the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Jun 2026
Improving global and regional ocean heat content by consistently combining GRACE gravity, satellite altimetry and Argo profile observations in a joint inversion framework
Abstract. The current energy imbalance at the top of atmosphere and corresponding heating of the Earth system is the main driver of steric sea level change through ocean heat uptake (OHU). A global constant heat capacity factor is commonly applied to retrieve ocean heat content (OHC) from observed ocean-average steric sea level. We propose an extension to this methodology, which focuses on the leading modes of steric variability, which are derived from an ocean model and fitted to GRACE gravity, satellite altimetry and in situ Argo observations within a joint inversion framework. These modes are utilized to obtain data driven OHC estimates by establishing a mapping between modeled OHC and steric sea level, and rescaling each mode individually based on observed steric sea level change. On global scales for the period 2005-01 till 2024-12, our OHU results (0.62 W/m2) agree well with a variety of published datasets from in situ Argo data, model reanalyses and space-geodetic approaches as well as independent estimates from the CERES project. At basin scales, we demonstrate the global OHU to be driven mainly by warming of the Pacific Ocean (0.23 W/m2), followed by contributions from the Indian (0.20 W/m2) and Atlantic (0.13 W/m2) oceans. Minor contributions are found from the Arctic Ocean (0.01 W/m2), the Southern Ocean (0.02 W/m2) and the residual ocean (0.03 W/m2). Our results also indicate a shift from dominant heating in the Indian Ocean driven by heat transport from the Pacific Ocean, e.g. found during 2005–2015, towards a more evenly distributed global ocean heat budget.
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Status: open (until 05 Aug 2026)
- RC1: 'Comment on essd-2026-368', Giuseppe M.R. Manzella, 17 Jun 2026 reply
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RC2: 'Comment on essd-2026-368', Anonymous Referee #2, 21 Jul 2026
reply
The manuscript introduces a budget method to reconstruct global and regional ocean heat content (OHC) and uptake (OHU) rates over 2005–2024. Although budget methods have been used to estimate global OHC time series widely, it is less commonly used to derive regional OHC changes. The manuscript provides a new dataset for understanding OHC, which is valuable for the ocean community and fits the scope of ESSD perfectly. However, I think the authors should provide the uncertainty of their indirect OHC datasets. The uncertainty of this method is closely associated with the challenges of regional sea level budget. The uncertainty of regional sea level and ocean mass changes is much larger than that of global mean time series. Thus, some studies have pointed out that sea level budgets are not balanced in some basins, such as North Atlantic. The authors should add some discussions. This could influence the confidence of the work and should be addressed before publication. The authors should be cautious when they compare their results with other products, such as observations and ocean reanalyses. The calculation of the ocean reanalyses ensemble mean in this study is not acceptable. The ocean reanalyses products do not have the same periods, resulting in inconsistent errors. I believe that this manuscript must address these two major issues before publication.
Major comments:
- Previous studies have highlighted the challenges of closing regional budgets, which means there is still great uncertainty in sea level, ocean mass, and steric sea level. The budget gaps can be induced by satellite altimetry, GRACE/GRACE-FO, or Argo observations. But it seems that this method mainly adds the budget gaps into steric sea level. This is not reasonable. I know it is hard to separate budget gaps into three parts, so I hope the authors can discuss the uncertainty of this method.
- The authors give the comparison among different products to validate their results. This comparison is important to increase the reader’s confidence. But it is not wise to use ‘overestimate’ or ‘underestimate’ in the observations when they are compared with the indirect method. I think the uncertainty of observations is smaller than the method. If the authors can point out the limitations of observations, such as instrument bias and other problems, I think the description is acceptable.
- I am confused about the resolution. The output of this manuscript is 0.25 degree. I know the satellite altimetry and GRACE have the resolution of 0.25 degree, but the salinity observation only have a resolution of 1 degree. Can the authors provide more details?
Minor comments:
L94: Another challenge is that the uncertainty of regional sea level observations are much larger than that of global mean time series.
L123: It is more proper to use EOF. PCA is used in time series decomposition generally, and EOF involves spatial and temporal decomposition.
L159: Why choose 700m as a divided range? Some studies use 700m as a specific depth because it is the maximum observation range of XBT (the major source of ocean temperature before Argo). The Argo observations can cover upper 2000m ocean. Maybe 2000m is a better choice.
L160: Please clarify how to remove artificial trend and salinity drifts
L160: The authors should point out the depth range. The ORAS5 covers the full-depth ocean, but some of the Argo-based observations (such as SCRIPPS) only provide the upper 2000m.
L169: ORAS5 has a resolution of 0.25 degree, but the Argo-based observations generally only have 1 degree.
L178: It is unusual to use along-track satellite altimetry. I do not think it is damage, but I think the authors should point out why they do not use the gridded products and the corrections used in altimetry (such as GIA, wet troposphere correction).
L351: The number is odd. Maybe the authors want to express “(1.34 ±0.12)*1022”. I recommend using “ZJ”.
L354: Point out the computed period.
L355: The number is odd.
Fig. 3: I do not trust the ocean reanalyses time series in this figure. For example, it seems the ocean reanalysis time series has a fake increase in 2024 in the Atlantic Ocean. The increase is induced by the number of ocean reanalysis ensembles. I recommend using the ocean reanalyses, which cover the full analysis period, such as CIAGR, SODA4 and ORAS5.
L425: I think the authors should explain the Arctic time series with caution. The sea level observations in the Arctic is limited, which greatly reduces the reader confidence. The authors should point out limited observations here.
L565: I do not think so. The sea level budget is an indirect method to estimate OHU, and it is hard to be a baseline to judge other methods. If the authors can give evidence to show that the uncertainty of their method is smaller than that of observations, the description is acceptable. In Meyssignac et al., (2023) supplement, the Indian Ocean exhibited a great budget residual, and the residual is mainly to be included in the steric sea level with such a method. It is not the fact. The sea level and ocean mass observation also possibly contribute the budget gaps. That’s why the authors get a higher trend in Indian Ocean.
Meyssignac, B., Ablain, M., Guérou, A., Prandi, P., Barnoud, A., Blazquez, A., et al. (2023). How accurate is accurate enough for measuring sea-level rise and variability. Nature Climate Change, 13(8), 796–803. https://doi.org/10.1038/s41558-023-01735-z
L575: The authors can add more discussion on the uncertainty of this method. And in my opinion, the authors should add the discussion about the regional sea level budget (Mu et al., 2024; Bouih et al., 2025). Also, the GIA correction in GRACE/GRACE-FO and limited observation of deep ocean (below 2000m) salinity/temperature are important source of uncertainty.
Mu, D., Church, J. A., King, M., Ludwigsen, C. B., & Xu, T. (2024). Contrasting Discrepancy in the Sea Level Budget Between the North and South Atlantic Ocean Since 2016. Earth and Space Science, 11(8), e2023EA003133. https://doi.org/10.1029/2023EA003133
Bouih, M., Barnoud, A., Yang, C., Storto, A., Blazquez, A., Llovel, W., et al. (2025). Regional sea level trend budget over 2004–2022. Ocean Science, 21(4), 1425–1440. https://doi.org/10.5194/os-21-1425-2025
Citation: https://doi.org/10.5194/essd-2026-368-RC2
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General Comment
The paper calculates ocean heat content and its changes over time starting from a principal components analysis. The approach adopted is convincing and supported by the results. The authors' work makes an important contribution to one of the most debated issues in the scientific and general context. The article therefore deserves publication after some minor corrections.
Specific Comment
The section requiring further clarification concerns the principal components used to calculate the fingerprint. The authors state that they use 75 components (out of 236, I assume—but the text should explain this better) accounting 80% of the total variance. A figure (better) or a comment on how the variance is distributed in the various modes would be helpful in understanding whether the remaining 20% can be considered just noise.
Although of little practical importance, there is a formal difference between Singular Value Decomposition and Empirical Orthogonal Function. In 2.2, the authors define PCA and write EOF on 124 line. Again, this has no practical consequences, but formally, it is inaccurate.
Specific Comments
In Formula 1, it would be better to include all the coordinates so as to emphasize the fact that the integration is performed only on the vertical coordinate.
In the same formula, it is necessary to indicate the value of -H in the integral.
The use of CERES (which are not completely independent data) can only be used for comparison of results. This needs to be made clearer in the discussion.