## 3 Methods
### PROSAILH-BGC Description  
BIOME-BGC was coupled with the leaf and canopy radiative transfer (RT) models named PROSPECT and SAILH [19], respectively, resulting in the coupled model referred to hereafter as PROSAILH-BGC. The objectives of the coupling were twofold: to improve the BIOME-BGC description of the canopy radiation regime and to simulate the NDVI as a function of LAI and overpass characteristics (sensor and sun geometry) of MODIS observations. BIOME-BGC computes net shortwave radiation using a constant surface albedo during the year. This assumption is violated in deciduous ecosystems where the albedo is closely related to foliar phenology [41]. Moreover, the radiation transmitted and absorbed by the canopy is modeled according to Lambert-Beer's law. The radiation absorbed by the canopy is therefore a function of the incoming PAR radiation, the LAI and of biome-specific canopy light extinction coefficients. The Lambert-Beer formulation neglects multiple scattering in the vegetated medium. To overcome such limitations we replaced the RT subroutine of the model with the PROSAILH model. PROSAILH is a combination of two models: PROSPECT [42], which describes leaf optical properties and SAILH [43], which computes top-of-the-canopy spectral bidirectional reflectance. PROSPECT is a plate model that simulates reflectance and transmittance of a leaf as a function of four state variables: leaf structure parameter, chlorophyll a+b concentration, water content and leaf mass area. SAILH is a one-dimensional bidirectional turbid medium RT model that simulates canopy bidirectional reflectance for a given sun-sensor geometry, canopy background reflectance, LAI, mean leaf inclination angle, hot-spot-size parameter and background brightness factor. The choice of SAILH is justified by its theoretical simplicity and advantages for application purposes. Nevertheless, this model assumes a dense canopy, which may not be the case with young poplar plantations. Sparse canopies in fact originate shadowing (between crowns and on the soil background) which are not simulated by the RT model. Shadowing effects were minimized by working with the vegetation optical index NDVI. Moreover, it must be noted that when using MODIS data at 250 m spatial resolution (so-called medium resolution) the 1D approach can accurately represent the reflected, transmitted and absorbed fraction of vertical fluxes, irrespective of local variability exhibited by the canopy at a finer spatial scale [18]. On the contrary, the retrieved variables (e.g. LAI) are the domain-average effective variables instead of the actual ones. We believe that this is not a major problem because these effective variables are used to feed BIOME-BGC, which is indeed a simplification of the real world, using effective variables as well. The PROSAILH requires a total of eight input parameters (Table 1). LAI was provided with the daily step by BIOME-BGC, while the other input parameters were kept constant and parameterized according to a previous study on poplar plantations [17]. Fixing leaf parameters to constant values represented a simplification of the RT problem because of leaf age and darkening during the growing season. Another simplification that was applied regards the fact that our modelling approach does not include the understory vegetation that may be present in poplar plantations. Both natural processes (changes of leaf optical properties, understory growth) are to some extent picked up by NDVI, but neglected in our modelling approach. The PROSAILH-BGC flowchart is reported in Figure 1. Daily LAI, simulated by the BIOME-BGC, is used as input for the PROSAILH which simulates NDVI, daily shortwave radiation, PAR, PAR absorbed by the canopy and site albedo. These variables are then forced into the BIOME-BGC and used for daily simulations.