## 2 Materials and Methods
### eWUE Model Development  
The monthly values of eWUE were parametrized as a function of biophysical and meteorological variables. The monthly data scale is widely used in studies related to NEE and eWUE [24; 70] due to its ability to provide a comprehensive view of these ecological processes over time. Monthly data reduce the extreme values, allowing researchers to analyze and identify long-term trends in measurement, which is crucial for understanding carbon fluxes and the overall health of ecosystems. To this end, we considered time series of the Normalized Difference Vegetation Index (NDVI) [71] and meteorological variables such as air temperature (Tair), VPD, precipitation (P), and reference evapotranspiration (ETo). NDVI is a widely used indicator of vegetation health and density, calculated from the reflectance values in both near-infrared and red spectral bands captured by remote sensing [72]. Based on NDVI time series from Sentinel-2A and Sentinel-2B (sensor MSI, granule 30 SWJ) and Landsat 8 (sensor OLI, scenes 199-033 and 200-033) satellite images, data were extracted from the WebGIS platform developed by the University of Castilla-La Mancha [73]. Four pixels (10 m resolution) within the study site were selected and averaged monthly to avoid georeferencing errors in the EC tower; this sampling approach, however, remained representative of the footprint area of the flux tower. In Las Tiesas, trees start with an age of only 2 years, whereas in Tarazona, the data begins with 3-year-old trees but with a higher planting density. While Tair, ETo and P were obtained from La Gineta-SIAR [61], vapor pressure deficit (VPD) values were directly measured by the instrumentation placed at the EC tower. In this analysis, a multiple linear regression model was developed to predict the eWUE using the set of variables NDVI, Tair, VPD, P and ETo as independent inputs. The independent variables in the multiple linear regression model for predicting eWUE were chosen based on their relevance to vegetation health and meteorological conditions. NDVI was included for its role in indicating vegetation density, while Tair, VPD, P, and ETo were selected for their direct effects on plant physiology and water use efficiency. These variables were included to offer a comprehensive view of the factors affecting eWUE and were readily accessible. Variables not included were either less relevant or could introduce unnecessary complexity, risking overfitting. The full dataset was divided into randomly selected calibration (75% data) and validation sets (25% data). The approach was calibrated as a multiple linear regression model with the calibration data; following this correlation, the Akaike Information Criterion (AIC) was analyzed [74] using R free software, the function being part of the stats package. The AIC is designed to balance the trade-off between the goodness of fit of a model and its complexity, thereby helping to prevent overfitting. The AIC is a widely employed model selection metric that balances a model's fit to data with its complexity [25; 75; 76]. The absolute value of AIC alone is not greatly informative; its usefulness lies in comparing AIC between different models. Two squared errors were computed, R\({}^{2}\) and R\({}^{2}\) adjusted (R\({}^{2}\) adj), as the latter penalizes the inclusion of unnecessary variables. Subsequently, the model performance was evaluated on the validation data, measuring R\({}^{2}\), Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) [77]. The AIC is a criterion intended to strike a balance between the model's fit to the data and its complexity. In other words, the AIC penalizes more complex models to avoid overfitting. A model that fits the data well but is overly complex might have a higher AIC than a simpler model with a slightly worse fit. The absolute value of AIC alone is not very informative; its usefulness lies in comparing AIC between different models. Meanwhile, R\({}^{2}\) measures the proportion of variability in the dependent variable explained by the model.