The nature tile is simulated with the ISBA scheme [24; 25], which computes the exchanges of energy and water between the continuum soil-vegetation-snow and the atmosphere above. In ISBA, a 3-layer soil scheme is used (surface 0-1 cm, root zone 0-2 m, and deep soil 2-3 m). The soil prognostic variables (temperature, water content, and intercepted water content) are calculated using the force-restore method [25]. The force terms for temperature are radiation, latent and sensible heat flux. The restore term relaxes the temperature to the mean soil temperature. The force terms for soil water content are precipitation and evaporation. The restoring term describes how the system reaches equilibrium.  
A more recent version of the model named ISBA-A-gs [26; 27; 28; 29] accounts for a simplified photosynthesis model where the evaporation is controlled by the aperture of the stomata and this mechanism regulates the balance between the transpiration and the assimilation of CO\({}_{2}\). The model is suitable for describing the evolution of the vegetation because biomass is a prognostic variable. The growing of vegetation is due to photosynthesis (CO\({}_{2}\) assimilation) while its decrease is due to soil moisture stress or senescence. The model considers the soil moisture stress in photosynthesis [28]. Plants can have two strategies to the stress: a drought avoiding and a drought tolerant strategy. The growth of the biomass is proportional to the daily net assimilated CO\({}_{2}\), while the decrease is described by an exponential function.  
One of the carbon-fluxes, GPP (Gross Primary Production), is the assimilated CO\({}_{2}\) by the plants. Photosynthesis is first calculated at the leaf scale. The sensitivity of the plant to the specific humidity of the air is also included in the calculations. The net assimilation is integrated over the canopy, and GPP is calculated as the sum of the total assimilation and the dark respiration. NEE is the net CO\({}_{2}\) flux of the ecosystem.