Validation of tropospheric ties at the test setup GNSS co-location site in Potsdam

. Atmospheric ties are the differences of atmospheric parameters between antennas or stations at the same site and meteorological conditions. However, there is often a discrepancy between the expected zenith delay differences and those estimated from geodetic analysis, potentially degrading a combined solution employing atmospheric ties to constrain atmospheric delay differences. To investigate the possible effects on GNSS atmospheric delay, this study set up an experiment with four co-located GNSS stations of the same type, both antenna and receiver. Specific height differences for each antenna w.r.t. one 5 reference antenna have been measured. One antenna was equipped with a radome of the same height and type as an antenna close to the ground. Additionally, a meteorological sensor was used for meteorological data recording. The results show that tropospheric ties from the analytical equation based on meteorological data from Global Pressure and Temperature 3 (GPT3) model, Numerical Weather Models, in-situ measurements, and ray-traced tropospheric ties, reduced the bias of zenith delay roughly by 72%. However, the in-situ tropospheric ties yielded the best precision in this study. These results demonstrate that 10 the instrument effects on GNSS zenith delays were mitigated using the same instrument. In contrast, although the effects of the radome on atmospheric delays are well known, the magnitude of the effects determined in this study is unexpectedly large. at observations degraded the tropospheric gradients. To extract the instrument effect, we set up another experiment with three GNSS stations and four different antennas. The height differences between the three stations were on one centimeter level. One of the three stations could be adjusted in height to control the height displace- ment after changing antenna. We succeeded in keeping the shift in the GNSS zenith delays within 2 mm level. The bias on GNSS zenith delays and tropospheric gradients agrees with the result of the previous experiment in this study. Moreover, we successfully detected the antenna-dependent effect on both the GNSS zenith delays and gradients from this experiment.

1 Introduction 2 GNSS co-location experiments 2.1 A20 rooftop experiment We designed the GNSS co-location experiment to assess whether the expected atmospheric parameter differences that are calculated employing either in-situ meteorological observations or numerical weather model match those estimated from the 90 independent geodetic analysis of data collected at these co-located stations. At any site, we expect from nodes of the same observing system a decreasing ZTD with increasing height at any given time. To prove this statement, we set up the experiment on the rooftop of the A20 building at Telegrafenberg, the campus of GFZ, Potsdam, Germany. This experiment utilized four Septentrio choke-ring antennas (IGS standard name: SEPCHOKE B3E6) and Septentrio PolaRx5 receivers. Figure 1 shows the setup of the experiment. We installed the antenna A201 at the highest place. A202 and A203 were placed lower than A201 with 95 two meters and four meters height differences, respectively. Antenna A204 was placed on the same level as A203 but installed with a radome from Aeroantenna manufacturer (SPKE:SPECTRA PRECISION conical dome with spike; sold by Aeroantenna and NovAtel). Due to the fact that the radome induces some additional signal propagation delay on GNSS observations owing to its material and shape (Schmid, 2009), we expect it to increase the atmospheric zenith delays. A meteorological sensor (Vaisala WXT530) was installed to record air pressure, temperature, and relative humidity; the meteorological data logging interval was set to 300 s. The precision of the meteorological information can be found in Sect. 3.3. The horizontal separation was less than 15 m in this experiment, assuring that all GNSS antennas and the meteorological sensor were subjected to the same atmosphere condition. This experiment was conducted from 30 th January to 7 th March 2020. Additionally, we used this experiment to assess whether there is any benefit in applying tropospheric ties in sub-daily resolution (every hour in this study) with the analytical equation, NWM, and in-situ measurements for GNSS intra-technique combination. 105

A17 rooftop experiment
As various GNSS antennas are used in worldwide networks of the IGS, the error from the antenna types could differently show up in tropospheric parameters. Therefore, instrumental effects in GNSS-derived tropospheric parameters needs to be determined. For this purpose, we designed an experiment on the rooftop of the A17 building of GFZ Potsdam Telegrafenberg campus, Potsdam, Germany. The purpose of the second experiment was to quantify the instrumental effect of GNSS-derived 110 tropospheric parameters. This experiment was conducted using three GNSS stations, two permanent GNSS stations, and one experimental GNSS station. The unique feature of this experiment is able to adjust the height of the antenna pole (see Fig.   2). The antenna pole is a steerable device that allows to alter the height of the antenna at a level of 10 cm. Thus, the heights of the reference point of the different antenna types are controlled to coincide at a level of a few millimeters. In other words, independent of the antenna type, the reference point positions agree after an initial phase where the antenna position is assessed 115 and then adjusted according to the average height displacement estimated by a PPP. This special setup allows us to avoid any significant displacements between the tested antenna types, so that all changes in GNSS-derived tropospheric parameters can be attributed to instrumental effects. GNSS observations at the experiment station were simultaneously collected with two different receivers; therefore, the experiment GNSS station names were given as A17F and A17G. This experiment involved two permanent GNSS stations 120 from the IGS and GFZ networks, namely, POTS and POTM (Ramatschi et al., 2019), which are located on the rooftop of the A17 building. The distance between the three antennas were less than two meters in horizontal component and one decimeter for the vertical component. Five different GNSS antennas were employed sequentially in this experiment applying the abovementioned "technical adjustment of the position, so that the reference points of all the antennas can be considered as not displaced". This specific set up is of high importance as we attempt to avoid effects on tropospheric parameters induced by 125 different antenna positions. The effects might be caused, for example, by differences of multipathing or by different height of antenna reference points in the atmosphere typically cause tropospheric parameters to differ systematically. The list of equipment in this experiment is shown in Tab. 1. The experiment was conducted from 1 st November 2021 to 10 th January 2022.  At the time when the photo was taken a JG5 antenna was installed on A17F/G (see Tab. 1). Meanwhile, two reference antennas were continuously operated that are part of the permanent IGS and GFZ networks named POTS and POTM equipped with JG5 and LR4 antennas, respectively.

GNSS processing
In this study, we analyzed GNSS observations using the Bernese GNSS software version 5.2 (Dach et al., 2015). Precise Point Positioning (PPP) approach was utilized based on CODE final orbit and clock information (Dach et al., 2020). The GNSS processing included the estimation of daily station coordinates, hourly zenith wet delays, and hourly horizontal gradients. The orbits are given in the IGS14 reference frame (Rebischung and Schmid, 2016), which is a GNSS-subset of the ITRF2014, and 135 are consistent with the IERS Conventions 2010 (Petit and Luzum, 2010). The observation sampling rate was five minutes. Dualfrequency GPS and GLONASS code and carrier phase observations were applied to perform an ionosphere-free combination eliminating first-order ionospheric effects. The receiver clock parameters were estimated per observation sampling epoch. A priori ZHD was calculated based on grid model from the Vienna Mapping Function 1 (VMF1) (Böhm et al., 2006). The Vienna Mapping Function 1 (VMF1) was also applied to map the slant delays to zenith delays. The Chen and Herring (1997) model was 140 utilized as the gradient mapping function. A cut-off elevation angle of seven degrees was applied and also elevation-dependent downweighting of observations following 1/cos 2 (z) where z is zenith angle.

Tropospheric ties of the A20 experiment
A difference in atmospheric parameters between GNSS antennas is expected due to the different antenna reference point locations in this experiment, primarily height differences. These can be called "tropospheric ties" (Teke et al., 2011;Heinkelmann 145 et al., 2016). We determined tropospheric ties at the GNSS atmospheric parameter's estimation epochs with various methods and meteorological information and examined their performance. In this study, we defined tropospheric ties using an analyt- . The effect of horizontal distance was not investigated in this study because the expected gradient differences are well below the capability of the modern GNSS system, as described in Sect. 2.1.
Since the height is an essential information in tropospheric tie derivation, we investigated its precision in this study. The variations of the heights of the four antennas for the entire experiment were within 1 cm, as presented in Fig. 3. The standard deviations of height residuals were roughly 2 mm. This variation is expected because of many reasons, such as the building 160 has some physical motion due to thermal expansion, satellite orbits and clock errors, and satellite's geometry during the day.
However, this variation cannot affect the derivation of tropospheric ties significantly because the ZTD differences at the level of 1 mm require height differences at the level of 4 m due to the hydrostatic part (Bock et al., 2010).  (2007). Additionally, the magnitude of the tropospheric ties increased with increasing height differences. Figure 4 shows hourly tropospheric ties between A201 and A203 stations during the experiment. The tropospheric ties from T2, T3, and T4 showed similar variability; however, tropospheric ties based on GPT3 showed almost no variation, which is expected given that GPT3 features only annual and semi-annual waves and the duration of the experiment was five weeks only. This shows that all tropospheric ties derivation methods account for the sub-daily atmosphere variation except T1, which contains only annual 170 and semi-annual variations.

The uncertainties in meteorological parameters of the A20 experiment
The uncertainties of meteorological information, such as pressure, temperature, water vapor pressure, provided by GPT3, the meteorological sensor, and Numerical Weather Models, are described in Tab. 3. Unfortunately, the meteorological sensor cannot provide the water vapor pressure directly. For this study, we converted relative humidity to water vapor pressure using relative 175 humidity and saturated water vapor pressure. We calculated the saturated water vapor pressure using the Magnus equation with coefficients from Alduchov and Eskridge (1996) and temperature from the meteorological sensor. Then, we performed error propagation to calculate uncertainties of water vapor pressure for the meteorological sensor at the estimation epoch.
Regarding the formal errors of NWM, we obtained the uncertainties from Balidakis (2019). However, these numbers are valid only for this experiment because the formal errors of NWM vary with location and time. Unfortunately, it is impossible 180 to extract formal errors from GPT3 as this information is not provided. Therefore, we determined formal empirical errors of GPT3 by computing the differences w.r.t the meteorological sensor for each meteorological information. Then, the RMS of the differences was extracted. We applied these values as formal errors for GPT3. Therefore, these numbers are only valid for this experiment.

A20 experiment
We formed six pairs of GNSS stations in the experiment, as presented in Tab. 2. We calculated the weighted mean biases of the differences and the weighted root-mean-square (WRMS). Regarding ZTD comparison, we calculated five types of ZTD differences, following Table 4. Firstly, we calculated ZTD differences without applying tropospheric ties (S0). Secondly, we applied tropospheric ties using the analytical equation (Teke et al., 2011) based on meteorological information from GPT3 (S1), NWM 190 (S2), and the meteorological sensor (S3), as well as ray-traced tropospheric ties (S4) before calculating ZTD differences to assess the performance of tropospheric ties from the individual methods. We performed error propagation from input parameters to calculate the uncertainty of tropospheric ties for each method. The uncertainties in meteorological parameters from GPT3, NWM, and the meteorological sensor can be found in Sect. 3.3. We also compared the tropospheric gradients and calculated the time series of the differences between estimated gradients for each comparison case. Then, weighted mean biases, weighted standard deviation, and WRMS were calculated for each comparison case. As the GNSS antennas in this experiment observed the same tilt of the atmosphere, we expect no differences in the estimated gradients. Thus, we compared the estimated gradients directly without applying corrections.
According to Fig. 8, the observation geometry is similar for all antennas of the experiment. Therefore, the effects from observation geometry can be neglected in this study.

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The cut-off elevation angle is a factor that affects GNSS-derived atmospheric parameter accuracy because the difference in number of observations and elevation angle-dependent errors contribute to the estimated GNSS-derived atmospheric parameters. Thus, this could affect the differences in GNSS-derived atmospheric parameters as well. Based on this, we briefly investigated the impact of using different elevation angles on the differences of ZTD and horizontal gradients by selecting two different cut-off elevation angles, such as seven and ten degrees, with the strategy described in Sect. 3.1. According to Fig. 5,205 the bias of estimated ZTD differences using seven degrees cut-off elevation angles was higher than the bias of using ten degrees cut-off elevation angle. Meanwhile, the bias of the estimated horizontal gradients of seven degrees cut-off elevation angle was less than using 10 degrees cut-off elevation angle. In contrast, the variations in the estimated ZTD and horizontal gradients differences using seven degree cut-off elevation angles were less than those using ten degrees cut-off elevation angle. This suggests that using high elevation angles reduces the impact of elevation-dependent systematic errors on the GNSS-derived 210 ZTD differences. However, it increases the error in estimated horizontal gradients because the number of observations in the low-elevation angle, which is important for the horizontal gradients, is decreased. This finding agrees with a previous study by Ning and Elgered (2012).

A17 experiment
The A17 experiment consisted of two phases for each antenna following the first one. The first phase was to determine the horizontal gradients) differences between A17F/G and POTS/POTM were calculated. In this phase, we can assume that the change in the antenna reference point position does not exhibit significant effects on the tropospheric parameters differences.

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In order to quantify the instrumental effects in GNSS-derived tropospheric parameters, we performed a double-differencing process. We took the mean difference of the JG5 antenna from the first observing period at A17F as the reference. We compared this with the mean differences of the other antennas at the same station in this experiment, including the JG5 antenna that  observed again in the last period. With this approach, we expected that the systematic effects from the reference station would be eliminated. Therefore, the remaining biases are attributed to the instrument effect. This approach was utilized in the analysis 230 of both ZWD and horizontal gradients in the A17 experiment. We present a comparison of ZTD for each case described in Tab. 4. A selection of the results is provided in Fig. 6 and Tab. 5,

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while the complete set of results can be found in the electronic supplement. Figure 6 shows the ZTD differences between A201 and A203 for all scenarios during the experiment. The bias between A201 and A203 for S0 was -1.5 mm, with an empirical standard deviation of 1.7 mm. Meanwhile, the biases for S1, S2, S3, and S4 were roughly -0.2 mm with a similar empirical standard deviation of S0 for all cases. This result shows that significant biases are mainly caused by height differences and atmospheric conditions. Moreover, tropospheric ties determined using the 240 above-mentioned methods significantly reduced the biases. However, there was no improvement in the empirical standard deviation of the ZTD differences when applying tropospheric ties since the variation of tropospheric ties was less than 0.1 mm, as demonstrated in Fig. 4. This agrees with a previous study by Heinkelmann et al. (2016). According to Tab. 5, this situation also applied to the comparison between A201 and A202, A202 and A203. In contrast, we found an unexpected bias in the S0 case between A201 and A204. The bias was smaller than expected (less than 0.3 mm) despite roughly four meters of height 245 difference that should result in a 1 mm bias. Thus, applying tropospheric ties increased the biases of ZTD differences, as shown in S1, S2, S3, and S4. These unexpected biases could also be seen when comparing A202 vs. A204, and A203 vs. A204. They are related to the radome, which has significant effects on the GNSS-derived atmospheric parameters. Therefore, installing a radome should be avoided unless necessary, as recommended in the IGS site guidelines (IGS, 2019).
Additionally, we calculated formal errors of tropospheric ties for the particular method in the experiment. The formal errors 250 of T1, T2, T3, and T4 were 34.8, 3.2, 1.6, and 14.1 mm, respectively. T3 yielded the best precision in this study because the meteorological sensor provides high precision of the meteorological parameters, as presented in Sect. 3.3.  Figure 6. The ZTD differences (smoothed with a four-hours running median filter) between A201 and A203 for all case studies. The height difference is approximately four meters. S1, S2, S3, and S4 lines are relatively identical line because the means and variation are approximately equivalent, see Tab. 5.

Tropospheric horizontal gradients
In this section, we present a comparison of the tropospheric gradients. For each comparison case, we analyzed both north and east estimated gradients, as mentioned in Sect. 3.4. 255 Figure 7 shows the comparison of the estimated east gradients between the GNSS antennas during the experiment. The best agreement was found between A201 and A202. The bias and WRMS were 0.018 mm and 0.221 mm, respectively. These are expected because both antennas were installed horizontally close. In contrast, the biases were mostly between 0.1 and 0.2 mm, and the WRMS were at the level of 0.4 mm for the rest of the comparison. These results show that some effects degraded the estimated east gradients observed at A203 and A204. According to Fig. 1, some obstacles exist around A203 and A204, e.g., 260 shadowing of refractor building, and the antennas were placed close to the ground. Therefore, there is a possibility of larger multipath effects for both antennas. According to Fig. 8, we found large residuals for low-elevation observations in A203 and A204, especially in the east-west direction. This shows that multipathing causes effects on the estimated east gradients in A203 and A204 antennas because the sensitivity of gradient estimates to low-elevation observations is much larger.
Additionally, the biases of the north gradient differences were at the level of 0.100 mm or better for all comparisons, see Tab. 265 6. The best agreement of the north gradients was found again for A201 and A202. The bias was 0.008 mm, and the WRMS was roughly 0.299 mm, whereas the WRMS for the rest of the differences was approximately 0.500 mm. This situation also similarly appeared in the east gradients. Therefore, multipathing also causes effects on the estimated north gradients. The north gradient biases were smaller than those of the east gradients in this experiment, except for the small difference between A201 and A202 because the residuals of north-south observations were smaller than the residuals of east-west observations, as shown in Fig. 8. It is obvious that the north-south and east-west observations affect north-south and east-west gradient parameters, respectively. However, the WRMS of the north gradient differences were larger than the east gradient differences. According to Fig. 8, there are few observations in the northern part of the skyplot because of the inclination of the GNSS orbits. The deteriorated geometry might contribute to the high variation in the estimated north gradient.    and standard deviation (wstd)) are shown for both parameters. Figure 9 shows a comparison between POTS and POTM, which are the reference stations in this experiment. The bias and standard deviation of ZWD differences were −0.56 and 1.29 mm, respectively. This result agrees with the results from the 280 A20 experiment where the height difference between two antennas was less than one meter and using a different instrument.
According to Fig. 10, the average height differences of A17F/G w.r.t. reference stations (POTM/POTS) for each antenna approximately agreed at the 2 mm level. These results show the success of steering the reference point positions, which is the target of the A17 experiment. The J3T antenna was not considered in this study because we could not control the average height difference in the J3T to agree within two millimeters with the rest antennas. Figure 11 shows the comparison of ZWD 285 parameters as well as height differences of the test antenna w.r.t the reference stations. The results show that there were shifts in the time series of ZWD differences, whereas the shifts in the height difference time series were negligible. This demonstrates that the shift in the ZWD difference time series was not affected by changing reference position. It is likely that the different bias for each experiment antenna was caused by the instrumental effect. Moreover, severe weather events (heavy rainstorm) occurred in the L20 and SEP antennas. These clearly affected the biases of ZWD differences as well. The JG5 antenna in two 290 different periods showed similar mean biases, according to Fig. 12. This demonstrates that the instrument effect in GNSSderived tropospheric parameters is probably time-independent. However, the insignificant difference was due to the different weather conditions between the two observation periods.  We also performed a comparison of tropospheric gradients. Figure 13 shows the mean of the tropospheric gradient differences between A17F and POTS/M for the individual test antennas. Similar to the ZWD comparison results, the biases in 295 tropospheric horizontal gradients were different for an individual antenna. The biases of east gradient differences were larger than those of north gradients. These were where multipathing occurred in the low-elevation observations of the test station, as shown in Fig. 14. The JG5 antenna also showed similar biases for two different observing periods, similar to ZWD parameters.
These prove that the instrumental effect occurs in both parameters, GNSS-derived ZWD and gradients.
To extract the instrumental biases, we performed double-differencing as described in Sect. 3.4.2. Figure 15 shows the double-300 differenced ZWD biases for A17F/G w.r.t. POTS/POTM stations. The potential biases from the reference stations are supposed to cancel during the double-difference process. Therefore, these biases reflect the instrumental bias in GNSS-derived atmospheric parameters. As mentioned previously, we expect the same bias for the same instrument. However, a small bias remains in the JG5 antenna. Similar findings were also obtained for tropospheric gradients. of tropospheric ties on ZTD decreases the mean differences between the antennas by 72%, i.e., from −1.7 mm to −0.5 mm, while the standard deviations remain unaffected for small height differences. These results confirm that the ZTD bias between antennas depends only on height differences and atmospheric conditions if using the same instrument at a co-location site.

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Moreover, applying tropospheric ties in sub-daily resolution shows insignificant improvements for small height differences, as presented in this study. Nevertheless, the radome causes an additional effect on the GNSS measurements.  The best agreement of tropospheric gradients was found between A201 and A202, which was expected. However, the multipath effects on low-elevation observations degrade the agreement of tropospheric gradients from GNSS in this study.
Therefore, the GNSS antenna should not be installed close to the ground or in the vicinity of an obstacle that causes multipath 325 signals, as recommended by the IGS site guidelines (IGS, 2019). Moreover, lacking observations in the northern part of the sky limited through the orbit inclination caused a larger variation in the north gradients compared to the east gradients in the A20 rooftop experiment.
In the A17 rooftop experiment, we successfully minimized the height shift during antenna changing within millimeter level.
Additionally, the height difference between the reference station and experiment station was on one centimeter level. Accord-330 ing to the A20 rooftop experiment, this number was not significantly affected in observed tropospheric ties. Moreover, the bias due to the height shift was insignificant. However, the severe weather event caused a shift in the GNSS-derived atmospheric parameters time series. Therefore, we conclude that the biases on observed tropospheric ties reflect the instrumental biases on GNSS-derived atmospheric parameters, if no severe weather event happens. We also succeeded in extracting the instrumen- tal bias on GNSS-derived atmospheric parameters from this experiment using double-differencing process, despite that the 335 instrumental biases for the same antenna (JG5) were slightly different at different observing period.
The technique-dependent systematic effects, such as radome and multipath effects, are considered the primary source of biases of the GNSS-derived atmospheric parameters in this study. This statement agrees with previous findings from Steigenberger et al. (2013) that showed multipath effects and radome-induced biases in the estimated coordinates that simultaneously affect ZTD parameters. Systematic errors due to uncalibrated radome and multipathing need to be avoided as they impose the 340 thread of introducing noise-like and systematic errors that can be at the size or even larger than the tropospheric ties for the zenith delays. Therefore, these effects need to be avoided, especially multipath effects, to determine precise ZWD parameters from GNSS, necessary for Precipitable Water Vapor determination for climate studies. In this dedicated best case study, four tropospheric ties models perform comparably well as corrections due to height difference. From this experiment, there is no clear preference for one of the tropospheric ties models. Another potential systematic error source of the zenith delays is the 345 instrumental bias when operating different antenna types. This error source was investigated in this study and successfully determined. The gradients are even more vulnerable. Since they are small, typically at the sub-mm level, the small systematic effects, e.g., due to multipathing, have a larger effect on them, relatively. With the application of the tropospheric delay model, however, the values of the gradients get amplified, and thereby they can have significant effects on the refraction model and consequently on other parameter groups. Concluding, although the gradients do not require a height-dependent correction for 350 small height differences, such as the tropospheric ties for the zenith delays, they can be affected by systematic errors more significantly than the zenith delays. Hence, it is questionable whether gradients can provide an accurate way of inter-technique combination. In comparison to zenith delays, the parameterization of gradients a longer time intervals should be applied.
Further investigation is required as both experiments were conducted only for a short period of about five weeks and a single dedicated site. Additional effects could occur in a long time series of GNSS-derived atmospheric parameters. Moreover,

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increasing the distances (both horizontal and vertical) between the GNSS antennas could determine how much the errors of the atmospheric parameters depend on distance or at least, the limitation of the application of tropospheric ties in the combination of atmospheric parameters.
Data availability. The datasets obtained for the experiments are available upon request from the corresponding author.
Author contributions. CK did most of the data analysis and writing of the manuscript. CK, RH, and MR participated in the design of the experiment and helped to improve the manuscript. KB, BM, and HS contributed to discussion of the results and improving the manuscript.
All the authors read and approved the final manuscript.