## Introduction

The dissolved gases carbon dioxide (CO2) and oxygen (O2) in seawater are of much biogeochemical interest1. Carbon dioxide is important because of its role as a greenhouse gas, with about one quarter of the anthropogenic CO2 produced by fossil fuel combustion and land use changes being absorbed by the ocean2. The coupling of atmospheric CO2 and O2 is used to derive land/ocean carbon sink partitioning3 and serves as a reference to verify ocean model results used in the global carbon budget2. Time-series observations at some specific locations (mostly in the northern hemisphere4), as well as distributed measurements of the partial pressure of CO2 (pCO2) at the global scale5,6 show that surface seawater pCO2 is rising at a similar rate to the mole fraction of CO2 in the atmosphere, which has increased by more than 40% since pre-industrial times (from 280 to over 400 ppm or μmol mol−1). Global change is also affecting oceanic O2 concentrations; warming decreases oxygen solubility and enhances water column stratification, thereby reducing ventilation of subsurface waters with atmospheric oxygen and leading to a decline in oxygen in the global ocean7,8,9. Oxygen is biologically linked to CO2, for instance during photosynthesis which simultaneously uses CO2 and generates O2.

There have been some attempts to jointly investigate dissolved O2 and CO2 in different ocean basins (e.g., refs. 1,10,11,12,13,14,15). However, in these studies the two gases were usually treated differently, for instance O2 as a concentration ([O2]) or percent saturation and CO2 as a partial pressure (pCO2) (refs. 10,13,16,17); in addition, oxygen values are sometimes reported relative to argon (Ar) (e.g., refs. 18,19,20). Analyses in which O2 and CO2 are calculated in different units, or as percentages, cannot take straightforward advantage of the stoichiometric relationships (i.e., Redfield ratios) between carbon, oxygen, and nutrients21,22. An improved O2-CO2 analysis method was proposed by Torgersen and Branco23 and Vachon et al.24 to compare deviations of O2 and CO2 concentrations away from saturation, or in other words disequilibria (discrepancies compared to equilibrium with atmospheric values). This approach was shown to provide insights into river and lake ecosystems, and has the potential to be applied more broadly to marine systems. Investigating co-variations of O2 and CO2 concentrations can help improve understanding of the drivers of surface ocean carbon dynamics.

In this study we extend the application of the O2-CO2 approach to the global surface ocean and name the approach CORS (Carbon and Oxygen Relative to Saturation). We treat O2 and CO2 identically and compare dissolved concentrations of O2 and CO2 ([CO2] and [O2]) in surface seawater to saturation values (values at which the net air-sea gas exchange rate is zero). The saturation values for O2 and CO2 are strongly temperature-dependent, as was already shown by the first plot of [O2] against temperature over much of the global surface ocean in the early 1980s using GEOSECS data25 (Supplementary Fig. 1). The global database has been greatly expanded in recent decades, providing wider spatial and temporal coverage, culminating in the Global Ocean Data Analysis Project (GLODAPv2.202026,27,28; used throughout this study, for simplicity, it is referred to as GLODAPv2 hereafter), which is by far the largest high-quality observational dataset of both carbon and oxygen. This expanded dataset has not previously been used to compare [O2] and [CO2] to each other and to saturating values.

Furthermore, a potential application is to compare patterns in CORS plots from GLODAPv2 with those from float data from the Southern Ocean Carbon and Climate Observations and Modeling (SOCCOM) project. Equipped with biogeochemical sensors (e.g., oxygen, nitrate, pH, and bio-optical sensors), ~200 autonomous biogeochemical Argo floats were deployed by the SOCCOM project29 and have enabled a better understanding of carbon and oxygen cycles in the Southern Ocean30,31. They strikingly found that the high-latitude Southern Ocean (i.e., Antarctic-Southern Zone, ASZ) has released much more CO2 to the atmosphere than previously estimated31,32,33, which attracted community concerns on the sensor bias and data quality control (QC) of pH and associated carbonate parameters34. Funding has recently been announced (Global Ocean Biogeochemistry GO-BGC Array project) for the construction and deployment of 500 floats (as a contribution towards an anticipated eventual fleet of 1000 floats) to provide float coverage similar to that provided by the SOCCOM project but across the global ocean. A consensus is urgently required on how to calibrate and validate float carbonate data to ensure the highest accuracy and comparability among different studies and datasets34. Given that the float O2 data is likely to be more accurate than pH and the calculated carbonate system data (refs. 29,31,35; see also descriptions in Methods), O2 in the context of CORS plots could provide a strong constraint for detecting questionable float CO2 data, if compared to GLODAPv2.

To advance knowledge of oceanic oxygen and carbon cycling and address the above concerns, our study had two main objectives: (1) to construct CORS plots from the GLODAPv2 database, to be used later as a reference to compare against. These plots show the CORS analysis to be capable of identifying regions and periods where processes have driven both O2 and CO2 away from their equilibrium with the atmosphere. (2) to apply this method to the SOCCOM dataset and compare the resulting plots to the GLODAP reference, in order to investigate the potential of CORS as a tool for interpreting and validating data collected by autonomous platforms.

## Results

### Overall patterns in CORS plots from GLODAPv2 data

To first order, both [CO2] and [O2] from GLODAPv2 follow the solubility relationship with temperature (decreasing values with increasing temperature) (Fig. 1), as found previously for [O2] in GEOSECS data (Supplementary Fig. 1). However, deviations occur in certain regions and seasons (Supplementary Figs. 26). Deviations of O2 from its equilibrium with the atmosphere are usually of the opposite sign to the corresponding CO2 deviations (Supplementary Fig. 2).

In both hemispheres, the distributions of [CO2] and [O2] show strong seasonal variations: [CO2] and [O2] deviate furthest from their temperature-dependent saturation values in spring and summer while staying close to saturation in autumn and winter (Fig. 1). We do not discuss further the Indian Ocean because deviations of [CO2] and [O2] from saturation are less pronounced there than in other ocean basins. Individual CORS plots for each basin are presented as supporting information (Supplementary Figs. 36).

In spring, supersaturation of O2 usually accompanies CO2 undersaturation. Strong supersaturation of CO2 (together with undersaturation of O2) is observed in parts of the northeast and eastern equatorial Pacific for water temperatures close to 10 and 18 °C (Supplementary Fig. 2a). However, other Pacific data exhibit CO2 undersaturation and accompanying O2 supersaturation (Fig. 2a). In the Atlantic Ocean, 73% of all spring data are undersaturated in CO2 while supersaturated in O2 (Fig. 2a).

In summer, the undersaturation of CO2 is less pronounced in the Atlantic Ocean (Figs. 1c and 2b), whereas in the Pacific Ocean it is more or less similar to that in spring. In summer, some simultaneous CO2 and O2 undersaturations are observed in the Southern Ocean at latitudes polewards of 60°S where ice melt occurs in coastal regions (Fig. 1c, d): 20% of the summer Southern Ocean data show undersaturation in both CO2 and O2.

In autumn and winter, there is less data across the global oceans but it appears that both gases stay closer to saturation as biological activity weakens and air-sea gas exchange strengthens. There are striking opposite changes to CO2 and O2 in the Southern Ocean (Figs. 1 and 2), where [CO2] is elevated (on occasion to as high as 30 µmol kg−1) and [O2] is depleted (sometimes to as low as 260 µmol kg−1) (Fig. 1). Overall, both gases deviate more strongly from saturation in winter than in autumn in the Southern Ocean.

### Processes causing deviations in CORS plots from GLODAPv2 data

Figures 1 and 2 show, for the global surface ocean, the coupling of CO2 deviations and O2 deviations from saturation across geographic and seasonal scales, with four specific features (F1–F4 in Fig. 2) warranting further investigation: (F1) CO2 undersaturation in conjunction with O2 supersaturation in the high-latitude Atlantic and Pacific Oceans in spring; (F2) CO2 supersaturation paired with O2 undersaturation in the eastern equatorial Pacific and California coast in spring and summer; and (F3–F4) supersaturation of CO2 together with undersaturation of O2 in the Southern Ocean in winter and to a lesser extent in spring and autumn. Processes known to simultaneously affect ΔCO2 and ΔO2 include warming/cooling, ice melting, respiration and photosynthesis, and upwelling. The impacts of these processes on ΔCO2 and ΔO2 are shown in the inset to Fig. 2d (see Methods—Predicted effects of different processes—for the explanation of the inset figure).

With additional plots, we explore the possible causes of these features. Figure 3a shows a CORS plot of Atlantic and Pacific spring data, colored by in-situ nitrate concentration. The data falling in the fourth quadrant (negative ΔCO2 and positive ΔO2) are associated with depleted nitrate concentrations and are located primarily in the Irminger Basin in the North Atlantic and the Oyashio region in the western subarctic Pacific Ocean (Supplementary Fig. 2a, b), regions where intense spring blooms are observed36,37,38,39. The data patterns are generally consistent with phytoplankton blooms (photosynthesis) as the driver of the F1 deviations (although the lack of correlation (Supplementary Table 1) between CORS and NO3 is surprising). Data in quadrant two of Fig. 3a (F2) are mainly from off the northern California coast, a region where seasonal coastal upwelling is known to bring subsurface waters (depleted in O2 and enriched in CO2 and nutrients from decomposition of organic matter) to the surface ocean40. CORS and NO3 are strongly correlated in these data (Supplementary Table 1).

Figure 3b shows the relationship between ΔCO2, ΔO2, and the NO3 anomaly in the Southern Ocean in winter, where the NO3 anomaly is the difference of surface in situ nitrate concentration from its annual mean value in the surface Southern Ocean based on GLODAPv2. The nitrate anomaly is strongly correlated with ΔCO2 and ΔO2 (Supplementary Table 1). The winter data in the Southern Ocean (Fig. 2d) imply that respiration or, more likely, upwelling of ‘old’ water into which organic matter has been respired, is responsible for F3 and F4. The calculation of ΔCO2 (Eq. 2) is made relative to atmospheric CO2 at the time of measurement, even for water that has recently upwelled and never previously had contact with anthropogenic ΔCO2. For this reason, data from recently upwelled water will tend to plot lower on CORS plots than it would if its [CO2] value was compared to the [CO2] value in equilibrium with pre-industrial atmospheric CO2. In addition, decreases in [CO2] because of CaCO3 dissolution41,42 (which does not affect [O2]) are likely to contribute to the lower-than-expected slope. Figure 3c (and Supplementary Fig. 7) shows that Southern Ocean surface waters with the largest deviations (those furthest from the origin of the CORS plots) in winter are those which have recently upwelled (neutral density > 27.8 kg m−3, refs. 43,44,45,46). We, therefore, conclude that the large excursions in the Southern Ocean in autumn and winter are driven by the upwelling of deep waters that have previously been altered by the decomposition of sinking organic matter.

### Near-zero y-intercepts in CORS plots from GLODAPv2 data

We investigated CORS plots to look for common features in them, when generated from the high-quality data in GLODAPv2. For quiescent regions not experiencing intense biogeochemical activity, gas exchange is the dominant control for both dissolved gases, keeping them close to equilibrium with the atmosphere. In such regions, we would expect the centroid of the data in the CORS plots to then be close to the origin (i.e. $${\overline{\triangle {{{\mbox{O}}}}_{2}}}$$ and $${\overline{\triangle {{{\mbox{CO}}}}_{2}}}\approx 0$$ μmol kg−1), and this is what is seen when CORS plots are constructed from the HOT and BATS time-series data (Supplementary Fig. 8; $${\overline{\triangle {{{\mbox{O}}}}_{2}}}=1{{\mbox{.}}}9$$ μmol kg−1 and $${\overline{\triangle {{{\mbox{CO}}}}_{2}}}=-0{{\mbox{.}}}2$$ μmol kg−1 at HOT; $${\overline{\triangle {{{\mbox{O}}}}_{2}}}=3{{\mbox{.}}}2$$ μmol kg−1 and $${\overline{\triangle {{{\mbox{CO}}}}_{2}}}=-0{{\mbox{.}}}3$$ μmol kg−1 at BATS) from sub-tropical gyres. However, in less quiescent regions, the centroid can be shifted away from the origin (as seen for instance in the Southern Ocean in winter—Fig. 3b—where upwelling leads to a displaced centroid: $${\overline{\triangle {{{\mbox{O}}}}_{2}}}=-26.9$$ μmol kg−1 and $${\overline{\triangle {{{\mbox{CO}}}}_{2}}}=1.4$$ μmol kg−1). The distance of the centroid from the origin cannot, therefore, be considered a reliable indicator of data quality.

Several other statistical properties can be calculated (see for instance Vachon et al.24), of which we found the y-intercept value (i.e., the value of ΔCO2 when ΔO2 is zero) to be the most useful. The application of CORS to the GLODAPv2 dataset shows that, when strongly influenced by a dominant biogeochemical process, the departures of O2 and CO2 from atmospheric equilibrium are coupled and the best-fit lines of ΔO2 and ΔCO2 still tend to intersect close to the coordinate origin (Fig. 4). Across the global oceans, we found y-intercepts close to zero (range −1.10 to −0.16 µmol kg−1 in different basins (Fig. 4), with a value for the global dataset of −0.18 µmol kg−1). Due presumably to the effect of ice melt in the summer Southern Ocean, the Southern Ocean y-intercept is significantly lowered compared to other ocean basins (Fig. 4e). The relative uniformity of y-intercept values suggests their usefulness as indicators of data quality.

### CORS plots from all float data, regardless of QC flag

Below we show that CORS plots are capable of distinguishing ‘questionable’ or ‘bad’ float data from QCed ‘good’ data. As an illustration, we examined data from floats F9096 and F9099 deployed in the high-latitude Southern Ocean, using which Williams et al.33 found significantly higher sea surface pCO2 and air-sea CO2 efflux in wintertime. Unlike Williams et al.33 in Fig. 5 we have plotted both data flagged as ‘questionable’ or ‘bad’ and data flagged as ‘good’. The figure shows some abnormally high (up to 20 µmol kg−1) and low (down to −20  µmol kg−1) ΔCO2 values, neither of which are coupled with equivalent ΔO2 values. The resulting CORS plots are significantly different from the general CORS pattern across the global ocean (Fig. 4). All of these abnormal data have been flagged ‘questionable’ or ‘bad’ by SOCCOM’s QC procedure but CORS plots also reveal the data to be problematic.

### CORS plots using only float data flagged as ‘good’

Below we show that CORS plots are also useful for analyzing and examining ‘good’ float data. In order to be comparable with the GLODAPv2 database, we first selected 12 biogeochemical Argo floats (Supplementary Fig. 9) around the Drake Passage or south of Tasmania to get as many overlaps as possible with the shipboard dataset28. When CORS plots were produced for the float data, we found (Fig. 6) a pattern that is overall rather similar to that from GLODAP data in the Southern Ocean (Figs. 3b and 4f), consistent with upwelling of CO2-rich deep waters. However, a discrepancy was found with regards to the y-axis intercepts of the best-fit regressions of ΔCO2 and ΔO2: in contrast to the global GLODAP y-intercepts, which are all similar to each other (range of less than 1.0 between the minimum and maximum), the float-derived y-intercepts are highly variable (range of −3.81 to +0.99 µmol kg−1; Figs. 4 and 6, Table 1). We adopted a subsampling strategy (see Methods) to treat the GLODAP and float datasets identically, with the result showing that half of the selected floats have y-intercepts greater than the GLODAP-derived value of −1.10 µmol kg−1 (Fig. 6, Table 1). Among these floats, F9096 and F12545 deviate more strongly from the GLODAP pattern along the positive y-axis direction, whereas some other floats, e.g., F9275 and F9646 deviate along the opposite direction (Fig. 6). The average difference in y-intercepts (calculated as GLODAPv2 minus float values) is −0.12 µmol kg−1, implying that, overall, float y-intercepts are more positive (or less negative) than GLODAP ones (Table 1).

Applying CORS to the whole SOCCOM dataset south of 55°S (48 floats with QCed O2 and CO2 data, Supplementary Table 2), we also found that y-intercepts were on average greater than the GLODAP-derived ones, with an average difference (GLODAPv2 minus float) of −0.36 µmol kg−1 (Supplementary Table 2). Given that oxygen sensors are accepted as more established, reliable, and accurate than pH sensors from which the CO2 values were calculated29, the anomalous float y-intercepts suggest offsets most likely due to pH-related biases, such as the uniform crossover correction assuming a fixed offset of pH from 1500 m depth to surface29,33,34. While unusual y-intercept values are suggestive of data quality issues, they are not necessarily definitive proof. It is also possible, we believe, that, in some locations, local processes produce real CORS patterns that differ from those normally seen. For instance, surface water near to where rivers enter the sea, or in regions of strong mixing with deeper waters, could potentially exhibit persistent unusual CORS patterns. Data displaying unusual behavior on CORS plots should therefore not be immediately discounted but should instead be flagged as requiring further investigation before it can be accepted as valid. Detailed investigation of this issue is beyond the scope of this manuscript, but we note that a correction of −0.36 µmol kg−1 to [CO2] corresponds to a correction to pCO2 of −5.8 µatm under typical Southern Ocean conditions. Our finding is in line with some recent studies47,48,49 based on different approaches (airborne observations of atmospheric CO2 gradients, uncrewed surface vehicle observations during circumnavigation of Antarctica, and reconstructed estimates of winter observations and CO2 fluxes) that indicate the possible overestimation of CO2 outgassing from SOCCOM float data.

## Discussion and conclusions

An improved analysis technique (CORS) for paired O2-CO2 data has been presented here, treating both gases identically and accounting for the atmospheric pressure effect on both gas saturation concentrations. The CORS technique was applied to the large, high-quality, global dataset GLODAPv2, as well as to the SOCCOM float dataset. CORS plots provide a detailed insight into the identity and intensity of processes impacting CO2 and O2. Although both gas concentrations were seen to be often close to the temperature-determined equilibrium value in GLODAP2 data, several noteworthy deviations from equilibrium with the atmosphere and the possible processes driving them were discussed: in spring, phytoplankton blooms (most notably in the Irminger Basin of the North Atlantic and in the Oyashio region of the western subarctic Pacific Ocean) drive undersaturation of CO2 and coincident supersaturation of O2, whereas upwelling in the California coast and equatorial Pacific drives the opposite; in autumn and winter, upwelling in the Southern Ocean produces supersaturation of CO2 and undersaturation of O2. CORS plots can serve as a useful tool for the detection of processes (e.g., blooms and upwelling) that simultaneously affect both oxygen and carbon.

Recent developments in sensors mounted on gliders, floats, and moorings have become increasingly important because they provide opportunities for sampling in remote regions and in inclement weather where traditional shipboard measurements are difficult and expensive to obtain31,32,50,51,52,53,54. Along with the basic hydrological parameters (i.e., temperature and salinity), biogeochemical variables such as nutrients, oxygen, and CO2 (or pH, from which CO2 can be estimated) are now being measured30,31,32,33,55. ΔCO2 and ΔO2 can therefore be obtained from measurements made autonomously, and CORS plots generated from them. Even though oxygen returns to gas exchange equilibrium more rapidly than does carbon dioxide56,57, ΔCO2 and ΔO2 have been shown here to exhibit coupled (simultaneous and proportional) changes in CORS plots from GLODAPv2 data. Moreover, oxygen data from sensors is generally more accurate and reliable than CO2 derived from pH measured on Argo floats29,35. Because of this, it makes sense to exploit the O2 data to improve the CO2 data. Here we have shown that CORS plots can often identify questionable data (data shown to be questionable by other QC methods) immediately. In addition, our results suggest that CORS plots can also reveal issues with supposed ‘good’ data (i.e., quality issues not picked up by other QC methods). This is because systematic errors in either [CO2] or [O2] tend to stand out in CORS plots, and to lead to anomalous y-intercept values relative to the GLODAPv2 reference (Table 1). Our approach provides a more straightforward way to assess and potentially improve CO2 data quality by comparison to other float measurements. CORS plots allow a check on sensor performance, which is important for instruments on these unmanned platforms which operate without servicing or recalibration.

As the oceanographic community becomes increasingly reliant on data collected from autonomous platforms50,58, techniques such as CORS will be beneficial for diagnosing data quality, and for immediate detection of questionable data.

## Methods

The surface ocean is defined41,59 as shallower than 30 m at latitudes greater than 30°, and shallower than 20 m at latitudes less than 30°. The Southern Ocean is defined as south of 50°S. Boreal spring is taken as from April to June, and austral spring from October to December, and so on for the other seasons (following global scale studies60).

### Dataset descriptions

#### GLODAP dataset

Data for this study were obtained from GLODAPv2.202026,27,28 (denoted ‘GLODAPv2’ in this manuscript), which includes data from 946 cruises conducted during the period 1972–2019. Only open ocean data (seafloor depth > 200 m) were included. We excluded data from the Arctic Ocean (>65°N) because of data scarcity and strong perturbations from river inputs61. The observed CO2 concentration was calculated using the MATLAB version62 of CO2SYS, from in-situ temperature, salinity, DIC, TA, phosphate, and silicate in the GLODAPv2 database. In this study, the dissociation constants for carbonic acid and sulfate were taken from Lueker et al.63 and Dickson64, respectively, and the total borate-salinity relationship from Lee et al.65. We used data only when both O2 and carbonate system measurements are available and when the quality control of data is flagged as ‘good’.

The accuracies of measured O2, DIC, and TA from GLODAPv2 are stated as 1% (≈3 μmol kg−1), 4 μmol kg−1, and 4 μmol kg−1, respectively28. The uncertainty of calculated CO2 concentration is dominated by the uncertainties from DIC and TA66, and is assessed using an add-on to the CO2SYS program that calculates uncertainty propagation66. The propagated uncertainty of CO2, taking into account the uncertainties in the input variables as well as in the equilibrium constants, is 0.4 µmol kg−1. We also evaluated the uncertainty ourselves using a Monte Carlo analysis (following Wu et al.67), which produced a similar uncertainty of 0.5 µmol  kg−1.

#### SOCCOM float dataset

The SOCCOM project (https://soccom.princeton.edu/) has deployed ~200 biogeochemical profiling floats in the Southern Ocean since 2014. The floats are mounted with a combination of biogeochemical sensors including ones for measuring water column pH, oxygen, and nitrate29. Carbonate system parameters including pCO2 and others are first calculated from sensor-measured temperature, salinity, pH, LIAR algorithm-estimated TA, and silicate and phosphate concentrations33,68,69. The nutrient data are derived from a matched GLODAP database as a function of potential density (see details in Williams et al.33); ignoring silicate and phosphate concentrations has anyway only a negligible effect on carbonate system calculation33. The CO2 concentration [CO2] is then calculated from pCO2 and CO2 solubility using Henry’s Law ([CO2] = KH × pCO2). The pH-dependent bias correction and quality control29,33 has been applied to the accessible data from https://soccompu.princeton.edu/www/index.html. The quality control of pH data is based on the crossover analysis for deep waters between float and shipboard (including available Southern Ocean dataset and SOCCOM deployment cruises) measurements (see also ref. 33,69). The empirical algorithm for estimating in-situ pH as a function of temperature, salinity, pressure, and O2 is determined for shipboard bottle measurements at 1000–2000 m depth, which is then applied to float-measured temperature, salinity, pressure, and O2. By comparing the two pH values at 1500 m depth, an offset in pH is applied to the entire float profile. The measured oxygen and pH have reported uncertainties of 1% and 0.01 respectively, and the estimated TA and pCO2 have reported uncertainties of 5.6 µmol kg−1 and 2.7% respectively33. Only data with a quality-control flag of ‘good’ were used.

The propagated uncertainty of float [CO2] calculated following Orr et al.66 is 0.8 µmol kg−1, which is twice the uncertainty of [CO2] from GLODAPv2. The float oxygen sensors have been shown to perform robustly and with good stability (100% good data return29). The oxygen data can be calibrated every time a float surfaces because it can measure oxygen above the sea surface; this calibration is then used to adjust the entire profile29. From the crossover comparison to GLODAPv2, the float-measured oxygen data was seen to be closely correlated with GLODAPv2 data and to follow a 1:1 relationship. In contrast, the float-measured pH data exhibited large offsets from adjacent GLODAPv2 data and there was a significant departure from a 1:1 relationship (e.g., fitted line deviated from 1:1 line by 0.03 at pH = 8.05; ref. 29).

Converting pCO2 to [CO2] is obtained by multiplying pCO2 by the Henry’s constant for CO2 (KH), based on an average sea surface temperature of 1 °C in the Southern Ocean (i.e., KH ≈ 0.06).

### Calculation of saturation values for O2 and CO2 and their uncertainties

$${\Delta {{{{{\rm{O}}}}}}}_{2}=\left[{{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{obs}}}}}}}\right]-\left[{{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}\right]$$
(1)
$${\Delta {{{{{\rm{CO}}}}}}}_{2}=\left[{{{{{{\rm{CO}}}}}}}_{2,{{{{{\rm{obs}}}}}}}\right]-\left[{{{{{\rm{C}}}}}}{{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}\right]$$
(2)

where the subscript ‘obs’ indicates the observed concentration, and ‘sat’ indicates the saturation concentration (in equilibrium with the atmosphere).

The saturation concentration for O2 was calculated using the equation introduced by Garcia & Gordon70,71 for the solubility of O2. It is noteworthy that Garcia & Gordon70,71 determined the O2 saturation value at an assumed atmospheric pressure of 1 atm, which means that their approach (Eq. 3) needs to be modified to account for local in-situ sea level pressure (SLP) using a parallel equation (Eq. 4):

$${{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}^{1{{{{{\rm{atm}}}}}}}={{{{{\rm{K}}}}}}\times p{{{{{{\rm{O}}}}}}}_{2}^{1{{{{{\rm{atm}}}}}}}={{{{{\rm{K}}}}}}\times x{{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{air}}}}}}}\times ({{{{{{\rm{P}}}}}}}_{1{{{{{\rm{atm}}}}}}}-{{{{{{\rm{P}}}}}}}_{{{{{{\rm{sw}}}}}}}),$$
(3)
$${{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}^{{{{{{\rm{SLP}}}}}}}={{{{{\rm{K}}}}}}\times p{{{{{{\rm{O}}}}}}}_{2}^{{{{{{\rm{SLP}}}}}}}={{{{{\rm{K}}}}}}\times x{{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{air}}}}}}}\times ({{{{{{\rm{P}}}}}}}_{{{{{{\rm{SLP}}}}}}}-{{{{{{\rm{P}}}}}}}_{{{{{{\rm{sw}}}}}}}),$$
(4)

where ‘1atm’ and ‘SLP’ denotes two different pressures, K is the solubility of O2, $${{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}^{1{{{{{\rm{atm}}}}}}}$$ is the result of the calculation based on Garcia & Gordon70,71 methodology, Psw is the water vapor pressure calculated from surface ocean temperature and salinity72.

Substituting (3) into (4):

$${{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}^{{{{{{\rm{SLP}}}}}}}={{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}^{1{{{{{\rm{atm}}}}}}}\times ({{{{{{\rm{P}}}}}}}_{{{{{{\rm{SLP}}}}}}}-{{{{{{\rm{P}}}}}}}_{{{{{{\rm{sw}}}}}}})/({{{{{{\rm{P}}}}}}}_{1{{{{{\rm{atm}}}}}}}-{{{{{{\rm{P}}}}}}}_{{{{{{\rm{sw}}}}}}})$$
(5)

where $${{{{{{\rm{O}}}}}}}_{2,{{{{{\rm{sat}}}}}}}^{{{{{{\rm{SLP}}}}}}}$$ is the O2 saturation value corrected for local sea level pressure and Psw. PSLP is from National Center for Environmental Prediction/National Center for Atmospheric Research (NCRP/NCAR) reanalysis data at the time of the measurement (https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.surface.html).

In order to account for the impacts of bubble injection on O2 saturation in the surface ocean, we applied a saturation anomaly of 0.75%56 to O2 saturation (i.e., the saturation of O2 in the surface ocean is here calculated as 100.75% of the value from the saturation equations). The bubble injection effect on the more soluble CO2 is negligible (<0.1%, ref. 73) and therefore it is not applied to the CO2 calculations.

The saturation concentration for CO2 was calculated using Henry’s Law ([CO2,sat] =  KH × pCO2,eq), where pCO2,eq refers to the partial pressure of CO2 in seawater when it is in equilibrium with atmospheric CO2. This was calculated as: pCO2,eq = xCO2,air  × (PSLP−Psw), where xCO2,air is the mole fraction (ppm) of CO2 in dry air. The values of xCO2,air are subject to spatiotemporal variabilities; we used the monthly mean atmospheric xCO2 values for each ocean basin for each year from the NOAA/ESRL/Global Monitoring Division (ftp://aftp.cmdl.noaa.gov/data/trace_gases/co2/flask/). We used data from the following monitoring sites: BMW (Tudor Hill, Bermuda) and ASC (Ascension Island) in the north and the south Atlantic Ocean, respectively; SEY (Mahe Island) in the Indian Ocean; MLO (Mauna Loa, Hawaii) and SMO (Tutuila) in the north and the south Pacific Ocean, respectively; and PSA (Palmer Station, Antarctica) in the Southern Ocean (>50°S). PSLP and Psw are described in Eqs. 35. The solubility (KH) of CO2 was calculated following Weiss74.

### Predicted effects of different processes

ΔCO2 and ΔO2 exhibit some co-variation (Figs. 1 and 2) and so predicted joint effects of different processes were calculated (inset to Fig. 2d), based on global average sea surface conditions (unless specified otherwise) calculated from GLODAPv2 data: salinity of 34.6, temperature of 15 °C, TA of 2300 µmol kg−1, and atmospheric pCO2 of 380 µatm (for the year 2005), which yields saturation concentrations of CO2 and O2 of 14.3 µmol kg−1 and 248.5 µmol kg−1 respectively, and DIC of 2072 µmol kg−1.

To predict the effects of warming and cooling, we calculated saturation gas concentrations along a temperature gradient, and then compared the saturation value at 15 °C (T0) to that at another temperature (T1) using Eq. 1:

$$\triangle {{{{{\rm{Gas}}}}}}={[{{{{{{\rm{Gas}}}}}}}_{{{{{{\rm{sat}}}}}}}]}^{{T}_{0}}-{[{{{{{{\rm{Gas}}}}}}}_{{{{{{\rm{sat}}}}}}}]}^{{T}_{1}}$$
(6)

Instantaneous warming and cooling would have an immediate impact on the CORS values (ΔCO2 and ΔO2) because changes in temperature alter gas solubility. Warming decreases the gas solubility (equilibrium value), so warming increases both ΔCO2 and ΔO2, whereas cooling decreases them. The calculated molar ratio between changes in [CO2,sat] and changes in [O2,sat] for warming is 0.086 and for cooling is 0.091.

To predict the effect of ice melt, we assumed that ice contains so little dissolved CO2 and O2 that melting adds insignificant amounts75,76, so [DIC] and [O2] are subjected to the same degree of dilution during ice melting. A degree of dilution gradient (e.g., diluted by 5, 10, 20, and 30%) was then assumed for salinity, TA, DIC, and O2 at a temperature of −1.8 °C, which is the average value for regions subject to ice melt. Each dilution step yielded a new carbonate system, for each of which [CO2] was recalculated using CO2SYS. By comparing each of [CO2] and [O2] to their original values, the ratio between the changes induced by ice melt was calculated as 0.125.

To predict the effects of photosynthesis and respiration, DIC changes were made proportional to changes in O2 of ±25, ±50, ±75, and ±100 µmol kg−1. The corresponding DIC changes were calculated by multiplying the O2 changes by the Redfield ratio21 of DIC/O2 = −117/170. So, for instance, DIC changed by −17.2 µmol kg−1 when O2 changed by +25 µmol kg−1 due to photosynthesis. Using CO2SYS62, [CO2] was then calculated to change by −1.28 µmol kg−1 for this example. The same logic was applied to changes in [CO2] and [O2] due to respiration. The ratio of [CO2] change to [O2] change is not perfectly linear; the ratio (slope) of a line fitted to the results is −0.044 for photosynthesis and −0.067 for respiration. Since temperature dominates solubility and carbonate system dissociation constants, and because spring blooms at high latitudes occur in cold water, we also made the same calculation at a temperature of 5 °C, resulting in −0.070 for photosynthesis and −0.116 for respiration (shown by the gray shading in the inset to Fig. 2d). Although the Redfield ratio refers to changes in DIC and [O2], our choice of plotting [CO2] rather than DIC versus [O2] has advantages: (1) the y-axis value on the CORS plot relates directly to the tendency for air-sea CO2 exchange to occur; (2) assessing [CO2] relative to saturation is quite straightforward whereas assessing [DIC] relative to its saturation value requires an additional step involving alkalinity.

Since there is spatial variation in the parameters (i.e., salinity, temperature, TA, and DIC) used to calculate the slopes for photosynthesis and respiration in different ocean basins, the theoretical slopes in Fig. 3a, b were calculated based on the average condition in each specific ocean basin.

The formation and dissolution of CaCO3 affects [CO2] but not [O2] and is therefore only inducing changes along the ΔCO2 axis. It is also noteworthy that in addition to the processes above, upwelling and entrainment of subsurface waters (characterized by CO2-rich and O2-depleted due to remineralization) also account for the departures from equilibrium of both gases, where these effects tend to drive CORS towards the second quadrant.

### Subsampling treatment of GLODAP dataset

Because the GLODAP and SOCCOM float datasets have different amounts of data, we adopted a subsampling approach in order to treat the two datasets equally. The procedure is described using the following scenario as an imagined example:

GLODAP Southern Ocean data from all seasons: N = 2500, y-intercept = −1.5;

Float dataset from all seasons: N = 300, y-intercept = −3.0;

To test statistically whether the second y-intercept is significantly lower than the first, we set up a null hypothesis (H0) that the float-derived y-intercept is greater than or equal to the GLODAP-derived y-intercept. We repeatedly (10,000 times) took random subsamples (size N = 300) from the GLODAP Southern Ocean data, calculated the y-intercepts of the fitted lines, and then calculated the frequency with which y_float ≥ y_GLODAP (subsample). If frequency < 5% then y_float is significantly lower than y_GLODAP. Furthermore, we calculated the value of a term (y_diff) for the difference in y-intercepts by subtracting y_float from y_GLODAP.