# Modelling High-Resolution Actual Evapotranspiration through Sentinel-2 and Sentinel-3 Data Fusion
## 2 Materials and Methods
### Input Data Sources
#### 2.3.1 Satellite Data  
The main satellite data inputs come from the Sentinel-2 (both A and B) and Sentinel-3 (A only) satellites. Sentinel-2 and Sentinel-3 were chosen as the primary satellite data sources for this study for a number of reasons. Firstly, as mentioned previously, when treated as a constellation those satellites are able to satisfy the need for temporally dense observations at high spatial resolution and with good radiometric accuracies. Secondly, they are part of the Copernicus programme, meaning that there is a guaranteed long-term continuity of data into the future. Thirdly, the data from those satellites is free and open and will remain so, again due to being part of the Copernicus programme. High-resolution shortwave observations needed to characterise the state of vegetation in the evapotranspiration model as well as to sharpen TIR data were obtained by the MultiSpectral Instrument (MSI) on board of the Sentinel-2A & 2B satellites. MSI acquires reflectance information in 13 spectral bands (with central wavelength ranging from 444 nm to 2202 nm) with a spatial resolution of 10 m, 20 m, or 60 m (depending the spectral band) and global geometric revisit of at least 5 days when both satellites are considered [6]. The MSI sensor has 3 spectral bands in the leaf-pigment sensitive red-edge part of the electromagnetic spectrum and two bands in water-content sensitive shortwave-infrared part of the spectrum, in addition to the more traditional visible and near-infrared bands, which makes it well suited for vegetation mapping and monitoring [69]. For each of the validation sites, all Sentinel-2 images for year 2017 were visually scanned and the ones which were cloud, fog and shadow free in the closest vicinity of the flux towers locations were selected for processing. L1C top of the atmosphere images were converted to bottom-of-atmosphere (BOA) reflectances (L2A) using the Sen2 Cor atmospheric correction processor [70] v2.5.5. BOA reflectance values were then used as input to the Biophysical Processor [71] available in the SNAP software v6.0.1 (step.esa.int--last accessed 28 November 2018) in order to obtain effective values of green Leaf Area Index (LAI), Fractional Vegetation Cover (FVC), Fraction of Absorbed Photosynthetically Active Radiation (FAPAR), Canopy Chlorophyll Content (CCC) and Canopy Water Content (CWC). The outputs of the SNAP Biophysical Processor have been validated in a number of studies, with good performance in herbaceous crops [72; 73] but overestimation of LAI in bare-soil cases and underestimation of LAI in forests [74]. Those inaccuracies could have an impact on the results of this study in semi-arid and forested areas. The fraction of vegetation which is green and transpiring (\(f_{g}\)) was estimated based on [PERSON] et al. [75] (Equation (7)):  
\[f_{g}=FAPAR/FIPAR \tag{7}\]  
where FIPAR is the fraction of photosynthetically active radiation intercepted by green and brown vegetation. FAPAR was obtained from the biophysical processor as described above, while FIPAR was derived iteratively from Equation (8) of [PERSON] and [PERSON] [51]:\[FIPAR=1-\exp\frac{-0.5 PAI}{\cos\theta} \tag{8}\]  
where \(\theta\) is the solar zenith angle at the time of the S2 overpass, and PAI is the plant area index with initial PAI equal to LAI and in subsequent iterations  
\[PAI=LAI/f_{g} \tag{9}\]  
until \(f_{g}\) converges. Two assumptions made in Equation (8) are that all intercepted PAR comes from the solar beams, and that both FAPAR and FIPAR are computed from a canopy with a spherical leaf inclination distribution. Indeed, from the the average leaf angle histogram, from which the training database was built in [PERSON] and Baret (2017), most training cases in the Biophysical processor correspond to a spherical distribution (mode at 60\({}^{\circ}\) leaf angle). Equation (9) was subsequently used within the land surface models to convert LAI, which was assumed to represent green LAI (2017), into PAI.