GPS STDs, i.e. the signal delays along each single signal path, have been derived from the EPOS software using a time resolution of 2.5 min and an elevation cutoff angle of 7∘. In EPOS the precise point positioning (PPP) based on the undifferenced phase and code observations with proper weights scaled according to elevation angles is implemented. In PPP mode, the precise orbits and clocks of all GPS satellites required by the PPP analysis are determined by further refining the IGS (International GNSS Service) routine products . Each station is processed independently by PPP and the processing of a large number of stations can be easily parallelized in near real time. ZTDs are processed using a 12 h sliding window shifted each hour, and STDs are reconstructed every 150 s. Tropospheric delays are estimated using the Saastamoinen model of the ZHD (zenith hydrostatic delay) and the global mapping function (GMF) . The remaining tropospheric impact is parameterized in zenith delays with 15 min resolution, and the gradients are estimated every hour. Then STDs are retrieved as a combination of different estimates : STD=mh⋅ZHD+mw⋅(ZWD+D)+δD=cot⁡ϵ(GNcos⁡α+GEsin⁡α), where ZHD and ZWD are the hydrostatic and the wet zenith delay, mh and mw are the hydrostatic and the wet mapping function, GN and GE are the delay gradient parameters in the northern and eastern direction, ϵ is the elevation angle, α is the azimuth angle and δ is the postfit phase residual.

As described above, STDs can be obtained by GPS data processing techniques, but WVR provides IWV along a given line of sight. Therefore, GPS STDs are converted into SIWV for the validation. The STD delay can be divided into a hydrostatic and a wet component. The hydrostatic part can be calculated with the Saastamoinen ZHD model using the surface pressure (P0) at the station : ZHD=0.0022768P01-0.0026cos⁡(2ϕ)-0.00028h, where h is the height above geoid in km, P0 is the surface pressure in hPa and ϕ is the geodetic latitude of the observing site. ZHD can be mapped onto the individual slant path by using the hydrostatic global mapping function mh: SHD=mh⋅ZHD.

Secondly, the slant wet delay (SWD) or the zenith wet delay can be separated from the STD/ZTD by the estimated hydrostatic delay (SHD/ZHD): ZWD=ZTD-ZHDSWD=STD-SHD. Then the ZWD/SWD is converted into the IWV/SIWV using a relationship based on the surface temperature : IWV=Π⋅ZWDSIWV=Π⋅SWD, where Π is a temperature dependent factor: Π=106ρRv(C1Tm+C2), where C1=373 900 K2hPa-1 and C2=22.1 KhPa-1 are the refractivity coefficient, ρ is the mass density of liquid water, Rv is the gas constant for water vapor, and Tm is a weighted temperature of the atmosphere: Tm=∫eTdh∫eT2dh≈70.2+0.72T0, where T0 is the surface temperature in K and e is the water vapor pressure. This approximation is accurate to 2 % for all weather conditions .

The GFZ HATPRO WVR exploits the microwave spectrum emitted by atmospheric water molecules at different wavelengths to derive information on atmospheric liquid water and IWV. It can clearly identify the spatial and temporal distribution of clouds and IWV by measuring the absorption lines of atmospheric water vapor at frequencies between 22.24 and 27.84 GHz and a window channel at 31.4 GHz for the liquid water. The HATPRO can measure the SIWV directly in satellite direction by applying the GPS tracking mode. For the tracking, GPS ephemeris data derived via HATPRO's built-in GPS receiver are used to determine the satellite positions. Then, the radiometer can periodically scan a number of visible GPS satellites. This allows a comparison of the measured WVR SIWVs with the GPS SIWVs without interpolation.

The rain-flagged data are excluded. In addition, only WVR data observations with atmospheric liquid water (ALW) below 1 kgm-2 were used for the comparison. If the ALW is too large, ALW can distort the measurement of the brightness temperature. As a consequence, the measured WVR SIWVs can be extremely high.

There were differences between elevation and azimuth angles of the GPS and WVR data due to small time differences (∼ 1.25 min). The derived GPS SIWVs were matched to the nearest WVR measurements where a maximum deviation in the intersection angle of 2∘ was accepted. The zenith-mapped SIWVs were calculated with the following formula: IWVz=SIWV/mw.

The elevation angle plays an important role in data processing. The mapping function error is large on the low elevation angle , and the scattering and multipath effects on the GPS signal are typical problems at low elevation angles in the GPS data processing . Also, WVR data at low elevation angles can be influenced by ground radiation sources. Therefore, it is necessary to study the dependency of the GPS - WVR variations on the elevation. The SD of ΔSIWV strongly increases with decreasing elevation angles (Fig. ). The data with elevation angles below 15∘ have obviously larger biases with a larger SD, but, above about 30∘, the bias and SD of ΔSIWV show no significant dependence on elevation. In contrast, the variations in ΔIWVz and also relative ΔSIWV (not shown here) have a low dependence on elevation for the whole elevation range (Fig. ). ΔIWVz are mainly in the range of [-4 kgm-2, 4 kgm-2], while ΔSIWV show a strong variability at low elevation angles.

Furthermore, the relation between ΔSIWV and humidity conditions is studied. Typically, the amount of IWV shows strong variations with time. To classify the humidity conditions, within this study we used WVR IWVs measured within time periods close to each other. About 203 202 observations have corresponding WVR IWVs within a time interval of ± 3 min. It was checked whether the bias and SD of ΔSIWV depend on atmospheric humidity.

As shown in Fig.  (top), the SD of ΔSIWV increases slightly with increasing WVR IWVs. For WVR IWVs above 25 kgm-2, the biases of ΔSIWV drift slightly towards negative values, while rather positive values are observed below 10 kgm-2. The variations in ΔSIWV generally increase at higher WVR IWVs, and GPS SIWVs are increasingly smaller than WVR SIWVs. Regarding the bias tendency, a similar behavior can be seen for relative ΔSIWV (Fig. , bottom), while the SD shows the opposite behavior to the absolute comparisons as it decreases with increasing WVR IWVs. Due to observation values near the expected measurement accuracy, relative bias and SD reach large values at very dry conditions (WVR IWV below 3 kgm-2). Instead of the relative ΔSIWV, the relation between ΔIWVz and WVR IWV is shown in Fig. . The same tendency is observed with the bias and SD of ΔIWVz. A linear tendency of the differences from positive values to negative values is observed in the figures.

Pressure (P), temperature (T) and relative humidity (RH) were measured by the meteo sensor of the type Vaisala PTU200 near the POTS station with high accuracy. Pressure and temperature were used to calculate the GPS SIWV and have an effect on the estimated SIWV. Therefore, pressure and temperature may also influence the comparison results.

The comparisons between RH, T, P and the differences are shown in Fig. . ΔIWV is the difference between the WVR-measured IWV in zenith direction and the GPS-ZTD-derived IWV. The GPS IWV has a temporal resolution of 15 min. Due to the WVR measurements periodically switching between GPS satellite tracking and zenith IWV observation mode every 5 min, only about 14 132 GPS IWVs have the corresponding WVR IWVs within the time interval of ±3 min. In Fig.  (middle), the biases of ΔSIWV, ΔIWVz and ΔIWV change considerably with the variation in pressure. It is difficult to find the dependency between pressure and the differences because of the strong variability. Similarly to pressure, no clear relation between the relative humidity and differences is found (Fig. , top). In contrast, the biases of ΔSIWV, ΔIWVz and ΔIWV decrease with increasing temperature, and the corresponding SDs increase at the same time (Fig. , bottom). A similar tendency is observed between the differences and WVR IWVs (see Figs. , ). The relation between the IWV and temperature is shown in Fig. . The amount of water vapor increases with temperature, showing the temperature effect on the atmospheric water-holding capacity. In Fig. , the water vapor amount of GPS observations at high temperatures is smaller than the measured WVR IWVs.