## 2 Materials and Methods
### LUE Model
#### 2.2.3 \(\varepsilon\) Estimation  
The estimation of \(\varepsilon\) is based on the determination of a maximum \(\varepsilon\) value (\(\varepsilon_{\text{max}}\)), which is reduced by environmental parameters/conditions. The value of \(\varepsilon_{\text{max}}\) (gC/MJ) is specific to each land cover and even to each species [45], with variations also depending on the geographical area. In this case, a value of 3 g/MJ was used for xeric shrublands, which is similar to the values for woody cover in semi-arid zones [46, 47], and a value of 2 g/MJ was used for swamps, since the dominant species can be an intermediate value between grasslands [48] and annual crops [49]. To reduce \(\varepsilon_{\text{max}}\) to these maximum values at both sites, two approaches were applied using meteorological variables and a water stress index. \(\varepsilon\) Reduction with Meteorological Variables  
The value for \(\varepsilon_{\text{max}}\) is modified according to the meteorological variables that reduce the efficiency of the system, the daily minimum air temperature (Tmin), and the vapor pressure deficit (VPD) according to Equation (2) [50]. \[\varepsilon=\varepsilon_{\text{max}}\times\text{Tmin\_sc}\times\text{VPD\_sc} \tag{2}\]  
where \(\varepsilon\) is the light use efficiency parameter, \(\varepsilon_{\text{max}}\) is its maximum value defined in the previous section, and Tmin_sc and VPD_sc (dimensionless) are simple linear functions between 0 and 1 derived from the daily values of Tmin and VPD (Figure 2). These linear functions are obtained using threshold values, where the minimum and maximum values for Tmin are 0 and 1 of the scalar Tmin (increasing function), respectively; and the minimum and maximum values for VPD correspond to 1 and 0 of the scalar VPD (decreasing function), respectively. Upper and lower thresholds for both variables were taken from the Biome-Property-Look-Up-Table (BPLUT) [50], using open shrubland cover (\(-8\) and \(8.8\)\({}^{\circ}\)C for Tmin; and 0.65 and 4.8 kPa for VPD) for xeric shrubland grassland cover (\(-8\) and \(12.02\)\({}^{\circ}\)C for Tmin; and 0.65 and 5.3 kPa for VPD) for marshland. Tmin was obtained from the ERA5-Land, 1278 daily aggregated arrays corresponding to the temperature_2m_min dataset. VPD was obtained using Equation (3). \[\text{VPD}=(\text{es}-\text{a}) \tag{3}\]  
where VPD is the vapor pressure deficit (kPa), es is the saturated vapor pressure (kPa) obtained from Equation (4), while ea is the actual vapor pressure (kPa) obtained from Equation (5):  
\[\text{es}=(0.611\times\text{exp}\left((17.27\times\text{Tmed})/(237.3+\text{ Tmed})\right)) \tag{4}\]  
where Tmed is the mean air temperature (\({}^{\circ}\)C) obtained from the ERA5-Land, 1278 daily aggregated arrays corresponding to the temperature_2m dataset. \[\text{ea}=\text{es}\times\text{RH} \tag{5}\]  
where RH is the relative humidity (%) obtained from Equation (6):  
\[\text{RH}=\text{exp}((17.269\times\text{Td})/(273.3+\text{Td})-(17.269\times \text{Tmed})/(237.3+\text{Tmed})) \tag{6}\]  
where Td is the dew point temperature (K) obtained from the ERA5-Land, 1278 daily aggregated arrays corresponding to the dewpoint_temperature_2m dataset. \(\varepsilon\) Reduction with a Water Index  
For this reduction, the Land Surface Water Index (LSWI) [51] (Equation (3)) was used as a water availability index. This dimensionless index was previously applied to evaluate moisture content in vegetation as well as to evaluate soils associated with humidity in semi-arid ecosystems [52]. It is computed using Sentinel-2 bands B8 (near infrared, NIR: 835.1 nm for S2A, 833 nm for S2B) and B12 (shortwave infrared 2, SWIR: 2202.4 nm for S2A, 2185.7 nm for S2B) according to Equation (7). \[\text{LSWI}=(\text{B8}-\text{B12})/(\text{B8}+\text{B12}) \tag{7}\]  
where B8 and B12 are NIR and SWIR2 bands from Sentinel-2.