Please see attached PDF report. Overall it is a very well written paper covering an important subject. I feel a few modifications to the manuscript text will improve clarity.

In this manuscript Camargo and colleagues analyze the regional sea level budget (i.e., the sum of individually measured/modelled contributions) to satellite altimetry over the 1993 to 2016 period. They specifically focus on the effect of spatial averaging on the uncertainties in budget closure. For spatial averaging they incorporate an a priori pattern recognition (two different approaches) step, which identifies clusters of homogeneous regions that are then averaged for the budget analysis. They demonstrate that clustering generally improves the budget closure and works significantly better than just using larger blocks. They also demonstrate the importance of the inclusion of an ocean bottom pressure term to the sterodynamic component. Overall, this is a very well written paper using novel approaches with several interesting findings. I therefore have no major reservations regarding the publication of the paper in Ocean Science. Below I provide a couple of comments and suggestions:

General:

I hope I did not overlook anything, but it seems that the authors compare geocentric sea level from satellite altimetry to relative sea level from the budget components, as their budget components also seem to contain crustal components of GRD terms due to contemporary mass change!? To my understanding one must either add those components to satellite altimetry, or only consider the geoid variations in the budget. The term has a substantial contribution to regional sea level according to Frederikse et al. (2017a)

Specific

Line 20: The inverse barometer contribution is missing here

Line 32: or for individual coastline stretches characterized by coherent variability (Frederikse et al., 2016, 2017b; Dangendorf et al., 2021). It has also been closed at a tide gauge level by Wang et al. (2021).

Line 69: I was wondering how the authors treated missing data due to the presence of sea ice at higher latitudes? This might also affect some of the budget misclosures/uncertainties mentioned farther below in the manuscript.

Line 83: How does that compare the deep ocean contribution from Zanna et al. 2019?

Line 85 following: As mentioned as a general comment, the approach seems to be inconsistent with respect to geocentric sea level as measured by satellites.

Line 94: It might be good to provide a little more information here, given that this other paper is still under review. I was also wondering how the estimates differ from those in Frederikse et al. (2020)?

Line 174 following: I am wondering how sensitive the two approaches are to temporal filtering? Former assessments such as Thompson and Merrifield (2014) have focused on decadal scales (which is likely more relevant for trends). Did the authors test sensitivity to smoothing? Also, have the time series been deseasonalized before applying the clustering technique?

Line 207: Or atmospheric teleconnections. Not all of them are connected by coasts

Line 231: does this mean a positive bias?

Line 344: The authors might consider Calafat et al. (2013) & Dangendorf et al., (2014), who initially established that link

Line 349: Southern Hemisphere

References:

Calafat, F. M., Chambers, D. P., & Tsimplis, M. N. (2013). Inter‐annual to decadal sea‐level variability in the coastal zones of the Norwegian and Siberian Seas: The role of atmospheric forcing. Journal of Geophysical Research: Oceans, 118(3), 1287-1301.

Dangendorf, S., Calafat, F. M., Arns, A., Wahl, T., Haigh, I. D., & Jensen, J. (2014). Mean sea level variability in the North Sea: Processes and implications. Journal of Geophysical Research: Oceans, 119(10).

Frederikse, T., Riva, R., Kleinherenbrink, M., Wada, Y., van den Broeke, M., & Marzeion, B. (2016). Closing the sea level budget on a regional scale: Trends and variability on the Northwestern European continental shelf. Geophysical research letters, 43(20), 10-864.

Frederikse, T., Riva, R. E., & King, M. A. (2017a). Ocean bottom deformation due to present‐day mass redistribution and its impact on sea level observations. Geophysical Research Letters, 44(24), 12-306.

Frederikse, T., Simon, K., Katsman, C. A., & Riva, R. (2017b). The sea‐level budget along the N orthwest A tlantic coast: GIA, mass changes, and large‐scale ocean dynamics. Journal of Geophysical Research: Oceans, 122(7), 5486-5501.

Zanna, L., Khatiwala, S., Gregory, J. M., Ison, J., & Heimbach, P. (2019). Global reconstruction of historical ocean heat storage and transport. Proceedings of the National Academy of Sciences, 116(4), 1126-1131.

Review of “Regionalizing the Sea-level Budget With Machine Learning Techniques” by Camargo et al.

General comments:

Global sea level budgets are examined using two machine learning techniques. Through identifying regions of similar sea level variability, the authors examined sea level budget in different basins of the world oceans. It is found that for most of the ocean regions, sea level variation can be explained using steric height changes and mass transport between ocean and land. But for some highly dynamic regions, the sea level budget closure may be affected by the mass redistribution associated with strong western boundary currents. All these make sense to this Reviewer. This is an excellent example of SOM application in oceanography and climate research community. I would like to recommend the manuscript be accepted after some minor revision. Specific comments are listed as follows.

Specific comments:

1. Pioneer work on SOM analysis of sea level variability should be properly mentioned. These include the first time SOM analysis of the satellite altimetry data (Liu et al., 2008), and the dual-SOM applications including the regionalizing of sea level variability in the Gulf of Mexico (Liu et al., 2016). It would be good to add the following information to the paragraph explaining the SOM (L138 - L156) or the Introduction part (L44-45):

“SOM has been used to extract patterns of sea level variability from satellite altimetry data (Liu et al., 2008; Weisberg and Liu, 2017, Nickerson et al., 2021). Dual-SOM application has been proposed to analyse sea level data, one focused on the characteristic spatial patterns, and the other focused on the characteristic time series, using sea level in the Gulf of Mexico as an example (Liu et al., 2016). The latter resulted in regionalizing the sea level variability, and is pursued here in this study to analyse global sea level data.”

2. L361-L362 indicate the challenges of sea level budget in coastal regions. This is true, as coastal ocean dynamics of sea level (e.g., Liu et al., 2007) are more complicated than that of deep ocean, and key dynamics may not be properly represented in the global data. It would be good to add a sentence to L364 about the sea level budget issues for coastal regions:

“Note that sea level budget for coastal regions is more challenging (Liu et al., 2007) with some of the dominant coastal ocean dynamics are not properly represented in the global data sets.”

3. Throughout the manuscript, “sea-level” should be changed to “sea level” ––– no hyphen.
4. The abbreviations of “sea level change” and “sea level budget” are not necessary at all. They do not save much space in text, rather they may cause inconveniences to readers, as readers may need to go back to search what they stand for, particularly for the case of many other acronyms are used later.
5. L23, it would be good to provide an example, Chambers et al. (2014), for this sentence.

6. L90, GRD is not defined.

7. Line 139, it would be good to insert a sentence to mention the powerfulness of the SOM technique: “It was demonstrated to be more powerful than conventional feature extraction methods (e.g., Liu and Weisberg, 2005).

References:

Chambers, D.P., A. Cazenave, N. Champollion, H. Dieng, W. Llovel, R. Forsberg, K. von Schuckmann, Y. Wada (2014), Evaluation of the global mean sea level budget between 1993 and 2014, Integrative study of the mean sea level and its components, 315-333, Springer, Cham.

Liu, Y., and R.H. Weisberg (2005), Patterns of ocean current variability on the West Florida Shelf using the self-organizing map, Journal of Geophysical Research, 110, C06003, http://dx.doi.org/10.1029/2004JC002786.

Liu, Y., and R.H. Weisberg (2007), Ocean currents and sea surface heights estimated across the West Florida Shelf, Journal of Physical Oceanography, 37(6), 1697-1713, http://dx.doi.org/10.1175/JPO3083.1.

Liu, Y., R.H. Weisberg, and Y. Yuan (2008), Patterns of upper layer circulation variability in the South China Sea from satellite altimetry using the self-organizing map. Acta Oceanologica Sinica, 27(Supp.), 129-144.

Liu, Y., R.H., Weisberg, S. Vignudelli, and G.T. Mitchum (2016), Patterns of the Loop Current system and regions of sea surface height variability in the eastern Gulf of Mexico revealed by the self-organizing maps, Journal of Geophysical Research Oceans, 121, 2347-2366, http://dx.doi.org/10.1002/2015JC011493.

Weisberg, R.H., and Y. Liu (2017), On the Loop Current penetration into the Gulf of Mexico, Journal of Geophysical Research: Oceans, 122, 9679-9694, http://dx.doi.org/10.1002/2017JC013330.

Nickerson, A.K., R.H. Weisberg, and Y. Liu (2022), On the evolution of the Gulf of Mexico Loop Current through its penetrative, ring shedding and retracted states, Advances in Space Research, 69(11), 4058-4077, https://doi.org/10.1016/j.asr.2022.03.039

The authors offer a new perspective on regional sea level budget (SLB) closure by focusing on two machine learning (ML) algorithms. They show how self organizing maps (SOM) and d-MAPS allow to identify spatially coherent regions and (i) close the SLB in most of those regions and (ii) further reduce the undertainties otherwise present when using the gridded data alone. Importantly, by focusing on two ML tools they are able to demonstrate the robustness of their conclusions under the models architecture considered.

This is a good, well written paper and it further demonstrate the benefit of focusing on coherent patterns rather than gridded data. I reccomend publication after some minor revisions.

(a) Section 2.1. Is terrestrial water storage included in the sea level budget? If not, can the authors give an explanation on why it was not considered?