## 4 Results  
### Performance  
The different performance measures of Case A, B, and C are shown on the example of the revised [PERSON] et al., 2001 and the [PERSON] and [PERSON] 1990 algorithm only. The relation of the performances of the different cases is very similar for all algorithms; therefore the following detailed presentation of the results from the two revised algorithms is sufficient. Figure 7 will later give an overview over all algorithms. The left-hand side of Figures 3-6 show the \(r^{2}\), the MAD, the RMS, and the STDEV separately for each view angle, columnar water vapour class and daytime coefficient sets. Thereby, case C shows the best agreement in all columnar water vapour classes. \(r^{2}\) values are very high except for extremely humid conditions, and MAD values stay below 0.5 K ([PERSON] and [PERSON] 1990) and around 1 K ([PERSON] et al., 2001) except for very humid conditions and extreme view angles. Case B does show only slightly lower accuracies, except in the case of very low temperatures. There, this coefficient set is not sufficient. Case A shows the lowest accuracies in all cases, MAD values do hardly fall below 1 K. There is a general decrease with higher view angles and with higher columnar water vapour, a result that was expected from other studies [38]. The right-hand side of Figures 3-6 show the same data but this time split up by ranges of initial guess LST. The relations between cases A, B, and C as well as the influence of the view angle are the same. Furthermore, all algorithms work better in case of very low temperatures, which is due to the usually very low water content in the atmosphere in such conditions. Interestingly, the case B and case C give slightly better performance in high temperature conditions (310-320 K) than in moderate temperature conditions (270-290 K). Figure 4: Performance measures (**a**) \(r^{2}\); (**b**) MAD; (**c**) RMS; (**d**) STDEV for the revised [PERSON] et al., 2001 algorithm for different LST ranges (daytime coefficients). Figure 3: Performance measures (**a**) \(r^{2}\); (**b**) MAD; (**c**) RMS; (**d**) STDEV for the revised [PERSON] et al., 2001 algorithm for different CWV ranges (daytime coefficients). The performance measures of the night-time coefficients are very similar to the daytime values both in magnitude and in tendency. Figure 7 shows overviews over all methods, plotted for the different ranges of columnar water vapour, a sensor view angle of 0\({}^{\circ}\), an initial guess LST range from 270 to 310 K, and separated for the day and the night coefficient sets. Where possible, the coefficient sets from case C are taken, as these were identified as the best performing coefficient sets. Most methods show the same relation with columnar water vapour classes. The methods work well in low humidity  
Figure 5: Performance measures (**a**) \(r^{2}\); (**b**) MAD; (**c**) RMS; (**d**) STDEV for the revised Becker and Li 1990 algorithm for different CWV and LST ranges (daytime coefficients). Figure 6: Performance measures (**a**) \(r^{2}\); (**b**) MAD; (**c**) RMS; (**d**) STDEV for the revised Becker and Li 1990 algorithm for different CWV and LST ranges (daytime coefficients). atmospheres, but decrease in accuracy when using more humid profiles. For the split-window algorithms, the MAD stays below 0.4 K, however the mono-window algorithms have partly higher MAD values. The [PERSON] et al., 2001 and the linear method stay below 1 K, but the [PERSON] 1983 algorithm reaches almost 2 K, while the Jimenez-Munoz and Sobrino 2003 is even higher. The Jimenez-Munoz and Sobrino 2003 algorithm shows low accuracies in humid conditions (mostly out of the range in Figure 7). Especially the night coefficients give lowest accuracies in very humid conditions. This is in line with the findings described in [1]. Figure 8 shows an extract of the statistical data for a columnar water vapour range of 0-35 kg\(\cdot\)m\({}^{-2}\), a sensor view angle of 0\({}^{\circ}\), and separated for the initial LST classes.