Controls of ocean carbon cycle feedbacks from different ocean basins and meridional overturning in CMIP6

The ocean response to carbon emissions involves a competition between the increase in atmospheric CO2 acting to enhance the ocean carbon storage, characterised by the carbon-concentration feedback, and climate change acting to decrease the ocean carbon storage, characterised by the carbon-climate feedback. The contribution from different ocean basins to the carbon cycle feedbacks and its control by the ocean carbonate chemistry, physical ventilation and biological processes is explored in diagnostics of 10 CMIP6 Earth system models. To gain mechanist insight, the dependence of these feedbacks to 5 the Atlantic Meridional Overturning Circulation (AMOC) is also investigated in an idealised climate model and the CMIP6 models. The Atlantic, Pacific and Southern Oceans contribute equally to the carbon-concentration feedback, despite their different size. This large contribution from the Atlantic Ocean relative to its size is associated with an enhanced carbon storage in the ocean interior due to a strong local physical ventilation and an influx of carbon transported from the Southern Ocean. The Atlantic Ocean provides the largest contribution to the carbon-climate feedback relative to its size, which is primarily 10 due to climate change acting to reduce the physical ventilation. The Southern Ocean provides a relatively small contribution to the carbon-climate feedback, due to a compensation between the climate effects of the combined decrease in solubility and physical ventilation, and the increase in accumulation of regenerated carbon in the ocean interior. In the Atlantic Ocean, the AMOC strength and its weakening with warming has a strong control on the carbon cycle feedbacks that leads to a moderate dependence of these feedbacks to AMOC on global scale. In the Pacific, Indian and Southern Oceans there is no 15 clear correlation between AMOC and the carbon cycle feedbacks, suggesting that other processes control the ocean ventilation and carbon storage there.


Introduction
Carbon emissions drive an Earth system response via direct changes in the biogeochemical carbon cycle and the physical climate. These changes in the biogeochemical carbon cycle and physical climate further amplify or dampen the Earth system 20 response, with this indirect effect often refer to as a feedback (Sherwood et al., 2015). The physical climate feedback involves the combined effect from changes in atmospheric water vapour, lapse rate, surface albedo and clouds (Ceppi and Gregory, 2017), and from a shift in the regional patterns of ocean heat uptake due to changes in the ocean circulation (Winton et al., 2013). For the carbon cycle, an initial increase in atmospheric CO 2 leads to a carbon uptake and storage in land and ocean. 1999; Crueger et al., 2008;Schwinger et al., 2014). However, the net effect of AMOC weakening with climate change on the carbon storage is highly uncertain and sensitive to the representation of the vertical carbon gradient and ocean biological processes in Earth system models. This uncertainty motivate us to explore the control of AMOC on the carbon cycle feedbacks in CMIP6 models, and the relative importance of changes in biological processes and physical ventilation for the carbon storage in different ocean basins. 70 Our aim is to provide insight for the relative contribution from different ocean basins to the ocean carbon cycle feedbacks, and the processes that drive this relative contribution and its uncertainty amongst CMIP6 Earth system models, with particular emphasis on the control of AMOC. In the next section, we provide a theoretical separation of the ocean carbon cycle feedbacks into contribution from carbonate chemistry, physical ventilation and biological processes, and explore how the interplay of these processes drives the global response of 10 CMIP6 Earth system models (Table 1). In section 3, we explore the geographical 75 distribution of the ocean carbon cycle feedbacks, and the processes that control their relative distribution in the Atlantic, Pacific, Indian and Southern Oceans. In section 4, we investigate the effect of the AMOC on the global and basin-scale carbon cycle feedbacks, firstly in an idealised climate model that provides a mechanistic insight, and then in diagnostics of the CMIP6 models. Section 5 summarises our conclusions and discuss our results in the context of previous studies.
2 Ocean carbon cycle feedbacks and their control by different processes 80 Anthropogenic carbon emissions drive an increase in atmospheric CO 2 which in turn leads to an increase in the ocean carbon inventory relative to the pre-industrial, ∆I ocean . At the same time the increase in atmospheric CO 2 modifies the physical climate system, such as for example leading to ocean warming and increase in stratification, which further influences the ability of the ocean to absorb carbon from the atmosphere. Hence, the ocean carbon uptake due to anthropogenic carbon emissions can be expressed as a function, F , of changes in the atmospheric CO 2 and the physical climate 85 ∆I ocean = F (CO 2,0 + ∆CO 2 , T 0 + ∆T ) − F (CO 2,0 , T 0 ), where the surface air temperature, T , is used as a proxy for the physical climate and subscript 0 is the pre-industrial. By expanding the function F into a Taylor series (Schwinger et al., 2014;Williams et al., 2019), the ocean carbon inventory changes relative to the pre-industrial, ∆I ocean , are expressed as where R 3 contains the derivatives of third order and higher. By ignoring the second and higher order terms but keeping the terms for the non-linear relationship between atmospheric CO 2 and climate change, Eq.
(3) is rewritten as where the ocean carbon-concentration feedback parameter is defined as β ocean = ∂F ∂CO2 0 , the ocean carbon-climate feedback 95 parameter is defined as γ ocean = ∂F ∂T 0 and the non-linearity of the ocean carbon cycle feedbacks is defined as N = ∂ 2 F ∂CO2∂T 0 .
The carbon cycle feedback parameters, β and γ , are traditionally estimated using Earth system model simulations with the couplings between the carbon cycle and radiative forcing either switched on or off: a fully coupled simulation, a radiatively coupled simulation and a biogeochemically coupled simulation (Friedlingstein et al., 2006;Arora et al., 2013;Jones et al., 2016;Arora et al., 2020). Any combination of these three simulations can be used to estimate the carbon cycle feedback 100 parameters, however, each combination yields somewhat different results due to the non-linearity of the system (Gregory et al., 2009;Zickfeld et al., 2011;Schwinger et al., 2014;Arora et al., 2020). Here, we estimate the carbon cycle feedback parameters using the fully coupled simulation (COU) and the biogeochemically coupled simulation (BGC) under the 1% yr −1 increasing CO 2 experiment, in which the atmospheric CO 2 concentration increases from its pre-industrial value of around 285 ppm until it quadruples over a 140-year period, following the recommended C 4 MIP protocol of experiments (Jones et al., 2016;Arora 105 et al., 2020). To exclude model biases, the control run was used to estimate the changes relative to the pre-industrial in the Earth system models. For simplicity, we ignore the effect of the air temperature increase in the BGC simulation to the feedbacks, which has a contribution of less than 5% (Arora et al., 2020), such that 110 where ∆CO 2 is the increase in atmospheric CO 2 and ∆T the increase in air surface temperature in the fully coupled earth system (i.e COU simulation). The carbon-climate feedback parameter, γ ocean , in Eq. (5) corresponds to the effect of climate change under rising atmospheric CO 2 and hence includes the effect of the non-linearity, N ∆CO 2 in Eq. (4) (Schwinger et al., 2014).
To gain insight for the driving mechanisms of the carbon cycle feedbacks and their uncertainty amongst Earth system models, 115 β ocean and γ ocean may be separated into contribution from the regenerated, the saturated and the disequilibrium ocean carbon pools following Williams et al. (2019) and Arora et al. (2020). The ocean dissolved inorganic carbon, DIC, may be defined in terms of these separate carbon pools (Ito and Follows, 2005;Williams and Follows, 2011;Lauderdale et al., 2013;Bernardello et al., 2014),

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where DIC pref is the DIC at the surface that is transferred into the ocean interior due to the physical ventilation, involving the circulation, and DIC reg is the DIC accumulated into the ocean interior due to biological regeneration of organic carbon. The DIC pref can be further split into two idealised carbon pools: (i) the DIC sat representing the amount of DIC that the ocean would have if the whole ocean reached a full chemical equilibrium with the contemporary atmospheric CO 2 ; and DIC dis representing the extend that the ocean departs from a full chemical equilibrium with the contemporary atmospheric CO 2 .

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Assuming the changes in the biological organic carbon inventory are small, the changes in the ocean carbon inventory relative to the pre-industrial era may then be related to the volume integral of the changes in each of the DIC pools, where m = 12.01 · 10 −15 PgC mol −1 is a unit conversion.
By substituting Eq. (7) into Eq. (5) the ocean carbon cycle feedback parameters may be expressed in terms of these different 130 ocean carbon pools as Arora et al., 2020) 2.1 Contribution from the saturated carbon pool to β ocean and γ ocean The changes in the saturated carbon pool relative to the pre-industrial in Eq. (7) can be expressed as where ∆ is the change relative to the pre-industrial, T ocean is the ocean temperature , S is the ocean salinity, P is the ocean phosphate concentration, Si is the ocean silicate concentration, Alk pre is the preformed alkalinity and f is a non-linear function representing the solution to the ocean carbonate chemistry for the contemporary atmospheric CO 2 . Here, f is estimated following the iterative solution for the ocean carbonate chemistry of Follows et al. (2006) and by considering the small con-140 tribution of minor species (borate, phosphate, silicate) to the preformed alkalinity. The preformed alkalinity is estimated from a multiple linear regression using salinity and the conservative tracer P O (Gruber et al., 1996), with the coefficients of this regression estimated based on the upper ocean (first 10 m) alkalinity, salinity, oxygen, and phosphate in each of the Earth system models.
To understand how the ocean carbonate chemistry operates and the mechanisms that control β sat , consider an ocean buffer factor, B, where the fractional change in the atmospheric CO 2 and saturated carbon inventory is defined relative to the preindustrial (Katavouta et al., 2018) where subscript 0 is the pre-industrial.
Substituting Eq. (12) into Eq. (8) the saturated part of β can be expressed as where B(CO 2 , T ocean,0 , S 0 , Alk 0 ) is the ocean buffer factor for the contemporary atmospheric CO 2 under the pre-industrial 155 ocean state for temperature, salinity and alkalinity, as is the case in the BGC run.
Expression (13) shows that β sat is proportional to the ocean capacity to buffer changes in atmospheric CO 2 with no changes in the physical climate, B(CO 2 , T ocean,0 , S 0 , Alk pre,0 ) −1 . The rise in atmospheric CO 2 leads to an increase in the saturated ocean carbon inventory, ∆I sat , (Fig. 2a, red shade) but also to a decrease in the ocean capacity to buffer changes in atmospheric CO 2 as the ocean acidifies, such that the buffer factor, B, increases and β sat decreases in all the Earth system models ( Fig.   160 2b, red shade). The buffer factor, B, and so β sat also depend on the pre-industrial ocean state due to the non-linearity of the ocean carbonate system. Hence, there is a spread in β sat amongst the Earth system models forced by the same increase in atmospheric CO 2 (Fig. 2b, red shade) related to their different pre-industrial ocean temperature, salinity and alkalinity.
To understand the mechanisms that control γ sat consider the solution to the saturated part of DIC as dictated by the carbonate chemistry where and K o is the solubility, K 1 and K 2 are the ocean carbon dissociation constants, and [H + ] sat is the ocean hydrogen ion concentration at a chemical equilibrium with the contemporary atmospheric CO 2 . K o , K 1 and K 2 are a function of the ocean temperature and salinity and so depend on the physical climate change, while [H + ] sat depends primary on the changes in atmospheric CO 2 . Combining Eq. (14) with Eq. (7) and Eq. (8), and assuming that the ocean temperature and salinity remain 175 at their pre-industrial value in the BGC run with no climate change, γ sat can be expressed as The term inside the first {} brackets in the right hand side of Eq. (16) contributes to the linear part of γ sat and is controlled 180 by changes in climate only; specifically by the effect of changes in the ocean temperature to the solubility and ocean carbon dissociation constants. Under warming due to changes in climate this term is negative. The term inside the second {} brackets in the right hand side of Eq. (16) contributes to the non-linear part of γ sat , and it depends on changes in pH, due to the increase in atmospheric CO 2 , and changes in climate. Under rising atmospheric CO 2 and warming this term is negative as [H + ] sat increases and K o decreases, and is smaller than the linear term as ∆[H + ]sat [H + ]sat < 1. The adjustment of γ sat due to changes in the pH, represented by this non-linear term, depends on the increase in atmospheric CO 2 ; for example, the non-linear term is about 30% and 50% of the linear term for a doubling of atmospheric CO 2 and for a quadrupling of atmospheric CO 2 , respectively. Hence, the non-linearity of the carbonate chemistry acts to reduce the magnitude of the negative γ sat consistent with the carbonate system being less sensitive to change in temperature under higher ocean DIC (Schwinger et al., 2014).
Expression (16) shows that γ sat is proportional to the changes in solubility due to climate change, and is further modified by 190 changes in the ocean carbon dissociation constants with warming and by the non-linearity of the carbonate chemistry. Ocean warming due to climate change leads to a decrease in the saturated carbon inventory, ∆I sat , in all the Earth system models ( Fig.   2c, red shade) primary driven by a decrease in solubility. This decrease in ∆I sat with warming drives a nearly constant negative γ sat (Fig. 2d, red shade) with the deviations from a constant value being associated to the non-linearity of the carbonate system.
The small spread of γ sat amongst the Earth system models (Fig. 2d, red shade) is associated with different pre-industrial ocean 195 states in the models.
2.2 Contribution from the regenerated carbon pool to β ocean and γ ocean Assuming that the oxygen concentration is close to saturation at the surface, DIC reg can be calculated from the apparent oxygen utilization, AOU , and the contribution of biological calcification to the alkalinity, Alk, (Ito and Follows, 2005;Williams and Follows, 2011;Lauderdale et al., 2013), such that ∆I reg in Eq. (7) is expressed as where R CO and R N O are constant stoichiometric ratios, and Alk pre is the preformed alkalinity such that Alk − Alk pre gives the contribution to alkalinity from biological calcification.
Substituting Eq. (17) in Eq. (8) the regenerated part of β ocean and γ ocean are expressed as The regenerated part of β ocean is associated with changes in ocean biological processes due to the atmospheric CO 2 increase.
∆I BGC reg and β reg are effectively negligible in the Earth system models ( Fig. 2a and b, green shade) as these models do not include an explicit dependence of biological production to an increase in carbon availability or decrease in seawater pH. The 210 regenerated part of γ ocean is associated with changes in ocean biological processes due to changes in climate, including the effect of changes in the circulation on the sinking rate of particles, the effect of warming on the solubility of oxygen and the effect of changes in alkalinity on the dissolution of the calcium carbonate shells of calcifying phytoplankton. ∆I COU reg −∆I BGC reg and γ reg are positive and increase in time in all the Earth system models ( Fig. 2c and d, green shade), as γ reg is dominated by the weakening in the ocean physical ventilation due to climate change. This weakening in the ocean physical ventilation leads 215 to a longer residence time of water masses in the ocean interior and so to an increase in the accumulation of carbon from the regeneration of biologically cycled carbon in the deep ocean (Schwinger et al., 2014;Bernardello et al., 2014).

Contribution from the disequilibrium carbon pool to β ocean and γ ocean
The disequilibrium part of β ocean and γ ocean are estimated using Eq. (8) as and The disequilibrium part of the carbon cycle feedback parameters is controlled by the ocean physical ventilation. Specifically, β dis is a function of the pre-industrial ocean physical ventilation and the rate of transfer of the anthropogenic carbon from the ocean surface into the ocean interior. The rise in atmospheric CO 2 leads to an increase in the magnitude of the negative 225 disequilibrium ocean carbon inventory, ∆I dis , in all the Earth system models (

Combined effect of saturated, disequilibrium and regenerated carbon pools to β ocean and γ ocean
On a global scale, the ocean carbon-concentration feedback parameter, β ocean , is positive in all the Earth system models and 240 explained by the chemical response involving the rise in ocean saturation, β sat , opposed by the effect of the relatively slow ocean ventilation, such that the physical uptake of carbon within the ocean is unable to keep pace with the rise in atmospheric CO 2 , β dis (Fig. 2b). There is no significant contribution from biological changes to β ocean in the Earth system models (Fig. 2b, green shading). The spread in β ocean amongst the Earth system models is relatively small (coefficient of variation, CV, of 0.10) when compared with the spread in γ ocean (CV of 0.46) ( Table 2). The spread in β sat is small (Fig. 2b, red shading) reflecting the 245 use of similar carbonate chemistry schemes and bulk parameterizations of air-sea CO 2 fluxes across marine biogeochemical models in CMIP6 , and is driven from differences in the pre-industrial ocean state, involving ocean temperature, salinity and alkalinity, amongst the models due to the non-linearity of ocean carbonate chemistry. The spread in β dis is also small (Fig. 2b, blue shading) as all the Earth system models have a broadly similar general pre-industrial circulation and physical ventilation.

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The ocean carbon-climate feedback parameter, γ ocean , is negative in the Earth system models, suggesting that the ocean takes up less carbon in response to climate change. The decrease in solubility and in the physical ventilation with warming act to reduce the ocean carbon uptake leading to a negative γ sat and γ dis , respectively (Fig. 2d). However, the decrease in the physical ventilation with warming also acts to increase the residence time in the ocean interior leading to an increase in the regenerated carbon and a positive γ reg (Fig. 2d, green shading). The combined γ sat and γ dis dominate over the opposing 255 γ reg leading to an overall negative γ ocean . The model spread in γ ocean is mainly driven by the spread in γ dis and γ reg (Fig.   2d) and it is associated with the different response of the ocean ventilation to warming in these models. The spread in γ reg is larger than the spread in γ dis due to the different parametrizations of ocean biogeochemical processes in the models. The spread in γ sat is relatively small (Fig. 2d, red shading) as all the models use similar carbonate chemistry schemes, and is driven by the non-linearity of the carbonate system that leads to a small sensitivity of γ sat to the spread in the pre-industrial ocean 260 temperature, salinity and alkalinity.

Regional ocean carbon cycle feedbacks in CMIP6 Earth system models
The carbon cycle feedbacks for the global ocean in Eq. (4) can be further separated into contribution from different ocean

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where γ n includes the non-linearity of the ocean carbon cycle feedbacks, n notes the different ocean regions, ∆I n is the change in the ocean carbon inventory relative to the pre-industrial in the region n, ∆CO 2 and ∆T are the global changes in atmospheric CO 2 and the surface air temperature, respectively, and β n and γ n are the carbon cycle feedback parameters for each ocean region n expressed as In Eq. (23) the regional feedback parameters are defined by the regional ocean carbon storage rather than the regional cumulative ocean carbon uptake, so that they include the effects from local air-sea carbon exchange and from the ocean transport of carbon between the different regions.
This effect of the ocean transport on carbon storage is important and when accounted for leads to different spatial patterns 275 for the carbon cycle feedback parameters (Fig. 3). Specifically, the carbon-concentration feedback parameter, β, estimated from the regional cumulative ocean CO 2 uptake (Fig. 3b) is large in the Southern Ocean, the North Atlantic, the Kuroshio Extension and the eastern boundary upwelling regions, and small in the subtropical gyres. The carbon-concentration feedback parameter, β, estimated from the regional ocean carbon storage (Fig. 3a) is also large in the North Atlantic, but instead large in the South hemisphere subtropical gyres and small in the Southern Ocean south of 50 o S. This difference in the β estimated 280 from the cumulative ocean CO 2 uptake and the ocean carbon storage is due to the northward transport of anthropogenic carbon from the Southern Ocean associated with subduction and transport of mode and intermediate waters.
The carbon-climate feedback parameter, γ, estimated from the regional cumulative ocean CO 2 uptake due to climate change like the Arctic and around Antarctic. The transport effect redistributes spatial asymmetries in γ, driven by the regional air-sea carbon exchange, and leads to a more uniform and less negative γ in the Southern Ocean, a less negative γ in the North Atlantic high latitudes and a switch to a negative γ in the Arctic (Fig. 3.a). For diagnostics of the net effect of the ocean transport on the carbon storage and the carbon cycle feedbacks in the Atlantic, Pacific and Southern Oceans see the Appendix.
Here, we focus on the ocean carbon cycle feedbacks estimated from the regional ocean carbon storage to gain more mech-290 anistic insight, so as (i) to account explicitly for the ocean transport of carbon, and (ii) to enable estimates of the regional contribution from the changes in the saturated, disequilibrium and regenerated carbon pools.

Contribution from different basins to β ocean and γ ocean
The Atlantic, Pacific and Southern Oceans contribute equally to the ocean carbon-concentration feedback parameter, β ocean , ( Fig. 4a) with an inter-model mean of 0.22, 0.25 and 0.23 PgC ppm −1 , respectively ( Table 2). The Indian Ocean contributes 295 less than half than the other 3 basins to β ocean (Fig. 4a) with an inter-model mean of 0.10 PgC ppm −1 (Table 2). In contrast, the contribution to the saturated and disequilibrium carbon pools, β sat and β dis , follows the basin size, with the Pacific Ocean having the largest contribution and the Indian Ocean the smallest contribution (Fig. 4a). In all basins, β reg is more than an order of magnitude smaller than β (Fig. 4a). There is a relative small spread in β, as shown by the coefficient of variation, CV<0.13 in all basins, (Table 2), and in β sat and β dis amongst the Earth system models (Fig. 4a).

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The Pacific, Atlantic, Southern and Indian Oceans contribution to the ocean carbon-climate feedback parameter, γ ocean , is on average -5.0, -4.5, -3.1 and -1.2 PgC K −1 , respectively (Table 2 and Fig. 4b). The basin-wide variability in γ amongst the models, as described by the coefficient of variation, CV, varies from 0.56 in the Pacific Ocean to 0.92 in the Southern Ocean (Table 2). The variability in γ amongst the models for each basin is substantially larger than that of the global ocean (Table 2), which suggests that variability in different basins can compensate each other.

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In the Southern Ocean, the contribution of the saturated, disequilibrium and regenerated carbon pools to γ is of a similar magnitude (Fig. 4b, blue circles), such that the decrease in solubility, the reduction in the physical ventilation and the increase in the regenerated carbon accumulation in the ocean interior due to climate change are equally important. In the Atlantic Ocean, γ is dominated by the disequilibrium carbon pool (Fig. 4b, red circles) and the reduction in the physical ventilation due to climate change, with the contribution of the regenerated and the saturated carbon pools being of a smaller magnitude.

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In the Indian Ocean, γ is mainly controlled by the compensation between saturated and regenerated carbon pools (Fig. 4b, yellow circles). In the Pacific Ocean, the magnitude of γ is dominated by the saturated carbon pool and the decrease in carbon solubility due to warming (Fig. 4b, purple circles). In all basins, the spread in γ dis and γ reg amongst the models is relative larger compare to the spread in γ sat (Fig. 4b). Hence, in all the ocean basins, the spread in γ amongst the models is mainly driven by the inter-model variability in the response of the physical ventilation and the regenerated carbon to climate change.
3.2 Processes controlling the contribution from different basins to β ocean and γ ocean The discrepancy between the basins volume relative to the global ocean, and the basins fractional contribution to β ocean and γ ocean (Fig. 5) suggests that larger regions do not necessary store more carbon, but rather the ocean carbon cycle feedbacks depend upon a complex interplay between ocean transport, air-sea interaction and biological processes.
The Southern and Indian Oceans contribute 27% and 12%, respectively, to the ocean carbon-concentration feedback param-320 eter, β ocean , following their fractional volumes of the global ocean (Fig. 5a). The Atlantic Ocean contributes 26% to β ocean , significantly more than its fractional volume of 18% of the global ocean. In contrast, the Pacific ocean contributes only 30% to β ocean despite its fractional volume of 42% of the global ocean. By definition, the contribution of each basin to β sat and β dis is approximately proportional to the ocean volume contained in each basin. However, β dis is relatively low in the Atlantic Ocean and high in the Pacific Ocean compared with their respective volumes, which is consistent with the Atlantic Ocean interior 325 being more ventilated and closer to equilibrium with the contemporary atmospheric CO 2 , and the Pacific ocean interior being less ventilated than the rest of the ocean. Hence, the relative large contribution to β ocean from the Atlantic Ocean is associated with a strong and rapid transfer of anthropogenic carbon into the ocean interior from both a strong local physical ventilation and a transport of carbon from the Southern Ocean.
The Atlantic Ocean has a contribution of 30% to γ ocean , much larger than expected from its fractional volume of 18% of the 330 global ocean (Fig. 5b). This large contribution of the Atlantic Ocean is primarily due to the disequilibrium part of γ (Fig. 5b), and the reduction in the physical ventilation due to climate change. In the well ventilated Atlantic Ocean, the additional heat penetrates into the ocean interior and is not confined to the ocean surface, which limits the effect of the reduction in solubility with warming, so that there is only a 11% contribution to γ sat there.
The Pacific and Indian Ocean contributions to γ sat are consistent with their fractional volumes (Fig. 5b). These basins 335 experience a significant decrease in solubility despite having warmed less per unit volume than the rest of the ocean (Fig. 1d), as much of this warming is confined in the ocean mixed layer. The Pacific and Indian Ocean contributions to γ dis and γ reg are smaller than expected from their fractional volumes, as there is no significant effect from changes in ventilation. This absence of any significant effect from changes in the ventilation with warming in the Pacific and the Indian Oceans leads to their smaller contribution to γ ocean relative to their volumes (Fig. 5b).

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The Southern Ocean has a contribution of 38% to γ dis , and of 52% to γ reg , much larger than expected from its fractional volume (Fig. 5b), which suggests that changes in the physical ventilation and the accumulation of regenerated carbon due to climate change drive large changes in ocean storage. The Southern Ocean contribution to γ sat is also larger than expected from its fractional volume (Fig. 5b), consistent with a large warming per unit volume in this basin (Fig. 1d). Hence, the apparent small contribution of the Southern Ocean to γ ocean , of 20%, is due to a compensation between the large decrease in ocean The model is first integrated to a pre-industrial steady state, with the distribution of temperature and DIC depending on the pre-industrial strength of the overturning. The model is then forced by a 1% yr −1 increase in atmospheric CO 2 concentration 370 from a pre-industrial value of 280 ppm until atmospheric CO 2 quadruples over a 140-year period. This increase in atmospheric CO 2 drives a radiative forcing: R = a ln (CO 2 /CO 2,0 ), where a = 5.35 W m −2 (Myhre et al., 1998) and subscript 0 is the preindustrial. This radiative forcing then drives a radiative response, λ∆T air , and a net downward heat flux entering the system at the top of the atmosphere, N T OA , (Gregory et al., 2004) such that R = λ∆T air + N T OA , where T air is the temperature of the slab atmosphere and λ is the climate feedback parameter that is assumed constant and equal to 1 W m −2 K −1 for simplicity.

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The ocean heat uptake, N , is distributed equally over the ocean surface and estimated as N = N T OA − c(∆T surf − ∆T air ), where c=50 W m −2 K −1 is an air-sea heat transfer parameter and T surf is the ocean temperature at the surface. For this model closure, the ocean heat uptake is more than 95% of the net downward heat flux entering the system at the top of the atmosphere.
This additional ocean heat reduces the conversion of light to dense waters in the North Atlantic, q N A , and leads to an overturning weakening, following where A is the model area covered by the low and mid latitudes, ρ is a referenced ocean density, C p is the specific heat capacity for the ocean, and T contrast is the temperature contrast between light waters in the low and mid latitudes, involving the mixed layer and thermocline, and the dense waters in the deep ocean.
Three experiments were conducted using this idealised model forced by 1% yr −1 increase in atmospheric CO 2 : (i) a control 385 experiment with a strong pre-industrial AMOC that experiences a reduction with warming as described by Eq. (24) (solid line in Fig. 6b); (ii) an experiment with a weak pre-industrial AMOC that experiences the same reduction with warming as in the control experiment (dotted line in Fig. 6b); and (iii) an experiment with a strong pre-industrial AMOC that experiences a doubled reduction with warming than in the control experiment, such that the right hand of Eq. (24) is multiplied by a factor of 2 (dashed line in Fig. 6b). In all the experiments, a fully coupled simulation (COU) and a biogeochemically coupled simulation 390 (BGC) are used to estimate the carbon-cycle feedback parameters β ocean and γ ocean .
In the idealised model, a weaker pre-industrial meridional overturning leads to a smaller carbon-concentration feedback parameter, β ocean , during the centennial transient response to the increase in atmospheric CO 2 (Fig. 6c, black lines). The saturated part of β does not directly depend on the AMOC strength (Fig. 6c, red lines). In contrast, a weaker pre-industrial AMOC leads to a more negative disequilibrium part of β (Fig. 6c, blue lines) due to a weaker and slower transfer of anthropogenic 395 carbon below the ocean surface. Hence, the pre-industrial AMOC controls β ocean through its effect on the physical ventilation via the disequilibrium carbon pool.
The strength of the pre-industrial meridional overturning has only a small impact on the carbon-climate feedback parameter, γ ocean , that is associated with the saturated carbon pool (Fig. 6d, solid and dotted lines). In the idealised model, a different pre-industrial overturning is associated with a different pre-industrial ocean state, in terms of temperature and DIC, which has 400 a small effect in the the saturated part of γ due to the non-linearity of the carbonate chemistry. The carbon-climate feedback parameter, γ ocean , is primarily controlled by the changes in AMOC with warming, and specifically by the dependence of the negative γ dis to the AMOC reduction with warming (Fig. 6d, solid and dashed lines). Hence, a more pronounced reduction in AMOC with warming drives a more negative γ ocean , as it leads to a larger reduction in the physical transfer of carbon into the ocean interior.

Results from CMIP6 Earth system models
There is a large spread in the pre-industrial strength of AMOC amongst the Earth system models (Fig. 7) with a range of 11.3 Sv in IPSL-CM6A-LR to 23.2 Sv in NorESM2-LM (Table 3). There is also a large spread in the response of the AMOC to climate change amongst the models (Fig. 8), with the magnitude of the AMOC weakening ranging from -3.6 Sv in IPSL-CM6A-LR to -17.47 Sv in MRI-ESM2 (Table 3). Generally, the models with a stronger pre-industrial AMOC simulate a larger reduction in AMOC with warming. Linear correlations are used to relate the AMOC variability amongst the models with the variability in the carbon-cycle feedbacks for the global ocean and the different ocean basins (Table 4).
For the global ocean, there is a moderate positive correlation between the pre-industrial AMOC and the ocean carbonconcentration feedback parameter, β ocean , (r=0.70, Table 4), such that models with stronger pre-industrial AMOC have a more positive β ocean . However, there is no significant correlation between the pre-industrial AMOC and the saturated or 415 disequilibrium part of β (Table 4) on global scale. In the Atlantic Ocean, β is strongly correlated with the pre-industrial AMOC in the Earth system models (r=0.87) and this correlation is due to β dis (Table 4 and Fig. 9a and c), which suggests that a stronger pre-industrial AMOC leads to a larger β via a stronger physical transfer of anthopogenic carbon below the ocean surface there, similar to the behaviour of the idealised model (Fig. 6c).
In the Southern Ocean, there is a statistically significant correlation between the pre-industrial AMOC and β (r=0.82), that is 420 not associated with either the saturated, the disequilibrium or the regenerated carbon pools (Table 4). A stronger pre-industrial AMOC is associated with a stronger return flow of interior water into the surface in the Southern Ocean upwelling branch of the overturning circulation (Marshall and Speer, 2012), and hence with a stronger local anthropogenic carbon uptake from the atmosphere in the BGC run there. However, in the Southern Ocean both the anthopogenic carbon uptake from the atmosphere and its export to the other basins are also controlled by subduction (Sabine et al., 2004;Sallée et al., 2012Sallée et al., , 2013 and the 425 residual circulation involving the wind-driven Ekman transport and eddy fluxes (Lauderdale et al., 2013). Hence, there is no significant correlation between the pre-industrial AMOC and β dis in the Southern Ocean as other processes like subduction and the residual circulation are important in setting the pre-industrial physical ventilation and transport of carbon to other basins.
There is also no significant correlation between the pre-industrial AMOC and β in the Pacific and Indian Oceans, suggesting that other processes dominate the ocean ventilation there.

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For the global ocean, the carbon-climate feedback parameter, γ ocean , and its disequilibrium part, γ dis , are positively correlated with the AMOC weakening due to climate change in the Earth system models (r=0.67, and r=0.76, respectively, Table   4). This correlation for the global ocean is driven by the Atlantic Ocean, as there is no significant correlation between γ and AMOC weakening in the Pacific, Indian and Southern Oceans (Table 4). In the Atlantic Ocean, a more pronounced AMOC weakening due to climate change is associated with a larger reduction in the physical transfer of carbon below the ocean surface 435 and so with a more negative γ and γ dis (Fig. 10a and c), consistent with the inferences for the idealised model (Fig. 6d)..
In the Atlantic Ocean, the correlation between γ reg and AMOC weakening is negative (r=-0.67, Table 4), when excluding the CNRM-ESM2-1 model which has a much larger γ reg than the rest of the Earth system models (Table 3). A more pronounced AMOC weakening leads to a longer residence time in the Atlantic Ocean interior and so to a larger accumulation of regenerated carbon there and a more positive γ reg (Fig. 10d). The substantially larger change in the regenerated carbon pool with warming in 440 CNRM-ESM2-1 than the rest of the models is probably due to a revised parametirization for organic mater remineralization (in PISCESv2-gas), its parametrisation of sedimentation and its interactive riverine input; see Séférian et al. (2020) for differences in ocean biogeochemistry amongst the Earth system models.
tribution of the Atlantic, Pacific, Indian and Southern Oceans to the ocean carbon cycle feedbacks in a set of CMIP6 Earth system models. Experiments using an idealised climate model and diagnostics of the CMIP6 models suggest a dependence of the ocean carbon cycle feedbacks on the strength of the pre-industrial Atlantic Meridional Overturning Circulation (AMOC) and on the magnitudes of the AMOC weakening with warming, primarily due to the control of the AMOC on the physical ventilation in the Atlantic Ocean. .

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The ocean carbon-concentration feedback in CMIP6 models is controlled by a competition between opposing contributions from the saturated and the disequilibrium carbon pools, such that (i) the carbonate chemistry drives a positive β ocean that decreases with the increase in atmospheric CO 2 as the ocean acidifies and its capacity to buffer atmospheric CO 2 decreases, and (ii) the physical ventilation drives a negative β ocean that becomes less negative in time as the anthropogenic carbon is transferred from the ocean surface into the ocean interior. The ocean carbon-climate feedback in CMIP6 models is controlled 455 by a competition between the combined decrease in the saturated and disequilibrium carbon pools and the increase in the regenerated carbon pool, such that (i) the decrease in solubility and weakening in physical ventilation with warming drive a negative γ ocean , and (ii) the increase in the accumulation of regenerated carbon, associated with a longer residence time in the ocean interior with climate change, drives a positive γ ocean .
5.1 Regional ocean carbon cycle feedbacks 460 The regional ocean carbon storage is controlled by the local air-sea carbon exchange and the transport of carbon by the ocean circulation. Here, we estimated the regional carbon cycle feedbacks based on the regional ocean carbon storage such that the effect of the ocean transport of carbon is explicitly accounted for. This transport effect acts to decrease the carbon-concentration feedback parameter, β, in the Southern Ocean, and increase β in the Southern hemisphere subtropical gyres and the western boundary of the Atlantic Ocean in CMIP6 models. The transport effect on β is consistent with the view that while almost half 465 of the anthopogenic carbon enters through the Southern Ocean, much of this carbon is transferred and stored into the Atlantic, Pacific and Indian Oceans (Sabine et al., 2004;Khatiwala et al., 2009;Frölicher et al., 2015). The transport effect also leads to a more spatially uniform and negative carbon-climate feedback parameter, γ, almost everywhere in the ocean in CMIP6 models.
The Atlantic, Pacific and the Southern Oceans provide comparable contributions, of 26% to 30%, to the global ocean carbon-470 concentration feedback, despite their different size. This large contribution from the Atlantic Ocean relative to its volume is associated with an enhanced physical transfer of anthropogenic carbon into the ocean interior due to a strong local ventilation and a transport of carbon from the Southern Ocean. The inter-model variability in the carbon-concentration feedback parameter, β, amongst the CMIP6 models is small in all the ocean basins, reflecting the use of a similar carbonate chemistry scheme in these models  and a similar general large-scale circulation.
The Atlantic Ocean has the largest contribution to the ocean carbon-climate feedback relative to its size in CMIP6 models, which is mainly due to the disequilibrium carbon pool and the reduction in the physical ventilation with climate change.
Specifically, the negative γ per unit area is largest in the high latitudes of the North Atlantic in CMIP6 models, consistent with previous studies suggesting the effect of climate-driven changes in the circulation to the carbon storage is significant there (Sarmiento et al., 1998;Winton et al., 2013;Bernardello et al., 2014).

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The relative small contribution from the Southern Ocean to the carbon-climate feedback in CMIP6 is due to a partial compensation between the combined decrease in solubility and physical ventilation with warming, driving a negative γ, and the large increase in accumulation of regenerated carbon in the ocean interior with climate change, driving a positive γ. This compensation between the decrease in solubility and physical ventilation with warming and the increase in accumulation of regenerated carbon with climate change in the Southern Ocean is also supported by previous studies based on experiments 485 using a single model (Sarmiento et al., 1998;Bernardello et al., 2014); and a significant increase in the regenerated carbon pool of the Southern Ocean with climate change was also found in CMIP5 models (Ito et al., 2015).
In the Indo-Pacific Ocean, the carbon-climate feedback in CMIP6 is primarily attributed to the saturated carbon pool and the decrease in solubility with warming. This response in the Indo-Pacific Ocean is consistent with a feedback triggered by warming and the reduction in solubility dominating in low and mid-latitudes, as was shown in a CMIP5-generation Earth 490 system model (Rodgers et al., 2020). The inter-model variability in γ amongst CMIP6 models is relatively large compared with β in all the ocean basins, and is mainly driven by the spread in the response of physical ventilation and circulation to climate change, and in the parametrization of ocean biogeochemical processes amongst the models.

Control of the Altantic Meridional Overturning Circulation
Our sensitivity experiments with an idealised climate model show that a weaker pre-industrial Atlantic Meridional Overturning 495 Circulation (AMOC) leads to a smaller ocean carbon-concentration feedback parameter, β ocean . This dependence of β ocean to the pre-industrial AMOC is controlled by the disequilibrium carbon pool, and the physical transfer of anthropogenic carbon from the surface to the ocean interior. The ocean carbon-climate feedback parameter, γ ocean , is instead primarily controlled by the reduction in AMOC with warming, where a weakening in AMOC reduces the physical ventilation and leads to the disequilibrium part of γ becoming more negative.

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Turning to the CMIP6 models, in the Atlantic Ocean, the carbon-concentration feedback parameter, β, is controlled by the strength of the pre-industrial AMOC, similarly to the behaviour in the idealised climate model. This control of AMOC on β is associated with the disequilibrium carbon pool and the effect of physical ventilation, such that Earth system models with stronger AMOC have a more efficient transport of anthopogenic carbon into the ocean interior in the Atlantic Ocean.
However, there is only a moderate correlation between AMOC strength and β ocean on a global scale, which suggests that other 505 processes related to ocean ventilation, involving the wind-driven gyre circulation, mode water formation and subduction and the Southern Ocean residual circulation, are also important for regulating the ocean carbon-concentration feedback. In contrast with our results based on the idealised model and the CMIP6 models, Roy et al. (2011) found no direct dependence of β ocean to the AMOC strength in older generation Earth system models, which suggests that either: (i) the sample of 4 models used in is more pronounced when considering estimates at the quadrupling of atmospheric CO 2 rather than estimates from years 2010 to 2100 in a high-emission scenario as in Roy et al. (2011).
In the Atlantic Ocean, the carbon-climate feedback parameter, γ, is controlled by the AMOC weakening with climate change in the CMIP6 models, similarly to the behaviour in the idealised climate model. This control of the AMOC weakening on γ is: (i) primarily due to the disequilibrium carbon pool, with a more pronounced AMOC weakening driving a larger reduction in 515 the physical transfer of carbon into the ocean interior and a more negative γ; and (ii) to a lesser extend due to the regenerated carbon pool, with a more pronounced AMOC weakening driving a larger accumulation of regenerated carbon in the ocean interior and a more positive γ. The dependence of the carbon-climate feedback to the AMOC weakening in the Atlantic Ocean is consistent with previous studies based on experiments using a single older generation Earth system model (Crueger et al., 2008;Yoshikawa et al., 2008).

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On global scale, we found only a moderate dependence of γ ocean to AMOC weakening with climate change that is attributed to the Atlantic Ocean, as there is no significant correlation between γ and AMOC weakening in the Pacific, Indian and Southern Oceans. Hence, the weakening in the AMOC due to climate change has only a modest impact on ocean carbon uptake on the global and centennial scale, consistent with previous studies (Sarmiento et al., 1998;Joos et al., 1999;Zickfeld et al., 2008).
Future work should focus on the control of the ocean carbon cycle feedbacks from other ventilation processes beyond the 525 AMOC, such as the formation and subduction of mode and intermediate waters involving the seasonal mixed-layer cycle, and the horizontal and vertical circulation. Additionally, the regional ocean cumulative carbon uptake and carbon storage may be estimated in a dynamically based density space (Sallée et al., 2013;Meijers, 2014;Iudicone et al., 2016) to reveal the contribution of different water masses to β and γ (Roy et al., 2020, personal communication). Finally, we note that for a quadrupling of atmospheric CO 2 and on centennial time scale the carbon-concentration feedback is substantially larger than 530 the carbon-climate feedback; however, this will not necessary be the case after the emissions cease and there is an ongoing carbon cycle and climate response as the system adjusts towards equilibrium.
Appendix A: Contribution of air-sea flux and ocean transport to the carbon cycle feedbacks in different ocean basins The Southern Ocean accounts on average for about half of the ocean anthopogenic carbon uptake (Fig. A1a red line) in CMIP6 Earth system model despite covering only 30% of the global ocean consistent with results from CMIP5 model during the 535 historical period (Frölicher et al., 2015), as well as observational based estimates (Mikaloff-Fletcher et al., 2006). However, a large portion of the anthropogenic carbon entering through the Southern Ocean is transferred through the ocean circulation into the Atlantic, Indian and Pacific Oceans, with the Atlantic Ocean receiving most of this carbon (Fig. A1a) in CMIP6 models, consistent with observational-based estimates (Sabine et al., 2004;Khatiwala et al., 2009). Consequently, the carbonconcentration feedback parameter β is substantially larger in the Southern Ocean, but smaller in the other ocean basins when 540 estimated based on the local air-sea cumulative carbon flux (Fig. A1b, red lines) than when estimated based on the changes in the local ocean carbon storage (Fig. A1b, black lines). Turning to the carbon-climate feedback, the net effect of climate change  Table 4. Correlation between the ocean carbon-concentration feedback parameter, β, and the pre-industrial strength of the Atlantic Meridional Overturning Circulation (AMOC) and correlation between the ocean carbon-climate feedback parameter, γ and the AMOC weakening due to climate change, along with the contribution from the saturated, disequilibrium and regenerated carbon pools based on 10 CMIP6 models (Table 1). For the regenerated part of γ, correlations estimated excluding the CNRM-ESM2-1 model, which has substantially larger changes in the regenerated carbon with warming than the rest of the Earth system models, are presented as γreg. The correlation is expressed as a correlation coefficient, r, and a p-value.     (Table 1). The feedback parameters are based on the fully coupled simulation (COU) and the biogeochemically coupled simulation (BGC) .The control run was used to estimate the changes relative to the pre-industrial to exclude model biases. Figure 3. Geographical distribution of the CMIP6 inter-model mean carbon cycle feedback parameters normalised by area, β (gC ppm −1 m −2 ) and γ (gC K −1 m −2 ), as estimated: (a) based on the regional ocean carbon inventory changes; and (b) based on the regional cumulative ocean carbon uptake from the atmosphere. The estimates are based on the fully coupled simulation (COU) and the biogeochemically coupled simulation (BGC) under the 1% yr −1 increasing CO2 experiment. The control run was used to estimate the changes relative to the preindustrial to exclude model biases. Diagnostics are from years 121 to 140 (the 20 years up to quadrupling of atmospheric CO2). The intermodel mean is based on the models in Table 1 Figure 5. The fractional contribution (in %) of different ocean basins to the total volume of the ocean and to the ocean carbon cycle feedback parameters, along with the contribution from the saturated, disequilibrium and regenerated carbon pools based on the inter-model mean of 10 CMIP6 models (Table 1): (a) carbon-concentration feedback parameter, β, and (b) carbon-climate feedback parameter, γ. The estimates are based on the fully coupled simulation (COU) and the biogeochemically coupled simulation (BGC) under the 1% yr −1 increasing CO2 experiment. The control run was used to estimate the changes relative to the pre-industrial to exclude model biases. Diagnostics are from years 121 to 140 (the 20 years up to quadrupling of atmospheric CO2). The regenerated part of β is omitted as its contribution to β is negligible in all basins (Fig. 4). run was used to estimate the changes relative to the pre-industrial to exclude model biases. The intermodel mean is based on the models in Table 1 excluding NorESM2-LM for which the air-sea carbon flux for the BGC run was unavailable.