## 2 Materials and Methods
### Model Input Specifications and Parameterization for STEPS, SCOPE, and TSEB  
Particular attention is given to the specific inputs of STEPS, SCOPE, and TSEB and their requirements to ensure transparency over the Mediterranean region. For STEPS, incoming solar radiation is first partitioned into direct and diffuse components using latitude, slope, aspect, and elevation data from the HydroSHEDS Digital Elevation Model (DEM). This partitioning is necessary for canopy radiative transfer calculations, which STEPS employs in its empirical scheme to simulate eco-hydrological processes [31]. For the parameterization of soil and surface variables, literature-based ranges are selected to determine soil texture-specific hydraulic properties (wilting point, field capacity, porosity, etc.). The same approach is followed for biological parameters, i.e., the maximum carboxylation capacity (Vcmax), canopy clumping index, precipitation interception, and stomatal conductance for each land cover class (forests, croplands, grasslands, and shrublands).  
The STEPS model simulates daily LAI values (LAIdaily) using its phenology module. It considers daily air temperature and the maximum LAI (LAImax) of the growing season for each vegetation type and applies the classical growing degree days (GDD) concept, where LAImax is a crucial variable for simulating biophysical processes, i.e., photosynthesis, respiration, etc. [31]. STEPS and SCOPE both acquired the high-quality maximum LAI product, MOD15A2H V6. While TSEB acquired the daily LAI product from SEVIRI-MSG ([[https://landsaf.ipma.pt/en/products/vegetation/lai/](https://landsaf.ipma.pt/en/products/vegetation/lai/)]([https://landsaf.ipma.pt/en/products/vegetation/lai/](https://landsaf.ipma.pt/en/products/vegetation/lai/))) accessed on 5 November 2022. Table 2 summarizes the model-specific inputs and model specifications for STEPS, SCOPE, and TSEB.  
To ensure consistency across models, all surface and subsurface parameters were resampled to a fixed 10 km resolution (Table 2). These parameters include the following:  
* LAI;
* Volumetric Soil Moisture Content (VSMC) for SCOPE and STEPS;
* International Soil Reference and Information Centre (ISRIC) SoilGrids containing soil texture and soil depth information for STEPS;
* European Space Agency (ESA) Worldcover 100 m land use/cover for STEPS and SCOPE and GLCNMO-LULC for TSEB.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Variable** & **Dataset** & **Units** & **STEPS** & **TSEB** & **SCOPE** \\ \hline Accumulated Rainfall & ERA5 Total Precipitation & mm & + & - & - \\ \hline Volume of water in soil layer (0–7 cm) & ERA5 Volumetric Soil water content & mm\({}^{3}\) & + & - & + \\ \hline Temperature of air at 2 m above & ERA5 Air Temperature & \({}^{\circ}\)C & + & + & + \\ \hline Pressure (force per unit area) of the & ERA5 Surface Pressure & kPa & + & + & + \\ atmosphere on the surface & ERA5 Windspeed & ms\({}^{-1}\) & + & + & + \\ \hline Relative Humidity & ERA5\_Relative Humidity & \% & - & + & - \\ \hline Atmospheric Vapor Pressure & ERA5\_Atmospheric Vapor Pressure & kPa & - & - & + \\ \hline Hydrologically Conditioned DEM & WWF\_Hydrosheds\_DEM\_1 km & m & + & - & - \\ \hline \hline \end{tabular}  
* indicates used in the model, *- indicates not used in the model and *- indicates not required in this model.  
\end{table}
Table 1: Cont.  
To enhance the accuracy of ET estimations, adjustments were made to the SCOPE and TSEB model outputs. Initial simulations with SCOPE indicated overestimated ET values in dry, arid regions. To address this, additional soil moisture constraints were added from ERA5 data (volumetric soil water content at 0-7 cm depth) to balance the energy budget [38]. For TSEB, gap-filling was carried out for LST, and cloud-contaminated pixels using a ratio of actual ET to ASCE-based reference ET, assuming this ratio remained constant over ten days; its rational method is explained in [36].