# Modelling High-Resolution Actual Evapotranspiration through Sentinel-2 and Sentinel-3 Data Fusion
## 2 Materials and Methods
### Description of ET Models  
The energy balance can be expressed as (1)  
\[R_{n}\approx G+H+\lambda E \tag{1}\]  
where net radiation \(R_{n}\) is a key element in the energy budget of the land surface as it determines the available energy that the land utilises for water evapotranspiration (latent heat flux, \(\lambda E\)) and for heating up the overlying air layer (sensible heat flux, \(H\)). Equation (1) assumes that other energy terms (heat advection, heat storage in the canopy layer, and energy for photosynthesis) are negligible. Since ET is the combined process of soil evaporation and canopy transpiration, \(R_{n}\) can be also be partitioned into soil (\(R_{n,S}\)) and canopy net radiation (\(R_{n,C}\)), with both sensible and latent heat flux also partitioned between soil (i.e., evaporation process) and canopy (transpiration).  
Using remote sensing data to derive \(R_{n}\) has proven to be a sound alternative to ground-based measurements of both shortwave and longwave net radiation. Different approaches have been proposed to estimate surface albedo, ranging from empirical relationships between ground measured albedo and the different reflective bands in satellite [45] to more physically based methods relying on modeling the surface anisotropic effects [46; 47]. Indeed, one of the major challenges when estimating albedo with satellite remote sensing data is that such sensors typically measure the outgoing radiance at a given direction while the estimation of albedo needs to account for the outgoing radiance in all the directions of the hemisphere [48; 49]. Methods based on the modelling of those bidirectional effects have proven to be effective to overcome this challenge. In this study, we use a method for retrieving soil and canopy shortwave net radiation, proposed by [PERSON] and [PERSON] [50], based on the different spectral behaviour of soil and vegetation for the photosynthetically active radiation (PAR) and near infrared (NIR) regions of the spectrum. Such approach is based on the radiative transfer model (RTM) described in [PERSON] and [PERSON] [51] to obtain estimates of soil and canopy albedo as well as canopy transmittance in the PAR and NIR. This approach requires as inputs Leaf Area Index and leaf inclination distribution [52], the different bihemispherical reflectances and transmittances of soil and a single leaf, and the proportion of diffuse irradiance. However, this approach assumes homogeneous canopies and it requires some corrections when dealing with clumped canopies [53], which were also used in this study.  
On the other hand, longwave net radiation is primarily driven by the thermal radiation emitted by the surface, which depends on surface emissivity and skin temperature following the Stefan-Boltzmanlaw. Besides, [PERSON]'s law can be applied to derive the atmospheric longwave radiation that is absorbed by the surface. When running OSEB models (i.e., METRIC), only those two components are taken into account. However, when using TSEB models (i.e., TSEB-PT and ESVEP), surface anisotropy can also be accounted for when estimating the net longwave radiation, considering that leaves and soil have different temperatures and hence emit different amounts of thermal radiation [50].  
Soil heat flux \(G\) is usually assumed to be a ratio of the soil net radiation. [PERSON] et al. [54], [PERSON] et al. [31] suggested that \(G\) is ca. 35% of net radiation of the soil around midday hours and this is the approach used in this study by TSEB models. Since net radiation of the soil cannot be computed when using OSEB models, a specific equation suggested by [PERSON] et al. [31] is used instead.  
In all three evaluated models, \(\lambda E\) is estimated as residual of Equation (1). The main difference between the models is in the way in which \(H\) is calculated, as briefly described in the sections below.