Improving Spatial Resolution of Ice Sheet Mass Change using a Data Combination of Satellite Gravimetry and Altimetry

Wiese, David N.; Nilsson, Johan; Schlegel, Nicole-Jeanne; Gardner, Alex S.; Ellmer, Matthias; Landerer, Felix W.

doi:10.5194/egusphere-2026-4404

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https://doi.org/10.5194/egusphere-2026-4404

Preprints

25 Aug 2026

| 25 Aug 2026

Improving Spatial Resolution of Ice Sheet Mass Change using a Data Combination of Satellite Gravimetry and Altimetry

David N. Wiese, Johan Nilsson, Nicole-Jeanne Schlegel, Alex S. Gardner, Matthias Ellmer, and Felix W. Landerer

Abstract. We present two decades of monthly Antarctic mass change at a spatial resolution of (100 km)², representing an order of magnitude improvement over the current state-of-the-art for gravity-derived estimates. This advancement is achieved by leveraging the accuracy of satellite gravimetry over larger spatial scales and the spatial resolution of altimetry at finer spatial scales. We do this through a formal data combination of satellite gravimetry and altimetry observations at the level of the gravimetry normal equations, estimating 1° circular disk mascon elements. The data combination yields independent mascon estimates, yielding effective spatial resolution of 1°. Gravimetry observations dominate the solution at long wavelengths, while altimetry observations are the dominant contributor at the spatial scale of an individual mascon. This yields a mass change solution that is closely aligned with gravimetry-only solutions from GRACE and GRACE-FO over larger spatial scales, yet spatially resolves mass change variability at finer scales. Additionally, we provide a set of gain factors to further downscale the mass within each mascon, providing monthly mass change estimates at a 1.92 km spatial scale. Uncertainties from measurement systems and model corrections (glacial isostatic adjustment, firn air content) are propagated through the data combination and presented. The methodology presented is extensible to other regions around the globe.

Received: 21 Jul 2026 – Discussion started: 25 Aug 2026

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David N. Wiese, Johan Nilsson, Nicole-Jeanne Schlegel, Alex S. Gardner, Matthias Ellmer, and Felix W. Landerer

Status: final response (author comments only)

RC1: 'Comment on egusphere-2026-4404', Matthias O. Willen, 08 Oct 2026

Summary
This manuscript extends a GRACE/GRACE-FO Level-1-based mascon approach by incorporating an additional observation type (satellite altimetry over the Antarctic Ice Sheet) in order to improve estimates of ice sheet mass change.

The approach unites two important advantages: the high spatial resolution of satellite altimetry and the complete mass information provided by satellite gravimetry (GRACE/GRACE-FO).

The resulting product will be of great value for the community in investigating and understanding cryospheric processes. The methodology is presented clearly and in a comprehensible manner, and the use of flat mascon disks for this application is both interesting and promising. I have two general comments relating to the study design and the focus of the manuscript. My specific comments mainly concern points that remained unclear to me during reading.

General comments
1. Inconsistency in the processing levels of the two observation types

In my view, there is a certain inconsistency in the use of the two observation types, as they originate from very different processing levels. For GRACE/-FO, Level-1B data are used. To the best of my knowledge, this is the first time that L1B data have been used in a combination study of this kind as the authors write. An essential argument for doing so is that it avoids the use of more extensively post-processed observations, even though the methodological effort involved is considerably higher. At the same time, however, a highly processed altimetry product is used. Deriving surface elevation changes from the various satellite altimetry missions requires a large number of post-processing steps (retracking, calibration, interpolation, filtering, etc.). The same line of reasoning that motivates the use of L1B data for GRACE could equally be applied to the altimetry product, e.g. by starting from retracked heights rather than interpolated grids.

Furthermore, it would be interesting to demonstrate how the final result depends on the choice of altimetry product, or on processing decisions made during the altimetry data processing. Are there significant differences at small spatial scales when a different altimetry product is used? The authors show very nicely in Sect. 3.3 and Fig. A5 that the contribution of altimetry at short spatial scales is considerable. Moreover, the authors demonstrate how the additional information from altimetry improves the estimation by showing that the correlation between mascons is removed. In the polar gap of the altimetry data, however, this additional information comes solely from an interpolation, which may introduce systematic errors, e.g. by inter-mission calibration. In the combination result (Figure 9a) and in the gain-factor downscaled result (Figure 9b), the mission-specific polar gap transition becomes visible. This may be particularly relevant in Envisat-only months, when the polar gap starts already at a latitude of ~81.5°. This further suggests that the solution adopts systematic altimetry errors. This is neither discussed nor investigated further in the manuscript.
2. Conclusions about ice sheet dynamics

The authors conclude that the product "improves knowledge of ice sheet dynamics". I fully agree that the data combination product presented here makes it possible to investigate the dynamics of the Antarctic Ice Sheet in greater detail. However, this is not the subject of the present manuscript. The phenomena driving the mass changes of the ice-sheet system are neither investigated nor discussed further. The manuscript primarily presents a method for combining two satellite datasets, along with the resulting product, and in this respect it is certainly an important and very useful contribution.

Nevertheless, I have some reservations as to whether the manuscript in its present form fits the scope of The Cryosphere. The manuscript essentially reads as a methods or data description paper presenting a data product that meets certain community baselines. Given this, the statement in the conclusions that the product "improves knowledge of ice sheet dynamics" raises the question of what this claim is based on. What have we learned about ice-sheet dynamics from the data combination that we could not have learned from GRACE-only and altimetry-only solutions? The authors may wish to consider whether the manuscript in its present form, with revisions, might be better suited to a data journal such as ESSD, or to a journal focusing on processing methods in satellite geodesy. Alternatively, the manuscript could be extended with analyses demonstrating what the improved spatial resolution allows us to learn about ice-sheet processes that was not previously possible. I appreciate that this is ultimately an editorial decision and this is not a criticism of the scientific quality of the presented work, which I consider high.

Specific comments
l. 20: Please explain why the spatial resolution and accuracy currently provided by GRACE/GRACE-FO are insufficient for capturing cryospheric processes.
l. 40: It would be appropriate to also cite our study (doi.org/10.1093/gji/ggag059) at this point, in which, very similarly to the study presented here, we introduced satellite altimetry over Antarctica into a joint global inversion framework that uses GRACE and GRACE-FO alongside further datasets in order to increase the spatial resolution of the derived Antarctic mass changes to up to 50 km.
l. 46: The direct processing of Level-1 data within such a combination approach is indeed novel. At this point in the introduction, however, I would appreciate a justification for the necessity of taking this methodologically much more demanding way. What are the limitations of previous combination methods that use Level-2 data and the full covariance information? What can be overcome by using Level-1 data?
l. 51: It would be helpful to provide the reader with somewhat more background on the community goals and recommendations. Which scientific questions lie behind them? Can the data combination presented here answer these questions?
Eq. 1: An explanation of why the normal equation system was set up in this particular form would be desirable. This only became clear to me after reading further, or after consulting the cited literature. Without prior knowledge of mascon approaches, it would arguably be more intuitive to first set up a normal equation system of the form

H^T W H x = H^T W y

where W is then the inverse of the observational covariance matrix. Through the addition of P^-1, the representation given in the manuscript corresponds to a regularized least-squares problem, for which additional information is required. This only becomes clear later (l. 267) and is due to the chosen mascon parameterization, since linear dependencies would otherwise arise, is that correct? For the altimetry, however, the system of equations reduces to an unregularized problem (l. 255). I found it somewhat confusing that the mathematical description initially introduces the system differently from the way it is subsequently implemented in practice.
l. 73: I can follow the reasoning behind the parameterization with 1° flat mascon disks in the region where ice altimetry observations are also available, since their determination is constrained by the additional observations. Outside this region, however, where no additional information is available, a 1° parameterization constitutes an over-parameterization and necessarily requires regularization in order to obtain a stable solution. A parameterization oriented towards the GRACE-only resolution would seem more appropriate there unless the authors see specific advantages in retaining a globally uniform parameterization.
l. 88: It states that each mascon disk is centred at body-fixed spherical coordinates, while l. 74 states that the disks are distributed on the surface of an ellipsoidal Earth. Other studies have shown that neglecting the oblateness of the Earth leads to significant differences, particularly for mass changes in the polar regions (doi.org/10.1007/s00190-018-1128-0). Or is this not critical here, because the actual distance between the satellites and the mascon is considered in the determination of the mascons?
Eq. 2: A suggestion: a simple sketch illustrating the flat disk mascon and its parameters could be helpful here.
l. 118: As a reader, one has to take this statement on trust. Is there a reference demonstrating this numerical benchmark, or could it be shown in a supplement?
l. 196: An extended explanation of the relationship between depth-averaged density and FAC would be helpful for all readers who are not familiar with firn processes.
l. 205: Does the FAC uncertainty depend solely on the magnitude, or would it also be sensible to introduce some form of noise level?
l. 214: I appreciate the practical rationale for a percentage-based uncertainty estimate, and Fig. A1 convincingly demonstrates that the solution is largely insensitive to this choice. It might nevertheless strengthen the manuscript to complement the operational argument with a brief physical justification for the 30 % value specifically.
l. 250: How many parameters are estimated, and how many observations are used per month?
l. 258: The necessity of the stepwise procedure surprises me, given that satellite altimetry is also used. I would have expected that the information from satellite altimetry leads to a system of equations which is overdetermined, i.e. that the spatial allocation over the ice-covered regions is already constrained and that regularization is therefore not necessary. The authors also show very nicely in Sect. 3.4 that the spatial correlation between the mascons is considerably reduced (effectively removed) by the addition of altimetry. The authors may wish to provide somewhat more insight into the system of equations, the degrees of freedom, the resolution matrix, etc.

More general: The authors conclude on an effective spatial resolution of 1° from the reduction of inter-mascon correlation to 0.02. Decorrelation of estimated parameters and spatial resolving capability are not necessarily the same thing, particularly when a regularization term is present. An analysis of the resolution matrix, or the response to a synthetic point-mass input, would provide a more direct demonstration of the claimed resolution.
l. 275: The 13-month running mean acts as a temporal low-pass filter, and the authors admit that the formal uncertainties are artificially low (l. 305). This suggests that this step adds information that is not strictly observational. It would be helpful if the authors could discuss what this implies for the interpretation of sub-annual variability in the final product, and whether the reported effective spatial resolution is partly a consequence of this constraint rather than of the altimetry information alone.
Sect. 2.7: Temporally correlated errors are neither accounted for nor discussed. The uncertainty determined in Eq. 15 therefore describes only part of the total uncertainty, as the authors themselves note in l. 309 and following. Satellite altimetry, for example, has temporally correlated errors, which presumably propagate into the combination result. Furthermore, both GIA and FAC have a trend error, i.e. an uncertainty that increases with temporal distance from a chosen reference epoch. Other GRACE-based ice-mass balances provide a more comprehensive uncertainty characterisation (see, e.g., Table S1 in https://doi.org/10.3390/rs13091736). An estimate of the trend errors, and their inclusion in Table 1, would be desirable in order to allow the values presented here to be assessed and compared. In addition, neither the interpolation across the satellite altimetry polar gap nor the hypsometric interpolation of low quality data (Sect. 2.3) appears to contribute separately to the overall uncertainty (Eq. 15) and are difficult to assess as a user of the data set.
Sect. 2.8: Are the results presented here consistent, within the stated uncertainties, with https://doi.org/10.1038/s41597-026-08088-0?
Sect. 2.8: The validation promised in the section heading is, to be honest, rather a comparison, is it not? In particular, expectation 2 in Sect. 2.8 states that mass change at scales <300 km should more closely follow altimetry observations. Since altimetry is itself an input to the combination, this criterion appears to be satisfied by construction rather than independently verified. The same may hold for the first expectation, although, admittedly, there are no genuinely independent observations available to validate it.

However, a validation against independent datasets would indeed be interesting. Given the high spatial resolution that the authors achieve with their product, a comparison with GNSS-measured elastic loading effects, for example, would be very interesting. Admittedly to the applied GIA correction, no agreement in the trend is to be expected, but possibly on shorter time scales (e.g. seasonal signals). A comparison with independent GNSS data could validate/falsify the data combination to a certain extent.
Fig. 2 + Fig. 3 + Fig. 5: Why is the altimetry-only uncertainty larger than the assessed uncertainty of the data combination product?
Fig. 7: The figure indicates that beyond approximately degree 25, the a priori information is the largest contributor to the global solution, acting comparably to a 330 km Gaussian smoothing operator, while altimetry contributes only a few percent globally. Fig. 6, in contrast, shows altimetry to be dominant at the mascon scale over Antarctica. These two representations are not easily reconciled by the reader. A brief discussion of how the global spectral picture relates to the regional contribution maps would help to clarify to what extent the reported 100 km resolution over Antarctica is supported by observations rather than by the a priori constraint.
Sect. 3.5 + Fig. 9: A difference map between Fig. 9b and Fig. 9c would be very interesting, together with a brief discussion of the differences. And one further question for my understanding: would it also be possible to arrive at the downscaled result directly from a classical mascon solution? It remains unclear to me why it is preferable to first determine mascons jointly from GRACE and altimetry, which are then downscaled using the gain-factor approach, rather than determining mass changes directly at the high resolution from a GRACE-only mascon solution.
Sect. 4: A critical discussion of the limitations of the presented dataset is missing. At the very least, the considerable uncertainty that propagates from the GIA correction into the derived mass estimates should be discussed here (cf. Table S1 in https://doi.org/10.3390/rs13091736). In addition, further systematic error sources arising from the altimetry processing and the post-processing (l. 279ff) should be discussed.
Sect. 5: The conclusions are very methodological. Are there any conclusions about the estimated mass changes in space and time that the authors have found?

Technical comments:
Eq. 5: Please introduce kappa.
l. 330: "Independent" may be misleading here, as as both the gravimetry-only and the altimetry-only solutions are derived from the same observations that enter the data combination.
Fig. 2 + Fig. 3: The diagrams are difficult to read. A larger presentation, as well as grid lines, would be helpful. In addition, the use of red and green within the same figure may be a barrier for some readers.
Table 1: Please specify the time period over which the trends were estimated. Given the uncertainties of Antarctic mass balance estimates, reporting two decimal places does not seem appropriate.
Fig. 4 and similar figures: Highlighting the mascons shown in the figure would be helpful.

Citation: https://doi.org/10.5194/egusphere-2026-4404-RC1
RC2: 'Comment on egusphere-2026-4404', Ingo Sasgen, 07 Nov 2026

Dear David and co-authors,
Please find below my assessment of the manuscript. Having worked on combining gravimetry and altimetry myself, I read it with great interest and noted a number of points that need clarification. I hope that addressing them will help to strengthen the manuscript.
Best,

Ingo
Summary

The manuscript by Wiese et al. presents a combined estimate of Antarctic ice mass change from satellite gravimetry and altimetry. The approach builds on the established JPL mascon estimation from Level-1 GRACE/GRACE-FO data and extends it by including Level-3 altimetry data at the normal-equation level. The benefit of the combination arises from the complementary spatial sensitivity of the two observing systems: gravimetry is accurate at long wavelengths, while altimetry resolves mass change at fine spatial scales. Further downscaling beyond the 1° target grid is achieved by applying gain factors derived from the high-resolution (~2 km) altimetry fields. Uncertainties from the gravimetry measurements (Level-1), the altimetry measurements, and the model corrections are propagated through the data combination. The resulting spatio-temporal fields are analysed with respect to the relative contribution of the gravimetry and altimetry data at different spatial scales. The approach is designed to be extensible to other regions and to the future GRACE-C mission.

General assessment

The analysis represents a unique way of combining gravimetry and altimetry at low-level (Level-1) GRACE/GRACE-FO data. I understand that it extends the established JPL mascon estimation procedure by including altimetry over Antarctica, aiming at a generalized approach that is extensible to other regions of the globe. The manuscript is clearly structured, the figures are mostly appropriate. However, I missed important details in some places, in particular on the derivation of the altimetry uncertainties and their aggregation to the mascon scale, the computation of basin-scale uncertainties for the combined solution, the mascon grid definition, and how the 3° gravimetry-only solution is mapped onto the 1° mascons for comparison with the combined estimate.
My greatest concern is, however, that the product claims to be validated, where instead consistency checks at different spatial scales are presented, which largely investigate the behavior of formulation of the combination problem itself (Eq. 1). Moreover, I found it somewhat difficult to track how exactly signal and noise structures of the input data map to the output of the combination. Part of the reason is that an independent product (JPL RL06.3M at 3°) that is not part of the combination algorithm and has its own regularization and leakage correction is used as the gravimetry-only reference at 1° mascon scale, without uncertainties. The authors should clarify which other processing choices were made or adapted for the independent mascon product (e.g. leakage correction, Coastline Resolution Improvement (CRI) filter, gain factors) and show that it can serve as a gravity only reference.

Moreover, it would be important to clearly discuss advantages and disadvantages of performing the combination at the level of Level-1 data, which is elaborate, in the context of other combination approaches at higher level. Furthermore, the effects of assuming uncorrelated errors in the altimetry input and the corrections should be discussed.
Overall, I see considerable value in this contribution. Extending the Level-1 mascon processing by including altimetry is a unique and interesting approach to data fusion and a useful enhancement of the mascon products. However, the study somewhat overclaims that this approach, or combination with altimetry in general, is optimal or the “gold standard”. Please clearly show its limitations in view of alternative approaches. My largest concerns are the lack of independent validation (which, I acknowledge, is not straightforward) and the inconsistencies in the treatment of the gravimetry and altimetry uncertainties in the final cross-check analysis. Before the product’s uncertainty estimates and effective resolution can be relied upon for glaciological applications, the validation, the treatment of correlated errors, and the sensitivity to the relative weighting and regularization need to be demonstrated more clearly. Addressing these points would substantially strengthen the manuscript and raise the maturity level of the intended product. Finally, as the methods and data description focus strongly on gravity field estimation and the manuscript does not derive new insights into ice-sheet processes, it may not fully fit the scope of The Cryosphere. Personally, I would suggest that the authors consider transferring the manuscript to EGU’s Earth Observation (EO), provided the review process can be continued there.

Major comments

+ M1 Validation

• Sect. 2.8 (L313 ff.): This should not be called “validation”, as it is merely a consistency check of the combination procedure. All three criteria are more or less experiments of the behavior of Eq. 1. Please rename this section, e.g. “Consistency checks” or “Solution characterization”.

• L315: “Validation campaign” is misleading, as no independent data are used. Please rephrase, e.g. “our assessment is restricted to …”.

• Suggestions for an independent validation are given under M8 (i).

+ M2 Altimetry uncertainties and their spatial correlation

• L148–154: Please give more details on how the uncertainties of the ~2 km product are aggregated to mascon level.

• L148–154: Please state clearly the limitation that correlated uncertainties are omitted for altimetry. Also point out that these correlations, caused by penetration/retracking and cross-calibration, are mission-dependent and therefore also time-dependent.

• Sect. 2.3 (L131–154): The combination relies on a single altimetry product (Nilsson et al., 2022), which uses one retracker per CryoSat-2 mode. An alternative altimetry product could be a useful sensitivity test, but also demonstrate the empirical uncertainty of the input altimetry data.

• L330–339: For the altimetry-only solution, uncertainty correlation lengths of 100 km and 500 km are assumed here, but WA in the combination is diagonal. Why? This seems inconsistent…

• Fig. 8: The purpose of this figure is a bit unclear to me. The vanishing correlation is surprising, and needs further explanation. Isn’t this just a result of the diagonal structure of WA, i.e. the uncertainty model, that dominates the combination at the scale of neighboring mascons? And what about leakage? Decorrelated uncertainties does not mean no leakage. It should be part of the validation to show decorrelation of the signal as well. Please clarify what the figure is meant to demonstrate and/or consider moving it to the supplement.

• Relative weighting (Eq. 1, Fig. A1): I have the impression that the altimetry is weighted quite strong relative to gravimetry. It would be really helpful to perform a sensitivity test on the relative weighting (maybe for a selected month), e.g. by scaling WA (for instance by factors of 0.25 and 4) and/or by introducing a spatially correlated error model for the altimetry (e.g. with the 100 km and 500 km correlation lengths used for the altimetry-only solution). Fig. A1 varies only the FAC error amplitude and therefore addresses this only partly.

+ M3. Formulation of the combination and error model

• L47–50: This sentence is too long and confusing, particularly for a non-specialist readership of TC. What is meant by “data types”? Please emphasize that gravimetry and altimetry enter at very different levels. The simultaneous estimation of mass change and nuisance parameters seems to be an important advantage of this approach. A shorter explanation of this benefit, together with the remaining limitations and the different processing levels of the two inputs, would make the contribution more accessible.

• L70–79: Please be more explicit about the variance/covariance content of the design and uncertainty matrices. Please state clearly why approximating WG and WA as diagonal may be justified.

• L177–182: Please explain the implications of treating GIA model uncertainty through the ensemble rather than in the observation covariance model.

+ M4. Consistency of the uncertainty estimates

• L303–305: I appreciate the effort to avoid unrealistically small formal uncertainties. However, please clarify in what sense the Step-2 uncertainties provide a suitable estimate for the final Step-3 product, and assess whether they account adequately for regularization effects and the data-derived prior.

• L330–339: It is not clear how the basin-scale uncertainties of the combined solution are computed.

• L330–339: Although W_G is described as consistent with RL06.3M, please clarify how the product-level uncertainty estimates compare, particularly with respect to regularization and leakage.

+ M5. Gravimetry-only reference at the mascon scale

• L353–354: Please describe how the 3° RL06.3M solution is mapped onto the 1° mascons, as Fig. 4 seems to show different time series for adjacent 1° mascons.

• L354–355: I understand that sampling the gravimetry-only solution below its native resolution is not straightforward. Still, it would be very helpful to show uncertainties for the gravimetry-only curves at the 1° scale, e.g. by propagating errors, including leakage, from the RL06.3M product or from a Level-2 solution.

+ M6. Scale-dependent contributions of gravimetry and altimetry

• Fig. 6: The figure suggests that the solution is almost entirely driven by altimetry and you wonder why use a prior? However, the key point of the combination is that the contributions are scale-dependent. Please show the contributions at different spatial scales, e.g. mascon, basin and ice-sheet level, or refer to the spectral analysis instead. I think it is very important to show that gravimetry outperforms altimetry at the basin level, as has been shown in the time series and previous studies. Otherwise, I would recommend to put the figure into the supplement.

• Fig. 7: The global spectral analysis is informative, but it does not directly establish the wavelength-dependent contributions over Antarctica. Could the authors provide a regionally focused analysis, or qualify the Antarctic interpretation of Fig. 7 accordingly? Also, I would recommend not to introduce spherical harmonics at this stage (which may cause confusion with L2-data combinations), but instead use a grid-based spatial metric.

+ M7. A priori information and regularization

• L275–278: Step 3 constrains the solution towards the 13-month running mean of Step 2. Please discuss to what extent real subseasonal signals, e.g. from strong snowfall events, are damped by this constraint. Would you think an approach using temporally correlated uncertainty would be a way forward?

• Sect. 2.6 (L285–290): Could the authors clarify how the altimetry constraint and the subsequent CRI separation interact in coastal mascons, especially where only part of a mascon is covered by altimetry?

+ M8. Discussion

• Sect. 4 (L416 ff.): The discussion focuses on meeting mission requirements but does not address the limitations of the approach. For readers who want to build on or modify this method, or develop a new one, a clear statement of the underlying assumptions and limitations would be very valuable – so would be users of a product. In particular, please discuss: (i) the lack of independent validation, and consider e.g. a comparison of along-coast mass change profiles with surface ice velocities (as done in Sasgen et al., 2019), or of sub-basin scale results with input–output; (ii) the neglected spatial error correlations in WA and their effect on the weighting and on the uncertainties; (iii) the scale-dependent contributions of gravimetry and altimetry, which are claimed but not rigorously demonstrated (Figs. 6 and 7); and (iv) the influence of the a priori information and the regularization, in particular the 13-month running-mean prior in Step 3, which is derived from the Step 2 solution and may damp real sub-seasonal signals.

• L444–446: Personally, the claim that this combination or altimetry / gravimetry combination is “optimal” and will remain the “gold standard” is not justified, or supported by the results. Please tone down this statement.

+ M9. Scope of the manuscript

• General: The manuscript primarily presents a methodology and the development of a data product, but does not derive new insights into ice-sheet processes. In its present form, I think it may fit better in a journal focusing on observing methods and data products, such as the new EGU journal Earth Observation. Alternatively, the authors would need to demonstrate what the improved spatial resolution allows us to learn about ice-sheet processes that was not possible before. I acknowledge that this is ultimately an editorial decision and I would only recommend transfer if the review process can be continued.
Minor and technical comments

• L1: I suggest naming the grid dimensions explicitly for the spatial resolution.

• L5: On what grid?

• L6: “yielding effective” → “yielding an effective”.

• L9: Please briefly indicate in the abstract that the gain factors are derived from altimetry, and clarify how their calculation and limitations differ from the formal data combination.

• L10: “1.92 km” → “about 2 km” would make the abstract more readable.

• L20: Writing (300 km)² is a bit confusing, also because of anisotropy. Just give one approximate length scale here and in the following (about 300 km).

• L22–24: Better: “sampling the gravitational effects of near-surface …”.

• L28: Model corrections for altimetry, gravimetry, or both? Please be more specific.

• L29–30: Statement not precise enough. At what spatial scale?

• L30–32: For radar altimeters, there is also the uncertainty from changes in the dielectric properties caused by changing surface processes, and from the interpolation of scattered data to smooth surfaces.

• L33–34: The sentence is vague. Please specify the spatial scales at which the stated complementarity applies.

• L46: Please write GRACE/GRACE-FO consistently (currently GRACE/GRACE-FO, GRACE and GRACE-FO, GRACE/-FO).

• L54–55: Please make explicit whether “community reports” refers to the documents cited in the following sentences.

• L55–62: A brief explanation of the cryospheric applications underlying these spatial and accuracy requirements would help the readership understand their relevance.

• L56: Globally? For ice sheets? Please reconcile the 1 cm accuracy target in the Introduction with the 15 mm target in the Discussion, and clarify whether they refer to the same requirement.

• L66–69 (Eq. 1): Please remove the brace, as the summed system is solved. Is the altimetry prior omitted in the implementation?

• L73–74: Please briefly describe the mascon grid (1° latitude bands with a varying number of cells per band?) and define the “bounding quadrilateral” used in Eq. 13. A short note on how the disks relate to the cells, e.g. regarding coverage and the polar cells, would also help.

• L125–126: “gravity estimation” → “surface mass change estimation from gravity”.

• L131–136: Do you use the pre-2002 data for anything in the analysis? If not, this paragraph could be shortened and joined with the next one.

• L139–143: Has this interpolation uncertainty been accounted for in WA?

• L217–218: Yes, that is good. But please state that the ratio hA(GIA) / hG(GIA) depends on the Earth structure and on the loading history.

• Fig. 1: Please sort the panels according to Eq. 15 and state the time reference of the uncertainties (monthly value, anomaly relative to the reference epoch, or trend). If feasible, please also show the altimetry uncertainty aggregated to mascon level and the measurement uncertainty of a gravimetry-only solution. This would make clear where each dataset controls the combined solution. This could be moved to the supplement.

• Fig. 1 / Sect. 3: Please briefly discuss the spatial structure of the uncertainties (Fig. 1) in Sect. 3. This would deserve its own subsection if the gravimetry and altimetry uncertainties were shown as well.

• Table 1: Please briefly clarify the MAD, e.g. whether it is computed after detrending or after removing the mean offset.

• Fig. 9: Again, the similarity of (b) and (c) is expected, as the spatial scale shown is dominated by the altimetry. The subtle difference between (b) and (c), or between (a) and (c) resampled at mascon level, would be more instructive. Please also state the trend period in the caption.

Citation: https://doi.org/10.5194/egusphere-2026-4404-RC2

David N. Wiese, Johan Nilsson, Nicole-Jeanne Schlegel, Alex S. Gardner, Matthias Ellmer, and Felix W. Landerer

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Short summary

Tracking Antarctic ice loss is vital for predicting sea-level rise. Satellite gravity measurements reliably track overall mass changes, while height measurements capture fine local details. We combined two decades of both satellite records into a unified model. This boosts mapping clarity tenfold, revealing ice loss from broad regional scales down to individual glaciers. These refined maps help scientists monitor vulnerable ice streams and improve climate projections.


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