## 4 Results
### Comparisons of Satellite and GPS IWV Monthly Means  
From the satellite and GPS IWV values of all matched and valid satellite-GPS cases within the German domain climatologies were computed in the form of monthly means. The monthly means were produced by spatially and temporally aggregating all valid IWV values within a one-month time period. Figure 5 shows the annual cycle of IWV, in the form of monthly means and accompanying standard deviations for the IWV dataset from each satellite instrument and the corresponding GPS IWV dataset. IWV shows a maximum in July and a minimum in February-March, except for MODIS, which shows the lowest value in January. Also, for all datasets the absolute standard deviation is highest in the summertime and lowest in the wintertime. The overall biases found before, are naturally also reflected in the monthly mean comparisons. IASI shows an underestimation of IWV for all months. In an absolute sense, the agreement is better in winter than in summer, resulting in an overall bias of \(-1.7\) kg/m\({}^{2}\) and a RMSE of \(1.77\) kg/m\({}^{2}\). The monthly standard deviations compare well with the GPS  
Figure 4: Bias (inner circle colors ranging from blue to red) and standard deviation (std; outer circle colors in greyish colors) at each GPS station for all matched IWV observations within one year. Only the GPS stations are included with at least 20 valid satellite-GPS data pairs. standard deviations. MIRS shows a good agreement in the summertime and an overestimation in the wintertime. The standard deviations compare well throughout the year. The overall bias is 1.53 kg/m\({}^{2}\) and the RMSE is 1.84 kg/m\({}^{2}\). MODIS and MODIS-FUB show larger seasonal amplitudes and larger standard deviations than IASI and MIRS, reflecting the more observed extreme IWV values related to a higher spatial resolution. For MODIS, the IWV is overestimated in the summertime, where also the standard deviation is larger than the GPS standard deviation, and slightly underestimated in the wintertime, where the standard deviations are in better agreement. The bias is 0.75 kg/m\({}^{2}\) and the RMSE is 1.45 kg/m\({}^{2}\). The best match can be found for MODIS-FUB. In the summertime there is a slight underestimation of IWV, while in the wintertime the mean IWV values agree best. Throughout the year, the standard deviation is generally slightly larger than the GPS standard deviation. The bias is \(-\)0.2 kg/m\({}^{2}\) and the RMSE is 0.55 kg/m\({}^{2}\). IWV climatologies can be computed for different time scales, e.g., days to seasons. To assess the impact of averaging time period on the computed satellite-based IWV climatologies and their difference to the corresponding GPS climatologies, the bootstrap technique was used. This means that from each IWV dataset all available IWV values belonging to 10,000 averaging time periods, randomly obtained from the one-year IWV dataset, were collected and averaged. Figure 6 shows the results in terms of mean satellite-GPS IWV difference as a function of averaging time period for three different settings. The reference climatology from which the mean IWV difference (error) always is computed is the GPS climatology for which all valid 15 min IWV values within each averaging time period are used. Various satellite-based climatologies are compared to the GPS climatologies. First, the satellite-based climatologies are computed using the GPS IWV values for all matched satellite pixels (Figure 6 left panel). This was done to ignore the impact of satellite retrieval issues on the results, but only focus on the impact of satellite temporal sampling. All satellite-based climatologies show an underestimation for all averaging time periods. The median ranges from about \(-\)0.2 kg/m\({}^{2}\) to \(-\)0.5 kg/m\({}^{2}\) for IASI and MIRS, and from about \(-\)1.5 kg/m\({}^{2}\) to \(-\)2 kg/m\({}^{2}\) for MODIS and MODIS-FUB.