In this study, numerical experiments on the ocean carbon cycle were performed using an offline ocean biogeochemical tracer model based on within the framework of the CCSR Ocean Component Model version 4.0 . This model has an approximate horizontal resolution of 1°, and it includes 44 vertical layers with thicknesses ranging from 5 to 250 m.

The ocean biogeochemical cycle model is forced with monthly averaged output from a climate model simulation designed specifically for the last deglaciation and run with the MIROC 4m atmosphere–ocean general circulation model (AOGCM) . The boundary conditions include horizontal advection velocity, sea surface height, vertical diffusivity, temperature, salinity, shortwave radiation, wind speed above the sea surface, and sea ice concentration.

Prognostic variables for the ocean biogeochemical cycle model include phosphate, DIC, alkalinity, dissolved organic phosphate, dissolved oxygen, iron, silicate, and carbon isotopes of DIC (13C and 14C). The availability of light, phosphate, and iron is used to determine the rate of phosphate uptake by phytoplankton. Notably, sedimentation processes on the seafloor are not considered, and all particles reaching the seafloor are assumed to dissolve in the deepest layer of the model.

To evaluate the transient response of the global ocean carbon cycle during the last deglaciation, we conducted offline ocean carbon cycle experiments forced with the outputs of the AOGCM MIROC 4m simulation, covering the period 21 to 11 ka BP. The MIROC 4m simulation focusing on the last deglaciation was performed according to the PMIP protocol with respect to the changes in orbital parameters and greenhouse gases during this period . However, the ice sheets were fixed at their 21 ka BP state of the ICE-5G reconstruction. Freshwater inflow from the Northern Hemisphere ice sheets deviates from the PMIP protocol after the latter half of Heinrich Stadial 1 (HS1). This approach seeks to align the simulated AMOC variations with those reconstructed from 231Pa/230Th sediment core records and the associated climate changes that occurred during the Bølling–Allerød (BA) and Younger Dryas (YD) periods.

Figure  shows the calculated variations in Δ14C–CO2, δ13C–CO2, and pCO2 in the atmosphere (solid lines), together with their estimated values (dashed lines). Additionally, it illustrates the variations in the average of ΔΔ14C (i.e., the difference in Δ14C between the ocean and the atmosphere), δ13C, and DIC in the middle (500–2000 m) and deep (>2000 m) layers of the Atlantic, Southern (<40° S), and Pacific oceans.

Analysis of the modeled differences between the LGM and the Holocene indicates that the AMOC is weaker (9.0 Sv) during the LGM (21 ka BP) than during the Holocene (11 ka BP), i.e., 17.4 Sv (Figs. a and S1 in the Supplement). The basin-wide distributions of ΔΔ14C and δ13C in the Atlantic and Pacific oceans during specific periods are presented in Figs.  and , respectively. The model results demonstrate that ΔΔ14C, an indicator of ocean ventilation, is lower in the deep Atlantic at 21 ka BP than at 11 ka BP (Figs. c and a, f), which is in qualitative agreement with reconstructions from sediment core records . Notably, however, the simulated ΔΔ14C values are less negative than the reconstruction ΔΔ14C values at 21 ka BP in the Atlantic below 3000 m and in the Pacific below 2000 m (Fig. a).

Regarding δ13C, the model results show a stronger vertical gradient between the surface and the deep ocean in the Atlantic (Fig. h), corresponding to a shallower and weaker AMOC at 21 ka BP compared to that at 11 ka BP. This qualitative difference is consistent with the reconstructed δ13C. However, similar to the finding for ΔΔ14C, our model experiment underestimates the reconstruction of δ13C in the deep ocean, particularly in the Southern Ocean (Fig. i).

Our previous study, which involved numerical experiments under the climatic conditions of the LGM and accounted for the enhanced stratification in the Southern Ocean and iron fertilization from glaciogenic dust, showed improved quantitative agreement between the model results and the sediment core data for dissolved oxygen, δ13C, and Δ14C . The triangles in Fig.  illustrate the changes in the carbon isotope signatures reported in that study. Comparison of the results from the two studies highlights the advances made by in capturing the dynamics of the Southern Ocean, suggesting that the incorporation of the processes considered in their research could improve model–data agreement. However, their LGM simulation also slightly overestimated the changes in the glacial Pacific, and these discrepancies highlight the difficulty in achieving consistent scenarios that account for all changes in the global ocean within a model.

Atmospheric pCO2 was predicted by running the ocean carbon cycle model. Its value is 278.1 ppm at 21 ka BP and 306.9 ppm at 11 ka BP, i.e., a difference of 28.8 ppm that is relatively small compared to the difference of approximately 80 ppm reconstructed from ice cores (approximately 188–267 ppm in the EPICA Dome C record and approximately 193–273 ppm in the WAIS Divide record ). This discrepancy could be attributed to several factors, including the relatively small differences in sea surface temperature (SST) observed between the two intervals (Fig. b). Using proxy and data assimilation, the global mean SST difference between the LGM and the Holocene has been reported to be 1.7–3.6 °C , whereas the SST difference in our experiment is only 1.6 °C. A small difference in SST leads to a small difference in CO2 solubility between the two periods, which causes underestimation of the magnitude of atmospheric pCO2. Furthermore, it is important to note that this study did not consider specific processes that might have contributed to the reduction in atmospheric pCO2 during the LGM, such as enhanced salinity stratification, iron fertilization from glaciogenic dust, and carbonate compensation, as discussed in .

The differences in the steady-state ocean carbon cycles at 21 and 11 ka BP highlight the difficulty in accurately reproducing the actual changes in atmospheric pCO2 in the transient experiment connecting these periods. Therefore, our analysis focuses on investigation of the impacts of climate change, particularly the notable variations in the AMOC and on the ocean carbon cycle, and reveals the successes and deficiencies of the model through model–data comparison of carbon isotope signatures.

Figure k shows the calculated changes in atmospheric pCO2 driven by variations in the climate and the carbon cycle during the last deglaciation. To investigate the factors driving the change in atmospheric pCO2, we decomposed the factors relevant to the partial pressure of CO2 at the sea surface (pCO2os). This parameter controls atmospheric pCO2 through gas exchange between the atmosphere and the ocean. Oceanic pCO2 is affected by temperature, salinity, DIC, and alkalinity, and the influence of those factors on pCO2os can be represented as follows: 1pCO2os=f(sDIC,sALK,SST,SSS), where sDIC is sea surface DIC, sALK is sea surface alkalinity, SST is sea surface temperature, and SSS is sea surface salinity. The function f is determined based on the inorganic chemistry of the carbonate system . We can assess the contribution of each variable to the changes in pCO2os by examining the change in each variable from its original value.

Comparison of ΔΔ14C variations between models and data enables assessment of the accuracy of calculated ocean circulation changes. The reconstructed ΔΔ14C in the deep ocean rises notably during the latter half of HS1 , in contrast to the less pronounced shift seen in the model experiment (Fig. b–e). Two primary factors contribute to this discrepancy. Firstly, the model underestimates the increase in deep-ocean ventilation during the latter half of HS1 period, which is crucial for determining the trend in Δ14C changes in the deep ocean. Secondly, the model calculates higher ΔΔ14C values compared to the reconstructed lower values of ΔΔ14C in the deep ocean during the LGM. These aspects indicate a potential oversight in the model's representation of ocean dynamics, affecting both the simulation of ventilation changes during the latter half of HS1 and ΔΔ14C values during the LGM. The difficulty in reproducing changes in ΔΔ14C might also be related to underestimation of variations in atmospheric pCO2 during this period (Fig. k). Processes that might contribute to this problem are discussed in more detail in Sect. 4.2.

After the BA transition, the calculated variations in ΔΔ14C in synchrony with the significant changes in the AMOC are generally consistent with those observed in the reconstruction . Corresponding to the AMOC change, ΔΔ14C increases in the deep ocean from the Atlantic to the Pacific Ocean (Fig. c–e). Subsequently, ΔΔ14C decreases from the Atlantic to the Southern Ocean during the YD period in response to weakening of the AMOC (Fig. c–e). This change is consistent with the reconstruction , but there is an overestimation of the quantitative changes in the deep Atlantic Ocean, as illustrated in Fig. e. This overestimation may be related to the challenges in accurately reproducing the deep-ocean circulation fields, which is a topic that is discussed further below.

Assessment of the AMOC changes during the last deglaciation by involved conducting transient model simulations using the Bern3D model. They performed multiple model–data comparisons including carbon isotope ratios, εNd, and 231Pa/230Th. Their research results suggest gradual weakening of the AMOC during HS1, recovery at the BA transition, and subsequent weakening during the YD period, albeit without a complete collapse. The proposed pattern of AMOC change is qualitatively consistent with the ocean modeling of (Fig. a). The Bern3D study indicates that the proportion of deep water originating from the North Atlantic during the YD period is little different to that during the BA because of the short duration of the YD period. Conversely, this study shows drastic changes in the distribution of Δ14C and δ13C at the basin scale in response to AMOC variations over a period of approximately 1000 years (Figs. e and e). This extended period of the AMOC stagnation in our model helps to explain the observed discrepancies between the model and the reconstructed data in the deep Atlantic during the YD period.

The carbon isotope ratios calculated by our model suggest that the AMOC during the YD period might be represented as excessively weak or that the duration of the weak AMOC state may be overly extended. However, it is important to acknowledge the inherent differences among models in representing broader deep-ocean circulation patterns, including the AABW and Pacific meridional overturning. These differences result in distinct chemical tracer distributions at the basin scale, underscoring the challenge of conclusively explaining past AMOC variations through a single model or study. Given the systematic biases present in physical and biogeochemical processes within models, a comparative analysis across multiple models is essential for exploring past AMOC variations.

Further information can be obtained by comparing the results of model–data comparisons for ΔΔ14C and δ13C. For δ13C, both the model and the data show similar trends, depicting an increase in deep-water δ13C during the BA period as in ΔΔ14C. However, there is a discrepancy during the subsequent YD period. The model indicates a reduction in deep-water δ13C during the YD period, whereas this feature is absent in the reconstruction of (Fig. g–j). There are several possible factors that could potentially influence this discrepancy. For example, discrepancies in the directions and magnitudes of changes observed across different sediment cores could reflect inherent variability in environmental signals. Additionally, potential dating inaccuracies within individual sediment core data could result from smoothing effects such as bioturbation and coring artifacts. These complexities in interpreting the sediment core record stem from both natural variability and methodological challenges, highlighting the need for caution when comparing model simulations with sediment core data. Another important factor is the weakening of the simulated AMOC during the YD period. Comparison of the model and sediment data for ΔΔ14C and δ13C suggests that the weakening of the AMOC during the YD period might be overly pronounced in the model (Figs. e and e). Additionally, the calculated increase in export of biogenic organic matter in the Southern Ocean during the YD period compared to that in the BA period (Fig. S6f and g) contributes to the decrease in δ13C in the deep ocean. This emphasizes the importance of accurately simulating nutrient and iron cycles, especially in iron-limited regions affected by changes in dust-derived iron supply. As the Southern Hemisphere warms and becomes more humid, the supply of iron from dust might decrease . Reproducing changes in δ13C is challenging owing to the intricate interconnections between ocean circulation, biological processes, and atmosphere–ocean gas exchange. Understanding the discrepancies between the model and the data in terms of the δ13C changes will require future sensitivity experiments to clarify their respective contributions and to provide deeper understanding of these factors.

Ocean modeling with freshwater-forcing experiments has provided insights into the link between the shutdown and resumption of the AMOC and the changes in atmospheric pCO2. demonstrated that cessation of the AMOC causes increase in atmospheric pCO2 owing to several factors. Firstly, the efficiency of the biological carbon pump in the North Atlantic is relatively high compared to that in the Southern Ocean. Therefore, reduction in the NADW inflow leads to a decrease in biological carbon sequestration in the deep ocean. Secondly, weakening of Southern Ocean stratification associated with shutdown of the AMOC increases the outgassing of CO2 from the ocean to the atmosphere.

The results of this study confirm the gradual increase in atmospheric pCO2 during HS1 and the YD period in parallel with the weakened state of the AMOC; however, such an increase is not directly related to reduction in the regenerated nutrient inventory, as suggested by . The reason for this difference is that the contribution of the changes in temperature and alkalinity to the change in pCO2os during the YD period is greater than the contribution of the change in DIC in this study. When the AMOC changes, the non-thermal effects on changes in pCO2os mainly depend on the magnitude of the relative contributions of DIC and alkalinity to pCO2os based on the vertical gradient of DIC and alkalinity between the surface and the deeper ocean (Figs. S7 and S8).

Although our results show the impact of drastic changes in the AMOC on atmospheric pCO2 during the last deglaciation, the model does not fully explain the variations in atmospheric pCO2 during the early deglaciation. Ice core records indicate a rise of approximately 40 ppm in atmospheric pCO2 accompanied by a reduction in atmospheric δ13C–CO2 and Δ14C–CO2 during HS1. However, the calculated variations are insufficient in terms of their amplitude (Fig. a, f, and k). A key contributor to this discrepancy is the limited extent of the change in ventilation, evident from the ΔΔ14C changes in the ocean (Fig. b–e). However, the current model has difficulty fully reproducing these substantial changes in ventilation.

In addition to the changes in ventilation, biological processes are important in explaining the deglacial carbon cycle changes. indicated that iron fertilization from glaciogenic dust increases biological production in the subantarctic region, thereby contributing to the reproduction of low δ13C in the deep Southern Ocean during the LGM (triangles in Fig. i). However, their study did not reproduce the profoundly old deep water in the deep glacial Southern Ocean, as suggested by radiocarbon data (triangles in Fig. d), but it did reproduce the low δ13C values (triangles in Fig. i). The change in glaciogenic dust deposition was not considered in this study; therefore, the model might underestimate the glacial–interglacial variation in biological production in the subantarctic region, potentially contributing to the underestimation of the changes in atmospheric and deep-sea δ13C during HS1.

Moreover, while many studies focused primarily on environmental changes in the Atlantic, the contributions from other ocean basins are also important. For example, sediment core records from the North Pacific indicate an increase in ΔΔ14C at depths near 1000 m during HS1 . Analysis of radiocarbon and boron isotopes in sediment cores by revealed that the extent of the NPIW expanded during HS1. These ventilation changes have the potential to contribute to the rise in atmospheric pCO2. compared two coupled climate models, i.e., MIROC version 3.1 and LOVECLIM, and showed consistent results for activation of ventilation of NPIW triggered by freshwater inflow into the North Atlantic. The processes of activation of ocean ventilation and subsequent degassing of CO2 in the North Pacific during the early deglaciation could contribute to the currently unexplained increase in atmospheric pCO2.

The high-resolution ice core data obtained from the WAIS Divide record provides valuable insights into the timescale of the changes in the carbon cycle during the last deglaciation. It is suggested that there are two modes of change in relation to atmospheric pCO2: a slow increase on the millennial scale and a rapid increase on the centennial scale . The rapid increase in atmospheric pCO2 of 10–15 ppm at the end of HS1 (14.8 ka BP) and at the end of the YD period (11.7 ka BP) over a short period of 100–200 years is synchronized with the resumption of the AMOC . However, this study did not reproduce such abrupt changes in atmospheric pCO2. Several factors might contribute to this discrepancy, including insufficient temperature rise in the Southern Hemisphere associated with change in the AMOC, inadequate representation of the vertical concentration gradients of DIC and alkalinity, limitations in capturing atmospheric and oceanic dynamics in the general circulation model, and the influence of small-scale phenomena. Previous modeling studies have suggested that deeper convection in the Southern Ocean and strengthening of westerly winds in the Southern Hemisphere could contribute to the abrupt jump in atmospheric pCO2 during the middle of HS1 (16.3 ka BP) by transporting sequestered carbon from the deep Southern Ocean to the surface . These processes are related to the challenges in reproducing carbon isotope ratios described above; therefore, this discussion points to the necessity of improving our AOGCM and of refining its experimental setup in future studies, as previewed in Sect. 4.3.

Model–data comparisons of carbon isotope signatures underscore the importance of refining our climate models to more accurately represent the complex interactions that govern changes in the carbon cycle. Future improvements to the AOGCM used in this study might address the following considerations.

Currently, the AOGCM does not account for temporal changes in ice sheets, and it underestimates the changes in Southern Ocean SST . Moreover, there is some uncertainty regarding the volume of meltwater flow across the North Atlantic during HS1 and the BA period . It suggests that the problem is integral to the AOGCM because the AMOC response is not consistently and realistically observed, even when realistic freshwater variations are applied. Furthermore, as identified by , the magnitude of ocean warming during the last deglaciation varies depending on the response characteristics of each model, resulting in a range across multiple models. demonstrated that the alteration of parameters associated with cloud thermodynamic phase fractions in a climate model reduces the warming bias of SST in the modern Southern Ocean. Using a model with a reduced Southern Ocean warming bias, we expect to obtain different responses in Southern Ocean SST and ocean circulation during the glacial period and in their changes during the deglaciation compared to those derived in this study. Some studies proposed potential alterations in the westerly winds over the Southern Ocean throughout the last deglaciation , but there is a substantial degree of uncertainty concerning the anticipated changes in the atmospheric dynamics. Those uncertainties could have a substantial impact on the results of ocean biogeochemical cycle modeling and, consequently, on atmospheric pCO2. Efforts to reduce bias and to facilitate comprehensive discussion regarding climate model consistency are critical to advancing future climate–carbon cycle modeling. These endeavors are essential to refine our understanding of the complex interactions between climate and the carbon cycle.

In addition to those factors mentioned above, there are several other factors that could contribute to improving the simulation of the ocean carbon cycle during the last deglaciation. One important consideration is the inclusion of critical processes for lowering atmospheric pCO2 during the LGM, which are identified in . Those processes include enhanced stratification of the Southern Ocean, iron fertilization from glaciogenic dust, and carbonate compensation. Understanding the changes in those processes during the deglaciation is critical, and their proper incorporation into future modeling efforts might lead to both improved simulations and better understanding of the dynamics during this period. Studies have also reported that inclusion of the parameterization of vertical mixing, which depends on tidal mixing energy and stratification, could help better reproduce the deep-ocean circulation in the Pacific . The introduction of tidal mixing parameterization has also proven effective in reproducing δ13C and Δ14C in the glacial ocean . Incorporating the insights from these model developments has the potential to lead to more realistic representation of carbon cycle variations during the glacial period and subsequent deglaciation. Moreover, glacial–interglacial changes in ocean volume due to ice sheet changes also have an impact on the carbon cycle. A recent study analyzing PMIP model outputs highlighted the importance of accurate representation of ocean volume changes and their associated effects on alkalinity adjustments . For more accurate simulations, it is critical to perform numerical integration that accounts for temporal changes in ocean volume during the deglaciation.

It is also worth noting that carbon exchange between the atmosphere and the ocean is not the sole driver of deglacial variation in atmospheric pCO2. Changes in terrestrial and soil carbon storage also play important roles in modulating atmospheric δ13C–CO2 and pCO2 during the last deglaciation . Comparison of Δ14C–CO2 and δ13C–CO2 provides a consistent explanation if carbon uptake by vegetation expands during the BA period and declines during the YD period, as suggested by . Vegetation growth, prompted by CO2 fertilization, can act as a carbon sink, offsetting the increase in atmospheric pCO2 . In this study, we applied the same sea surface restoring terms for the carbon isotopes used during the initial spin-up of the LGM throughout the deglaciation experiment. In other words, this approach did not consider changes in vegetation or changes in 14C production in the atmosphere. Future studies using Earth system models that include both terrestrial and oceanic carbon cycle processes would enhance our comprehensive understanding of glacial changes in carbon cycles. A study of the carbon cycle associated with the glacial Dansgaard–Oeschger events, conducted using an Earth system model, revealed that the changes in terrestrial carbon storage at this timescale are as important as those in the oceans . Moreover, in previous studies using Earth system models of intermediate complexity, temporal variations in atmospheric pCO2 are primarily used to calculate changes in radiative forcing, and several studies have explored the interaction between the carbon cycle and the climate . Although fully coupling a carbon cycle model to a climate model is a more advanced endeavor, we are eager to explore this avenue in future research.