# Assimilation of Earth Observation Data Over Cropland and Grassland Sites into a Simple GPP Model
## 3 Methods
### Radiative Transfer Model  
The assimilation of EO data into the model is achieved by linking the canopy reflectance RT model PROSAIL5B [16] to the GPP model described in Section 3.1. While the GPP model simulates the temporal trajectory of the leaf area index (LAI), the link with the canopy RT model allows simulating the NDVI that the MODIS sensor would observe for the satellite overpass time. The RT simulation is performed using the actual sun-target-sensor geometry as specified by the MODIS observations. In order to minimize the number of free parameters, all RT parameters are fixed to nominal values except LAI, SLA, and background reflectance. Although the leaf chlorophyll content can exhibit a seasonal cycle affecting GPP, we opted to keep the model simple and we assumed that actual variation in chlorophyll can be represented in the model by LAI variation alone, having the effect of modulating the total canopy chlorophyll content (LAI x leaf chlorophyll content [38]) when the leaf chlorophyll content is fixed. The values used for the fixed parameters are presented in Table 2. Values refer to literature data for green vegetation (e.g., [39; 40]). The fraction of diffuse incoming solar radiation is fixed and was determined by MODTRAN5 [41] simulations for mid-latitude clear sky conditions in summer time.  
The reflectance spectrum of the canopy background needed by the RT model to simulate the top of canopy reflectance is determined as follows. For a given pixel, we first select all original NDVI observations with a value smaller than the 5 th percentile of the entire NDVI historical distributions (i.e., year 2000--time of simulation). Under the assumption that the time series contains NDVI observations acquired when the green grassland or crop cover is minimal or absent, such observations are considered representative of the background reflectance. As this subset of low-NDVI observations may contain unrealistic outliers (low NDVI values due to undetected cloud cover), we subsample it by selecting the five observations showing the minimum difference between the original NDVI and the NDVI temporally smoothed with the Savitzky-Golay filter [42]. In this way, we discard low-NDVI observations that are far from the smoothed temporal profile (i.e., negative spikes) and may be thus due to undetected clouds rather than absence of vegetation. Background reflectance in the seven MODIS bands coming with MxD09A1 products (see Section 2.2) is computed averaging the reflectances of the selected five observations. Finally, as a full spectrum at 1-nm sampling step is needed by the RT model, the MODIS reflectances are fitted using the Price functions for the soil reflectance [43].  
Once the full top of canopy reflectance spectrum (i.e., 400-2500 nm) is simulated with the 1-nm sampling interval used by the RT model, the MODIS relative spectral response functions ([[http://mcast.gsfc.nasa.gov/calibration/parameters](http://mcast.gsfc.nasa.gov/calibration/parameters)]([http://mcast.gsfc.nasa.gov/calibration/parameters](http://mcast.gsfc.nasa.gov/calibration/parameters))) are used to convolve the spectrum into the MODIS bands. The NDVI is then computed from the MODIS-like red and near infrared bands.  
FAPAR used in Equation (1) of the Sim model is computed by PROSAIL5B as the actual instantaneous spectral canopy absorption in the PAR region at 10:00 local solar time. The absorption at this local time is close to the daily integrated value under clear sky condition [44]. The FAPAR value is computed as the weighted average of the spectral canopy absorption in the PAR region (400 to 700 nm). Spectral observations are weighted by their contribution to total incident irradiance at ground level using MODTRAN5 simulations for mid-latitude clear sky conditions in summer time.