Biological export production controls upper ocean calcium carbonate dissolution and CO₂ buffer capacity

Abstract

Marine biogenic calcium carbonate (CaCO₃) cycles play a key role in ecosystems and in regulating the ocean’s ability to absorb atmospheric carbon dioxide (CO₂). However, the drivers and magnitude of CaCO₃ cycling are not well understood, especially for the upper ocean. Here, we provide global-scale evidence that heterotrophic respiration in settling marine aggregates may produce localized undersaturated microenvironments in which CaCO₃ particles rapidly dissolve, producing excess alkalinity in the upper ocean. In the deep ocean, dissolution of CaCO₃ is primarily driven by conventional thermodynamics of CaCO₃ solubility with reduced fluxes of CaCO₃ burial to marine sediments beneath more corrosive North Pacific deep waters. Upper ocean dissolution, shown to be sensitive to ocean export production, can increase the neutralizing capacity for respired CO₂ by up to 6% in low-latitude thermocline waters. Without upper ocean dissolution, the ocean might lose 20% more CO₂ to the atmosphere through the low-latitude upwelling regions.

Marine heterotrophic respiration drives calcium carbonate dissolution and intensifies oceanic absorption of atmospheric CO₂.

INTRODUCTION

Biogenic calcium carbonate minerals (mostly calcite and aragonite) are produced by organisms in the euphotic zone, the sunlit layer closest to the ocean surface. When the organisms die and sink through the water column, a portion of CaCO₃ minerals dissolves while the remaining portion is dissolved or buried in marine sediments. The magnitude of surface CaCO₃ export and subsequent dissolution in the water column—a process called the carbonate pump (1)—can influence the ocean’s ability to absorb atmospheric CO₂ through a distribution of seawater alkalinity. Sinking biogenic CaCO₃ can also act as a ballast mineral for sinking organic particles (2, 3), which in turn can control food supplies for marine organisms at depth and contribute to long-term carbon sequestration. Ocean acidification, caused by oceanic absorption of anthropogenic CO₂, has adverse effects on marine calcifiers by reducing calcification rates and decreasing seawater saturation state with respect to CaCO₃ minerals (4). However, the sensitivity of biogenic CaCO₃ cycling to seawater acidity is difficult to assess globally because of the diversity of calcifying organisms and their differing sensitivities to environmental conditions (4, 5). Furthermore, our incomplete understanding of the drivers of CaCO₃ export and dissolution challenges a reliable projection of the future strength and efficiency of the carbonate pump and the oceanic carbon sink (6). The global ocean patterns of the carbonate pump’s strength and efficiency and their environmental and biological controls can help constrain future sensitivities of the carbonate pump to climate and environmental changes.

The association between the spatial pattern of the carbonate pump and its environmental controls is yet to be underpinned by solid theoretical and observational lines of evidence. Satellite observations tend to point to higher calcification rates in high-latitude surface waters, whereas sediment trap data point to higher CaCO₃ export rates in waters at low latitudes (7, 8), implying decoupling between the surface production and vertical export of biogenic CaCO₃ (9). The absence of global data on various types of calcifying organisms, ranging from those containing less soluble calcite (constituting coccolithophores and foraminifera) to those having more soluble aragonite or high-Mg calcite (constituting pteropods and fish bones), is another source of uncertainty with respect to the global ocean CaCO₃ cycle (9, 10). A related uncertainty lies in where and how sinking CaCO₃ particles dissolve. While studies based on laboratory and in situ experiments focused on the abiotic effects of CaCO₃ solubility in acidified deep waters (11–15), studies based on sediment traps and alkalinity data highlighted that approximately 50% of CaCO₃ exported from the ocean surface is dissolved either in slightly oversaturated or close to saturated waters for calcite and aragonite minerals (8, 15–19). These studies hypothesized that CaCO₃ particles are dissolved in organic matter aggregates or zooplankton guts where the release of CO₂ from the oxidation of organic matter and digestive acids generates highly acidic microenvironments. A tight association between metabolic respiration of sinking organic particles and CaCO₃ dissolution within the upper part of the twilight zone (upper 100 to 300 m) was confirmed in direct observations in the North Pacific (15, 18) and in the North Atlantic (20); however, the relative importance of the abiotic versus biotic controls of the global ocean CaCO₃ dissolution rates and their effects on the seawater neutralizing capacity for atmospheric CO₂ have remained somewhat uncertain.

To estimate the global ocean cycling of biogenic CaCO₃, we use an ocean biogeochemistry model where CaCO₃ export and dissolution are empirically formulated in terms of the CaCO₃ mineral saturation states and organic carbon remineralization rates (see Materials and Methods). The model of CaCO₃ cycling is optimized against global observational datasets of alkalinity (21), dissolved inorganic carbon (DIC) (21), and the burial fluxes of inorganic carbon into marine sediments (see Materials and Methods) (22). The model also includes an observationally constrained ocean circulation field (23), satellite-based estimates of net primary production (NPP) (24, 25), observed riverine inputs of nutrients and carbon (26, 27), and the effects of water-column nitrification and denitrification (28) on alkalinity distribution (29). Hence, our model takes into account the lateral advection and mixing of alkalinity from coastal margins and alkalinity input from alkalinity-rich deep waters that are essential to accurately quantify CaCO₃ dissolution rates throughout the water column (30, 31). We note that although some of the input data (e.g., NPP, riverine carbon inputs, and CaCO₃ burial fluxes into marine sediments) include coastal features, our coarse resolution model (2° × 2° horizontal resolution and 24 vertical layers) does not resolve the regional details of coastal ocean currents, shelf processes, and neritic CaCO₃ cycling. Hence, our global ocean estimates are inevitably limited to the CaCO₃ cycles in the open ocean.

An important aspect of this study is that we assess the model performance using the global observational compilations of sediment trap-based CaCO₃ flux data (15, 20, 32, 33) and large-volume pump–based CaCO₃ concentration data (34–36), both measured within the ocean’s upper twilight zone (upper 300 m). As shown below, the observed relationships between the vertical attenuations of CaCO₃ and particulate organic carbon (POC) fluxes or concentrations provide crucial constraints on the biogenic control of vertical CaCO₃ transfer efficiency above 300 m that is only weakly constrained by the observed tracer concentrations alone. This study builds upon a previous study of constraining the global ocean’s organic carbon cycles (37) and includes both organic and inorganic carbon cycling from their surface export to sedimentary burial fluxes in a self-consistent manner. A more realistic representation of the upper ocean physical and biogeochemical processes, compared to previous global-scale assessments (16, 19), helps elucidate the regional hotspots for the abiotic versus biotic drivers of CaCO₃ dissolution. Our numerical model framework also allows us to explore the global effects of CaCO₃ dissolution on the CO₂ buffer capacity of seawater. Below, we report the best estimates that are optimally consistent with the observational constraints (figs. S1 and S2). Uncertainties for our estimates are derived on the basis of a suite of model experiments, considering uncertainties in satellite-based NPP estimates and model formulations for CaCO₃ export and dissolution (see Materials and Methods).

RESULTS

Spatial patterns of CaCO₃ export and shallow (≤300 m) dissolution

Our model reveals large horizontal variability in the export ratio of CaCO₃ to POC at the base of the euphotic zone that is correlated with the degree of supersaturation at the sea surface (fig. S3). The CaCO₃ export ratio ranges from near-zero at high latitudes to 17% with an uncertainty range of 10 to 21% at low latitudes (averaged over 30°S to 30°N). When total organic carbon export (the sum of dissolved and POC) is considered, the range becomes slightly narrower from near-zero at high latitudes to 16% (with an uncertainty range of 9 to 19%) at low latitudes where dissolved organic carbon (DOC) is exported to the subsurface via the subduction of mode and intermediate waters. Although such spatial correspondence does not prove a causal relationship, saturation state–dependent calcification rates were commonly obtained in laboratory, culture, and mesocosm experiments (4, 5). Higher CaCO₃ export ratios toward the low-latitude surface are also consistent with previous sediment trap- and model-based studies (38, 39). Using the constrained CaCO₃ export ratio and the model estimate of POC export (37), we obtain the CaCO₃ export from the euphotic zone that ranges from near-zero in polar and oligotrophic regions to 20 g C m⁻² year⁻¹ in highly productive regions (Fig. 1A) where POC export can reach as high as 150 g C m⁻² year⁻¹ (fig. S3). When zonally averaged, the large spatial range is reduced to a meridional variation of 0 to 9 g C m⁻² year⁻¹ for CaCO₃ and 11 to 94 g C m⁻² year⁻¹ for POC export (Fig. 2A) due to substantial longitudinal heterogeneity.

Fig. 1. CaCO₃ export from the euphotic zone and dissolution fractions within the upper 300 m.

(A) The vertical export of CaCO₃ from the euphotic zone. The base of the euphotic zone in our model varies from a depth of 73 m in eutrophic regions to 114 m in oligotrophic and highly convective high-latitude regions. (B) The fraction at which the CaCO₃ exported from the euphotic zone is dissolved until it reaches a depth of 300 m. The shading shows our best estimate. The regions with very low CaCO₃ export leading to spurious fractions are masked as white. The filled circles show the sediment trap data–based estimates (see Fig. 3 and figs. S5 and S6 for details). The filled diamonds show the CaCO₃ concentration data–based estimates (see Fig. 4 and fig. 7 for details).

Fig. 2. The zonally averaged vertical transfer efficiencies of sinking CaCO₃.

The transfer efficiencies (middle) are compared with the zonally averaged CaCO₃ and POC export from the euphotic zone (top) and zonally averaged burial fluxes (bottom). The zonal averages from the North Atlantic to the Southern Ocean, and to the North Pacific are shown. (A) The vertical CaCO₃ fluxes are normalized with respect to the export from the euphotic zone in each water column. The zonal average of the vertical transfer efficiency is shown as shading. The depth by which 30% of the surface exported CaCO₃ is transferred (or 70% dissolves) is marked with purple lines. The solid black line represents the calcite saturation horizon, and the dotted black line represents the aragonite saturation horizon. (B) Same as (A), except that the vertical CaCO₃ fluxes are normalized with respect to the export from a depth of 300 m. (C) Uncertainties of the CaCO₃ export, the 30% transfer depths, and the burial fluxes are added as shade to the best estimates (respective solid lines).

The subsequent dissolution of CaCO₃ in the ocean’s interior (water column and sediments combined) is highly variable in space (fig. S4). The most intensive dissolution occurs close to the base of the euphotic zone (roughly corresponding to the upper twilight zone shallower than 300 m) under areas where the surface is highly productive. When the vertical fluxes are normalized with respect to the export from the euphotic zone, the fraction at which the CaCO₃ exported from the base of the euphotic zone is dissolved (also termed dissolution efficiency hereinafter) within the upper 300 m exhibits a large horizontal variability of 0 to 70% in our optimal solution (Fig. 1B). A meridional variability of the zonally averaged dissolution fraction at 300 m ranges from 8 to 52% (Fig. 2A). When the uncertainty from the suite of model experiments is considered, the meridional variability extends to a range from 0 to 75%. To put it another way, the depth by which 70% of the surface exported CaCO₃ is dissolved varies from a depth of 240 to 3900 m in our best estimate and from a depth of 130 to 4300 m when the uncertainty is considered (Fig. 2C).

The most rapid vertical attenuation of CaCO₃ flux occurs in the mid-latitude North Atlantic and North Pacific around 40°N where the POC export is largest (Figs. 1B and 2A). Such rapid attenuation of sinking CaCO₃ fluxes was observed in the upper twilight zone of the North Pacific subpolar gyre (i.e., station 4 in fig. S5) (15), where our model indicates 53% (with an uncertainty of 0 to 76%) dissolution between 73 and 300 m at a grid cell located at 42°N, 158°W (Figs. 1B and 3B and fig. S5). Our model-based estimate agrees reasonably well with the observed value of 63 ± 3% dissolution (15) (Fig. 3 and fig. S5). The rapid attenuation of sinking CaCO₃ fluxes in the North Atlantic subpolar gyre is also qualitatively supported by sediment trap CaCO₃ fluxes reported to diminish by 84 ± 5% from 51 to 184 m at the Porcupine Abyssal Plain (PAP) station located at 49°N, 16°W (Fig. 3 and fig. S6) (20).

Fig. 3. The relationships between the POC export and remineralization and the CaCO₃ dissolution efficiency within the upper twilight zone (≤300 m) estimated using the sediment trap data and the model.

(A) The relationship between the POC export from the euphotic zone and the upper ocean CaCO₃ dissolution fraction estimated using the sediment trap data. The Pacific (Pac.) data are from (15, 32, 33) with “Stn.” representing station (see fig. S5 for vertical fluxes) and the Atlantic (Atl.) data are from (20) (see fig. S6 for vertical fluxes) with PAP representing Porcupine Abyssal Plain. A data point closest to the sea surface is assumed to represent the base of the euphotic zone, which varies from 50 to 150 m depending on the stations. Data points located between 151 and 300 m are taken or averaged to estimate the dissolution fraction within the top 300 m. (B) Estimates based on our model. The x axis shows the POC export from the euphotic zone and the y axis shows the CaCO₃ dissolution fraction from the base of the euphotic zone to a depth of 300 m. The best estimates sampled from the grid cells corresponding to the sediment trap locations are marked as symbols and the uncertainties are shown as error bars. Gray dots show the best estimates from all grid cells except for the regions where the bathymetry is shallower than 300 m. (C and D) Same as (A) and (B) except that the x axes show the POC flux attenuation (i.e., remineralization) from the euphotic zone to a depth of 300 m. Error bars for the observations are based on the reported values, except that for Pac. K2 and Pac. Aloha the differences in the two measurements are regarded as their uncertainties.

The dissolution hotspots within the upper twilight zone of the Northern Hemisphere mid-latitudes are followed in amplitude by large dissolution fractions within the upper twilight zone of the equatorial upwelling regions and the subantarctic zones where our model suggests that ~30% of the exported CaCO₃ dissolves within the upper 300 m (Figs. 1B and 2A). Relatively higher transfer efficiency (~90%) or slower attenuation of sinking CaCO₃ fluxes (~10%) occur under oligotrophic regions, where POC export from the euphotic zone is lowest. Such biological export-dependent (or remineralization-dependent) transfer/dissolution efficiencies are qualitatively consistent with the observed contrasts between the eutrophic and oligotrophic regions, found for the North Pacific (15) and the North Atlantic (Fig. 3 and figs. S5 and S6) (20). The sediment trap data thus provide independent support for our best estimates constrained by the CaCO₃ burial fluxes and alkalinity distribution.

Further independent support for the tight association between POC remineralization and shallow CaCO₃ dissolution comes from the suspended particle concentration data collected using large-volume pumps (34–36), although a direct comparison is made difficult because we do not explicitly simulate CaCO₃ concentrations in our model (see Materials and Methods). The data along the eastern equatorial Pacific (35) (chosen based on the best quality control; see Materials and Methods) exhibit a large range of 26 to 88% in the vertical attenuation of CaCO₃ concentration within the upper 300 m (Fig. 4 and fig. S7). The percent attenuation of CaCO₃ is positively correlated with the magnitude of POC attenuation with a correlation coefficient of 0.76 (P < 0.01 based on a t test). Together, the flux and concentration data support a wide range of CaCO₃ dissolution fractions within the upper 300 m of the global ocean (Fig. 1B), which in our model is primarily driven by the POC remineralization rates within the upper twilight zone (see Materials and Methods).

Fig. 4. The relationship between the vertical attenuations of POC and CaCO₃ concentrations within the upper twilight zone (≤300 m) estimated using the particle concentration data and the model.

(A) The relationship between the vertical attenuations of POC and CaCO₃ concentrations. The particle concentration data measured using large-volume pumps from (36) are used. For each vertical profile, a maximum CaCO₃ concentration (within a depth range of 50 to 150 m) and a minimum CaCO₃ concentration (within a depth range of 150 to 300 m) are taken to estimate the vertical CaCO₃ attenuation fraction. The POC attenuation in the x axis is estimated using POC concentrations at the corresponding depths. The CaCO₃ attenuation fraction in the y axis is also color-coded in each circle. See fig. S7 for the vertical profiles. (B) The CaCO₃ attenuation fractions are shown at the sampling locations as filled circles. The circles are tagged with the longitude of the sampling locations. The three circles of “78 W (1),” “78 W (2),” and “78 W (3)” fall in a range of 77°30′W to 78°30′W and offshore directed from (1) to (3).

Spatial patterns of CaCO₃ dissolution below 300 m and burial fluxes

Below the upper twilight zone, the CaCO₃ dissolution patterns are characterized primarily by basin-scale contrasts of the seawater undersaturation states with respect to calcite and aragonite (fig. S4). Distinct dissolution peaks occur in the deep and bottom waters that are undersaturated with respect to aragonite or calcite. The deep ocean dissolution hotspots follow the progressive shoaling of the saturation horizons, the depth above which supersaturated waters lie and below which undersaturated waters lie. When the vertical CaCO₃ fluxes are normalized with respect to the vertical fluxes at 300 m, the depth of 30% transfer efficiency (i.e., 70% dissolution) rises from ~4.5 km in the North Atlantic, to ~4 km in the Southern Ocean, and to ~2.5 km in the North Pacific (Fig. 2, B and C). That is, the vertical transfer efficiency of the exported CaCO₃ from a depth of 300 m to the seafloor tends to decrease as deep waters become more corrosive (more acidic) from the North Atlantic to the Southern Ocean, and to the North Pacific. The acidity and seawater undersaturation state of deep water appear to be primary drivers of the basin-scale differences in deep ocean CaCO₃ dissolution and CaCO₃ burial fluxes into sediments.

Spatially varying fractions (e.g., a zonal average ranging from 1 to 52% with an uncertainty range of 1 to 78%) of the surface exported CaCO₃ are buried in marine sediments. In general, the burial fractions are higher in less corrosive North Atlantic seafloor and lower in more corrosive North Pacific seafloor (Fig. 2 and fig. S1). Our model captures the observed basin-scale contrasts of CaCO₃ burial fluxes arising from the bottom water saturation state, e.g., disproportionately higher burial fluxes in the Atlantic basin than the other basins and near the absence of burial fluxes in the North Pacific (fig. S1). We also find that surface CaCO₃ export exerts a large control over the spatial pattern of CaCO₃ burial fluxes (40), especially for some of the regional burial hotspots in the Atlantic and in the southeastern Pacific. When zonally averaged, the latitudinal bands of elevated burial fluxes coincide with those of higher CaCO₃ export from the euphotic zone except for the North Pacific (Fig. 2). More efficient upper water dissolution (i.e., less transfer efficiency) of surface exported CaCO₃ under eutrophic surface, relative to oligotrophic surface, tends to dampen the meridional variability of the CaCO₃ fluxes reaching the seafloor (fig. S4). Yet, substantial fractions of the surface exported CaCO₃ remain undissolved and are buried under highly productive regions, exhibiting burial peaks (Fig. 2 and fig. S1). This direct connectivity from the sea surface to the seafloor makes the CaCO₃ burial fluxes a useful constraint for the estimation of the water column CaCO₃ export and dissolution (38).

Global budget of CaCO₃ export, dissolution, and burial

The spatial patterns of the CaCO₃ export and dissolution discussed above are consistent with previously suggested global ocean CaCO₃ budgets. Globally, our model estimates that 0.40 Pg C year⁻¹ (with an uncertainty of 0.26 to 0.46 Pg C year⁻¹) of DIC is transferred from land to the open ocean. The estimate is slightly greater than our prescribed riverine DIC flux of 0.30 Pg C year⁻¹ (27), yet still falls within the uncertainty range. The global integral of the terrestrial DIC fluxes is partly balanced by the global integral of CaCO₃ burial fluxes into marine sediments, where our estimate of 0.20 Pg C year⁻¹ agrees with an observation-based estimate (41). The globally integrated CaCO₃ exported from the euphotic zone is estimated to be 1.40 Pg C year⁻¹ with an uncertainty range of 0.77 to 1.94 Pg C year⁻¹ (Fig. 5A). Global CaCO₃ export has been previously suggested to range from 0.4 to 1.8 Pg C year⁻¹ (8) based on various methodologies, including satellite data in conjunction with CaCO₃ sinking flux estimates (42), analysis of seasonal decrease in surface alkalinity (43), and global ocean and Earth system models (44–47). Our estimate falls within the upper bound of existing estimates. However, our estimate is substantially larger than the Earth system model-based estimates of 0.66 Pg C year⁻¹ provided by the Climate Model Intercomparison Project (CMIP) phase 5, and 0.4 to 1.2 Pg C year⁻¹ provided by the CMIP phase 6 (6). The upward revision in this study is likely because our estimate implicitly includes the dissolution effects of not only calcite but also more soluble forms of CaCO₃ and allows for dissolution above the saturation horizon. Of the CaCO₃ exported from the euphotic zone, 37% (with an uncertainty of 5 to 52%) dissolves in the twilight zone shallower than 300 m, where sinking aggregates fluxes rapidly attenuate due to heterotrophic respiration (20, 33). Because of the intensive dissolution in shallow waters, only 0.88 Pg C year⁻¹ (with an uncertainty of 0.71 to 0.99 Pg C year⁻¹) is exported to depths >300 m, which approximates a recent alkalinity-based estimate of 0.91 ± 0.14 Pg C year⁻¹ (16) and an inverse model–based estimate of 1.0 Pg C year⁻¹ (Fig. 5A) (19). At a depth of 2000 m, CaCO₃ export is further reduced at 0.43 Pg C year⁻¹ (with an uncertainty of 0.41 to 0.50 Pg C year⁻¹), which is close to a reported value of 0.6 Pg C year⁻¹ derived from sediment trap data (8).

Fig. 5. CaCO₃ export and dissolution integrated over the global ocean and basins.

(A) Globally integrated estimates for the vertical export of CaCO₃. The total export from this study is decomposed into the export through three distinct saturation zones and the export that ends up being buried in marine sediments. The three distinct saturation zones include the water supersaturated with respect to calcite and aragonite (supersat), the water supersaturated with calcite, but undersaturated with aragonite (midsat), and the water undersaturated with calcite and aragonite (undersat). The total CaCO₃ fluxes at different depth levels from this study (best estimate as yellow circles and the uncertainty as yellow error bars) are compared with the estimates from previous studies. (B) CaCO₃ dissolution rate is integrated over the three distinct saturation zones. (C) Same as (B), except that the integrated estimates are normalized with respect to the mass of the distinct water.

CaCO₃ dissolution effects on the CO₂ buffer capacity by seawater

To gain an insight into potential drivers of CaCO₃ dissolution and its implications on the global carbon cycle, we divided the ocean’s interior into three domains depending on the saturation states with respect to CaCO₃ minerals: the water that is supersaturated with respect to both calcite and aragonite (referred to as “supersat” zone hereinafter); the water that is supersaturated for calcite, but undersaturated for aragonite (referred to as “midsat” zone); and the water that is undersaturated with both calcite and aragonite (referred to as “undersat” zone) (Fig. 6B). We divided the CaCO₃ vertical export and dissolution into the components that occur within the distinct saturation zones (Fig. 5 and fig. S8). We also diagnosed the distribution of the regenerated DIC and alkalinity, exclusively attributed to the dissolution in each zone (Fig. 6), and assessed how the dissolution contributes to the CO₂ buffer capacity (fig. S9) and air-sea CO₂ exchange (see Discussion and Fig. 7). Dissolution in each zone includes the combined effects of CaCO₃ dissolution within the water column and sediments. For clarity, the diagnostics and implications are based on the “Ex_all” experiment where the biological cycling of phosphorus and nitrogen does not influence ocean alkalinity distributions while all else are kept equal to our best solution of the optimization (see Materials and Methods).

Fig. 6. Zonally averaged regenerated alkalinity from CaCO₃ dissolution in distinct saturation zones.

This is estimated using the Ex_all experiment where the biological sources and sink of phosphorus and nitrogen are turned off in the best solution of the optimization. (A) Total regenerated alkalinity. (B) The ocean is grouped into three: the water supersaturated with respect to calcite and aragonite, referred to as supersat; the water supersaturated with respect to calcite, but undersaturated with aragonite, referred to as midsat; and the water undersaturated with calcite and aragonite, referred to as undersat. (C) Regenerated alkalinity contribution from the supersat dissolution. (D) Regenerated alkalinity contribution from the midsat dissolution. (E) Regenerated alkalinity contribution from the undersat dissolution.

Fig. 7. Implications of the CaCO₃ dissolution within the water that is supersaturated with calcite and aragonite on the air-sea CO₂ exchange.

(A) The buffer capacity (defined as ∂[DIC]/∂[CO₂] × [CO₂] where [CO₂] is the concentration of aqueous CO₂ in seawater) at the sea surface estimated using the Ex_all experiment. (B) The percentage contribution from the supersat dissolution to the sea surface buffer capacity. (C) Shading shows the inferred effects of the supersat dissolution on air-sea CO₂ exchange, i.e., a difference in the air-sea CO₂ exchange between the Ex_all experiment and the case where the effects from the supersat regenerated alkalinity and DIC are removed from the Ex_all experiment. Positive values denote the anomalous fluxes into the ocean (or less efflux into the atmosphere) in mol m⁻² year⁻¹. The contour lines show the preindustrial CO₂ fluxes (in mol m⁻² year⁻¹) simulated from the Ex_all experiment. Positive values (solid lines) denote fluxes into the ocean and negative values (dotted lines) denote fluxes into the atmosphere.

When the CaCO₃ dissolution is integrated over the distinct saturation zones, the largest portion of total CaCO₃ dissolution occurs within the supersat water (i.e., 54% dissolution with an uncertainty of 13 to 66%) (Fig. 5B). When the integrated value is normalized with respect to the mass of water in a unit of micromoles per kilogram per year, the supersat dissolution is two times larger than the global average (Fig. 5C), highlighting the importance of biological controls of CaCO₃ dissolution. Despite the global and regional significance in total CaCO₃ dissolution (Fig. 5 and fig. S8), the alkalinity regenerated from the supersat dissolution (also known as excess alkalinity) is only up to 15 μeq kg⁻¹ and mainly confined in the upper ocean (Fig. 6C) that has relatively short residence time in the ocean’s interior. The magnitudes of the regenerated alkalinity are comparable with the model observation misfits (fig. S2). This renders a relatively weak constraint over the upper ocean dissolution, explaining the large uncertainty for the estimated shallow CaCO₃ dissolution (Figs. 2C; 3, B and D; and 5; and figs. S5 and S6). Because the supersat dissolution mostly occurs in upper waters below highly productive and upwelling-dominated surfaces (Fig. 2 and fig. S4), an important portion of the regenerated alkalinity would be entrained back to the surface and recycled within the upper ocean with quick turnover timescales, leaving only little imprints on subsurface alkalinity locally. Another portion of the regenerated alkalinity is transported to the equator where the convergence of global thermocline water results in an accumulation of regenerated alkalinity. Because CaCO₃ dissolution increases alkalinity twice as much as an increase of DIC, the CaCO₃ dissolution within the supersaturated water has a net effect of up to 6% increases in the CO₂ buffer capacity of the thermocline water (fig. S9).

The effects of CaCO₃ dissolution in the midsat and undersat zones, constituting 29% (with an uncertainty of 24 to 58%) and 17% (an uncertainty of 11 to 29%) of total dissolution in the ocean interior (Fig. 5B), respectively, are different from that of the supersat dissolution. Much longer residence times of deep waters allow regenerated DIC and alkalinity to accumulate over longer time periods, elevating alkalinity by up to 50 μeq kg⁻¹ for the midsat dissolution and 60 μeq kg⁻¹ for undersat dissolution (Fig. 6, D and E). Coupled with the slow deep ocean overturning circulations from the North Atlantic to the Southern Ocean, and to the deep Pacific, dissolutions in the midsat and undersat waters are responsible for the large lateral gradients of alkalinity from relatively young deep Atlantic to old deep Pacific waters. Because of the strong imprints on the large-scale distributions of alkalinity and CaCO₃ burial fluxes, the deep ocean CaCO₃ dissolution is relatively well constrained in this study, as reflected by relatively smaller uncertainty ranges for the estimated deep ocean dissolution rates (Fig. 5). Figure 6 (D and E) also show that non-negligible portions of the alkalinity regenerated from the deep ocean CaCO₃ dissolutions intrude the supersat domain through mixing, as suggested by (30). The alkalinity regenerated from the midsat and undersat dissolution contributes to up to 10% of the buffer capacity by mid-depth (1 to 2 km) and deep (3 to 4 km) waters, respectively (fig. S9). The maximum effect of the midsat dissolution is found at mid-depth around ~1500 m in the equatorial Pacific and Indian oceans where a substantial amount of CaCO₃ dissolution occurs in the mid-depth aragonite undersaturated water (figs. S4 and S8). On the other hand, the maximum effect of the undersat dissolution is found in the deep North Pacific at depths of ~3500 m where both local dissolution and cumulative effects of remote CaCO₃ dissolution contribute to the maximum effects on alkalinity and the CO₂ buffer factor.

DISCUSSION

Our results reveal a previously overlooked sensitivity of upper-ocean CaCO₃ dissolution and air-sea CO₂ exchange to organic carbon respiration. We estimated that a global average of 37% (with an uncertainty of 5 to 52%) of the CaCO₃ exported from the euphotic zone is dissolved within the upper 300 m, an upper layer of the ocean’s twilight zone where most heterotrophic respiration of sinking POC occurs. The fraction at which the surface exported CaCO₃ is dissolved (i.e., dissolution efficiency) within the upper 300 m is highly variable in space, which is explicitly tied to the export and remineralization of POC in the ocean’s upper twilight zone. This important portion of CaCO₃ dissolution has been neglected in previous global-scale assessments, which either focus on the ocean below 300 m or use observed tracer distributions alone as constraints (16, 19, 44). Our estimated shallow CaCO₃ dissolution is only loosely constrained by the observed alkalinity distributions and sedimentary burial fluxes. The weak constraint is reflected by the large error bars for the shallow dissolution (Figs. 2C; 3, B and D; and 5; and figs. S5 and S6) which encompass model solutions with no dependency on POC remineralization (i.e., near zero slopes inferred from Fig. 3, B and D), possibly reconciling this study with previous global-scale estimates.

On the other hand, the data from sediment traps (15, 20, 32, 33) and large-volume pumps (34–36) indicate that the connection between the vertical attenuations in POC and CaCO₃ fluxes (or concentrations) within the upper twilight zone might be more robust than our conservative estimate, leaning toward the upper limit of the uncertainty range (i.e., the steepest slopes inferred from Fig. 3, B and D). The optimal solution in our model is obtained using a linear dependency of the CaCO₃ dissolution efficiency on POC remineralization rates with a slope and an intercept determined by the model formulation and optimization (see Materials and Methods). Despite the qualitative agreements, however, there exist large quantitative disparities in the relationships of POC export (and remineralization) versus CaCO₃ dissolution efficiency between our model- and observation-based estimates. Part of the differences could be due to the spatial and temporal biases in the flux/concentration measurements and the model uncertainty. The large uncertainties in the observations and in our diagnostic model hamper us from providing a conclusive guideline for the model implementation of the organic carbon respiration control of shallow CaCO₃ dissolution. As proven useful in this study, better spatial and temporal coverages of sediment trap and particle concentration data deployed at shallow depths would certainly help better constrain the global ocean CaCO₃ cycle and its drivers.

The factors responsible for the biogenic dissolution of sinking CaCO₃ in the supersaturated upper water beneath the highly productive surface ocean are still not clearly understood. As constrained in this study, the CaCO₃ to POC molar ratio in the exported particles from the euphotic zone tends to be lower in subpolar eutrophic regions compared to low-latitude oligotrophic regions (fig. S3), indicating that sinking aggregates contain more organic carbon per unit CaCO₃ under eutrophic regions. The disproportionately larger amount of organic carbon associated with sinking CaCO₃ would promote higher rates of respiration-driven dissolution under the eutrophic surface. Moreover, it is also likely that sinking organic carbon under the eutrophic surface is more labile and susceptible to biologically mediated grazing than that under the oligotrophic surface (48), the latter which is known to host the microbial community that produces more recalcitrant forms of organic matter (49). Disproportionately larger fractions of labile POC or simply larger bulk POC fluxes within the twilight zone below the highly productive surface might attract more heterotrophic respiration, creating corrosive microenvironments for CaCO₃ dissolution. The role of heterotrophic respiration in driving CaCO₃ dissolution could be effective in slowly sinking particles (34, 50) produced through zooplankton-mediated fragmentation and egestion processes under the eutrophic surface (51). The positive correlation between the vertical POC attenuation and the CaCO₃ attenuation efficiency shown in Fig. 4 is dominated by small (1 to 53 μm) size classes where the majority of suspended POC and CaCO₃ exist (34). This implies coccolith calcite and potentially other small biogenically produced carbonates as the dominant substrate for shallow dissolution, whereas larger organisms such as pteropods and foraminifera sink very quickly due to their large size (34). All these potential drivers emphasize the complex interplay between twilight zone biogeochemical processes and upper ocean CaCO₃ dissolution.

The dissolution of CaCO₃ in shallow waters carries notable implications for the ocean’s role in regulating atmospheric CO₂. When the regenerated alkalinity from the supersat dissolution is upwelled to the surface, the excess alkalinity can increase the surface water’s CO₂ buffer capacity regionally by up to 5% (Fig. 7B). This implies a reduction of natural CO₂ efflux through the low-latitude upwelling regions (Fig. 7C)—the largest areas of natural CO₂ outgassing in the contemporary climate (52). If the supersat dissolution did not occur, then the CO₂ outgassing across the global ocean’s 30°S to 30°N band would increase by 20% (a net efflux of 1.0 Pg C year⁻¹ with the supersat dissolution versus a net efflux of 1.2 Pg C year⁻¹ without the supersat dissolution). This difference in magnitude is comparable to the variability in the equatorial Pacific air-sea CO₂ exchange induced by the El Niño Southern Oscillation, which ranges from 20 to 70%, despite differing drivers (physical versus biological) and timescales (interannual versus a broader spectrum dependent on ecological responses to climate/environmental change).

Should the same controls influencing the spatial patterns of CaCO₃ dissolution also apply to temporal sensitivity or future climate conditions, a matter requiring validation in future studies, our findings suggest that upper ocean CaCO₃ dissolution may not be as responsive to ocean acidification as previously believed. Instead, the response of upper ocean CaCO₃ dissolution and the associated change in the ocean’s CO₂ buffer capacity would be more influenced by organic carbon export and respiration within the twilight zone. This interplay of CaCO₃ dissolution and its subsequent burial into marine sediments introduces a previously unrecognized feedback loop in Earth system models, with far-reaching impacts on marine ecosystems, the global carbon cycle, and climate change.

MATERIALS AND METHODS

Experimental design

We aim to constrain the global ocean patterns of CaCO₃ export, dissolution, and burial fluxes into marine sediments and their primary drivers using a numerical model. To this end, we optimized the model parameters representing CaCO₃ cycling against multiple observational datasets. To support the biogenic control of CaCO₃ dissolution in the upper 300 m, we also analyzed the global compilations of sediment trap data and particle concentration data, both of which are not used to optimize the model and hence provide independent constraints on CaCO₃ cycles. Using the constrained numerical model, we performed sensitivity experiments to attribute the simulated tracer distributions and oceanic CO₂ uptake to the CaCO₃ dissolution in distinct ocean domains characterized by different saturation states with respect to CaCO₃ minerals.

Analyses of CaCO₃ and POC flux and concentration data

We used the particle flux data based on sediment traps (15, 20, 32, 33) and the particle concentration data based on large-volume pumps (36) to estimate the vertical attenuation of the flux and concentrations within the upper 300 m. For the sediment trap data, we assumed that a trap depth closest to the sea surface corresponds to the base of the euphotic zone, which varies from 50 to 150 m depending on the stations. To represent the flux below the euphotic zone, we took or averaged the data points located between 151 and 300 m. A difference between the two data points (one above 151 m and the other below 150 m) is used to estimate the dissolution fraction of CaCO₃ flux and the remineralization of POC within the top 300 m. We excluded the sediment trap data where the CaCO₃ export from the euphotic zone is very small (<1 g C m⁻² year⁻¹) or the dissolution fractions are negative.

For the particle concentration data (36), we subsampled the data within the upper 300 m where both CaCO₃ and POC concentrations (in both small and large size classes) have the data quality flag of “0,” indicating the best quality control. This criterion screens out most of the data presented in (34), giving us only the data collected along the eastern equatorial Pacific (35). We combined the small (1 to 53 μm) and large (>53 μm) size classes to represent the CaCO₃ and POC concentrations. For each vertical profile, a maximum CaCO₃ concentration and a minimum CaCO₃ concentration, the latter located below a depth of the maximum value, are taken to estimate the vertical CaCO₃ attenuation fraction. The POC attenuation is estimated using POC concentrations at the corresponding depths. This approach helps us link the strongest vertical CaCO₃ attenuation with the associated POC attenuation while minimizing potential biases from vertical sampling. We excluded the data where the vertical attenuations of CaCO₃ or POC concentrations are negative.

Ocean biogeochemistry model

The model uses a steady-state global ocean circulation inverse model (23) that is optimally consistent with observed ocean temperatures, salinity, CFC-11, and deep ocean natural radiocarbon. The horizontal resolution of the model is 2° × 2°, and the vertical grid size increases with depth from 36 m near the surface to 633 m near the bottom with a total of 24 layers. The model has prognostic tracers of phosphate, alkalinity, DIC, and semi-labile and refractory dissolved organic phosphorus and DOC. The model parameters controlling the export and remineralization of organic carbon and organic phosphorus were previously optimized against the global ocean databases of phosphate, dissolved organic phosphorus, DOC, and DIC (37). Built upon the already optimized organic carbon cycle model, in this study, we further elaborated the model formulations and parameterizations representing the export, dissolution, and burial fluxes of CaCO₃, and optimized the model parameters against the observed alkalinity and CaCO₃ burial fluxes into marine sediments. Below, we briefly review the relevant model formulations representing organic carbon cycling and describe the added formulations for the CaCO₃ cycle.

The governing equations for alkalinity (ALK) and DIC are the following

$$\begin{array}{c}\frac{\mathrm{\partial }[\text{ALK}]}{\mathrm{\partial }t}+U·\nabla [\text{ALK}]-\nabla (K\nabla [\text{ALK}])=\hfill \\ {\mathit{Jb}}_{\text{ALK}}+{\mathit{Jt}}_{\text{ALK}}+{\mathit{Jl}}_{\text{ALK}}+J{v}_{\text{ALK}}\hfill \end{array}$$ (1)

and

$$\begin{array}{c}\frac{\mathrm{\partial }\left[\text{DIC}\right]}{\mathrm{\partial }t}+U·\nabla \left[\text{DIC}\right]-\nabla (K\nabla \left[\text{DIC}\right])=\hfill \\ {\mathit{Jb}}_{\text{DIC}}+{\mathit{Jt}}_{\text{DIC}}+{\mathit{Jl}}_{\text{DIC}}+J{v}_{\text{DIC}}+J{g}_{\text{DIC}}\hfill \end{array}$$ (2)

where the three terms on the left-hand side represent the time rates of change in tracer concentrations, and the advective and mixing effects on tracer concentrations. The terms on the right-hand side represent the biological sources and sinks (Jb), the terrestrial inputs to the ocean (Jt), the sedimentary burial loss (Jl), the concentrating and diluting effect due to evaporation and rainfalls (Jv), and the air-sea gas exchange (Jg). We refer readers to (37) for the descriptions of the Jv and Jg terms, and here, we mainly describe Jb, Jt, and Jl terms.

The net community production of organic carbon is formulated on the basis of the satellite-based estimates for NPP as

$$\text{prodC}=\mathrm{\alpha }\frac{{\left(\text{NPP}\right)}^{\mathrm{\beta }}}{{\left[{\text{PO}}_4\right]}_{\text{obs}}·Z_{\text{eu}}}{\left[{\text{PO}}_4\right]}_{\text{mod}}$$ (3)

where NPP is the satellite-based estimate for the column-integrated net primary production from (24, 25) in moles of C m⁻² s⁻¹. Z_eu is the thickness of the euphotic layer that varies from 73 m in eutrophic regions to 114 m in oligotrophic and highly convective high-latitude regions. [PO₄]_obs and [PO₄]_mod are the observed and modeled phosphate concentrations, respectively, the former taken from the World Ocean Atlas (53). The ratio of the two can modulate the satellite-based NPP to yield the spatial pattern of net community production (e.g., more production in regions where upwelling increases the ratio of modeled PO₄ to observed PO₄ at the sea surface). Globally uniform values for the two parameters α and β were optimized for the two NPP products separately with the estimates for one NPP presented in table S1 and the estimates for the other NPP presented in (37). The export of POC out of the euphotic zone at a horizontal location r [termed as F_POC(z_eu, r)] is scaled with the net community production with the scaling factor that depends linearly on the euphotic zone temperature. The remaining portion of the net community production is transported as DOC by ocean circulations. The exported POC is assumed to be remineralized instantaneously while sinking. The vertical attenuation profile for downward POC fluxes at r follows Martin’s power law curve with the exponent linearly scaled with temperatures at 200 m [T₂₀₀(r)] as

$$F_{\text{POC}}(z_n,\mathbf{\text{r}})=F_{\text{POC}}(z_{\text{eu}},\mathbf{\text{r}})·{\left(\frac{z_n}{z_{\text{eu}}}\right)}^{-b_C\left(\mathbf{\text{r}}\right)}$$ (4)

where z_n is the depth of the nth grid cell, which is positive and increases downward. The exponent is formulated as b_C(r) = δ_C · T₂₀₀(r) + γ_C in which δ_C and γ_C were optimized (table S1). The temperature at a depth of 200 m is chosen to represent temperatures (an important environmental factor controlling biological respiration) in the upper twilight zone. b_C is constrained to range from 0.8 in warm subtropical thermocline to 1.0 in cold high-latitude thermocline, possibly reflecting greater lability and grazing of sinking POC in eutrophic waters. Yet, the spatial differences are not statistically significant and depend on the NPP product (37).

Similar to POC, CaCO₃ is not an explicit tracer in our model, and hence, its biogenic export and dissolution are implicitly represented through downward flux attenuation. The biological sources and sinks for alkalinity are expressed as

$${\mathit{Jb}}_{\text{ALK}}=2{\mathit{Jb}}_{\text{Ca}}-{\mathit{Jb}}_{\text{NO}3}-5.8{\mathit{Jb}}_{\text{PO}4}$$ (5)

where Jb_Ca represents the alkalinity sources and sinks due to biogenic CaCO₃ cycles, Jb_NO3 due to biogenic NO₃ cycles, and Jb_PO4 due to biogenic PO₄ cycles. The factor of two in Jb_Ca arises from two moles of alkalinity equivalents consumed and released when a mole of CaCO₃ is produced and dissolved, respectively. The factor of −5.8 (−1 − 2 × 2.4) in Jb_PO4 comes from the assumption that a globally uniform stoichiometric ratio of S:P is 2.4 and that two moles of alkalinity equivalents are released and consumed when a mole of SO₄ is produced and remineralized (29). Although NO₃ is not a major tracer simulated in our model, its biogenic sources and sinks (Jb_NO3) affect alkalinity as shown in Eq. 5. Hence, we linearly scaled the production of organic nitrogen with that of organic carbon using a spatially varying stoichiometric ratio of phytoplankton N:C ratio of rN:C = 125‰ + 30‰ × [NO₃]_eu/(0.32 μmol kg⁻¹ + [NO₃]_eu) where [NO₃]_eu is the observed NO₃ in the euphotic zone (54). We also assumed that the remineralization profile for particulate organic nitrogen and the e-folding timescale for dissolved organic nitrogen remineralization are equal to those of organic carbon. Our Jb_NO3 term also includes the effects of additional nitrogen sources and sinks due to nitrification and denitrification, taken from (28). Hence, the biological source and sink term for NO₃ is Jb_NO3 = rN:C·Jb_oc + nitrification + airborne NO₃ inputs – water column and sediment denitrification (29), where Jb_oc represents biological sources and sinks of organic carbon. Jb_DIC is the sum of Jb_oc and Jb_Ca.

The Jb_Ca term constitutes the export of CaCO₃ from the euphotic zone and dissolution throughout the water column and in sediments. The export of CaCO₃ from the euphotic zone is proportional to the export of POC with a ratio that depends on the saturation state of surface water (4, 5). We used the following two formulations for the CaCO₃ export ratio at the base of the euphotic layer: (i) The export ratio of CaCO₃ to POC is linearly scaled with the saturation state of water with respect to calcite as

$$F_{\text{Ca}}(z_{\text{eu}},\mathbf{r})=[\mathit{Al}·{\mathrm{\Omega }}^C(z_{\text{eu}},\mathbf{r})+\mathit{Bl}]·F_{\text{POC}}(z_{\text{eu}},\mathbf{r})$$ (6)

where Ω^C(z_eu, r) is the saturation state with respect to calcite in the euphotic zone, taken from the Global Ocean Data Analysis Project (GLODAP) version 2 (21). The globally uniform parameters Al and Bl are optimized in this study (table S1). (ii) The CaCO₃ export ratio follows a Michaelis-Menten equation of the saturated state as

$$F_{\text{Ca}}(z_{\text{eu}},\mathbf{r})=\mathit{Am}·\frac{[{\mathrm{\Omega }}^C(z_{\text{eu}},\mathbf{r})-1]}{\mathit{Bm}+[{\mathrm{\Omega }}^C(z_{\text{eu}},\mathbf{r})-1]}·F_{\text{POC}}(z_{\text{eu}},\mathbf{r})$$ (7)

a formulation similar to that used in (55). The maximum value of the export ratio Am and a half-saturation constant Bm are globally uniform and optimized in this study. The divergence of sinking CaCO₃ fluxes (i.e., water column dissolution) is formulated with a first-order rate constant dissf that is horizontally and vertically varying as

$$\frac{F_{\text{Ca}}(z_n,\mathbf{r})-F_{\text{Ca}}(z_{n-1},\mathbf{r})}{z_n-z_{n-1}}=-\mathit{\text{dissf}}(z_n,\mathbf{r})·F_{\text{Ca}}(z_{n-1},\mathbf{r})$$ (8)

where F_Ca(z_n, r) is a downward CaCO₃ flux exiting the nth grid cell, F_Ca(z_n−1, r) is equivalent to a CaCO₃ flux entering the nth grid cell. The rate constant dissf is a dissolution constant normalized with respect to the CaCO₃ flux from above (in m⁻¹) and can be interpreted as the dissolution rate normalized with respect to the mass of CaCO₃ (in a unit of g g⁻¹ day⁻¹) divided by the sinking velocity of CaCO₃ (in a unit of m day⁻¹). When dissf(z_n, r) is set to zero, none of the CaCO₃ dissolves in the grid cell and all CaCO₃ passes to the next grid cell. A globally uniform value of dissf would yield an exponentially decaying profile of downward CaCO₃ fluxes, which was adopted in the simple Ocean Carbon-Cycle Model Intercomparison Project protocol (56).

Here, we formulated the dissolution constant dissf as

$$\begin{array}{c}\mathit{\text{dissf}}(z_n,\mathbf{r})=\hfill \\ \frac{C·\text{max}{[0,1-{\mathrm{\Omega }}^C(z_n,\mathbf{r})]}^{2.2}+D·\text{max}{[0,1-{\mathrm{\Omega }}^A(z_n,\mathbf{r})]}^{1.5}+E·R_{\text{POC}}{(z_n,\mathit{r})}^G}{\mathit{\text{vel}}}+H\hfill \end{array}$$ (9)

where Ω^C (z_n, r) is the saturation state with respect to calcite at a grid cell, Ω^A (z_n, r) is the saturation state with aragonite. The exponents 2.2 and 1.5 are from field- or lab-based studies (15, 57) and were adopted in a previous modeling study (19). The use of 4.7 (58) instead of 2.2 as an exponent of [1 − Ω^C (z_n, r)] does not make discernible differences in our conclusion, and the optimal solutions using an exponent of 4.7 are incorporated into our uncertainty range. The previously reported values for C and D (units of g g⁻¹ day⁻¹ have large spreads with more than an order of magnitude differences) (15, 57, 58). Hence, we chose to optimize C and D (table S1). The sinking velocity of CaCO₃ particles, vel, is in nature determined by the size and density of sinking particles as well as the viscosity of seawater. Previous studies reported the sinking velocity of CaCO₃ ranging from <10 to >150 m day⁻¹ (50). We assumed that the sinking velocity is a second-order polynomial function of depth as

$$\mathit{\text{vel}}=\text{min}(\mathit{vm},v\mathit{1}·{z_n}^2+v\mathit{2}·z_n+v\mathit{3})$$ (10)

where vm is a threshold close to zero, needed to avoid zero or negative sinking velocity, and the coefficients v1, v2, and v3 are optimized. Our optimization yields the v1, v2, and v3 values such that vel is converged to a threshold of vm, possibly due to dominant controls of the other terms in Eq. 9 on the CaCO₃ dissolution constant. Hence, we only report the prescribed vm value in table S1. For the respiration control of CaCO₃ dissolution, we explored the following two formulations: (iii) R_poc is a function of the remineralization rate of POC at a grid cell that is nondimensionalized with an arbitrary constant R_iii (in mol m⁻³ s⁻¹) as

$$R_{\text{poc}}(z_n,\mathbf{r})=\left[-\frac{F_{\text{POC}}(z_n,\mathbf{r})-F_{\text{POC}}(z_{n-1},\mathbf{r})}{z_n-z_{n-1}}\right]·{R_{\text{iii}}}^{-1}$$ (11)

(iv) R_poc is a function of the remineralization rate of POC normalized with respect to POC flux from above that is nondimensionalized with an arbitrary constant R_iv (in m⁻¹) as

$$R_{\text{poc}}(z_n,\mathbf{r})=\left[-\frac{F_{\text{POC}}(z_n,\mathbf{r})-F_{\text{POC}}(z_{n-1},\mathbf{r})}{z_n-z_{n-1}}\right]·\frac{1}{F_{\text{POC}}(z_{n-1},\mathbf{r})}·{R_{\text{iv}}}^{-1}$$ (12)

The scaling factor E (a unit of day⁻¹) and the exponent G (unitless) are globally uniform parameters to be optimized (table S1). The formulation (iii) would give a dissf pattern that is highly variable vertically and horizontally with higher values in the water where POC remineralization is strong. The formulation (iv), which is equivalent to b_C(r)_⋅(z_eu/z_n) _⋅R_iv⁻¹, would give a dissf pattern that is variable mainly vertically [i.e., due to a relatively smaller horizontal variation in b_C(r) than z_n⁻¹]. Because all POC fluxes reaching the bottom layer of the ocean model are assumed to be remineralized there [i.e., F_POC(z_bottom, r) = 0], both (iii) and (iv) would give two peaks vertically, the largest peak below the euphotic zone and a secondary peak at the bottom grid cell, the latter depending on bathymetry. The last term in Eq. 9, H (a unit of m⁻¹), is included to dampen the horizontal heterogeneity produced by the other terms in Eq. 9 if necessary.

The CaCO₃ flux exiting the bottom layer of the ocean model is partitioned into two: A fraction is added to the bottom grid cell representing dissolution in sediments and a remaining fraction is permanently removed from the water column. This removal rate becomes burial fluxes (B_Ca) in Jl_ALK and Jl_DIC in Eqs. 1 and 2 with a 2:1 ratio. The CaCO₃ burial flux at a given location is parameterized as

$$B_{\text{Ca}}(z_{\text{bottom}},\mathbf{r})=F_{\text{Ca}}(z_{\text{bottom}},\mathbf{r})·\mathit{\text{buryfrac}}\left(\mathbf{r}\right)$$ (13)

where F_Ca(z_bottom, r) is the CaCO₃ flux exiting the bottom layer of the ocean. The fraction of burial [buryfrac (r)] is assumed to be linearly scaled with the global patterns of the saturation state with respect to calcite, dissolved O₂ concentrations [O2 where the observed O₂ (in μmol kg⁻¹) is taken from the World Ocean Atlas (59)], and the respiration rate of POC (R_POC in Eq. 11) at the bottom grid cells of the ocean as

$$\begin{array}{c}\text{buryfrac}\left(\mathbf{r}\right)=I·\text{max}{[0,1-{\mathrm{\Omega }}^C(z_{\text{bottom}},\mathbf{r})]}^{\text{2.2}}+\hfill \\ J·\mathrm{O}2(z_{\text{bottom}},\mathbf{r})+K·R_{\text{POC}}(z_{\text{bottom}},\mathbf{r})+M\hfill \end{array}$$ (14)

The globally uniform parameters, I, J, K, and a constant M are optimized along with other parameters (table S1). We do not distinguish the dissolved CaCO₃ in the water column from that in sediments when discussing the results due to the uncertainty in model bathymetry and our simple representation of sedimentary dissolution.

The terrestrial alkalinity source (Jt_ALK) includes riverine and non-riverine inputs, the latter of which is estimated in this study. The terrestrial alkalinity fluxes are set to be equal to the terrestrial DIC fluxes given that terrestrial DIC fluxes are mostly in the form of HCO₃⁻ (60). The riverine DIC fluxes are prescribed on the basis of the GEMS-GLORI database (27, 61) and integrated globally to 0.30 Pg C year⁻¹ (61). To address the uncertainty in the prescribed riverine DIC inputs, and to include additional sources from coastal sediments and aquifers (62), we added a spatially uniform flux of DIC at the sea surface around the global coastlines except Antarctica. Assuming a steady-state condition for the preindustrial times, the terrestrial alkalinity sources need to be balanced by the alkalinity burial sink from the downward CaCO₃ fluxes. For this, the magnitude of the non-riverine alkalinity source is estimated such that the globally integrated terrestrial alkalinity source is precisely balanced by the burial fluxes of alkalinity described above. The terrestrial carbon inputs (Jt_DIC) include the inorganic (= Jt_ALK) and organic forms, the latter prescribed using (26, 63) with a global integral of 0.31 Pg C year⁻¹ [see (61) for details of the prescribed riverine and air-bourn inputs of terrestrial carbon].

Optimization experiments

We optimized the model parameters (table S1) simultaneously using FMINSEARCH in MATLAB, which uses the unconstrained Nelder-Mead simplex direct search method (64). We did not impose any constraints on the signs or ranges of the model parameters so that they are all freely determined by the optimization algorithm. The cost function to be minimized is set as

$$\begin{array}{c}\text{CF}=\frac{\sum \text{Vol}(z_n,\mathbf{r})·{[\text{ALK}{(z_n,\mathbf{r})}^{\text{mod}}-\text{ALK}(z_n,\mathbf{r}{)}^{\mathrm{obs}}]}^2}{\sum \text{Vol}(z_n,\mathbf{r})·{[\text{ALK}{(z_n,\mathbf{r})}^{\text{obs}}-⟨\text{ALK}{(z_n,\mathbf{r})}^{\text{obs}}⟩]}^2}+\hfill \\ \frac{\sum \text{Vol}(z_n,\mathbf{r})·[\text{DIC}{(z_n,\mathbf{r})}^{\text{mod}}-\text{DIC}(z_n,\mathbf{r}{)}^{\mathrm{obs}}{]}^2}{\sum \text{Vol}(z_n,\mathbf{r})·{[\text{DIC}{(z_n,\mathbf{r})}^{\text{obs}}-⟨\text{DIC}{(z_n,\mathbf{r})}^{\text{obs}}⟩]}^2}+\hfill \\ \frac{\sum \text{Area}(z_{\text{bottom}},\mathbf{r})·{[B_{\mathit{Ca}}{(z_{\text{bottom}},\mathbf{r})}^{\text{mod}}-B_{\text{Ca}}(z_{\text{bottom}},\mathbf{r}{)}^{\mathrm{obs}}]}^2}{\sum \text{Area}(z_{\text{bottom}},\mathbf{r})·{[B_{\mathit{Ca}}{(z_{\text{bottom}},\mathbf{r})}^{\text{obs}}-⟨B_{\text{Ca}}{(z_{\text{bottom}},\mathbf{r})}^{\text{obs}}⟩]}^2}\hfill \end{array}$$ (15)

where Vol(z_n, r) is a grid-cell volume, Area(z_bottom, r) is a horizontal area, the angle brackets represent the volume- or area-weighted global averages, and the superscripts mod and obs indicate modeled and observed fields. The alkalinity (ALK) and DIC observations are from the GLODAPv2 dataset (21) and the observed CaCO₃ burial rates (B_Ca) are from (22). The global datasets are regridded to match the model grid cells (figs. S1 and S2). The estimated distribution of anthropogenic DIC is added to the simulated preindustrial DIC for comparison with observed DIC (37). We assumed that the present-day distribution of ocean alkalinity and CaCO₃ cycles remain fixed at the preindustrial values.

We performed two sets of optimization experiments with one set using the NPP estimate of (24) and the other set using the NPP estimate of (25). For each set, four experiments are performed using either one of the formulations for F_Ca(z_eu, r) (Eq. 5 or Eq. 6) and dissf (z_n, r) (using Eq. 11 or Eq. 12). Of the total eight experiments, the best estimate is chosen from the optimal solution of the best model configuration that yields the minimum value of the cost function. The configuration using the NPP estimate of (25) and Eqs. 5 and 11 turns out to yield the best solution after optimization, although other configurations also yield solutions that fall within the uncertainty range. For the uncertainty estimation, we aggregate all the optimization results that use the NPP estimate of (25) and apply the criterion of an averaged 1.0% increase in the unexplained variance of alkalinity, DIC, and CaCO₃ burial rates relative to the minimum cost function (i.e., a 1.0%-point increase in the cost function). Thus, the uncertainty in model formulations (which is a dominant source of uncertainty than the use of different NPP products) is partly taken into consideration in our uncertainty estimation.

An optimal formulation for CaCO₃ dissolution

Here, we provide a formulation of CaCO₃ dissolution (both water column and sediments combined) that is optimal for the multiple datasets used in this study. Note that we do not intend to overinterpret individual terms and parameter values obtained in this study (table S1) because some terms are not independent of each other. Moreover, the formulations are meant to be diagnostic for the present-day climate. Nevertheless, it could be informative to describe the optimal formulations obtained in this study.

With our optimized parameter values (table S1), Eq. 8 becomes

$$\begin{array}{c}\frac{F_{\text{Ca}}(z_n,\mathbf{r})-F_{\text{Ca}}(z_{n-1},\mathbf{r})}{z_n-z_{n-1}}=\hfill \\ -\left\{\frac{0.15·\text{max}{[0,1-{\mathrm{\Omega }}^C(z_n,\mathbf{r})]}^{2.2}+0.009·\text{max}{[0,1-{\mathrm{\Omega }}^A(z_n,\mathbf{r})]}^{1.5}+0.46·R_{\text{POC}}(z_n,\mathbf{r})}{10}\right\}\hfill \\ ·F_{\text{Ca}}(z_{n-1},\mathbf{r})\hfill \end{array}$$ (16)

where the optimized constant of H = 0.0002 (in m⁻¹) is neglected from Eq. 9 due to its relatively minor contribution. By scaling our optimized values of C = 0.15 and D = 0.009 to C = 0.50 g g⁻¹ day⁻¹ and D = 0.028 g g⁻¹ day⁻¹, the values previously used in a global ocean modeling study (19) based on (15, 57, 58), the inferred sinking velocity of CaCO₃ particles can be scaled from 10 to approximately 30 m day⁻¹, which falls into a reasonable range reported in (50). Note however that the large uncertainty in the thermodynamic rate constants (15, 57, 58) would be directly propagated into an uncertainty in the inferred CaCO₃ sinking velocity in this case.

Equation 16 provides further insight into the relationship between the CaCO₃ dissolution efficiency and POC remineralization rates in the upper twilight zone where Ω^C and Ω^A are greater than 1 in the majority of the global ocean. The dissolution fraction within the upper 300 m can be approximated as

$$\frac{F_{\text{Ca}}(z_{\text{eu}},\mathbf{r})-F_{\text{Ca}}(300,\mathbf{r})}{F_{\text{Ca}}(z_{\text{eu}},\mathbf{r})}=0.012·\langle R_{\text{POC}}(z_{\text{eu}~300},\mathbf{r})\rangle \prime ·(300-Z_{\text{eu}})$$ (17)

where Z_eu is either 73 or 114 m in our model, which gives rise to two distinct slopes in Fig. 3 (B and D). 〈R_POC(z_eu~300, r)〉′ is the POC remineralization rate averaged from the base of the euphotic zone to a depth of 300 m and now expressed in a unit of g C m⁻³ year⁻¹ with a scaled coefficient of 0.012 [with a unit of m² year (g C)⁻¹]. This implies a 12% increase in CaCO₃ dissolution fraction when the exported POC increases by 10 g C m⁻² year⁻¹ or a 12% increase in CaCO₃ dissolution fraction when the average POC remineralization rate increases by 0.05 g C m⁻³ year⁻¹, which approximate the slopes of the gray dots shown in Fig. 3 (B and D). The intercepts of gray dots in Fig. 3 (B and D) are equal to H ∙ (300 − Z_eu).

Although it is not a primary focus in this study, we also briefly describe the optimized fraction at which the CaCO₃ flux exiting the bottom grid cells of the ocean is buried (buryfrac in Eq. 14). The fraction increases from 50% in the shallow regions of the North Pacific and Indian Oceans to 100% in the majority of the Atlantic Ocean. The resulting CaCO₃ dissolution in fig. S4 and the burial flux in fig. S1 result collectively from the optimized model formulations described here.

Diagnosing regenerated DIC and alkalinity due to CaCO₃ dissolution

On the basis of the optimal model configuration and parameter values, we diagnosed the distributions of alkalinity and DIC that are regenerated from CaCO₃ dissolution in three distinct saturation zones (the undersat, midsat, and supersat zones) (Fig. 6B). This diagnostic has been useful because alkalinity concentration at a given grid cell is the superposition of preformed and regenerated components, the former defined as the alkalinity transported from the sea surface by ocean circulation and the latter defined as the alkalinity added by CaCO₃ dissolution. The regenerated component of alkalinity is again the superposition of the effects of CaCO₃ dissolution at different grid cells. For clarity in our analyses and interpretation, we first turned off the Jb_NO3 and Jb_PO4 terms in Eq. 5 while keeping the other terms and parameterizations fixed at those for the optimal solution. A steady-state solution from this modified model configuration is named “Ex_all.” Then, we performed the following model experiments based on the Ex_all configuration.

In the “Ex_No_undersat” experiment, we turned off the CaCO₃ dissolution (i.e., dissf = 0 and buryfrac = 1) in the undersat zone, while CaCO₃ dissolution is allowed to occur in the supersat and midsat zones. In the “Ex_No_under_midsat” experiment, we turned off the CaCO₃ dissolution in the undersat and midsat zones, while CaCO₃ dissolution is allowed to occur in the supersat zone. In the “Ex_No_diss” experiment, we turned off the CaCO₃ dissolution in all of the three saturation zones so that all of the CaCO₃ exported from the euphotic zone passed through the water column and was buried in sediments. In each experiment, we obtained steady-state solutions and subtracted the estimated preformed alkalinity from the simulated alkalinity to obtain the regenerated (i.e., excess) alkalinity from CaCO₃ dissolution, which is equivalent to two times regenerated DIC, following the approach of (65).

The difference in regenerated alkalinity between the Ex_all and Ex_No_undersat experiments is attributed to the regenerated alkalinity originating from the CaCO₃ dissolution in the undersat zone. Likewise, the difference in regenerated alkalinity between the Ex_No_undersat and Ex_No_under_midsat experiments is attributed to the regenerated alkalinity originating from the CaCO₃ dissolution in the midsat zone. The difference in regenerated alkalinity between the Ex_No_under_midsat and Ex_No_diss experiments, the latter of which is confirmed to be zero everywhere, is attributed to the regenerated alkalinity originating from the CaCO₃ dissolution in the supersat zone. The resulting distributions of regenerated alkalinity and DIC are used to assess their effects on seawater buffer capacity of CO₂ as described below.

We estimated the CO₂ buffer capacity in the ocean’s interior by applying the simulated DIC and alkalinity obtained from the Ex_all experiment following the method of (66). To quantify the effects of the CaCO₃ dissolution in the three distinct zones on the buffer capacity, we first removed the respective regenerated components of DIC and alkalinity from the simulated DIC and alkalinity in the Ex_all experiment. The reconstructed DIC and alkalinity were then used to diagnose the CO₂ buffer capacity. The departure from the buffer capacity in the Ex_all experiment is regarded as the contribution from each zone CaCO₃ dissolution. This approach was necessary because the preformed components of DIC and alkalinity are unrealistic in the experiments where the water column CaCO₃ dissolutions were turned off. The suppression of CaCO₃ dissolution in each zone results in increasing the CaCO₃ removal rates into marine sediments, which in turn elevates the non-riverine inorganic carbon inputs to the ocean surface and the preformed concentrations in our steady-state model.

We further explored how the supersat CaCO₃ dissolution might influence the CO₂ buffer capacity and air-sea CO₂ exchange at the sea surface. For the Ex_all case, we simply used the simulated surface DIC and alkalinity to estimate the CO₂ buffer capacity and air-sea CO₂ fluxes using the preindustrial atmospheric CO₂ concentration of 280 ppm. To reconstruct the surface DIC and alkalinity fields that would be obtained if there were no CaCO₃ dissolution in the supersat zone, we first removed the contributions of the regenerated DIC and alkalinity from the DIC and alkalinity simulated in the Ex_all experiment. This reconstructed aphotic zone fields of DIC and alkalinity (without dissolution effects at the supersat zone) were then propagated to the euphotic zone as

$$\text{ALK}\left({\mathbf{r}}_{\text{eu}}\right)={\mathrm{\sum }}_{\mathbf{r}\mathrm{apho}\mathbf{}}\text{ALK}\left({\mathbf{r}}_{\text{apho}}\right)·{\mathrm{f}}_{\mathbf{r}\text{apho}}\left({\mathbf{r}}_{\text{eu}}\right)$$ (18)

and

$$\text{DIC}\left({\mathbf{r}}_{\text{eu}}\right)={\mathrm{\sum }}_{\mathbf{r}\mathrm{apho}}\text{DIC}\left({\mathbf{r}}_{\text{apho}}\right)·{\mathrm{f}}_{\mathbf{r}\mathrm{apho}}\left({\mathbf{r}}_{\text{eu}}\right)$$ (19)

where r_eu is a grid point within the euphotic zone in a three-dimensional space, r_apho is a grid point within the aphotic zone in a three-dimensional space, f_rapho(r_eu) is a propagator based on the steady-state ocean circulation field denoting the volume mixing ratio of water at r_eu that was transported from r_apho (67). This approach is the same as the one we used to compute the preformed alkalinity except that the direction is reversed from the aphotic zone to the euphotic zone. The estimated euphotic zone DIC and alkalinity were then vertically averaged to compute the CO₂ buffer capacity at the sea surface and air-sea CO₂ exchange in the absence of the CaCO₃ dissolution in the supersat zone. The potential contributions from the supersat dissolution to the surface water CO₂ buffer capacity and air-sea CO₂ exchange are then estimated by taking differences from the corresponding estimates based on the Ex_all experiment.

Supplementary Materials

This PDF file includes:

Figs. S1 to S9

Table S1