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: open (until 25 Mar 2026)
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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
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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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Interactive computing environment
Improving-GNSS-NTL Aino Schulz https://github.com/ainoschulz/Antarctica_NTL
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General comments
Minor comments