## 2 The BEAM Toolbox and the Land Surface Temperature Processor
### The LST Processor as a BEAM Plug-In
#### 2.2.2 Description of the LST Processor in BEAM
Therefore, the underlying algorithm is recursive and takes as input TOA reflectance data for the solar reflective AATSR bands at both nadir and backward views (resulting in a total of eight channels), and the 14 MERIS bands at all non-absorbing \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Name** & **Unit** \\ \hline \(F_{0}\) & Solar irradiance at TOA & \(Wm^{-2}nm^{-1}\) \\ \(L_{0}\) & Radiance at TOA & \(Wm^{-2}sr^{-1}nm^{-1}\) \\ \(\rho_{0}\) & Reflectance at TOA & \(dl\) \\ \(\theta_{s}\) & Solar zenith angle & rad \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variables of Equation (4). Figure 3: Logical flow of the L1b product collocation. channels (excluding O2 absorption band). All of these bands are available from the cloud screening output product described in the previous paragraph. SDRs for all input channels are calculated using look-up tables (LUTs). The SDRs depend on initial aerosol parameters, sun-sensor geometry, and surface pressure. This atmospheric correction retrieval scheme is illustrated in Figure 4.  
The output of the algorithm are aerosol optical depth (AOD) at a reference waveband (550 nm) Angstrom exponent (an exponent that expresses the spectral dependence of aerosol optical thickness (\(\tau\)) with the wavelength of incident light (\(\lambda\)). The spectral dependence of aerosol optical thickness can be approximated (depending on size distribution) by \(\tau_{a}=\beta\lambda^{a}\), where \(\alpha\) is Angstrom exponent (\(\beta\) = aerosol optical thickness at 1 \(\upmu\)m)), an estimate of the aerosol model, and atmospherically corrected surface reflectances (SDRs) for all bands used. Moreover, an error metric is provided where a low value of this metric corresponds to a set of surface reflectances (and hence atmospheric profile) that is realistic. Consequently, the algorithm needs to be applied recursively until an optimal aerosol/SDR solution is retrieved. However, although aerosol parameters and SDRs are available as output at the same time, the retrieval is in practice split into an aerosol and SDR part for performance reasons. As the spatial variation of aerosol in the atmosphere is generally much lower than the variation of the reflectances, the iterative retrieval scheme is first applied on a coarser grid, keeping just the optimal aerosol result. In return, this result is downscaled to the original resolution, and the algorithm is applied just one more time to derive the corresponding SDR result. For the final LST retrieval, only these SDRs will be used, and the aerosol quantities are not explicitly needed. The SDR result product contains all the flag bands, the \"latitude\" and \"longitude\" tie point grids, and the AATSR brightness temperatures  
Figure 4: Logical flow of the retrieval of surface reflectances and aerosol properties. copied from the input product, and as additional bands the SDRs for MERIS wavelengths 620 nm and 753 nm, and the SDRs for AATSR nadir/forward at wavelengths 555 nm and 659 nm (Table 2). In the SEN4 LST processor realization, the SDR product serves as final result of the first major processor module (\"SEN4 LST SDR Synergy Processor\"), and it is written to disk. Land Surface Temperature Retrieval  
Necessary input variables for the LST retrieval are the atmospheric water vapour, the surface emissivity, and regression coefficients (Figure 5). The atmospheric water vapour W is obtained from the MERIS Level 2 product corresponding to the given L1b input. This product gives the total column water vapour per pixel in \(gcm^{-2}\). If such a product is not available, the water vapour is set to a constant value of \(W=2.0\)\(gcm^{-2}\) within the retrieval. Input surface emissivities into the LST algorithms are retrieved using the NDVI Thresholds Method described in Section 2.2.1. The MERIS/OLCI bands selected for the calculation of the NDVI are 560 nm and 665 nm.