Following the input pre-processing of all AC solutions, the weekly position SINEX files of all contributors were merged to obtain a series of combined weekly position SINEX solutions. Since each AC solutions included at least 5 EPN stations, the EPN weekly position SINEX solutions are used as skeleton to connect all AC contributions. Although before GPS week 1400 only a small number of non-EPN stations were available in the national solutions, we included weekly solutions from GPS week 1000 (March 1999) up to GPS week 1933 (January 2017) in order to assure the better compatibility with the EPN-only long-term multi-year solution.
Reference frame definition
Due to the inherited features of the GNSS technique, the GNSS positions and velocities are expressed in an earth-centered, earth-fixed geometric reference system, ITRS, defined by its origin, scale, orientation, and time evolution. The actual realization of the ITRS is ITRF2014 (Altamimi et al. 2016) including long-term inputs from all space geodetic techniques such as GNSS, satellite laser ranging (SLR), very long baseline interferometry (VLBI), and doppler orbitography and radiopositioning integrated by satellite (DORIS).
In order to tie a GNSS network to any ITRS realization (ITRFyy), a set of reference stations need to be identified. The preferred method to tie a solution to a reference frame is the Minimum Constraint (MC) approach (Altamimi et al. 2002), because as pointed out in Sillard and Boucher (2001), and shown by other studies, the reference frame constraints applied in individual geodetic solutions can distort the position and velocity estimates. To avoid such biases in the MC approach, the reference frame implementation is performed through a geometric transformation; constraints are only applied on the transformation parameters between the processed and the reference network, instead of constraining any reference stations positions/velocities part of the treated network.
The reference frame for the EPN Densification is ITRF2014, and we aligned the network to the published ITRF2014 reference frame solution using a selected set of European ITRF2014 reference stations. The selection was an iterative process, identifying stations having long, stable, uninterrupted time series, representing the secular EURA plate motion well and evenly covering the stable part of Europe. Following a preliminary exclusion, we started with 63 reference stations and 180 solutions and ended up with 57 reference stations and 157 solutions. In order to make the best alignment with ITRF2014, we applied MC over all 14 transformation parameters. If MC is properly realized, then the estimated positions of reference stations should agree with their ITRF2014 values at the level of 2 mm in 2D and 5 mm in the UP component and the transformation parameters estimated between the reference frame solution and the computed multi-year solution, given exactly the same reference stations, should be zero: no translation, scale factor or rotation and no rate of change of these parameters should exist. The final set of selected ITRF2014 reference stations is shown in Fig. 5.
The CATREF combination software handles the weighting of the different solutions, both on the weekly integration and also during the multi-year combination. Using the variance component estimation method (Altamimi et al. 2002), we applied a weighting approach that re-scales the variance–covariance matrices of each individual solution. Starting with variance factors equal 1, a preliminary combination was computed and then the a posteriori variance factor for each individual solution was estimated in the inversion, which was then applied to the variance–covariance matrix of the corresponding individual solutions. After one iteration, the variance of unit weights of the combination was checked and if it was not close to unity, then the solution was re-checked for blunders or systematic errors.
Solution and its quality
The presented EPN Densification solution, in agreement with the naming convention of the EPN long-term maintenance solutions, was labeled D1933. The complete solution includes 3192 stations, where the corresponding positions and velocities are published in SINEX format and expressed in ITRF2014, ETRF2000, and ETRF2014 frames.
The quality of the results was assessed and demonstrated in different ways, including
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(1)
The weighted RMS of the integrated weeks, as illustrated in Fig. 6,
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(2)
Comparison of the latest ITRF2014 solution and this densification solution in terms of positions and velocities in the common stations shown in Figs. 7 and 8,
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(3)
Browsing the individual residual times series of the stations.
Items 1–2 are useful to check and detect any biases in the solution in general, and item 3 is necessary to check each station for remaining outliers, offsets or any conflicts in overlapping cases.
The weighted RMS series shown in Fig. 6 clearly demonstrates the high quality and stability of the solution. The average WRMS for the East and North components are 1.1 mm, while 3.5 mm for the UP component. No increase in the WRMS can be observed around GPS week 1400 when the inclusion of the densification networks gradually starts. Some seasonality is still present in the series mainly due to the Nordic stations, where the snow accumulation on the antennae causes apparent temporary position biases during wintertime, although at several extreme cases, such as KIRU, KIR0, KUUS, SODA, VAAS, those data periods were removed before the final combination.
Figures 7 and 8 illustrate the position and the corresponding velocity differences, between the ITRF2014 reference frame solution and the D1933 densification solution. The plots demonstrate the successful alignment of the multi-year solution to the ITRF2014; no systematic biases are observed in the position or in the velocity estimates.
The standard deviations of the 14 transformation parameters between ITRF2014 and D1933, i.e., translation (tr), rotation (rot), scale (sc), for the positions and velocities are as follows: trX = 0.04 mm, trY = 0.04 mm, trZ = 0.04 mm, SC = 0.005 ppb, rotX = 0.012 mas, rotY = 0.016 mas, and rotZ = 0.011 mas.
D1933 is considered to be a high-quality, homogeneous, dense position and velocity data set aligned to ITRF2014 and created under full compliance with EUREF standards. The position estimates of the D1933 solution can be used for the validation and inter-comparison of official national ETRS89 positions used for the practical geodetic applications of the CORS networks.
Velocity field
An important product of the EPN Densification is the estimated velocity field, which has multiple scientific applications. At the European level, within the EUREF community the discussion has just started about the future introduction of semi-kinematic or kinematic reference frame realization, where the dense velocity field may effectively support the kinematic modeling. On the other hand, the homogeneous, dense velocity field from Svalbard to Crete shall be used as a reference from large to local scale or inter-regional interpretations and strain modeling.
The estimated 2D and UP velocity fields of the D1933 solution are shown in Figs. 9 and 10, respectively. In both cases, only the velocities of stations with more than 3 years of time series are plotted. As it is widely known that for achieving reliable velocity estimate in ideal cases observation series of at least 2.5 years are needed to reduce the bias that may be caused by apparent seasonal cycles (Blewitt and Lavallée 2002). Velocity estimate based on shorter series are most likely biased and in the presence of heightened noise level, the required time span should be considerably longer. This is especially valid for the UP component. Considering all arguments, we exclusively publish station positions and velocities based on longer than 3 years of observations.
The 2D velocities in Fig. 9 are expressed in the ETRF2000 reference frame. We do easily distinguish the stable part of the continent and the active regions in the Mediterranean and Fennoscandia. The height variations are shown in Fig. 10, where we can also easily identify the main patterns: (1) large regions, where the general subsidence is primarily due to the sediment compaction, (2) Fennoscandian and Scottish post-glacial uplift, and (3) the moderate rise of the Alps and the Southern Apennines. The detailed interpretation of the tectonic patterns that may be observable in the data set is out of the scope of this paper. The delivered high-quality and fully homogeneous position and velocity solution, however, is offered to be used as reference for such geophysical studies.
Despite the elimination of the velocities based on less than 3 years of data, both maps show some stations with velocities affected by local conditions, which are not well representing their tectonic environment. Assuming that the data analysis had been done correctly, corresponding to station time series without noisy sections and all offsets had been identified, the station specific biases may group as small- to medium-scale anthropogenic effects and monumentation issues. Water extraction and mining mostly cause locally significant, easily identifiable biases; stations such as Lorca in Spain, Katowice in Poland, Cluj in Romania, and Karaman in Turkey are removed from Figs. 9 and 10. As a lot of permanent GNSS stations are installed on buildings, the occasional instability of the building or the monument itself may distort the velocity estimation at a level of 1 mm/year or less. Such biases can be identified and marked using careful mathematical testing including geophysical information in the background. Assuming that on a given tectonic unit the 2D velocity pattern can be described as a spherical rotation and the residual velocities within a threshold should be considered as zero, then efficient and reliable filtering can be designed. Such filtering could be critically important in regions with lower tectonic activity, where the separation of the real signal and the (sub-)millimeter-level biases is essential to suppress velocities which are apparently do not represent the displacement field of the actual tectonic unit. Such velocity separation approach and its results will be treated in later.