The US Global Positioning System (GPS) became operational in 1995 as the first Global Navigation Satellite System (GNSS). Since that time, this technology has been transformed into a fundamental technique for positioning and navigation in everyday life. Hundreds of GPS permanent stations have been deployed for scientific purposes throughout Europe and the world, and the first stations have collected GPS data for approximately the last two decades. In 1994, a science-driven global network of continuously operating GPS stations was established by the International GNSS Service, IGS (Dow et al.m 2009), of the International Association of Geodesy (IAG) to support the determination of precise GPS/GNSS orbits, and clock and earth rotation parameters, which are necessary for obtaining high-accuracy GNSS analyses for scientific applications. A similar network, but regional in its scope, was also organized by the IAG Reference Frame Sub-Commission for Europe (EUREF) in 1996, which was called the EUREF Permanent Network (EPN; Bruyninx et al., 2012). Although its primary purpose was to maintain the European Terrestrial Reference System (ETRS), the EPN also attempted to develop a pan-European infrastructure for scientific projects and co-operations (Ihde et al., 2014). Since 1996, the EPN has grown to include approximately 300 operating stations, which are regularly distributed throughout Europe and its surrounding areas. Today, EPN data are routinely analysed by 18 EUREF analysis centres.

Throughout the past two decades, GPS data analyses of both global and regional networks have been affected by various changes in processing strategy and updates of precise models and products, reference frames and software packages. To reduce discontinuities in products, particularly within coordinate time series, homogeneous reprocessing was initiated by the IGS and EUREF on a global and regional scale, respectively. To exploit the improvements in these IGS global products, the second European reprocessing was performed in 2015–2016, with the ultimate goal of providing a newly realized ETRS.

Currently, station coordinate parameter time series from reprocessed solutions are mainly used in the solid earth sciences as well as to maintain global and regional terrestrial reference systems. Additionally, from an analytical perspective, the long-term series of estimated parameters and their residuals are useful for assessing the performances of applied models and strategies over a given period. Moreover, tropospheric parameters derived from this GNSS reanalysis could be useful for climate research (Yuan et al., 1993), due to their high temporal resolution and unrivalled relative accuracy for sensing water vapour when compared to other techniques, such as radio sounding, water vapour radiometers and radio occultation (Ning, 2012). In this context, the GNSS zenith tropospheric delay (ZTD) represents a site-specific parameter characterizing the total signal path delay in the zenith due to both dry (hydrostatic) and wet contributions of the neutral atmosphere, the latter of which is known to be proportional to precipitable water (Bevis et al., 1994).

With the second EUREF reprocessing, the secondary goal of the Geodetic Observatory Pecný (GOP) was to support the activity of Working Group 3 of the COST Action ES1206 (Guerova et al., 2016), which addresses the evaluation of existing and future GNSS tropospheric products and assesses their potential uses in climate research. For this purpose, the GOP provided several solution variants, with a special focus on optimal tropospheric estimates, including VMF1 vs. GMF mapping functions, the use of different elevation cut-off angles and estimates of tropospheric horizontal gradients using different time resolutions. Additionally, in order to enhance tropospheric outputs, we improved the processing strategy in a variety of ways compared to the GOP Repro1 (first EUREF reprocessing) solutions (Douša and Václavovic, 2012): (1) by combining tropospheric parameters during midnights and across GPS week breaks, (2) by checking weekly coordinates before their substitutions in order to estimate tropospheric parameters and (3) by filtering out problematic stations by checking the consistency of daily coordinates. The results of this GOP reprocessing, including all available variants, were assessed using internal evaluations of applied models and strategy settings and using external validations with independent tropospheric parameters derived from numerical weather model (NWM) reanalyses.

The processing strategy used in the second GOP reanalysis of the EUREF Permanent Network is described in Sect. 2, and the new approach that is developed to guarantee a continuity of estimated tropospheric parameters during midnights as well as between different GPS weeks is summarized in Sect. 3. The relationship between mean tropospheric horizontal gradients and the quality of low-elevation GNSS tracking is explained in Sect. 4. The results of internal and external evaluations of GOP solution variants and processing models are presented in Sect. 4, and the assessment of impacts of specific variants on estimated ZTD trends are is presented in Sect. 5. The last section concludes our findings and suggests avenues of future research.

The EUREF GOP analysis centre was established in 1997 and contributed to operational EUREF analyses until 2013 by providing final, rapid and near-real-time solutions. Recently, the GOP changed its contributions to that of a long-term homogeneous reprocessing of all data from the EPN historical archive. The GOP solution of the first EUREF reanalysis (Völksen, 2011) comprised the processing of a subnetwork of 70 EPN stations during the period of 1996–2008. In 2011, for the first time, the GOP reprocessed the entire EPN network (spanning a period of 1996–2010) in order to validate the European reference frame and to provide the first homogeneous time series of tropospheric parameters for all EPN stations (Douša and Václavovic, 2012).

In the second EUREF reprocessing (Repro2), the GOP analysed data obtained from the entire EPN network from a period of 1996–2014 using the Bernese GNSS Software version 5.2 (Dach et al., 2015). The GOP strategy relies on a network approach utilizing double-difference observations. Only GPS data from the EPN stations were included according to official validity intervals provided by the EPN Central Bureau (http://epncb.oma.be). Two products were derived from the reprocessing campaign in order to contribute to a combination at the EUREF level performed by the coordinator of analysis centres and the coordinator of troposphere products: (1) site coordinates and corresponding variance–covariance information in daily and weekly SINEX files and (2) site tropospheric parameters in daily Solution (Software/technique) INdependent EXchange Format for combination of TROpospheric estimates (SINEX_TRO) files.

This GOP processing was clustered into eight subnetworks (Fig. 1) and then stacked into daily network solutions with pre-eliminated integer phase ambiguities when ensuring strong ties to the IGS08 reference frame. This strategy introduced state-of-the-art models (IERS Conventions, 2010) that are recommended as standards for highly accurate GNSS analyses, particularly for the maintenance of the reference frame. Additionally, the use of precise orbits obtained from the second CODE (Centre of Orbit Determination in Europe) global reprocessing (Dach et al., 2014) guaranteed complete consistency between all models on both the provider and user sides. Characteristics of this GOP data reprocessing strategy and their models are summarized in Table 1. Additionally, seven processing variants were performed during the GOP Repro2 analysis for studying selected models or settings: (a) applying the tropospheric mapping function model GMF (Böhm et al., 2006a) vs. VMF1 (Böhm et al., 2006b), with the latter based on actual weather information; (b) increasing the temporal resolution of tropospheric linear horizontal gradients in the north and east directions; (c) using three different elevation cut-off angles, namely 3, 7 and 10∘; (d) modelling atmospheric loading effects; and (e) modelling higher-order ionospheric effects. Table 2 summarizes the settings and models of solution variants selected for generating coordinate and troposphere products, which are supplemented with variant rationales.

Within the processing, we screened station coordinate repeatabilities from weekly combined solutions and we identified any problematic station for which the north/east/up residuals exceeded 15/15/30 mm or RMS of the north/east/up coordinate component exceeded values 10/10/20 mm. Such station was a priori excluded from the tropospheric product for the corresponding day. There were other standard control procedures within the processing when the individual station could have been excluded, e.g. if (a) less than 60 % of GNSS data were available, (b) code or phase data revealed poor quality, (c) station metadata were found inconsistent with data file header information (receiver, antenna and dome names, antenna eccentricities), and (d) phase residuals were too large for all satellites in the processing period, indicating a problem with the station. Tropospheric parameters were estimated practically without constraints (a priori σ greater than 1 m); thus, parameter formal errors reflect the relative uncertainties of estimates. Usually, large errors indicate the lack of observations contributing to the parameter. During the tropospheric parameter evaluations, we applied the filter for exceeding formal errors of estimated parameters (ZTD σ greater than 3 mm, normal cases stay below 1 mm).

When site tropospheric parameter time series generated from the second EUREF reprocessing are applied to climate research, they should be free of artificial offsets in order to avoid misinterpretations (Bock et al., 2014). However, GNSS processing is commonly performed on a daily basis according to adopted standards for data and product dissemination. Thus far, EUREF analysis centres have provided independent daily solutions, although precise IGS products are combined and distributed on a weekly basis. Station coordinates are estimated on a daily basis and are later combined to form more stable weekly solutions. According to the EUREF analysis centre guidelines (http://www.epncb.oma.be/_documentation/guidelines/guidelines_analysis_centres.pdf), weekly coordinates should be used to estimate tropospheric parameters on a daily basis, but there are no requirements with which to guarantee the continuity of tropospheric parameters during midnights. Additionally, there are also discontinuities on a weekly basis, as neither daily coordinates nor hourly tropospheric parameters are combined across midnights between corresponding adjacent GPS weeks.

The impact of a 3-day combination was previously studied when assessing the tropospheric parameters stemming from the second IGS reprocessing campaign 2016 in the GOP-TropDB database (Győri and Douša, 2016). We compared two global tropospheric products provided by the analysis centre CODE differing only in the procedure of combining tropospheric parameters from the daily original solutions. The first product, COF, was based purely on a single-day solution while the second product, COD, was based on a 3-day combination (Dach et al., 2014). Sub-daily statistics were calculated by comparing 2 h ZTD estimates from both products during 2013. There were no significant biases observed, but mean standard deviation estimated from differences reached 0.8 mm in ZTD over a day and almost 1.8 mm close to the day boundaries. Similarly, a dispersion characterized by 1σ over all stations reached 0.5 mm for the former but up to 1.2 mm for the latter. Actual differences in ZTDs could even be larger, because this case used approximations leading to smooth low-resolution values close to the day boundaries.

During the first GOP reprocessing, there was no way to guarantee tropospheric parameter continuity at midnight, as the troposphere was modelled by applying a piecewise constant model. In these cases, tropospheric parameters with a temporal resolution of 1 h were reported in the middle of the hour, as was originally estimated. In the second GOP reprocessing, using again hourly estimates, we applied a piecewise linear model for the tropospheric parameters. The parameter continuities during midnights were not guaranteed implicitly, but only by an explicit combination of parameters at daily boundaries. For the combination procedure we used 3 consecutive days while the tropospheric product stems from the middle day. The procedure is done again for 3 consecutive days shifted by 1 day. A similar procedure, using the piecewise constant model, was applied for estimating weekly coordinates which aimed to minimize remaining effects in consistency at the breaks of GPS weeks (on Saturday at midnight). The coordinates of the weekly solution corresponding to the middle day of a 3-day combination were fixed for the tropospheric parameter estimates. In the last step, we transformed the piecewise linear model to the piecewise constant model expressed in the middle of each hourly interval (HR:30), which was saved in the SINEX_TRO format to support the EUREF combination procedure requiring such sampling. The original piecewise linear parameter model was thus lost, and, to retain this information in the official product in the SINEX_TRO format, we additionally stored values for full hours (HR:00). Figure 2 summarizes four plots displaying tropospheric solutions with discontinuities in the left panels (a, c) and enforcing tropospheric continuities in the right panels (b, d). While the upper plots (a, b) display the piecewise constant model, bottom plots (c, d) indicate the solution representing the piecewise linear model. The GOP Repro1 implementation is thus represented by the Fig. 2a plot while the GOP Repro2 solution corresponds to Fig. 2d and, alternatively, Fig. 2b.

These theoretical concepts were practically tested using a limited dataset in 1996 (Fig. 3). The panels in Fig. 3 follow the organization of the theoretical plots shown in Fig. 2; corresponding formal errors are also plotted along with estimated ZTDs. Discontinuities are visible in the left-hand plots and are usually accompanied by increasing formal errors for parameters close to data interval boundaries. As expected, discontinuities disappear in the right-hand plots. Although the values between 23:30 and 00:30 on 2 adjacent days are not connected by a line in the top-right plot, continuity was enforced for midnight parameters anyway, as seen in the bottom-right plot. Formal errors also became smooth near day boundaries, thus characterizing the contribution of data from both days and demonstrating that the concept behaves as expected in its practical implementation.

Recently, we have developed a new interactive web interface to conduct tropospheric parameter comparisons in the GOP-TropDB (Győri and Douša, 2016), which is being prepared for the IGS Tropospheric Working Group web (http://twg.igs.org/; Dousa et al., 2017). Using the interface, we observed large systematic tropospheric gradients during specific years at several EPN stations. Generally, from GNSS data, we can only estimate total tropospheric horizontal gradients without being able to distinguish between dry and wet contributions. The former is mostly due to horizontal asymmetry in atmospheric pressure, and the latter is due to asymmetry in the water vapour content. The latter is thus more variable in time and space than the former (Li et al., 2015). Regardless, mean gradients should be close to zero, whereas dry gradients may tend to point slightly more to the equator, corresponding to latitudinal changes in atmosphere thickness (Meindl et al., 2004). Similarly, orography-triggered horizontal gradients can appear due to the presence of high mountain ranges in the vicinity of the station (Morel et al., 2015). Such systematic effects can reach the maximum submillimetre level, while a higher long-term gradient (i.e. that above 1 mm) is likely more indicative of issues with site instrumentation, the environment or modelling effects. Therefore, in order to clearly identify these systematic effects, we also compared our gradients with those calculated from the ERA-Interim.

It is beyond the scope of this paper to investigate in detail the correlation between tropospheric horizontal gradients and effects such as antenna tracking performance. However, we do observe a strong impact in the most extreme case identified when comparing gradients from the GNSS and the ERA-Interim for all EPN stations. Figure 4 shows the monthly means of differences in the north and east tropospheric gradients from the MALL station (Mallorca, Spain). These differences increase from 0 mm up to -4 mm and 2 mm for the east and north gradients, respectively, within the period of June 2003–October 2008. Such large monthly differences in GNSS and NWM gradients are not realistic and were attributed to data processing when long-term increasing biases dropped down to zero on 1 November 2008, immediately after the antenna and receiver were changed at the station. During the same period, yearly mean ZTD differences in the ERA-Interim steadily changed from about 3 mm to about -12 mm and immediately dropped down to -2 mm in 2008 after the antenna change.

The EPN Central Bureau (http://epncb.oma.be), operating at the Royal Observatory of Belgium (ROB), provides a web service for monitoring GNSS data quality and includes monthly snapshots of the tracking characteristics of all stations. The sequence of plots displayed in Fig. 5, representing the interval of interest (2002, 2004, 2006 and 2008), reveals a slow but systematic and horizontally asymmetric degradation of the capability of the antenna to track low-elevation observations at the station. Therefore, we analysed days of the year (DoY) 302 and 306 (corresponding to 28 October and 1 November 2008) with the in-house G-Nut/Anubis software (Václavovic and Douša, 2016) and observed differences in the sky plots of these 2 days. The left-hand plot in Fig. 6 depicts the severe loss of dual-frequency observations up to a 25∘ elevation cut-off angle in the southeast direction (with an azimuth of 90–180∘), which causes the tropospheric linear gradient of approximately 5 mm to point in the opposite direction. Figure 10 also demonstrates that an increasing loss of second frequency observations appears to occur in the east (represented as black dots). The right-hand plot in this figure demonstrates that both of these effects fully disappeared after the antenna was replaced on 30 October 2008 (DoY 304), resulting in the appearance of normal sky plot characteristics and a GLONASS constellation with one satellite providing only single-frequency observations (represented as black lines).

This situation demonstrates the high sensitivity of the estimated gradients on data asymmetry, particularly at low-elevation angles. The systematic behaviour of these monthly mean gradients, their variations from independent data and a profound progress over time seem to be useful indicators of instrumentation-related issues at permanent GNSS stations. It is also considered that gradient parameters can be a valuable method as a part of ZTD data screening procedure (Bock et al., 2016).

Although the station MALL represented an extreme case, biases at other stations were observed too, e.g. GOPE (1996–2002), TRAB (1999–2008), CREU (2000–2002), HERS (1999–2001), GAIA (2008–2014) and others. Site-specific, spatially or temporally correlated biases suggest different possible reasons such as site-instrumentation effects including the tracking quality and phase centre variation (PCV) models, site-environment effects including multipath and seasonal variation (e.g. winter snow–ice coverage), edge-network effects when processing double-difference observations, spatially correlated effects in reference frame realization and possibly others. The problematic stations and periods mentioned above were however still included in comparisons and trend analysis because of the lack of objective criteria for their identification, which should be studied in future.

The GOP variants and reprocessing models were assessed by a number of criteria, including those of the internal evaluations of repeatability of station coordinates, residuals at reference stations and the external validation of ZTDs and tropospheric horizontal gradients with data from numerical weather model reanalyses.

We assessed the impact of solution variants on long-term ZTD trend estimates by analysing 172 EUREF stations providing a time series of data longer than 10 years. For each station, the trend analysis was performed without any data homogenization or outlier rejection as our focus was only on assessing the impact of solution variants on the trend estimates. The ZTD trends were estimated using the least squares regression method applied on the model (Weatherhead et al., 1998): Yt=μ+βXt+St+εt, where μ is the constant term of the model; βXt is the linear trend function, with β representing the trend magnitude; St represents the term modelled by the sine wave function of time Xt including annual, second harmonics and daily variations; and finally εt is the noise in the data.

Site-by-site-estimated ZTD trends from all the variants are provided in the Supplement completed by time span information, number of records and estimated mean formal errors calculated over all variants. In total, trends range from -0.99 to 0.96 mm year-1. Although the individual station trend provided in the Supplement could be compared to other studies – e.g. Baldysz et al. (2016), Klos et al. (2016), or Nilsson and Elgered (2008) – it should be strongly emphasized here that our trends are estimated without any preceding time-series homogenization and the formal errors of the trend estimates are underestimated by a factor 2–4 (Nilsson and Elgered, 2008).

Table 6 summarizes the statistics of estimated trend differences at all 172 stations, always between particular variants as defined in Sect. 5.5. Interestingly, the most significant impact is observed due to the non-tidal atmospheric loading effects reaching differences below ±0.55 mm year-1 in ZTD trends for some extreme cases from the ensemble of 172 stations and an overall 1σ scatter of 0.50 mm year-1 from the ensemble of stations. Changes in elevation cut-off angle, particularly from 3 to 10∘, also reveal a significant impact characterized by differences below ±0.34 mm year-1 and the scatter of 0.32 mm year-1. The impact of mapping function on trend estimates remains small, with a maximum difference of 0.12 mm year-1 and the 1σ scatter below 0.08 mm year-1, while other strategy changes, due to time resolution of tropospheric gradients and higher-order ionospheric effects, remain negligible, always below ±0.04 mm year-1 for all 172 stations, with the scatter of the same magnitude. All mean biases over differences also stay below 0.05 mm year-1. These results are consistent with a study performed by Ning and Elgered (2012) spanning a broader span of cut-off angles. They demonstrated a significant impact of this parameter on integrated water vapour trend estimates.

Finally, we selected 12 stations available over the entire second reprocessing period. All estimated trends are displayed in Fig. 16, ranging from -0.05 to 0.38 mm year-1. Consistent with the overall results reported in Table 5, the most significant impact for the selected 12 stations is observed in the change of elevation cut-off angle (GO2 and GO3 vs. GO1) and atmospheric loading (GO4 vs. GO1) when reaching differences up to 0.1 mm year-1 in estimated ZTD trends. Impacts of other strategies are generally below 0.05 mm year-1 – variants GO4, GO5 and GO6 are very similar, but not consistent again with GO1, meaning the non-tidal atmospheric loading has a significant impact on trend estimates for selected stations with the longest data time series.

In this paper, we present results of the new GOP reanalysis of all stations within the EUREF Permanent Network during the period of 1996–2014. This reanalysis was completed during the second EUREF reprocessing to support the realization of a new European Terrestrial Reference System. In the second reprocessing, we focused on analysing a new product – the GNSS tropospheric parameter time series for applications to climate research. To achieve this goal, we improved our strategy for combining tropospheric parameters during midnights and week breaks. We also performed seven solution variants to study optimal troposphere modelling; we assessed each of these variants in terms of their coordinate repeatability by using internal evaluations of the applied models and strategies. We also compared tropospheric ZTD and tropospheric horizontal gradients with independent evaluations obtained by numerical weather reanalysis via the ERA-Interim.

Results of the GOP Repro2 yielded improvements of approximately 50 and 25 % for their horizontal and vertical component repeatability, respectively, when compared to those of the GOP Repro1 solution. Vertical repeatability was reduced from 4.14 to 3.73 mm when using the VMF1 mapping function, a priori ZHD, and non-tidal atmospheric loading corrections from actual weather data. Increasing the elevation cut-off angle from 3 to 7∘/10∘ increased RMS errors of residuals from these coordinates' repeatability. All of these factors were also confirmed by the independent assessment of tropospheric parameters using NWM reanalysis data.

We particularly recommend using low-elevation observations along with the VMF1 mapping function as well as using precise a priori ZHD values together with the consistent model of non-tidal atmospheric loading. While estimating tropospheric horizontal linear gradients improves coordinates' repeatability, 6 h sampling without any absolute or relative constraints revealed a loss of stability due to their correlations with other parameters. On the other hand, 24 h piecewise linear gradients did not indicate a worse repeatability of coordinates estimates. For saving the time needed for the processing of 4 times fewer gradient parameters, we could recommend using the unconstrained 24 h piecewise model for the modelling of the first-order tropospheric asymmetry.

The impact of processing variants on long-term ZTD trend estimates was assessed at 172 EUREF stations with time series longer than 10 years. The most significant impact was observed due to the non-tidal atmospheric loading effect reaching differences below ±0.55 mm year-1 in ZTD trends for some extreme cases from the ensemble of 172 stations. Changes in elevation cut-off angle, particularly from 3 to 10∘, also revealed a significant impact reaching differences below ±0.35 mm year-1. The change of mapping function was observed to be rather small, with a maximum difference of 0.12 mm year-1, while other strategy changes, due to time resolution of tropospheric gradients and higher-order ionospheric effects, remained negligible, always below ±0.04 mm year-1 for all 172 stations.

Assessing the tropospheric horizontal gradients with respect to the ERA-Interim reanalysis data revealed some long-term systematic behaviour linked to degradation in antenna tracking quality. We presented an extreme case at the Mallorca station, in which gradients systematically increased up to 5 mm from 2003 to 2008 while pointing in the direction of prevailing observations at low-elevation angles. However, these biases disappeared when the malfunctioning antenna was replaced. More cases similar to this, although less extreme, have indicated that estimated tropospheric gradients are extremely sensitive to the quality of GNSS antenna tracking, thus suggesting that these gradients can be used to identify problems with GNSS data tracking in historical archives.

One of the main difficulties faced during the second reprocessing was that of the quality of the historical data, which contains a large variety of problems. We removed data that caused significant problems in network processing when these could not be pre-eliminated from normal equations during the combination process without still affecting daily solutions. To provide high-accuracy, high-resolution GNSS tropospheric products, the elimination of such problematic data or stations is even more critical considering the targeting static coordinates on a daily or weekly basis for the maintenance of the reference frame or the derivation of a velocity field. Before undertaking the third EUREF reprocessing, which is expected to begin after significant improvements have been made to state-of-the-art models, products and software, we need to improve data quality control and clean the EUREF historical archive in order to optimize any future reprocessing efforts and to increase the quality of tropospheric products. These efforts should also include the collection and documentation of all available information from each step of the second EUREF reprocessing, including individual contributions, EUREF combinations, time-series analyses and coordinates, and independent evaluations of tropospheric parameters.