We used the global warming experiments conducted by Yamamoto et al. (2015) with the MIROC 4 m AOGCM. This model is based on the MIROC 3.2 (K-1 Model Developers, 2004) that contributed to the Coupled Model Intercomparison Project phase 3 (Meehl et al., 2007), which was extensively cited in the Intergovernmental Panel on Climate Change Fourth Assessment Report. In the MIROC 4 m, the coefficient of the isopycnal layer thickness diffusivity is set as 7.0 × 10-6 cm2 s-1 instead of the value of 3.0 × 10-6 cm2 s-1 used in the original MIROC 3.2. The atmospheric GCM has a horizontal resolution of T42 (∼ 2.8∘) and 20 vertical levels. The oceanic GCM has a zonal resolution of 1.4∘ and a spatially varying meridional resolution that is approximately 0.56∘ at latitudes lower than 8∘ and 1.4∘ at latitudes higher than 65∘; the resolution changes smoothly between these latitudes. The vertical coordinate is a hybrid of sigma-z, resolving 44 levels in total: eight sigma-layers near the surface, 35 z layers beneath, and one bottom boundary layer (Nakano and Suginohara, 2002). The sea ice component is based on a two-category thickness representation, zero-layer thermodynamics (Semtner, 1976), and dynamics using elastic–viscous–plastic rheology (Hunke and Dukowicz, 1997). A model spin-up has been performed under preindustrial boundary conditions such as insolation and an atmospheric CO2 concentration of 285 ppm.

The ocean carbon cycle was calculated by the MIROC-based offline biogeochemical model (Yamamoto et al., 2015), which enables us to conduct numerous sensitivity experiments of the ocean carbon cycle forced by outputs from AOGCM climate simulations with low computational cost. The horizontal and vertical resolutions are the same as in MIROC 3.2. For the tracer calculation, the monthly output data of velocity, temperature, salinity, sea surface height, sea surface wind speed, sea ice fraction, and sea surface solar radiation from MIROC are applied to an offline tracer scheme (Oka et al., 2011).

This biogeochemical model is a modified version of the nutrient–phytoplankton–zooplankton–detritus (NPZD) ecosystem model of Keller et al. (2012). The model includes two phytoplankton classes (nitrogen fixers and other phytoplankton), zooplankton, particulate detritus, nitrate (NO3), phosphate (PO4), dissolved oxygen (O2), dissolved inorganic carbon (DIC), alkalinity (ALK), two carbon isotopes (13C and 14C), and an ideal age tracer. Constant stoichiometry relates the C, N, and P content of the biological variables and their exchanges to the inorganic variables (NO3, PO4, O2, ALK, and DIC). Optimal uptake kinetics, which assume a physiological trade-off between the efficiency of nutrients encountered at the cell surface and the maximum assimilation rate (Smith et al., 2009), are adopted for the nutrient limitation of the growth rate of phytoplankton. The maximum phytoplankton growth and microbial remineralization rates are assumed to increase with seawater temperature according to Eppley (1972).

The formulations of air–sea gas exchange and carbon chemistry follow the protocols of the Ocean Carbon Cycle Model Intercomparison Project – Phase 2 (OCMIP-2; http://ocmip5.ipsl.jussieu.fr/OCMIP/, last access: 6 July 2018) (Najjar and Orr, 1999). The production rate of calcium carbonate (CaCO3) is assumed to be proportional to that of particulate organic carbon (POC, CaCO3 : POC = 0.03) and the settling flux of particulate CaCO3 in the water column decreases with an e-folding depth of 3500 m (Schmittner et al., 2008). Although iron cycling is not explicitly calculated in our model, we adopted the iron limitation for the phytoplankton growth rate using monthly dissolved iron concentration outputs from preindustrial experiments conducted using the biogeochemical elemental cycling model (AOU_06 case in Misumi et al., 2013). Thus, we cannot consider changes in iron cycling and their impact on ecosystems in the global warming experiment. This model does not include a marine-sediment module because the reaction of the dissolved CO2 with CaCO3 in deep-ocean sediments only plays an important role at timescales of thousands of years or longer (Archer et al., 1998).

As we forced the offline ocean biogeochemical model with monthly mean data from the AOGCM, a certain amount of short-term variability was averaged over. To confirm the validity of the offline calculations and their sensitivity to the forcing frequency, we compared the passive salinity distribution in the offline model to online salinity distribution in the AOGCM. There were no significant differences in basin-scale distributions between the two simulations, suggesting that short-term processes had limited impact on our results.

The biogeochemical model was initialized from the annual mean climatology data based on the World Ocean Atlas 2005 (WOA2005: Garcia et al., 2006) for dissolved NO3 and PO4 and the GLobal Ocean Data Analysis Project (GLODAP; Key et al., 2004) for DIC and ALK. For the spin-up, the last 50 years of data in the MIROC preindustrial experiment were cyclically applied to the offline ocean biogeochemical model. A model spin-up of more than 8000 years has been performed in order to eliminate the model drift in the global inventory of all tracers. In the last century of the spin-up run, the global net atmosphere–ocean CO2 exchange is 3.0 × 10-4 PgC yr-1, which is smaller than the OCMIP2 threshold of 0.01 PgC yr-1 (Orr, 2002). The resultant initial storage of ocean carbon (35 400 PgC), ocean net primary production (49.6 PgC yr-1), and export production (8.1 PgC yr-1) are comparable to observations and other estimates (Antoine et al., 1996; Schlitzer, 2000; Ciais et al., 2014). The simulated basin-scale distributions of nutrients (PO4 and NO3), DIC, and ALK under preindustrial conditions are generally in agreement with the modern distributions in the WOA2005 and GLODAP datasets (Fig. S1 in the Supplement). All physical and biogeochemical tracers, except salinity, have correlation coefficients with observational data of more than 0.85 and normalized standard deviation values between 0.7 and 1.1 (Fig. S2).

After the spin-up, the prescribed atmospheric CO2 concentration for the climate model was increased by 1 % per year from the preindustrial value (285 ppm) until it reached 4 × CO2 levels (1140 ppm) at year 140. This value was then held constant until reaching 2000 model years. Using the output of the global warming experiment conducted by the climate model, the offline biogeochemical model was integrated for 2000 years (GW_bio in Table 1).

The prescribed CO2 concentrations during the first 140 years of our experimental design are higher than the business-as-usual scenarios such as SRES A2 and RCP8.5, so the response of climate and oceanic carbon cycle would be somewhat different. After year 140, the influence of the initial difference would weaken because of the similar CO2 concentrations between the 4 × CO2 and business-as-usual scenarios. Therefore, the CO2 differences between these scenarios would have a limited impact on the long-term response of climate and ocean carbon cycle to global warming. We compare our results with previous long-term simulations under the business-as-usual scenario in Sect. 3.

In the real world, the climate and carbon cycle change in response to CO2 emissions; our simulation with prescribed CO2 concentrations is thus highly idealized. However, there is an advantage to simulations with prescribed CO2 concentrations as opposed to those with prescribed emissions: the former allow for a more rigorous separation of feedback processes since carbon sinks respond to the same atmospheric CO2 concentration in all simulations (Zickfeld et al., 2011).

We conducted additional experiments for the first 500 years using the offline biogeochemical model (Table 1). In the constant-climate run (CTL_bio), the same prescribed CO2 concentration as used in GW_bio but with the climate conditions of the MIROC preindustrial experiment were applied to the offline biogeochemical model. This experiment relied on the same concept as the uncoupled simulation in Friedlingstein et al. (2006), in which changing atmospheric CO2 concentrations did not affect the radiation balance and therefore the climate. The total change in oceanic CO2 uptake due to global warming is obtained from the difference between GW_bio and CTL_bio (“Total” in Table 2). We conducted three sets of experiments to isolate the sensitivity of CO2 uptake with respect to changes in sea surface temperature (SST), ocean circulation, biology, freshwater flux, and sea ice (Table 1).

In this section, we briefly describe the regional changes in climate and ocean biogeochemical variables; a full summary of global mean changes was reported in Yamamoto et al. (2015). At the end of the global warming simulation, the global mean surface air and ocean temperature increase by 8.4 and 6.5 ∘C, respectively. The AMOC decreases from 16.5 to 3.8 Sv in the first 500 years and does not recover by the end of the simulation. The strength of the Antarctic Bottom Water (AABW) formation decreases from 6.2 to 2.4 Sv in the first 500 years. Thereafter, the strength of the AABW formation recovers and overshoots the preindustrial condition after year 1000. These global mean changes are comparable to previous long-term simulations with EMIC and AOGCM (see Yamamoto et al., 2015, for a more detailed discussion).

At the time of CO2 quadrupling (year 140), polar amplification occurs only in the Northern Hemisphere (Fig. 2a). The surface temperature over the Southern Ocean and Antarctica gradually increases, and polar amplification in both hemispheres is observed at approximately year 1000. This slow southern polar warming is related to deep-ocean heat uptake in the Southern Ocean. According to the slow deep-ocean heat uptake, the ocean interior is still warming up at the end of the simulations (Fig. 2b). Slow southern polar warming and ocean heat uptake have also been reported in previous multi-millennial simulations conducted by ECHAM5–MPIOM (Li et al., 2013). In the ocean, greater warming of the upper ocean (above 2000 m) occur in the Southern Hemisphere (Fig. 2c). This is because the drastically weakened AMOC and enhanced AABW formations cause the heat transport to be larger in the Southern Hemisphere than in the Northern Hemisphere (Fig. 2d). Weakening in AMOC reduces the heat transport from 1.8 to 0.8 PW across 30∘ N. By contrast, the enhanced AABW increases heat transport by 0.7 PW in the Southern Hemisphere.

Strengthening and poleward shifting of the subpolar westerlies occurs in the Southern Hemisphere (Fig. 2e), which is consistent with the observations and a robust feature of climate projections in global warming experiments (Fyfe and Saenko, 2006; Meijers, 2014). A 12 % strengthening and a 2.8∘ poleward shift of the maximum annual mean zonal wind stress occur at the time of CO2 quadrupling. Subsequently, the subpolar westerlies in the Southern Hemisphere are gradually weakened but are still slightly stronger than the preindustrial conditions. This weakening occurs because the slow southern polar warming weakens the thermal gradient between the tropical and polar areas. The contributions of ocean circulation change caused by strengthened westerlies to the ocean carbon cycle are discussed in Sect. 4.2.

Global PO4 and NO3 concentration at the surface decreases by about 25 and 20 %, respectively. These decreases are attributed to reduced nutrient supply into the euphotic zone due to enhanced stratification and slower deep-ocean circulation. As a result, the global export production decreases by 22 % (see Fig. 1d in Yamamoto et al., 2015), which is comparable with CMIP5 models (7–18 % reduction in export production from the 1990s to 2090s for RCP8.5) (Bopp et al., 2013). Remarkable reductions in surface PO4 concentration occurs in the tropical ocean and the North Atlantic (Fig. 2f). Consistent with this reduction, the largest declines in export production are also located around the Equator and in the North Atlantic (Fig. 2g). The increases in export production are primarily observed in the Southern and Arctic oceans. These increases are related to reductions in light limitation and/or increased growth rates due to rising temperatures as shown by Steinacher et al. (2010).

The efficiency of the oceanic biological pump is calculated following Ito and Follows (2005) as the biologically sequestered fraction of the total phosphate inventory, Premi / Ptot. Here, Ptot is the total phosphate inventory and Premi is remineralized phosphate concentration (Premi = AOU × RP:O), where AOU is the apparent oxygen utilization (AOU = O2sat - O2), O2 is the dissolved oxygen concentration, and RP:O is a constant phosphorous-to-oxygen ratio. Premi / Ptot increases from its preindustrial value of 0.47 to 0.51 in the first 200 years. This increased efficiency of the biological pump is consistent with CMIP5 models (calculated in terms of AOU) (Schwinger et al., 2014). After 500 model years, Premi / Ptot decreases to 0.34 by the end of the simulation. Preformed PO4 is accumulated in AABW (Fig. S3). This reduced efficiency of the biological pump is associated with enhanced AABW formation after 500 model years (Yamamoto et al., 2015).

Global primary production increases by 2.5 PgC yr-1 from the preindustrial value, which is consistent with previous studies (Schmittner et al., 2008; Taucher and Oschlies, 2011). Both diazotrophs and other phytoplankton increase slightly. Taucher and Oschlies (2011) showed that increases in primary production are caused by temperature effects on biological processes such as remineralization and the microbial loop.

Due to the constant production ratio of POC to CaCO3 in the model formulation and the increase in the global primary production, CaCO3 production is increased by 6 %. The export of CaCO3 also increases in spite of a reduction in the POC export, resulting in the rain ratio increasing from 0.09 to 0.13. Two distinct export responses are caused by faster and shallower remineralization of POC in a warmer ocean; however, the remineralization rate of CaCO3 is independent of the seawater temperature in our model. The enhanced CaCO3 production decreases (increases) alkalinity in the surface (deep) oceans as shown by changes in the salinity-normalized alkalinity (dashed lines in Fig. 2h). Reduced surface alkalinity is also caused by the longer residence time of surface waters, allowing a more efficient biological utilization of the carbonate ions. The enhanced surface-to-deep gradient of the salinity-normalized alkalinity and the alkalinity associated with changes in CaCO3 cycling and ocean circulation have been reported in previous long-term simulations (Plattner et al., 2001; Schmittner et al., 2008).

Changes in the freshwater flux also alter the alkalinity. At low latitudes, enhanced evaporation concentrates the surface alkalinity. Dilution of the surface alkalinity by enhanced precipitation at high latitudes reduces the alkalinity in the deep ocean. As a result, changes in the freshwater flux cause weaker surface-to-deep alkalinity gradients. The effects of changes in the CaCO3 cycling and freshwater flux cancel each other out, resulting in apparently slight changes in the surface-to-deep alkalinity gradient in our model (solid lines in Fig. 2h). The effects of changes in the CaCO3 cycle and freshwater flux to the CO2 uptake change are quantitatively discussed in Sect. 4.1.

We first show the cumulative oceanic uptake of CO2 and the reduction of oceanic CO2 uptake due to global warming. At the time of CO2 quadrupling (year 140), the cumulative CO2 uptake is 567 PgC in the global warming run (GW_bio) and 654 PgC in the constant climate run (CTL_bio), a projected reduction due to global warming of 13 %. These values are close to those of corresponding simulations in the Coupled Model Intercomparison Project 5 (CMIP5; Taylor et al., 2012) in which the modeled mean CO2 uptake is 613 PgC and the uptake reduction is 11 % (Arora et al., 2013). Even though oceanic CO2 uptake is decreased during constant atmospheric CO2 after year 140, a new equilibrium is not yet reached by the end of the simulation. In the last decade of the experiments, the ocean still takes up approximately 0.31 PgC yr-1 due to the millennial timescale of the deep-ocean ventilation (Key et al., 2004). At the end of the simulation, the cumulative CO2 uptake is 2028 PgC and the uptake reduction due to global warming increases to 30 % (Fig. 3a and Table 1). These values and the increasing trend in the uptake reduction are also comparable to the results of previous long-term EMIC simulations (Plattner et al., 2001; Schmittner et al., 2008).

The time evolutions of oceanic CO2 uptake in each basin are shown in Fig. 3b. During the first few decades, the Pacific Ocean is the dominant sink of atmospheric CO2 because it possesses the largest area. After atmospheric CO2 stops increasing, the surface Pacific waters are close to saturation and CO2 uptake rapidly decreases because the deep Pacific waters are slowly ventilated. Conversely, the decrease in CO2 uptake in the Southern Ocean is slower than that in the Pacific Ocean. Carbon transport from the surface to deep ocean via these well-ventilated waters causes continuous CO2 uptake there. In the preindustrial condition, the pCO2 in the Southern Ocean is kept higher than the atmospheric pCO2 owing to the upwelling of carbon-rich deep waters, resulting in a source of atmospheric CO2. The Southern Ocean alters from a source to a sink of atmospheric CO2 immediately after the atmospheric CO2 increase. This phenomenon is consistent with observation-based reconstructions of present-day and preindustrial air–sea CO2 fluxes (Gruber et al., 2009). After excess CO2 is mixed throughout the deep ocean, the pCO2 in the Southern Ocean again exceeds the atmospheric pCO2. The Southern Ocean returns to being a source of atmospheric CO2 at approximately year 1400. At the end of the global warming experiment, the Atlantic and Southern oceans are the major sink and source basins of atmospheric CO2, respectively, as in the preindustrial condition.

We also investigate the regional differences in uptake reduction due to global warming. In the first 500 years, approximately half of the total uptake reduction occurs in tropical and subtropical regions between 32.5∘ S and 32.5∘ N (Figs. 3c, and S4). The contributions of the high latitudes in the Northern Hemisphere and Southern Hemisphere have similar magnitudes. At a basin scale, the contributions of the Atlantic and Pacific oceans have similar magnitudes and that of the Indian Ocean is approximately half those contributions. These regional differences have also been found in similar long-term simulations by Plattner et al. (2001).

Figure 4 shows the zonal mean distribution of the salinity-normalized DIC (sDIC) in the global warming run. In the first 500 years, changes in sDIC from the preindustrial condition decrease from the surface to the deep oceans. Significant sDIC changes in the deep water are observed in the North Atlantic. The shallower CO2 invasion into the North Atlantic compared to the constant climate run (Fig. S4) is caused by the weaker and shallower AMOC. After year 1000, due to the enhanced AABW formation, AABW with a relatively high sDIC concentration intrudes into the deep North Atlantic below 2000 m. As a result, the largest sDIC change in the deep water occurs in the North Atlantic at the end of the simulations. The smallest sDIC change is found in the deep North Pacific in accordance with the millennial ventilation timescale.

In the abiotic experiments, the reduction in oceanic CO2 uptake associated with global warming is caused by changes in the ocean circulation and increases in the SST that reduce the global CO2 uptake by 308 and 140 PgC, respectively (Table 2). Weaker AMOC and AABW formations decrease the downward transport of CO2 from the surface to the deep ocean, leading to a significant drop in the CO2 uptake at high latitudes (Fig. 5a) and thus a reduction in sDIC in the deep ocean (Fig. 6a).

An increase in sDIC also occurs in the Antarctic intermediate water. As previously mentioned, the intensification of the Southern Hemisphere westerly winds enhances the mixing and overturning circulation of the Southern Ocean (Fig. 6a), increasing the CO2 uptake and sDIC (Fig. 5a). An enhanced CO2 uptake due to intensified westerly winds in the Southern Ocean has also been observed in previous studies using simple box models and coupled general-circulation models (Zickfeld et al., 2007; Matear and Lenton, 2008). A similar redistribution of carbon due to wind-stress-induced circulation changes is found in Swart et al. (2012), in which the Agulhas leakage and overturning circulation are linked.

The contribution of the SST increase to CO2 uptake diminishes continuously from south to north. Biological changes calculated as the residual enhance CO2 uptake at high latitudes and reduce it at low latitudes; the resulting global CO2 uptake increases by 46 PgC due to biological changes. These global and regional contributions of individual mechanisms are consistent with previous estimations using abiotic experiments and other methods (Sarmiento et al., 1998; Matsumoto et al., 2010).

The contributions of changes in the ocean circulation and the biological pump to the reduced CO2 uptake differ between the abiotic and CTL-base and GW-base experiments even when using the same model and scenario, as suggested in previous studies (Sarmiento et al., 1998; Zickfeld et al., 2008; Matsumoto et al., 2010). Our results show that these different results are caused by the estimation methods used.

We attribute these different results to the vertical gradient of DIC under the preindustrial conditions of the abiotic and biotic experiments (i.e., CTL-base and GW-base) (Fig. 1). With regards to the circulation effect of the abiotic experiments, the enhanced CO2 uptake associated with reduced upward transport of natural CO2 from the deep ocean to the upper ocean is underestimated because the vertical DIC gradient in the abiotic experiments is much smaller than in the biotic experiments. The effect of circulation change in the abiotic experiments primarily represents reduced CO2 uptake due to reduced downward transport of anthropogenic CO2 from the surface to deep ocean. In the CTL-base and GW-base experiments with a realistic vertical DIC gradient, the effect of the circulation change represents both a reduced upward transport of natural CO2 and a reduced downward transport of anthropogenic CO2. Therefore, the reduction in CO2 uptake due to weaker deep-ocean circulation is larger in the abiotic experiments than in the CTL-base and GW-base experiments. An increase in CO2 uptake associated with weaker equatorial upwelling is found only in the CTL-base and GW-base experiments.

In the abiotic experiments, the biological contribution is calculated as the residual. The enhanced CO2 uptake owing to the reduced upward transport of natural CO2 is included in the biological effect. This effect overcomes the reduced CO2 uptake due to the weakening of the biological pump, leading to an enhanced CO2 uptake due to the biological change. Therefore, the CTL-base and GW-base experiments are more useful for quantifying the contributions of circulation and biological change. We conclude that changes in the organic matter cycle and increases in the SST are the primary contributors to the reduction in CO2 uptake due to global warming in our model. Although our experimental design differs from that used in some previous studies (e.g., Joos et al., 1999; Plattner et al., 2001), the identification of differences in feedback mechanism among all experimental designs is beyond the scope of this work and should be the subject of future research.