## Methods
### GPP Models: Definition, Inversion and Analysis  
According to [PERSON] [2], _GPP_ results from the product of the incoming _PAR_, the fraction of it absorbed by green vegetation (\(f_{\text{PAR}}\)) and the Light Use Efficiency (\(\epsilon\)) (Equation (3)). Optically-based _GPP_ predictive models can be developed using SVI as proxies of the parameters in the [PERSON]'s model [4]. \[GPP=PAR\cdot f_{PAR\cdot\epsilon}, \tag{3}\]  
In this work, we fit and test the performance of four different _GPP_ models considering different degrees of complexity, and of spatial and temporal mismatch between optical and EC observations. The first three models (MOD1-MOD3) make use of _PAR_ and optical information and have already been tested by several authors using field spectroscopy data [56; 32; 57]. These models replace [PERSON]'s equation parameters by linear functions of SVI. We used the Normalized Difference Vegetation Index (_NDVI_) [58] (Equation (4)) and Photochemical Reflectance Index (_PRI_) [59] (Equation (5)) to represent \(f_{\text{PAR}}\) and \(\epsilon\) respectively. Moreover, we assessed the performance of different _PRI_ formulations designed to minimize the effect of vegetation structure and pigment contents in the estimation of \(\varepsilon\). Specifically, we tested \(PRI_{515}\) (Equation (6)) [60] which was found less sensitive to canopy structure than \(PRI\); the Normalized \(PRI\) (\(PRI_{\text{nom}}\), Equation (7)) [61] which was related to water stress and normalizes for different canopy chlorophyll concentrations; and the Calibrated \(PRI\) (\(CPRI\), Equation (8)) [62] also normalized by pigment content. Notice that all \(PRI\)-based indices are formulated in such a way that they are positively related with \(\varepsilon\). \[NDVI=\frac{HDRF_{800}\ -\ \ HDRF_{680}}{HDRF_{800}\ +\ \ HDRF_{680}}, \tag{4}\]  
\[PRI=\frac{HDRF_{531}\ -\ \ HDRF_{570}}{HDRF_{531}\ +\ \ HDRF_{570}}, \tag{5}\]  
\[PRI_{515}=\frac{HDRF_{531}\ -\ HDRF_{515}}{HDRF_{531}\ +\ \ HDRF_{515}}, \tag{6}\]  
\[PRI_{norm}=\frac{PRI}{RUVI\cdot\left(\frac{HDRF_{700}}{HDRF_{670}}\right)}\, \tag{7}\]  
where \(RDVI\) is the Renormalized Difference Vegetation Index [63]. \[CPRI=PRI-(0.645*\ln(mNDVI_{705})+0.0688)\ \, \tag{8}\]  
where \(mNDVI_{705}\) is the Red-Edge Normalized Difference Vegetation Index [64]. The fourth model (MOD4) is based on the algorithm of the MODerate-resolution Imaging Spectroradiometer (MODIS) \(GPP\) product (MOD17A2) [65]. MOD4 models the \(\varepsilon\) parameter as the product of the maximum \(\varepsilon\) (\(\varepsilon_{\text{max}}\)) and a scalar ranging between 0 and 1 that expresses photosynthetic down-regulation; the last is formulated combining linear ramp functions of vapor pressure deficit (\(VPD\)) and air temperature (\(T_{\text{air}}\)) (Equation (9)). \[\varepsilon=\ \varepsilon_{max}\cdot\left(\frac{VPD_{\text{max}}-VPD}{VPD_{ \text{max}}-VPD_{\text{min}}}\right)\cdot\left(\frac{T_{\text{air}}-T_{\text {MINmin}}}{T_{\text{MINmax}}-T_{\text{MINmin}}}\right), \tag{9}\]  
where \(VPD_{\text{max}}\) and \(T_{\text{MINmin}}\) are the maximum \(VPD\) and the minimum \(T_{\text{air}}\) values at which photosynthesis is completely down-regulated (\(\varepsilon=0\)). Complementarily, \(VPD_{\text{min}}\) and \(T_{\text{MINmax}}\) are the minimum \(VPD\) and the minimum \(T_{\text{air}}\) at which photosynthesis is not regulated (\(\varepsilon=\varepsilon_{\text{max}}\)). In addition, \(f_{PAR}\) is described by the Beer's law (Equation (10)) depending on an extinction coefficient (\(k\)) and the Leaf Area Index (\(LAI\)) [66]; the second was modeled using a linear function of \(NDVI\) (Table 3). As the MOD17A2, we assume \(k=0.5\)[65]. \[f_{PAR}=1-e^{(-k\ LAI)}\, \tag{10}\]  
Table 2 shows the parametric equations of the models fit against observed half-hourly footprint-weighted SVI, \(GPP_{\text{hh}}\) and micro-meteorological data (\(PAR\), \(VPD\) and/or \(T_{\text{air}}\)). \(PAR\) was assumed to be the 45% of \(R_{\text{g}}\)[65] measured in the EC towers.