Review of esd-2024-1, " Estimating ocean heat content from the ocean thermal expansion parameters using satellite data", submitted by Kondeti and Palanisamy for possible publication in Earth System Dynamics.

This manuscript presents a methodology for making maps of ocean heat content (and thermosteric sea level) using an artificial neural network that incorporates Argo CTD data together with what the authors identify as satellite SST and SSS data, as well as the results of the application of that method. There are some very major issues that will need to be resolved prior to publication.  Specific minor comments follow, first major, then minor, indexed by line number (L) where possible.

1. ince ocean heat content and thermometric anomalies are generally surface-intensified, so integrating from the surface to each depth of mapping does little to reveal how well the method works for mapping ocean heat content or thermometric anomalies at depths below the thermocline.  In that respect it would be much more useful, and transparent, to map these quantities in distinct pressure or depth layers.  Typical layers for using Argo might be 0-100 m, 100-300 m, 300-450 m, 450-700 m, 700-1000 m and 1000-2000 m, but others might be chosen if desiring more vertical resolution.  The statistics for these would be much more revealing of the skill of the method below the surface layers than as it is currently formulated

2. The maps of ocean heat content (or thermometric sea level) are validated only against another machine learning estimate, but there are a number of objectively mapped and machine learning mapped products out there which are more widely used against which this work should be compared.  See Johnson et al. (2023, https://doi.org/10.1175/BAMS-D-23-0076.2) and/or von Schuckman et al. (2023, https://doi.org/10.5194/essd-15-1675-2023) for an idea of the range of products available.

3. Sea surface height is more directly related to both ocean heat content and of course themosteric anomaly, so why aren't say CNEMS SSH maps, available since 1993, used as the neural network analysis?

4. Why are only Argo data used in the training? There are many more temperature profiles from shipboard CTDs, XBTs, marine mammals, and other sources readily available from the WOD that expand the spatial and temporal coverage Argo data considerably. Furthermore, Argo data should be downloaded directly from an Argo global data assembly centre, not WOD at NCEI, for the most recent version, as the data are subject to delayed-mode quality control and revisited frequently. As a result NCEI archives may be out-of-date.  

5. The data section covers only the in situ data, and not the fields used for prediction. Please consider moving the description of the SST and SSS "data" into the data section. Also, hopefully SSH data too, as that should certainly be useful in constructing the network. Another point, the ORAS5 "SSS" data are not from satellite measurements!  Those maps are output of an ocean reanalysis , that is to say, an assimilation of in situ data (including all the Argo profile data) into a numerical ocean model.  So ORAS5 SSS fields are certainly not independent from Argo data, in fact, they directly incorporate those data. This fact, and the model used and datasets ingested, are all well documented on the ORAS5 websites.  Please study the documentation and revise the analysis, manuscript, and claims within accordingly. 

6. Section 4.1. Given the relatively large (100s to 1000s of km) and long (30-120 days) decorrelation scales of ocean temperature anomalies, it is misleading to call or treat these points as "independent". Almost all of them will be well correlated with some of the data used to construct the ANN.  This probably means the true uncertainties are much higher than estimated here.

7. What is the point of section 5?  It gives neither new oceanographic information nor insight into the accuracy or usefulness of the maps generated.  It might better to compare and contrast trends with trends from other products. If a section on the topic is retained, it would be beneficial to recruit a co-author familiar with oceanography, as the section as written is haphazard.

Minor comments

8. L24. 93% is an old estimate at this point. See von Schuckman et al. (2023) for an update.

9. L27. The statement that this understanding is "inevitable" seems an odd word choice.  It is important, or societally relevant, but that does not make it inevitable.

10. L32-33. Actually, just temperature profiles with depth information are also useful (e.g. XBT data). Measurements of conductivity on all profiles are not strictly necessary.

11. L42-87. This paragraph is very long and rather stream-of-consciousness in style. Consider breaking it up into a few paragraphs covering the different topics to better organize the exposition.

12. L48. There is a recent Zhao manuscript on the subject that should be referenced.

13. L177-178. Here and elsewhere in the manuscript, sentences like "blah blah blah are shown in Figure 3" generally duplicate figure captions and interrupt the flow of ideas.  It's much better to write a sentence that communicates the main thing the authors want the readers to get out of the figure and refer to it parenthetically.

14. L241-249.  The more energetic regions of the oceans will of course be more difficult to model.  It might be appropriate to reference studies that have documented the spatial variability of eddy energy in the oceans, highlighting the western boundary current extensions and Antarctic Circumpolar Current, among other regions.

15. L466. The phrase "Future releases of WOA will certainly resolve the complex patterns..." again seems odd, arguably incorrect, and out of place.  Please consider deleting or rephrasing this sentence.

This manuscript has the potential to provide some key strengths, by seeking to contribute to addressing the thorny problem of geoinformation retrieval from satellite data through information-technologically assisted inverse modeling: more precisely ocean "heat" content from proxy parameters derived from satellite data and assisted by artificial neural network data-based modeling.

Overall, the initiative is welcome and courageous, given the minefield of caveats across the retrieval and estimation workflow, which can easily hinder the accuracy and reliability of the formal results and condition the confidence with which novel insights can effectively be drawn from the whole process.

Notwithstanding the complexity and fragility of the overall procedure, the authors have made efforts to document the workflow and underlying reasoning. That does not mean that the results can be taken for factual and fail-proof. However, that does not mean that they should be entirely discarded either without a further attempt to strengthen the methodological and operational robustness of the study workflow, namely in terms of enabling assumptions, limitations and implications.

(For instance, Pearson correlation suffers from various disqualifying shortcomings, especially when relating such complex data, that the reliance on such basic linear metric for relating environmentally relevant datasets is highly questionable).

To that end, it will be crucial to aptly and thoroughly explain and clarify all the fundamental and operational assumptions, limitations and respective mitigation strategies. That is required to more confidently be able to legitimize the research procedure and allow for interpretable results to be drawn and effectively assessed as valid outcomes. While the authors have invested considerable efforts in explaining such in the original manuscript, further diligence is needed, as also pointed out by the other reviewer.

Crucial attention needs to be placed in the formal algorithmic procedures, the underlying mathematical details, and the physical justifications for each conducted step, so that a more detailed feedback can be provided pertaining the associated intricacies and underpinnings beyond these more general remarks. Currently, as also shared by the other referee, major concerns hover over the solidity of the research procedure, which will require thorough clarification and revision.

On a more minor (yet still relevant) aspect, the density scatterplots require some visualization improvement, namely in terms of color scale, so that the different shades can be more easily seen and grasped.

While not repeating the concerns of the other reviewer, I reiterate my overall agreement with them and the need to overcome such for strengthening the contribution. Notwithstanding the difficulties faced by the submitted study and the lack of detail that precludes a clear conclusion on the validity of the procedure and quality of the data (which require thorough clarification and exploitation in the revised version), I hope that the authors can clarify the questions, overcome the shortcomings and produce a much more solid revised manuscript.