Thank you very much for the very kind, appreciative and helpful review of our manuscript. In the following, we will briefly respond to the comments and outline how we plan to revise the manuscript. The referee comments are marked in italics.

According to section 2, the method builds upon the work from Rietbroek et al. (2016), which uses a variety of sea level fingerprints generated from mass change blocks or modes as basis functions to decompose the observations from GRACE and Altimetry. I would expect a paragraph describing the fingerprint dataset to be included in the manuscript for clarification.

Thank you for pointing to this. In the revision, we will extend and add the explanation of the fingerprint inversion and the patterns that we implement.

I am not sure if the inversion method in Rietbroek et al. (2016) works well when mass change blocks used to generate fingerprints are vertically superimposed. For example, GIA signals and ice mass change are overlapped, and their fingerprints are correlated. Therefore, they may not be well separated. If you are facing such a problem, please clarify how you have addressed it. In Rietbroek et al. (2016), I believe they initially removed an a priori GIA model. Please explain how you handled this problem in this study.

Indeed, the fingerprints of GIA and ice mass change in Antarctica are strongly correlated. A separation is only possible because we apply an inversion approach that make jointly use of data sets, i.e. different observation types at the same time. In our case, these are observations from satellite gravimetry and satellite altimetry over ice sheets. Both observation types differ in their sensitivity towards GIA and ice mass change, so that a separation of the signals is possible, as we demonstrated in Willen et al. (2022). A GRACE-only inversion would not work with the chosen parametrization due to the correlated patterns. We will clarify this in the revised manuscript.

The input GRACE/GRACE-FO products are unfiltered spherical harmonic solutions complete to degree 96. We know that filtering techniques will introduce artefacts, but they also remove errors especially when the truncation degree is high. So, I was wondering if the authors have checked whether the filtering/smoothing will have a large impact on the final results. Looking at Figure 3, we see negative signals over DML and TA, which is not being found in other studies I think. Could this be caused by the unfiltered stripes? Also, why do not use Mascon solutions as input?

We agree that filtering is very helpful in minimizing error effects in the data sets. Filtering is a means of preventing the noise components of the GRACE/GRACE-FO gravity field from influencing the results too much. The same purpose is fulfilled by incorporating the GRACE/GRACE-FO error covariance information. In this way, the inversion procedure is "informed" about the noisiness of high-degree components. And this information is incorporated in a theoretically more rigorous way than by isotropic filtering. Furthermore, the large scale patterns are hardly sensitive to small-scale spatial noise. We discuss possibilities for filtering in section 4.4. In the approach presented here, we try to determine GIA effects and estimate high-resolution mass changes at the same time. The latter would not be achievable if input data sets are filtered. However, we implemented a regularization of the GIA parameters in Antarctica, which results in a smoothing similar to a Gaussian filter. In the joint inversion presented here, the regularization has the advantage that it is applied to the parameters that we assume to be smooth. A smoothing is not applied to the observations.

The implemented globally-consistent parametrization would not work in its current form with mascon products, i.e. we would need to set-up newly developed normal equations. In addition, mascon solutions have already been corrected for the GIA effects, which we want to determine here. The GIA effect would have to be back-processed. Furthermore, these products are already based on many processing decisions, so that a rigorous propagation of the error-covariance information, as presented, would not be possible as long as it is not completely provided along with the mascon products.

We will better clarify in the revised manuscript our strategy to reduce that errors affect the estimate. Additionally, we will explain why we make use of GRACE/GRACE-FO level-2 products for the presented approach instead of level-3 products.

In Figure 3, the GIA results are compared with previous efforts. I am unsure if the GIA result in panel (a) contains the present-day GIA or not. The output GIA is compared with GNSS observations over Antarctica, so I assume it includes the present-day GIA effect. If it does contain present-day GIA, it may not be fair to compare it with the GIA from Caron et al.

Thank you for pointing out that it is not clear which effects are indicated here. We assume that by "present-day GIA effect" the referee refers to the elastic response to recent ice mass change. This can be confusing, because with "present-day GIA effect" we refer to effects that are observable today but had their cause in loading changes, e.g., thousands of years ago. With “GIA-effect”, we only refer to effects associated with the adjustment process to an isostatic state caused by glacial mass changes in the past. This is to be distinguished from effects associated with the instantaneous elastic response to contemporaneous ice-mass loading changes (Thomas et al., 2011). We removed the elastic effects from the GNSS observations as described in Sect. 2.3, so that GNSS and the GIA estimate from the inversion, e.g. in Fig. S10, represent the same signal.

In the revised version of the manuscript, we will clarify what we mean by “GIA effects”.

Table 1 shows the AIS FAC result, but the signal appears to have a smaller value than the error. It's not clear if this has physical significance. Please provide clarification.

Table 1 shows integrated values, so that negative and positive values can balance each other out. In fact, based on the uncertainty given, we cannot make a significant statement as to whether the FAC rate integrated over Antarctica has a positive or negative sign. Signal and error varies spatially (Figure 2 c+f). We will expand the discussion on FAC in Sect. 4.3.

We will consider all minor concerns in the revision.

References:

Rietbroek, R., S.-E. Brunnabend, J. Kusche, J. Schröter, and C. Dahle (2016). “Revisiting the contemporary sea-level budget on global and regional scales”. In: Proc. Natl. Acad. Sci. USA 113.6, pp. 1504–1509. ISSN : 0027-8424. DOI: 10.1073/pnas.1519132113.

Thomas, I.D., M.A. King, M.J. Bentley, P.L. Whitehouse, N.T. Penna, S.D.P. Williams, R.E.M. Riva, D.A. Lavallee, P.J. Clarke, E.C. King, R.C.A. Hindmarsh, and H. Koivula (2011). “Widespread low rates of Antarctic glacial isostatic adjustment revealed by GPS observations”. In: Geophys. Res. Lett. 38.22, p. L22302. ISSN : 0094-8276. DOI: 10.1029/2011GL049277.

Willen, M.O., M. Horwath, A. Groh, V. Helm, B. Uebbing, and J. Kusche (2022). “Feasibility of a global inversion for spatially resolved glacial isostatic adjustment and ice sheet mass changes proven in simulation experiments”. In: J. Geod. 96.10, pp. 1–21. ISSN : 0949-7714. DOI: 10.1007/s00190-022-01651-8.

We are very pleased with the favorable assessment of the manuscript and the very helpful comments. We acknowledge that Sect. 4.3 in particular falls short and needs improvement in terms of content and structure. In the revision of the manuscript, we will revise this section and we are very grateful for the detailed comments that will improve the manuscript.

In the revised manuscript, we plan to re-structure the interpretation section (Section 4.3) as follows:

• validity of spatially-resolved GIA effects and ice mass changes, in particular in East Antarctica
• interpretation of resolved GIA patterns in context of their origin (loading change and rheology) with GIA modelling results/other inversion results
• interpretation of estimated GIA in terms of rheological features in West Antarctica and the Antarctic Peninsula
• interpretation of implications given by the utilized uncertainty information with a focus on FAC

We will improve the alignment of the content with the other subsections of the discussion.

We will revise all technical comments.

Thank you very much for the supportive and helpful comments on our manuscript. This helps us a lot to improve the article. In the following, we will respond to the comments and outline how we plan to revise the manuscript. The referee comments are marked in italics.

1) I find the split of figures between then main paper and the supplementary information imbalanced. There are only 3 figures in the main body of the paper but 16 contained in the supplementary information. I think this manuscript could be improved by moving some figures to the main body, such as one figure for each assessment method detailed in Section 2.3. E.g. S10 for (1), Fig S9 or S13 for assessment (3). Furthermore, each assessment is clearly set out in section 2.3 and described in separate paragraphs. In Section 3, it would be useful to describe the results of each assessment by referring to the number (1,2,3) as described in Section 2.3

Thank you for the helpful advice to keep the structure of the assessment methods from 2.3 in the other sections. This will increase the clarity of the article. We admit that the comprehensibility of the assessments will be increased if figures are shown in the main text already. We will transfer Fig. S10 and Fig. S13 from the Supplement to the main text.

2) I have a slight issue with the treatment of the Antarctic Peninsula as described in the supplementary information. As the authors point out, the expected mantle viscosity here is low (see also Nield et al 2014, Samrat et al 2020). As such, using the ICE6G loading model, which neglects any ice loading in the Late Holocene, will produce incorrect results – since the Late Holocene ice mass changes will dominate the present-day signal. Combined with SELEN, which is likely not high resolution enough to capture GIA here, I think this limitation in the method should be mentioned in the main text to make it clear this area is from a forward model (Pg 5, Line6-7). What was the reason for not using the Caron forward model of GIA in the Peninsula?

We agree and are aware that the applied variant of considering GIA in the Antarctica Peninsula is rather limited to address the actual GIA effects here. We acknowledge that this is an information that should be communicated transparently in the main part of the article and should not just appear in the Supplement. We will clarify this and highlight in the main part of the article that GIA in this area comes from a forward model.

The main reason that we use SELEN outputs is that with the publicly available software we have the facility to calculate a globally consistent GIA effect that is only due to load changes on the Antarctic Peninsula. We do not have this option when using the forward model output from Caron et al. From this model we could extract only a regional GIA effect in the Antarctic Peninsula, but not the global GIA fingerprint that we need in the applied framework. Furthermore, the forward model output from Caron et al., like other global 1-D GIA models, is limited in explaining actual GIA effects on the Antarctic Peninsula, too. In the future, we expect improvements from 3-D GIA model outputs, utilizing a more realistic rheology. Nevertheless, an essential open point remains: the centennial loading history. Further development of combination methods using new high-quality data sets, as e.g. from ICESat-2, hold some promise to determine GIA on the Antarctic Peninsula and may be useful to validate future GIA forward model outputs. We will expand the discussion on the consideration of GIA effects in the Antarctic Peninsula region in the main text.

Last but not least, we thank you for the minor comments, which we will revise.

Publisher’s note: this comment is a copy of AC3 and its content was therefore removed.