# Modelling High-Resolution Actual Evapotranspiration through Sentinel-2 and Sentinel-3 Data Fusion
###### Abstract
In this study we focus on different, but possibly complementary, approaches: empirical and semi-empirical methods that exploit relationships between shortwave bands and thermal or ET data (hereinafter called image sharpening methods); and physically-based ET downscaling methods (hereinafter called ET disaggregation). Thermal image sharpening uses information from the thermal and shortwave images themselves to calibrate empirical or semi-empirical models. Those models relate coarse resolution \(T_{rad}\) (or ET) with coarse resolution (or fine resolution aggregated to coarse resolution) shortwave bands, and then apply the calibrated model to the fine scale shortwave image, producing either a sharpened \(T_{rad}\), or directly an ET product. One of the first attempts to sharpen \(T_{rad}\) was TsHARP [11], who tested different regression models between \(T_{rad}\) and NDVI. Since then, TsHARP has been utilised as reference method for developing and testing other sharpening methods [8; 12; 13]. The Data Mining Sharpening (DMS) approach [8] used local and global regression trees between reflective bands and \(T_{rad}\) of homogeneous samples at coarse scale (based on coefficient of variation threshold). Residual analysis was performed to ensure energy conservation (based on emitted radiances) between original resolution and sharpened images. To avoid overfitting of regression trees such as in DMS the use of random forests was proposed instead [14]. Following with the machine learning algorithms, [PERSON] et al. [15] used an Artificial Neural Network with Genetic Algorithm and Self-Organizing Feature Mapping trained with different land surface parameters for each land cover class (vegetation, bare soil, urban and water). A different approach used an unmixing method to derive brightness temperature and emissivity at fine scale [16]. The unmixed brightness temperature and emissivity were then the inputs to a generalized split-window algorithm to retrieve fine resolution \(T_{rad}\). The use of a contextual algorithm can also be applied in sharpening, such as is the case of DISPATCH-LST (DISaggregation based on Physical And Theoretical scale CHange) by [PERSON] et al. [7] who used shortwave information on fractional vegetation cover and fractional photosynthetically active vegetation cover in contextual scatterplots of fractional green vegetation cover versus \(T_{rad}\) and albedo versus \(T_{rad}\) to define minimum and maximum soil and canopy endmember temperatures. Finally, two or more different methods can be used together and combined through weighted averaging, such as in [PERSON] et al. [17], who combined TsHARP and a Thin Plate Spline interpolation by weighting their corresponding residuals. Besides of the fact that all methods described above can be used as well to sharpen ET, other studies have already suggested methods to directly downscale coarse scale ET using shortwave data [18; 19; 20; 21]. In any case, shortwave images provide limited information related to some surface energy balance processes, such as turbulent transport, soil moisture, and meteorological forcing. Therefore ancillary variables could be included in \(T_{rad}\) or ET sharpening such as land cover maps (to account for different aerodynamic roughness), local meteorology, or surface geometry [22]. A previous study [4] found that using a \"disaggregation\" approach [10; 23] significantly enhanced the accuracy of turbulent fluxes derived with sharpened \(T_{rad}\). That approach ensures spatial consistency between fluxes derived at fine and coarse spatial scales by first estimating them at the coarse scale at which the thermal observations were acquired. In the following step, the low-resolution air temperature is varied to adjust the flux estimates for all high-resolution pixels falling within one low-resolution pixel. This is repeated until a consistency between the two scales is obtained. This approach assumes that since the coarse scale estimates are derived with \(T_{rad}\) at original spatial resolution they are of higher accuracy.