# Assimilation of Earth Observation Data Over Cropland and Grassland Sites into a Simple GPP Model
## 3 Methods  
### GPP Model  
The vegetation growth model used in this study is composed by a set of equations similar to that of GRAMI model ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). The model runs at daily time step and is built around the core equation describing the conversion of absorbed light into gross primary production, \(GPP\)([PERSON] et al., 2018):  
\[GPP(\mathrm{i})=\varepsilon_{m}\varepsilon_{\mathrm{ws}}(\mathrm{i})\ FAPAR( \mathrm{i})\ PAR(\mathrm{i}) \tag{1}\]  
where i is the day of the year, \(GPP\) is the daily gross primary production, \(\varepsilon_{m}\) is the maximum light conversion factor (i.e., the light use efficiency coefficient), \(\varepsilon_{\mathrm{ws}}\) is the water stress reduction factor to the light use efficiency, PAR is the photosynthetically active radiation and FAPAR is the fraction of the absorbed PAR. The value of \(\varepsilon_{m}\) for crop and grassland targets is set to 1.7 and 1.1 gC m\({}^{-2}\) d\({}^{-1}\) MJ\({}^{-1}\)  
Figure 1: Location of eddy covariance (EC) sites and period covered by flux measurements. Green cross are for grassland sites whereas orange dots are for cropland sites. respectively. These values were derived from a preliminary optimization procedure against EC data of four sites as described in Section 3.4. FAPAR is computed as a function of LAI by the same RT model used to simulate NDVI to ensure internal consistency (see Section 3.2). PAR is estimated as 0.48 * Global Radiation from ECMWF (in MJ m\({}^{-2}\)) according to [PERSON] and [PERSON] [29]. Despite we do not account for direct effect of temperature on \(\varepsilon_{m}\) with an additional stress reduction factor, temperature plays a role in determining \(\varepsilon_{us}\) and leaf senescence (introduced below). In addition, we assume that no photosynthesis occurs when the mean daily temperature is below the base temperature used for the computation of growing degree days (Equation (4)). A fraction of _GPP_ is used by the plants for respiration, while the remaining net primary production (_NPP_) is used for the growth. In this simplified modelling we neglect temperature, nitrogen and biomass dependency of maintenance respiration and, based on the findings of [PERSON] et al. [30], and we consider respiration proportional to _GPP_. The ratio \(\gamma\) between respiration and _GPP_ was set to 0.25 as in [PERSON] et al. [31]. \[NPP(\mathrm{i})=(1-\gamma)\;GPP(\mathrm{i}) \tag{2}\]  
A fraction of the daily _NPP_ is allocated to leaf tissues according to the following equation:  
\[\Delta LAI(\mathrm{i})=NPP(\mathrm{i})\;Pl(\mathrm{i})\;CF\;SLA-\;LAI_{sen}( \mathrm{i}) \tag{3}\]  
where \(\Delta LAI\) is the daily variation of leaf area index (_LAI_), _Pl_ is the dynamic coefficient of partitioning into leaves, _CF_ is the constant conversion factor from carbon (gC) to dry matter content, _SLA_ is the constant specific leaf area (leaf area per unit weight) and \(LAI_{sen}\) is leaf area that is lost through leaf senescence. _CF_ is set to 1/0.45 as in [PERSON] et al. [32]. _SLA_ (m\({}^{2}\) g\({}^{-1}\)) is subject to optimization (described in Section 3.5) as it is crop- and grassland-type specific and plays a major role in controlling leaf area expansion. Senescence (_LAI_sen) and partitioning into leaves (_Pl_) are modelled using growing degree days (_GDD_), defined as the sum of the following daily quantity from emergence:  
\[\Delta GDD(\mathrm{i})=Max\;[T(\mathrm{i})-Tb,0] \tag{4}\]  
where \(T\) is the mean daily air temperature and Tb is the base temperature. Tb is set to the standard value of 0 \({}^{\circ}\)C for crops and to \(-5\)\({}^{\circ}\)C for grassland according to [PERSON] et al. [33]. Leaf senescence is empirically modelled as proposed by [PERSON] [14] for the GRAMI model. The LAI emerged at time i with _GDD_(i) is removed after (i) growing degree days.