# Modelling High-Resolution Actual Evapotranspiration through Sentinel-2 and Sentinel-3 Data Fusion
## 2 Materials and Methods
### Thermal Data Sharpening Approach  
The thermal data sharpening approach used in this study is based on ensemble of modified decision trees. The basic scheme of the method (Figure 1) is based on [PERSON] et al. [8] and has been previously applied by [PERSON] and [PERSON] [4] to sharpen thermal data to be used as input to evapotranspiration models. Each S3 scene is matched with an S2 scene acquired at most ten days before or after the S3 acquisition and the regression model used for sharpening is derived specifically for each scene pair.  
Briefly, the atmospherically corrected Sentinel-2 shortwave data (all the 10 m and 20 m spectral bands) with a spatial resolution of 20 m is resampled to match the pixel sampling of the SLSTR sensor (around 1 km spatial resolution). Concurrently, the SRTM DEM is used to derive slope and aspect maps which, together with S3 overpass time, are used to estimate the solar irradiance incident angle of a flat tilted surface. The DEM and the solar angle maps are also resampled to the SLSTR resolution. A multivariate regression model is then trained with the three resampled datasets used as predictors and the \(T_{rad}\) used as the dependent variable. The selection of training samples is performed automatically by estimating the coefficient of variation (CV) of all the high-resolution pixels falling within one low-resolution pixel and selecting 80% of pixels with lowest CV. The regression model is based on bagging ensemble [85] of decision trees. The decision trees are additionally modified such that all samples within a regression tree leaf node are fitted with a multivariate linear model, as proposed by [8].  
The regression models are trained on the whole S2 tile (100 km by 100 km) as well as on subsets of 30 by 30 S3 pixels in a moving window fashion. Once they are trained they are also applied on the whole  
Figure 1: General thermal sharpening workflow. Explanatory variables include both shortwave bands as well any other ancillary explanatory variable, such as elevation, land cover type or exposure. Model could be any regression model, such as multivariate linear regression or machine learning techniques.  
scene and on each window. The bias between the predicted high-resolution \(T_{rad}\) pixels aggregated to the low-resolution and the original low-resolution \(T_{rad}\) is calculated and the outputs of the whole-scene and moving-window regressions are combined based on a weight inversely proportional to the bias [8]. Finally, the \(T_{rad}\) predicted by the regression model is corrected by comparing the emitted longwave radiance of the sharpened fine \(T_{rad}\) versus the original coarse \(T_{rad}\). A bias-corrected \(T_{rad}\) is therefore re-calculated by adding an offset all fine scale pixels falling within coarse scale pixel in order to remove any residual bias. This is done to ensure the conservation of energy between the two thermal images with different spatial resolutions [8]. The output of the sharpening is a 20 m representation of the LST.  
This image sharpening approach relies on the direct or indirect relationship that different regions of the shortwave spectrum have with the radiometric temperature and/or the ET process. For instance the temperature of denser canopies, with higher contrast between visible and near-infrared bands, is lower than the temperature of bare soils [86; 87]. In addition, surfaces with higher water content (i.e., larger absorption in the short-wave infrared) have a larger evaporative capability and hence lower temperature [88]. Likewise, higher chlorophyll concentrations (i.e., larger absorption in the red and red-edge regions) might lead to higher light and water use efficiency and hence lower temperatures. The information contained in the DEM (i.e., the altitude and solar illumination conditions) also has a direct relationship with radiometric temperature, with sunlit areas having higher temperatures than shaded ones and lower altitude surfaces having higher temperatures than higher altitude surfaces.