1. Introduction

The ocean’s carbon cycle impacts atmospheric carbon dioxide (CO₂) and hence Earth’s energy budget and climate [1]. Lower atmospheric CO₂ during glacial periods, for example, has been attributed to increased carbon storage in the ocean, although the mechanisms for the changes in ocean carbon remain controversial [2,3]. The isotopic ratio R = ¹³C/¹²C, commonly expressed asδ¹³C = (R/Rstd—1), that is the deviation from a standard ratio R_std (Equation A in S1 Text), is widely used in paleoceanography to trace past changes in carbon cycle and ocean circulation [4].

Understanding ocean C and ¹³C cycling is complicated because they are influenced by different physical, chemical, and biological processes. As a gas, CO₂ dissolves is sea water and exchanges with the atmosphere. Solubility depends strongly on temperature [5], whereas the rate of air-sea flux is a function of wind speed [6]. Once in the ocean, CO₂ reacts with sea water and forms bicarbonate (HCO₃) and carbonate (CO₃) ions. At present-day pH levels, roughly 90% of the carbon is in bicarbonate form, about 10% is in CO₃ and only about 1% is CO₂ [7]; thus, the ocean is highly buffered with respect to CO₂. DIC = CO₂ + HCO₃ + CO₃ makes up the vast majority of ocean carbon (~37 Eg; 1 Eg = 10¹⁸ g = 10³ Pg), whereas Dissolved Organic Carbon (DOC) amounts to ~0.7 Eg [8] and Particulate Organic Carbon (POC) is negligible in terms of global inventories. During air-sea gas exchange δ¹³C fractionates such that the heavy isotope preferentially dissolves [7]. Isotopes are also fractionated between the different carbonate species, a process that is strongly temperature dependent [9]. As a result, at equilibrium, tropical DIC is enriched in ¹³C with respect to atmospheric CO₂ by ~7.5 ‰ and polar DIC by ~10.5 ‰ [10], indicating that temperature changes can have an important impact on δ¹³C_DIC. Photosynthesis by phytoplankton removes carbon, preferentially ¹²C, from surface waters creating POC and leaving surface waters depleted in DIC and enriched in δ¹³C_DIC (~ +2 ‰). Calcifying organisms remove additional carbon from the surface together with alkalinity, but calcium carbonate production does not fractionate the isotopes. Eventually, sinking POC and calcium carbonate are returned to DIC in the subsurface ocean by respiration and dissolution, where it can be sequestered for centuries or longer. These processes are called the soft-tissue and carbonate pumps, terms coined in analogy to a cellular ion pump, which actively transports ions up gradient from lower to higher concentrations [11]. Together they are referred to as the biological carbon pump.

The biological pump continuously removes carbon from the surface to the deep ocean, thus contributing to lower atmospheric CO₂, and increasing DIC concentrations and decreasing δ¹³C_DIC with depth. However, surface processes and transport of surface properties into the deep ocean also contribute to vertical variations in C and δ¹³C_DIC. Temperature-dependent solubility of C and fractionation of ¹³C tends to increase the C content and δ¹³C_DIC of polar waters, which fill the deep ocean and dominate the global inventory/average; this is the solubility pump [11]. Slow exchange with the atmosphere creates substantial disequilibria for both C and ¹³C, which propagate into the interior [12–14]. On a global basis, the equilibration time with the atmosphere is about 1 year for C and 10 years for δ¹³C_DIC [5,10], but it can be larger, e.g. in sea ice covered regions.

In principle, these processes are well known and represented in global ocean models. However, most ocean models only carry total DIC as a prognostic tracer, and thus cannot separately quantify how different processes contribute to a given change in DIC, which impedes interpreting and understanding DIC changes. Efforts to separate the different processes affecting DIC and δ¹³C have a long history [10,11,15,16]. In models, biology can be switched off to simulate carbon in an abiotic ocean [11,13,14], however it is not often done to interpret results from a full model. Relationships between biological carbon and other substances involved in biological cycling such as phosphorous and oxygen have been used to estimate the contributions of biology. The storage of carbon from remineralization of organic matter C_soft ≅ C_soft,AOU = r_C:O·AOU, also known as the soft-tissue biological pump, has been suggested to be related to Apparent Oxygen Utilization (AOU = O_2,sat—O₂), which is the deviation of oxygen from its temperature-dependent saturation concentration O_2,sat [17], using a constant carbon-to-oxygen ratio r_C:O [18–21]. Similarly, C_soft ≅ C_soft,PO4 = r_C:P·(PO₄—PO_4,0), the deviation of phosphate from a reference value such as the globally-averaged surface-mixed-layer concentration PO_4,0 has been used [11,16], assuming a constant carbon-to-phosphorous ratio (r_C:P). A popular approximation in paleoceanography attempts to isolate the effect of air-sea exchange, δ¹³C_as = δ¹³C –(2.7–1.1×PO₄), by using phosphate to remove the effect of biology on δ¹³C [10,15,22,23]. A recent variant is to use AOU to approximate δ¹³C_soft ≅ δ¹³C_soft,AOU = AOU·(– 1.1)/170 [24]. However, all these approximations are problematic. Oxygen, notwithstanding its much shorter equilibration time with the atmosphere (~1 month) than carbon (~1 year), is substantially undersaturated in regions of deep water formation and the degree of undersaturation is time dependent, which can lead to large errors in the AOU approximation [25–27]. Similarly, preformed PO₄ shows substantial variations for different deep-water masses [28] and almost certainly has varied in time, which affects δ¹³C_as, as shown herein. Moreover, the ratio of carbon to phosphorous r_C:P in organic matter is spatiotemporally variable [29,30].

Recently, models have started to include additional diagnostic tracers that can be used to decompose ocean carbon storage thereby avoiding the large errors associated with the above approximations [12,31,32]. These studies have emphasized the role of disequilibrium carbon storage C_dis, but they were incomplete, which hampered the interpretation of C_dis. Complete decompositions, separating C_dis into biological and physical contributions (Fig 1) has facilitated that interpretation and led to additional mechanistic insights into the modern and glacial ocean [1,2,33]. Here we extend a complete and accurate decomposition of DIC to δ¹³C_DIC.

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Fig 1. Disequilibrium schematic in Southern Ocean.

In an ocean without biology (A) upwelling of North Atlantic Deep Water (NADW) occurs in the Antarctic divergence. Subsequent flow to the south leads to heat loss to the atmosphere (red wiggly line). This increases its solubility, which causes uptake of carbon (green wiggly line), and a surface flux that tends to increase δ¹³C (orange wiggly line). However, due to incomplete air-sea gas exchange before waters sink to depths as Antarctic Bottom Water (AABW) negative disequilibria remain for both carbon and δ¹³C. Soft-tissue biology (B), conversely, causes upwelling of respired carbon that is depleted in δ¹³C, which leads to outgassing of carbon, but a surface flux that tends to increase δ¹³C. This results in a positive disequilibrium for carbon, but a negative disequilibrium for δ¹³C.

https://doi.org/10.1371/journal.pclm.0000434.g001

δ¹³C_DIC in past oceans can be reconstructed by measuring δ¹³C_cib in shells of the fossil foraminifera genus Cibicides extracted from sediment cores [34]. Since δ¹³C_cib is one of the most measured paleoceanographic tracers, a better understanding of δ¹³C_DIC would benefit paleoceanography and Earth science in general. One of the best studied periods in paleoclimate is the Last Glacial Maximum (LGM, ~20,000 years ago), because climatic changes were large (good signal-to-noise ratio), and samples can be well dated with radiocarbon. Shackleton [35] first noted a decrease in ocean δ¹³C_DIC during glacial periods, which he attributed to the transfer of isotopically light terrestrial organic carbon to the ocean. The general decrease in whole ocean δ¹³C_DIC has subsequently been confirmed. The most recent study used hundreds of sediment cores combined with an inverse model to estimate a decrease in global mean ocean δ¹³C_DIC of 0.32±0.20 ‰ in the LGM relative to the PI [36; G15]. An unequivocal interpretation of those observations, however, remains lacking. While a transfer of land carbon to the ocean is still a viable possibility [36,37], another possibility is an increase in the biological pump [3,38], which would decrease deep ocean and hence whole ocean δ¹³C_DIC ≅ Δ¹³C_pre + Δ¹³C_soft. However, Sigman & Hain’s [3] argument is based on an estimate by Vollmer et al. [24] of global ocean preformed Δ¹³C_pre changes being close to zero, which used the AOU approximation. Moreover, in Khatiwala et al.’s [2; K19] data-constrained model, the biological pump (C_soft) was weaker during the LGM, whereas C_dis,bio was greatly enhanced.

Here we build upon the modeling efforts mentioned above, specifically the work of K19. Those authors had implemented additional diagnostic tracers in an offline model, which was used to simulate LGM and PI equilibrium states. We have implemented a slightly modified method in an online model, which can be used for transient simulations, and we have extended the decomposition to δ¹³C_DIC. The latter has not been attempted before in the literature that we are aware of. We apply the method to data-constrained simulations of the PI and LGM oceans.

2. Model description

The Oregon State University version of the University of Victoria (OSU-UVic) climate model [39] includes a simple energy-moisture-balance atmospheric component, a land surface and dynamic vegetation model, a three-dimensional coarse-resolution ocean general circulation model component and the Model of Ocean Biogeochemistry and Isotopes (MOBI). MOBI features three phytoplankton functional types (diatoms, diazotrophs and other phytoplankton), nitrogen, phosphorous, silicate, and iron as growth-limiting nutrients, carbon, oxygen, zooplankton, detritus (POC), variable P:C ratios in phytoplankton, DOC, nitrogen (¹⁵N) and carbon (¹³C, ¹⁴C) isotopes. Implementation of δ¹³C is described in detail in Schmittner et al. [20]. The version used here does not include interactive sediments. OSU-UVic/MOBI has been validated against modern observations and against paleoceanographic data from the LGM [2,40–43]. Noticeable differences with previous versions are some details of the ocean ecosystem model such as the use of variable P:C ratios of phytoplankton, variable half-saturation constants for nutrient uptake, and different parameters [44]. Tracer distributions in the PI state are similar to previously published versions and agree well with observations, including DIC and δ¹³C_DIC (Figs A-C and Section D in S1 Text). The LGM state used here is also very similar to K19 and agrees well with reconstructions of surface temperatures, whole ocean temperatures, δ¹³C_DIC, Δ¹⁴C and δ¹⁵N, and features a shallower and weaker Atlantic Meridional Overturning Circulation (AMOC; Figs D-E and Section E in S1 Text) and enhanced iron fertilization in the Southern Ocean [41].

In addition to the prognostic equations for DIC and DI¹³C we have implemented equations for C_pre, C_sat, C_soft, C_CaCO3, ¹³C_pre, ¹³C_sat, ¹³C_soft, and ¹³C_CaCO3 (see Section A in S1 Text for notation). C_pre and ¹³C_pre are set to DIC and DI¹³C, respectively, in the surface layer and are transported into the subsurface. In contrast to DIC and DI¹³C, however, for C_pre and ¹³C_pre there are no interior sources and sinks from biology. C_sat and ¹³C_sat are calculated as the DIC concentration in equilibrium with the atmosphere, implying no surface fluxes, with zero interior sources and sinks. The disequilibrium C_dis = C_pre−C_sat is diagnosed. C_soft (C_CaCO3) and ¹³C_soft (¹³C_CaCO3) are set to zero at the surface and in the subsurface they are subject to the same sources and sinks as DIC related to the production and regeneration of organic matter (CaCO₃). To separate biological and physical effects we have created a model version without biology (NoBio), in addition to the Full model described above. Model NoBio is used to determine the physical components C_sat,phys, C_dis,phys and a model version without CaCO₃ cycling (NoCaCO₃) is used to diagnose the effect of the hard-tissue pump. The biological preformed components C_sat,bio = C_sat−C_sat,phys and C_dis,bio = C_dis−C_dis,phys are calculated as differences from the full model, which has been shown to be a good approximation [14].

3. Experiments

After a 7,000-year spin-up to equilibrium with prescribed pre-industrial forcing, including CO₂ and δ¹³C_CO2, the model was run for 5,000 years with prognostic (variable) CO₂, which reaches 278 ppm (Table 1), in good agreement with preindustrial ice core observations [45]. At this point, the same LGM boundary conditions as in Muglia et al. [41] were applied instantaneously: increased soluble iron fluxes in the Southern Ocean, reduced sedimentary iron fluxes due to lower sea level, increased salinity, prescribed ice sheets and radiative forcing from methane and nitrous oxide, prescribed wind stress anomalies and decreased meridional moisture fluxes in the Southern Hemisphere. The latter causes an AMOC shoaling, which leads to a good agreement with δ¹³C_cib and radiocarbon data from LGM ocean sediments [43]. This state has also been used in K19. Although, atmospheric CO₂ was allowed to vary, δ¹³C_CO2 = -6.5 ‰ was kept fixed, consistent with ice core measurements [46]. Imposition of prescribed ice sheets affects terrestrial carbon storage, which instantaneously decreases by ~400 Pg (in exp NoCaCO₃ only by ~360 Pg; Table 1), because of the loss of vegetation and soil carbon where the ice was added. This can be thought of as land carbon buried by the ice [47], but it is unclear how much carbon was permanently buried and how much was transported by ice movement to the margins, where it could have been respired and entered the atmosphere. Note that our model does not have permafrost and the expansion of land carbon into the exposed continental shelves during the LGM is not considered. Given these uncertainties, we decided to fix δ¹³C_CO2, which provides realistic boundary conditions for the ocean. The LGM simulations were brought to equilibrium after a 7,000-year spin-up. The results below are from 200-year-averaged analysis simulations starting at the end of the LGM and variable CO₂ PI spin-ups.

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Table 1. Global carbon budget and temperatures.

C_A, C_O = DIC + DOC, and C_L are the atmospheric, ocean, and land carbon contents, respectively, and C = C_A + C_O + C_L is their sum. SAT is surface air temperature and T_O is whole ocean temperature.

https://doi.org/10.1371/journal.pclm.0000434.t001

4. Results

4.1. Climate and carbon

As a result of imposing LGM boundary conditions, atmospheric CO₂ drops and eventually reaches ~190 ppm in the Full and NoCaCO₃ models (Table 1), consistent with ice core observations [48]. The similarity of those models indicates that changes in the CaCO₃ cycle play no significant role in the reduction of atmospheric CO₂ in the Full model. Global cooling of surface air temperatures by ~-5.7°C and of whole ocean temperatures by -2.5°C in those models is in good agreement with observation-based estimates [49–51]. However, model NoBio only cools by -4.0°C because its atmospheric CO₂ decline is only 27 ppm and thus much less than the ~87 ppm in the models with the soft-tissue biology included. Thus, changes in soft-tissue carbon cycling reduce atmospheric pCO₂ in the full LGM model by 60 ppm. Note that this large effect of the soft-tissue pump is amplified by reducing atmospheric pCO₂ and cooling temperatures, which enhances carbon storage further, and thus is entirely consistent with a total effect of temperature causing 45 ppm of the LGM-PI pCO₂ changes in K19.

The land carbon inventory decreases in the full model by 512 Pg, which includes 400 Pg buried by ice plus 110 Pg reduction simulated by the land model outside of ice covered areas. This implies that its atmospheric CO₂ decrease is due to the 293 Pg increase in ocean carbon (C_O = DIC + DOC), which is almost exclusively driven by DIC. The increase by 309 Pg in the sum of the components of the carbon decomposition reproduces the total DIC increase within 5% accuracy (x symbols in Fig 2C). Although the absolute DIC inventories of the PI and LGM runs are overestimated by ~100 Pg they are reproduced within 0.3% accuracy (x symbols in Fig 2A). We conclude that the errors of the decomposition are small enough to allow an accurate and complete assessment of the simulated changes in total DIC. A more detailed error analysis is presented in Section F in S1 Text.

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Fig 2.

Components of global ocean C (panel A, C) in units of Exagram (1Eg = 10¹⁸g = 1,000 Pg) and δ¹³C (panels B, D) in units of permille. Panels A & B show absolute values from the PI (red colums) and LGM (blue columns). Panels C & D show LGM-PI differences. In panel A, the left axis applies to DIC and C_sat,phys, whereas the right axis applies to the other components. X-symbols in the leftmost columns indicate the sum of the individual components; compared to the total, they indicate the accuracy of the method. Plus-symbols represent AOU approximations. Other symbols indicate observation-based estimates [1,52–54]. We have corrected the LGM-PI change in δ¹³C_DIC from [52] (-0.32 ‰) by subtracting 0.05 ‰ due to a decrease in global mean [CO₃] by 20.5 μmol/kg in the model using the regression slope of -0.0026 ‰/(μmol/kg) estimated by [34].

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4.2. Ocean carbon components

We decompose DIC = C_pre + C_reg into preformed and regenerated components. The preformed component C_pre = C_sat + C_dis consists of saturation C_sat = C_sat,phys + C_sat,bio and disequilibrium C_dis = C_dis,phys + C_dis,bio carbon, both of which are separated into physical and biological contributions. Regenerated carbon C_reg = C_soft + C_CaCO3 results from the accumulation of respired soft-tissue carbon and dissolved calcium carbonate. Thus, total DIC = C_sat,phys + C_sat,bio + C_dis,phys + C_dis,bio + C_soft + C_CaCO3 = C_phys + C_bio can also be written as the sum of physical C_phys = C_sat,phys + C_dis,phys and biological C_bio = C_sat,bio + C_dis,bio + C_soft + C_CaCO3 processes. Biological carbon storage can be regarded as the direct or active part of the biological pump (C_reg = C_soft + C_CaCO3) plus contributions from biology on preformed carbon C_pre,bio = C_sat,bio + C_dis,bio.

The carbon components and their changes, shown in Figs 2A, 2C, 3A, 3C, 4A, 4C and 4E, and Section G in S1 Text, are very similar to those of K19. For this reason, they will not be discussed in detail here. Instead, we will only present a summary except for significant differences with that study. The model’s PI DIC inventory is with 37,348 Pg close to, but slightly larger, than that estimated by DeVries [1; 37,100 Pg]. Simulated PI DIC concentrations at the surface and in the deep ocean are in good agreement with observations (Figs 3A and 4A). The bulk of the model’s DIC storage is due to physical saturation C_sat,phys = 36,025 Pg (Table 2). However, the actual DIC storage in model NoBio (C_phys = C_sat,phys + C_dis,phys) is 761 Pg lower (C_dis,phys = -761 Pg). The physical disequilibrium is negative mainly because surface waters flowing south in the Southern Ocean lose heat to the atmosphere, which increases their solubility (Fig 1A), but slow ingassing from the atmosphere prevents equilibration to be reached before waters subduct and sink to the deep ocean [14]. Thus, the deep ocean’s carbon storage is less than it would be at equilibrium. Our estimate of C_dis,phys is in good agreement with that of DeVries [1; -700 Pg].

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Fig 3.

Zonally averaged surface values of DIC concentrations (left) and δ¹³C_DIC (right) and their decompositions for the PI (red) and the LGM (blue). Observations (square symbols) of PI DIC and δ¹³C_DIC are from (A) GLODAP2.2021 [55,56] and (B) Kwon et al. [54], respectively, corrected for anthropogenic carbon. Legend in panels (A) and (C) also apply to panels (B) and (D), respectively.

https://doi.org/10.1371/journal.pclm.0000434.g003

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Fig 4.

Horizontally averaged profiles of DIC (left) and δ¹³C_DIC (right) and their decomposition in the PI (red) and LGM (blue) runs. Top panels show DIC (thick solid) and C_pre (dashed). The difference is C_reg = DIC–C_pre. Thin lines show the sum of the components for comparison with DIC. Observations (square symbols) are from GLODAP2.2021 [55,56] and Kwon et al. [54] corrected for anthropogenic carbon. Panels C & D show physical components C_phys and Δ¹³C_phys (solid), and C_sat,phys and Δ¹³C_sat,phys (dashed), respectively. The difference is the physical disequilibrium e.g. C_dis,phys = C_sat,phys−C_phys. Panels E & F show the biological components.

https://doi.org/10.1371/journal.pclm.0000434.g004

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Table 2. Global Components for C (Pg) and Δ¹³C (‰).

https://doi.org/10.1371/journal.pclm.0000434.t002

C_sat,phys and C_dis,phys do not change much in the LGM. C_sat,phys is determined by the surface DIC(T, S, pCO_2o, ALK) concentration in NoBio. At equilibrium, the ocean pCO₂ (pCO_2o) is equal to that of the atmosphere (pCO_2a). Thus, C_sat,phys depends on temperature T and pCO_2a, both of which changed considerably in the LGM. Effects of salinity (S) and alkalinity (ALK) changes in NoBio are minor. However, cooler temperatures would have increased C_sat,phys, while lower pCO_2a would have decreased it, resulting in a small net effect. Overall, DIC in NoBio’s LGM simulation decreased by 45 Pg compared to the PI, which together with the loss of 56 Pg from the atmosphere (27 ppm) is compensated by an increase in land carbon by ~100 Pg (after the burial of 400 Pg by ice; Table 1).

In the PI control run, biological saturation carbon storage C_sat,bio = C_sat−C_sat,phys = -812 Pg is negative due to the effect of biology on alkalinity. Biological production of CaCO₃ reduces alkalinity at the surface. Since pCO_2a is identical in the PI simulations of models Full and NoBio, surface DIC equilibrium concentrations must be lower in the Full model compared with NoBio and hence C_sat,bio < 0. The spatial distribution of C_sat,bio at the surface features large negative concentrations in the tropics, particularly in the Indian ocean, and in the North Atlantic (Fig I panel A in S1 Text). It is strongly correlated with the effect of biology on alkalinity because T, S, pCO_2a and the circulation are all identical between the Full model and NoBio. From the surface, large negative concentrations (-80 to -100 mol/m³) of C_sat,bio are advected into the mid-depth North Atlantic (Fig I panel D in S1 Text), whereas bottom waters in all ocean basins have less negative concentrations (~-40 mol/m³; Fig I panels D,G in S1 Text). In the LGM, C_sat,bio = -1,297 Pg becomes 485 Pg more negative than in the PI (Fig 2C). This reduction is affected by changes in the pCO_2a and T differences between the Full model and NoBio. Since LGM pCO_2a is lower in the Full model than in NoBio, surface DIC at saturation in the Full model will be reduced more than in NoBio (ΔC_sat = C_sat,LGM = C_sat,PI < ΔC_sat,phys = C_sat,phys,LGM = C_sat,phys,PI). CaCO₃ cycling decreases C_sat,bio by 1,051 Pg in PI and by 801 Pg in the LGM (Full–NoCaCO₃).

As in K19, the largest driver of the increase in ocean carbon storage is the biological disequilibrium C_dis,bio. It approximately doubles from 1,155 Pg in the PI to 2,360 Pg in the LGM. It is likely that, as in K19, sea ice, iron fertilization, and circulation changes all conspire to force the large increase in C_dis,bio in the LGM simulation. Our estimate of C_dis,bio in the PI is larger than that from a recent study using a data-assimilated model including the soft-tissue pump only [33; 487 Pg]. However, this discrepancy is not due to the presence of the CaCO₃ cycle in our model. In model NoCaCO₃ C_dis,bio is 1,244 Pg, slightly higher than in the Full model. The large difference between our model and that of Nowicki et al. is disconcerting and should be investigated further but is beyond the scope of this work.

Regenerated components C_soft = 1,175 Pg and C_CaCO3 = 690 Pg in our PI model are in good agreement with estimates by Carter et al. [53; 1,300+-230 and 540+-60 Pg, respectively]. Both components decrease in the LGM by 180–190 Pg, consistent with decreased export production, as in K19. Even though enhanced iron fertilization in the Southern Ocean forces C_soft to increase, reduced meridional overturning circulation and increased sea ice cover decrease productivity and hence C_soft through increased nutrient and light limitation of phytoplankton growth (K19). However, despite reduced C_reg and C_sat,bio biological carbon storage as a whole C_bio increases by 355 Pg in the LGM, due to the large increase in C_dis,bio.

4.3. Ocean carbon-13 components

The decomposition of DI¹³C is analogous to that of DIC. Expressing the components in delta notation δ¹³C_DIC = Δ¹³C_pre + Δ¹³C_reg, we use capital delta (Δ) to refer to weighted-average, additive components (Section A in S1 Text), where preformed contributions Δ¹³C_pre = Δ¹³C_sat + Δ¹³C_dis = Δ¹³C_sat,phys + Δ¹³C_sat,bio + Δ¹³C_dis,phys + Δ¹³C_dis,bio are the sum of saturation and disequilibrium components and regenerated components Δ¹³C_reg = Δ¹³C_soft + Δ¹³C_CaCO3 include contributions from soft and hard tissue pumps, although the latter are negligible as will be shown below.

Whole ocean δ¹³C_DIC (Fig 1) is 0.58 ‰ in the PI and 0.18 ‰ in the LGM, in good agreement with observation-based estimates [22,52,54]. Note that the LGM-PI estimate of -0.32 ‰ from [52], mentioned earlier, was not corrected for the effect of carbonate ion changes. Doing so, using the modeled carbonate ion change yields -0.37 ‰, in excellent agreement with our model estimate of -0.39 ‰. The sum of the components in our decomposition precisely reproduces this value as well as the absolute values in the PI and LGM, even though locally small differences occur (Section F in S1 Text). The spatial distribution of δ¹³C_DIC in both PI and LGM simulations is also in good agreement with observations (Figs 3B, 4B and 5A). The PI features high values (2–2.5 ‰) near the surface, except near Antarctica where they drop to ~1 ‰, and lower values at depth (~0.5 ‰). The model also reproduces the PI interbasin differences with relatively high values (~1 ‰) in the deep Atlantic and lower values (~0 ‰) in the deep Pacific (Fig 5D and 5G, Fig B in S1 Text).

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Fig 5.

Horizontally-averaged profiles of δ¹³C_DIC and its decomposition in the Atlantic (A,B,C), Southern Ocean (south of 40°S; D,E,F), and Pacific and Indian (G,H,I). Panels A,D&G show absolute values for the PI (red) and LGM (blue). Thick solid lines are model results. Observation-based estimates are shown as thick red dotted [54], tick red dashed [22], thick blue dashed [52] corrected according to calibration LA1 of Schmittner et al. [34], and thin blue dashed line are the uncorrected data from [52]. Panels B,E&H show LGM-PI differences. Panels C,F&I show the three dominant terms in the δ¹³C_DIC decomposition for the LGM-PI. The thick solid purple line is the same as in panels B,E&H. The thin purple line is the sum of the three components (Δ¹³C_sat,phys, Δ¹³C_soft, Δ¹³C_dis,bio).

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A striking long-known feature of the LGM distribution in Atlantic sediment reconstructions is the increased vertical gradient at mid depths [57,58], which the model reproduces, although it somewhat overestimates it. In the model, this steepened gradient is due to enhanced iron fertilization in the Southern Ocean, which increases productivity there and injects more isotopically light carbon in deep waters, a shoaling of the Atlantic Meridional Overturning Circulation (AMOC), which shifts the southward penetration of relatively isotopically high North Atlantic Deep Water to shallower depths and an increase in sea ice cover, which prevents equilibration with the atmosphere. The decrease in observed deep Atlantic δ¹³C_DIC by about 1 ‰ is well reproduced by the model (Fig 5B), although it extends to slightly shallower depths. This may be due to a too shallow and weak simulated AMOC (Fig E in S1 Text). The decrease in the deep Southern Ocean is slightly underestimated, while that in the Indian and Pacific is slightly overestimated by the model (Fig 5E and 5H). Nevertheless, we conclude that the model captures the main features in the sediment data and thus is a viable representation of the LGM state that justifies further analysis. One caveat of this model state is hypoxic conditions in the northern North Pacific, which are inconsistent with sediment data. These biases suggest more carbon and less oxygen in the North Pacific and less carbon and more oxygen in the Southern Ocean in the model compared to the reconstructions.

Figs 2D, 4F, 5C, 5F and 5I reveal that Δ¹³C_dis,bio is by far the dominating term in the δ¹³C_DIC decrease. Globally, it amounts to -0.67 ‰ (Table 2) and in the deep ocean it decreases δ¹³C_DIC by about 1 ‰. The fact that deep ocean δ¹³C_DIC decreases less than that is owed to positive changes in Δ¹³C_sat,phys and Δ¹³C_soft by 0.2–0.3 ‰ (Fig 4D and 4F). Globally, each of those components increases δ¹³C_DIC by 0.16–0.17 ‰ (Table 2).

The spatial distribution of Δ¹³C_dis,bio, shown in Fig 6 reveals that it is dominated by the Southern Ocean. In the PI, minimum values of Δ¹³C_dis,bio of ~-1.2 ‰ are simulated in the marginal polar seas, which propagate as AABW into the abyssal waters of all ocean basins. In the LGM, values twice as large (~-2.4 ‰) extend more spatially at the surface around Antarctica and penetrate not only abyssal waters but also much of the mid depth oceans. The LGM-PI changes in Δ¹³C_dis,bio (Fig 6F) feature a minimum in the North Atlantic around 3.5 km depth, due to AMOC shoaling.

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Fig 6.

Modelled distribution of Δ¹³C_dis,bio (‰) in the PI (A,D,G), LGM (B,E,H) and the difference (LGM-PI; C,F,I) at the surface (A,B,C) and zonally-averaged in the Atlantic (D,E,F) and Pacific and Indian (G,H,I).

https://doi.org/10.1371/journal.pclm.0000434.g006

5. Discussion and conclusions

We have demonstrated that widely used approximations of respired carbon and δ¹³C_DIC, based on the AOU approximation or phosphate (δ¹³C_as) lead to large errors, in this case even wrong signs, and thus should not be used anymore. They confuse air-sea disequilibrium of oxygen with that of carbon and preformed phosphate with that of δ¹³C_DIC, which makes them invalid. Conclusions based on those approximations need to be re-evaluated. For example, the conclusion of Sigman and Hain [3], that the changes in preformed δ¹³C_DIC in the LGM were zero, thus implying that the observed whole ocean decrease in δ¹³C_DIC was due to respired carbon indicating an increased biological pump, was based on the AOU approximation of Δ¹³C_soft by Vollmer et al. [24]. In contrast, here we find that the whole ocean decrease in δ¹³C_DIC of -0.39 ‰ was caused by a large decrease in preformed Δ¹³C_pre of -0.55 ‰, dominated by the biological disequilibrium Δ¹³C_dis,bio change of -0.67 ‰.

The soft-tissue biological pump is driven by the sinking flux of organic matter, which is isotopically light and leads to depletion of surface DIC and enrichment of δ¹³C_DIC (Fig 1A), resulting in uptake of CO₂ from the atmosphere at mid and low latitudes and a tendency of air-sea fluxes to decrease δ¹³C_DIC there. In the subsurface ocean, the remineralization of the organic matter increases DIC and decreases δ¹³C_DIC. Thus, C_soft > 0 and Δ¹³C_soft < 0. In other words, the sinking flux of organic matter is a source for biological carbon and a sink for δ¹³C_DIC. If this was the only process operating, ocean carbon would increase, and its δ¹³C_DIC would decrease, indefinitely. This is obviously not the case. At equilibrium, this source for biological carbon has an equal sink in upwelling and outgassing of C_bio to the atmosphere, which increases δ¹³C_DIC. If air-sea gas exchange was infinitely fast, the disequilibrium would be zero. However, since gas exchange is slow, a disequilibrium C_dis,bio > 0 and Δ¹³C_dis,bio < 0 remains near Antarctica (Fig 3C and 3D), which fills the deepest layers of the ocean (Fig 6).

Physical processes, in contrast, lead to cooling at the surface, which causes negative disequilibria (C_dis,phys < 0 and Δ¹³C_dis,bio < 0) and surface fluxes in the polar Southern Ocean overturning circulation branch that tend to increase both CO₂ and δ¹³C_DIC (Fig 1A). Thus, while for carbon the biological and physical disequilibria oppose and diminish each other, for δ¹³C_DIC they collaborate and strengthen one another (Fig 2). This leads to a much larger effect of the disequilibrium for δ¹³C_DIC than for carbon.

Two processes affect biological carbon storage. First, the active biological pump, the source of biological carbon, which transports carbon against a gradient in analogy to Volk and Hoffert’s [11] cellular ion pump, associated with photosynthesis, sinking of organic matter and accumulation of regenerated carbon at depth, quantified as C_reg. Second, the sink of biological carbon associated with upwelling and outgassing, which, because it is ineffective, especially near Antarctica, leaves a substantial disequilibrium (C_dis,bio, Δ¹³C_dis,bio), thus adding to the storage of isotopically light biological carbon. It is useful to distinguish between these because regenerated carbon is impacted by processes that affect productivity such as nutrient or light limitation and the residence time of waters in the subsurface, whereas the disequilibrium is impacted by processes that affect gas exchange such as sea ice and the proportion of the deep ocean that is ventilated from Antarctic polar waters. Even though biological carbon increased in our LGM simulations, the active part of the biological pump decreased (C_reg), which leads to an increase in Δ¹³C_reg. Instead, we attribute the increase in biological carbon storage and decrease in Δ¹³C_bio to changes in the biological disequilibrium, representing a diminished sink of biological carbon.

Shackleton’s [35] hypothesis, that a reduction in terrestrial carbon would have caused the whole ocean decrease in δ¹³C_DIC, implies that Δ¹³C_sat is the dominant term in our model’s decomposition. However, that is not the case. Rather, our results suggest that processes that affect the biological disequilibrium are the main drivers of the observed decrease in δ¹³C_DIC, such as increased sea ice cover, iron fertilization and shoaling of the AMOC. However, here we have not performed single forcing experiments such as in K19. Therefore, a quantification of each forcing variable on the simulated changes in the carbon isotope components will need to wait until further study. Nevertheless, another argument against Shackleton’s hypothesis and studies that support that idea [36,37], is that it assumes a closed land-ocean-atmosphere system in which carbon and carbon-13 are conserved. However, ample evidence suggests that sediment interactions played a role on glacial-interglacial timescales [60,61], and that they have affected both carbon and δ¹³C [62]. Thus, estimates of terrestrial carbon changes from whole ocean δ¹³C_DIC based on the assumption of a closed system are likely flawed.

Our simulations also assume a closed system. Sediment interactions, specifically the dissolution of calcium carbonate, would have increased ocean carbon and alkalinity, more than in our model, and further reduced atmospheric CO₂. This effect could have compensated for the respiration of some or all the terrestrial carbon that was buried under ice in our simulations. However, the effect of the dissolution of ~970 Pg of calcium carbonate with a δ¹³C of 1.5 ‰ [38] would have increased whole ocean δ¹³C_DIC by only ~0.04 ‰, a relatively small effect, and thus does not affect our estimated δ¹³C_DIC decomposition much. Nevertheless, simulations with a more complete carbon cycle, including sediments, permafrost and sea level are desirable.

Supporting information

Acknowledgments

We thank Samar Khatiwala for contributing ideas to calculate ¹³C_sat as described in Section C in S1 Text. We are grateful for constructive reviews from Michel Crucifix and one anonymous reviewer.