## 2 The BEAM Toolbox and the Land Surface Temperature Processor
### The LST Processor as a BEAM Plug-In
#### 2.2.1 Theoretical Background of the LST Algorithm  
A large number of land surface temperature (LST) and land surface emissivity (LSE) algorithms have already been published ([12; 13]). Many of these algorithms are based on the split-window (SW) or the two-channel (TC) techniques. The SW is based on the differential absorption concept [14], in which the atmospheric effect over the measured signal is corrected using the difference signal in  
Figure 1: BEAM-VISAT overview. two thermal (TIR) bands at two different wavelengths, or by one TIR band on two different view angles, the dual-angle (DA) algorithms. The two types of algorithms depend on the surface emissivity. The retrieval of the emssivity values can be done in many ways ([15; 16; 17]). The approach selected here is based on vegetation indices (VIs) [18] and on classification-based approaches [19]. To allow for near real-time retrievals and to avoid nighttime acquisitions, methods based on day/night pairs are not considered. The proposed algorithm finally selected has the expression [20]:  
\[T_{S}=T_{i}+c_{1}(T_{i}-T_{j})+c_{2}(T_{i}-T_{j})^{2}+c_{0}+(c_{3}+c_{4}W)(1- \varepsilon)+(c_{5}+c_{6}W)\Delta\varepsilon, \tag{1}\]  
where \(T_{s}\) is the LST (in K), \(T_{i}\) and \(T_{j}\) are at-sensor brightness temperatures (in K), \(W\) is the atmospheric water vapor content (in \(gcm^{-2}\)), \(\varepsilon\) is the mean land surface emissivity, LSE: 0.5-(\(\varepsilon_{i}+\varepsilon_{j}\)), and \(\Delta\varepsilon\) is the LSE difference (\(\varepsilon_{i}-\varepsilon_{j}\)). Sub-indices \"\(i\)\" and \"\(j\)\" refer to two different thermal infrared (TIR) bands, thus leading to the SW algorithm, or to one TIR band but two different view angles (e.g., nadir \"\(n\)\" and oblique \"\(o\)\" views), thus leading to the DA algorithm. Coefficients \(c_{0}\) to \(c_{6}\) are obtained from statistical regressions performed over simulated data. This algorithm is physically-based, and it explicitly includes the atmospheric water vapor (\(W\)) content and surface emissivity (LSE). Furthermore, it can easily incorporate external sources of W and LSE. Input of the emissivity value is calculated using the normalized difference vegetation index (NDVI) thresholds method (THM) first established by [18] (Equation (2)). The threshold method is applied on each thermal band (i) because it has a spectral base:  
\[NDVI<NDVIs:\varepsilon_{i}=a_{i}+b_{i}\rho_{rad}, \tag{2}\] \[NDVIs\leq NDVI\leq NDVIv:\varepsilon_{i}=\varepsilon_{is}(1-Pv)+ \varepsilon_{ip}Pv+C_{i},\] \[NDVI>NDVIv:\varepsilon_{i}=0.99,\]  
where \(\rho_{rad}\) is the reflectance at the red band, \(\varepsilon_{s}\) and \(\varepsilon_{v}\) are reference values of surface emissivity for soil and vegetation, respectively, \(C\) is a cavity term for rough surfaces that depends on geometrical factors (and it is neglected for operational purposes or assumed constant; in the present case is assumed to be 0.005 [21]), and \(Pv\) is the fractional vegetation cover, which can be obtained from the scaled NDVI [22]:  
\[Pv=\frac{NDVI-NDVIs}{NDVIv-NDVIs}, \tag{3}\]  
where NDVI is the current value and NDVIs and NDVIv are reference values of NDVI for bare soil and fully vegetated surfaces, respectively. Values of 0.15 for NDVIs and 0.99 for NDVIv are considered representative of global conditions [23]. A simplified version of the NDVI-THM method is selected because it requires reduced computing time and allows contemporary implementation. More details ca be found in Section 2.2.2 and Equations (5) and (6). It has the advantage that whenever improved products of \(W\) and LSE are available, the potential LST product generated with this algorithm can be easily reprocessed to provide a new product version. It is important to highlight again that the scope of this paper is not to provide a detailed description of the atmospheric correction and the cloud screening methodologies. In the SEN4 LT project documentation, there is a review and adaptation of both approaches for potential application on S3.