# Assimilation of Earth Observation Data Over Cropland and Grassland Sites into a Simple GPP Model
## 3 Methods
### Inversion Set-Up  
Selected model parameters are derived through model inversion [49]. Here we use model-recalibration as assimilation strategy [8; 9] to retrieve the set of model parameters described in Table 3. Recalibration is performed by searching those parameter values that maximize the agreement between the observed MODIS NDVI temporal profile and the simulated one. This is computationally achieved minimizing a cost function defined by the sum of square differences of the two temporal profiles of NDVI. Numerical optimization is performed using Levenberg-Marquardt least-squares constrained minimization (IDL routine MPFIT [50]). Since NDVI may be biased towards low values owing to the presence of undetected clouds, the optimization is adapted to the upper envelope of the observations using an iterative weighting scheme similar to that proposed by [PERSON] et al. [51]. When two growing cycles per solar year are present, they are treated separately.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Units** & **Description** & **First Guess** & **Range** & **Reference** \\ \hline \multirow{3}{*}{DOY0} & \multirow{3}{*}{Day of year} & Day at which the simulation & \multirow{3}{*}{LSP} & \multirow{3}{*}{\(\pm\)60 days} & \multirow{3}{*}{-} \\  & & & the “emergence” date. & & \\ \hline LAI0 & m\({}^{2}\)m\({}^{-2}\) & Leaf area index at DOY0 & 0.02 & 0.01–0.08 & - \\ \hline SLA & m\({}^{2}\)g\({}^{-1}\) & Specific Leaf Area & 0.012 & 0.002–0.025 & [52; 53; 54; 55] \\ \hline \multirow{3}{*}{c} & \multirow{3}{*}{GDD} & Multi-annual & \multirow{3}{*}{250-FG \({}^{*}\) 1.5} & \multirow{3}{*}{-} \\  & & & average of & \\ \cline{1-1} \cline{5-5}  & & & GDD from SOS & \\ \cline{1-1} \cline{5-5}  & & & to TOM & \\ \hline d & - & Leaf lifespan gain Equation (5) & 0.0 & 0–3 & [14] \\ \hline \multirow{3}{*}{Pl\({}_{\text{max}}\)} & \multirow{3}{*}{-} & Maximum leaf partitioning ratio & \multirow{3}{*}{0.3} & \multirow{3}{*}{0.1–0.8} & [56] \\  & & Equation (6) & & & \\ \hline \multirow{3}{*}{GDD\({}_{\text{max}}\)} & \multirow{3}{*}{GDD} & GDD from emergence after & \multirow{3}{*}{Same as parameter c} & \multirow{3}{*}{-} \\  & & which no partitioning to leaves & & \\ \cline{1-1} \cline{5-5}  & & occur Equation (8) & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model parameters subject to optimization. LSP stands for Land Surface Phenology, the satellite-based phenological timings described in Section 3.3. FG stands for first guess.  
The iterative minimization requires setting initial values and boundaries for the model parameters (first guess in Table 3).  
The water stress factor of Equation (9) is defined on precipitation and evapotranspiration and does not obviously take into account that irrigation water might be administrated to both crops and grasses. As irrigation practices cannot be known a priori, we adopted the following strategy. Optimization is performed twice, without and with water limitation according to Equation (9). The run proving the best fit to observed NDVI is retained. The forward model and the inversion procedure are implemented in IDL (Harris Geospatial Solution).