Quantification of ocean heat uptake from changes in atmospheric O 2 and CO 2 composition

The ocean is the main source of thermal inertia in the climate system1. During recent decades, ocean heat uptake has been quantified by using hydrographic temperature measurements and data from the Argo float program, which expanded its coverage after 20072,3. However, these estimates all use the same imperfect ocean dataset and share additional uncertainties resulting from sparse coverage, especially before 20074,5. Here we provide an independent estimate by using measurements of atmospheric oxygen (O2) and carbon dioxide (CO2)—levels of which increase as the ocean warms and releases gases—as a whole-ocean thermometer. We show that the ocean gained 1.33 ± 0.20 × 1022 joules of heat per year between 1991 and 2016, equivalent to a planetary energy imbalance of 0.83 ± 0.11 watts per square metre of Earth’s surface. We also find that the ocean-warming effect that led to the outgassing of O2 and CO2 can be isolated from the direct effects of anthropogenic emissions and CO2 sinks. Our result—which relies on high-precision O2 measurements dating back to 19916—suggests that ocean warming is at the high end of previous estimates, with implications for policyrelevant measurements of the Earth response to climate change, such as climate sensitivity to greenhouse gases7 and the thermal component of sea-level rise8. As shown in Fig. 1, recent temperature-based hydrographic estimates of ocean warming9–12 show good agreement for the years 2007– 2016 (1.09 ± 0.10 × 1022 to 1.16 ± 0.20 × 1022 J yr−1), but a larger spread when extending back to include the sparser data of the 1990s (0.90 ± 0.09× 1022 to 1.36 ± 0.10 × 1022 J yr−1 for 1993–2015). The spread is mostly caused by gap-filling methods and systematic errors5,9, which together introduce uncertainties of up to 25%–50% in warming trends4. Because temperature-based estimates also use the same upperocean observations and linear warming trend for depths below 2,000 m (ref. 11), they may share additional unknown systematic errors12. An alternative method based on the top of the atmosphere energy balance13 is also not truly independent, because it is subject to large systematic errors when estimating long-term trends and therefore depends on the same hydrographic measurements for calibration13–15. Here we introduce a third method, based on changes in the abundances of gases in the atmosphere, which respond to whole-ocean warming through the temperature dependence of gas solubility in sea water. This method is not limited by data sparseness, because fast mixing in the atmosphere efficiently integrates the global ocean signal. Changes in ocean heat content on seasonal16 and glacial–interglacial17 timescales have been reconstructed using measurements of noble gases in modern or ancient air. Our method is similar, but instead of relying on noble gases (for example, ratios of argon to nitrogen), which lack sufficient accuracy as yet16, we rely on measurements of atmospheric O2 and CO2, which can be summed to yield a tracer ‘atmospheric potential oxygen’ (APO) that responds to warming similarly to a noble gas18. When the ocean warms, the solubility of O2 and CO2 drops, and the amount of gas lost by the ocean can be quantified with the complementary change observed in the atmosphere. Precise atmospheric O2 measurements began in 1991 (CO2 in 1958), enabling APO-based reconstructions of ocean heat content that span nearly three decades6. APO (O2 + 1.1 × CO2) is computed using observed atmospheric O2/N2 molar ratios and CO2 molar fractions (see Methods)6,19. By design, APO is insensitive to exchanges with land ecosystems, which produce changes in O2 and CO2 that largely cancel in APO owing to their approximate 1.1 O2/C oxidative ratio. Time-series measurements at remote sites show a global long-term decline in APO, with ΔAPOOBS being −243.70 ± 10.10 per meg (units defined in the Methods) between 1991 and 2016. ΔAPOOBS is driven by four primary contributors, illustrated in Fig. 2:

O 2 measurements began in 1991 (CO 2 in 1958), enabling APO-based reconstructions of ocean heat content that span nearly three decades 6 .
APO (O 2 + 1.1 × CO 2 ) is computed using observed atmospheric O 2 /N 2 molar ratios and CO 2 molar fractions (see Methods) 6,19 . By design, APO is insensitive to exchanges with land ecosystems, which produce changes in O 2 and CO 2 that largely cancel in APO owing to their approximate 1.1 O 2 /C oxidative ratio. Time-series measurements at remote sites show a global long-term decline in APO, with ΔAPO OBS being −243.70 ± 10.10 per meg (units defined in the Methods) between 1991 and 2016. ΔAPO OBS is driven by four primary contributors, illustrated in Fig. 2: where ΔAPO FF is the decrease in APO caused by industrial processes (fossil-fuel burning and cement production), which in aggregate consume more than 1.1 moles of O 2 for each mole of CO 2 released; ΔAPO Cant accounts for the oceanic uptake of excess anthropogenic atmospheric CO 2 ; ΔAPO AtmD accounts for air-sea exchanges driven by ocean fertilization from anthropogenic aerosol deposition (increased fertilization leads to increased photosynthesis, with a concomitant release of O 2 and uptake of CO 2 ); and ΔAPO Climate accounts for air-sea fluxes of O 2 , CO 2 and N 2 driven by ocean processes, including warminginduced changes in solubility, in ocean circulation, and in photosynthesis and respiration (N 2 influences O 2 /N 2 ratios). Here, we derive ΔAPO Climate from equation (1) and show that it tracks ocean warming. We estimate ΔAPO FF using fossil-fuel and cement inventories 20 , finding ΔAPO FF = −119.70 ± 4.00 per meg (Fig. 3). ΔAPO Cant is controlled by the increase in atmospheric CO 2 and by ocean mixing, which is quantified by the distribution of transient tracers including chlorofluorocarbons (CFCs) 21 ; we find that ΔAPO Cant = −154.30 ± 4.20 per meg. ΔAPO Cant is relatively precise because it excludes the effects of changing ocean biology and circulation on natural carbon fluxes that are included in ΔAPO Climate . ΔAPO AtmD is derived from ocean model simulations with and without aerosol fertilization (phosphate, iron and nitrogen; Extended Data Fig. 1) 22 . ΔAPO AtmD is uncertain, owing in part to uncertainties in iron availability to photosynthetic organisms, but is relatively small compared with the other terms: ΔAPO AtmD = 7.00 ± 3.50 per meg. From equation (1), we thereby find that ΔAPO Climate = 23.20 ± 12.20 per meg, corresponding to a leastsquares linear trend of +1.16 ± 0.15 per meg per year-larger than the trends expected from 26-year natural variations alone in four Earthsystem models (the Community Earth System Model (CESM) and the Geophysical Fluid Dynamics Laboratory (GFDL), Institut Pierre Simon Laplace (IPSL) and University of Victoria (UVic) models). As shown in Fig. 3, a clear increase in ΔAPO Climate emerges over the period January 1991 to the end of December 2016.
A starting point for understanding ΔAPO Climate is to imagine that O 2 and CO 2 behave like inert gases, such that the air-sea fluxes are dominated by temperature-driven solubility changes. In this case, Letter reSeArCH APO would increase by around 0.8 per meg per 10 22 J of warming, with changes in O 2 and CO 2 solubility accounting for an increase of +1.0 per meg per 10 22 J, partly offset by the N 2 contribution of −0.2 per meg per 10 22 J (Methods). Support for the dominance of solubility in ΔAPO Climate can be found in the natural distribution of O 2 and carbon in the ocean. Ocean potential oxygen (OPO) is a dissolved tracer that mirrors APO Climate and tracks changes in air-sea O 2 and CO 2 fluxes 18 . Observed OPO abundance is strongly tied to ocean potential temperature ( Fig. 4): warming induces OPO loss, and cooling induces OPO gain. The observed OPO-to-temperature trend of −4.45 nmol J −1 is within 17% of the trend of −3.70 nmol J −1 expected from solubility alone (OPO sat -to-temperature). Biological effects (related to changes in ocean circulation and photosynthesis/respiration) on CO 2 and O 2 substantially cancel in OPO (Extended Data Fig. 2), while thermal impacts reinforce each other, with warming waters releasing both O 2 and CO 2 to the atmosphere and increasing ΔAPO Climate .
Further support for the dominance of solubility in ΔAPO Climate is found on multidecadal timescales in the four Earth-system models mentioned above, which yield OPO-to-temperature ratios of between −4.71 and −4.38 nmol J −1 , bracketing the ratio of −4.45 nmol J −1 found in hydrographic observations (Extended Data Fig. 3). The models also simulate a very close relationship between ΔAPO Climate and the change in global ocean heat content (ΔOHC) that occurs during the simulations (1920-2100), with an atmospheric build-up in APO of between 0.83 and 0.99 per meg per 10 22 J (Extended Data Figs. 3, 4) -close to the ratio expected from temperature-driven solubility changes alone (0.8 per meg per 10 22 J). By dividing the simulated APO change into separate biological and thermal components, we show that solubility changes account for more than 80% of ΔAPO Climate , while biologically driven changes account for 5% to 20% (Extended Data Fig. 4). This partitioning found in response to transient warming is very similar to the partitioning found in hydrographic data (where solubility and biology contribute 83% and 17%, respectively, to the OPO-to-temperature ratio; Fig. 4).
Small differences between individual model ΔAPO Climate -to-ΔOHC relationships (0.83 to 0.99 per meg per 10 22 J) reflect systematic differences in biological fluxes. Models with stronger biological effects (IPSL and UVic) yield stronger oceanic loss of OPO and stronger release of APO for a given ocean warming (more negative OPO-to-temperature and higher ΔAPO Climate -to-∆OHC; Extended Data Fig. 3b). Using this relationship, we find that a ∆APO Climate -to-∆OHC ratio of 0.87 ± 0.03 per meg per 10 22 J is compatible with the observed OPO-totemperature ratio. Combining this constrained ΔAPO Climate -to-ΔOHC ratio (0.87 ± 0.03 per meg per 10 22 J) with the observation-based trend in ΔAPO Climate (1.16 ± 0.18 per meg yr −1 ) yields a warming trend of 1.33 ± 0.20 × 10 22 J yr −1 between 1991 and 2016. As shown in Fig. 1, this APO-based estimate of ocean heat uptake agrees well, within uncertainties, with the highest temperature-based estimates (from the Pacific Marine Environmental Laboratory (PMEL) 10   Industrial processes (fossil-fuel burning and cement production; ΔAPO FF ) and the ocean sink for anthropogenic carbon (ΔAPO Cant ) remove APO from the atmosphere. The fertilization effect of anthropogenic aerosol deposition (ΔAPO AtmD )-which promotes marine photosynthesis-and the changes in solubility, biology and ocean circulation due to warming (ΔAPO Climate ) release APO into the atmosphere. Our study shows that ΔAPO Climate can be used to estimate long-term changes in global ocean warming.  Letter reSeArCH  and marginally with the two next estimates (from Cheng et al. 12 (CHEN) and the Japanese Meteorological Institute (MRI) 9 ). The APO data provide a much-needed independent confirmation of the recent upward revisions in estimates of ocean warming 5,9 . A higher value of ΔOHC compatible with both APO Climate and in situ temperature approaches (1.13 to 1.46 × 10 22 J yr −1 ) calls for a steric sea level rise of 1.34-1.74 mm yr −1 (Methods), in full agreement with satellite constraints on thermal expansion, corrected for the freshwater contribution (1.50 ± 0.40 mm yr −1 ) 8, 23 .
A higher ΔOHC will also affect the equilibrium climate sensitivity, recently estimated at between +1.5 K and +4.5 K if CO 2 is doubled 1 . This estimated range reflects a decrease in the lower bound from 2 K to 1.5 K owing to downward revision of the aerosol cooling effect (in the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report, as compared with the Fourth Assessment Report) 1,24 , but relied on a low ΔOHC value (0.80 × 10 22 J yr −1 for 1993-2010). An upward revision of the ocean heat gain by +0.5 × 10 22 J yr −1 (to 1.30 × 10 22 J yr −1 from 0.80 × 10 22 J yr −1 ) would push up the lower bound of the equilibrium climate sensitivity from 1.5 K back to 2.0 K (stronger warming expected for given emissions), thereby reducing maximum allowable cumulative CO 2 emissions by 25% to stay within the 2 °C global warming target (see Methods).
We find that the APO-heat coupling (APO Climate ) is most robust on decadal and longer timescales. Strong cancellation of biological O 2 and CO 2 fluxes is not expected on all temporal scales 25 . On seasonal timescales, air-sea O 2 fluxes driven by marine photosynthesis are around eight times larger than those of CO 2 owing to slow equilibration of CO 2 (ref. 25 ). More complex coupling is also possible on interannual timescales 26 , such as the weaker lagged air-sea CO 2 flux compared with the O 2 flux during El Niño events 27 .
Atmospheric O 2 and CO 2 measurements have been applied previously to estimate global land and ocean CO 2 sinks, but relied on estimates of ocean heat content and model-based oceanic O 2 -to-heat ratios to correct for climate-driven O 2 outgassing 28-30 . Here we have reversed this logic, using estimates of other quantities to constrain the ocean heating. Our approach exploits the APO-heat relationship, which is stronger than the O 2 -heat relationship. Further work to constrain the separate contributions of O 2 and CO 2 to APO is needed to refine estimates of land and ocean carbon sinks using atmospheric O 2 and CO 2 .

Online content
Any methods, additional references, Nature Research reporting summaries, source data, statements of data availability and associated accession codes are available at https://doi.org/10.1038/s41586-018-0651-8. 28. Keeling where (δO 2 /N 2 ) is the atmospheric change in δO 2 /N 2 ratios (in per meg); X CO 2 is the CO 2 concentration in the air parcel (in p.p.m., that is, μmol mol −1 ) and 350 is an arbitrary reference; 1.1 is the approximate O 2 /CO 2 ratio of terrestrial ecosystems 33 ; and X O 2 (= 0.2094) is the reference value of atmospheric mole fraction of O 2 necessary to convert X CO 2 from p.p.m. to per meg units. ΔAPO OBS is computed from in situ atmospheric changes in CO 2 concentrations and O 2 /N 2 ratios 19 measured at stations of the Scripps Institution of Oceanography network (available online at http://scrippso2.ucsd.edu) 6 . The global average ΔAPO OBS is based on data from the three stations with longest record (1991 to 2016), that is, La Jolla (32.9° N, 117° W), Alert (82.5° N, 62.5° W) and Cape Grim (40.5° S, 144.5° E) and weighted by the stations' latitudinal distribution 34 . Station annual means are based on bimonthly data fit to a four-harmonic seasonal cycle and a stiff long-term trend 6 . The uncertainty on ΔAPO OBS was computed by generating 10 6 time series with noise scaled to the random and systematic errors of APO data detailed in Extended Data Table 3. The uncertainty is taken as the 1σ interval (±1 standard deviation) from these 10 6 realizations (Fig. 3). Effects of fossil-fuel burning and cement production on APO. ΔAPO FF is estimated using annual CO 2 emissions from oil, coal, gas, flaring and cement production (ΔCO 2(i) in moles) 20 weighted by their O 2 /C combustion ratios, R i (ref. 6 ): where M air is the number of moles of dry air in the atmosphere (convert moles of CO 2 to p.p.m.). The uncertainty on ΔAPO FF includes uncertainties in CO 2 emissions (ΔCO 2(i) ) 35 and in combustion ratios (R i in Extended Data Table 3) 36 . Uncertainties on ΔCO 2(i) are not independent in time and were estimated using an autoregressive model 37 (1,000 realizations); uncertainties on R i were computed using a Monte Carlo approach (1,000 realizations). The uncertainty on ΔAPO FF was then estimated by combining the 1,000 realizations of ΔCO 2(i) and the 1,000 realizations of R i , yielding a set of 10 6 estimates of ΔAPO FF . Effect of ocean anthropogenic carbon uptake on APO. We represent the ocean CO 2 uptake (ΔCO 2 ) as the sum of three contributions: where ΔCant 0 is the flux driven by the rise in CO 2 assuming steady ocean circulation (ΔCant 0 is negative, corresponding to uptake by the ocean); ΔCO 2Climate is the flux driven by the action of climate on natural carbon in the ocean (ΔCO 2Climate is positive, that is, warming reduces the uptake of natural carbon); and ΔCant′ is the remainder, which accounts for impact of circulation changes on the uptake of carbon driven by rising CO 2 (ΔCant′ is positive, that is, warming reduces the uptake of C ant ). ΔAPO Cant can be expressed as the weighted sum of the two terms ΔCant 0 and ΔCant′: where ΔCant 0 and ΔCant′ are in moles. Note that ΔCO 2Climate is accounted for in ΔAPO Climate . ΔCant 0 is taken from a recent ocean inversion scheme with assimilation of observed potential temperature, salinity, radiocarbon and CFC-11 (ref. 21 ), updated to 2016. ΔCant′ cannot be derived from observations and was estimated at 0.05 Pg C yr −1 , equivalent to a trend of +0.2 per meg −1 , using model simulations (see 'Model anthropogenic ΔCant′').
The uncertainty on ΔAPO Cant is related to uncertainties in ΔCant 0 and ΔCant′. We allow for uncertainty in ΔCant 0 following ref. 21 , using the ten sensitivity experiments (on ocean vertical and isopycnal diffusivities, data constraint, gas-exchange coefficient and so on) available for the ocean inversion and an estimate of the interannual variability in the ocean sink of a 0.2 Pg C yr −1 . We also allow an additional 1% uncertainty (less than 0.03 Pg C yr −1 ) in ΔCant 0 resulting from imperfectly known atmospheric CO 2 history 38 , taking account of sensitivity to start date (1765 versus 1791), to degree of temporal smoothing, and to using different versions of the record since 1958 (Mauna Loa record versus average of Mauna Loa and South Pole records). This estimate used a variant of the box-diffusion model 39 , and CO 2 data from ref. 40 and the Scripps CO 2 program (https://library.ucsd.edu/ dc/collection/bb3381541w). Uncertainties on ΔCant′ are assumed to be 100% of the model-based estimate of ΔCant′. Ocean fertilization and atmospheric deposition of aerosols. Deposition of anthropogenic aerosol from fossil fuel, biomass burning and other processes fertilizes the ocean with nutrients and increases surface photosynthesis and subsurface respiration [41][42][43] . The effect of aerosol fertilization is partly counterbalanced by biological processes such as a decline in nitrogen fixation, which would be immediate, and an increase in denitrification in the water column, which would be on timescales of several hundred years 44 . Fixed anthropogenic nitrogen also fertilizes the land biosphere and coastal oceans by river runoffs, but, in these cases, efficient denitrification returns fixed nitrogen to the atmosphere and has little impact on the APO budget on the decadal timescales considered here. The impact of anthropogenic aerosol on O 2 , CO 2 and APO air−sea fluxes is evaluated with the IPSL ocean model NEMO-PISCES v2 (ref. 45 ), using the difference between simulations with aerosols and a simulation in which the aerosol deposition is fixed to a constant preindustrial value (equivalent to year 1850, Extended Data Fig. 1) 22 . We use four simulations with varying aerosols: one includes the combined effect of nitrogen (N), iron (Fe) and phosphorus (P) aerosol deposition, whereas the other three include only their individual contributions (N-only, Fe-only or P-only; Extended Data Fig. 1 and Extended Data Table 5). Uncertainties at the 1σ level on ΔAPO AtmD are assumed to be ±50%. See Extended Data Table 4.  Table 5). The overall impact on ΔAPO AtmD is +0.27 per meg yr −1 over 27 years of simulation , which we extrapolate to our 1991-2016 period. Increased O 2 outgassing accounts for an increase in APO of +0.51 per meg yr −1 , and CO 2 uptake accounts for a change in APO of −0.24 per meg yr −1 (APO AtmD(O2) and APO AtmD(CO2) in Extended Data Table 3).
The overall effect of N, Fe and P is smaller than the sum of the individual effects (Extended Data Fig. 1), because of the interplay between the aerosol deposition pattern and nutrient co-limitations in the ocean. Phytoplankton growth in the ocean depends on the availability of the most limiting nutrient. While more available N will promote photosynthesis in regions where N is limiting (for example, the tropical Atlantic Ocean), the effect is negligible in regions where Fe, P or any other nutrient is limiting (such as the Southern Ocean; see Fig. 2 in ref. 22 ).
To our knowledge this is the first estimate of the effect of anthropogenic aerosol deposition on both O 2 and CO 2 air-sea fluxes at the global scale. Note however that ref. 6 used anthropogenic aerosol N inventories and scaling arguments to estimate an ocean O 2 loss due to anthropogenic N deposition only of about 10 ± 10 Tmol yr −1 , slightly lower than our model estimate of 15.5 Tmol yr −1 . ΔAPO Climate trends and uncertainty analysis. We compute the APO response to climate change (ΔAPO Climate ) via: We combine the estimates of ΔAPO FF , ΔAPO Cant and ΔAPO AtmD to obtain 10 6 time series of ΔAPO FF + ΔAPO Cant + ΔAPO AtmD , and obtain 10 6 time series of ΔAPO Climate using the 10 6 time series of ΔAPO OBS . We computed the ΔAPO Climate least-squares linear trend using the standard deviation of the 10 6 realizations of ΔAPO Climate as the error. We find a ΔAPO Climate trend of 1.16 ± 0.15 per meg yr −1 for 1991-2016. Hydrography-based estimates of ocean heat uptake. We used four global-ocean estimates of ΔOHC, based on hydrographic measurements, in Fig. 1. Ocean warming rates from the surface to 2,000 m are from ref. 10  where O 2sat is the dissolved O 2 concentration at saturation with the observed temperature and salinity 48 ; and C pisat is the dissolved inorganic carbon concentration expected at the observed temperature and salinity and assuming equilibrium with a preindustrial partial pressure of CO 2 of 280 p.p.m., using pre-formed alkalinity 49 . Solubility-driven changes in OPO and APO. Extended Data Fig. 2 shows a tight and quasilinear link between observed OPO and potential temperature (−4.4 nmol J −1 ; r 2 = 0.95), similar to the link found between OPO sat and potential temperature (−3.7 nmol J −1 ; r 2 = 0.93). This suggests that changes in OPO and hence ΔAPO Climate are driven primarily by changes in thermal air-sea fluxes. In these observations, departures of dissolved oxygen and carbon concentrations (O 2 * and C pi *) from their respective saturation curves (O 2sat and C pisat ) due to biological activity tend to balance (Extended Data Fig. 2). By contrast, thermal effects reinforce each other (O 2sat and C pisat both decrease with increasing temperature) and biological effects compensate for each other (O 2 * > O 2sat and C pi * < C pisat ). The change in APO expected from changes in gas solubility in the ocean is an increase of 3.0 nmol per J of warming, which includes the outgassing of O 2 and CO 2 following OPO sat (3.7 nmol J −1 ) and the release of N 2 (0.7 nmol J −1 ) (Extended Data Fig. 2b) 58 .
For GFDL, IPSL and UVic, we used the CMIP5 business as usual 'historical-RCP8.5' scenario, the feedback experiment 'esmFdbk3' (which includes only warming-driven changes associated with anthropogenic emissions, such as radiation effects), and the fixed-climate experiment 'esmFixClim3' , which includes only the direct biogeochemical effects of increasing atmospheric CO 2 (for example, uptake of anthropogenic carbon, acidification and so on). For CESM, we also used the historical-RCP8.5 experiment and the separation between anthropogenic carbon from the natural carbon available in this model (carbon tracer separation approach). The feedback approach used for GFDL, IPSL and UVic removes all direct biogeochemical effects of rising atmospheric CO 2 on the air-sea O 2 and CO 2 exchanges, whereas the natural carbon tracer separation approach used for CESM still includes the biogeochemical impacts of increasing atmospheric CO 2 on the carbon cycle (for example, acidification) even while it excludes the anthropogenic carbon itself. However, we expect the effect on our results to be small and negligible.
We also used the multicentury preindustrial control simulation 'piControl' with no increase in atmospheric CO 2 to correct for model drift and to estimate the natural internal variability of ΔAPO Climate (Fig. 2). We used model results over the 1920-2100 period, which were available for the four models.
Model OPO was computed as for the observations. Note that for CESM we removed subsurface regions of high denitrification in the Eastern Equatorial Pacific Ocean and the Bay of Bengal, where oxygen and O 2 * in this model have unrealistic values 59 . Model anthropogenic ΔCant′. The component ΔCant′ was derived from equation (2) (ΔCant′ = ΔCO 2 − ΔCant 0 − ΔCO 2Climate ) using CMIP5 model simulations. ΔCO 2 was taken from experiment RCP8.5, ΔCant 0 from experiment esmFixClim3, and ΔCO 2Climate from experiment esmFdbk3. Note that the control simulation was also used to correct model drift. We estimated ΔCant′ to be 0.05 ± 0.05 Pg C yr −1 for 1991-2016, based on the results of the three modelswhich individually yielded ΔCant′ values of 0.0 Pg C yr −1 (IPSL), 0.12 Pg C yr −1 (GFDL) and 0.12 Pg C yr −1 (UVic)-and assuming an uncertainty of ±100%. This corresponds to a trend of 0.12 ± 0.12 per meg yr −1 . Model ΔAPO Climate -to-ΔOHC ratios and uncertainty. Model ΔAPO Climate is computed using individual contributions from O 2 , CO 2 and N 2 as follows: where ΔF O 2 , ΔF CO 2 and ΔF N 2 are the changes in air-sea fluxes of O 2 , CO 2 and N 2 respectively (in moles); M air is the number of moles of dry air in the atmosphere; and X N 2 and X O 2 are the reference atmospheric mixing ratios of N 2 and O 2 respectively 60 . O 2 and CO 2 fluxes are simulated in the models. N 2 air-sea fluxes, which affect the O 2 atmospheric mixing ratio (because O 2 constitutes around 20% of the atmospheric composition), are quantified from the global ocean temporal changes in N 2 solubility computed from model changes in temperature and salinity 61 .
The link between long-term changes in APO Climate and ocean heat contentthat is, ΔAPO Climate -to-ΔOHC ratios-were computed for each model using the 180 years of simulations (1920-2100). Resulting ΔAPO Climate -to-ΔOHC ratios vary between 0.83 and 0.99 per meg per 10 22 J of warming (Extended Data Fig. 3). These ratios include uncertainty in the natural climate variations on interannual and decadal timescales and uncertainty in the O 2 /C oxidative ratio associated with global gains and losses of O 2 and CO 2 by terrestrial ecosystems. The uncertainty due to interannual variations was evaluated by computing ΔAPO Climate -to-ΔOHC ratios using multiple 26-year-long segments from the 180-year simulations. We obtained 616 ΔAPO Climate -to-ΔOHC ratios (154 time series of 26 years per model), and used the standard deviation between these ratios as a measure of the uncertainty.
The O 2 /C ratio is assumed to be 1.1 in our computation to follow the widely accepted definition of APO (APO = O 2 + 1.1 × CO 2 ), but is shown to have variations between 1 and 1.1 (ref. 33 ). An oxidative ratio lower than 1.1 would yield a weaker ΔAPO Climate -to-ΔOHC slope and hence a slightly higher estimate of ΔOHC for a given ΔAPO Climate . We evaluated the influence of the O 2 /C ratio for each model by using the difference between ΔAPO Climate computed with a ratio of 1.1 and ΔAPO Climate computed with a ratio of 1. The two contributions to the uncertainties on the simulated ΔAPO Climate -to-ΔOHC ratios (interannual variations and O 2 /C ratio) combine to yield ±0.01 per meg per 10 22 J for the CESM and GFDL models, ±0.02 per meg per 10 22 J for the UVic model, and ±0.05 per meg per 10 22 J for the IPSL model (1σ). These uncertainties are used in Extended Data Fig. 3. Steric component of sea-level rise. We evaluated the steric component of sea-level rise associated with a ΔOHC compatible with both APO Climate and existing in situ temperature constraints (that is, between 1.13 × 10 22 J yr −1 and 1.46 × 10 22 J yr −1 ) to be between 1.34 mm yr −1 and 1.74 mm yr −1 . Following ref. 62 , this calculation assumes that 45% of the warming occurs below 700 m, and that the steric rise is 1 mm per 0.60 × 10 22 J above 700 m, and 1 mm per 1.15 × 10 22 J below 700 m (that is, a global steric rise of 1 mm per 0.84 × 10 22 J). Assuming that 48% of the warming occurs below 700 m (ref. 10 ) would yield a global steric rise of 1 mm per 0.86 × 10 22 J and change our estimate by less than 3%. Our estimate is also consistent with the recent hydrography-based estimate of the WCRP Global Sea Level Budget Group 63 . Ocean heat uptake, sea level and climate sensitivity. Climate sensitivity has been estimated to fall within the range of +1.5 K to +4.5 K for a doubling of CO 2 (ref. 1 ). The impact of an increase in the ocean heat uptake on the effective equilibrium climate sensitivity (the apparent equilibrium climate sensitivity diagnosed from nonequilibrium conditions) can be estimated using a cumulative approach on the Earth energy balance (see Fig. 2 in ref. 1 where N is the global heat imbalance, which mostly consists of the ocean heat uptake; F is the radiative forcing (in W m −2 ); ΔT is the increase in surface temperature (in K) above a natural steady state; and α is the climate feedback parameter (in W m −2 K −1 ), which is inversely proportional to the effective equilibrium climate sensitivity 1 . All terms in equation (3) are time integrated over the period of interest. The IPCC Fifth Assessment Report gives a ΔOHC of 0.80 × 10 22 J yr −1 for 1993-2010, which is about 0.5 × 10 22 J yr −1 lower than the ΔOHC that is compatible with both APO and hydrographic constraints. By applying equation (3) 1 to surface temperature data over the period 1991-2016 (HadCrut4 version 4.5, ref. 64 , with a 1860-1879 preindustrial baseline), we found that the upward revision of the global heat imbalance, N, by +0.5 × 10 22 J yr −1 pushes up the lower bound of the equilibrium climate sensitivity from 1.5 K back to 2.0 K. An increase of the lower bound from 1.5 K to 2 K corresponds to a need to reduce maximum emissions by 25% to stay within the 2 °C global warming target (because of the almost linear relationship between warming and cumulative emissions; see Fig. SPM.10 in ref. 1 ). This corresponds to a reduction in maximum allowable cumulative CO 2 emissions from 4,760 Gt CO 2 to 3,570 Gt CO 2 .
We tested the sensitivity of the climate sensitivity by using three alternate temperature datasets (NASA GISS Surface Temperature Analysis GISTEMP 65 , available at https://data.giss.nasa.gov/gistemp; the NOAA/OAR/ESRL global surface temperature data 66 v4.0.1, available at https://www.esrl.noaa.gov/psd; and the ocean + land product of Berkeley Earth, available at berkeleyearth.lbl.gov/auto/ Global; all data were accessed on 7 August 2018) as well as two preindustrial baseline periods (1860-1879 and 1880-1899). We find changes in the climate sensitivity of the order of 5% owing to the choice of temperature dataset, and less than 1% due to the choice of preindustrial baseline. Link to global ocean deoxygenation. Our application of O 2 atmospheric measurements to constrain long-term ocean warming can be compared with earlier work that considers warming-driven oceanic O 2 outgassing. Multiplying our warming rate of 1.33 ± 0.20 × 10 22 J yr −1 by the O 2 -to-heat ratios simulated by the four ESMs (−3.70 ± 0.80 nmol O 2 J −1 ) yields an ocean loss of 49 ± 13 Tmol O 2 yr −1 . Adding a loss of around 19 ± 19 Tmol O 2 yr −1 due to anthropogenic aerosols (Extended Data Table 5) yields a global ocean outgassing of 68 ± 23 Tmol O 2 yr −1 , in the range of previous estimates based on atmospheric data 67 (about 40 Tmol O 2 yr −1 ), ocean data above 1,000 m (55-65 Tmol O 2 yr −1 , refs 68,69 ) and global ocean data 70 (96 ± 42 Tmol O 2 yr −1 ). This calculation suggests that ocean CO 2 uptake is reduced by warming at a ratio of around 0.70 nmol of CO 2 per joule (the difference between the O 2 -to-heat ratio of 3.70 nmol J −1 and the OPO-to-heat ratio of 4.45 nmol J −1 ). Code availability. ESM codes are available online for IPSL-CM5A-LR (cmc.ipsl. fr/ipsl-climate-models), GFDL-ESM2M (mdl-mom5.herokuapp.com/web/docs/ project/quickstart), UVic (climate.uvic.ca/model) and CESM (www.cesm.ucar. edu/models/).

Data availability
Scripps APO data are available at http://scrippso2.ucsd.edu/apo-data. APO Climate data, contributions to APO OBS