Introduction

The ocean serves as a vast carbon reservoir in the Earth’s carbon cycle1 and plays a crucial role in regulating decadal to millennia-scale climate by absorbing and sequestering CO2 and hence controlling atmospheric CO2 concentration2,3. Part of the CO2 dissolved in the ocean becomes fixed as organic carbon through upper ocean net ecosystem productivity. Although most of the organic carbon formed is eventually respired back into inorganic carbon, organic matter transported away from the upper ocean (commonly referred to as “export flux/production”) contributes to long-term oceanic carbon storage. These processes are the so-called “biological carbon pump”, which is one of the important processes responsible for ocean CO2 uptake. Recently, in addition to the gravitational settling of particulate organic carbon (POC) as the classical concept of the biological carbon pump, the transport of dissolved organic carbon4,5 (DOC) and the transport of DOC and POC by mesoscale eddies6,7,8 and sub-mesoscale structures9, as well as the transport associated with vertical movements of mesopelagic migrators10, are thought to contribute substantially to the export of organic carbon to the deep ocean11, that is, to the biological carbon pump.

Global observational quantification of the carbon fixed and exported to the deep ocean through the biological pump remains insufficiently constrained12,13,14 due to a lack of direct observations that can be mapped globally and a lack of understanding of the processes that can be modeled. Various approaches have been used to provide global estimates, including estimates from satellite data15,16 and chemical tracer fields17,18, extrapolation of in situ direct measurements19, combinations of observations and mechanical models20,21, and data assimilation using ocean biogeochemical models22,23, yielding estimates ranging from 4 to 13 Pg C year−1. This weak observational constraint stands in contrast to the relatively well-constrained global estimate of air–sea CO2 exchange for the recent decade (2.8 ± 0.4 Pg C year−1, mean ± SD)24, despite both being essential components of the global carbon cycle. This is partly because of the difference in the number of observations required to quantify them due to the different complexities among their underlying processes. The weakness of observational constraints complicates the validation of Earth system models (ESMs)25, potentially introducing one of the causes of uncertainties in the future climate projections by ESMs.

With recent technical advancements in the measurement of dissolved oxygen concentrations by autonomous profiling floats26, methodologies for indirect quantifying the biological carbon export from year-long dissolved oxygen data are also being developed and applied over spatially broader regions27, beyond the traditional ocean stations. Autonomous profiling floats, such as the Biogeochemical-Argo (BGC-Argo) float, provide relatively high-frequency (more than once per month), long-term (~5–7 years), and spatially broader observations of the upper ocean dissolved oxygen28. By subtracting dissolved oxygen changes induced by various physical processes from the observed oxygen time series, it is possible to obtain the net production of oxygen by biological processes. As the oceanic biological oxygen and organic carbon production are linked via the photosynthetic stoichiometry29, the net biological oxygen production can be converted into the net organic carbon production (total production minus autotrophic and heterotrophic respiration), which is referred to as the net community production (NCP). Under steady-state conditions (i.e., no net organic carbon accumulation) and with averages taken over a broader spatial extent in which lateral organic carbon exchanges become negligible, the upper ocean NCP is identical to the amount of organic carbon exported from the upper ocean into ocean interior. Recent expansion of the BGC-Argo network has led to a remarkable increase in the number of dissolved oxygen profiles obtained and improved spatial coverage. Consequently, estimates of NCP derived indirectly from float-based dissolved oxygen data have the potential to overcome the spatial limitations of previous estimates, and hence provide a more robust global constraint of the biological carbon pump.

To globally quantify the amount of organic carbon exported thorough the biological pump, we expanded previously established local framework for upper ocean dissolved oxygen budget30,31,32 to the global ocean, with explicitly incorporating lateral physical processes that could potentially play an important role in the global budget. An equation for the upper ocean dissolved oxygen budget indicates that upper ocean dissolved oxygen integrated vertically from sea surface to a depth (\({{{{{\rm{O}}}}}_{2}}_{{{\mathrm{int}}}}\)) varies because of fluxes due to physical processes, such as air–sea exchange (\({F}_{{{{\rm{A}}}}-{{{\rm{S}}}}}\)), horizontal and vertical advection (\({F}_{{{{\rm{ADV}}}}}\)), horizontal diffusion (\({F}_{{{{\rm{hDIFF}}}}}\)) and vertical diffusion (\({F}_{{{{\rm{vDIFF}}}}}\)), as well as the net biological production (\({F}_{{{{\rm{NCP}}}}}\)):

$$\frac{\partial {{{{{\rm{O}}}}}_{2}}_{{{\mathrm{int}}}}}{\partial t}={F}_{{{{\rm{A}}}}-{{{\rm{S}}}}}+{F}_{{{{\rm{vDIFF}}}}}+{F}_{{{{\rm{ADV}}}}}+{F}_{{{{\rm{hDIFF}}}}}+{F}_{{{{\rm{NCP}}}}}$$
(1)

Integrating Eq. (1) over a climatological annual cycle, the left side tends to zero. Further spatial integration over the global ocean gives the global net biological oxygen production (\({{{{\rm{NBP}}}}}_{{{{{\rm{O}}}}}_{2}}\)) as

$${{{{\rm{NBP}}}}}_{{{{{\rm{O}}}}}_{2}}=-{\int }_{\!\!\!{{{\rm{year}}}}}\,{\int }_{\!\!\!{{{\rm{global}}}}}\,\left({F}_{{{{\rm{A}}}}-{{{\rm{S}}}}}+{F}_{{{{\rm{vDIFF}}}}}+{F}_{{{{\rm{ADV}}}}}+{F}_{{{{\rm{hDIFF}}}}}\right){dtdA}.$$
(2)

This equation was applied to the climatological annual cycles computed from oxygen data from 1980 to 2022 for which the spatial data coverage becomes sufficient. We first estimated the four physical oxygen fluxes as their climatological monthly maps using multiple observational and reanalysis products and then determined the global annual net biological oxygen production using these maps. The annual net oxygen production obtained was then converted to annual net community production (ANCP) by using the photosynthetic quotient33, ΔO2/ΔC = 1.45 (see Methods for further details).

The biological carbon fixation primally occurs in the sunlit upper ocean, known as the euphotic zone. The fixed organic carbon exported to layers below has the potential to contribute to the long-term ocean carbon sequestration. However, given the typical upper ocean situation that the annual maximum of the surface mixed layer depth (MLD) is deeper than that of the euphotic layer depth (Zeu), with the exception of oligotrophic subtropical oceans (Fig. 1a, b), a considerable portion (~10–90%34) of the organic carbon exported during the warm productive season can be re-entrained into the mixed layer by the subsequent winter mixing. The re-entrained organic carbon can be respired back to the inorganic form and then utilized to production in the euphotic layer or exposed to the air–sea gas exchange again, thus is not able to contribute the long-term ocean carbon sequestration.

Fig. 1: Distribution of the water surface used to set the lower boundary of the upper ocean dissolved oxygen budget.
figure 1

a Annual maximum mixed layer depth73 (MLD). b Annual maximum euphotic layer depth74 (Zeu). c Defined surface for the lower boundary of the upper ocean dissolved oxygen budget calculation (depth H) as the deeper of the annual maximum of MLD and that of Zeu.

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In this study, to quantify the organic carbon export that escapes such upper ocean seasonal cycle and reaches to deeper layers, we defined the depth of the lower boundary of the upper ocean used in the calculation of the dissolved oxygen budget (here referred to as depth H) as the deeper of the annual maximum MLD or the annual maximum Zeu (Fig. 1c); therefore the resultant ANCPs represent the organic carbon fluxes crossing the H-plane over the course of one year with having more than one-year sequestration time-scale. As will be seen later in Results, it is noted that the ANCPs estimated in this study tend to be smaller than the traditional ANCPs defined in the euphotic layer, so we add a subscript H to distinguish the ANCPs in this study (ANCPH) from the traditional definition.

Results

Upper ocean dissolved oxygen balance

At the sea surface, oxygen is exchanged between the atmosphere and the ocean (Fig. 2a). In the mid- to high latitudes, the air–sea oxygen exchanges exhibit pronounced seasonality. The strong air–sea oxygen gradient in the cold season is a consequence of undersaturated sea surface oxygen, which results from the rapid cooling and continuous supply of relatively low oxygen water from below due to the surface cooling and associated convection. It promotes net oxygen uptake during winter, whereas net outgassing is driven by reduced solubility due to surface heating and increases in dissolved oxygen due to enhanced biological production during warm periods. Much of the global ocean experiences a net loss of oxygen on an annual average basis due to air–sea exchange. Some regions, such as the eastern equatorial Pacific, the southern subtropical Indian Ocean, high latitudes of the North Atlantic and the Southern Ocean, exhibit an annual net oxygen uptake. In addition to the typical diffusive air–sea oxygen flux driven by the air–sea gradient of the concentrations and the surface winds, air–sea oxygen exchange mediated by bubbles also contributes to the high-latitude net uptake (Supplementary Fig. 1). Globally integrated, 206 ± 246 Tmol O2 (mean ± estimated error; see Methods for uncertainty estimation) is being removed annually from the ocean, consistent with the sign inferred from global ocean deoxygenation35,36,37. Previous estimates derived from the bulk relationship between global ocean oxygen and heat content during the same period of analysis38,39,40,41,42 fall within the range of uncertainty range of our estimate.

Fig. 2: Annually integrated physical oxygen fluxes that contribute to the upper ocean dissolved oxygen balance.
figure 2

Spatial patterns of four annually integrated physical oxygen fluxes (left side of each panel) and their zonal mean seasonal cycles (right side of each panel). a Air–sea oxygen exchange (FA–S); b vertical diffusion of oxygen (FvDIFF) at the lower boundary (depth H); c advection of oxygen (FADV); and d horizontal diffusion of oxygen (FhDIFF). A negative flux indicates oxygen removal from the upper ocean. Note that the maps of the advection term (c) and the horizontal diffusion term (d) are spatially smoothed to match the horizontal mapping scale of the air–sea exchange and vertical diffusion term.

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At the lower boundary of the upper ocean (depth H), the vertical diffusion fluxes serve to reduce oxygen annually from the upper ocean over an entire region, as dissolved oxygen concentrations generally increase closer to the air–sea interface (Fig. 2b). The spatial distribution is more indicative of the spatial distribution of vertical oxygen gradient intensities at depth H, rather than of the vertical diffusion coefficient used (Supplementary Fig. 2). Pronounced downward fluxes occur in regions with strong vertical oxygen gradients, such as the subarctic North Pacific and the eastern equatorial Pacific. In regions where H is defined as the annual maximum MLD, such as in mid- to high latitudes (c.f., Fig. 1), winter diffusion fluxes tend to be stronger because the base of the winter mixed layer, i.e. strong diffusivity layer, is closer to the temporally fixed depth H.

Physical processes other than air–sea exchange and vertical diffusion also play a crucial role in the global upper ocean dissolved oxygen balance43. The advection fluxes result in an annual net removal of upper ocean oxygen, especially in regions of wind-driven upwelling (e.g., the eastern equatorial Pacific and Atlantic, and the Southern Ocean) and water-mass obduction44 (e.g., subarctic/subpolar gyres), as low-oxygen water from deeper layers moves above depth H (Fig. 2c). The horizontal diffusion fluxes exhibit higher values along regions characterized by strong currents (Fig. 2d). On a global scale, physical oxygen fluxes from vertical diffusion, advection, and horizontal diffusion, annually remove 248 ± 33, 316 ± 38, and 120 ± 49 Tmol O2 from the upper ocean, respectively.

The sum of these annual physical oxygen fluxes should balance the net annual biological oxygen production (equation [2]) under the assumption of the steady-state condition (Fig. 3). The global annual net biological oxygen production is estimated to be 889 ± 256 Tmol O2 year−1. Using the ΔO2:ΔC ratio33 of 1.45 ± 0.03, the climatological global ANCPH over the analysis period (1980–2022) can be estimated as 7.36 ± 2.12 Pg C year−1. Given the definition of depth H in this study, this result implies that, globally, through the biological pump, the equivalent amount of carbon, in either particulate or dissolved form, escapes from the predominant upper-ocean seasonal cycle of physical environmental conditions (e.g., mixing and restratification) and becomes sequestered into the ocean interior on longer timescales than, at shortest, one year.

Fig. 3: Annual upper ocean dissolved oxygen balance.
figure 3

Zonally integrated upper ocean dissolved oxygen balance for five latitudinal bands, including physical oxygen transfers by air–sea exchange (FA–S, the top numbers with arrows), diffusion (FvDIFF + FhDIFF, the first numbers in paratheses), and advection (FADV, the second numbers in paratheses), and net biological production of oxygen (FNCP, green bold numbers). The black line shows the zonal mean depth H. Global balance (Eq. (2)) is reported as the sums with their uncertainties in the bottom box (see Methods for uncertainty estimation). The unit of all budget terms are Tmol O2 year–1.

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Note that, during the derivation of Eq. (2), we made the assumption of a steady state in terms of the total amount of the upper ocean dissolved oxygen over the four decades of the analysis period, although the current state of ocean deoxygenation is an undeniable fact supported by evidence from multiple observations35,36,37. However, considering that a previous estimate37 of deoxygenation in the upper 200 m was approximately 10 Tmol O2 year−1 (c.f., global mean H = 186 m), the potential error from our assumption is smaller than the uncertainties from other sources of error, and hence its impact is considered minor in this budget calculation.

Global ocean ANCP based on dissolved oxygen budget

The estimated ANCPHs, which have a global mean of 1.7 ± 0.5 mol C m–2 year–1, exhibit a characteristic latitudinal variation, with substantial zonal variations over each ocean basin (Figs. 4a and 4f). The average ANCPH in the Northern Hemisphere (NH, 2.0 mol C m−2 year−1) is larger than that in the Southern Hemisphere (SH, 1.5 mol C m−2 year−1), implying hemispheric differences in vertical and lateral supplies of nutrients and atmospheric deposition that support productions. The result indicates that, considering the area of ocean in each hemisphere, almost the same amount of carbon is fixed and exported into the ocean interior through the biological pump.

Fig. 4: Global O2-based annual net community production (ANCP).
figure 4

a Spatial pattern of ANCP (positive values indicate net production) obtained from the sum of four oxygen fluxes due to physical processes. Green boxes and stars indicate the region defined as the Kuroshio-Oyashio Confluence Region (KOCR), and the locations of the Hawaii Ocean Time-series (HOT) and the Ocean Station P (OSP). b Zonal means of the four physical oxygen fluxes and the bolus component of oxygen advection (FADV*). The units were converted to carbon units with a ΔO2:ΔC ratio of 1.45. c–f Zonal mean O2-based ANCP estimated in this study (blue lines) and previous local estimates (blue, orange, and green dots). The dots’ colors represent the definition of the depth defined as the lower boundary of the upper ocean when determining the ANCP (depth H in case of this study); annual maximum MLD (blue), seasonally varying MLD or Zeu (orange), and the others (green). The horizontal lines accompanied by dots indicate their uncertainties where these are available (all data and their references are summarized in Supplementary Table 1). Blue shading indicates a range of two standard deviation of the zonal mean. The dash line in c–f shows the zonal mean climatological (1985–2018 mean) surface CO2 flux from an observation-based global monthly gridded products98 submitted to the ocean branch of phase two of the REgional Carbon Cycle Assessment and Processes (RECCAP2-ocean) project.

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Each ocean basin shares the meridional variation in ANCPHs, with relatively high ANCPHs in the high latitudes and equatorial regions and lower values in the subtropics (Fig. 4c, d). On the other hand, it indicates considerable differences in the average ANCPHs: 1.1 mol C m−2 year−1 in the Indian Ocean, 1.6 mol C m−2 year−1 in the Pacific Ocean, and 1.9 mol C m−2 year−1 in the Atlantic Ocean. A previous study45 has identified the similar contrast among basins, which is likely attributable to difference in nutrient supply from the Southern Ocean45 and/or low-latitude mesopelagic nutrient recycling46. Our method in which the dissolved oxygen budget is calculated should result in spatial patters of ANCPHs that reflect the sum of the terms in the physical oxygen fluxes (Fig. 4b). The results highlight that the physical processes such as advection and diffusion play a crucial role in closing the upper ocean dissolved oxygen budget at not only global scale but also regional scale, particularly in high latitudes and equatorial regions.

The obtained ANCPHs with their zonal variabilities show good overall agreement with previous local estimates (Fig. 4c–f). In general, the result of estimating ANCPH from tracer budgets highly depends on the definition of H (i.e., the depth at which the export is estimated). The ANCPHs in this study are derived from the net biological oxygen production, i.e., biological production minus autotrophic/heterotrophic respirations. Since the biological production dominates in the euphotic layer, and as it goes deeper, respirations become relatively dominant, the deeper the depth H, the smaller the ANCPs tend to be47. As this study uses a deeper H compared to the previous float-based and ocean station studies, which used the seasonally varying MLD48 or Zeu49, or fixed depths of 100 m or 200 m50,51, ANCPHs from this study could reflect a greater influence from subsurface respiration, leading to lower ANCPs. Furthermore, using a skin temperature correction52 when calculating air–sea oxygen exchanges could also be one of the reasons why our ANCPHs are on the smaller side (see also Supplementary Note 3 for further details).

In addition to such discrepancies with a part of previous estimates due to the difference in the definition for calculations, potential biases arising from limitations of data used in this study also warrant attention. Direct carbon export by meso-scale eddies and associated submeso-scale structures, known as the Eddy-pump, is believed to account for ~20% of the total in the eddy-rich Southern Ocean8. Although the bolus velocities from a reanalysis product were used in our budget calculations, the eddy transport of oxygen (FADV* in Fig. 4b) computed from the parameterized eddy transport and the spatially smoothed dissolved oxygen fields might be underestimated. And, in the air–sea oxygen flux calculations, we used raw profile values to calculate instantaneous oxygen flux, which are then smoothed into monthly temporal resolutions in the subsequent spatial mapping. This could lead to underestimations of episodic and intense biogenic oxygen releases that could occur on relatively short time scales. Both aspects require further verification through additional observational studies as more data is accumulated.

Local perspective for dissolved oxygen balance and NCP

Even within the same ocean basin, the seasonal upper ocean dissolved oxygen balances are distinct among the subtropics (near the Hawaii Ocean Time-series station, HOT), the region associated with the western boundary current (Kuroshio-Oyashio Confluence Region, KOCR), and the subarctic (near the Ocean Station P, OSP), which were selected as regions with an abundance of observations (c.f., Supplementary Figs. 3 and 4).

In the subtropics, situated far from strong currents, the oxygen tendency in the budget is primarily determined by the balance between air–sea exchange (FA–S) and net biological production (FNCP) (Fig. 5a). The NCP remains positive throughout the most of the year, resulting in a carbon export of about 1 mol C m−2 year−1 into the dark ocean annually through the biological pump. In the KOCR, oxygen reduction by advection (FADV) due to the obduction53 of low-oxygen water mass from the layer below the depth H also plays an important role in the upper ocean dissolved oxygen balance54 (Fig. 5c). Although there is a substantial seasonal amplitude of vertically integrated oxygen, the resultant ANCPH remains modest. In the eastern subarctic (OSP), the remarkably strong vertical oxygen gradient around the winter MLD makes vertical diffusion an important factor in oxygen reduction during the winter (Fig. 5e). The resulting seasonal cycle of NCP at OSP is more consistent with a previous case study that explicitly accounted for lateral physical oxygen fluxes55.

Fig. 5: Local upper ocean dissolved oxygen budgets and apparent oxygen utilization (AOU).
figure 5

a, c, e Monthly upper ocean dissolved oxygen budgets (Eq. (1)) near the Hawaii Ocean Time-series (HOT) station, the Kuroshio-Oyashio confluence region (KOCR), and the Ocean Station P (OSP), respectively. Shading along the lines indicates the uncertainties (see Methods for uncertainty estimation). b, d, f Seasonal cycles of the apparent oxygen utilization (AOU, [O2]sat – [O2]) at the same locations. Blue, red, and green lines indicate the surface mixed layer depth (MLD), euphotic layer depth (Zeu), and the lower boundary of the upper ocean as defined in this study (depth H), respectively.

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The relationship between the annual maximum MLD and Zeu reflects the processes that regulate the seasonal cycle of physical environments. In the region near HOT, where the annual maximum Zeu is deeper than the annual maximum MLD, positive NCPs are maintained by the strong production after spring, as suggested from the increase in dissolved oxygen (decrease in apparent oxygen utilization [AOU]) around the lower part of the mixed layer (Fig. 5b). On the other hand, in the KOCR, where the annual maximum MLD is substantially deeper than the annual maximum Zeu, the vertically integrated NCP becomes negative (i.e., respiration exceeds production) even during what is generally the productive period (spring to summer). This can be attributed to intense subsurface respiration during the productive periods in the thick layer below the Zeu but above H, which is implied from the strong AOU increases within this layer from April to September (Fig. 5d). This demonstrates that the upper ocean condition of the physical environments (here, the resultant relationship between MLD and Zeu) is one of the important controlling factors for determine the local carbon export. And, because of the considerable seasonality of subsurface respiration, estimates of ANCP derived from mesopelagic oxygen changes during the productive season only51,56,57 must be interpolated with caution.

Discussion

The ANCPHs estimated from oxygen differs in principal from those inferred from satellite data, allowing for an independent comparison with satellite-derived net primary production (NPP58,59,60). The latitudinal trends of both ANCPH and ANPP exhibit a decrease from the equator northward followed by an increase, showing a coherent pattern in the NH (Figs. 4f and 6). In the SH, ANCPHs increase southwards after reaching their minimum at 30°S, but ANPPs show the minimum values at the southern end of this analysis (60°S). Dividing the obtained zonal mean ANCPH by the satellite-derived ANPP yields the export ratio, under the assumption of the annual steady sate for the zonal-mean (i.e., ANCPH can be considered equivalent to the annual export production). The ratios indicate a relatively stable latitudinal variation in the NH, with slightly higher values at high latitudes (Fig. 6). On the other hand, in the SH, reflecting the different behaviors among ANCPH and ANPP, there is a marked latitudinal variation, with very low ratios in the subtropics and high ratios reaching up to 75% in the Southern Ocean. The previous parameterizations15,61 capture the latitudinal features of the export ratio in the NH but not in the SH. Given the latest global NPP estimate62 of 53 Pg C year−1, the global export ratio becomes 0.14.

Fig. 6: Latitudinal trend in the export ratio derived from the O2-based ANCP.
figure 6

Satellite-derived annual net primary production (ANPP; green line, left y-axis) and the export ratios (ANCP/ANPP, right y-axis) computed using the O2-based ANCP estimated in this study (blue line) and based on two empirical parametrizations (red15 and yellow61 lines). Shading around the lines indicates a range of one standard deviation among the three satellite-derived NPP products: vertically generalized production model (VGPM)58; carbon-based production model (CbPM)59; and carbon, absorption, and fluorescence euphotic-resolving (CAFE) model60. The export ratio following Laws et al. (2001) is calculated by their equation (2) (ef-ratio) with using the three products mean of ANPP and a sea surface temperature climatology92. The export ratio following Li and Cassar (2016) is calculated by their equation (7) with using a sea surface temperature climatology92.

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Combined with the air–sea inorganic carbon (CO2) fluxes, the present-day long-term mean distribution of biological-driven organic carbon export presented in this study implies a comprehensive view of the overall of upper ocean carbon cycle (Fig. 4c–f). In the Pacific (Fig. 4d), as is largely common across other ocean basins, the amount of carbon exported from the upper ocean by the biological pump exceeds the inorganic carbon supplied from the sea surface in the high latitudes. This divergence of carbon fluxes requires the net upward (and/or horizontal) physical supplies of inorganic carbon into the upper ocean supporting the substantial biological production, suggesting the dominant role of the biological pump in the ocean carbon pumps. On the other hand, in the subtropics of both hemispheres, more inorganic carbon is supplied by the air–sea flux than the amount of organic carbon exported from the upper ocean. This upper ocean convergence of carbon fluxes in subtropics indicates the anthropogenic accumulation of the inorganic carbon within the upper ocean and/or the net removal of inorganic carbon from the upper ocean due to the vertical/horizontal physical transport. Therefore, in this region, both physical and biological pumps contribute to the carbon export from the upper ocean. In tropical regions, the upper ocean carbon appears to be diverging due to strong surface CO2 release and biological-driven export. This divergence can be balanced by the physical supply of inorganic carbon from the depths due to equatorial upwelling, emphasizing again the important role of the biological pump in transporting carbon to deeper layers in the tropics. These global perspective of the upper ocean carbon cycle described here from the observational tracer budget support the results from a previous model study63.

Considering the sequestration time-scale of one year, our estimation of the global carbon export is consistent with the latest independent estimate obtained through an inversion64, falling within their range of uncertainties. We believe that our results could contribute to the observational constraints of the global biological pump. Although there are still some difficulties to be improved, such as uncertainties in the conversion of oxygen to carbon etc., the dissolved oxygen budget methodology has the great advantage of incorporating the results of most of diverse downward pathways of biological carbon pump which make the direct field measurement difficult. With further improvement in the spatiotemporal coverage of the data, the methodology that has been developed over nearly half a century65,66 has the potential to enable us to monitor inter annual, decadal or longer time-scale changes in the biological carbon export and to help us understand their roles on the changing climate.

Because of international efforts to develop and maintain a network of global observations, we are at the beginning of an era where the export production through the biological pump can be globally estimated from in situ observed data, without relying on conventional remote sensing data. The accumulation of multiple independent descriptions using various different tracers can facilitate a more comprehensive understanding of the biological processes themselves that drive the biological pump by revealing more detailed vertical structure and seasonal development beyond the vertically integrated and annual mean basis of this study. The ability to estimate the horizontal and vertical distribution of dissolved substances and their budget on nearly global spatial coverage from observational data must contribute to a more detailed three-dimensional picture of the ocean carbon cycle and should be useful for validation of ESMs. International collaboration to maintain these observations is indispensable for updating our knowledge and refining ocean biogeochemical models and then for understating ongoing and forthcoming global changes.

Methods

Dissolved oxygen data

In this study, we used dissolved oxygen profiles observed from 1980 to 2022, sourced from the World Ocean Database (WOD) 201867, the BGC-Argo data from the Argo Global Data Assembly Centre68, and the Global Ocean Data Analysis Project (GLODAP) version 2.202269 (Supplementary Figs. 3 and 4). From the WOD, profiles obtained by ship-base observations (datasets named as “OSD” and “CTD”) were used. We checked for duplicate observations by research cruises among the GLODAP and WOD based on the dates and locations of the observations, and prioritized them for use in the order GLODAP and WOD. Only dissolved oxygen values classified as “good” by the Quality Control (QC) procedure for each database were used: “Data mode = Adjusted or Delayed” and “Profile QC Flag = A or B” for BGC-Argo data70, and “QC flag = 0” for WOD data67. Furthermore, for analyses that require not only sea surface values but also vertical profiles, we excluded profiles where the shallowest oxygen observation layer was deeper than 15 m, profiles where the spacing of vertical observation layers was wider than 50 m above 150-m depth or wider than 100 m above the 400-m depth, and profiles with fewer than eight observations above 200-m depth (Supplementary Fig. 4). For profiles from autonomous profiling floats, we corrected biases at the base of the mixed layer due to the slow response time of the dissolved oxygen sensor following the method proposed by a previous study31.

To calculate the horizontal gradients of dissolved oxygen required for estimating physical oxygen fluxes through advection and horizontal diffusion (Methods “Calculation of physical oxygen fluxes”), we also used two global ocean dissolved oxygen gridded products, the World Ocean Atlas 201871 (WOA 2018) and Gridded Ocean Biogeochemistry from Artificial Intelligence-Oxygen72 (GOBAI-O2). Both products are based on observational data: WOA 2018 provides optimally interpolated monthly climatology of dissolved oxygen from profiles obtained by various observational platforms, including ships and autonomous profiling floats, which are archived in WOD 2018, and GOBAI-O2 contains dissolved oxygen data from BGC-Argo floats spatially interpolated using machine learning techniques at 1° (latitude) × 1° (longitude) horizontal resolution and monthly temporal resolution.

Upper ocean dissolved oxygen budget

Neglecting the cross-boundary flux due to molecular diffusion, dissolved oxygen concentration ([O2]) within a water parcel undergoes changes based on the difference between biological production and respiration (J, positive indicates net production),

$$\frac{D\left[{{{{\rm{O}}}}}_{2}\right]}{{Dt}}=J.$$
(3)

Integrating Eq. (3) vertically from the surface (z = 0) to a depth (z = –H) and rewriting it yields an equation for the upper ocean dissolved oxygen budget:

$$\frac{\partial }{\partial t}{\int }_{\!\!\!-H}^{0}\left[{{{{\rm{O}}}}}_{2}\right]{dz} =\, {F}_{{{{\rm{A}}}}-{{{\rm{S}}}}}-{\left.{\kappa }_{v}\left(-H\right)\frac{\partial \left[{{{{\rm{O}}}}}_{2}\right]}{\partial z}\right|}_{z=-H}+{\int }_{\!\!\!-H}^{0}{{{{\boldsymbol{\nabla }}}}}_{{{{\bf{h}}}}}\bullet {{{{\boldsymbol{\kappa }}}}}_{{{{\bf{h}}}}}{{{{\boldsymbol{\nabla }}}}}_{{{{\bf{h}}}}}\left[{{{{\rm{O}}}}}_{2}\right]{dz} \\ +{\int }_{\!\!\!-H}^{0}-\left({{{\bf{v}}}}{{{\boldsymbol{+}}}}{{{{\bf{v}}}}}^{{{{\boldsymbol{* }}}}}\right)\bullet {{{\boldsymbol{\nabla }}}}\left[{{{{\rm{O}}}}}_{2}\right]{dz}+{\int }_{\!\!\!-H}^{0}{Jdz},$$
(4)

where \({\kappa }_{v}\) and \({{{{\boldsymbol{\kappa }}}}}_{{{{\bf{h}}}}}\) are vertical and horizontal diffusion coefficients, and \({{{\bf{v}}}}\) and \({{{{\bf{v}}}}}^{{{{\boldsymbol{* }}}}}\) represent current velocities and their bolus components, respectively (Supplementary Note 1 for the derivation).

According to Eq. (4) (equivalent to Eq. (1)), the vertically integrated dissolved oxygen concentration is subject to variations caused by air–sea exchange at sea surface (FA–S), vertical diffusion at the depth H (FvDIFF, the second term on the right side of Eq. (4)), horizontal diffusion (FhDIFF, the third term on the right side of Eq. [4]), advection (FADV, the fourth term on the right side of Eq. [4]), and net biological production within the layer (FNCP, the last term on the right side of Eq. [4]). In this study, we applied Eq. (4) to a climatological annual cycle, resulting in the left side of Eq. (4) tending toward zero. We first obtained the climatological monthly maps of the dissolved oxygen fluxes due to the four physical processes over one year by gridding local estimates of the fluxes from individual profiles or using gridded products (Methods “Calculation of physical oxygen fluxes” for details), and then we obtained the monthly map of the net annual biological oxygen production as the residual.

In this study, we defined the lower boundary of the vertical integration of the dissolved oxygen budget (depth H) as the deeper of the annual maximum mixed layer depth (MLD) or the annual maximum euphotic layer depth (Zeu) (Fig. 1). We used the depth-sorted 95th percentiles of Argo temperature/salinity-based MLD73 and satellite-derived Zeu74. By using this definition of H, which is always deeper than MLD and remains constant over time, we avoided the direct calculation of considerably large vertical diffusion fluxes within the mixed layer and the entrainment fluxes due to time-varying MLDs, which could be substantial sources of error. In addition, choosing H deeper than (or equal to) the annual maximum Zeu throughout the year allows us to capture almost all of the photosynthetic production near the sea surface, including productions that occurs below the summer shallow MLD but above Zeu. However, note that in regions where winter convection reaches several times deeper than Zeu, the value obtained for net biological oxygen production (hence also ANCPH) may strongly reflect the respiration below Zeu.

Calculation of physical oxygen fluxes

We used a parameterization for estimating air–sea oxygen exchange based on numerical simulation75 and optimized using field measurements76. The air–sea oxygen exchange (FA–S) is represented as the sum of the diffusive flux (Fs) and the bubble fluxes (Fp and Fc):

$${F}_{{{{\rm{A}}}}-{{{\rm{S}}}}}=\left({F}_{{{{\rm{s}}}}}+\beta {F}_{{{{\rm{p}}}}}+\beta {F}_{{{{\rm{c}}}}}\right)\times (1-{f}_{{{{\rm{ice}}}}}),$$
$${F}_{{{{\rm{s}}}}} = {k}_{{{{\rm{s}}}}}\left(\frac{{P}_{{slp}}}{{P}_{{atm}}} {[{{{{\rm{O}}}}}_{2}]}_{{{{\rm{s}}}}}^{{{{\rm{sat}}}}}-{[{{{{\rm{O}}}}}_{2}]}_{{{{\rm{s}}}}}\right)$$
$${F}_{{{{\rm{p}}}}}={k}_{{{{\rm{p}}}}}\left((1+\Delta P)\frac{{P}_{{slp}}} {{P}_{{atm}}}{[{{{{\rm{O}}}}}_{2}]}_{{{{\rm{s}}}}}^{{{{\rm{sat}}}}}-{[{{{{\rm{O}}}}}_{2}]}_{{{{\rm{s}}}}}\right),$$
$${F}_{{{{\rm{c}}}}}={k}_{{{{\rm{c}}}}}{\chi }_{{atm}}^{{{{{\rm{O}}}}}_{2}},$$
(5)

where \(\beta\), \({f}_{{{{\rm{ice}}}}}\), \({P}_{{slp}}\), \({P}_{{atm}}\), and \({\chi }_{{atm}}^{{{{{\rm{O}}}}}_{2}}\) indicate a tuning parameter optimized by field measurements76 (\(\beta\) = 0.37), the sea ice fraction, the sea level pressure, one standard atmospheric pressure, and atmospheric mole fraction of oxygen, respectively. ks, kp, and kc are mass transfer coefficients for each of the fluxes that govern the air–sea oxygen exchange velocity and are given as a function of wind speed.

We used daily wind speed data from satellite observations (third generation of the Japanese Ocean Flux Data Sets with Use of Remote-Sensing Observation77, J-OFURO3), atmospheric reanalysis products (Japanese 55-year Reanalysis78, JRA55; Modern-Era Retrospective Analysis for Research and Applications version 279, MERRA2; and ECMWF Reanalysis version 580, ERA5), and their combination (Cross-Calibrated Multi-Platform version 2.081, CCMPv2), daily sea level pressure data from ERA5, and satellite-derived daily sea ice concentration data82 from the National Snow and Ice Data Center. Wind speeds, sea level pressure, and sea ice concentrations were spatially interpolated to get values at the locations of individual ship/float profiles. Sea surface oxygen saturation concentrations83 (\({[{{{{\rm{O}}}}}_{2}]}_{{{{\rm{s}}}}}^{{{{\rm{sat}}}}}\)) were calculated from sea surface temperature and salinity obtained from profiles, using a skin temperature correction following a previous study52. The three components of air–sea oxygen exchange were estimated from the interpolated wind speeds, sea level pressure and sea ice concentrations, and sea surface oxygen concentrations (\({[{{{{\rm{O}}}}}_{2}]}_{{{{\rm{s}}}}}\)) from individual profiles (see also Supplementary Note 2 for further details).

The vertical diffusion term (FvDIFF, the second term on the right side of Eq. [4]) was calculated as the product of the vertical gradient of dissolved oxygen and the vertical eddy diffusion coefficient at depth H. The vertical eddy diffusion coefficients at depth H are estimated on the basis of the upper ocean turbulence observations84 by assuming a profile that decreases exponentially with an e-folding scale of 20 m as it goes deeper from the diffusion coefficient at the base of the mixed layer (\({\kappa }_{v}^{{{{\rm{mb}}}}}\)), and approaches the background diffusion coefficient (\({\kappa }_{v}^{{{{\rm{bg}}}}}\)):

$${\kappa }_{v}\left(t,x,y,z=-H\right)={\kappa }_{v}^{{{{\rm{bg}}}}}+\left({\kappa }_{v}^{{{{\rm{mb}}}}}-{\kappa }_{v}^{{{{\rm{bg}}}}}\right){e}^{-\left(\frac{H-{{{\rm{MLD}}}}(t)}{20{{{\rm{m}}}}}\right)}.$$
(6)

We used monthly vertical diffusion coefficients at the base of the mixed layer85 obtained from the mixed layer temperature/salinity budget using time-series observations at the ocean stations located in the NH, which are also validated by observational estimates based on budgets using other tracers86,87. The monthly vertical diffusion coefficients shifted by six months were used for the SH profiles, and the annual means were used for profiles in the tropics (20°S–20°N). For the background vertical diffusion coefficient, we mainly used two global observational products based on an inverse estimation from the salinity distribution on isopycnal surfaces88 and a fine-structure parameterization89, in addition to a product based on energy-constrained parameterization of tidal mixing90. \({\kappa }_{v}^{{{{\rm{bg}}}}}\) was computed using the values from the products at depths sufficiently far from depth H (averaged over the depth from H + 100 m to H + 750 m, Supplementary Fig. 2). We calculated the vertical dissolved oxygen gradient at depths H and MLD from individual profiles that were vertically interpolated at 2-m intervals by using the Akima interpolation. With the estimated vertical diffusive coefficient at depth H from Eq. (6), we computed the oxygen fluxes due to vertical diffusion for individual profiles.

The spatially non-uniformly distributed profile values of vertically integrated oxygen concentration (\({{{{{\rm{O}}}}}_{2}}_{{{\mathrm{int}}}}\)) itself, the air–sea oxygen exchange (\({F}_{{{{\rm{A}}}}-{{{\rm{S}}}}}\)), and vertical diffusion (\({F}_{{{{\rm{vDIFF}}}}}\)) were mapped monthly to a 1° (latitude) ×1° (longitude) grid. First, we averaged the profile values in 1° (latitude) ×1° (longitude) bins, excluding values that are outside the range of two standard deviations of profile values within the bins (referred to as a grid value). Next, we conducted a Gaussian distance-weighted averaging for each grid point by searching for grid values over an elliptical shaped area with a latitude:longitude distance ratio of 1:2. The size of the ellipse (i.e., the influence radius) was increased at each grid point until there were at least seven grid values inside the ellipse. To avoid spatially excessive mapping due to the scarcity of original profile values, we also mapped the sea surface temperature obtained from the same profiles using the same mapping procedures. If the resulting mapped sea surface temperatures differed from the independent climatology of a satellite-derived sea surface temperature product (NOAA Extended Reconstructed SST version 591) by more than double the interannual standard deviation, the mapped values were masked as missing in the discussions of local dissolved oxygen balance.

We calculated the advection term (FADV, the fourth term on the right side of Eq. [4]) using two dissolved oxygen gridded products (WOA 2018 and GOBAI-O2) along with velocity estimated from observational temperature/salinity fields (the Roemmich-Gilson Argo Climatology92) and surface wind fields (J-OFURO3, JRA55, ERA5, MERRA2), and velocities from ocean reanalysis products (Estimating the Circulation and Climate of the Ocean version 4 release 493, ECCOv4r4; and Estimated State of Global Ocean for Climate Research version 05a94, ESTOC). The observation-based horizontal velocity was represented as the sum of the geostrophic current velocity and the Ekman current velocity. Except for the equatorial region (5°S–5°N), the geostrophic component was estimated from three-dimensional temperature and salinity fields92 with the assumption that the reference level is at a depth of 1975 dbar, and the Ekman component was obtained from the sea surface wind stress fields77,78,79,80 through non-stratified classical Ekman theory. The vertical velocities were then derived by integrating the continuity equation for an incompressible fluid using estimated horizontal velocities with the boundary condition of no vertical motion at the surface. The Gent-McWilliams ocean bolus velocity from the ECCOv4r4 was used as the bolus component of the velocity field.

We used observational gridded products for the horizontal diffusion coefficients based on an inverse estimation88 and a mixing-length parameterization95 using Argo salinity on isopycnal surfaces to calculate the horizontal diffusion of oxygen (FhDIFF, the third term on the right side of Eq. [4]). The horizontal diffusion fluxes were calculated at a horizontal resolution of 1° (latitude) ×1° (longitude) from horizontal diffusion coefficient and gridded dissolved oxygen products (WOA 2018 and GOBAI-O2). For purposes of visualization, the calculated horizontal diffusion and advection terms were spatially smoothed to align their spatial scales with those of mapped air–sea exchange and vertical diffusion terms (e.g., in Fig. 2c, d). This spatial smoothing does not impact the calculation of the globally integrated values summarized in Fig. 3.

The globally integrated values for physical oxygen fluxes summarized in Fig. 3 were computed with consideration for the data grids missing due to an insufficient number of profiles, or regions not covered by data products. After deriving the mean values for fluxes from values at available grid points which covers ~77% area of the global ocean, we obtained globally integrated fluxes by multiplying the mean values by the area of the global ocean.

Uncertainty estimation

In several previous studies on estimation of local ANCP through dissolved oxygen budgets30,32 and the syntheses of these96, the measurement error of dissolved oxygen concentration itself has been highlighted as a major source of uncertainty. In profiles from the BGC-Argo floats, which are the primary data source for this study, potential errors of 1% or 3 μmol O2 kg−1 have been reported, even after applying the QC procedures97. Our comparison of float observation data, which has been QCed uniformly through the millions of profiles following a common protocol, with shipboard observations (GLODAP), which has been extensively processed to ensure the accuracy and consistency of the data, also indicates the differences of ~1% in the surface oxygen concentrations (Supplementary Fig. 5). In the calculation of the air–sea oxygen exchange, an error of 0.5–1% in surface dissolved oxygen concentration (typically around 300 μmol O2 kg−1) could translate to an error in the flux estimate of 0.5–1 mol O2 m−2 year−1 (i.e., equivalent to an ANCP of 0.35–0.70 mol C m−2 year−1).

In the estimation of physical oxygen fluxes derived from individual profiles (air–sea exchange and vertical diffusion), a Monte Carlo approach was employed to quantify associated uncertainties. In order to calculate the air–sea flux, a randomly selected wind value was taken from a normal distribution with an average value of five spatially interpolated daily wind products and a standard deviation of five values. A surface oxygen concentration was also randomly taken from a normal distribution with the observed surface oxygen as the mean and the 1% error of the mean as the standard deviation. In the calculation of the vertical diffusion flux, a background diffusivity was randomly taken from the two independent products, and for the diffusivity at the base of the mixed layer a 100% error of the monthly diffusion coefficient was assumed, as reported by the previous study85. For each profile, these flux calculations were repeated 1,500 times using randomly selected values. The mean of these iterations was taken as the flux value, and its standard deviation was employed as a measure of uncertainty. Flux values and their errors, obtained from 1,500 repeated calculations across ~600,000 profiles, were spatially mapped to a 1° (longitude) ×1° (latitude) grid using the mapping method described above. The errors associated with the integrated fluxes (e.g. Fig. 3) are reported as the simple summation of the mapped errors.

In the estimation of physical oxygen fluxes with use of the gridded oxygen products (advection and horizontal diffusion), we assessed the uncertainties from differences in the products and methodologies (referred to as “methodological uncertainty”). We estimated the methodological uncertainties by using multiple plausible parameters, data products, and calculation methods to calculate each physical oxygen flux, and then by computing standard deviations of the results obtained from the combinations of these. For the advection, advection (bolus), and horizontal diffusion components, the numbers of combinations are 6 (2), and 4, respectively (Supplementary Table 2).

The uncertainties estimated for each physical oxygen flux propagate into the estimate of net biological oxygen production (Eq. [2]) as the square root of the sum of variances. The uncertainty in the photosynthetic stoichiometry (ΔO2/ΔC = 1.45 ± 0.03)33 was also taken into account when converting net biological oxygen production into ANCP.