Effect of temperature corrections

Figure 1 illustrates the effect of the two adjustments described above on a calculation of annual global ocean-atmosphere fluxes for this period, with calculations starting from the SOCAT v2019 database. To interpolate the SOCAT surface water fCO2 data in space and time we adopt as our standard method the two-step neural network approach described by Landschützer et al.8,18, (see also description below and Methods section). The interpolation was applied to the SOCAT data without modification, after adjusting the data to a subskin temperature and regridding (as described in refs. 12,19, see also Methods section) then additionally after repeating the flux calculation assuming a ΔT across the cool skin of 0.17 K15 salinity increase of 0.1 unit11 and the conservative “rapid transport” scheme of Woolf et al.11 (see Methods section). Each adjustment increases the calculated flux by ~0.4 PgC yr−1 when integrated over the global ocean. For the period ~2000, this approximately doubles the calculated flux into the ocean. Over the 27 years 1992–2018 inclusive, the cumulative uptake is increased from 43 to 67 PgC.

Fig. 1: Effect of near-surface temperature corrections.

Global air–sea flux calculated by interpolating SOCAT gridded data using a neural network technique8, followed by the gas exchange equation applied to the ocean mass boundary layer. The net flux into the ocean is shown as negative, following convention. The uncorrected curve uses the SOCAT fCO2 at inlet temperature as usually done. Correction of the data to a satellite-derived subskin temperature is shown, and the additional change in flux due to a thermal skin assumed to be cooler and saltier than the subskin by 0.17 K15 and 0.1 salinity units11. Excludes the Arctic and some regional seas—ocean regions included are shown in Supplementary Fig. 2.

Uncertainty estimates

Ocean-atmosphere fluxes calculated using the gas exchange equation are subject to two broad sources of uncertainty: (1) specification of the gas transfer velocity, which depends on the thickness of the MBL and is usually parameterized as a function of wind speed, and (2) specification of the CO2 concentration difference across the MBL. The recent study by Woolf et al.20 contains a detailed treatment of the uncertainties due to the gas transfer, concluding that a realistic estimate (approximately, a 90% confidence interval) is ±10% when applying this to global data.

The second source of uncertainty, due to the concentration difference, is dominated by that introduced by the interpolation in time and location of surface ocean CO2. This is relatively well constrained in the more densely observed regions such as the North and Equatorial Atlantic and North and Tropical Pacific. However, in more remote regions such as the Southern, South Pacific, and Indian Oceans, the observational coverage is patchier in space and time and often seasonally biased, with few winter measurements (see Supplementary Fig. 3). New sensors and designs of autonomous floats, as now being deployed in the Southern Ocean21, show promise to solve the problem of adequately observing surface CO2 in remote regions22, but for the gap-prone historical data, the interpolation method used can have a substantial influence on the results in these data-poor regions.

To evaluate the uncertainty in flux estimates introduced by the gap-filling procedure, we used three methods for interpolating in space and time, each applied to the global data divided according to three different spatial clustering schemes, for a total of nine mappings. The interpolation methods were as follows: (1) a time series (TS) of fCO2sw data, constructed by a least squares fit to all monthly averaged fCO2 values within the defined region. The model fitted was a seasonal cycle with three harmonics superimposed on a linear trend; (2) simple multilinear regression (MLR) of the fCO2 data on latitude, longitude, and four variables for which continuous comprehensive mappings are available, these being sea-surface temperature (SST), salinity (SSS), mixed layer depth (MLD), and atmospheric CO2 mixing ratio (XCO2); (3) the feed-forward neural network method of Landschützer et al.8,18 (FFN), which also seeks a regression on these four variables. The spatial clustering schemes applied to each of the techniques (shown in Supplementary Fig. 1) were as follows: (a) division into 14 regions along latitude–longitude lines; (b) division into the 17 biogeochemical divisions suggested by Fay and Mckinley23, and (c) division into 16 biomes using a self-organizing map technique employed by Landschützer et al.8.

Where the data are adequately distributed over space and time, the use of multiple mapping techniques and different clustering schemes to estimate uncertainty gives similar results to formal geostatistical techniques, such as kriging7,20. However, in regions of very sparse and uneven coverage, statistically based techniques can underestimate uncertainties because of the assumption that the available data are representative of the true data population over a region, which may not be the case if whole regions or seasons are poorly sampled. In this instance, different mapping techniques can give substantially different results. Altering the clustering of the data by changing the shape of the geographical divisions can also have a major effect, because unsampled areas are assumed to have the same statistical properties as the sampled regions with which they are grouped.

For each combined mapping-and-clustering technique, Table 1 shows the spread and mean of the residuals (the global set of predicted values minus observed values). The neural network FFN mapping method provides a much smaller spread of residuals, giving better agreement with data at a given location and time than do the other methods. This is to be expected given its much greater flexibility, with typically several hundred parameters being adjusted to provide a non-linear fit to each cluster, compared to only 8 and 11 fitted parameters for respectively the TS and MLR methods. Figure 2 shows estimates of global and hemispheric ocean-atmosphere CO2 flux over the period 1992–2018 by the nine interpolations (using a single parameterization of the gas transfer velocity). Despite the difference in the quality of the fits to the individual data as evidenced by Table 1, convergent results are obtained by all the calculations for the Northern Hemisphere over the whole period, and there is a good agreement in the Southern Hemisphere for much of the period after 2000. The average of all the methods is shown, with one and two standard deviations of the nine separate estimates. A few regions are excluded (see Supplementary Fig. 2) to ensure compatibility in the comparison between methods, but these affect the results by <0.05 PgC yr−1.

Table 1 Statistics of the residuals of the predictions to data.
Fig. 2: Global ocean-atmosphere CO2 fluxes 1992–2018.

Fluxes are integrated a globally, and b for northern and southern hemispheres, calculated using a standard gas exchange formulation (see Methods section) with the nine interpolation schemes for fCO2 described in the text shown as colored lines: TS red, MLR green, FFN blue. The line styles indicate the spatial clustering schemes used (illustrated in Supplementary Fig. 1): solid, Landschützer SOM; dashed, latitudinal regions; dotted, Fay and Mckinley biomes. The standard method, SOM-FFN as described in Landschützer et al.8, is shown as a thicker blue line. Shading indicates one- and two-standard deviations of the nine methods around the mean (thick black line).

The wider uncertainties indicated pre-2000 arise from the divergence of fits in the Southern Hemisphere. The majority of studies using the historical surface CO2 data find that the Southern Ocean sink was static or weakening during the 1990s and strengthened considerably after 200024,25. The simpler, linearly constrained interpolation methods show something of this change, but it is less pronounced than in the more flexible FFN calculations. However, we retain the wider spread pre-2000 as a realistic estimate of uncertainty then, given the paucity of the data and its uneven, and decadally changing, spatial distribution in the Southern Ocean and South Pacific (see Supplementary Fig. 3, which shows the distribution of the data in the Southern Hemisphere).

New CO2 surface fluxes compared to interior observations

We now compare our estimates for global CO2 flux into the ocean, with a recent independent synthesis of observations estimating the increase in oceanic anthropogenic carbon from interior repeat hydrography measurements, over the period 1994–200717. This comparison requires accounting for pre-industrial ocean-atmosphere fluxes: the ocean was pre-industrially a source of CO2 to the atmosphere, with a net dissolved river flux usually estimated as 0.45–0.6 PgC yr−1 flowing down rivers to the ocean, from ocean to atmosphere and from the atmosphere to the land surface26,27. We also have to add a flux for the Arctic Ocean, not included in our study but estimated at 0.12 PgC yr−128. In Fig. 3, we show our standard case estimate of the anthropogenic sink, with the ocean-atmosphere flux increased by 0.57 PgC yr−1, (0.12 PgC yr−1 Arctic plus a pre-industrial flux of 0.45 PgC yr−1), and with the uncertainty bands now widened to include the Woolf et al. estimate for gas transfer velocity uncertainty20. This is compared to the recent estimate for the accumulation of anthropogenic carbon from interior ocean observations, over the period 1994–200717. Two previously published estimates of the sink calculated from the surface data are also shown for comparison8,10. In contrast to these earlier estimates, our revised surface flux is consistent with the interior anthropogenic accumulation and most previous estimates of the pre-industrial ocean-to-atmosphere source.

Fig. 3: Observation-based estimates of anthropogenic CO2 uptake.

The black line is our standard case global ocean-atmosphere flux increased by −0.57 PgC Cyr−1 to account for pre-industrial and Arctic fluxes as described in the text. The shading gives one and two standard deviations of estimates around this value, including the uncertainty in gas transfer rates as assessed by Woolf et al.20. Red horizontal line and uncertainty is a recent estimate of the global inventory increase of anthropogenic carbon in the ocean between 1994 and 200717. Dashed lines: two previous estimates of global uptake based on surface data: blue dashed line from Landschützer et al.8, red dashed line from Rödenbeck et al.10, both as quoted in Le Quéré et al.31. Both are increased by the pre-industrial flux correction and Landschützer et al.8 also increased by Arctic correction.

In Table 2, we show uptake integrated over the 13 years from mid-1994 to mid-2007 in the northern and southern Pacific, Indian and Atlantic basins, and compare these with the inventory increases as given by Gruber et al.17. The inventory increase in each basin will not equal the flux through the surface of that basin, both because of the pre-industrial flux correction described above, and because subsurface ocean transport redistributes the CO2 away from the uptake regions. The comparison is revealing, however, because we should not expect a very large change in inter-hemispheric CO2 exchange in the ocean during this time. We expect some correspondence between these figures, therefore, at least at the hemispheric level. The global flux through the ocean surface is less than the inventory change by ~7 PgC over this period, an amount consistent with the expected pre-industrial ocean source. However, the Northern Hemisphere uptake, which is comparatively well constrained by the surface data, quite closely matches the inventory increase in the Northern Hemisphere. The majority of the difference between surface uptake and inventory increase is in the Southern Hemisphere, suggesting that excess river carbon that the natural cycle puts into the open ocean was pre-industrially compensated by net outgassing almost entirely in that hemisphere, and that its magnitude is ~0.5 PgC yr−1. A recent proposed upward revision of this flux to 0.78 Pg Cyr−129 was motivated in part by the clear mismatch between anthropogenic carbon uptake and the earlier, lower estimates of surface uptake, but our analysis is more consistent with the lower values of previous studies, which come from ocean inverse models26 and inventories of global dissolved riverine carbon27,30. We note also that the uncertainty on the South Pacific flux (including the Pacific sector of the Southern Ocean) is particularly large, reflecting the paucity of data there (Supplementary Fig. 3). However, over the entire Pacific basin, and globally, uncertainties are smaller, because there is inter-basin compensation with some mapping estimates that give high values in the southern Pacific giving lower values in the tropical and northern regions.

Table 2 Estimates of ocean CO2 uptake compared to interior inventory of anthropogenic carbon.

The agreement between the observational estimates of CO2 uptake by the oceans provides an important constraint on calculations of the global carbon budget and its rate of change. Supplementary Table 1 gives more detail on global fluxes calculated over decadal periods compared to those of earlier estimates, both of the net contemporary ocean-atmosphere flux and the ocean uptake of anthropogenic carbon. As indicated in Fig. 3, our best estimate of 2.5 ± 0.4 Pg yr−1 for anthropogenic carbon uptake during 1994–2007 agrees closely with that of Gruber et al. and has a similar uncertainty. This sink is stronger than most recent estimates and is ~0.5 PgCyr−1 larger than the central estimate of the Global Carbon Project31 for that period for example. That estimate is the average of a number of models, which however span a wide range, with a 2-σ uncertainty of ±0.6 PgC yr−1 for that period. The discrepancy between our value and that of the Global Carbon Project increases with time and approaches 1 PgC yr−1 after 2010.

We conclude that, when correctly applied, two data-led independent estimates for the ocean sink for CO2, based respectively on observations of the surface flux and the interior inventory of CO2, agree within relatively well-constrained uncertainties. The sink so determined is larger than most ocean carbon models predict, and suggests that some revision of the global carbon budget is required. Due weight should be given to the constraints that ocean interior and surface observations impose when calculating global carbon budgets, and near-surface temperature deviations need to be taken into account when using surface observations to calculate fluxes. Continued systematic observation of the surface and interior ocean carbon system remains essential to tracking how the global carbon cycle is changing in response to human activities.


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