the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Nov 2025
Improving the precision of Antarctic GNSS time series through non-tidal loading corrections
Abstract. Precise Global Navigation Satellite System (GNSS) measurements are essential for monitoring vertical land motion in Antarctica, where geophysical processes such as glacial isostatic adjustment (GIA) and ice mass change produce complex and often subtle deformation signals. However, a substantial portion of the variability in GNSS time series is caused by non-tidal loading (NTL), which can bias trend estimates and obscure geophysical signals if left uncorrected. This study evaluates the impact of 11 NTL correction model combinations from EOST (École & Observatoire des Sciences de la Terre, Strasbourg) and ESMGFZ (Earth System Modelling Group of GeoForschungsZentrum Potsdam) on vertical GNSS time series at three East Antarctic stations located in Dronning Maud Land (DML) using five datasets processed with distinct strategies. Results show that NTL corrections substantially reduce root mean square (RMS), noise, and seasonal amplitudes in datasets with high initial variability, particularly in precise point positioning (PPP)-based solutions, while network-based and combined solutions show limited improvement or even increased variability. Among loading components, non-tidal atmospheric loading (NTAL) consistently yielded the greatest reductions, while the added contribution of non-tidal oceanic (NTOL) and hydrological (HYDL) loading were beneficial only in specific GFZ model combinations in PPP-processed datasets. GFZ corrections generally outperformed EOST at two stations, where RMS values were reduced by more than 20 %. On the other hand, EOST corrections were more effective at one station, where RMS values were reduced by approximately 15 %. These results demonstrate the critical role of processing strategy, NTL model choice, and station environment in improving Antarctic GNSS time series for geophysical interpretation.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-5358', Anonymous Referee #1, 14 Feb 2026
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AC1: 'Reply on RC1', Aino Schulz, 18 Feb 2026
We want to thank the reviewer for their helpful and valuable comments. We realise that there is room for improvement in terms of clarity and presentation. As many of the comments concern clarification, we have revised the manuscript accordingly as detailed below.
General comments
- The abstract should make clear if the network-based processing solution excludes NTL before the comparative corrections are evaluated. Same comment for the combined solution. It should be clear that the experiment of testing NTL is on solutions that don’t already have NTL applied.
We have clarified in both the abstract and the introduction how non-tidal loading (NTL) is treated in the different GNSS solutions.
- Abstract – we now explicitly state that we test NTL models on datasets that do not already include NTL corrections, and that the network-based and PPP solutions are NTL-free prior our experiments. The following sentences were added:
“For the precise point positioning (PPP) and network-based double-differenced (DD) solutions, we first use coordinate time series generated without any NTL corrections and subsequently apply the various NTL models. In contrast, the combined PPP+DD solution already incorporates a standard non‑tidal atmospheric loading (NTAL) correction in its operational processing, so we investigate the impact of alternative NTL model configurations relative to this pre-corrected reference.”
- Introduction – we added explicit statements about the NTL status of each solution:
“Given this context, this study aims to evaluate the impact of NTL corrections on GNSS time series in East Antarctica, focusing on three stations located in Dronning Maud Land (DML). We analyse three types of GNSS solutions: (i) global PPP solutions, (ii) regional network-based DD solutions, and (iii) a combined PPP+DD solution. For the PPP and DD solutions, we first use time series generated without any NTL corrections and subsequently apply different NTL models to assess their effect on seasonal signals, noise characteristics, and vertical velocities. For the combined PPP+DD solution, standard NTAL corrections are already applied in operational processing. We therefore assess additional model variants and their impact relative to this baseline.”
Minor comments
- Cite some of these “global analyses” referenced.
We have clarified and given examples of global studies that include Antarctic stations by adding explicit citations in the introduction.
- An editor should confirm the use of commas throughout the manuscript for consistency with journal requirements.
We have done our best to adjust comma usage for clarity and internal consistency. We will, of course, defer to the journal editor for final adjustments to ensure full compliance with the journal’s style guidelines.
- L70 – 75. Based on the content of the abstract, I expected some content about the types of solutions to be compared, i.e. PPP processed, network-processing (aka. double-differencing solutions), or other.
We agree that this information should appear earlier in the manuscript. The introduction has been revised to briefly describe the different GNSS solutions considered in this study. As mentioned earlier, we now explicitly state that we use (i) global PPP solutions, (ii) regional network-based double-differenced (DD) solutions, and (iii) a combined PPP+DD solution, and we summarise their main characteristics.
- Figure 1 inset – Add the location of the south pole.
We revised the Figure 1 inset to include the location of the south pole.
- A brief compare and contrast about PPP vs. DD processing in the introduction or methods (section 2) would help unfamiliar readers. Also, how is the PPP+DD GR solution created? Perhaps some details would help.
We thank the reviewer for this suggestion. We have added a concise comparison of PPP and DD processing strategies in the introduction. The new text reads:
“GNSS coordinates can be derived using different processing strategies, most notably Precise Point Positioning (PPP) and network-based double-differencing (DD) (Zumberge et al., 1997; Kouba and Héroux, 2001; Blewitt, 1989). PPP analyses undifferenced dual-frequency code and carrier-phase observations for each station independently, relying on precise external satellite orbit and clock products to realize positions directly in a globally consistent reference frame. This makes PPP particularly suitable for sparsely distributed stations and facilitates combination with global geodetic solutions. In contrast, DD processing forms linear combinations of observations between pairs of satellites and receivers, which effectively eliminate satellite and receiver clock errors and reduce other common mode effects within a regional network (Blewitt, 1989). By exploiting the integer nature of double-differences carrier-phase ambiguities, DD typically yields highly precise relative positioning and can supress spatially correlated errors, but it requires simultaneous observations across a network and well-connected station geometry. “
In section 2.1 (GNSS data and processing), we have expanded the description of how the combined PPP+DD solution (GR dataset) is constructed, including the main processing steps and combination strategy:
“The GR dataset was constructed by combining four independently processed GNSS solutions contributed by the GIANT-REGAIN analysis centres (TUD, UTAS, OSU, NEWC). Each centre used different software and processing strategies (PPP or DD) but adopted a common reference frame and consistent station metadata (Buchta et al., 2025c). The combination involved three main steps: (i) each centre generated daily coordinate time series using its own PPP or DD strategy; (ii) the individual daily solutions were aligned to a common set of regional IGb14 core sites by estimating six-parameter Helmert transformations for each day; and (iii) the transformed coordinate time series were combined station by station using variance-scaled weighted averages, so that solutions with lower residual noise received higher weight in the final GR product. In the GR combination, NTAL was modelled in the NEWC processing and then applied consistently in the combined coordinates. Thus, the GR dataset used in this study already includes standard NTAL correction. “
This should make the nature of PPP+DD (GR) solution clearer to readers who are less familiar with the dataset or with GNSS processing in general.
- Table 2. Expand acronyms as much as possible.
We have revised Table 2 to expand the acronyms as much as possible while keeping the table readable and concise.
- Figure 3. Please add subscripts to the acronyms to indicate if the solution is PPP or DD. Adding subscripts to all solution acronyms throughout the manuscript to indicate PPP or DD processing strategy would help readers.
We agree that it is important to clearly distinguish PPP and DD solutions. We have therefore introduced a consistent notation where subscripts indicate the processing strategy: “P” for PPP, “D” for DD, and “C” for the combined PPP+DD solution (i.e., AYP, NGLP, TUDD, OSUD, GRC). We introduce this notation at the beginning of section 4 and use the notation from then on forwards in the manuscript, in the text, tables, and figure legends, to make the processing strategy of each solution immediately clear.
- Need to always specify for clarity in technical writing “This” what? For example, L285. Also specify articles when possible, like “it” in L287.
We thank the reviewer for this observation. We have revised the manuscript to replace ambiguous pronouns such as “this” and “it” with explicit nouns wherever needed.
- By the time I got to L290, it became quite difficult to follow all of the acronyms. Consider spelling out throughout the manuscript the acronyms for the noise types, i.e. White Noise and Power Law Noise to reduce the number of acronyms. Also spell out regions, like ACC (L517).
We agree that the number of acronyms may hinder readability. To address this, we have:
- Spelled out the names of the noise types (white noise and power-law noise) throughout the manuscript instead of relying on acronyms, except where abbreviations are unavoidable in figures or tables.
- Reduced the use of other acronyms where possible and ensured that all remaining abbreviations are defined at first use.
- Spelled out regional names such as the Antarctic Circumpolar Current (ACC) at first occurrence and, where helpful, repeated the full name in sections where the acronym might be unclear to non-specialist readers.
These changes should make the text easier to follow, particularly in the results and discussion sections where many terms appear together.
- As someone who processes GPS data, I really want it to be clearer in this manuscript which solution is PPP and which one is DD with the subscript suggestion (see comment #8) since there is some debate in the geodetic community as to which approach is the most appropriate given various factors.
We appreciate this comment and have taken several steps to improve clarity:
- In the introduction and methods, we explicitly label each solution as PPP, DD, or PPP+DD when first introduced, and we briefly summarise their characteristics as noted above.
- Throughout the manuscript we consistently use notation that distinguishes PPP and DD variants (i.e. by adding subscripts to dataset names). In particular, Figure 3 and other relevant figures have been updated so that each solution acronym includes a subscript indicating whether it is derived from PPP or DD processing.
- Where we discuss results, we explicitly remind the reader which processing strategy (PPP, DD, or PPP+DD) is being referred to, to avoid ambiguity.
- Section 4.2 might be repetitive.
We have streamlined Section 4.2 to reduce repetition. Specifically, we shortened the introductory paragraph by removing restatements of the station set, datasets, and metrics already described in Sections 2 and 4. We also trimmed some of the “Overall…” summary paragraphs in subsections 4.2.1–4.2.3. The revised Section 4.2 now focuses on the essential station-by-station results, with broader synthesis presented only once.
- Be sure that the sigma-level is stated for the uncertainties clearly.
We thank the reviewer for this remark. We have clarified the uncertainty convention used throughout the manuscript. In the Methods section we now explicitly state that all reported uncertainties (±) correspond to formal one standard deviation (1σ) estimated by Hector using a maximum-likelihood approach with temporally correlated noise. We have also updated the relevant figure captions and table notes (e.g. Figures 3–5, Appendix A) to indicate that the plotted error bars and quoted uncertainties represent 1σ.
Citation: https://doi.org/10.5194/egusphere-2025-5358-AC1
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AC1: 'Reply on RC1', Aino Schulz, 18 Feb 2026
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RC2: 'Comment on egusphere-2025-5358', Anonymous Referee #2, 16 Jul 2026
The manuscript evaluates the effect of 11 non-tidal loading (NTL) correction combinations from EOST and ESMGFZ on the vertical GNSS time series of three stations in Dronning Maud Land (ABOA, SYOG, VESL), using five differently processed datasets and the Hector software to estimate trends, seasonal amplitudes and noise parameters. The topic is relevant, the amount of work is considerable, and the demonstration that correction effectiveness depends strongly on the processing strategy (PPP versus double-difference or combined solutions) is a useful result, since few studies have examined NTL performance specifically in Antarctica. However, in its present form the manuscript is hard to read: it never explains why this analysis matters, its most striking result (correction-induced trend changes of up to 1 mm/yr at ABOA) is reported but not explained, the noise analysis adds little to the story, and the results sections largely recite numbers that are already in the figures and appendices. I therefore recommend major revisions.General comments1. The problem setting and the "why" of the study are missing.The introduction motivates NTL corrections with generic arguments (GGOS accuracy goals, ITRF and EOP quality, lines 44–52) that apply to any GNSS station in the world. What is never spelled out is why this matters in Antarctica in particular: (i) the continent has very few ground stations of any kind (meteorological, GNSS, tide gauges), so little ground truth enters the weather and ocean models on which the NTL corrections themselves are built — the corrections are therefore least reliable exactly where they are applied here, a circularity the reader should be made aware of; (ii) surface loading associated with ice-mass change produces both a seasonal signal and a secular vertical motion, and these, together with GIA, are key indicators of climate change — GNSS vertical rates in Antarctica are, for instance, essential for validating the GIA models used to correct GRACE/GRACE-FO mass balances; (iii) consequently, the long-term linear trend and the seasonal signal are the target quantities of this study, and RMS or noise reduction is only a means to estimate them better, not an end in itself.I strongly recommend rewriting the introduction (and the abstract) around these points: state which signals matter in Dronning Maud Land, how large they are expected to be (predicted GIA uplift rates, expected elastic response to present-day ice-mass change), and how unmodelled loading biases them. Without this framing the reader has no way to judge whether, for example, a trend change from −0.49 to +0.54 mm/yr is an improvement or a degradation.2. The correction-induced trend changes at ABOA are reported but not explained.At ABOA the uncorrected TUD solution shows subsidence (−0.49 ± 0.67 mm/yr) which every correction makes more positive, up to +0.54 ± 0.14 mm/yr with EOST4 (lines 320–323) — the sign of the vertical motion flips. At the same station the AY solution barely reacts (0.44 → 0.43–0.53 mm/yr). I do not understand why, and the manuscript does not tell me. Since all datasets at a given station receive the identical correction time series, a correction cannot by itself move one solution’s trend by 1 mm/yr and leave another’s unchanged; the difference must arise from the interaction of the correction with data gaps, offsets and noise levels that differ between solutions. Two analyses would clarify the mechanism: (a) report the linear trend contained in each NTL correction series itself over the analysis period 2003–2021 — any secular rate in, e.g., the modelled ocean bottom pressure or atmospheric pressure maps directly into the corrected GNSS trend, and the reader should know how much of the trend change is simply the trend of the correction; (b) quantify the coupling between seasonal signal and trend estimation in series with long gaps — ABOA has multi-month gaps in 2006 and 2021 (line 249), and changing the seasonal amplitude changes the estimated trend through this coupling (cf. Bos et al., 2010, already in the reference list). Without such an analysis the reader cannot tell whether the corrected trends are more accurate or merely different, which undermines the concluding claim (lines 576–578) that the results have critical implications for GIA research.3. The noise analysis adds little to the story in its current form.Section 4.2.3 enumerates power-law and white-noise amplitudes and spectral indices per station, dataset and model, but their physical meaning is not discussed, and several results look like estimator artefacts rather than changes in the data: the WN amplitude jumps from 0.46 to 2.46 mm while PL drops (AY EOST1 at ABOA, line 390), or collapses from 1.04 to 0.01 mm (OSU EOST2); the spectral index at ABOA flattens from −0.96 to −0.42 (AY GFZ3, Appendix A), and trend uncertainties shrink by factors of 3–5 (TUD at ABOA: 0.67 → 0.14 mm/yr). In a PLWN model the two amplitudes and the spectral index are strongly correlated parameters, so such trade-offs must be interpreted with caution before drawing conclusions about the noise itself — and the strongly reduced trend uncertainties may well be over-optimistic. I suggest either (a) tying the noise analysis to the motivation of general comment 1, i.e. translating the post-correction noise properties into trend detectability (how many years of data are needed to detect a given uplift rate, before and after correction), which would give the section a clear purpose, or (b) condensing it to a short paragraph plus a table.4. The results sections summarise too little and list too much.Large parts of Sections 4.1–4.2.4 (e.g. lines 259–282, 318–337, 353–369, 384–404) recite values that are already shown in Figures 3–7 and tabulated in Appendices A and B, so the reader receives the same numbers three times but the message not once. Each subsection should open with its finding in one or two sentences, support it with a few representative numbers, and refer to the figures and appendices for the rest. The excellent question the authors raise themselves at lines 297–300 — which dataset most accurately represents geophysical reality? — is asked and then dropped; the Discussion should attempt an answer, for example by confronting the corrected trends with independent GIA and elastic-loading predictions for Dronning Maud Land, which would also close the loop with general comment 1.5. Internal consistency of the comparison.The five datasets are expressed in different reference frames (IGS14, IGb14, IGS20) and the authors themselves note associated velocity differences of 0.1–0.3 mm/yr (lines 110–112) — the same order of magnitude as the trend effects under study — yet the frames are not harmonised and this is not propagated into the interpretation. The NTL corrections are provided in the CF frame, whereas only the AY solution is in CF (line 150) and the others are aligned to ITRF realizations; the neglected (seasonal) geocenter motion affects annual amplitudes and deserves discussion. Finally, the GR combination already contains NTAL applied during processing, yet EOST6/GFZ4/GFZ5 stack NTOL and HYDL from a possibly different model family on top of it; a comment on the consistency of that mixture is needed.Specific comments- Abstract: like the results sections, it is dominated by percentages. State the purpose (recovering trend and seasonal signals in a data-sparse, climatically critical region) and the main conclusion in physical terms.- Lines 82–84: the justification "computational constraints" for using only three stations is weak — a Hector analysis of a few additional stations is cheap. The record-length argument alone is the convincing one; consider dropping the computational one.- Line 103: NGL does not process ABOA, so ABOA is compared over four datasets and the other stations over five. Make this explicit in the figure captions to avoid confusion.- Lines 184–196: Eqs. (1)–(2) are textbook material and can be removed or moved to an appendix.- Lines 205–213: the PLWN choice is defended by citations only. Did the authors test alternative noise models, or use an information criterion (AIC/BIC as available in Hector) for model selection? Given general comment 3, this matters for the trend uncertainties.- Lines 214–217: clarify what "residuals" means here (post-fit residuals after removing trend, seasonal terms and offsets?) and therefore what the RMS reduction of Eq. (6) actually measures. If the seasonal signal is estimated and removed before computing RMS, the RMS change reflects mainly the stochastic part; state this explicitly.- Lines 250–252: "ABOA shows a quite even trend" contradicts the −0.49 mm/yr found for TUD later; the qualitative description of Figure 2 should be made consistent with Figure 3.- Lines 338–344: with three stations in one region, statements about "effects across Antarctica" are too strong; restrict conclusions to Dronning Maud Land here and elsewhere (also line 575).- Lines 374–376: phase shifts of the seasonal signal are mentioned but never shown; add a table or figure, or remove the statement.- Lines 412–414: state which dataset lacked formal errors; WRMS could still be reported for the other four datasets.- Lines 434–448: the attribution of the OSU/TUD behaviour to reference-network geometry is plausible but speculative; phrase it as a hypothesis or support it with a test (e.g. common-mode analysis).- Lines 474–479: the suggestion that increased snow accumulation produces elastic loading that slows the observed uplift (Medley et al., 2018) is exactly the kind of loading-trend mechanism that general comment 2 asks for — develop it quantitatively rather than in passing.Technical corrections- Figure 7 caption: refers to WRMS while the figure and Section 4.2.4 analyse RMS.- Line 147: format the process-noise unit properly (m/√s rather than "m/√sec" in text math).- Line 374: "Phase shits" → "Phase shifts".- Line 429: "benefits again the least form the corrections" → "from".- Line 549: "sparce" → "sparse".Citation: https://doi.org/
10.5194/egusphere-2025-5358-RC2 -
AC2: 'Reply on RC2', Aino Schulz, 17 Jul 2026
We want to thank the reviewer for the detailed and constructive assessment. We agree that the previous version motivated NTL corrections too generally and did not sufficiently frame the study around the Antarctic geophysical problem. In the revised manuscript, we have rewritten the abstract, introduction, results, and discussion to emphasize that the quantities of primary interest are vertical trends and seasonal signals relevant to GIA, present-day ice mass change, and Antarctic mass-balance studies. RMS and noise metrics are now presented as diagnostics of time series quality. We have ran again the analyses with all time series harmonized to the IGS20 reference frame and adjusted the rest of the text accordingly. We also softened interpretations that were not directly supported by the results.
General comments
- The problem setting and the "why" of the study are missing.
We agree that the original introduction relies too heavily on general GNSS and reference-frame motivations and did not sufficiently explain why NTL corrections are important and difficult in Antarctica. We will therefore rewrite the abstract and introduction to focus on Antarctic vertical land motion, where the primary target quantities are the long-term vertical trend and the seasonal signal. The revised will text focus on the role of GNSS in separating GIA, present-day ice-mass change, and elastic loading, and in validating GIA models used in Antarctica.
We also add text explaining that Antarctic NTL corrections are difficult to validate due to limited data and infrastructure. Concerning signal magnitudes, we will include published estimates of expected GIA and present-day elastic loading rates for the Dronning Maud Land sector to provide context.
- The correction-induced trend changes at ABOA are reported but not explained.
We agree with the reviewer that this point requires additional analysis. We are adding an analysis of the linear trend contained in each NTL correction series over 2003–2021, both for the complete correction series and after sampling the corrections at the epochs of each GNSS dataset. The results and discussion will be revised accordingly, and the interpretation of the sign change will be softened.
- The noise analysis adds little to the story in its current form.
We agree that the previous noise section listed too many stochastic parameters without sufficiently explaining their role in the study. We will condense the section and now emphasize the power-law amplitude, white noise amplitude, and spectral index are jointly estimated and can trade off in a PLWN model, especially in a gappy time series. The noise analysis will be used mainly to assess changes in low-frequency variability and formal trend uncertainty, rather than to interpret each noise parameter as a separate physical process. Overall, we will change the structure of the results section as discussed more in the response for comment 4.
- The results sections summarise too little and list too much.
We agree that the results section previously repeated too many numerical values and contained content more appropriate for the discussion. We will restructure our results into two headings “4.1 Comparison of uncorrected GNSS datasets” and “4.2 Impact of loading corrections on GNSS time series” so that the text would not be too repetitive and only gives the main representative values with the rest being shown in figures, table or appendices. We already moved interpretive explanations about processing strategy, GRC behaviour, and GIA implications from the results to the discussion.
- Internal consistency of the comparison.
We agree that reference-frame consistency is an important limitation. To reduce this inconsistency, we are currently reprocessing the comparison after transforming the GNSS time series to a common IGS20 frame. The methods, results, and discussion will be updated accordingly. We still note that residual differences may remain because the products were originally generated with different processing strategies, metadata, and a priori corrections.
The EOST and ESMGFZ loading series were requested in CF frame. We now clarify that this may not be fully consistent with all GNSS products, as the reference frame convention is not always documented. Therefore, we also did not apply a correction for seasonal geocenter motion, so any inconsistency between CF-, CE-, and CM-based products could contribute to small differences in the estimated seasonal signals and long-term trends.
Finally, we clarified the treatment of GRC. Because it already includes standard NTAL correction during operational processing (although we don’t know which model), the GRC-specific EOST/GFZ4/GFZ5 tests add NTOL and/or HYDL on top of a precorrected solution. These combinations are therefore sensitivity tests rather than internally homogeneous full NTL solutions. We will state that this model-family mixing may partly explain the limited or negative response of GRC to additional corrections.
Minor comments and technical corrections
We thank the reviewer for these detailed specific comments. We will revise the manuscript accordingly. The abstract will be rewritten to state the purpose and main conclusion more clearly. We removed “computational constraints” as a justification for selecting three stations and now justify the selection based on record length and environmental setting. We clarified also in the relevant figures that NGLP is unavailable at ABOA, so ABOA is compared using four datasets and SYOG/VESL using five. The coordinate transformation equations have been removed from the main text.
We clarified the stochastic modelling and RMS methodology. We did indeed test alternative noise models and found that the PLWN model generally performs slightly better than other combinations based on the AIC and BIC values. This has been added to the text. We also define residuals explicitly as post-fit residuals obtained after removing the estimated trend, seasonal terms, and offsets. Accordingly, the RMS reductions are interpreted as a reduction in remaining post-fit variability.
The qualitative description of ABOA will be revised to be consistent with the Hector-derived trends. Statements that previously generalized the results to all Antarctica have been restricted to Dronning Maud Land. The statement about seasonal phase shifts has been addressed. We now state which dataset lacks formal errors and report WRMS in the appendix where formal uncertainties are available.
The interpretation of OSUD/TUDD differences in terms of reference-network geometry has been rephrased as a hypothesis, since no common-mode or controlled-network test was performed. The statement concerning increased snow accumulation will also be revised. The technical corrections to the figure captions, units, and typographical errors have been noticed and made.
Citation: https://doi.org/10.5194/egusphere-2025-5358-AC2
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AC2: 'Reply on RC2', Aino Schulz, 17 Jul 2026
Interactive computing environment
Improving-GNSS-NTL Aino Schulz https://github.com/ainoschulz/Antarctica_NTL
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General comments
Minor comments