the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Aug 2026
Accounting for shelf-width in selecting altimetry observations for estimating coastal sea level changes improves its agreement with tide gauges
Abstract. Monitoring coastal sea level change is critical as sea level rise becomes inevitable due to climate change. The global tide gauge (TG) network is sparse and suffers from data gaps, while satellite altimetry performance near the coast remains spatially inconsistent. Here, a novel dynamically varying search radius algorithm (DSR algorithm) is developed that uses bathymetry to choose satellite observations that represent coastal sea level variability better. The DSR algorithm is applied to the low-resolution (1 Hz) coastal product, X-TRACK SLA L2P v2.2 (XTRACK), and is evaluated through comparison with TG and the high-resolution (20 Hz) coastal product, XTRACK/ALES (Along-track sea level anomalies and trends v3.0). To assess the benefit of DSR, existing observation-selection algorithms are applied to both XTRACK and XTRACK/ALES and compared against TG using detrended deseasonalized coastal sea level anomalies. This inter-algorithm comparison at 272 TG stations demonstrates broader applicability of DSR across various coastal regimes, with consistently higher median correlation and lower median Normalized Root Mean Square Error. The improvement using DSR is especially pronounced along narrow coastal shelf regions. Additionally, the DSR-applied XTRACK's ability to capture coastal sea level anomalies at multiple temporal scales is assessed at 264 stations, showing improved agreement for both seasonal (annual) and non-linear trend (interannual and trend) signals. In some regions, such as the eastern Australian coast and Gulf of St. Lawrence, lower correlation and higher Root Mean Square Error for residual signals are reported, which are discussed. Further, Coastal Sea Level Trends (CSLT) for 1994–2023 (30 years) from DSR-based XTRACK match TG trends within their uncertainties. Notably high CSLT values are observed in the Gulf of Mexico (5.09±0.57 mm/yr from altimetry and 5.2±0.67 mm/yr from TG) and the Baltic Sea (4.62±1.3 mm/yr from altimetry and 4.24 ±1.37 mm/yr from TG).
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-4902', Anonymous Referee #1, 13 Oct 2026
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AC1: 'Reply on RC1', Vandana Sukumaran Nair, 21 Oct 2026
We thank the reviewer for the time taken in reviewing our manuscript. We have addressed each comment individually by providing a detailed response and the corresponding actions taken to revise the manuscript. Please refer to the attached document for point-by-point response to all comments.
Since the main concern was readability, we will reduce the use of abbreviations throughout the manuscript. For several other comments, the points raised are already covered in the original manuscript; in those cases, we will point to the relevant sections and, will make necessary clarifications in the text to avoid any ambiguity. Looking forward to constructive comments.
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AC1: 'Reply on RC1', Vandana Sukumaran Nair, 21 Oct 2026
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RC2: 'Comment on egusphere-2026-4902', Anonymous Referee #2, 14 Oct 2026
General comments
This manuscript presents a Dynamic Search Radius (DSR) algorithm for selecting altimetry observations in coastal sea level monitoring, grounded on a physically sound hypothesis relating shelf-width to coastal sea level dynamics. The global validation across 272 tide gauge stations and the exhaustive inter-algorithm comparison represent a substantial contribution to the field. However, several issues need to be addressed before the manuscript can be accepted for publication.
Despite the clear effort invested, the manuscript suffers from a lack of organization in the presentation of the algorithms and their comparisons, which makes it difficult for the reader to follow the overall logic of the analyses. The large number of algorithms and metrics introduced, combined with changing station subsets across sections, results in a narrative that is hard to track even for a specialist reader. Related to this, the authors tend to emphasize the strengths of the DSR approach while the limitations and potential drawbacks receive insufficient attention.
On the methodological side, several points require clarification. The central comparison between X_DSR and ales_300 is problematic since both algorithms operate on products of fundamentally different spatial resolutions, making it difficult to isolate the effect of the algorithm from the effect of data resolution. Furthermore, the authors do not justify why DSR was not applied to XTRACK/ALES, which would have been a natural and informative comparison. Additionally, given that DSR selects observations over a relatively large area along the shelf, it is worth discussing whether averaging gridded altimetry products over a similar search radius would yield comparable results, which would put the actual added value of the algorithm in perspective. The physical interpretation of the NLT results also deserves deeper treatment, as the large spatial footprint of low-frequency signals may partly explain the high agreement at that temporal scale independently of the algorithm. Finally, the role of tidal and DAC corrections is mentioned only superficially, and the contribution of VLM to the results is unclear and should be clarified or streamlined.
Throughout the manuscript, two distinct problems in coastal altimetry appear to be conflated, which undermines the clarity of the contribution. The first is the problem of measurement precision: how to obtain reliable altimetric observations as close as possible to the coast, which is addressed by dedicated retracking strategies such as ALES or FF-SAR and specialized geophysical corrections. The second is the problem of observational representativeness: given a set of available observations, how to best select and combine them to represent coastal sea level variability at a given location. The DSR algorithm clearly belongs to the second category, as it selects and averages observations distributed along the shelf within a search radius that can reach up to 250 km, without necessarily bringing the measurements closer to the coast. These are fundamentally different objectives, and conflating them leads to misleading comparisons with high-resolution products such as XTRACK/ALES, whose added value lies primarily in improving measurement precision near the shore. The authors should explicitly position their contribution within this framework from the outset, and ensure that the comparisons and conclusions are interpreted accordingly throughout the manuscript.
Based on the above, I recommend Major Revision. The underlying idea is sound and the validation effort is commendable, but the manuscript requires substantial improvements in organization, depth of discussion, and methodological transparency before it can be considered for publication.
Specific comments
Page 1, line 12: replace “dynamically varying search radius” with “Dynamically varying Search Radius”
1 Introduction
Page 2, line 41: replace “significant wave height” with “Significant Wave Height”
Page 2, line 44: Add that part of the coastal altimetry is the use of global models to represent the dynamics of tides and sea level due to high frequency winds (tidal models and DAC).
Page 2, line 47: add “Adaptative Leading Edge Subwaveform” before “, Passaro et al., 2014)”
Page 2, line 51: delete “(Adaptative Leading Edge Subwaveform)”
Page 2, line 56: replace “coastal sea level trends” with “Coastal Sea Level Trends”
Page 3, line 65: replace “sea level anomaly” with “Sea Level Anomaly”
Page 3, lines 81-83: The authors state that ‘coastal sea level variability is more sensitive to local ocean dynamics, which is influenced by the continental shelf-width [...] we hypothesize that selecting altimetry points along the coast and within the shelf would represent the coastal sea level better.’ However, the logical connection between these two statements is not sufficiently justified. The fact that coastal sea level variability is influenced by shelf-width does not automatically imply that observations outside the shelf are less representative, and this assumption deserves a more explicit physical justification. Furthermore, it is not clearly discussed how this hypothesis and the resulting algorithm differ conceptually from the approach of Cazenave et al. (2022), who also averaged altimetry observations along and across tracks in the vicinity of each tide gauge and found substantial improvements in correlation. The added value of DSR with respect to that work should be explicitly stated.
Page 3, line 91: The term ‘non-linear trend (interannual and trend)’ is confusing. It is unclear whether the linear trend is included in or removed prior to computing the NLT component. The use of the term ‘non-linear trend’ to describe a signal that apparently includes a linear trend component is contradictory and should be clarified here. This will be further commented in the methodology section.
2 Data and Methods
Page 4, line 100: the corrections include the geophysical ones and here is a good place to introduce them.
Page 5, lines129-138: The discussion about temporal sampling differences between tide gauges and altimetry missions is valid, but it is misleading in this context since TG data used in this study corresponds to monthly means from PSMSL, and therefore altimetry observations are also averaged to monthly means. This should be clarified upfront to avoid confusion.
More importantly, the authors should explicitly describe how tidal correction is handled in both datasets. For the TG monthly means, it is commonly assumed that averaging over a month effectively removes the tidal signal. If this assumption holds, it would be worth discussing whether the same approach could be applied to the altimetry data, i.e., adding back the tidal signal to XTRACK and XTRACK/ALES observations before computing monthly means, and then comparing results with and without explicit tidal correction. This would provide a more consistent treatment of both datasets and could also serve as an interesting sensitivity test to evaluate the impact of tidal correction on the final results.
2.1.3 DAC and VLM products
I suggest explaining which is the purpose of DAC and VLM and what they represent.
2.2 Methods
Page 7, line 184: Table 1: The selection of algorithms applied to XTRACK and XTRACK/ALES differs substantially. It is not clear to this reviewer whether this choice is based on previous literature or on other criteria, and if so, the relevant references should be made more explicit. Furthermore, and more importantly, it is not explained why the DSR algorithm was not applied to XTRACK/ALES, which would have been a natural and informative comparison to isolate the effect of the algorithm from the effect of data resolution. This omission limits the interpretation of the results and should be addressed.
Page 9, lines 200-204: The description of the STL decomposition and its resulting components is insufficient and needs to be clarified. First, the term ‘non-linear trend’ is contradictory when the authors simultaneously state that it includes the linear trend. It should be explicitly stated whether the linear trend is removed prior to the STL decomposition or whether it is retained as part of the NLT component, and why. Second, there is an apparent overlap between the NLT and the residual components, as both are described as capturing interannual variability. The frequency bands effectively isolated by each component should be clearly defined. Third, the STL decomposition is sensitive to the choice of smoothing parameters, which are not reported. These should be specified, as they determine what signals are attributed to each component and are therefore critical for the interpretation of the results in sections 4.3 and 4.4.
Page 9, 2.2.4 Ellipsoidal Correction
The ellipsoidal correction described in this section is not clearly justified in the context of all analyses performed in this study. While I agree that TG and altimetry measure sea level with respect to different reference surfaces, and that this correction is necessary for long-term trend analysis, it is not required for the comparison of detrended sea level anomalies. In the case of detrended SLA derived from both TG and altimetry, removing the temporal mean over the same period is sufficient to eliminate any constant offset between the two reference surfaces. The authors should clarify in which specific analyses this correction is applied and why.
Furthermore, it is not clear how this correction relates to the VLM correction applied using GPS data. If the TG record is corrected for VLM and subsequently referenced to the ellipsoid, there is a risk of double-counting some components of vertical motion. The relationship between both corrections should be explicitly described, and it should be clarified whether the ellipsoidal correction and the VLM correction are applied independently or in combination, and to which subset of stations and analyses each applies.
Page 10, line 238: replace “2017” with “2022”
Page 14, lines 291-298: I suggest to summarize in a table or rewrite in a friendly way.
The manuscript does not clearly explain whether the altimetry time series compared against tide gauge records corresponds to a spatial average of all observations within the DSR search radius, or whether comparisons are performed point by point along individual satellite tracks. While the methodology section and the flowchart in Figure 2 suggest that a spatially averaged time series is computed for each tide gauge station, this is inconsistent with several figures throughout the manuscript. Figures 6, 7 and 8 display correlation and NRMSE values along individual altimetry tracks, and Figures 5, 9 and 10 show maps of correlation and NRMSE without clarifying whether these metrics derive from a spatially averaged altimetry series or from individual track comparisons. This ambiguity propagates through the results and should be resolved with a clearer and more explicit description of how the final altimetry time series is constructed and what exactly is being compared against the tide gauge record at each stage of the analysis.
4 Results and Discussion
Page 14-20: Sections 4.1 and 4.2: The distinction between these two sections is not sufficiently clear. Section 4.1 presents an inter-algorithm comparison based on correlation and NRMSE, while section 4.2 shifts to a geographical analysis of the performance of X_DSR and ales_300 against TG. However, this change of focus is not explicitly announced and the transition between both sections lacks a clear connecting narrative. The authors should either unify both sections under a common framework or provide a more explicit justification for treating them separately, ensuring that the reader can follow the overall logic of the results without having to infer the structure of the analysis.
Page 15, lines 334-339: While the improved performance of DSR along narrow shelf regions is a relevant result, the authors should provide a more thorough physical interpretation. Part of the improvement may be attributed to the fact that the continental shelf exhibits fundamentally different ocean dynamics compared to the open ocean, and restricting observations within the shelf selects a signal that is physically more coherent with what the tide gauge measures. Furthermore, since the compared signal is detrended and deseasonalized, the analysis is effectively focused on low-frequency residual variability, which tends to have a larger spatial footprint and is therefore more coherent along the shelf. This has important implications for the interpretation of the results and should be explicitly discussed.
Page 16, Figure 3a-b: It is not clear how the statistical metrics were computed for the nearest point algorithms (X_npoint and ales_np). Unlike the search radius or nearest pass approaches, which aggregate multiple observations, the nearest point method selects a single altimetry point per station. This raises the question of how a boxplot with a median and dispersion can be constructed for this algorithm: if only one point is selected per station, each station contributes a single correlation or NRMSE value, and the boxplot would only reflect the spread across stations within each region, not within each station. The authors should clarify how the nearest point time series is constructed and whether the boxplot representation is consistent across all algorithms shown in the figure, as mixing single-point and multi-point approaches without clarification may lead to misleading interpretations.
4.2 Comparing XTRACK/ALES and XTRACK with TG data
The choice of ales_300 as the benchmark for comparison with X_DSR is not sufficiently justified. It is unclear whether ales_300 was selected because it consistently outperformed all other XTRACK/ALES algorithms in section 4.1, and if so, this should be stated explicitly with reference to the relevant results. More importantly, the most natural and informative comparison would have been between X_DSR and a DSR-based version of XTRACK/ALES, which would allow isolating the effect of the algorithm from the effect of data resolution. The absence of this comparison is a significant limitation that undermines the conclusions drawn from this section, and the authors should provide a clear justification for this methodological choice.
Page 18, line 382: replace “Mar del Plata” with “Palermo”. Mar del Plata station is outside the Rio de la Plata estuary.
Page 18, lines 391-395: The physical interpretation of the discrepancy observed at Skagway and Juneau stations is not clearly stated. The authors describe seasonal changes in precipitation, freshwater runoff, heat content and salinity, but do not explicitly connect these factors to the altimetry-TG discrepancy. If the intended interpretation is that freshwater-driven buoyancy effects generate a local sea level signal that the altimeter cannot capture because the available observations are too far from the tide gauges, this should be stated explicitly. The current description leaves the reader to infer the physical mechanism, which weakens the discussion. The authors should clarify the causal chain between the hydrological forcing and the observed discrepancy in altimetry-TG agreement.
Page 20, Figure 6: This figure is confusing. First, it simultaneously shows point-by-point correlation coefficients along individual satellite tracks and spatially averaged time series compared against the tide gauge, without clarifying the relationship between these two representations. If X_DSR and ales_300 both produce a single spatially averaged time series per station, it is unclear what the track-by-track correlation map represents and how it was computed. Second, the time series comparison shows that both X_DSR and ales_300 perform similarly at this station, which raises the question of what this example is meant to illustrate. Third, and more importantly, the fact that the highest correlations are found along the western track rather than the closest track to Eden is physically relevant and deserves discussion, as it suggests that the spatial coherence of the sea level signal in this region does not follow a simple distance-to-coast gradient.
Page 20, line 411: This statement reinforces a concern raised earlier in this review. The authors acknowledge that XTRACK/ALES performs better at narrow coasts due to its ability to retrieve observations closer to shore, which is precisely the problem that the DSR algorithm aims to address. This makes the absence of a DSR-based version of XTRACK/ALES even more difficult to justify. Applying DSR to XTRACK/ALES would have been the most natural and fair comparison, and would have allowed isolating the contribution of the algorithm from that of the underlying data resolution. As noted previously, the lack of this comparison is a significant limitation of the study. More generally, it difficult to follow the overall logic of the analyses throughout sections, despite the clear effort made by the authors. A more systematic and transparent presentation of the algorithm comparisons would substantially improve the readability and impact of the manuscript
Page 22, Section 4.3: This section is confusing because the validation of interannual and detrended signals was already addressed in sections 4.1 and 4.2, and the reader struggles to identify what new information is being presented here. The key differences with respect to the previous sections, namely the use of a longer time period (1994-2023) and the explicit evaluation of the seasonal signal, are not clearly stated at the outset. The authors should revise the title and introductory sentences of this section to explicitly highlight these differences, making clear that the added value of this analysis lies in the extended temporal coverage and the inclusion of the annual signal, rather than presenting it as a repetition of previous results.
Page 23, line 449: The authors refer to ‘interannual sea level’ variability as part of the residual signal, which is inconsistent with the definition provided earlier where interannual variability is described as a component of the NLT. This contradiction reinforces the concern raised previously regarding the unclear separation between the NLT and residual components, and should be resolved with a consistent and explicit definition of the frequency bands captured by each component throughout the manuscript.
Page 23, line 454: For the discussion of coastal trapped waves, I recommend the following article: Passaro, M.: Can satellite altimetry observe coastally trapped waves on sub-monthly timescales?, Ocean Sci., 21, 2663–2679, https://doi.org/10.5194/os-21-2663-2025, 2025.
Page 23, line 457: The physical interpretation offered here is incomplete. If the poor residual signal correlation in tidally dominated estuaries is related to tidal influences, then the discussion should focus on the limitations of the global tidal model used for the altimetry correction, which is known to perform poorly in shallow and estuarine environments. In that case, the residual altimetry signal would contain uncorrected tidal energy that is not present in the monthly TG SLA, which already has the tidal signal effectively removed by temporal averaging. The SLA, as measured by both altimetry and TG, should ideally reflect halosteric and thermosteric variability, and the authors should clarify whether the observed discrepancy is due to inadequate tidal correction in the altimetry product rather than an inherent limitation of the DSR approach.
Page 23, lineas 466-470: The finding that no significant bias exists between TG referenced to the ellipsoid and altimetry-derived SLA is expected and not surprising. When the temporal mean is removed to compute SLA, any constant offset between the two reference surfaces is effectively cancelled, regardless of whether the TG is referenced to a local datum or to the ellipsoid. Therefore, this analysis does not provide additional insight for the comparison of detrended sea level anomalies. As noted in the comment on section 2.2.4, the ellipsoidal correction is relevant and necessary for the analysis of long-term trends, but its application and interpretation should be clearly restricted to that context throughout the manuscript. I recommend
Gregory, J. M., Griffies, S. M., Hughes, C. W., Lowe, J. A., Church, J. A., Fukimori, I., ... & van de Wal, R. S. (2019). Concepts and terminology for sea level: Mean, variability and change, both local and global. Surveys in Geophysics, 40(6), 1251-1289.
Page 28, line 521: I believe that the article https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2009JC005767 cited on the introduction will help with the discussion of the seasona-annual cycle
Page 28, Lines 528-530: These concluding statements raise several concerns that are not adequately addressed in the manuscript. First, the claim that XTRACK (1 Hz) performs comparably or better than XTRACK/ALES (20 Hz) deserves a much more careful interpretation. Both products may not be corrected by the same geophysical models, and differences in tidal and DAC corrections could explain part of the observed performance gap independently of the retracking strategy. The authors should clarify whether the same corrections were applied to both products and discuss the potential impact of differences in geophysical corrections on the results. It is worth noting that in coastal areas, high-resolution retracked products such as ALES have been shown to outperform standard products (e.g., Lago et al., 2017, in the San Matías Gulf), suggesting that the relationship between resolution and performance is not straightforward and may depend on the signal-to-noise ratio and the quality of geophysical corrections in each region.
Second, the conclusion that altimetry effectively captures coastal sea level variability at monthly and longer temporal scales is not surprising given that the compared signal is detrended and deseasonalized, retaining primarily low-frequency variability. As noted earlier in this review, low-frequency signals have a larger spatial footprint and are therefore more coherent over extended areas, which naturally favors agreement with tide gauge records independently of the algorithm used. This is particularly relevant for stations in dynamically complex areas such as Brest, where good agreement at long temporal scales would be expected precisely because the dominant low-frequency forcing operates at regional scales. This physical context should be explicitly acknowledged in the conclusions.
Lago, L. S., Saraceno, M., Ruiz-Etcheverry, L. A., Passaro, M., Oreiro, F. A., D’Onofrio, E. E., & González, R. A. (2017). Improved sea surface height from satellite altimetry in coastal zones: A case study in Southern Patagonia. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 10(8), 3493-3503.
Citation: https://doi.org/10.5194/egusphere-2026-4902-RC2 -
RC3: 'Comment on egusphere-2026-4902', Anonymous Referee #3, 22 Oct 2026
General comments
The manuscript introduces a Dynamic Search Radius (DSR) algorithm that uses continental shelf geometry to select satellite altimetry observations representative of coastal sea level at tide gauge (TG) locations. The method is evaluated against a large global TG dataset, compared with several existing selection strategies, and assessed at different temporal scales. The global coverage, the systematic intercomparison of selection strategies and the openly available code are valuable aspects of the study, and the topic is relevant to the coastal altimetry community.
In its current form, however, the manuscript does not demonstrate convincingly how much of the reported improvement is attributable to the use of shelf geometry itself. Part of it may instead come from differences in the number of averaged observations, the effective spatial averaging scale, or the characteristics of the altimetry products being compared. I also identified several further issues:
- inconsistencies in the treatment of VLM and the ellipsoidal referencing;
- statistical tests that do not support the conclusions drawn from them;
- insufficient documentation of the independence between parameter selection and performance evaluation;
- several unclear station counts and a number of reference errors.
I consider these issues addressable and recommend major revision. My specific comments follow.
Major comments
1- Isolating the contribution of the DSR algorithm
Fig. 3a compares DSR with fixed-radius, nearest-pass and nearest-point selections applied to XTRACK. These baselines, however, differ from DSR in two respects at once: they do not apply a shelf mask, and they use a fixed rather than a station-dependent radius. The reported gain therefore cannot be attributed to either element separately. I suggest the following:
-Shelf-masked baseline. Add a baseline using a fixed radius (e.g., 250 km, equal to SR2) restricted to on-shelf points. This would isolate the contribution of the dynamic radius from that of the shelf mask.
-Number of averaged points. Report, for each method and station, the number of averaged altimetry points and the number of contributing passes. Then show whether the correlation gain persists after accounting for this number. Averaging more points from more passes reduces noise and improves temporal sampling regardless of where the points lie, so part of the improvement may simply reflect averaging.
-Minor islands. For minor islands, DSR is not applied and a fixed 200 km radius is used instead (Lines 268–270), so X_DSR is effectively identical to X_200 at these stations. These stations should be reported separately or excluded from the DSR statistics. This likely concerns most stations in the PI region.
-Along-shelf averaging. Several examples (Santa Monica, Charleston II) show that DSR selects observations up to about 200 km along the shelf. The authors should discuss how this differs, physically and statistically, from conventional large-scale spatial averaging. They should also discuss whether the benefit is expected to hold where the along-shelf coherence of sea level is weak.
2- Comparability of XTRACK and XTRACK/ALES
The intercomparison is performed over the common 2002–2020 period, which is appropriate. Within this period, however, the two products still differ in several respects:
-Temporal sampling. XTRACK has about 10-day sampling and is averaged to monthly values by the authors. XTRACK/ALES is delivered as monthly values.
-Processing. The two products use different retracking and editing strategies, and possibly different geophysical corrections.
-Seasonal signal. XTRACK/ALES is delivered with the annual and semi-annual cycles already removed.
DSR is applied only to XTRACK, so the comparisons in Figs. 3b, 4b and 5 cannot separate the effect of the selection strategy from the effect of the product. Applying DSR to XTRACK/ALES under the same evaluation conditions would substantially strengthen the assessment. Without such a test, the conclusion that “XTRACK/ALES provides limited improvement over XTRACK” (Line 524) is not supported and should be removed or reformulated.
3- Vertical land motion, reference systems and ellipsoidal linking
The treatment of VLM and reference frames requires clarification, and part of the analysis appears internally inconsistent.
-VLM correction procedure: The PSMSL RLR system provides datum continuity but does not remove VLM. The authors should explicitly describe how the NGL-derived GNSS vertical velocities are applied to the tide gauge records, specifying the adopted sign convention and reference frame, the GNSS observation period relative to the 1994–2023 study period, how the spatial separation between the GNSS and tide gauge stations is accounted for, and the quality criteria used to identify and exclude stations with unreliable VLM estimates (Lines 149–150).
The manuscript does not cite Wöppelmann and Marcos (2016, Rev. Geophys., 54, 64–92, https://doi.org/10.1002/2015RG000502), a key reference for this topic. That paper sets out the relationship between relative sea level, geocentric sea level and VLM at tide gauges, the accuracy required for VLM in sea level trend studies, and the issue of differential motion between GNSS antennas and tide gauges. It also discusses altimetry minus tide gauge differences as an independent estimate of VLM. This framework should be used to define the sign convention adopted here and to interpret the trend discrepancies at the 70 stations where altimetry and TG trends disagree (Line 497), which may partly reflect residual VLM.
-Nonlinear VLM: A single linear VLM rate is unlikely to be valid over 1994–2023 at stations affected by nonlinear motion. The most prominent example is the post-2011 Tohoku deformation in Japan. The two most extreme trends discussed (Uragami and Onisaki, Lines 482–484) are both located in Japan. The large discrepancy at Uragami (8.8 vs 4.62 mm/yr) is not discussed and should be.
-Ellipsoidal linking and trends: In Eq. (2), H_RLR is a constant offset between the RLR datum and the ellipsoid, and a constant offset cannot change a linear trend. However, Lines 499–500 report that linking Onisaki to the ellipsoid changes the TG trend from 5.37 to 7.12 mm/yr. This change must therefore originate from another processing step, such as a different GNSS solution or a different VLM treatment in the ellipsoidal workflow. The authors should explain exactly what changes between the two configurations. They should also confirm that VLM is not applied twice in the ellipsoidal case, given that Line 223 states that the ellipsoidal SSH is additionally corrected for VLM.
-Bias test: Lines 214–215 state that the long-term mean is removed from TG sea level to obtain SLA. If both the TG and the altimetry series are anomalies relative to their own means, their mean difference is zero by construction. In that case the Student’s t-test for bias (Lines 225 and 467–468) is uninformative. Please clarify what quantity is tested.
-Which analyses need ellipsoidal referencing: The correlation and RMSE analyses of detrended or decomposed anomalies are essentially insensitive to the datum and to linear VLM. Only the trend comparison depends on them. This should be stated clearly, and the ellipsoidal analysis should be motivated accordingly.
4- Statistical evaluation of sea level trends
- The statement that altimetry trends fall within the TG uncertainty at 72% of stations compares the altimetry trend with the TG uncertainty only. Agreement should instead be assessed on the trend difference, using the combined uncertainty √(σ²_TG + σ²_ALT).
- A non-significant paired t-test does not demonstrate agreement, and the reported result (p = 0.08, 95% CI [−0.34, 0.02] mm/yr) is borderline. If equivalence is the claim, a formal equivalence test such as TOST, with a stated tolerance, is appropriate.
-The paired t-test assumes independent stations. Many stations are spatially clustered (e.g., Baltic Sea, Japan), which inflates the effective sample size.
-Please report the distribution of station-level trend differences, the mean bias and the RMSE, together with their regional breakdown.
(a) Please state whether serial correlation of the residuals was accounted for in the 95% confidence intervals. OLS uncertainties from monthly sea level data are known to be underestimated if it is ignored.
(b) Reporting only trends with p < 0.05 (Line 208) introduces selection bias. All trends should be reported, with significance indicated.
(c ) The abstract (Line 24) states that altimetry trends match TG trends within their uncertainties, and the conclusions (Line 526) state that they lie “well within” them. Both claims are inconsistent with the 70 stations reported outside the uncertainty limits (Line 497) and should be revised.
5- Parameter sensitivity and independence of validation
The sensitivity analysis over 396 parameter combinations is a positive feature of the study. However, its independence from the performance evaluation is not documented.
- The sensitivity analysis and the multi-scale evaluation in Sect. 4.3 cover the same period (1994–2023). The authors should state how many of the 264 evaluation stations were also used in the sensitivity analysis. The station count of the sensitivity analysis is also inconsistent between Line 264 (318 stations) and Line 286 (312 stations).
-The sequential filtering procedure in Sect. 3.2 removes parameter values one criterion at a time, so the final set may depend on the order in which the criteria are applied. Please justify this ordering or use a joint criterion.
-If the two station sets overlap, an independent validation such as leave-region-out or k-fold cross-validation across stations would show whether the selected parameters generalize. If this is not feasible, the possibility of optimistic performance estimates should be acknowledged explicitly.
-Since the six retained combinations perform similarly (Line 301), the statement that the chosen parameters “offer the best performance” (Lines 304–305) should be softened.
6- Definition and interpretation of temporal components
-Please state explicitly whether the nonlinear trend (NLT) component includes the linear trend. Lines 203 and 437 suggest that it does.
-The NLT is described as including interannual variability, while the residual is described as monthly to interannual (Lines 203–204). The frequency bands therefore overlap and need a clearer separation.
-Please report the STL parameters (seasonal and trend window lengths, robustness iterations), since they control how variance is partitioned among the components.
-The high agreement for the NLT (88%) and annual (97%) components should be discussed in light of the large spatial coherence of low-frequency and seasonal sea level variability. This coherence would favor broad spatial averaging regardless of the selection algorithm. The residual component, for which only 21% of stations meet the RMSE criterion, is the more discriminating test of DSR and deserves more weight in the conclusions.
7- Geophysical corrections and coastal processes
-The TG records are corrected with an ERA5-based DAC (Sect. 2.1.3), while the altimetry products carry their own standard DAC (Lines 129–130). Please confirm that the two corrections are consistent in model and forcing. Inconsistent atmospheric corrections can affect agreement at monthly scales.
-For each TG, the DAC grid point giving the largest variance reduction is selected among the nine closest points (Lines 147–148). This station-wise optimization against the TG record may itself improve the agreement with altimetry. Its effect should be quantified, for example by comparison with the nearest grid point.
-The consistency of tidal corrections in shallow water and estuaries should be discussed, since residual tidal aliasing from global tide models may degrade agreement there.
-The discussion should better acknowledge the role of wind-driven coastal sea level variability and its dependence on shelf width. Shelf width affects not only which observations are representative but also the amplitude of the local response to wind forcing.
8- Agreement metrics, consistency and presentation
-The criterion “r > 0.7 or NRMSE < 1” (Lines 310–311) is lenient, since NRMSE < 1 only means that the RMSE is smaller than the TG standard deviation. Using both criteria jointly, or justifying the thresholds, would make the evaluation more meaningful.
-Sect. 2.2.1 describes the selection of the 272 stations used in the intercomparison, but the 373-station set analysed in Sect. 4.2 (Lines 363–364) is not defined in the Methods. Please describe the station selection procedure for each analysis. Please also clarify whether it is a coincidence that the number of stations with good X_DSR correlation in this set (272) equals the size of the intercomparison sample. Finally, 272 of 373 corresponds to about 73%, not about 70%.
-The Results section contains long sequences of regional median values that would be clearer in summary tables. Please also state clearly which station subset and period each comparison uses: 272 stations for 2002–2020, and 264, 248 and 49 stations for 1994–2023.
-The discussion of the regions where DSR performs poorly (eastern Australia, Gulf of St. Lawrence, tidal estuaries) is useful. It should be framed as a limitation of the method, not only as a limitation of altimetry.
-Line 519 states that DSR ensures “at least 15 per month”. The threshold is defined as 15 spatial points within the search radius, which does not by itself guarantee 15 observations per month, particularly when the points come from a single pass. Please rephrase.
-The conclusions should not imply that improved agreement with TGs demonstrates superior performance of the underlying altimetry measurements. A larger averaging footprint can increase agreement while reducing the representativeness of truly local coastal signals.
Minor comments
1-Lines 43–44: The statement that observations closer than 50 km to the coast were neglected until 2010 is too categorical. Please qualify it or support it with a reference.
2-Line 131: “TG data represents true monthly SLA mean values” is overstated. TG records are also affected by local processes and instrumental errors.
3-Section numbering: Two subsections are numbered 2.1.3 (DAC and VLM products; Bathymetry product).
4-Figs. 3 and 4, captions: “Regions are shown on the y-axis” should read “x-axis”.
5-Fig. B3, caption: It states that combinations excluding more than 10% of stations were removed, whereas the text and Figs. B1–B2 state 15%.
6-Figs. 11 and A3, captions: They refer to a panel (c) that does not exist.
7-Region abbreviations: NEA (northeast America) and NEAt (northeast Atlantic Ocean) are easily confused. The region definitions also differ between Fig. 3 and Figs. 5, 9 and 11. Please harmonize them.
8-Line 304: Bhowmik and Sankarasubramanian (2019) addresses bias correction of precipitation–temperature cross-correlation and is not an appropriate reference for the Fisher Z-transformation. Please cite a standard statistical source.
9-Line 463: Abdallah and Eid (1989) is a Red Sea study and does not support a general statement about the drivers of the annual sea level cycle along global coastlines.
10-Line 32: Hughes et al. (2018) addresses ocean bottom pressure and the deep ocean circulation. Its relevance to coastal sea level processes should be checked.
11-Duplicate references: The following entries refer to the same papers and should be merged: Druon et al. (2001a, b), Johnson et al. (2023a, b) and Zhao and Guo (2011a, b).
12-Incomplete references: In Cazenave et al. (2025), the title is repeated and no journal, repository or DOI is given. Swallow (1963) is also incomplete.
13-Reference order: The entry “Stations with Ellipsoidal Links” is placed out of alphabetical order.
14-Line 498: Please state how many of the 70 stations with trends outside the TG uncertainty are located in regions of known nonlinear VLM.
Citation: https://doi.org/10.5194/egusphere-2026-4902-RC3
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- 1
Review of “Accounting for shelf-width in selecting altimetry observations for estimating coastal sea level changes improves its agreement with tide gauges” by Sukumaran & Vishwakarma.
In this paper a selection method for satellite altimetry data is proposed to produce a better agreement with data from tidal gauges. I find it difficult to form an opinion on the validity of the results, because on the one hand the text is filled with a large amount of details and abbreviations, which severely hampers readability, while on the other hand the text is short on crucial information.
For example, in the Introduction the authors phrase their central hypothesis as ”that selecting altimetry points along the coast and within the shelf would represent the coastal sea level better”. This is really too unspecific to form a meaningful and testable hypothesis.
In discussing altimetry data, the authors mention corrections that are included as “tidal correction and Dynamic Atmospheric Correction (DAC)”. This again lacks specificity, but I assume the authors refer to the long-period nodal tide and to the inverted barometer effect. However, when discussing the tide-gauge data, the long-period nodal tide is no longer mentioned and apparently is not corrected for. This makes the comparison between altimetry data and tide gauges problematic.
Another problem is that the tide-gauge data collected by national agencies worldwide, may not always have been fully corrected for land subsidence. The authors seem to suggest (in Section2.2.4) that the Revised Local Reference offers a fixed datum, but as explained on the PSMSL website it is rather a convenient and arbitrary choice: “The RLR datum at each station is defined to be approximately 7000mm below mean sea level, with this arbitrary choice made many years ago in order to avoid negative numbers in the resulting RLR monthly and annual mean values.”
In the same paragraph, the authors mention removing a “long-term mean”, without specifying what they mean by “long-term”.
The Results section in its present form is unreadable; again, it is buried under details (which would rather belong in a table) and abbreviations. Just to quote one paragraph: “DSR consistently outperforms other algorithms across most regions, with median r value of 0.97 (Baltic), 0.75 (Eaus), 0.79 (GoM), 0.72 (IO_SCS), 0.71 (NEAt), 0.84 (NSea), 0.71 (NZ), 0.51 (SA), 0.92 (WAus) (Fig. 3). It performs comparably with XTRACK/ALES algorithms in several regions: MedSea (0.77 for DSR, compared to 0.79 and 0.78 for ales_300 and ales_200), NEA (0.75 for DSR and 0.76 for ales_300), NPO (0.74 for DSR and 0.76 for ales_300), NWA (0.84 for DSR and 0.85 for ales_300) and PI (0.86 for DSR and 0.89 for ales_300 and ales_200) (Fig. 3(a)).” There should be better ways of conveying the essence of the information to the reader.
The Conclusions section raises a couple of points that perhaps require comment. First, the authors put forward as the central novelty of the paper that they developed a selection algorithm to choose points on the continental shelf rather than in the open ocean in order to determine sea-level change at the coast. But given the large regional variability in sea-level change, why would one even consider open-ocean data to get coastal trends? In other words, the author’s choice makes sense but is also obvious. Furthermore, they point out that coastal sea-level dynamics is very different from the open ocean - which is certainly true - but they identify as the primary cause the fact the currents have to follow the coastline (l. 514). First, it is not made clear why this would have an implication for sea-level change, but second, a much more important difference has to be the wind variability (also on inter-annual time scales) and its major effect on (annual-mean) sea level at the coast. This aspect would need to be considered in the analysis.
Given all these reservations, and the lack of readability of the manuscript, I recommend rejection.