*4.2. Absolute ZTD Estimations*

In order to evaluate the performance of our antenna calibrations on the absolute ZTD estimation several PPP computations were performed. The rover antennas were divided in two groups. The first group is formed by the LEIAR25.R3 LEIT and TRM55971.00 NONE from which we know the antenna patterns from existing type mean IGS ANTEX entries, and which provide an excellent reference for our own calibrations, as well as scenarios in which no or satellite-only antenna calibrations would be available. The results are summarized in Table 5 and Figure 7. Using no ANTEX file at all, the ZTD RMSE compared to the IGS reference is about 15 mm for both antennas in contrast to about 4 mm with applying the IGS PCO and PCV corrections. Supplying only satellite antenna corrections decreases the ZTD RMSE to 8 mm (LEIAR25.R3 LEIT) and to about 4 mm (TRM55971.00 NONE). It also shows that the LEIAR25.R3 LEIT antenna, caused by the antenna design and radome, has a phase pattern that deviates significantly from a sphere, resulting in a bias of about 6 mm when applying only satellite antenna corrections (and ignoring the receiver corrections). This makes it particularly important to correct for this error with this antenna type. The TRM55971.00 NONE antenna pattern suggests to have only little impact on the ZTD estimation with almost identical results comparing the original IGS ANTEX data results. It suggests that the PCV of this antenna has a spherical pattern. Applying the antenna PCV corrections from the conducted short baseline analysis demonstrated comparable results for the elevation-based ANTEX correction and slightly less precise results for the azimuth-elevation corrections. Especially the bias increased which suggests that more outliers are present in the azimuth analysis which is presumably caused by the lack of observing days to perform an azimuthal correction with the utilized calibration method. Except for the minor bias, the ZTD RMSE with self-calibrated antenna pattern entries are comparable to the results using the IGS ANTEX calibrations, and comparable to the IGS reference ZTD estimations.

The second group of antennas consisted of the GA530, AV28 and ANN-MB-00. Since no official antenna calibrations are available for these antennas, the performance could not be evaluated directly against official calibrations. However, the IGS supplies official ZTD estimations from DLF1 to which the results can be compared. Since the PPP processing scheme is not changed except for the supplied ANTEX files, the results demonstrate the antenna phase variation impact on the tropospheric delay. They are shown in Table 6 and Figure 7. The results of the GA530 antenna are comparable to the performance of the LEIAR25.R3 and TRM55971.00 antennas. Supplying no ANTEX file at all, high ZTD biases in the order of −20 mm and −15 mm for the AV28 and ANN-MB-00 antennas are evident with the rectangular bracket. Using a circular plane reduced them to about 12 mm and 6.5 mm, respectively, while maintaining similar RMSE. When applying satellite PCO and PCV corrections, the boxplots in Figure 7 (Satellite PCO/PCV column) demonstrate that the standard deviation decreased notably. The presented offsets and consequently RMSE values limit the application of the data for meteorological purposes. After applying the elevation-only antenna corrections to the data, the bias and RMSE

decreased significantly for the antennas AV28 and ANN-MB-00. Remarkably, the applied corrections did not only increase the performance of the antennas with a circular plane, but also significantly decreased the error from using the rectangular bracket as base. Applying the azimuth-elevation dependent corrections to the data slightly increased the performance of the low-cost antennas. The bias increased slightly for the GA530 antenna and is presumably caused by the short observation time and outliers present in the residuals. The results are encouraging and demonstrate that the applied corrections for low-cost antennas make the data more attractive for tropospheric analysis. Particularly, the performance of the patch antenna ANN-MB-00 with a circular ground plane after correcting the phase pattern yields comparable results (0.47 mm bias and 4.02 mm RMSE) to those from geodetic quality antennas. To confirm these findings, longer observation times are recommended. The utilized IGS I14.ATX ANTEX file consisting of the elevation-only calibrations (without PCO estimations) for the antennas LEIAR25.R3 LEIT, TRM55971.00 NONE, Trimble GA530 and Trimble AV28 and U-blox ANN-MB-00 using a circular plane is attached as Supplementary Material.

#### *4.3. Dual- versus Single-Frequency*

The ionosphere-free linear combination, which is applied to dual-frequency data in PPP to eliminate the ionospheric delay, almost triples the noise in the data. Considering that noise in the data, including the noise in the antenna calibrations, is the major contributor to the bias and RMSE in the ZTD estimation, it can be useful to use L1 data only. Also, although this could change in the future, single-frequency receivers are more readily available than cheap dual-frequency receivers. By applying the SEID algorithm to L1-only observations, an artificial second frequency is generated from the L1 data using the interpolated ionospheric delay from a network of dual-frequency reference receivers. We apply this method to investigate if L1-only measurements may be favorable for ZTD estimations. The results are shown in Table 7. Using the original L1-only data and IGS ANTEX file, the SEID results indicate a similar performance for the high-quality antennas LEIAR25.R3, TRM55971.00 and GA530 compared to the L1 + L2 processing using the original IGS ANTEX file (Tables 5 and 6). Compared to results obtained using only satellite PCO/PCV corrections, the performance of the AV28 and ANN-MB-00 antennas increased significantly after applying SEID on the original data. The lowest bias (−0.40 mm) and RMSE (4.23 mm) is observed with the ANN-MB-00 using a circular plane as base. The results with rectangular brackets demonstrate a ZTD RMSE of about 7 mm and a bias of −5 to −6 mm. Especially the bias of the datasets with rectangular brackets could be reduced to −0.36 mm (ANN-MB-00) and 2.26 mm (AV28) after applying elevation corrections to the L1 data. Applying the azimuth-elevation dependent corrections to the L1 input data resulted in minor improvements for the AV28 data and slight degradation of the ANN-MB-00 data.

These results suggests that the original L1 + L2 data is considerably affected by noise amplified by the ionosphere-free linear combination. Provided that a network of high quality surrounding stations exists, the approach demonstrates the strong advantage of the SEID algorithm to generate L2, which drastically reduces the noise on the target receiver data. There is, however, a trade-off between smoothing the true signal and the underlying noise. Utilizing this method almost eliminates the ZTD bias that was present in the data and the RMSE decreased to a level that is comparable to high-quality measurements which makes it attractive for meteorological applications such as water vapor estimation.
