## 4 Results
### Sensitivity  
The final accuracy of a product does not only depend on the model performance, but also on the quality of its input data. Considering the fact, that input data to LST estimation is never perfectly accurate, it is straightforward to analyse the sensitivity of each method to its input bands. In this study, sensitivity was evaluated by simple deterministic analysis. The results of an LST algorithm with first a reference input value and second with deviating input values was compared. The differences of the resulting LST from the first reference run and the other (deviating) runs show the sensitivity of an algorithm to that input variable. For this analysis, it is assumed that the deviations have a discrete uniform distribution. Figures 9-11 show the sensitivity of the [PERSON] et al., 2001 method to columnar water vapour, emissivity of band 4 and mean atmospheric temperature in form of boxplots for daytime conditions. In case of all input variables, the error increases with increasing deviation of the input variable from its 'true' value. The sensitivities for columnar water vapour, emissivity, and mean atmospheric temperature show larger scattering range with higher deviations. In single cases the error occurring in the LST due to a specific error in an input dataset might be considerably higher than the average error. In case of columnar water vapour for example, the maximum error occurring at 28 kg/m\({}^{2}\) for columnar water vapour is 11.1 K. In case of an emissivity input error of 0.0475 a maximal error of 3.3 K would occur. However, at lower ranges of input error, which might be the majority, the resulting errors in LST are  
Figure 10: Sensitivity of the [PERSON] et al., 2001 method to band emissivity for daytime conditions. Figure 9: Sensitivity of the [PERSON] et al., 2001 method to columnar water vapour for daytime conditions. much lower. The MAD at an input error of 8 kg/m\({}^{2}\) for columnar water vapour is 0.53 K and the MAD at an input error of 0.02 for emissivity is 0.65 K only. In nighttime conditions, the sensitivity is generally lower, but especially for the columnar water vapour. The MAD at an input error of 8 kg/m\({}^{2}\) for columnar water vapour is then 0.24 K.  
Figures 12-14 show the sensitivity of the Becker and Li 1990 method to total columnar water vapour, mean emissivity and emissivity difference. In addition, here, the error increases with larger deviation of the input variable. Figure 11: Sensitivity of the [PERSON] et al., 2001 method to mean atmospheric temperature for daytime conditions. Figure 12: Sensitivity of the Becker and Li 1990 method to columnar water vapour for daytime conditions. Similar to the mono-window algorithm, the sensitivities for columnar water vapour, emissivity and emissivity difference show larger scattering ranges with higher deviations for the split-window algorithm Becker and Li 1990. The maximum absolute error occurring at 28 kg/m\({}^{2}\) for columnar water vapour is 4.1 K. In case of an emissivity input error of 0.0475 also a maximal error of 3.3 K would occur. The MAD at an input error of 8 kg/m\({}^{2}\) for columnar water vapour is 0.81 K and the MAD at an input error of 0.02 for emissivity is 0.61 K. In nighttime conditions, the sensitivity is also lower for the columnar water vapour. The MAD at an input error of 8 kg/m\({}^{2}\) is then 0.26 K.  
In case all variables are incorrect the errors sum up to a total sensitivity. This is shown at the example of an input error of total water vapour of 8 kg/m\({}^{2}\), an emissivity error of 0.02, and--where applicable--an error of mean atmospheric temperature of 5 K and emissivity difference of 0.02. In case of the mono-window algorithms, the algorithms of [PERSON] 1983 and [PERSON] et al. 2001 show the lowest total sensitivities. [PERSON] 1983 has an almost neglectable sensitivity to emissivity, which is mainly due to the magnitude of the first constant in the formula. [PERSON] et al.