Though Global Navigation Satellite System (GNSS) data processing has been significantly improved over the years, it is still commonly observed that zenith tropospheric delay (ZTD) estimates contain many outliers which are detrimental to meteorological and climatological applications. In this paper, we show that ZTD outliers in double-difference processing are mostly caused by sub-daily data gaps at reference stations, which cause disconnections of clusters of stations from the reference network and common mode biases due to the strong correlation between stations in short baselines. They can reach a few centimetres in ZTD and usually coincide with a jump in formal errors. The magnitude and sign of these biases are impossible to predict because they depend on different errors in the observations and on the geometry of the baselines.

We elaborate and test a new baseline strategy which solves this problem and significantly reduces the number of outliers compared to the standard strategy commonly used for positioning (e.g. determination of national reference frame) in which the pre-defined network is composed of a skeleton of reference stations to which secondary stations are connected in a star-like structure. The new strategy is also shown to perform better than the widely used strategy maximizing the number of observations available in many GNSS programs. The reason is that observations are maximized before processing, whereas the final number of used observations can be dramatically lower because of data rejection (screening) during the processing. The study relies on the analysis of 1 year of GPS (Global Positioning System) data from a regional network of 136 GNSS stations processed using Bernese GNSS Software v.5.2. A post-processing screening procedure is also proposed to detect and remove a few outliers which may still remain due to short data gaps. It is based on a combination of range checks and outlier checks of ZTD and formal errors. The accuracy of the final screened GPS ZTD estimates is assessed by comparison to ERA-Interim reanalysis.

Outliers and gaps in ZTD (zenith total delay) series estimated from ground-based Global Navigation Satellite System (GNSS) data are detrimental to meteorology and climate monitoring applications (Bock et al., 2016). Though GNSS data processing has been significantly improved over the years, outliers are still frequently observed in ZTD time series. This study aims at understanding the main factors leading to these outliers and testing improved processing strategies capable of minimizing these effects in the context of post-processing of GNSS data from moderately sized networks (e.g. national scale). We show that the baseline design strategy in a double-difference network processing has a strong impact on the quality and continuity of ZTD time series.

Another approach of satellite data processing which can be used to estimate GPS (Global Positioning System) ZTD is the precise point positioning (PPP) technique. Since PPP allows one to process each station individually, there is no direct propagation of errors between stations. However, the accuracy of ZTD estimates from PPP processing depends strongly on the quality of satellite orbits and clocks. In our study, we focused on improving the double-difference processing because most EPN and E-GVAP analysis centres rely on a network approach utilizing double-difference observations, and many of them use Bernese GNSS Software v.5.2 (Dach et al., 2015).

The most widely used baseline strategy in double-difference processing is the so-called “obs-max” strategy which maximizes the number of double-difference observations from all stations of the network simultaneously (Dach et al., 2015). The optimization of the baselines is performed independently day after day. This strategy is especially convenient because it determines automatically the best baseline structure for every given day. The best stations (with most observations) are thus connected together to form the skeleton the network while the worst stations are relegated to the peripheral, hence minimizing their detrimental effects (biases and gaps) on the other stations. The obs-max processing strategy leads theoretically to the most accurate estimates (ZTD, coordinates, etc.) since it uses the maximum possible number of observations. This strategy has a drawback, however, which is the use of slightly different network geometry every day as the number of observations changes. Day-to-day changes in the baseline geometry have an impact on the stability and repeatability of the estimates. To circumvent this effect, other baseline designs have been introduced. Jaworski et al. (2011) and Bosy et al. (2012) used a pre-defined network which contains a baseline skeleton of EPN reference stations, which serves as the nodes to which national stations are connected in a star-like geometry. They show that this strategy leads to accurate and stable coordinates for a national network. In this study we show that both these strategies have limitations and are prone to ZTD outliers and gaps. Investigation of various case studies helped us to identify the weaknesses of these strategies. We propose and test an alternative baseline strategy that overcomes the most severe limitations and yields more stable ZTD time series with less outliers and gaps. We also describe an efficient outlier detection method for the final screening of the reprocessed ZTD time series and assess the quality of final ZTD data by comparison with ERA-Interim reanalysis.

Section 2 introduces the details of a standard initial processing strategy which is used to calculate the station coordinates in national GNSS networks. In Sect. 3, results from standard strategy are discussed and some case studies are shown. Section 4 describes the new, improved baseline strategy. In Sects. 5 and 6, the new baseline strategy is compared to the initial and obs-max strategies. Section 7 briefly describes the screening procedure used to remove the remaining outliers in the ZTD estimates and the solutions from the different strategies are objectively evaluated by comparison with ERA-Interim reanalysis. Section 8 concludes and draws perspectives.

In this study, GPS data from 136 stations were analysed for the year 2014. They
include 104 stations of the Polish national Ground Based Augmentation System
(GBAS) network ASG-EUPOS and 32 EPN stations (remote and in Poland;
Fig. 1). The remote EPN stations (i.e. with baselines longer than 500 km)
were included in order to provide absolute ZTD estimates (Duan et al., 1996;
Tregoning et al., 1998). Details of the baseline strategy are given below.
The processing was carried out for double-difference observations using
Bernese GNSS Software v.5.2 (Dach et al., 2015). A minimum-constraint
approach was followed consistently with the general EUREF recommendations. The
collected GNSS data were processed in 24 h sessions starting at 00:00 UTC
each day with data sampling of 60 s. The ionosphere-free linear
combination of carrier phase observations was used. An elevation cut-off
angle of 3

The initial baseline design was based on common practice for the analysis of national GNSS networks. All the EPN stations were used as reference stations and connected together (Fig. 1a) and ASG-EUPOS stations were connected to the nearest EPN stations in a star strategy (Fig. 1b). With this design, all baselines are independent. It allows the division of the network into sub-networks, which are processed independently with correct correlations and are combined afterwards (Dach et al., 2015). Starting with this initial baseline structure, the network is modified automatically by the Bernese software every day, depending on the availability of observations. When observations for an EPN station are missing for the whole day, the obs-max solution automatically creates new baselines with nearby stations (see e.g. Fig. 4 discussed later). This type of baseline design works well for positioning but has one major drawback for tropospheric monitoring. Indeed, when observations for a given station are missing only for a fraction of a day, the station will still be processed and all baselines connected to this station will be impacted by the data gap. Since station coordinates are estimated daily, they are not impacted much by a short data gap (e.g. a few hours). In contrast, since ZTD parameters are estimated every 2 h, a data gap of about a few hours will strongly impact the ZTD estimates of all stations connected to the station with the gap. The situation becomes problematic when the gap produces a break in the network structure and a cluster of stations is disconnected from the main network (i.e. the one made of reference EPN stations including long baselines). This situation can arise in (i) star clusters composed of ASG-EUPOS stations which are connected to the main network via a single EPN–EPN baseline and (ii) filaments and scattered clusters of stations created by obs-max as part of the automatic redesign of the baselines when no observations are available for some of the stations. Figure 2 shows an example of the first kind where station SULP is connected to the main network via USDL only. Other cases of this kind are BYDG, ZYWI, and GANP. Figure 4 (discussed later) shows an example of the second kind when the initial EPN station BOGO has no observations and stations LOMZ and OSMZ are connected to MYSZ in a filament style. This type of situation is actually very common. The expected impact of disconnections of small clusters from the main network is a common mode bias in the ZTD estimates at the disconnected stations. Indeed, when the baselines are too short (< 500 km), the ZTD estimates are highly correlated and absolute values cannot be properly recovered (Duan et al., 1996; Tregoning et al., 1998). The exact magnitude and sign of the bias is impossible to predict as it depends on the other errors in the observations, on the geometry of the baselines, and on the constraints applied on the ZTD parameters during the processing.

Example of common mode biases in ZTD affecting a cluster of
stations (SULP, BILG, CHEL, HOZD, HRUB, SHAZ) due to disconnection from the
reference network.

The analysis of results from the initial processing strategy revealed many outliers due to disconnections of stations, which showed up as spikes in ZTD and in formal error of ZTD. Here, we examine a few cases in order to quantify the magnitude of the biases and give an idea of their frequency.

Figure 2 illustrates the first kind of situation, with the case of a group of
five ASG-EUPOS stations connected in star configuration to EPN station SULP,
which itself is connected to the main network through a single baseline with
EPN station USDL. Let us first focus on the spike at the end of day 226 (the
errors at the beginning of day 226 are of a different nature and will be
discussed later). On day 226 the baseline USDL–SULP has observations only
until 18:52 UTC. At that time station USDL has a data gap which lasts until
day 230 at 05:46 UTC. From 18:52 UTC to the end of the day 226, the cluster
composed of EPN station SULP and its five ASG-EUPOS stations is disconnected
from the main network and common mode ZTD biases show up. The formal errors
increase simultaneously as a result of high correlation between the
estimated ZTD parameters. Table 1 reports the values for ZTD and formal
errors for two of the ASG-EUPOS stations (BILG and CHEL) connected to SULP,
as well as the values for SULP and USDL. The ZTD bias at BILG, CHEL, and
SULP varies as follows:

Estimated ZTD and formal error (

Maximum ZTD variation (positive or negative) at stations of the cluster based on SULP during data gap periods at station USDL (gap number 13 corresponds to day 226 on Fig. 2). Below is the corresponding formal error.

The second kind of situation (initial reference network modified
automatically by Bernese coincident with a gap in one of the connecting
stations of a small cluster) is exemplified in Fig. 4. In this case,
reference EPN station BOGI is not available and obs-max strategy connected
ASG-EUPOS stations OSMZ, LOMZ, and MYSZ in line. MYSZ is connected from the
initial design to EPN station LAMA. On day 73 a data gap at station LAMA
between 00:00 and 11:00 UTC causes a disconnection of the chain of
stations MYSZ–LOMZ–OMSZ. A common mode bias in the ZTD estimates of

Example of common mode biases in ZTD affecting a cluster of
stations (MYSZ, LOMZ, OSMZ) due to disconnection from the reference network.

Now let us come back to the spikes observed on beginning of day 226 (Fig. 2). Two sites (BILG and HRUB) show variations in ZTD of 15–20 cm between 00:00 and 02:00 UTC and 5–10 cm between 02:00 and 04:00 UTC. One site has no ZTD estimates (SHAZ) and the others show smaller variations which are more in the expected range of values. During this period, no disconnection was observed from station USDL, so the origin of the biases must be different. Inspection of post-fit residuals showed that during this period, few double-difference observations were available for the baselines connected to SULP (one to four satellites were observed at a time for BILG-SULP baseline, one to three satellites for HRUB-SULP, and three satellites for HOZD-SULP). Moreover, a lot of ambiguity parameters were estimated over this period, which might be due to many short data gaps at SULP. The formal errors in the lower plot of Fig. 2b reflect the differences in the number of observations. The biases in ZTD estimates can only be explained by increased errors during processing, e.g. ambiguity parameters not properly fixed (Dousa, 2002) or errors in satellite orbits (Dousa, 2010). It is clear that the larger biases are connected with the smaller number of used satellites (i.e. fewer observations, but also weaker geometry) and increased number of ambiguities. This kind of spike, due not to disconnections from main network but to data gaps at a station, was observed for many stations. Figure 5 shows the number of observations per day at SULP and two other EPN stations, ZYWI and KATO, which are good stations (their mean numbers are around 22 000 while the best stations reach mean numbers around 23 000). Station SULP has a mean of 16 547. This was the smallest number among all Polish EPN stations. It was thus decided to remove SULP from the new solution (Sect. 4). A threshold on the number of observations per day of 14 000 was also introduced for the reference EPN stations to limit the impact of their data gaps on the connected ASG-EUPOS stations. This test was applied daily.

Time series of the number of observations (or maximum when the station is involved in several baselines) for stations SULP, KATO, and ZYWI. The dashed line shows the threshold used to eliminate days with low numbers of observations.

In addition to the problems described above, we also noticed that in case of gaps in observations, spikes in ZTD and formal error often appear at the edges of the gaps. For example, station USDL has a data gap between day 226 at 18:52 UTC and day 230 at 05:46 UTC. The ZTD estimates at the edges of the gap (day 226 at 20:00 UTC and day 230 at 04:00 UTC) are expected to be less accurate because of fewer observations. Table 1 shows that the last ZTD estimate on day 226 is at 20:00 UTC, the value of which differs from the previous estimate by more than 4 cm while its formal error increases from 1.2 to 3.2 mm. The next ZTD estimate is for day 230 at 4:00 UTC, the value of which differs from the next one by 3 cm and its formal error is 12.4 mm. Though ZTD variations of 3 or 4 cm in 2 h are possible, they are very unlikely in this case based on the observed variations for the preceding and following ZTD values. We thus decided to systematically remove the ZTD estimates at the edges of gaps in the post-processing stage to avoid this kind of spike.

Map of reference network composed of EPN stations from Poland and nearby countries created using Bernese obs-max strategy on day 1 of year 2014, with the new baseline strategy. Remote stations are connected to the local reference network to strengthen the decorrelation between ZTD parameters.

A new baseline strategy was developed to fix the problems which appeared in
the initial solution and to ensure that all the stations remain connected to
the main reference network. Therefore, the main reference network composed
of local EPN stations from Poland and nearby countries was first optimized
every day using Bernese obs-max strategy. This ensured that the EPN stations
with small numbers of observations are relegated to the peripheral of the
network and thus limit the risk of disconnections as observed in the initial
strategy. Then the remote EPN stations were connected to this local
reference network to strengthen the decorrelation between ZTD parameters and
provide absolute ZTD estimates. For this purpose, 15 high-quality remote EPN
stations were chosen based on statistics and information available on the
EUREF server. We decided to discard two EPN stations (SULP, UZHL) because
of their small number of observations in 2014. Also, we chose station
BOGO instead of BOGI as a reference EPN station in Poland due to better
quality and stability of BOGO. Finally, we set a threshold of 14 000 for the
number of double-difference observations on EPN stations and removed
stations below this limit from the daily solution to minimize the risk of
disconnections. This number was chosen after numerous tests and appeared as
a good compromise between number of removals and baseline lengths. The final
procedure carried out for each daily session separately is given below
and illustrated with an example in Fig. 6:

Selecting the reference EPN stations in Poland and near countries, creating the reference network based on the results of a preliminary processing with Bernese using obs-max strategy, and removing those stations with fewer than 14 000 observations.

Connecting remote EPN stations to the reference network at peripheral stations (bad stations) which have only one baseline (e.g. BOR1, LAMA, USDL) using a shortest baseline approach, to reduce the risk of disconnections of parts of the stations.

Connecting additional remote EPN stations to Polish EPN stations with the highest number of observations (the best stations) to strengthen the decorrelation of ZTD estimates (e.g. BYGD, JOZE, SASS).

Finally, connecting the ASG-EUPOS stations to the reference EPN network using the shortest baseline approach and a “star” structure.

Comparison of ZTD estimates and formal error for the old (blue
lines) and new (red lines) baseline strategies.

Here, we compare the results from initial (old) and new baseline strategies. The ZTD estimates at the edges of gaps were removed beforehand. Figure 7 shows the results for station BILG. Overall, it is seen that most spikes in ZTD and formal error present in the old solution are avoided with the new strategy (Fig. 7a). Now let us focus on day 226 (Fig. 7b). With the new strategy, BILG is connected to EPN station USDL. Station USDL has good observations, with no interruptions in measurements at the beginning of the day, contrary to station SULP to which BILG was connected in the old solution (Fig. 2). The spikes at the beginning of the day seen at BILG in the old solution are thus avoided. However, USDL has a data gap from 18:52 UTC until the end of the day. After 20:00 UTC, station BILG has thus no more ZTD estimates. The point at 20:00 UTC is also removed since it precedes a gap. The large spikes seen in the old solution after 18:00 UTC because of disconnection of SULP and BILG are also avoided. On day 227, when USDL is not available, BILG is connected to KRA1 and the old and new solutions are fairly consistent.

Similar to Fig. 7 for station KUZA.

Another example is shown in Fig. 8 with station KUZA. In both solutions, this ASG-EUPOS station is connected to EPN station ZYWI. Overall, all spikes in ZTD except the one on day 102 are removed in the new solution (Fig. 8a). On day 102, the spike in ZTD is due to a data gap at ZYWI between 00:12 and 03:50 UTC. Since ZYWI had 17 742 observations on that day it was not removed and both the old and new solution estimated exactly the same ZTD values. Figure 8b shows a period when ZTD spikes are effectively removed. During days 26 to 30, ZYWI had many data gaps with maximum numbers of observations of 11 190, 10 686, 0, 6615, and 12 407, respectively, on these 5 days with the old strategy. As a consequence, large formal errors are observed at KUZA on days when the station is connected to ZYWI (all except day 28). The two large spikes in ZTD seen at the end of day 27 and beginning of day 30 are again due to very few observations in common with ZYWI (for 10–15 min only) on only one or two satellites at a time (similar to day 102). However, with the new strategy, the baseline KUZA-ZYWI is not used on these days because of too few observations (below 14 000). Instead, KUZA is automatically connected with EPN station KATO and the resulting ZTD and formal error time series are much smoother.

With the new baseline strategy, ASG-EUPOS stations are only connected to reference EPN stations and all these EPN stations have at least two baselines with the main reference network (local and remote EPN stations). Disconnection of clusters (Fig. 2) or chains of stations like MYSZ–LOMZ–OSMZ (Fig. 4) are avoided by construction. The only spikes remaining in the ZTD series in the new solution are thus due to small number of observations. We tested the idea of using constraints between successive ZTD parameters in order to smooth the ZTD time series and thus reduce the outliers. The idea works in general as both resulting ZTD variations and formal errors stay in a range consistent with the imposed constraints (e.g. 0.1 m), but outliers can still be detected in the time series. Using tighter constraints would further smooth not only outliers but also the variations in ZTD due to atmospheric variability. This is thus not a good solution to remove the remaining outliers and only the use of a proper screening method can help (see Sect. 7).

Statistics of ZTD estimates and formal errors (

Let us now quantify in a more statistical way the improvement of the new
strategy compared to the old one and compare them both to the standard
obs-max strategy taken as a reference. For this purpose, the same network has
been reprocessed with Bernese software using the obs-max strategy for all
stations (not distinguishing between EPN and ASG-EUPOS or between Polish
and remote stations). As a measure of the quality of each of three
solutions, we computed the standard deviations of the ZTD forward
differences and of the formal errors for each station. Taking the forward
differences of 2-hourly ZTD values allows us to remove almost completely the
seasonal variations and at the same time to magnify the outliers. Large
standard deviations are thus symptomatic of time series containing outliers.
However, in order to limit the impact of outliers that are too large (sometimes as
extreme as

Distribution of standard deviations of ZTD differences and formal error of ZTD for the 104 common ASG-EUPOS stations: the old solution is the blue line, obs-max is the green line, and the new solution is the red line.

Figure 9 shows the distribution of standard deviations of ZTD forward differences and of formal errors for 104 common ASG-EUPOS stations processed in all three solutions. Table 2 reports the mean values over all stations. We can see from Fig. 9 and Table 2 that the ZTD variations and formal errors are smaller, i.e. solutions are more stable and more accurate, for the new and obs-max solutions. Maybe surprisingly, the mean ZTD variability is smaller for the new solution compared to obs-max. However, the mean formal error is the smallest for obs-max (this is consistent with the fact that this strategy maximizes the number of observations). Obs-max also provides the largest number of ZTD estimates. However, the new solution achieves smaller ZTD variability and formal errors than obs-max at most sites (Table 2 reports the numbers of sites for which each solution is the largest among all; e.g. the new solution has the largest ZTD variations at only 11 sites, whereas obs-max has the largest number at 31 sites and the old solution at 62 sites). An explanation is given below.

Large variability in ZTD and formal error (Fig. 9) is observed with all three solutions at three3 sites: KOSZ, WLAD, and SHAZ. Inspection of time series shows many spikes in ZTD for these sites, which are in general associated with a low number of observations. Obs-max also has bad results for station OPLE, but these are due to large ZTD spikes on one specific day (17 January, not rejected by the light screening) when the station has many small data gaps. In general, the spikes in ZTD are coincident with spikes in formal error which can be detected and removed during the final screening step (Sect. 7).

Number of processed observations with the two processing variants (obs-max and new), on day 170, before and after residual screening carried out automatically by Bernese software.

The fact that the new solution provides better results than obs-max was investigated in more detail for special cases when outliers appeared in the obs-max solution that were not present in the new solution. One example is for station GDAN (Fig. 10). Spikes in ZTD and formal error are observed in obs-max solution on days 170–171 but not in the new solution. The number of epochs and observations collected at GDAN was high, so it is not the same case as described above for KUZA, KOSZ, WLAD, or SHAZ. Inspection of the design of the network in both processing variants (Fig. 11) shows that in obs-max solution, station GDAN was automatically connected to station WLAD and WLAD to EPN station REDZ, while in the new solution station GDAN was connected to EPN station REDZ (star structure). Table 3 shows the number of processed observations for the mentioned baselines with the two processing variants on day 170, before and after residual screening carried out automatically by Bernese software during processing. The numbers of observations are large before the screening for all the baselines, so there was no significant observation gap on that day. However, the numbers dropped strongly after screening, which reveals that observations were of bad quality, especially for station WLAD and to lesser extent for station GDAN. In this situation, the baseline design chosen by obs-max based on a priori number of observations did not reveal the best a posteriori. We counted 83 days of this kind in 2014 for station GDAN. A solution to this problem would be to optimize the baselines based on post-residual screening statistics. In the new solution, a preliminary selection of reference stations was applied and ASG-EUPOS stations were connected only to EPN stations which had more than 14 000 used observations.

Network design on day 170:

Similar to Table 2 but for other screening variants. The numbers in brackets in columns 6 and 7 indicate relative difference with the results of the “light screening” (values given in Table 2).

Distribution of standard deviations of ZTD forward differences and formal error of ZTD at 104 common ASG-EUPOS stations, for the new processing strategy and different screening variants (see text).

Despite the new processing strategy allowing us to produce more stable and more
accurate ZTD time series in comparison to the initial and obs-max
strategies, a few outliers may still remain due to short data gaps or
increased errors at the stations of a baseline, even if the first and the
last ZTD estimates around observation gaps are systematically removed (as
discussed earlier). The goal of the screening procedure described below is
to detect and remove these outliers. Following the approach proposed by Bock
et al. (2014), the procedure consists in applying first a range check on
the ZTD and formal errors

In screening variant no. 1, a range check on ZTD removes values outside of the interval [2.0;
2.6 m] and a range check on formal error removes values with

In screening variant no. 2, a range check on ZTD and formal error is performed as in variant no.
1 and a sigma outlier check removes values with

In screening variant no. 3, a range check and an outlier check are performed as in variant no. 2 and 00:00 UTC values are removed to avoid day boundary effects.

Mean statistics of ZTD differences and correlations between GPS and ERA-Interim computed over 103 common ASG-EUPOS stations. Column 5 (respectively 6) gives the number of stations for which the standard deviation of ZTD difference (respectively correlation) is maximum (respectively minimal) among the three solutions. The numbers in brackets are for the comparison of new and obs-max only. The best values are indicated in bold.

Distribution of mean differences, standard deviations of differences, and correlation coefficients of ZTD estimates from GPS and ERA-Interim at 103 common ASG-EUPOS stations. GPS data for the three different processing strategies, after screening variant no. 2, are shown.

Screening variant no. 3 was introduced to assess the weight of the day boundary effects in the overall statistics. When all 00:00 UTC estimates are removed, the stability and accuracy of ZTD estimates is significantly improved (Table 4). This screening option is, however, not to be used because it removes useful data. A better solution to the day boundary problem would be to combine solutions from successive days at the normal equation level (Dousa et al., 2017). The combination adjusts ZTD estimates across the 00:00 UTC boundaries for the central day and minimizes discontinuities between days.

As a final validation step, GPS ZTD estimates were compared to ERA-Interim
reanalysis (Dee et al., 2011). The reanalysis ZTD data were adjusted for
the height difference between the model topography and the GPS stations. The
GPS ZTD data were screened with screening variant no. 2. Mean and standard
deviation of ZTD differences between GPS and ERA-Interim and correlation
coefficients of 6-hourly time series are shown in Fig. 13. The results are
shown for 103 common ASG-EUPOS stations (station WAT1 is not displayed here
because of a bias of

Table 5 reports the mean values over all stations for the three variants.
The mean differences are around

This study aims at understanding the main factors leading to outliers in GPS ZTD time series in a sub-regional network (typically a permanent national GNSS network). We show that the baseline design strategy in a double-difference network processing has a strong impact on the quality and continuity of ZTD time series. ZTD outliers are most of the time caused by sub-daily data gaps at reference stations which provoke disconnections of clusters of stations from the reference network and common mode biases due to the strong correlation between stations in short baselines. We developed an alternative baseline strategy that minimizes such disconnections and yields more stable ZTD time series with less outliers and gaps. The new strategy ensures that all the stations remain connected to the main reference network. The reference network is optimized for each daily session separately using Bernese obs-max strategy and reference stations are removed from processing if their daily number of observations is lower than 14 000 (this is an empirical limit which can be adjusted). With the new baseline strategy, the stations of the sub-regional network (in our case ASG-EUPOS in Poland) are only connected to reference EPN stations and all these EPN stations have at least two baselines with the main reference network (to local and remote EPN stations); consequently disconnections of clusters or chains of sub-regional stations are avoided by geometry of the network. The only spikes remaining in the ZTD series in the new solution are due to small number of observations or short gaps at sub-regional stations. They are removed in a post-processing screening procedure which consists in (1) the removal of the first and the last ZTD estimates around observation gaps and (2) range check and outlier check on ZTD and formal errors. The range check and outlier check detect spikes in ZTD and formal errors based on constant and station-specific thresholds, respectively. The screening removed about 1.2 % of ZTD estimates, which remains at an acceptable level when high data continuity is required. Finally, screened GPS ZTD estimates were compared to ERA-Interim reanalysis to assess the quality of final ZTD data and detect smaller bias and jumps.

We investigate the cases when the new strategy provides better results than obs-max solution. Although obs-max maximizes the number of double-difference observations from all stations of the network simultaneously, the baseline design is chosen by obs-max based on a priori number of observations. In case of bad quality of observations, the number may drop strongly after residual screening carried out during processing. This leads to more ZTD outliers. A solution to this problem is to optimize the baseline based on post-residual screening statistics and apply a preliminary selection of the reference stations. This is done in the new baseline strategy.

PPP might be an interesting alternative to outliers arising from defects in the baseline geometry in a double-difference processing. PPP is based on single station observations, meaning that no baselines between stations are computed. Then, there is no problem of common mode biases when there are observation gaps in nearby stations. However, PPP is mainly affected by the quality of orbits and clocks for which very accurate products are not available in real time (e.g. for now-casting weather application). This is one of reasons why most of E-GVAP analysis centres use double-difference processing while the dependency on the clock products is much smaller.

The improved processing strategy may also be an interesting approach for reprocessing historical data to generate new data with fewer outliers or to the operational processing to improve future ZTD estimates. More accurate and stable ZTD series may be produced in this mode, and the impact of equipment changes may be more easily detected in the double-difference residuals than in zero difference residuals. Some scientific applications also use GNSS tropospheric gradient estimates (Dousa et al., 2017) which were not considered in this study. We argue that similar kind of outliers probably affect the gradient estimates and that the processing strategy proposed in this work would also similarly reduced them. The analysis of gradients and long time series will be considered in a future work.

GPS processing results and all the results in the form of
figures and tables for all types of presented comparisons and stations can be
provided by request to the authors. The GPS RINEX data from the EUREF
Permanent Network (EPN) stations are available from EPN Central Bureau
(

The authors declare that they have no conflict of interest.

This article is part of the special issue “Advanced Global Navigation Satellite Systems tropospheric products for monitoring severe weather events and climate (GNSS4SWEC) (AMT/ACP/ANGEO inter-journal SI)”. It is not associated with a conference.

This work has been supported by Polish National Science Centre grant no. UMO-2015/19/B/ST10/02758. The study was partially carried out during Short Term Scientific Mission (STSM) in the framework of ES1206 COST Action. Edited by: Jonathan Jones Reviewed by: two anonymous referees