the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Feb 2026
Consolidating Global Estimates of Ocean Heat Content: Toward a Consistent Earth Heat Inventory
Abstract. The Earth’s Energy Imbalance (EEI), defined as the difference between the incoming solar radiation and the outgoing terrestrial radiation at the top of the atmosphere, provides a fundamental measure of anthropogenic climate change. Today, this imbalance is positive, indicating that the Earth system is accumulating heat, of which more than 90 % is stored in the ocean. The evolution of Global Ocean Heat Content (GOHC) thus constitutes a critical indicator of planetary warming and underpins the Earth Heat Inventory, currently the only approach capable of quantifying the observed absolute value of the EEI. Yet, the lack of standardized calculation protocols and the diversity of methodological choices across studies hinder the comparability of GOHC estimates and obscure the traceability of associated uncertainties. Here, we present a comprehensive, transparent assessment of GOHC trends and uncertainties based on an ensemble of 13 gridded in situ ocean temperature products spanning 1960–2024. Building on prior community efforts, we systematically evaluate the sensitivity of GOHC trends to key methodological choices, including (i) the temperature product, (ii) the definition of the temperature variable, (iii) the treatment of seawater density and heat capacity, (iv) the ocean domain used for integration, and (v) the method used for trend estimation. Our results demonstrate that GOHC trends are remarkably robust across methodological configurations. Variations associated with the temperature variable definition, thermodynamic parameters, ocean domain, or trend estimation method remain below 0.1 W m⁻², well within the ensemble-mean uncertainty range of 0.21 W m⁻², across both recent decades and multi-decadal timescales. We further show that the substantial spread among published EEI estimates reflects pronounced temporal variability in ocean heat uptake rates. This variability renders EEI estimates highly sensitive to the selected averaging period, underscoring that present-day absolute EEI values can only be meaningfully interpreted in a long-term context. We demonstrate that the ensemble spread provides a practical and comprehensive proxy for GOHC uncertainty, consistent with product-specific uncertainty estimates. By consolidating international assessment practices, this study delivers a transparent characterization of the state of ocean warming and provides a fully documented, openly available framework for constructing a GOHC indicator. Together, these advances strengthen the Earth Heat Inventory estimate, establish a reliable benchmark for monitoring ocean warming and EEI, facilitate intercomparison across studies, and reinforce international climate assessments at the science and policy interface.
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Status: final response (author comments only)
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RC1: 'Comment on essd-2026-106', Don Chambers, 16 Mar 2026
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AC1: 'Reply on RC1', Audrey Minière, 04 Jul 2026
We thank the reviewer for the positive assessment of our work and for recognizing the value of the comprehensive comparison and uncertainty assessment presented in this study.
We also appreciate the reviewer's comment regarding the suitability of the manuscript for ESSD. While our study relies on existing temperature products, its primary objective is not only to analyse them but to provide a reproducible framework for deriving Global Ocean Heat Content estimates and associated Earth’s Energy Imbalance indicators. The manuscript introduces a harmonized ensemble dataset generated using a common methodology across multiple observational products, together with openly available code, standardized NetCDF outputs, and detailed documentation enabling full reproducibility and future updates.
In addition, the study provides a consolidated reference dataset and operational framework that can be readily reused by the community for climate monitoring and Earth Energy Inventory assessments. We therefore believe that the manuscript is well aligned with the scope of ESSD, particularly its emphasis on improving the accessibility, usability and standardization of Earth system data products.
We appreciate the reviewer's perspective and leave the final assessment of the manuscript's suitability to the Editor.
Citation: https://doi.org/10.5194/essd-2026-106-AC1
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AC1: 'Reply on RC1', Audrey Minière, 04 Jul 2026
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RC2: 'Comment on essd-2026-106', Anonymous Referee #2, 01 Jun 2026
This paper presents a comprehensive assessment of Global Ocean Heat Content (GOHC) trends using an ensemble of 13 gridded in situ ocean temperature products spanning 1960–2024 and systematically evaluates how five key methodological choices affect the results. The main finding is that GOHC trends are remarkably robust across methodological configurations, with variations from temperature variable definition, thermodynamic parameters, ocean domain, and trend estimation method all remaining below 0.1 W m⁻². In contrast, the choice of temperature product is the dominant source of uncertainty. I have several comments on this manuscript:
A. Introduction
1. [Line 34-50] First and second sentences are very general, as we can read them in many papers. I understand the authors want to make a smooth flow, but in this regard, I believe the authors can show a unique introduction
2. [Line 82] I think it will be good if the authors highlight the bias or difference between data sources.
3. [Line 88-92] The sentence is too long for a sentence.
4. [Line 69-73] In the Introduction, describe indirect OHC methods (reanalyses, sea-level budget, paleoclimate, atmospheric oxygen, neural networks) at considerable length, but since the paper explicitly states it focuses only on direct in situ estimates, this material should be condensed significantly5. The paper frames itself as building on "prior community efforts" but does not clearly articulate what is new compared to Minière et al. (2023) and von Schuckmann et al. (2023). A concise statement of novelty is missing.
6. The statement that GOHC "constitutes a critical indicator of planetary warming" is repeated nearly identically in lines 10–11 and 42–43. Redundancy should be removed.
7. The motivation for focusing on post-processing rather than pre-processing is stated (line 207) but appears only in Section 3, not in the Introduction. The scope limitation should be flagged early.
8. The claim of providing "for the first time, a depth-resolved perspective on the EEI" should highlight what Cheng et al. 2017, Levitus et al. 2012) related to depth-resolved OHC. The authors must clarify precisely what is novel.
9. The sensitivity of EEI estimates to the averaging period is an important conclusion, but the quantitative demonstration of this sensitivity is relegated to Fig. 2b without a dedicated analysis. A systematic test showing how trend estimates change as a function of window length would make this argument much more compelling.
10. The rationale for using anomalies rather than absolute values references for support. Given this is a methodologically relevant choice, at least a brief quantitative statement of the sensitivity to the climatology choice should appear in the main text.
11. The RFROM product uses a random forest regression trained on SSH and SST as predictors. Including a machine-learning-based product in an ensemble of objective analysis products introduces a fundamentally different source of structural uncertainty. The implications of this for ensemble interpretation should be discussed.
12. The recommendations are distributed across several paragraphs and are not consolidated. Practitioners reading this paper to guide their own GOHC calculations would benefit from a dedicated summary table or numbered list of best-practice recommendations. As written, the recommendations must be extracted from narrative text.
13. The paper does not discuss the deep ocean below 2000 m anywhere in the discussion. Given that deep ocean warming is an increasing contributor to EEI, the limitations imposed by restricting the analysis to 0–2000 m should be explicitly addressed, including an estimate of how much heat is potentially missing.
Citation: https://doi.org/10.5194/essd-2026-106-RC2 -
AC2: 'Reply on RC2', Audrey Minière, 04 Jul 2026
Point-by-point reply to reviewer 2
This paper presents a comprehensive assessment of Global Ocean Heat Content (GOHC) trends using an ensemble of 13 gridded in situ ocean temperature products spanning 1960–2024 and systematically evaluates how five key methodological choices affect the results. The main finding is that GOHC trends are remarkably robust across methodological configurations, with variations from temperature variable definition, thermodynamic parameters, ocean domain, and trend estimation method all remaining below 0.1 W m⁻². In contrast, the choice of temperature product is the dominant source of uncertainty. I have several comments on this manuscript:
Response : We thank the reviewer for the careful evaluation of our manuscript and for the constructive comments. We have taken these suggestions into account and revised the manuscript accordingly to improve clarity.
A. Introduction
1. [Line 34-50] First and second sentences are very general, as we can read them in many papers. I understand the authors want to make a smooth flow, but in this regard, I believe the authors can show a unique introduction
Response : The text has been revised accordingly [Lines 42–50].
2. [Line 82] I think it will be good if the authors highlight the bias or difference between data sources.
Response : We have revised the figure caption to explicitly clarify the heterogeneity in data sources and methodological approaches represented in Fig. 1, with further details provided in Fig. S1 and the Code and Data Availability section [Lines 109-115].
3. [Line 88-92] The sentence is too long for a sentence.
Response : We have changed the sentence accordingly [Lines 132-137].
4. [Line 69-73] In the Introduction, describe indirect OHC methods (reanalyses, sea-level budget, paleoclimate, atmospheric oxygen, neural networks) at considerable length, but since the paper explicitly states it focuses only on direct in situ estimates, this material should be condensed significantly
Response : The purpose of this paragraph is to illustrate the wide diversity of existing approaches used to estimate ocean heat content, thereby motivating the need for a harmonized assessment. Nevertheless, to improve the focus of the introduction and better align it with the scope of the present study, we have condensed the description of indirect methods while retaining representative examples and key references [Lines 86-95].
5. The paper frames itself as building on "prior community efforts" but does not clearly articulate what is new compared to Minière et al. (2023) and von Schuckmann et al. (2023). A concise statement of novelty is missing.
Response : We agree that the novelty relative to Minière et al. (2023) and von Schuckmann et al. (2023) was not sufficiently explicit in the original manuscript. To address this, we have added a concise paragraph in the Introduction [Lines 119-125] that states the specific contribution of this study and its distinction from previous work. In particular, we now emphasize that this study provides the first fully systematic and reproducible sensitivity framework quantifying the relative contribution of key methodological choices to GOHC trend uncertainty, building upon but extending prior community assessments and initial sensitivity analyses.
6. The statement that GOHC "constitutes a critical indicator of planetary warming" is repeated nearly identically in lines 10–11 and 42–43. Redundancy should be removed.
Response : We have changed the text accordingly [Line 60].
7. The motivation for focusing on post-processing rather than pre-processing is stated (line 207) but appears only in Section 3, not in the Introduction. The scope limitation should be flagged early.
Response : We agree that the scope of the study should be made explicit earlier in the manuscript. We have therefore revised the Introduction to indicate that our analysis focuses on post-processing methodological choices applied to gridded in situ temperature products [Lines 127-131].
8. The claim of providing "for the first time, a depth-resolved perspective on the EEI" should highlight what Cheng et al. 2017, Levitus et al. 2012) related to depth-resolved OHC. The authors must clarify precisely what is novel.
Response : We thank the reviewer for this helpful comment. We agree that previous studies (e.g., Levitus et al., 2012; Cheng et al., 2017) have already documented the vertical structure and temporal evolution of ocean heat content changes. The novelty of the present work does not lie in the computation of layer-integrated OHC itself, but rather in framing the temporal evolution of ocean heating rates across successive depth layers as a depth-resolved diagnostic of the Earth's Energy Imbalance. This is also based on the scientific method evolutions as presented in Minière et al. (2023), which have not been addressed in Levitus et al. (2012), or Cheng et al. (2017). We have revised the manuscript to make this distinction clearer [Lines 215-221].
9. The sensitivity of EEI estimates to the averaging period is an important conclusion, but the quantitative demonstration of this sensitivity is relegated to Fig. 2b without a dedicated analysis. A systematic test showing how trend estimates change as a function of window length would make this argument much more compelling.
Response : We thank the reviewer for this valuable suggestion. In the revised manuscript, we have expanded the sensitivity analysis to explicitly investigate the dependence of GOHC trend estimates on the analysis period itself. Specifically, new Fig. 4b–c systematically explores the sensitivity of GOHC trends to both window length and starting year, thereby quantifying how ocean warming rate estimates evolve across all possible temporal configurations. This new analysis complements the methodological sensitivity tests presented in Fig. 4a and demonstrates that, as suggested by Fig. 2, the choice of analysis period can have a larger influence on GOHC trends than most methodological assumptions, particularly for short averaging windows. The corresponding results and their implications are now discussed in Section 3 (Lines 465–480 and lines 523–541) and Discussion (Lines 665–677).
10. The rationale for using anomalies rather than absolute values references for support. Given this is a methodologically relevant choice, at least a brief quantitative statement of the sensitivity to the climatology choice should appear in the main text.
Response : In our case, changing the climatological reference period modifies the mean seasonal cycle computed from monthly GOHC time series and subsequently removed during anomaly calculation (Eq. 2.4 and 2.5). As a result, the choice of reference period primarily affects monthly values and introduces a constant offset in the anomaly time series (i.e., shifting the anomaly series upward or downward), without altering the associated trend estimates. This is further supported by the fact that all analyses in this study are based on annual-mean GOHC time series, which effectively removes the seasonal cycle prior to trend estimation. In this framework, the role of the reference period is therefore limited to centering the annual time series, enabling consistent comparison of temporal changes in ocean heat gain and its rate of change across products, rather than affecting the underlying long-term variability.
More generally, the influence of the climatological baseline adopted upstream of GOHC estimation and its trend has been discussed in the literature (e.g., Boyer et al., 2016; Cheng and Zhu, 2015; Lyman and Johnson, 2014), particularly in relation to choices involved in the construction of subsurface temperature fields and gridded OHC products. In this study, we do not revisit this aspect and focus instead on other methodological choices affecting GOHC time series analysis. We have clarified this distinction in the revised manuscript [Lines 326–332].
11. The RFROM product uses a random forest regression trained on SSH and SST as predictors. Including a machine-learning-based product in an ensemble of objective analysis products introduces a fundamentally different source of structural uncertainty. The implications of this for ensemble interpretation should be discussed.
Response :We acknowledge that RFROM differs from objective analysis products as it is based on a machine-learning reconstruction using sea surface height and sea surface temperature as predictors. We have clarified this point in the revised manuscript, by highlighting that RFROM represents a distinct methodological family within the ensemble [Lines 350-353].
12. The recommendations are distributed across several paragraphs and are not consolidated. Practitioners reading this paper to guide their own GOHC calculations would benefit from a dedicated summary table or numbered list of best-practice recommendations. As written, the recommendations must be extracted from narrative text.
Response :We thank the reviewer for this helpful suggestion. In the revised manuscript, we have added a detailed list and a dedicated summary table compiling the main methodological recommendations emerging from this study. This table consolidates the key findings currently distributed across the Discussion section and provides a clear and practical synthesis intended to facilitate the use of GOHC estimates by end users. We believe this addition significantly improves the accessibility and usability of the results [Lines 688–740].
13. The paper does not discuss the deep ocean below 2000 m anywhere in the discussion. Given that deep ocean warming is an increasing contributor to EEI, the limitations imposed by restricting the analysis to 0–2000 m should be explicitly addressed, including an estimate of how much heat is potentially missing.
Response : We thank the reviewer for this important comment. In the revised manuscript, we have extended Fig. 2 to include the estimated contribution of the ocean below 2000 m to the total ocean heat content, where available. We have also added a dedicated discussion [Lines 723–740] addressing the implications of restricting the main analysis to the upper 2000 m. This new section discusses the available estimates of deep-ocean warming, compares our inferred trends with published hydrography-based studies (e.g., Purkey and Johnson, 2010; Desbruyères et al., 2017; Johnson and Purkey, 2024), and highlights the limited observational constraints currently available for the global deep ocean. We further emphasize that improved monitoring of deep-ocean heat uptake remains essential for better constraining the full ocean heat inventory and, consequently, Earth's Energy Imbalance, particularly as new constraints emerge (e.g., Cazenave et al., 2026).
References
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Cazenave, A., Yang, C., Bouih, M., Storto, A., Chen, J., Lovell, W., von Schuckmann, K., and Leclercq, L.: Evidence of Increased Deep Ocean Warming From a Sea Level Budget Approach, Earth’s Future, 14, e2025EF007403, https://doi.org/10.1029/2025EF007403, 2026.
Cheng, L. and Zhu, J.: Influences of the Choice of Climatology on Ocean Heat Content Estimation, Journal of Atmospheric and Oceanic Technology, 32, 388–394, https://doi.org/10.1175/JTECH-D-14-00169.1, 2015.
Cheng, L., Trenberth, K. E., Fasullo, J., Boyer, T., Abraham, J., and Zhu, J.: Improved estimates of ocean heat content from 1960 to 2015, Science Advances, 3, e1601545, https://doi.org/10.1126/sciadv.1601545, 2017.
Desbruyères, D., McDonagh, E. L., King, B. A., and Thierry, V.: Global and Full-Depth Ocean Temperature Trends during the Early Twenty-First Century from Argo and Repeat Hydrography, Journal of Climate, 30, 1985–1997, https://doi.org/10.1175/JCLI-D-16-0396.1, 2017.
Forster, P. M., Walsh, T., Smith, C., Lamb, W. F., Lamboll, R., Cassou, C., Hauser, M., Hausfather, Z., Lee, J.-Y., Palmer, M. D., von Schuckmann, K., Slangen, A. B. A., Szopa, S., Trewin, B., Yun, J., Gillett, N. P., Jenkins, S., Matthews, H. D., Raghavan, K., Ribes, A., Rogelj, J., Rosen, D., Zhang, X., Allen, M., Andrew, R. M., Atkinson, C., Betts, R. A., Bombelli, A., Burgess, S. N., Cheng, L., Claxton, H. E., Friedlingstein, P., Frölicher, T. L., Domingues, C. M., Gasser, T., Gregory, C. H., Hoesly, R. M., Huppmann, D., Ishii, M., Kadow, C., Karwat, A., Kennedy, J., Killick, R. E., Kovilakam, M. V. M., Krummel, P. B., Lan, X., Lamarque, J.-F., Liné, A., Martín-Míguez, B., Monselesan, D. P., Morice, C., Mühle, J., Mussak, P., Peters, G. P., Pirani, A., Pongratz, J., Rigby, M., Rohde, R., Savita, A., Seneviratne, S. I., Smith, S. J., Taha, G., Tassone, C., Thorne, P., Wells, C., Western, L. M., van der Werf, G. R., Wijffels, S. E., Zecchetto, M., Zhong, J., Zhang, X.-Y., Masson-Delmotte, V., and Zhai, P.: Indicators of Global Climate Change 2025: annual update of key indicators of the state of the climate system and human influence, Earth System Science Data, 18, 3889–3933, https://doi.org/10.5194/essd-18-3889-2026, 2026.
Johnson, G. C. and Purkey, S. G.: Refined Estimates of Global Ocean Deep and Abyssal Decadal Warming Trends, Geophysical Research Letters, 51, e2024GL111229, https://doi.org/10.1029/2024GL111229, 2024.
Levitus, S., Antonov, J. I., Boyer, T. P., Baranova, O. K., Garcia, H. E., Locarnini, R. A., Mishonov, A. V., Reagan, J. R., Seidov, D., Yarosh, E. S., and Zweng, M. M.: World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010, Geophysical Research Letters, 39, https://doi.org/10.1029/2012GL051106, 2012.
Lyman, J. M. and Johnson, G. C.: Estimating Global Ocean Heat Content Changes in the Upper 1800 m since 1950 and the Influence of Climatology Choice, Journal of Climate, 27, 1945–1957, https://doi.org/10.1175/JCLI-D-12-00752.1, 2014.
Minière, A., von Schuckmann, K., Sallée, J.-B., and Vogt, L.: Robust acceleration of Earth system heating observed over the past six decades, Sci Rep, 13, 22975, https://doi.org/10.1038/s41598-023-49353-1, 2023.
Purkey, S. G. and Johnson, G. C.: Warming of Global Abyssal and Deep Southern Ocean Waters between the 1990s and 2000s: Contributions to Global Heat and Sea Level Rise Budgets, Journal of Climate, 23, 6336–6351, https://doi.org/10.1175/2010JCLI3682.1, 2010.
von Schuckmann, K., Minière, A., Gues, F., Cuesta-Valero, F. J., Kirchengast, G., Adusumilli, S., Straneo, F., Ablain, M., Allan, R. P., Barker, P. M., Beltrami, H., Blazquez, A., Boyer, T., Cheng, L., Church, J., Desbruyeres, D., Dolman, H., Domingues, C. M., García-García, A., Giglio, D., Gilson, J. E., Gorfer, M., Haimberger, L., Hakuba, M. Z., Hendricks, S., Hosoda, S., Johnson, G. C., Killick, R., King, B., Kolodziejczyk, N., Korosov, A., Krinner, G., Kuusela, M., Landerer, F. W., Langer, M., Lavergne, T., Lawrence, I., Li, Y., Lyman, J., Marti, F., Marzeion, B., Mayer, M., MacDougall, A. H., McDougall, T., Monselesan, D. P., Nitzbon, J., Otosaka, I., Peng, J., Purkey, S., Roemmich, D., Sato, K., Sato, K., Savita, A., Schweiger, A., Shepherd, A., Seneviratne, S. I., Simons, L., Slater, D. A., Slater, T., Steiner, A. K., Suga, T., Szekely, T., Thiery, W., Timmermans, M.-L., Vanderkelen, I., Wjiffels, S. E., Wu, T., and Zemp, M.: Heat stored in the Earth system 1960–2020: where does the energy go?, Earth System Science Data, 15, 1675–1709, https://doi.org/10.5194/essd-15-1675-2023, 2023.
Citation: https://doi.org/10.5194/essd-2026-106-AC2
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AC2: 'Reply on RC2', Audrey Minière, 04 Jul 2026
Data sets
Dataset and scripts supporting Consolidating Global Estimates of Ocean Heat Content: Toward a Consistent Earth Heat Inventory Audrey Minière https://zenodo.org/records/18485246
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This is a nice and very complete study comparing different strategies for computing changes in global ocean heat content. The authors examine all possible combinations of calculations that can be made to already analyzed temperature products and fully quantify the level of uncertainty introduced. As I expected when I began reading the manuscript, the primary source of difference in estimates relates to the length of the record (which can be controlled) and the processing decisions made by data centers for mapping raw temperature profiles (which cannot be controlled after the fact).
Unfortunately, as the authors conclude, the primary source of uncertainty is the very large range of values that come out of the data center statistical mapping, primarily before the introduction of Argo floats (but even continuing then to a certain extent).
This paper is well worth publishing and I have no suggestions for revisions. However, I am not convinced that ESSD is the best place for this manuscript. Yes, the authors provide code and their analyzed timeseries (which is useful to the community), but this is not really a NEW dataset. Overall, this is more of any analysis and synthesis of existing data and a discussion of "best practices" for analysis. Perhaps this is suitable for ESSD, but the editor might want to consider if it would be better suited in another EGU journal, such as Ocean Science or one of the climate-focused journals. I think it might get more views in another journal.