## 4 Results
### Direct Comparisons of Satellite and GPS IWV Values  
As a first step, all matched and valid IWV cases for the entire German domain and one-year time period are analyzed and the satellite and GPS IWV values are directly compared. Figure 3 shows the frequency of occurrence of all matched and valid satellite-GPS IWV data pairs for each satellite instrument. Statistical quantities related to these comparisons are presented in Table 2. The 2D histograms and accompanying statistical quantities show that the largest scatter and root mean square error (RMSE) can be seen in the MIRS-GPS comparison, while the lowest scatter and RMSE can be found for the MODIS-FUB-GPS comparison. The range of IWV values, both towards low and high IWV values, is largest in both MODIS-GPS and MODIS-FUB-GPS comparisons, while it is smallest in the IASI-GPS comparison. For the IWV datasets from IASI, MODIS and MODIS-FUB as well as for the corresponding IWV datasets from GPS, a maximum IWV can be seen between 5 and 10 kg/m\({}^{2}\). For MIRS, this maximum can be seen at around 18 kg/m\({}^{2}\). For the corresponding GPS IWV datasets in the IASI, MODIS and MODIS-FUB comparisons also a second maximum around 14 kg/m\({}^{2}\) can be seen. This bi-modal distribution can be observed for MODIS-FUB and IASI as well, and in a lesser extent also for MODIS. The slightly lower second maximum for MODIS and MODIS-FUB compared to GPS is likely related to undetected sub-pixel cloudiness, which results in lower retrieved IWV values. Comparing the distributions of both MODIS IWV products with IASI and MIRS more extreme IWV values for the former can be seen, related to the higher spatial resolution. Due to the lower spatial resolution of IASI and MIRS, the IWV is smeared out over a larger satellite pixel, thus smoothing out extreme values. The IASI linear fit shows a clear deviation from GPS, resulting in an overall bias of \(-\)1.77 kg/m\({}^{2}\). For MIRS, there is a clear overestimation for IWV values until about 25 kg/m\({}^{2}\), which switches to an underestimation at higher IWV values, which are less frequent, resulting in an overall bias of 1.36 kg/m\({}^{2}\). For MODIS, there is an overestimation of IWV values, which increases for higher IWV values, resulting in an overall bias of 1.11 kg/m\({}^{2}\). For MODIS-FUB, there is a minimal underestimation for larger IWV values, resulting in an overall small negative bias of \(-\)0.31 kg/m\({}^{2}\). \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Instrument** & **N** & **Bias** & **RMSE** & **Std** & **Mean (x)** & **Mean (y)** & **R** & **Slope** & **Intercept** \\ \hline IASI & 88336 & \(-\)1.77 \(\pm\) 0.006 & 2.74 & 2.09 & 16.17 & 14.40 & 0.959 & 0.866 \(\pm\) 0.001 & 0.387 \(\pm\) 0.015 \\ MIRS & 41948 & 1.36 \(\pm\) 0.016 & 3.77 & 3.50 & 15.98 & 17.36 & 0.881 & 0.807 \(\pm\) 0.002 & 4.453 \(\pm\) 0.037 \\ MODIS & 17438 & 1.11 \(\pm\) 0.021 & 3.11 & 2.91 & 16.18 & 17.28 & 0.959 & 1.117 \(\pm\) 0.003 & \(-\)0.781 \(\pm\) 0.046 \\ MODIS-FUB & 17437 & \(-\)0.31 \(\pm\) 0.019 & 2.52 & 2.50 & 16.18 & 15.87 & 0.955 & 0.967 \(\pm\) 0.002 & 0.226 \(\pm\) 0.041 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical quantities computed from the comparison shown in Figure 3. Presented are the number of matched measurements N, bias, root mean square error (RMSE) and standard deviation (STD) of the difference between the IWV dataset from GPS and satellite, the correlation (R) between GPS and each satellite IWV dataset and the slope and intercept of the linear fit shown by the dashed red-blue line in Figure 3. Units of bias, RMSE, Std, Mean(x), Mean(y) and Intercept are given in kg/m\({}^{2}\). In a next step, a direct comparison of satellite and GPS IWV values is performed at each GPS station to analyze the spatial distribution of bias and standard deviation within the German domain, see Figure 4. For this, only GPS stations are included for which at least 20 valid satellite-GPS data pairs in the one-year time period where found.