## 2 Materials and Methods  
### Model Description  
The ORCHIDEE land surface model deals with carbon, water and energy exchanges between the atmosphere and biosphere [42]. The vegetation is defined as a mosaic of 12 plant functional types (PFTs) based on morphology (tree or grass), leaf type (needle-leaf or broad-leaf), phenology (evergreen, summer-green or rain-green), photosynthetic pathway for crops and grasses (C3 and C4) and climatic regions (boreal, temperate and tropical). African vegetation includes 7 PFTs: C3 and C4 grass, C3 and C4 agriculture, evergreen and rain-green tropical broadleaved and temperate broadleaved evergreen trees. The GPP function that describes carbon assimilation, is based on the leaf scale equations for C3 and C4 PFTs from Farquhar and Collatz respectively [43, 44]. The scaling of GPP per layer within the canopy assumes an exponential attenuation of light following a big-leaf approximation. The foliage density (LAI) and plant water stress are prognostic and can impact GPP, carbon allocation, leaf age and senescence [42]. The variable fAPAR can be diagnosed from LAI output using the Ruimy formulation [45]: \(fAPAR=0.95\times(1-\exp(-0.5\times LAI))\).  
The energy exchanges (transport of radiation and heat) and water balance between the vegetation-soil-atmosphere are described in [46, 47]. Total ET is the sum of five components including evaporation of water intercepted by the canopy, transpiration by the vegetation and bare soil evaporation. The two other components of total ET in ORCHIDEE are snow sublimation (negligible in Africa) and evaporation from floodplains (river routing and floodplain hydrology scheme is not activated in this study). To simplify the transpiration parameterization, as well as for photosynthesis and light competition, ORCHIDEE does not account for fluxes from, and competition with, understory vegetation [42]. Bare soil evaporation is controlled by soil moisture and, thus, depends on the soil hydrology parameterization of ORCHIDEE. Transpiration is governed by the ability of the roots to extract water from the soil, assuming a PFT-dependent exponential root profile [47]. Simulated water stress from soil moisture availability influences photosynthesis and stomatal conductance through a scaling factor that is associated with relative soil moisture when the root zone relative soil moisture, _i.e._, volumetric soil moisture normalized by the difference between field capacity and wilting point, falls below a threshold value [48].  
The default ORCHIDEE hydrological scheme (hereafter, the two-layer version) is based on a simple two-layer bucket-type model [46]. The soil upper layer varies according to the water availability, and the deep soil layer is filled from top to bottom with precipitation. When ET is larger than precipitation, water is removed from the upper layer until it dries out, leaving only the deep soil layer. To analyze the role of a more realistic soil hydrology scheme on LUE and iWUE* trends (_i.e._, fAPAR, GPP and ET), we also use a second version of ORCHIDEE model with a soil diffusion model of 11 layers [49, 50, 51]. The 11-layer soil scheme represents a vertical soil flow based on physical processes from the Fokker-Planck equation that resolves water diffusion in non-saturated conditions from the Richards equation [52]. The soil physics in the 11-layer version is based on the CWRR (Center for Water Resources Research) model [53, 54]. The vertical discretization is not uniform: the grid being finer near the surface (the 3 topmost layers being 1 centimeter apart) where the soil moisture mostly varies, in order to represent the rapid exchanges of soil moisture near the surface [49]. Note that, in this study, the soil depth is uniformly fixed at 2 m for both ORCHIDEE versions.