## 2 Materials and Methods
### Methods
#### 2.3.3 Time Series of Vegetation Index  
The filtered and masked Sentinel-2 images were post-processed to calculate multiple VIs. Table 1 lists the VIs employed in this research together with their equations. In total eight VIs were computed per image and selected based on a literature review of GPP modeling for different ecosystem types (Table A1). Those VIs can be divided into two major classes, (i) greenness-sensitive VIs ((Normalized Difference Vegetation Index  
Figure 4: Climatological footprint of 2020 (**left image**) and 2021 (**right image**).  
(NDVI), Enhanced Vegetation Index (EVI), Two-bands Enhanced Vegetation Index (EVI-2), Red-edge Index (CLr), Modified Normalized Difference Vegetation Index (MNDVI)), and (b) water-sensitive VIs (the Modified Normalized Difference Water Index (MNDWI), Land Surface Water Index (LSWI), and Normalized Difference Infrared Index (NDII)). At first, we calculated the VI for each region within the climatological footprint, then we averaged them by a scaling factor. Finally, the total VI was computed as the sum of the VIs (Equation (2)):  
\[\text{VI}=\sum_{\text{j}=1}^{\text{k}}\left[\text{w}_{\text{j}}\times\sum_{ \text{i}=1}^{\text{n}}\text{VI}_{\text{i}}\right], \tag{2}\]  
where i is the number of pixels, j is the number of regions and \(\text{w}_{\text{j}}\) is the weight of the j region calculated as (Equation (3)):  
\[\text{w}_{\text{j}}=\frac{\text{OCL}_{\text{j}}-\text{ICL}_{\text{j}}}{\text{ n}_{\text{i}}} \tag{3}\]  
\(\text{OCLCL}_{\text{j}}\) and \(\text{ICLCL}_{\text{j}}\) being the outside and inner contour lines of the region j, respectively. With our approach, the weight is a constant value per region. This is a simplification of [PERSON] et al.'s approach [25] that reduces the computational time of the calculation of the VIs. For our study, we computed five regions within the climatological footprint, each of them accounting for 20% of the NEE measured at the Duque Fuente flux tower. Finally, we used the Akima [66] fitting algorithms to obtain a continuous time series. Fitting algorithms were not implemented as we addressed the noise in the time series through the filtering and masking processes of the satellite images. Figure 5 summarizes the processing chain applied on the Sentinel-2 images to obtain the VIs time series (pre-processing steps have been described in Section 2.2.1).  
Figure 5: Schematization of the processing chain applied on the Sentinel-2 images to obtain the VIs time series. At first, S2 L2A images (with orthorectification and atmospheric correction) are collected and filtered by cloud coverage (<30%). Then, pixels are filtered using (i) the supplementary band QA60 to mask the clouds; (ii) the SCL band to select pixels classified as vegetation, soil and water and (iii) a water mask to remove flooded pixels without standing vegetation (MNDVI < 0.05). Finally, the VI is calculated for each pixel within the climatological footprint, multiplied by their contribution weight and summed to obtain the final VI, a single value of VI per image per day. The Akima fitting algorithm is then applied to fill in the gaps and obtain a continuous time series.