Introduction

Over the past 40 years, the ocean has played a crucial role, absorbing 25% of anthropogenic carbon emissions1. This absorption has effectively slowed the growth of atmospheric carbon dioxide (CO2). However, this absorption has also increased seawater dissolved inorganic carbon (DIC), decreased pH, leading to ocean acidification, particularly impacting aragonite and calcite organisms2.

Traditionally, researchers have used aragonite saturation (Ωarag) to assess the impacts of ocean acidification on the growth of shellfish and other calcifying organisms. Thermodynamically, aragonite has a tendency to dissolve when Ωarag drops below the critical threshold Ωarag = 1 (Eq. 1)3. Some aragonite organisms exhibited a physiological negative response at Ωarag slightly above 14,5.

$${\varOmega }_{{arag}}=\frac{\left[{{Ca}}^{2+}\right]\left[{{CO}}_{3}^{2-}\right]}{{K}_{sp}}$$
(1)

Note: Ksp is the equilibrium constant for the dissolution of carbonate minerals.

In addition to the impact on calcifying organisms, there is concern about reducing seawater absorption capacity for CO2 due to acidification. The seawater absorption capacity for CO2 is defined as the increase in seawater DIC after CO2 is added to an equilibrium system and a new equilibrium is established. The carbonate equilibrium system primarily governs the seawater absorption capacity for CO2. It is influenced by various factors, including seawater temperature, salinity, biological activity, circulation transport, synthesis and degradation of organic matter, and crystallization and dissolution of calcium carbonate (Fig.1).

Fig. 1: Seawater carbon cycle.
figure 1

K0, K1, and K2 are Henry’s law constant for the dissolution of CO2, carbonate primary ionization constant, and carbonate secondary ionization constant. The model does not consider river and sediment inputs. Abbreviations in the figure include particulate inorganic carbon (PIC), dissolved inorganic carbon (DIC), particulate organic carbon (POC), and dissolved organic carbon (DOC). Seawater carbon cycling includes the Physical Solubility Pump, Carbonate Pump, and Biological Pump. The processes in the figure influence the seawater carbonate system, affecting its capacity to absorb CO2. Without the carbonate equilibrium, seawater would absorb about 1% of atmospheric CO2 through only physical dissolution10.

Full size image

Oceanographers have traditionally referred to seawater absorption capacity for CO2 as buffer capacity6,7,8, also known as the Revelle factor (RF). Since the absorption of CO2 by seawater does not alter its alkalinity (Alk), discussions of the RF typically assume a constant Alk9. The key to seawater absorption capacity for CO2 is Eq. 29,10, which enables seawater to enhance its CO2 absorption by about 15 times compared to pure physical absorption10. However, this seawater absorption capacity for CO2 is fundamentally limited, a concept first proposed by Roger Revelle11. Broecker proposed the RF (Eq. 3) based on seawater chemical equilibrium (Supplementary Method, Eqs. S1–S5) to measure the seawater CO2 Static Capacity12,13.

$${{\mbox{CO}}}_{2}+{{\mbox{CO}}}_{3}^{2-}+{{\mbox{H}}}_{2}{\mbox{O}}\leftrightarrow 2{{\mbox{HCO}}}_{3}^{-}$$
(2)
$$RF=\frac{\Delta p{{CO}}_{2}/p{{CO}}_{2}}{\Delta {DIC}/{DIC}}=\frac{\partial \,{ln}\,{{p}{CO}}_{2}}{\partial \,{ln}\,{DIC}}=\frac{{DIC}}{[{{CO}}_{2}]}\frac{\partial [{{CO}}_{2}]}{\partial {DIC}}$$
(3)

Note: pCO2 and [CO2] represent the partial pressure of CO2 and the concentration of CO2 (aq) in seawater, respectively. The equation is valid when ΔpCO2 is much smaller than pCO2, and ΔDIC is much smaller than DIC.

The RF measures the ratio of the relative change in pCO2 to the relative change in DIC12,14. It has been widely used in various oceanographic studies14,15,16 and models9,17,18 to assess the seawater sensitivity and absorption capacity for CO2. For example, a higher RF leads to a stronger pCO2 sensitivity to changes in surface temperature between ENSO phases7. Considering the RF into carbon sink models led to an increase of 9–11% in the estimated oceanic carbon sink while reducing the uncertainty by 42–59%15. The RF is higher in polar regions, indicating a lower capacity to absorb CO2 and buffer changes in pH6. Some researchers have proposed buffering factors similar to the RF9,19, such as γDIC, defined by Egleston9 (Eq. 4). DeVries proposed the concept of oceanic equilibrium carbon capacity (\({{{\mathcal{F}}}}\)) to evaluate the balance ratio between DIC and pCO214. A detailed discussion of these buffering factors can be found in the review by Middelburg et al.12.

$${{\gamma }_{{DIC}}=\left(\frac{\partial {ln}\left[{{CO}}_{2}\right]}{\partial {DIC}}\right)}^{-1}={\left(\frac{{\partial} \left[{{CO}}_{2}\right]}{\left[{{CO}}_{2}\right]\partial {DIC}}\right)}^{-1}={\left(\frac{\partial {{pCO}}_{2}}{{{pCO}}_{2}\partial {DIC}}\right)}^{-1}$$
(4)

Although the RF and its derived buffer indicators (e.g., γDIC) have been widely used to assess the seawater capacity to absorb and buffer CO2, their conceptual meaning and applicability remain debated. Conceptually, RF reflects “seawater static capacity of CO2” rather than its “acid-base buffering capacity” in the traditional chemical. However, RF is often confused with acid-base buffering as defined in analytical chemistry, leading to ambiguity in its interpretation and use. For instance, Middelburg12 and Egleston9 et al. noted that indicators such as RF and γDIC tend to reach their maximum or minimum values around pH = 7.5. They attempted to explain this pattern using “the minor species theory” from acid-base buffering theory.

Regarding applicability, it has been shown that RF is limited under certain environmental conditions. Takahashi et al. found that at high pCO2 and low pH, the relative changes in CO2 and DIC become similar, making RF a poor indicator of the buffer capacity. Furthermore, our results suggest that the applicability and physical interpretation of RF may become uncertain in the projected future ocean.

Here, we addressed the long-standing ambiguity of RF and γDIC in measuring seawater absorption capacity for CO2 and buffer capacity. We also found the limitations of the RF and γDIC under conditions of low pH and high pCO2, suggesting that it may become unsuitable in the future. Therefore, we proposed a new factor, γCO2, to quantify seawater absorption capacity for CO2 and acidification. Additionally, we analyzed the factors influencing γCO2 and examined its past and future global distribution.

Result and discussion

Limitations of RF and γDIC

The RF is commonly referred to as “buffer capacity” in various studies; however, it was initially defined as the seawater “Static Capacity” of CO213. We suggest that the so-called “Static Capacity” is more appropriately interpreted as the “CO2 absorption capacity”. This interpretation is conceptually distinct from the traditional “acid-base buffer capacity” definition and should not be conflated with it. The terminology “buffer capacity” can easily confuse the two. The traditional acid-base buffer capacity of a solution, defined by Eq. 512,20,21, represents the amount of strong base dCb or strong acid dCa (mol·kg−1) added to a 1 kg solution to increase or decrease its pH by one unit (dpH).

When RF and γDIC are used as indicators of acid-base buffer capacity, they show apparent inconsistent with β under the condition where pH < 7.5 (Fig. 2a, b, d) (The calculations were based on the 2020 average surface seawater conditions: Alk = 2250 μmol·kg−1, temperature = 18.3 °C, and salinity = 34.8). While RF and γDIC are suitable for characterizing the current acid-base buffer capacity, their applicability may be limited as seawater pH decreases. Therefore, we do not recommend using RF and γDIC as measures of acid-base buffer capacity, which may lead to confusion and conceptual misinterpretation.

$$\beta =\frac{{{dC}}_{b}}{{dpH}}=-\frac{{{dC}}_{a}}{{dpH}}=\frac{\partial {Alk}}{\partial {pH}}$$
(5.1)
$$\beta =2.303\left(\frac{{DIC}\,{K}_{1}\left[{H}^{+}\right]\left({K}_{1}{K}_{2}{\left[{H}^{+}\right]}^{2}+4{K}_{2}\left[{H}^{+}\right]\right)}{{\left({\left[{H}^{+}\right]}^{2}+{K}_{1}\left[{H}^{+}\right]+{{K}_{1}K}_{2}\right)}^{2}} \\ +\frac{{K}_{B}\left[{H}^{+}\right]{B}_{{TOT}}}{{\left({K}_{B}+\left[{H}^{+}\right]\right)}^{2}}+\left[{H}^{+}\right]+\frac{{K}_{w}}{\left[{H}^{+}\right]}\right)$$
(5.2)
Fig. 2: RF, γDIC, β, and γCO2 vary with pH and pCO2.
figure 2

The simulation conditions are at salinity = 34.8 and temperature = 18.3 °C. a, b, c The white solid line is Alk = 2250 μmol·kg−1. d The variation of the four factors with pH at Alk = 2250 μmol·kg−1. Neither the RF nor γDIC is suitable for assessing seawater absorption capacity for CO2 at pH < 7.5 (This critical threshold will vary in different Alk, temperatures, and salinity).

Full size image

Note: KB and Kw are the boric acid and water ionization constant. The \(\frac{2.303\,{DIC}\,{K}_{1}\left[{H}^{+}\right]\left({K}_{1}{K}_{2}{\left[{H}^{+}\right]}^{2}+4{K}_{2}\left[{H}^{+}\right]\right)}{{\left({\left[{H}^{+}\right]}^{2}+{K}_{1}\left[{H}^{+}\right]+{{K}_{1}K}_{2}\right)}^{2}}\) indicates the carbonate buffer capacity of seawater. The \(\frac{{2.303\,K}_{B}\left[{H}^{+}\right]{B}_{{TOT}}}{{\left({K}_{B}+\left[{H}^{+}\right]\right)}^{2}}\) indicates the borate buffer capacity of seawater. Other weaker buffer systems are neglected in the calculations.

However, if RF is used to measure the seawater absorption capacity for CO2, it also becomes inapplicable at pH < 7.5. Since the Alk of seawater remains nearly constant during seawater CO2 absorption, we use the white line in Fig.2a–c to simulate seawater chemistry changes following CO2 absorption. The results show that with the absorption of CO2 by seawater, the extreme points of RF and γDIC are evident after pH < 7.5. However, in theory, as seawater [CO2] increases, its absorption capacity for CO2 should decrease because CO2 (aq), along with the HCO3- and CO32- formed, constitutes part of DIC and should not exhibit extremum points.

This phenomenon arises because the RF was defined under the condition that the change is much smaller than the original value (Eq. 3). This definition, which later evolved into a natural logarithmic form, also leads to the following limitation: At pH < 7.5, there is minimal change in \(\frac{{DIC}\,\partial p{{CO}}_{2}}{\partial {DIC}}\) within the RF, with its value depending on pCO2. The RF reaches its maximum value as seawater pH decreases towards 7.5. At the pH < 7.5, the measured absorption capacity for CO2 tends to increase. Consequently, the RF cannot accurately measure the future seawater absorption capacity for CO2.

Similarly, according to the definition proposed by Egleston et al.9, γDIC is similar to the RF in terms of its physical meaning. As shown in its formulation (Eq. 4), γDIC is essentially derived by removing the DIC term from the RF expression, and therefore does not resolve the issues associated with RF. Under low pH and high pCO2 conditions, the value of γDIC also depends on pCO2. As a result, like RF, it cannot accurately reflect the seawater acid-base buffer capacity or its CO2 absorption capacity in a more acidified ocean.

Definition and meaning of γCO2

In the present ocean, surface seawater pH has already dropped to around 7.5 in some regions strongly affected by acidification22,23. At the same time, with global warming and rising atmospheric CO2, the global surface ocean pH is projected to approach 7.5 by 2100 under the high-emission scenario (SSP5-8.5). This trend will further challenge the applicability of the RF and γDIC under conditions of low pH and high pCO2.

We need a new indicator to better measure the seawater CO2 absorption capacity under severe ocean acidification. The indicator should have several key features. First, its value should consistently decrease with declining pH and increasing pCO2 and maintain this monotonic trend even under extremely low pH conditions. Second, it should minimize direct dependence on absolute values of pCO2 and DIC to better ensure comparability and applicability across different climate scenarios and oceanic regions.

Based on these features, we have proposed a new indicator, γCO2, to evaluate the seawater absorption capacity for CO2 (Eq. 6). The explicit equation for γCO2 could be derived from the METHODS. The inverse is taken because \(\frac{\partial \left[{{CO}}_{2}\right]}{\partial {DIC}}\) represents the sensitivity of CO2 (aq) to the change in DIC12, and taking the inverse reflects seawater absorption capacity for CO2. Partial derivatives are used because [CO2] in seawater depends on the carbonate equilibrium and Alk systems.

$${\gamma }_{{CO}2}{=\left(\frac{\partial \left[{{CO}}_{2}\right]}{\partial {DIC}}\right)}^{-1}$$
(6.1)
$${\gamma }_{{CO}2}= {\left(\frac{\partial \left[{{CO}}_{2}\right]}{\partial {DIC}}\right)}^{-1}=\left(1+\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{{K}_{1}{K}_{2}}{{10}^{-2{pH}}}\right)\\ -\frac{{K}_{0}\,p{{CO}}_{2}{(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{2{K}_{1}{K}_{2}}{{10}^{-2{pH}}})}^{2}}{{{{K}}}_{0}\,{{p}}{{{CO}}}_{2}\left(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{4{K}_{1}{K}_{2}}{{10}^{-2{pH}}}\right)+\frac{{10}^{-{pH}}{K}_{B}\,{B}_{{TOT}}}{{\left({K}_{B}+{10}^{-{pH}}\right)}^{2}}+{10}^{-{pH}}+\frac{{K}_{w}}{{10}^{-{pH}}}}$$
(6.2)

Unlike RF and γDIC, which show non-monotonic trends during pH decrease (Fig. 2c, d), γCO2 decreases as seawater pCO2 increases and pH decreases. This monotonic trend remains under extreme acidification, reflecting the continuous decline in the ocean’s CO2 absorption capacity as acidification intensifies. In addition, the definition of γCO2 avoids direct dependence on the values of DIC and pCO2, making it more suitable and comparable under different ocean conditions and climate scenarios. More importantly, γCO2 has a clear physical meaning. It represents the ratio between the CO2 absorbed by seawater and the amount absorbed by pure physical dissolution. This meaning is based on a simple condition. If only physical dissolution occurs and no chemical reactions of the carbonate system occur, all added DIC exists as CO2 (aq), and the change in DIC equals the change in CO2 (aq). In this case, γCO2 equals 1.

Regarding applicability, the change in seawater [CO2] can be calculated using Eq. 79. Atmospheric CO2 dissolution has a minimal impact on seawater Alk24, leading to the general expression \({d}[{CO}_{2}]=\frac{{dDIC}}{{\gamma }_{{CO}2}}\). From the definition of γCO2, Eq. 8 can be derived, allowing the prediction of DIC changes resulting from variation of surface seawater pCO2.

$${d}[{CO}_{2}]=\frac{\partial \left[{{CO}}_{2}\right]}{\partial {DIC}}{dDIC}+\frac{\partial \left[{{CO}}_{2}\right]}{\partial {Alk}}{dAlk}=\frac{{dDIC}}{{\gamma }_{{CO}2}}+\frac{\partial \left[{{CO}}_{2}\right]}{\partial {Alk}}{dAlk}$$
(7)
$$\Delta {DIC}={\gamma }_{{CO}2}\,{K}_{0}\,\Delta p{{CO}}_{2}$$
(8)

Using area-weighted calculation, the mean surface seawater γCO2 in 2020 was 15.50, corresponding pCO2 at 392.8 µatm (temperature = 18.4 °C and salinity = 34.8). Future change in seawater DIC could be predicted using the slight variation of pCO2 based on Eq. 8. If the future surface seawater pCO2 increases from 392.8 μatm in 2020 to 402.8 μatm (ΔpCO2 = 10.0 μatm), Consequently, the seawater DIC is anticipated to increase from 2048.0 to 2053.3 μmol·kg−1 (ΔDIC = 5.3 μmol·kg−1), resulting in a seawater pH decreases from 8.058 to 8.049 (ΔpH = −0.009) and Ωarag decrease from 2.799 to 2.753 (ΔΩarag = −0.046).

In contrast, when surface seawater pCO2 is 1109.3 μatm, and γCO2 is 4.71 in SSP5-8.5 (temperature = 22.8 °C and salinity = 34.0, Supplementary Table 1), an increase in pCO2 from 1109.3 to 1119.3 μatm (consistent with ΔpCO2 = 10.0 μatm). Consequently, the DIC increases slightly from 2170.5 to 2171.9 μmol·kg−1 (ΔDIC = 1.4 μmol·kg−1), while pH remains nearly constant at 7.658 and Ωarag decreases from 1.463 to 1.452 (ΔΩarag = −0.011). Despite the same increase in surface seawater CO2, the amount of CO2 absorbed by the seawater is only one-third of the current absorption capacity. Moreover, as the degree of acidification intensifies, the acidification rate gradually decreases.

Variation of γCO2 with seawater carbonate parameters

At the same pH, changes in Alk have minimal impact on γCO2 (Fig. 3a). This is because the increased Alk does not alter the position of the carbonate equilibrium, and the proportion of CO2 (aq) in DIC remains nearly unchanged, resulting in a stable γCO2. In contrast, when at the same pCO2, an increased Alk enhances seawater capacity absorption for CO2. These phenomena can be explained by the method of ocean Alk enhancement employed in current seawater CO2 removal. As shown in Fig. 3a, b, adding Alk (such as olivine) to seawater immediately raises Alk25,26,27, causing a simultaneously increased pH and decreased pCO2, leading to a marked increase in γCO2. Subsequently, the system absorbs atmospheric CO2 until the surface seawater pCO2 equals that of the atmosphere, returning to its initial value. As a result, pH increases slightly above its initial level, while Alk remains at its elevated value. Consequently, γCO2 gradually decreases but remains higher than its initial value, which indicates that increasing Alk is an effective method for enhancing seawater absorption capacity for CO2.

Fig. 3: Variation of γCO2 with pH, pCO2, DIC, Ωarag, SST and SSS.
figure 3

a–d The simulation conditions are temperature = 18.3 °C and salinity = 34.8. The legend of (a–d) is uniformly placed in (d). e–h The simulation conditions are at Alk = 2250 μmol·kg−1. a, b The figure represents the process of ocean Alk enhancement. Point A is the starting point of Alk addition, and point C is the endpoint. Segment AB is the process of adding seawater Alk, while segment BC is the process of seawater CO2 absorption. a At the same pH, an increased Alk has minimal impact on γCO2. b At the same pCO2, increased Alk leads to a marked increase in γCO2. c γCO2 reaches its minimum value when DIC slightly exceeds Alk. d Under different Alk, γCO2 is generally less than 3 when Ωarag < 1.0. e, f Variation of γCO2 with temperature and salinity. γCO2 is strongly influenced by temperature and salinity, decreasing as temperature and salinity decline. g, h Variation of γCO2 with Ωarag at different temperatures and salinity. At different temperatures and salinity, γCO2 is generally less than 3.0 when Ωarag < 1.0.

Full size image

γCO2 decreases as seawater DIC increases (Fig. 3c), and at the same DIC, higher Alk enhances seawater absorption capacity for CO2. Additionally, γCO2 approaches 1 when DIC slightly exceeds Alk. It implies that the additional absorption of atmospheric CO2 by seawater ceases, and CO2 can only enter seawater through physical dissolution. Without this additional absorption, seawater would absorb only about 1% of atmospheric CO2 through only physical dissolution10.

Variation of γCO2 with temperature and salinity

γCO2 shows considerable variation in different temperatures and salinity. For instance, at Alk = 2250 μmol·kg−1, seawater absorption capacity for CO2 decreases with decreasing temperature and salinity (Fig. 3e, f).

Although γCO2 exhibits considerable variation at different temperatures and salinity, it strongly correlates positively with Ωarag. Furthermore, as Ωarag decreases, γCO2 under different Alk, temperatures, and salinity conditions tend to converge (Fig. 3d, g, h). It is because, at low Ωarag, γCO2 primarily depends on [CO32−], and the Ωarag is also determined by [CO32−] according to Eq. 1. When Ωarag falls below the thermodynamic threshold of 1, γCO2 is generally less than 3 under most conditions. Therefore, we define γCO2 < 3.0 as the threshold for harmful conditions to aragonite-based organisms.

Global surface seawater γCO2 and changes over the last 30 decades

The area-weighted average of γCO2 for the global ocean in 2020 was 15.50 ± 0.21. The global distribution of surface seawater γCO2 shows a roughly symmetric pattern centered around the equator (Fig. 4a). From low to high latitudes, γCO2 increases and then decreases. This pattern is consistent with its relationship to pCO2, pH, and SST, as discussed earlier. A typical low-value region appears near the equator, which is related to the influence of upwelling28,29. Upwelling brings colder, high-pCO2, and low-pH seawater from deeper layers, leading to weaker CO2 absorption capacity. In addition, the North and South Pole exhibit weaker seawater absorption capacity, nearly approaching its minimum of γCO2 = 1.0. Although the Southern Ocean is considered a powerful carbon sink30,31,32, its CO2 absorption capacity may be close to the limit. The CO2 that enters the Southern Ocean through physical processes may not be effectively converted into HCO3− and CO32−.

Fig. 4: Global surface ocean γCO2 distribution, seasonal and interannual variation.
figure 4

Calculated using model temperature, salinity, pH, and pCO2. For details, please refer to the METHODS. a The left panel shows the global distribution of surface ocean γCO2 in 2020, while the right panel presents its latitudinal distribution. b, c Monthly variations of surface ocean γCO2 in the Northern and Southern Hemispheres during 2016–2020. d Interannual variations of surface ocean γCO2 from 1992 to 2020, with the wavy lines representing the seasonal fluctuations of γCO2. γCO2 was a 13% in global ocean decline over the past 30 years.

Full size image

The Southern Ocean has a substantial carbon sink but low absorption capacity. It can be explained by the differences of K0 in Eq. S1 between 0 °C and 18.3 °C, which are 0.063 mol·kg-1 and 0.034 mol·kg−1, respectively. The higher solubility of CO2 at lower temperatures leads to lower surface seawater pCO2 (about 162.0 to 354.0 μatm)30. The pronounced air-sea pressure difference enhances the transfer of large amounts of atmospheric CO2 into seawater. Meanwhile, elevated CO2 leads to an increased DIC and a decreased Ωarag (about 1.40–2.32), resulting in a lower γCO2 (Fig. 3c, d), which leads to lower seawater absorption capacity for CO2.

Egleston et al. suggested that the low CO2 absorption capacity of the Southern Ocean is primarily due to limited biological use of nutrients, and the upwelling processes bring up relatively high DIC from deep ocean9. We think of “absorption capacity” as the additional CO2 the system can absorb after re-establishing air-sea CO2 equilibrium. At the same time, “carbon flux” represents the actual annual dynamic absorption amount before the system reaches equilibrium. In other words, the strong carbon sink in the Southern Ocean causes more CO2 to stay in CO2 (aq), bringing the ocean’s CO2 absorption capacity close to its limit.

In addition to typical regional distribution, γCO2 also shows marked seasonal variation, with opposite trends in the Northern and Southern Hemispheres (Fig. 4b, c). Analysis shows that temperature is the primary driver of the seasonal changes in γCO2 and the key reason for the different seasonal patterns between the two hemispheres. In the Northern Hemisphere, temperature even causes γCO2 to be negatively correlated with pH and positively correlated with pCO2, although this is opposite to the general trend discussed earlier. Although the seasonal variations in pCO2 and pH are relatively small in the Southern Hemisphere, γCO2 still shows large seasonal fluctuations due to the influence of temperature changes.

Regarding long-term trends, γCO2 has shown a clear decreasing pattern over the past 30 years (Fig. 4d). The mean γCO2 in 1992 was 17.78 ± 0.18, 2.28 higher than in 2020. It indicates that the absorption capacity for CO2 has decreased by 13% over the last three decades. Consequently, if the mean surface ocean pCO2 continues increasing, as it did from 341.9 µatm to 393.2 µatm (ΔpCO2 = 52.3 μatm), and the DIC increases from 1991.4 μmol·kg−1 in 1992 to 2048.0 μmol·kg−1 in 2020 (ΔDIC = 56.6 μmol·kg−1), the mean ocean pCO2 would be assumed to increase from 392.2 in 2020 to 444.5 μatm (ΔpCO2 = 52.3 μatm) to maintain consistency. In this scenario, the mean DIC would only increase from 2048.0 μmol·kg−1 to 2071.0 μmol·kg−1 (ΔDIC = 23.0 μmol·kg−1), signifying a marked decrease in the rate of DIC increase in seawater.

In addition, γCO2 in the Northern Hemisphere is higher than in the Southern Hemisphere (Fig. 4b, c). It may be related to the higher average temperature in the Northern Hemisphere. At the same time, the rate of decline in γCO2 is slightly lower in the Northern Hemisphere (Fig. 4d). It could be due to the slightly stronger warming in the Northern Hemisphere over the past 30 years33, which may have partly slowed the decrease in γCO2.

Forecast of future seawater γCO2

We analyzed the future surface seawater CO2 absorption capacity based on the Share Socioeconomic Pathways (SSPs) models from the CMIP6 project (Supplementary Table 1). Under the SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios, by 2100 compared to 2020, the global surface ocean γCO2 will decrease by 11.6%, 37.3%, 58.7%, and 69.6%, respectively (Fig. 5a–d).

Fig. 5: Prediction of γCO2 under different scenarios.
figure 5

Calculated using CMIP6 model temperature, salinity, pH, and pCO2. For details, please refer to the METHODS. a–d Global oceanic 2100 γCO2 at SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5, respectively. The ocean has largely lost its absorption capacity for CO2 in SSP5-8.5. e The latitudinal distribution of γCO2 in 2100 under different scenarios. f The latitudinal distribution of γCO2 in SSP5-8.5 under different years. g Future interannual variability of γCO2 for each scenario. h RF, γCO2, pH, and pCO2 in the Southern Ocean in 2100 at SSP5-8.5. In this condition, the limitation of the RF is apparent (In the Southern Ocean in 2100 at SSP5-8.5, Alk = 2203 μmol·kg−1, temperature = 2.0 °C, and salinity = 33.2). The RF increases and then decreases, as seen in the h-amplified plot, which is unsuitable for assessing the future seawater absorption capacity for CO2.

Full size image

Based on the latitudinal distribution of γCO2 under different scenarios (Fig. 5e), by 2100, surface seawater γCO2 of low and mid-latitudes generally remain above the critical value of γCO2 = 3.0 in all scenarios. However, in high-latitude regions, γCO2 is close to or below this threshold under all scenarios except SSP1-2.6.

Notably, under the SSP5-8.5 scenario in 2100, by as early as 2050, surface seawater γCO2 of high-latitude will already be close to the critical γCO2 = 3.0, which will be a potential threat to the future carbon sink and ocean ecosystem stability. Further analysis showed that, by 2100, areas where γCO2 < 3.0 account for 61.5% of the global ocean. Since Ωarag usually decreases with depth, a surface γCO2 below the critical level may indicate that Ωarag also falls below its thermodynamic threshold (Ωarag = 1.0). It could exert negative physiological impacts on aragonite organisms.

Under different scenarios, the applicability of traditional factors RF and γDIC also faces serious challenges. In the SSP1-2.6 and SSP2-4.5 scenarios, neither RF nor γDIC reaches an extreme value before 2100. However, under the high-emission scenario SSP5-8.5, both RF and γDIC show clear extrema in the Southern Ocean when pH = 7.7 (Alk = 2203 μmol·kg−1, temperature = 2.0 °C, salinity = 33.2; Fig. 5h and Supplementary Table 1). Specifically, at 90°N, RF reaches its maximum in 2081 (Supplementary Fig. 2a), and γDIC reaches its minimum in 2077 (Supplementary Fig. 2b). In the simulation, γCO2 does not exhibit a maximum or minimum value (Supplementary Fig. 2c). The results under the SSP3-7.0 scenario are shown in Supplementary Fig. 2d–e. As pCO2 increases and pH decreases, RF and γDIC fail to reflect the seawater CO2 absorption capacity accurately.

In summary, compared with RF and γDIC, γCO2 can better overcome their limitations under high pCO2 and low pH conditions. It provides a more stable and reliable indicator for evaluating the seawater CO2 absorption capacity in the future. It is worth further exploring whether γCO2 can also be used to reveal its links with other biogeochemical processes, such as nutrient distribution and phytoplankton productivity. In addition, the potential application of γCO2 under extreme environments should be considered. For example, it may help assess the carbon uptake capacity of high-pCO2 ocean systems on Earth-like planets. We hope that γCO2 can contribute to more accurate assessments of ocean conditions, support global climate response strategies, and help evaluate global warming and ocean acidification.

Methods

RF, γDIC, and γCO2 explicit equation calculation

Using Egleston’s solution, we could derive the explicit equations of the RF and γDIC (Eqs. 9–15). The derivation is as follows.

DIC, Alk, [CO2], and [H+], two of the variables are known to give the other two, which gives Eqs. 9 and 10.

$$\left(\begin{array}{c}{dDIC}\\ {dAlk}\end{array}\right)=J\,\left(\begin{array}{c}d\left[{{CO}}_{2}\right]\\ d\left[{H}^{+}\right]\end{array}\right)$$
(9)
$$J=\left(\begin{array}{cc}\frac{\partial {DIC}}{\partial \left[{{{CO}}}_{2}\right]} & \frac{\partial {DIC}}{\partial \left[{{H}}^{+}\right]}\\ \frac{\partial {Alk}}{\partial \left[{{CO}}_{2}\right]} & \frac{\partial {Alk}}{\partial \left[{{H}}^{+}\right]}\end{array}\,\right)$$
(9.1)
$$\left(\begin{array}{c}d\left[{{CO}}_{2}\right]\\ d\left[{H}^{+}\right]\end{array}\right)={J}^{-1}\left(\begin{array}{c}{dDIC}\\ {dAlk}\end{array}\right)$$
(10)
$${J}^{-1}=\left(\begin{array}{cc}\frac{\partial \left[{{CO}}_{2}\right]}{\partial {DIC}} & \frac{\partial \left[{{CO}}_{2}\right]}{\partial {Alk}}\\ \frac{\partial \left[{H}^{+}\right]}{\partial {DIC}} & \frac{\partial \left[{H}^{+}\right]}{\partial {Alk}}\end{array}\right)$$
(10.1)

From Eq. 9 and Eq. 10, we could find the four elements of matrix J.

$$\frac{\partial {DIC}}{\partial \left[{{CO}}_{2}\right]} =1+\frac{{K}_{1}}{\left[{H}^{+}\right]}+\frac{{K}_{1}{K}_{2}}{{\left[{H}^{+}\right]}^{2}}=\frac{{DIC}}{\left[{{CO}}_{2}\right]} \\ \frac{\partial {\mbox{DIC}}}{\partial \left[{{H}}^{+}\right]} =-\left[{{CO}}_{2}\right]\left(\frac{{K}_{1}}{{\left[{H}^{+}\right]}^{2}}+\frac{2{K}_{1}{K}_{2}}{{\left[{H}^{+}\right]}^{3}}\right) \\ =-\frac{\left[{{HCO}}_{3}^{-}\right]+2\left[{{CO}}_{3}^{2-}\right]}{\left[{H}^{+}\right]}=\frac{-{{Alk}}_{c}}{\left[{H}^{+}\right]}$$
$$\frac{\partial {Alk}}{\partial \left[{{CO}}_{2}\right]} = \frac{{K}_{1}}{\left[{H}^{+}\right]}+\frac{2{K}_{1}{K}_{2}}{{\left[{H}^{+}\right]}^{2}}=\frac{\left[{{HCO}}_{3}^{-}\right]+2\left[{{CO}}_{3}^{2-}\right]}{\left[{{CO}}_{2}\right]} \\ = \frac{{{Alk}}_{c}}{\left[{{CO}}_{2}\right]} \frac{\partial {Alk}}{\partial \left[{H}^{+}\right]}=-\left\{\left[{{CO}}_{2}\right]\left(\frac{{K}_{1}}{{\left[{H}^{+}\right]}^{2}}+\frac{4{K}_{1}{K}_{2}}{{\left[{H}^{+}\right]}^{3}}\right)\right.\\ \left.+\frac{{K}_{B}{B}_{{TOT}}}{{\left({K}_{3}+\left[{H}^{+}\right]\right)}^{2}}+1+\frac{{K}_{W}}{{\left[{H}^{+}\right]}^{2}}\right\}=\frac{-S}{\left[{H}^{+}\right]}$$

Note34: where \(S=\left[{{HCO}}_{3}^{-}\right]+4\left[{{CO}}_{3}^{2-}\right]+\frac{{K}_{B}\left[{H}^{+}\right]{B}_{{TOT}}}{{\left ({K}_{B}+\left[{H}^{+}\right]\right)}^{2}}+\left[{H}^{+}\right]+\frac{{K}_{W}} {\left[{H}^{+}\right]}\), \(P=2\,[{CO}_{2}]+[{H{CO}}_{3}^{-}]\), \({A{lk}}_{C}=[{H{CO}}_{3}^{-}]+2\,[{{CO}}_{3}^{2-}]\). [CO2], DIC, Alk, and [H+] are in mol·kg−1.

We could find J-1 from Eq. 11.

$${J}^{-1}=\frac{1}{\left|J\right|}\left(\begin{array}{cc}\frac{\partial {Alk}}{\partial \left[{H}^{+}\right]} & -\frac{\partial {DIC}}{\partial \left[{H}^{+}\right]}\\ -\frac{\partial {Alk}}{\partial \left[{{CO}}_{2}\right]} & \frac{\partial {DIC}}{\partial \left[{{CO}}_{2}\right]}\end{array}\right)=\frac{\left[{H}^{+}\right]\left[{{CO}}_{2}\right]}{{{Alk}}_{c}^{2}-{DIC}\,S}\left(\begin{array}{cc}\frac{-S}{\left[{H}^{+}\right]} & \frac{{{Alk}}_{c}}{\left[{H}^{+}\right]}\\ -\frac{{{Alk}}_{c}}{\left[{{CO}}_{2}\right]} & \frac{{DIC}}{\left[{{CO}}_{2}\right]}\end{array}\right)$$
(11)

Note: |J| is the Jacobian determinant.

Equation12 could be found from the corresponding equivalence of Eq. 10 and Eq. 11.

$$\frac{\partial \left[{{CO}}_{2}\right]}{\partial {DIC}}=\frac{\left[{H}^{+}\right]\left[{{CO}}_{2}\right]}{({{Alk}}_{c}^{2}-{DIC}\,S)}\frac{-S}{\left[{H}^{+}\right]}=\frac{S\left[{{CO}}_{2}\right]}{{{DIC}\,S-{Alk}}_{c}^{2}}$$
(12)

The explicit equations Eqs. 13–15 for RF and γDIC could be derived from Eq. 12.

$${\gamma }_{{CO}2}= {\left(\frac{\partial \left[{{CO}}_{2}\right]}{\partial {DIC}}\right)}^{-1}=\left(1+\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{{K}_{1}{K}_{2}}{{10}^{-2{pH}}}\right) \\ -\frac{{K}_{0}\,p{{CO}}_{2}{\left(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{2{K}_{1}{K}_{2}}{{10}^{-2{pH}}}\right)}^{2}}{{K}_{0}\,p{{CO}}_{2}\left(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{4{K}_{1}{K}_{2}}{{10}^{-2{pH}}}\right)+\frac{{K}_{B}\,{B}_{{TOT}}{10}^{-{pH}}}{{\left({K}_{B}+{10}^{-{pH}}\right)}^{2}}+{10}^{-{pH}}+\frac{{K}_{w}}{{10}^{-{pH}}}}$$
(13)
$$RF =\frac{{DIC}}{p{{CO}}_{2}}\left(\frac{\partial p{{CO}}_{2}}{\partial {DIC}}\right) \\ =\frac{\left({K}_{0}\,p{{CO}}_{2}(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{4{K}_{1}\,{K}_{2}}{{10}^{-2{{pH}}}})+\frac{{K}_{B}\,{B}_{{TOT}}\,{10}^{-{pH}}}{{\left ({K}_{B}+{10}^{-{pH}}\right)}^{2}}+{10}^{-{pH}}+\frac{{K}_{W}}{{10}^{-{pH}}}\right)\left(1+\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{{K}_{1}\,{K}_{2}}{{10}^{-2{pH}}}\right)}{\left(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{4{K}_{1}\,{K}_{2}}{{10}^{-2{pH}}}+\frac{{K}_{B}\,{B}_{{TOT}}{10}^{-{pH}}}{{\left ({K}_{B}+{10}^{-{pH}}\right)}^{2}}+{10}^{-{pH}}+\frac{{K}_{W}}{{10}^{-{pH}}}\right)\left(1+\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{{K}_{1}\,{K}_{2}}{{10}^{-2{pH}}}\right)-{K}_{0}\,p{{CO}}_{2}{\left(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{{K}_{1}{K}_{2}}{{10}^{-2{pH}}}\right)}^{2}}$$
(14)
$${{{{\gamma }}}}_{{{{DIC}}}}\;{{=}}\;{\left(\frac{{{{\partial }}}{{{ln}}}\left[{{{{CO}}}}_{{{{2}}}}\right]}{{{{\partial }}}{{{DIC}}}}\right)}^{{{-}}{{{1}}}} =\, {K}_{0}\,p{{CO}}_{2}\left(1+\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{{K}_{1}\,{K}_{2}}{{10}^{-2{pH}}}\right)\\ -\frac{{({{{K}}}_{0}\,p{{{CO}}}_{2}(\frac{{{{K}}}_{1}}{{10}^{-{{pH}}}}+\frac{2{{{K}}}_{1}{{{K}}}_{2}}{{10}^{-2{{pH}}}}))}^{2}}{{K}_{0}\,p{{CO}}_{2}\left(\frac{{K}_{1}}{{10}^{-{pH}}}+\frac{4{K}_{1}{K}_{2}}{{10}^{-2{pH}}}\right)+\frac{{K}_{B}\,{B}_{{TOT}}\,{10}^{-{pH}}}{{\left({K}_{B}+{10}^{-{pH}}\right)}^{2}}+{10}^{-{pH}}+\frac{{K}_{w}}{{10}^{-{pH}}}}$$
(15)

The RF calculated using the explicit equation showed a deviation of only 0.8% (Supplementary Fig. 1) compared to the infinitesimal method calculation (Eq. 3), which is commonly used today. It proved the reliability of the calculation method. Egleston ignores the \(\frac{{10}^{-{{pH}}}\,{K}_{B}\,{B}_{{TOT}}}{{\left({K}_{B}+{10}^{-{pH}}\right)}^{2}}\) when calculating the RF, the mean RF was thus calculated to be 33.8% larger. The calculated RF would be small in the region of high values if the \(\frac{{10}^{-{pH}}\,{K}_{B}\,{B}_{{TOT}}}{{\left({K}_{B}+{10}^{-{pH}}\right)}^{2}}\) is included as a constant. Therefore, in our calculations, we used variable borate alkalinity.

Carbonate chemistry calculation

The carbonate chemistry was calculated using CO2SYS.Matlab_v3.2.135. The carbonate ionization and K2SO4 constants were derived from the literature values provided by Schockman36 and Dickson37. The borate formula38 and the [Ca2+] formula were used in Eq. 16 and Eq. 17, respectively. All pH mentioned in this study were calculated on the total scale.

$$\left[{B}_{{TOT}}\right]\left ({{{\rm{mol}}}}\cdot {{\mbox{kg}}}^{-1}\right)=\frac{0.0004326 \, {Sal}{inity}}{35}$$
(16)
$$[{{Ca}}^{2+}]\left({{{\rm{mol}}}}\cdot {{\mbox{kg}}}^{-1}\right)=\frac{0.01026 \, {Sal}{inity}}{35}$$
(17)

γCO2 global grid data calculation

γCO2 can be calculated using any two of the four parameters: CO2, pH, DIC, and Alk, along with temperature and salinity data. The global surface seawater γCO2 can be calculated using 1° × 1° global grid data products by pCO239, pH40, temperature, and salinity41.

γCO2 projections for 2100 based on IPCC report

We analyzed data from the IPCC 6th Assessment Report and CMIP6 to calculate the global ocean γCO2 in 2100 under various scenario models, using projected temperature, salinity, pCO2, and pH data42,43,44,45.