The primary objective of this study is to analyse and provide a data set that includes all GNSS observations on bedrock for the period from January 1995 to December 2021. Before going into detail, we want to briefly emphasise the usage of the terms GNSS and GPS. The first GNSS deployments tracked only GPS satellites. Many of these sites have since been upgraded with receivers capable of tracking multi-GNSS constellations, making it more correct to refer to these specific sites as GNSS stations. However, the processing strategies applied in this study were limited to GPS observations, resulting in coordinate time series based on GPS-only observations. Therefore, we use the terms GPS stations and GPS coordinate time series throughout the rest of this paper. The required GPS observational data, in the form of raw binary files or the RINEX format, were (to the extent possible) obtained from publicly accessible repositories. The Geodetic Facility for the Advancement of Geoscience (GAGE) manages the observational data and metadata for POLENET-associated stations and makes them publicly available. Observational data for GPS sites contributing to the global IGS network are made publicly available via multiple repositories (e.g. the CDDIS – Crustal Dynamics Data Information System). The observational data from smaller networks or past measurement campaigns are included in GAGE, scattered over smaller data repositories, or not publicly available at all (see Table S1 in the Supplement for the complete list of DOIs for the observational data).

Following a first call for data contribution by the initiators of the GIANT-REGAIN project in 2016, more than 20 station operators and national Antarctic research programmes supported the provision of GPS data for this project. This included stations with already processed and published time series as well as GPS stations with so far unpublished coordinate time series. Figure provides an overview of the spatial distribution of the GPS sites and their associated networks. To observe geodynamic processes related to solid-Earth deformation, the measurements need to refer to specifically marked points in the bedrock. With only 0.18 % of the Antarctic continent consisting of ice-free bedrock , suitable locations for GPS sites are limited to the coastal regions and mountain ranges.

Antarctic GPS sites have been occupied in two ways: in a campaign-style manner with episodic measurements (eGPS) or as continuously operating installations (cGPS). Episodic measurements are realised using the antenna on a fixed marker in the bedrock, with equipment removed at the end of each campaign and reinstalled after an interval typically of a year or more. Occupations typically last a few days to a few weeks.

The first cGPS sites were set up near research stations in the early and mid-1990s. These sites contribute to the global IGS network and provide the longest and most complete observation record within this study. The IGS sites were set up at staffed Antarctic stations, namely, Casey (CAS1), Mawson (MAW1), Dumont d'Urville (DUM1), Davis (DAV1), McMurdo (MCM4), and Syowa (SYOG). Later, additional sites were incorporated into the IGS network, such as Scott Base (SCTB), Mount Coates (COTE), O'Higgins (OHI2 and OHI3), Arrival Heights, McMurdo (ARHT), Rothera (ROTH), and Palmer Station (PALM), while other sites lost their IGS status (e.g. Vesleskarvet – VESL) or were decommissioned (PALV and OHIG).

Starting in 1995, several projects were launched to establish additional regional and local GPS networks. The SCAR Epoch Crustal Movement Campaigns from 1995 to 1999 focused on the regions of the Antarctic Peninsula and Dronning Maud Land and comprised coordinated episodic measurements with contributions and support from several national polar programmes . The TAMDEF (Transantarctic Mountains Deformation) project, with its first observations in 1996, established a GPS network covering large parts of the Transantarctic Mountains, consisting of 25 episodic, 6 quasi-continuous, and 2 continuous sites . The first sites of the VLNDEF (Victoria Land Network for DEFormation Control) network were installed during field campaigns in 1999–2000 and 2000–2001 , with 28 sites in the final configuration. The WAGN (West Antarctic GPS Network) was operated between 2001 and 2006 and covered yet unobserved regions of West Antarctica . A small GPS array of episodic sites was installed in the region of western Marie Byrd Land over 1999–2002 and around the Amery Ice Shelf in East Antarctica .

The harsh Antarctic conditions, such as low temperatures and the polar night, introduce particular technological and logistical challenges to the establishment and maintenance of GPS stations. Establishing a continuous and resilient energy supply has posed significant problems. Moreover, undertaking maintenance work presents a significant logistical challenge, and data transfer must be accomplished either remotely or through manual collection. An essential increase in the spatial coverage of remote cGPS was achieved following the International Polar Year (IPY) from 2007 to 2009 (see Fig. b). The POLENET-embedded network ANET formed the nucleus of the initiative. The ANET network extends from Victoria Land to the Amundsen Sea embayment and Filchner–Ronne Ice Shelf, covering major parts of West Antarctica. Within the POLENET initiative, some of the previous eGPS sites of the WAGN, TAMDEF, and Marie Byrd Land network were reoccupied and upgraded to cGPS sites. International partners contributed to the ANET network. Three sites of the VLNDEF (VL01, VL12, and VL30) network were upgraded to cGPS sites and included in the POLENET network in the 2014–2015 season . The POLENET–UKANET network of cGPS sites covers large parts of the Antarctic Peninsula and the surroundings of the Filchner–Ronne Ice Shelf . It includes sites of the LARISSA (LARsen Ice Shelf System, Antarctica) network, consisting of six cGPS sites (installed in 2008 and 2010) covering the northern part of the Antarctic Peninsula , and the CAPGIA (Constraints on Antarctic Peninsula GIA) network , installed in the 2009–2010 Antarctic summer season and consisting of nine cGPS sites. In addition to these large-scale networks, networks with a smaller spatial extent exist that are operated by various institutions. TUD continues to operate eGPS stations in the area of the Antarctic Peninsula, in Dronning Maud Land, and in the Amundsen Sea embayment, which in part represent the continuation of the initial measurements of the SCAR Epoch Crustal Movement Campaigns . The Japanese Antarctic Research Expedition (JARE) operates a local network at the Lützow-Holm Bay (69–70° S, 37–40° E) . In addition to the IGS station SYOG, episodic measurements were initially carried out and later partially upgraded to cGPS stations (the observational data from the cGPS stations were not available for this study). installed a network of six cGPS sites, providing observations for the so far barely covered coastal area of East Antarctica between Davis and Casey stations (70–120° E). Observational data from five sites were available for this study. Several sites are not affiliated with larger networks and are often co-located with research stations (e.g. ABOA , NONS, SVEA, KOH2, VESL, and LXAA). These sites can contribute significantly to an increased spatial coverage, especially in East Antarctica where the coverage is otherwise very sparse. The number of daily observations within Antarctica increased steadily from 1995 (Fig. b) with a significant increase in 2008 with the initiation of the POLENET project. The peak number of daily site observations (100) was reached in 2016 and has remained somewhat steady since. However, the observation count decreased in 2020, partly due to the COVID pandemic, when maintenance work and manual data retrieval were not possible for some sites.

Correct metadata are essential to determine consistent time series from GPS. In the context of GPS data processing, the metadata contain information about the hardware set-up. Incorrect information can lead to biased, more noisy time series and, subsequently, to errors in derived deterministic parameters, such as linear trends. Correct metadata are of utmost importance for eGPS , as errors in the metadata (e.g. antenna heights) can bias measurement campaigns and are not necessarily detectable by the analysis of the coordinate trajectories (depending on the number of measurements).

Basic information is usually provided in the RINEX header section and includes, among others, information about the installed antenna (type and serial number), receiver (type, serial number, and firmware version), and antenna eccentricities. For past sites, the RINEX header often contains incomplete or even false information. For this study, we confirmed or corrected the metadata information, using metadata logs, observation protocols, images of the GPS stations (with a focus on the antenna set-up), published metadata information, or personal communication with site operators.

To ensure the reproducibility of the processing and to enable possible future reprocessing, the metadata are provided in the established and comprehensive format of the station log files (https://files.igs.org/pub/station/general/sitelog_instr.txt, last access: 15 July 2024) of the IGS .

Multiple studies have reported on the effect of snow intrusion into the GPS antenna radomes through drainage holes in the ground plates for a subset of ANET and UKANET cGPS sites, leading to offsets and quasi-periodic (annual) signals in the coordinate time series. As a countermeasure, the drainage holes were initially closed with tape and later sealed with permanent plugs. A comprehensive list of efforts regrading the sealing of drainage holes was provided for this study (David Saddler, OSU, personal communication, 11 October 2023). Understanding the sealing efforts is crucial to accurately interpret the coordinate time series, as this can significantly alter the coordinate trajectory. The antenna sealing efforts are listed within the auxiliary data published in conjunction with the coordinate time series .

The individual analysis methods of the ACs differ with respect to the analysis software, the processing strategies (e.g. double-differencing or zero-differencing strategies), auxiliary products, and the strategies to realise the terrestrial reference frame, while all ACs adopted the same version of the International Terrestrial Reference Frame (ITRF) to ensure consistency. At the time of the initial processing, the latest version, the ITRF2020 was not available. Therefore, all ACs realised the IGb14 reference frame, the GNSS-only realisation of the ITRF2014 , and adopted the associated absolute antenna corrections for satellite and ground antennas provided by the IGS (igs14.atx). As mentioned in Sect. , we did not include observations of all GNSS but, rather, restricted our analysis to GPS observations.

The TUD analysis centre adopted a standard network-processing approach based on double-differenced phase observations using the Bernese GNSS Software v5.2 . The Antarctic GPS network was processed together with a selection of long-running IGS sites surrounding Antarctica. Satellite orbits and Earth rotation parameters were fixed to final products provided by the Center for Orbit Determination in Europe (CODE) . A priori zenith path delay (ZTD) values were realised by employing the dry ZHD (hydrostatic delay in zenith) and the Vienna mapping function (VMF3) . In order to apply the VMF3, a modified version of the Bernese GNSS Software v5.2 was used. The ZTD was parameterised as a piecewise linear function with a 1 h resolution. A horizontal tropospheric gradient was estimated once a day. First-order ionospheric effects were mitigated by forming the ionospheric-free linear combination. Second-order and third-order ionospheric effects were considered, based on global ionosphere maps (GIMs) provided by CODE. Ocean tidal loading corrections and atmospheric tidal loading corrections were applied at the observation level using the ocean tide model FES2014b and the atmospheric tide model of , respectively. Non-tidal loading corrections were not applied. Solid-Earth tide and solid-Earth pole tide corrections were applied according to the IERS2010 conventions . Only observations above 5° elevation were considered. Phase ambiguities were fixed to integers if possible, using a sophisticated scheme of baseline-length-dependent strategies . The Bernese Software v5.2 allows one to consider the misalignment of ground antennas from true north. If the station metadata included information on the antenna orientation, the azimuth-dependent phase centre corrections were applied accordingly. This does not apply to reference stations to maintain consistency with the IGb14 conventions. The geodetic datum was defined using a minimum-constraint approach imposing a no net translation (NNT) condition on a set of regional IGS core stations with respect to the IGb14 reference frame, when solving the daily normal equations for station coordinates and tropospheric parameters.

The University of Tasmania (UTAS) analysis centre analysed the GPS data using the GIPSY v6.4 software and non-fiducial NASA Jet Propulsion Laboratory (JPL) orbit and clock products (repro3). A zero-differenced precise point positioning (PPP) methodology was adopted . Pseudorange data were phase-smoothed, and all data were down-sampled to a 300 s interval. Only observations above 10° elevation were used. Receiver clock corrections were estimated every 300 s as a white noise process. Wet tropospheric zenith delays and gradients were estimated every 300 s with a random-walk process noise of 5×10-8 and 5×10-9 kms-0.5, respectively . The gridded VMF1 tropospheric mapping function was used, with hydrostatic and a priori zenith wet delays extracted from these grids which were based on ECMWF (European Centre for Medium-Range Weather Forecasts) products . Second-order ionospheric effects were corrected based on JPL IONEX (ionosphere exchange) files from the year 1999 onwards. Solutions prior to 1999 instead used the International Reference Ionosphere model. A shell height of 600 km was used in both cases . Solid-Earth tide and solid-Earth pole tide corrections were made as per the IERS2010 conventions . Ocean tidal loading displacements were modelled based on the TPXO7.2.2010 ocean tide model in the CM frame as is appropriate for JPL orbits which are also in a centre of mass (CM) frame , with 342 companion tidal constituents computed using the hardisp programme . Ambiguities were fixed to integers where possible . Daily site coordinates were then transformed from the fiducial-free frame of the orbits to the IGS14 using the JPL seven-parameter transformation files.

The OSU processing was performed with double differences in the “GPS At MIT/Global Kalman filter” (GAMIT/GLOBK) software 10.71 using the Ohio State high-performance computing facility and a parallelised Python wrapper for GAMIT known as Parallel.GAMIT (available through GitHub at https://github.com/demiangomez/Parallel.GAMIT, last access: 2 August 2024). The GPS data were processed using the IGS14 final orbits.VMF1 grids were used with piecewise linear functions of 1 h resolution to estimate the atmospheric delay. FES2014b was applied to correct for ocean tidal loading. The Antarctic data were processed together with a regional network spanning most of the Southern Hemisphere to improve the ambiguity resolution and network stability. Due to the large number of stations, we split the processing into sub-networks of about 40 sites, which include stations from a daily “backbone” network (of about 50 sites with an aperture that spans the entire region of interest) and up to 9 stations from neighbouring sub-networks. The daily solutions of the sub-networks were combined using GLOBK to produce daily GPS polyhedrons. The IGb14 frame was realised following the regional methodology of , where position, velocity, and seasonal (periodic) parameters were inherited from the parent frame (60 stations of the IGb14) using a highly consistent combination of daily solutions of about 400 stations.

The NEWC Antarctic Centre analysed GPS observables using the “GPS At MIT/Global Kalman filter” (GAMIT/GLOBK) software 10.70 . The GAMIT software employs double-difference network solutions based on ionospheric-free linear combination of GPS observables to mitigate phase biases resulting from errors in receiver and satellite clocks. The NEWC Antarctic processing strategy is similar to , utilising a two-step approach . In the first step, GPS phase observations from each day were used to generate loosely constrained position and covariance solutions. The solutions obtained from the first step were then utilised in the second step within the Kalman filter to estimate a consistent set of coordinates, time series, and velocities. Satellite orbit parameters remained fixed to the IGS final repro3 orbit product values. This might introduce a small scaling effect due to the inconsistency of the repro3 product series with IGb14 and igs14.atx. Second-order ionospheric corrections were applied using the combined IGS IONEX files. The zenith wet delay (ZWD) was modelled using a piecewise linear function with a process noise uncertainty constraint of 20 mmh-0.5, with three north–south and east–west atmospheric gradients per day. We implemented the time-varying a priori zenith hydrostatic delay (ZHD) and Vienna mapping function (VMF1), derived from the ECMWF model . An elevation cut-off angle of 10° was used, and observations were weighted using an elevation-dependent scheme based on the post-fit residuals. We considered the effects of ocean tide loading by using the FES2014 model . Non-tidal atmospheric pressure loading (NTAL) deformation was considered at the observational level . We determined the deformation from VMF1 grids of the atmospheric pressure by convolution in the spatial domain using Green's functions in the CM frame. In order to ensure consistency with the solutions of the other ACs, the mean daily NTAL deformation was restored to the final coordinate time series. To perform a double-difference solution in GAMIT, a network of stations needs to be defined. For computational efficiency, the NEWC Antarctic network was divided into seven sub-networks, each containing up to 45 stations. The stations in each sub-network were chosen based on geographic location to minimise station baseline lengths, which improves integer phase ambiguity resolution. IGS tie stations, which are common to all sub-networks, were included to allow the combination of the sub-networks into a single full-network solution using GLOBK. To ensure past data integrity, a set of 40 global IGS stations is included for processing data before the year 2000, enhancing ambiguity resolution. In addition to Antarctic networks, we processed a global network based on IGS14 core stations, facilitating the integration of all subnetworks into a unified network solution using the GLOBK Kalman filter. Daily solutions were aligned with the ITRF2014 reference frame through estimation of rotations and translations, minimising position residuals at specified reference frame stations.

The site-wise tropospheric delay, in the form of the zenith total delay (ZTD), was estimated together with the daily station coordinates by each AC, as described in Sect. . We provide the site-wise time series of ZTD estimates as an auxiliary data set . The TUD, OSU, and NEWC ACs parameterise the ZTD as piecewise linear functions, leading to duplicate estimates at the day boundaries. To form a continuous time series, the estimates for each AC were averaged at the day boundaries. The high-rate UTAS solution was down-sampled by forming hourly averages. Here, we decided against the combination of ZTD results and, instead, provide the individual AC solutions.

As the major product, we provide the combined coordinate time series for 286 bedrock sites in Antarctica . The individual ACs provided solutions for 286 (TUD), 286 (UTAS), 258 (OSU), and 270 (NEWC) sites. The differences in the number of solutions are due to different approaches and thresholds concerning the quality or completeness of the observational data. The combination leads to a small increase in the total number of daily solutions. The comparison of the number of daily solutions per site between the combination and the individual solution with the most solutions results in a mean increase of 0.3 %. The resulting mean time base of the combined product is 10.5 years. Figure  shows an example coordinate time series comprising both the individual and combined solutions. To assess the repeatability and noise characteristics of the individual and the combined solutions, we analysed the coordinate time series of 29 stable cGPS sites. These sites were selected to cover a time span of at least 6 years, to have no reported snow intrusions, to not be subject to other external disturbances, and to be well distributed over the Antarctic continent (see Fig. ).

First, residual time series were formed by fitting and subtracting a deterministic model (Eq. ) from the time series (see Fig.  for an example time series). Post-seismic deformation terms were neglected for the selected sites. Steps were consistently introduced for all ACs and the combined time series. The repeatability of the coordinate time series is then described by the derived RMS over the residual time series. Table  displays the median RMS for each AC and the combined solutions. The NEWC solution shows the lowest RMS for the lateral components, with a median RMS of 1.4 and 1.2 mm for the north and east components, respectively. The solution of OSU reaches the smallest median RMS for the vertical coordinate component with 4.1 mm. The repeatability for the TUD and UTAS solutions show higher values for the north and up components. The RMS values of the combined time series resemble the lowest RMS of the best-performing individual solutions for the lateral components with -0.1 and -0.1 mm for the north and east components, respectively, compared to the best-performing individual solution. The RMS for the vertical component is found to be 0.4 mm larger than that of the OSU solution.

To further characterise the spectral properties of the residual time series, we calculated the Lomb–Scargle periodogram (LSP), a representation of the power-spectral density for non-uniformly sampled data . We used un-normalised LSPs where the power-spectral density takes values similar to those of a fast Fourier transform (FFT) analysis, differing by a factor of 2 in the case of a complete time series. LSPs were computed for all sites and each coordinate component for each AC and for the combined solutions. Subsequently, the median LSP was formed over all 29 sites, allowing for the direct comparison between the solutions (Fig. ).

Firstly, the periodograms confirm the generally lower noise levels of the lateral coordinate components of the NEWC and OSU solutions compared to the TUD and UTAS solutions, especially at high frequencies. All solutions follow the well-known power-law-like behaviour of GPS coordinate time series, close to flicker noise (spectral index equals -1) and white noise for very high frequencies . Differences between the solutions become apparent for distinct frequencies. Dominant peaks are visible for the otherwise very low noise periodograms of the NEWC (north, east, and up) and OSU (east) solutions at the fortnightly periods of 13.63 and 14.16 d, possibly resulting from “direct” and “indirect/aliased” errors in tidal models . Smaller peaks are visible at 9.4 d for UTAS (up) and at 9.14 d for NEWC (up), also resulting from direct and indirect errors in tidal models, respectively. At lower frequencies, distinct peaks at harmonics of the GPS draconitic year (351 d) are apparent . The combined time series reveals reduced amplitudes for the spurious signals at high frequencies, whereas the draconitic harmonics remain at high amplitudes. Combining the individual solutions, as described in Sect. , has several advantages over the individual solutions: the repeatability is similar to the best-performing single AC solution, the amplitudes of high-frequency interfering signals have been reduced, and the overall spatiotemporal coverage has been increased.

The effect of NTAL-induced deformations was removed from the combined coordinate time series to infer the final data set. A number of studies have discussed the influence of NTAL effects on GPS time series, leading to a reduction in the amplitude of annual signals and the residual RMS depending on the site location . For the selection of stable sites, we find a mean reduction in the residual RMS of 0.2, 0.0, and 0.9 mm (see Table ) and a mean reduction in the annual amplitude of 0.1, 0.0, and 0.6 mm for the north, east, and up components, respectively. The maximum reduction in the vertical annual amplitude of 2.5 mm was found for the FALL site. An increase in the annual amplitude was identified for sites in Dronning Maud Land, with a maximum of 1.6 mm for the ABOA site.

We realised the terrestrial reference frame IGb14 using a regional selection of reference sites for the individual AC solutions (see Sect. ). As shown by , using a sparse set of regionally distributed reference sites can introduce a (secular) bias in the coordinate solutions. This adds to the uncertainty in the reference frame itself, which shows a secular bias of 0.2 mmyr-1 on the polar axis when comparing ITRF2014 to ITRF2020 . Uncertainties in the reference frame realisation, especially on the Z axis, map onto the uncertainty in the local vertical coordinate component of sites in the polar regions and must be taken into account when using them for geodynamic studies (e.g. GIA).

In order to evaluate our results using an independent solution, we compared and validated the results of our GIANT-REGAIN (GR) combined solution with the data products of the Nevada Geodetic Laboratory (NGL), University of Reno . Their publicly available “living data set” consists of coordinate time series of more than 17 000 globally distributed GPS stations with more than 10 000 stations updated every week. The NGL processing employs the PPP processing strategy of the GipsyX software, which provides a computationally efficient method to process an immense number of data. The processing uses GPS observations only as well as JPL orbit and clock products (Earth orientation parameters, satellite clocks, and ephemerides). The coordinate solutions are realised in the IGS14 reference frame. We refer to web resources (http://geodesy.unr.edu/gps/ngl.acn.txt, last access: 2 August 2024) for further details on the NGL processing set-up. In their solutions, the critical metadata (including antenna types and heights) are extracted from the header section of RINEX observation files.

To compare the data sets we selected 157 sites (55 % of the GR data set) available in both data sets and downloaded the final, cleaned NGL time series of geocentric coordinates (Fig. ). For this comparison, neither data set was corrected for NTAL deformation.

To check the consistency of the data sets, we compared the linear rates of coordinate change derived from both data sets. For this purpose, the NGL data set is limited to the GIANT-REGAIN period from 1995 day of year (DOY) 001 to 2021 DOY 365. Further, we limited the analysed stations to those that have an observation span of at least 3 years in both data sets, resulting in a selection of 143 sites. We used the local topocentric coordinate representation (north, east, and up) for the analysis. The Hector software package v1.9 was used to fit a deterministic model (Eq. ) to the time series, while assuming a white and flicker noise stochastic model. The deterministic model is limited to a linear trend and potential offsets for eGPS sites. We extracted information on discontinuities for the NGL data set from the provided master step file database (http://geodesy.unr.edu/NGLStationPages/steps.txt, last access: 2 August 2024). Steps in the GR data set are consistent with those used in Sect. .

Sites with large trend differences exceeding 10 mmyr-1 in either the north, east, or up components were considered outliers and excluded from the subsequent analysis. Five sites exceeded this threshold: MBL3, SLTR, VL06, VL20, and VLHG. The large differences can be explained by different assumptions regarding antenna heights and the different identification of jumps in the GR and NGL data sets. The distribution of trend differences (GR – NGL) for the remaining stations reveals a high level of consistency (Fig. ). The mean differences and standard deviations can be considered small, with values of 0.1±0.6, 0.0±0.8, and 0.2±1.1 mmyr-1 for the north, east, and up components, respectively. The estimated rates are sensitive to the assumed steps in the deterministic models. We repeated the estimation of the trends for the NGL data set but introduced step information consistent with the GR data set. The increased consistency of the deterministic models leads to a further reduction in the trend differences for the lateral components to 0.0±0.4 and 0.0±0.5 mmyr-1 for the north and east components, respectively. The differences in the estimated rates reflect differences a user would obtain using either data set for the defined time span. They do not solely describe differences that result from the different processing strategies. Individual site time series may have different temporal coverage for either data set and, therefore, be affected differently by non-linear loading variations .

The NGL data set originates from a highly automated processing and retrieves the necessary metadata from the header section of the observational RINEX file , which can be prone to errors. The NGL data set provides antenna heights along with the coordinate time series, enabling comparison with the revised metadata information of the GR data set. The comparison reveals different antenna heights for 57 sites and antenna height differences greater than 4 mm (approximate noise level of the up component; see Table ) for 43 sites, equaling 36 % and 27 % of sites, respectively. Differences in the antenna heights do not necessarily result in differences in estimated trajectory models, e.g. if the antenna height difference is constant for the whole observation time or between estimated steps. We quantify the impact of the improved antenna height information by modifying the NGL time series of the up component uNGL(t) for the 57 sites as follows: 5uNGLmod(t)=u(t)NGL+HNGL(t)-HGR(t), where HNGL(t) is the antenna height provided by NGL at time t and HGR(t) is the antenna height provided by the GR data set at time t. We detrended uNGL(t) and uNGLmod(t) and computed the residual RMS for all 57 sites. The mean RMS shows a reduction from 21.3 mm to 8.5 mm, while the median RMS shows a reduction from 9.1 to 7.9 mm. The RMS reduction results from the correction of outliers and the reduction in the steps associated with antenna changes. Example coordinate time series displaying the effect of corrected antenna heights are given in the Supplement.