| 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.
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.