1 Introduction

Sea level change is a major threat for the coastal communities and one of the prominent signs of global change. Thanks to long-term tide gauge records and supported by several space-borne altimeters since 1991, sea level changes can be observed with high accuracy. For the past century, Church and White (2011) estimated an absolute sea level trend from tide gauges of 1.7±0.2 mm yr−1 which was later revised to 1.56±0.33 mm yr−1 (Frederikse et al. 2020). In recent years, the global sea level change rate increased. For example, AVISO (2021) reports a trend of 3.4 mm yr−1 based on radar altimeter data between 1993 and 2020. However, especially for coastal regions the relative local sea level trend may differ significantly but is an important key indicator to determine the impact on coastal regions. The differences between geocentric and relative trends are caused by specific environmental conditions, like differences in water temperature, salinity stratification or coastal ocean currents and surge but also strongly on the vertical land motion (i.e., coastal uplift and subsidence). An extensive review on sea level variability in coastal regions is provided in Woodworth et al. (2019). Knowing the vertical land motion is essential to project the local and regional sea level trends and to support societal decision-making and effective coastal protection mechanisms (Siriwardane-de Zoysa et al. 2021; Bott et al. 2021). According to Wöppelmann and Marcos (2016) the required accuracy for vertical station velocities at tide gauges is at the level of 0.5 mm yr−1.

To support the estimation of accurate vertical land motion, the International GNSS Service (IGS, Johnston et al. 2017) initiated the IGS Tide Gauge Benchmark Monitoring Pilot Project (TIGA) in 2001 (Schöne et al. 2009). The main objective, to derive vertical land motion in a well-defined global reference frame, also includes the support of installing and maintaining the global network of GNSS at tide gauges and the collection of GNSS data of stations at or close to tide gauges as well as data processing, time series analysis, and distribution of results. Over the past 20 years, the institutes supporting TIGA performed regularly extensive reprocessing campaigns to derive the best possible and most consistent time series solutions. Previous TIGA solutions were presented for example by Rudenko et al. (2010, 2013), Deng et al. (2016), Santamaría-Gómez et al. (2012). Within the IGS third reprocessing campaign (repro3) a new TIGA reprocessing effort was undertaken and supported by GFZ and University of La Rochelle (ULR). The main motivation of the current TIGA reprocessing was to keep the consistency with the updated IGS reprocessing setup especially regarding the satellite modeling as well as to extend the individual coordinate time series to ensure up-to-date vertical land motion estimates.

In this publication we present the GFZ TIGA contribution computed within the repro3 framework. Following this introduction, the station selection and the applied processing strategy is described in Sect. 2. Section 3 discusses the derive time series and the estimated vertical velocities whereas comparisons with sea level records and altimetric data sets are presented in Sect. 4. Within Sect. 4 we assess also the quality of sea level records corrected by the GNSS-based trends. The paper closes with a brief summary and some conclusions in Sect. 5.

2 Station Selection and Data Processing

Compared to the previous GFZ TIGA contribution (Deng et al. 2016) with in total 794 stations a smaller station set was defined for the GFZ contribution to the TIGA reprocessing associated with the IGS third reprocessing campaign. In total 341 stations were selected containing 101 TIGA stations and 153 stations co-located to tide gauges. The geographical distribution of these stations is shown in Fig. 1. Due to the overall distribution of GNSS stations linked to tide gauges station clusters are visible along the European, Japanese, and partly the North American coastlines. To ensure a reliable definition of the geodetic datum the 66 GNSS stations defined as simplified IGS14 core network in the repro3 station priority listFootnote 1 were selected additionally (indicated by circles in Fig. 1). Obviously, 36 of these core stations are without connection to tide gauges and mostly located far from coastlines. However, eight datum stations are also TIGA stations and additional 21 are co-located with a tide gauge. Moreover, 30 additional stations without connection to tide gauges were processed, most of them located close to shorelines. Exceptions are NAUS (Manaus, Brazil) which was selected for further investigations regarding loading effects as well as WTZR (Wettzell, Germany) and ZIMM (Zimmerwald, Switzerland), which were added for quality control. Three other stations are located close to the Great Lakes in North America (SAG1, STB1, WIS1). The associated station meta-data are taken from the GFZ SEnsor Meta Information SYStem (semisys, Bradke 2020).

Fig. 1
figure 1

Station selection: IGS14 core stations used to define the geodetic datum (circle) and freely estimated stations (triangle); symbol size identifies TIGA stations, stations with closeby tide gauges and stations without tide gauge connection; the color-coding represents the time series length. Regions with dense stations networks are plotted additionally: Japan (top, right), Europe (right, bottom)

The number of stations processed for each day between 1994 and 2020 are presented in Fig. 2. While less than 100 stations were available for the years before 2000, this number increased especially in 2003 with the addition of TIGA stations from Japan. The decrease visible for the recent years is mostly associated to the decommissioned stations previously co-located to tide gauges and similarly visible in the repro3 submissions (Rebischung 2021). A rather stable number of 70–80 and 40–50 stations were processed from 2003 onwards for the TIGA and IGS core stations, respectively.

Fig. 2
figure 2

Number of stations contained in each daily solution, stations are grouped accordingly; IGS core refers to the simplified IGS14 core network defined in repro3

For the processing, a network approach was chosen with ambiguity fixing according to Ge et al. (2005) but without orbit determination. Therefore, we introduced the orbit and clock products provided in the GFZ repro3 solution (Männel et al. 2021). The main reason for this strategy (compared for example to the GFZ TIGA solution GT2 described in Deng et al. 2016) was to reduce the computational and personnel work load. To ensure consistency, the TIGA processing strategy followed the IGS repro3 settingsFootnote 2 and is described in detail in Table 1. This is especially true for the antenna corrections where the igsR3_2135.atx file was used with GPS transmitter offsets adjusted to the pre-launch calibrated Galileo PCOs provided by EUSPA. The derived coordinates are thus given in the consistently derived IGSR3 reference frame whose terrestrial scale differs from the ITRF2014 scale by around 1.2 ppb at epoch 2010.0 plus a drift of 0.03 ppb yr−1, which corresponds roughly to 0.2 mm yr−1 as described in IGS-mail 8026.Footnote 3 In addition, only GPS was processed compared to the three-constellation-solution of the GFZ repro3 solution.

Table 1 Summary of estimation and processing strategy; time span 1994–2020; GFZ software EPOS.P8 was used to process the GNSS data

To describe the processed TIGA solution some relevant indicators are discussed in the following. Figure 3 presents the number of daily processed phase observations in the commonly used ionosphere-free linear combination. Between 2008 and 2020 more than 600,000 observations were processed daily while their overall distribution follows naturally the characteristics of Fig. 2. For a few days the number of observations dropped due to a rather rigorous outlier exclusion. Additionally, the residual statistics are provided in Fig. 3. Residuals are defined here as the difference between GNSS observations and adjusted values in the GNSS processing. Except for the first years the RMS computed over all residuals within one day ranges between 7 and 9 mm. The associated number of ambiguities, given in Fig. 4, follows the distribution of the observations. Except for a lower fixing rate before 2000, mostly 99% of the ambiguities are successfully fixed during the processing. Exceptional high resolution rates in the early years for example in 1995 are related to periods when anti-spoofing was switched off (Steigenberger 2009). The derived daily solutions are stored in conventional SINEX files for a later combination. They are available for further investigation via Männel et al. (2022).

Fig. 3
figure 3

RMS of residuals averaged over all stations and satellites (red) and number of processed observations per day (blue)

Fig. 4
figure 4

Number of ambiguities per day (grey) and ratio of fixed narrow (blue) and widelane (red) ambiguities

3 Time Series Analysis

After converting the derived cartesian station coordinates (X,Y,Z) into topocentric coordinates (north, east, up) the time series analysis was performed using the Bernese GNSS Software FODITS programme (Ostini 2012; Dach et al. 2015). The fully functional model was set up including initial coordinates d0 and velocities v0, discontinuities dk, outliers sk, velocity changes vk, and components of periodic functions pa,k, pb,k (Dach et al. 2015):

$$\displaystyle \begin{aligned} f(t_i) = {\mathbf{d}}_0(t_0) + {\mathbf{v}}_0(t_i-T_0) \\\ + \sum_{k=1}^{n_d}{\mathbf{d}}_k\eta_{d,k}(t_i) + \sum_{k=1}^{n_s}{\mathbf{s}}_k\eta_{s,k}(t_i) + \sum_{k=1}^{n_v}{\mathbf{v}}_k\eta_{d,k}(t_i)\\\ + \sum_{k=1}^{n_p}[{\mathbf{p}}_{a,k}cos(\omega_k(t_i-t_0)) + {\mathbf{p}}_{b,k}sin(\omega_k(t_i-t_0))]\eta_{p,k}(t_i). \end{aligned} $$

Indicator functions ηx describe the validity of the corresponding components. Overall, 332 vertical time series were reliably assessed, whereas nine stations with less than 1000 daily coordinate estimates were excluded from the further investigations. The averaged time series length amounts to 5314 coordinate sets which corresponds to around 14 years. Overall 2327 coordinate discontinuities (i.e., on average seven per station) were found, they are mostly caused by hardware replacements and earthquakes. More important to vertical land motion, 275 velocity changes are identified mostly associated with earthquakes while 145 stations show constant linear trends. Annual and semi-annual signals were found for nearly all stations with globally averaged amplitudes of 3.9 and 1.1 mm, respectively. However, these amplitudes vary significantly as they depend strongly on station specific environmental conditions especially on non-tidal loading. As shown, for example in Männel et al. (2019) especially continental hydrology has a strong annual (i.e., periodic) component which needs to be estimated in the time series analysis if corresponding loading corrections are not considered. The remaining residuals, i.e., the difference between coordinate and trajectory model, is summarized in Fig. 5 averaged over all stations. While the corresponding RMS values (also known as repeatabilities) are higher in the earlier years, a stable behavior with 1–2 mm for the horizontal and 4–5 mm for the vertical component can be noticed from 2005 onwards. The mean values averaged over all stations per coordinate direction are 2.9, 3.3, and 5.6 mm for north, east, and up.

Fig. 5
figure 5

RMS between coordinates and trajectory model (repeatabilities) averaged daily in north (orange), east (green), and up (blue) direction

Figure 6 shows the vertical land motion rates estimated for the remaining 323 stations, i.e., after removing the nine stations with only short time series. Overall dedicated velocity patterns are visible. The formal errors are derived based on a white and power-law noise model. Driven by glacial isostatic adjustment (GIA) large uplift rates are visible for many stations above 45N. In Fennoscanida associated uplift rates of up to 8.2±0.4 mm yr−1 (VAAS, Finland) and 10.5±0.2 mm yr−1 (SKE0, Sweden) are determined. For stations in Iceland and Greenland strong uplift is visible as well reaching for example 12.9±0.4 mm yr−1 (KSNB, East Greenland), 15.0±0.4 mm yr−1 (SRMP, West Greenland), and 13.7±0.2 mm yr−1 (HOFN, Iceland). Similar values were reported in dedicated studies by Bevis et al. (2019), Wake et al. (2016), Ludwigsen et al. (2020) and others. Especially, in Greenland the GIA-driven viscoelastic uplift is superimposed by a significant elastic response on the negative mass balance of the Greenland Ice Sheet since 1992 (IMBIE Team 2020). This is visible for the long time series of KELY (West Greenland) where we determine a subsidence of −1.6±0.8 mm yr−1 before 2005 (in line with Dietrich et al. 2005) and a significant uplift of 6.6±0.3 mm yr−1 afterwards. A similar increase is found at KULU (East Greenland) where the uplift increased from 3.7±0.6 mm yr−1 to 10.0±0.3 mm yr−1 in 2005. While stations in Canada and Alaska are also subject to GIA overlaying effect dominate the vertical land motion locally. For example, stations DSL1 (−3.3±0.2 mm yr−1) and PBOC (−7.3±0.3 mm yr−1) located at Prudhoe Bay show strong subsidence related to local oil production (Ludwigsen et al. 2020). The region around the Kenai Fjords with stations SELD (8.4±0.3 mm yr−1) and AC67 (8.3±0.2 mm yr−1) are subject to strong postseismic uplift caused by the Prince Willam Sound earthquake in 1964 (Huang et al. 2020). Strong uplift rates are present also for southeast Alaska (AB44 with 16.6±0.4 mm yr−1 and AB50 with 17.5±0.4 mm yr−1) caused by rapid viscoelastic relaxation following the retreat of Little Ice Age glaciers (Larsen et al. 2005). Significant subsidence rates occur along the US coastlines of the Atlantic Ocean and Gulf of Mexico related mostly to ground water depletion and sediment compaction (Karegar et al. 2015, 2016). Largest values are visible for the Mississippi delta (GRIS, −7.2±0.1 mm yr−1) and the New York Bay area (SHK5, −3.6±0.2 mm yr−1). For Japan plotted velocity rates indicate land uplift for the northern part including Honshu while stations at Kyushu and Shikoku show mostly subsidence. Interesting to note is also the significant uplift signal of 24.3±0.4 mm yr−1 for PBRI (Andaman islands) which is related to postseismic signal following the Sumatra earthquake 2004 (Paul et al. 2012).

Fig. 6
figure 6

Vertical velocity rates for all datum (triangle) and freely estimated stations (circle), velocity rates determined for periods shorter than 2.5 yrs are not plotted. If velocity change were estimated the velocity with the longest interval is given. Regions with dense stations networks are plotted additionally: Japan (top, right), Europe (right, bottom)

To assess the derived vertical land motion, we computed the differences between our solution and the rates provided in the ALTIGAPS solution (Pfeffer and Allemand 2016) based on the ULR5 solution. Overall, no offset (0.04±0.1 mm yr−1) could be detected, however, the RMS of all possible 137 differences reaches still 1.7 mm yr−1. This is mostly caused by the different handling of velocity changes in the ALTIGAPS dataset. Compared to the newer ULR6a solution (Santamaría-Gómez et al. 2016) a difference of −0.1±0.1 mm yr−1 (RMS 1.7 mm yr−1) was determined. For the previous GT2 solution (Deng et al. 2016) available at SONELFootnote 4 we found an underestimation with respect to ALTIGAPS (mean difference -0.3±0.1 mm yr−1) and ULR6a (−0.4±0.1 mm yr−1).

4 Tide Gauge Records

An assessment of the new TIGA repro3 solution on sea level estimates was performed based on selected tide gauges. Overall, a distance shorter than 10 m between the tide gauges and the GNSS stations was found for 62 stations, while distances of larger than 1 km were found for 140 stations. A largest distance allowed is 31 km for the tide gauge at Helsinki (Finland, PSMSL ID 14) and the IGS station at Metsahovi (METS) both located at a stable craton. Revised Local Reference (RLR) monthly dataFootnote 5 provided by the Permanent Service for Mean Sea Level (PSMSL, Holgate et al. 2013) were used to derive the local sea level trends. In summary, 258 tide gauge records were available on PSMSL for the co-located tide gauges, with 241 records being in the RLR format (93%). For tide gauges without RLR data, metric data (i.e., records not adjusted to a local reference) were applied after a careful manual screening (17 records). After excluding 28 records where measurements ended before 1990, 230 records have been used in this investigation. Relative sea level changes were computed using a basic linear regression. A comparison between the derived sea level trends and values reported by NOAAFootnote 6 reveals a good consistency with an average difference of 0.1 mm yr−1 and an RMS of 0.8 mm yr−1. Overall 76 tide gauges available in both solutions were considered in this assessment. In general, strong relative sea level trends are visible especially for tide gauges in the Baltic Sea (around −7 mm yr−1), along Alaska’s Pacific coast (up to −18 mm yr−1), at the Gulf of Mexico (up to +9 mm yr−1).

After correcting the monthly tide gauge records for the GNSS-based vertical land motion the associated sea level changes were computed similar to the relative trends, i.e., by using a basic linear regression. While changes in the vertical land motion were considered as recommended by Klos et al. (2019) the GNSS-based velocities were extrapolated back in time for correcting the full tide gauge record. This strategy is discussed in more detail in Wöppelmann et al. (2007). In addition, for a few tide gauge records discontinuities had to be introduced. As pointed out by Rudenko et al. (2013) trend changes for January 1998 and 2009 had to be considered for the tide gauge at Churchill (Canada, PSMSL 447) to account for increase discharge into Hudson Bay. Related to groundwater removal a velocity change was set up for February 2003 for the tide gauge Hillarys (Australia, PSMSL 1761). For Aomori (PSMSL 1092) and Ogi (PSMSL 1344), both located in Japan, discontinuities related to the Tohoku earthquake (March 2011) were set up. Figure 7 shows the derived geocentric mean sea level trends for all considered tide gauges. For most of the tide gauges positive trends, i.e., increasing geocentric sea level can be noticed. The spatial variability between the trends of individual stations in terms of RMS is 2.0 mm yr−1 (which is significantly smaller than for the relative sea level with a variability 3.3 mm yr−1). Negative trends at some stations are caused by local effects. For example at Porto Garibaldi a relative sea level trend of +1.0 mm yr−1 is determined from the RLR data. However, after considering the local subsidence rate of −3.2 mm yr−1 the geocentric sea level trend results to −2.2 mm yr−1 which agrees to the finding of Meli et al. (2021).

Fig. 7
figure 7

Mean sea level trend for all tide gauges corrected for the estimated vertical land motion. Regions with dense stations networks are plotted additionally: Japan (top, right), Europe (right, bottom)

Based on AVISO’s multi-mission altimetric trend map (AVISO 2021) the derived tide gauge trends were compared to the closest grid point. Overall, a difference of −0.7 mm yr−1 shows systematic smaller trends observed by the tide gauges which could be related to the different time periods as the altimetry covers only the time between 1993 and 2020. For this period AVISO reports a global trend of 3.4 mm yr−1 compared to 2.3±0.1 mm yr−1 averaged from the 230 tide gauges considered in this study. The global trend derived from tide gauges increases to 3.0±0.2 mm yr−1 if considering only data records between 1993 and 2020. Correspondingly, the difference to the AVISO map decreases to 0.2±0.2 mm yr−1. The individual differences have an RMS of 2.5 mm yr−1 showing the discrepancy between local tide gauge observations and multi-mission altimetry. Comparing our solution with the previous GT2 solution (Deng et al. 2016), we found a comparable difference to AVISO of −0.6 mm yr−1, but with GT2 having a larger RMS of 3.2 mm yr−1.

5 Summary and Conclusions

Estimating vertical land motion is important to transfer relative sea level measurements at tide gauges into geocentric sea level trends. With the IGS TIGA project vertical land motion patterns are determined based on co-located GNSS stations. In the framework of the third IGS reprocessing campaign we processed long-term observations for 341 GNSS stations globally distributed and mostly located at or close to tide gauges. Based on a network approach and subsequent time series analysis vertical velocities were estimated for 230 recently active tide gauges. The repeatabilities of the GNSS time series are 1–2 mm for the horizontal components and 4–5 mm for the vertical. After assessing the GNSS-based vertical land motion estimates they were used to compute geocentric sea level trends. Comparing the derived sea level trends to AVISO’s multi-mission altimetric trend map reveals an overall difference of −0.7 mm yr−1 (0.2 mm yr−1 for tide gauge data to 1993–2020).