# Modelling High-Resolution Actual Evapotranspiration through Sentinel-2 and Sentinel-3 Data Fusion
###### Abstract
The disaggregation was shown to improve ET model skill when compared with outputs produced at either coarse or fine resolution alone [4; 23; 24]. The sharpened \(T_{rad}\) can be used as input to land-surface energy flux models. The latent heat flux \(\lambda E\) (or energy used for ET) can be estimated as the residual of the surface energy budget, using estimates of the net radiation (R\({}_{n}\)), soil heat flux (G) and sensible heat flux (H). The thermal-based ET models were originally formulated for computing H, which is governed by the bulk resistance equation for heat transfer [25], and is driven by the gradient between an ensemble surface temperature, called the \"aerodynamic surface temperature\" (\(T_{0}\)), and the surface layer air temperature. Besides of the estimation of that surface-to-air temperature gradient, the estimation of H requires the modelling of an aerodynamic resistance term, which can be viewed as a simplification of the complex turbulent transport of heat, momentum and water vapour, by using a similarity with [PERSON]'s law for electric transport. These resistances therefore represent how efficiently a scalar (heat, momentum or water vapour) is transported from one point to another following a gradient (i.e., vertical differences of temperature and/or vapour pressure). Several formulations and/or parametrizations have been proposed to describe these turbulent transport processes but generally they include variables related to surface aerodynamic roughness, wind speed as well as wind attenuation through the canopy, and atmospheric stability [26]. The challenge in resistance energy balance models is that \(T_{0}\) cannot be directly estimated by remote sensing [27; 28]. Hence, remote sensing ET models differ from each other on how the existing difference between the radiometric temperature (\(T_{rad}\)) observed by satellite sensors and \(T_{0}\) is considered. Single-source or bulk transfer schemes for modelling H treat soil and canopy as a single flux source and often employ an additional resistance term (\(R_{AH}\), usually dependent on the Stanton number \(kB^{-1}\)) because heat transport is less efficient than momentum transport from land surface (see e.g., [PERSON] [29] or [PERSON] et al. [30]). Appropriately calibrated, one-source energy balance (OSEB) models have shown satisfactory estimates of surface energy fluxes in heterogeneous landscapes [31; 32; 33; 34]. However, due to the difficulty in robustly and parsimoniously parametrizing \(R_{AH}\) for OSEB schemes at different landscapes, climates, and observational configurations [35], the two-source energy balance (TSEB) modelling approach was developed [36]. TSEB models partition the surface energy fluxes and the radiometric temperature between nominal soil and canopy sources, and include a more physical representation of processes related to \(T_{rad}\) and \(T_{0}\) without requiring any additional input information beyond that needed by single-source models using more sophisticated \(kB^{-1}\) parametrizing. However, because direct measurements of canopy (\(T_{C}\)) and soil (\(T_{S}\)) temperatures rarely are available, in most applications these component temperatures are derived from a measurement of the bulk surface radiometric temperature \(T_{rad}\). Partitioning of \(T_{rad}\) between \(T_{C}\) and \(T_{S}\) requires some assumptions related to the evaporative efficiency of soil or canopy [36; 37; 38]. Finally, like all remote sensing retrievals, satellite radiometric temperature is prone to uncertainty due to sensor noise, surface emissivity and atmospheric effects. To overcome this issue in ET estimation, several methods have been proposed based on either contextual models [39; 40; 41], by constraining the ET range between hot (no ET) and cold (potential ET) pixels [31; 32], or using time-differenced morning temperature rise [42; 43]. Regarding the contextual methods, all of them require homogeneous forcing and coupling between land surface/atmosphere which is a disadvantage when applied at large scales.