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Projected ocean warming constrained by the ocean observational record


The ocean absorbs most of the excess heat from anthropogenic climate change, causing global ocean warming and sea-level rise with a series of consequences for human society and marine ecosystems. While there have been ongoing efforts to address large uncertainties in future projections, to date the projected ocean warming has not been constrained by the historical observations. Here, we show that the observed ocean warming over the well-sampled Argo period (2005–2019) can constrain projections of future ocean warming and that the upper-tail projections from latest climate models with high climate sensitivities are unrealistically large. By 2081–2100, under the high-emission scenario, the upper 2,000 m of the ocean is likely (>66% probability) to warm by 1,546–2,170 ZJ relative to 2005–2019, corresponding to 17–26 cm sea-level rise from thermal expansion. Further narrowing uncertainties requires maintenance of the ocean observing system to extend the observational record.

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Fig. 1: Ocean heat content changes in observations and climate-model simulations.
Fig. 2: Contributions of the individual forcing to historical ocean warming and the association between historical changes and future projection.
Fig. 3: Emergent constraints on the global OHC and thermosteric sea-level projections under the high-emission scenario.

Data availability

The CMIP5 and CMIP6 climate-model outputs are available at All observational datasets used in this study are publicly available online (links are listed in Supplementary Table 2).

Code availability

The code used to generate the main figures and to derive the constrained projections based on the emergent constraint methodology is available from a Figshare repository64.


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This study was supported by the Centre for Southern Hemisphere Oceans Research (CSHOR), jointly funded by the Qingdao National Laboratory for Marine Science and Technology (QNLM, China) and the Commonwealth Scientific and Industrial Research Organisation (CSIRO, Australia). J.A.C. was also funded by the Australian Research Council’s Discovery Project funding scheme (project DP190101173). This research was undertaken with the assistance of resources from the National Computational Infrastructure (NCI Australia), an NCRIS enabled capability supported by the Australian Government. We thank Q. Wu for helpful discussions. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP. We thank the climate modelling groups (listed in Supplementary Table 1) for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data and providing access, and the multiple funding agencies who support CMIP and ESGF. Argo data were collected and made freely available by the International Argo Program and the national programmes that contribute to it (, The Argo Program is part of the Global Ocean Observing System.

Author information




J.A.C. initiated the idea of this study. K.L. carried out the analysis under the guidance of J.A.C. and X.Z. and wrote the first draft. All authors contributed to designing the study, interpreting the results and revising the manuscript.

Corresponding authors

Correspondence to Kewei Lyu or John A. Church.

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The authors declare no competing interests.

Additional information

Peer review information Nature Climate Change thanks Dewi Le Bars and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Relationship between the equilibrium climate sensitivity (ECS) and global OHC projections.

Scatterplot of projected 0–2000 m global OHC changes (2081–2100 relative to 2005–2019) against the ECS values from the CMIP6 (black) and CMIP5 (grey) models. The linear fits are shown although their relationship might not be expected to be linear31,32. (a) high-emission scenarios; (b) medium-emission scenarios; (c) low-emission scenarios.

Extended Data Fig. 2 Impact of the decadal ENSO variability on the observed near-global OHC change over the Argo period.

a, The Niño 3.4 index (black) and its linear fit (red) over 2005–2019. b, The near-global OHC time series over 2005–2019 from the Scripps Argo product (black) and its linear fit (red). The magenta line shows the multiple linear regression based on both the linear trend and the Niño 3.4 index (see Methods).

Extended Data Fig. 3 Emergent constraints on the global OHC projections under medium- and low-emission scenarios.

Scatterplot of projected 0–2000 m global OHC changes (2081–2100 relative to 2005–2019) against simulated 0–2000m near-global OHC changes over 2005–2019 from the CMIP6 ensemble. (a) medium-emission scenario SSP2-4.5; (b) low-emission scenario SSP1-2.6. Triangles are for the individual CMIP6 models (labelled by letters defined in Supplementary Table 1), with colours indicating the equilibrium climate sensitivity (ECS) range. The solid black line shows the linear regression across the CMIP6 ensemble and the dashed black lines show the prediction errors for the linear fit (68% confidence intervals). The vertical magenta line shows the observed trend over 2005–2019 averaged from eight observational datasets after correcting for decadal ENSO effect. The dashed magenta lines show the ±1 standard deviation uncertainty range in the observed trend, considering both spread between different datasets and uncertainty due to internal variability (see Methods).

Extended Data Fig. 4 The probability density function (PDF) for the linear regression from the model-derived emergent relationship and its combination with the observational estimate.

a, The PDF for the linear regression between projected 0–2000 m global OHC changes (2081–2100 relative to 2005–2019) under SSP5-8.5 and simulated 0–2000 m near-global OHC changes over 2005–2019 from 28 CMIP6 models as shown in Fig. 3a. b, The product of the linear regression PDF and the PDF from the observational estimate. The solid black line shows the linear regression across the model ensemble and the dashed black lines show the prediction error for the linear fit (68% confidence intervals). The vertical red lines in (b) show the observed trend over 2005–2019 after correcting for decadal ENSO effect and its uncertainty range.

Extended Data Fig. 5 The histogram of the residuals for the linear regression in Fig. 3a and the fitted probability distributions.

(black) normal distribution; (blue) logistic distribution; (brown) t location-scale distribution.

Extended Data Fig. 6 Emergent relationship between the simulated ocean warming over 2005–2019 and the projected future ocean warming from the CMIP5 ensemble under the high-emission scenario.

Scatterplot of projected 0–2000 m global OHC changes (2081–2100 relative to 2005–2019) against simulated 0–2000 m near-global OHC changes over 2005–2019 from 23 CMIP5 models under RCP8.5. Grey triangles are for the individual CMIP5 models. The solid black line shows the linear regression across the model ensemble and the dashed black lines show the prediction error for the linear fit (68% confidence intervals).

Extended Data Fig. 7 Emergent relationship between the simulated ocean warming over 2005–2019 and the projected future warming in four ocean basins under the high-emission scenario.

a, Southern Ocean (30°–90°S); b, Indian Ocean (20°–120°E, 30°N–30°S); c, Pacific Ocean (120°E–80°W, 70°N–30°S); d, Atlantic Ocean (80°W–20°E, 70°N–30°S). Triangles are for the individual CMIP6 models (labelled by letters defined in Supplementary Table 1), with colours indicating the equilibrium climate sensitivity (ECS) range. The solid black line shows the linear regression across the model ensemble and the dashed black lines show the prediction errors for the linear fit (68% confidence intervals).

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Lyu, K., Zhang, X. & Church, J.A. Projected ocean warming constrained by the ocean observational record. Nat. Clim. Chang. (2021).

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