cGENIE is an Earth system model of intermediate complexity, with a 3D frictional-geostrophic ocean (36×36 equal-area horizontal grid, 16 depth levels), 2D energy–moisture balance atmosphere with prescribed wind fields, and interactive atmospheric chemistry and ocean biogeochemistry. The model code and user handbook can be found in the cGENIE GitHub repository . We run a version of cGENIE with the same phosphorus-plus-iron (Fe) co-limitation scheme as used in the iron cycle model inter-comparison study of . The model branch enabled for use with flexible C/P ratios (see Sect. ) is tagged as release v0.9.5, and the model configurations used in this paper are included in this release see Code availability for details.

In the original version of the cGENIE Earth system model , as well as in the version of , the stoichiometric ratios are based on . Thus, there is a fixed relationship between the number of moles of the elements that are taken up (positive) or released (negative) during production of organic matter in the ocean. This relationship is P/C/O2=1/106/-138, where O2 is dissolved oxygen (nitrogen is assumed only implicitly for the purpose of accounting for organic matter creation and remineralization-related alkalinity transformations in the ocean; ). An exception is iron, where Fe/C varies as a function of iron availability as described in .

Although the average elemental composition of organic matter in the ocean is close to the Redfield ratios, the stoichiometry of production of new organic material has shown high in situ variability. Variability occurs between species, but also within the same species, and has been shown to depend on environmental factors such as nutrient availability, water temperature, and light e.g.. We test the importance of this variability for glacial ocean CO2 storage by running the same experiments with the fixed Redfield stoichiometry version of cGENIE and with a model version where we have implemented the linear regression model presented by (Eq. ). These two model versions are henceforth denoted RED and GAM.

The flexible stoichiometry in GAM depends on the ambient concentration of dissolved phosphate ([PO4]) in the water: 1P/C=1/PO4144.9µmolL-1+0.0060-1.

This relation shows that, when [PO4] is low, organisms bind more C per atom of P than they do under high-[PO4] conditions (Fig. ). Equation () is applied in cGENIE in the calculations of biological C uptake at the surface ocean based on the surface concentration of PO4. In Sect. , Eq. () is also used to translate model surface PO4 fields to the corresponding surface C/P ratios for the organic matter produced in each grid cell. Note that, while we change the ratio of C/P, the ratio of C/O2 remains the same in all experiments. As a result, the P/O2 ratio changes between experiments.

We start all experiments from an interglacial–modern (IG-M) control state, which has been run for 10 000 years to steady state, using either Redfield (CtrlRED) or variable (CtrlGAM) stoichiometry. The control states have a prescribed pCO2atm of 278 ppm and the same climate (Table ). However due to the differences in C/P, they have different ocean carbon inventories (Table S1 in the Supplement). In CtrlGAM, the export flux of organic matter see has a global average C/P composition of 121/1, and thus the global ocean carbon storage is larger than in CtrlRED. This also suggests that a perturbation, which increases ocean storage of P through the biological pump, could cause storage of 15 (i.e. 121–106) more carbon atoms in simulations using GAM compared to RED, simply because the average composition of the formed biological material is different. To distinguish between the role of the flexibility of the stoichiometry and the change in the mean composition of organic material, we add a control state with fixed stoichiometry where C/P = 121/1 (henceforth denoted Ctrl121).

In order to explore the effects of variable stoichiometry, we make a sensitivity study where we apply changes to boundary conditions, individually and in combination (see Sect. ), that may be representative of changes that occurred during glacial periods. All experiments are listed in Table .

The applied changes in boundary conditions are

physical perturbations (colder climate) of –

radiative forcing corresponding to LGM CO2 = 185 ppm and

By applying the above perturbations, we aim to approach, but not fully resolve, some of the characteristics of the LGM ocean, which appears to have had a global average ocean temperature (Toce‾) 2.57 ±0.24 ∘C colder than the Holocene , a weakly ventilated deep ocean e.g., and a more efficient biological pump e.g.. We also aim to increase carbon retention in the deep ocean .

The physical perturbations serve to achieve a colder climate (Toce‾ cools by 2.1 ∘C compared to Ctrl, thus 80 % of the observed 2.6 ∘C; see Sect. ) and weaker overturning (see Sect.  and Fig. ) with a longer residence time of the Antarctic Bottom Water (AABW) cell compared to Ctrl. Colder conditions achieve a stronger solubility pump, thereby strengthening the retention of carbon in the deep ocean. As the physical perturbations affect the ocean circulation and temperature, they also affect the nutrient distribution and the rates of nutrient upwelling and biological growth (slower growth in colder water). They thereby affect the biological productivity .

The biological perturbations serve to achieve a more efficient biological pump, which is connected with increased retention of nutrients and carbon in the deep ocean, and lower surface nutrient concentrations in productive regions (see Sect.  and ). With flexible stoichiometry, lower surface nutrient concentrations result in higher C/P ratios, further increasing the export production and thereby the carbon retention in the deep ocean. In our experiments, we show that the flexible stoichiometry amplifies the response of the biological pump to both physical and biological perturbations.

The perturbations and the experiments are described in detail in Sect. –.

For comparison and validation of model results, we use records of ocean-state variables from climatological mean fields of modern observations and proxy observations from the LGM.

Modern data of ocean temperature, oxygen, and nutrients are retrieved from the World Ocean Atlas 2018 and we use the proxy estimates of LGM ocean temperature from . Average modern-day strength of the Atlantic meridional overturning circulation (AMOC) is estimated by from the RAPID-MOCHA array at 26∘ N.

We use model–data comparison of benthic δ13C to assess the statistical similarity (correlation) between both the model control state and glacial-like state (see Sect. ) to benthic δ13C data representing the late Holocene (0–6 ka, HOL) and Last Glacial Maximum (19–23 ka, LGM) . Locations of core sites can be seen in Fig. S1 in the Supplement (see also Fig. 1 in ). Note that LGM benthic δ13C is more 13C-depleted than that in the Holocene due to the addition of 13C-depleted terrestrial carbon to the glacial ocean , which is not simulated in our model experiments. Therefore, to compare our glacial-like simulations (GLcomb) to LGM observations, we subtract a Holocene–LGM global average difference of 0.32 ‰ from the GLcomb experiments. state that the wide range of error for the estimate of glacial-to-modern change in benthic δ13C of 0.32±0.20‰ suffers from a lack of observations in all ocean basins but the Atlantic. Therefore, we place more emphasis on the results of the model–data comparison in the Atlantic than in the Indo-Pacific sector.

The extent to which biology succeeds in using the available nutrients can be determined by calculating the nutrient utilization efficiency P*‾ , 2P*‾=Prem‾Ptot‾, which is the fraction of remineralized (Preg) to total (Ptot) nutrients (in this case, PO4) in the ocean. Overlines denote global averages. Remineralized nutrients have been transported from the surface to the interior ocean by the biological pump, and Prem is given by 3Prem=Ptot-Ppre.

Here, Ppre is preformed PO4 – the concentration of PO4 that was present in the water parcel as it sank, and thus the fraction that was not used by biology in the surface ocean. In cGENIE, the concentration of preformed tracers is set in the surface ocean and then passively advected through the ocean interior . The biological pump also captures carbon, and a similar relationship can be used for concentrations of DIC, where 4DICrem=DICtot-DICpre. DICrem is used to compute the ocean storage of remineralized acidic carbon (ACrem; see Appendix ). ACrem is biological carbon that entered the ocean in the form of CO2 in soft tissue (as opposed to carbonates in hard tissue), measured independently of oxygen consumption and/or remineralized phosphate.

In cGENIE, Ppre and DICpre are modelled as passive tracers . Hence, we can use the model output for Ppre in Eq. () to compute P*‾ (Eq. ).

In a model with a fixed Redfield ratio, P*‾ determines the effect of the biological pump on pCO2atm. For example, it has been found that a higher P*‾ in the initial state gives a lower potential for drawdown of pCO2atm in response to similar perturbations . However, with variable stoichiometry this is no longer true, since the amount of carbon retained in the deep ocean is not necessarily proportional to P*‾.

The applied changes listed in Table  cause changes in ocean characteristics such as overturning circulation, temperature, surface nutrient distributions, and biological productivity, which result in changed pCO2atm. The resulting steady-state global average values for temperature (Toce‾), dissolved oxygen (O2‾), and nutrient utilization efficiency P*‾, as well as the maximum and minimum of the Atlantic meridional overturning stream function, are listed in Table .

We show the results of two different combined simulations; Acomb and GLcomb. GLcomb is the “glacial-like” simulation, which combines all the sensitivity experiments (Table ). Acomb omits the reduction in wind stress.

The representation of ocean biology in general circulation models (GCMs) tends to be oversimplified and the development of the models is often held back by constraints imposed by maintaining the computational efficiency of the model. The empirical model is simple and based on nutrient variables that are already present in biogeochemical models (nitrate and phosphate). By implementing the GAM parametrization, or possibly a power law such as that described by , an additional facet of the complexity of ocean biology can be implicitly accounted for at a relatively small computational cost. Previous model ensemble studies have shown that this type of dynamical response of the biology to changes in the modelled ocean state can improve the model's ability to realistically simulate ocean biogeochemistry . In pre-industrial and future simulations respectively, and find that the flexible stoichiometry acts to stabilize the response of ocean DIC to changes in the physical (circulation) state. In our glacial-like simulations, we find that the response of ocean DIC, and thus pCO2atm, to the combined perturbations is greater in the simulations with flexible stoichiometry. Nonetheless, our study confirms the potential importance of dynamical biological response for the outcome of model studies.

The approach taken by both and is to adapt a function to species-independent C : P observations. This means that they account for the adaptation of plankton to the surrounding conditions, in terms of both species composition and individuals being more frugal in low-nutrient conditions. This is one of the main advantages of such an approach, as it can be applied in a model without different plankton functional types, which is what we use here. appear to succeed with full glacial–interglacial CO2 cycles in CLIMBER-2, which does not have flexible stoichiometry for primary producers but which has a temperature limitation on growth and explicit phyto- and zooplankton with different C uptake rates. This combination may perhaps achieve a similar response in carbon export in their simulations, when moving into a colder climate, as the flexible stoichiometry does in our simulations. The next step to approach a more realistic modelling of the biological pump would be to include a representation of preferential remineralization of nutrients e.g., but this goes beyond the scope of the present study.

One drawback of the approach is that it assumes that the C/P ratio continues to increase continuously with increasing [PO4]. As such, in a high-surface-[PO4] region like the Southern Ocean, GAM does not represent the effects on C/P of temperature and light and the associated non-linear effects that could be of importance here e.g.. Up to [PO4]=1.7µM, the GAM parametrization fits the binned observational data well see Figs. 1 and S2 in. To account for the lack of observational data at higher [PO4] in , we have tested the effect of saturation of the C/P ratio at higher [PO4] in Ctrl and GLcomb simulations where we kept C/P=55/1 at [PO4]>1.7µM. The increase in ocean carbon storage and decrease in pCO2atm between Ctrl and GLcomb are nearly identical with GAM; thus saturation of the C/P ratio at very high [PO4] causes no noticeable impact on our results.

Our sensitivity experiments RLS ×0.75 and RLS ×1.25 reveal that the response in pCO2atm to the perturbation is enhanced in GAM compared to RED for both increased and decreased RLS. While increased RLS would be an effect of ocean cooling, and thus of interest for glacial studies, reduced RLS would be a consequence of ocean warming . describes how decreased RLS would have a positive feedback on pCO2atm in a future warming climate. Our results imply that flexible C/P could have a further reinforcing effect on this feedback. It would therefore be of interest to apply a parametrization of flexible C/P in models used for simulations of future climate feedbacks.

Many studies have suggested increased ocean storage of organic carbon as a potentially important contributor to the low glacial pCO2atm e.g.. However, biological production depends on water temperature and decreases in cold conditions. This temperature effect is parameterized in cGENIE as a local temperature-dependent uptake rate modifier proportional to e(T/15.9∘C), and we see overall reduced productivity in our cold climate simulations (see e.g. LGMphy, Table S1). As the climate cools, the temperature effect leads to a decrease in biological productivity and a subsequent decrease in P*‾ (see LGMphy in Fig. ). If productivity decreases, other mechanisms are needed to offset this decrease, if the total ocean storage of organic carbon is to increase. Mechanisms that can contribute to increased deep-ocean carbon retention are for example reduced SO overturning circulation increased residence time of the AABW; and deeper remineralization , which we apply through our perturbations in winds (Sect. ) and RLS (Sect. ). From our results, it is evident that variable stoichiometry can be another contributing factor. In our simulations, global average export production decreases, in terms of both POP (particulate organic phosphorus) and POC (particulate organic carbon), by 15 % between CtrlRED and GLcombRED because of the colder climate. However, the variable stoichiometry in GAM partly offsets this decrease in biological carbon capture – while the export production in terms of POP decreases by 17 %, the corresponding decrease in POC is only 10 %. Thus, in GLcombGAM we achieve an increase in ocean inventory of remineralized carbon, which exceeds the one of GLcombRED (Fig. ).

Due to the competing effects between decreased export production and increased retention that are introduced by the different forcing components, the net change in Prem, and thus in P*‾, is very small when moving from the control state (Ctrl) to the glacial-like state (GLcomb) (Fig. ). In the fixed stoichiometry case (RED), there is a small net increase in P*‾ of 0.020 in GLcomb compared to Ctrl, which is linearly related to a small increase in storage of ACrem in the ocean. In the case with variable stoichiometry (GAM), there is instead a very small decrease in P*‾ of 0.003. With a linear response, we would thus expect a decrease in storage of ACrem as well. Instead, we see a reasonably large increase in global average ACrem. In summary, we suggest this is a result of changes in surface P fields (see Fig. 7).

The reduced pCO2atm in GLcombGAM, compared to GLcombRED, can be explained by the non-linearity introduced by the local variability in C/P. When changes in ocean circulation, remineralization depth, and dust deposition cause the local nutrient availability in the surface waters to change, this affects the elemental composition of the exported organic material (Fig. S5). In GLcomb, there is a reduction of the surface layer P concentration compared to Ctrl in some key (HNLC) regions. In GAM, this decrease in surface P results in an increase in C/P. This further strengthens the biological pump in these key regions, resulting in a non-linear relationship between storage of remineralized phosphate and biologically sourced carbon (Fig. ). In CtrlGAM, the average elemental C/P composition is 121/1. In GLcombGAM, this average is 134/1 (Table S1, Fig. S5). This means that even though the same amount of P is exported to the deep ocean, the organic molecules carry more carbon, which is released in the deep ocean during remineralization. In CtrlGAM, the global average concentration of Prem is 1.16 µmolkg-1 (compared with 1.17 µmolkg-1 in GLcombGAM). By increasing the average C/P composition of 1.16 µmolkg-1 organic molecules from 121 to 134 (i.e. by 13 units), this causes an increase in Csoft by ∼15 µmolkg-1, which corresponds to the observed increase in ACrem. From this, we conclude that, in a system where stoichiometry is variable on a local scale, ocean storage of biologically sourced CO2 can change while the amount of remineralized nutrients remains constant.

Note also that CtrlGAM has a larger inventory of DIC as well as Csoft compared to CtrlRED. found that drawdown of pCO2atm in response to a perturbation is larger when the control state has a smaller inventory of DIC and Csoft. Yet, the effect of applying the same perturbation results in a larger drawdown of pCO2atm in GAM than in RED. This is opposite of the conclusions of . The reason is that the flexible stoichiometry in effect increases the drawdown potential, which more than compensates for the increased carbon inventory in the control state. In GLcombGAM, the C/P in global average export production increases from the control 121/1 to 134/1, which reflects the increased storage of organic carbon allowed by the flexible stoichiometry.

Studies have shown that deep-ocean O2 concentrations were lower during the LGM than in the Holocene e.g.. Here, we discuss implications of using flexible C/P for the model's ability to reproduce ocean oxygen patterns and concentrations in the different time periods.

In the Atlantic, CtrlGAM (Fig. 4e) reproduces the climatological mean extent of the oxygen minimum zone (OMZ) (Fig. 4a) better than CtrlRED (Fig. 4c) does. In the Pacific Ocean, the O2 gradient in the climatological mean fields (Fig. 4b) is more gradual compared to that of the control states (Fig. 4d, f), but the core of the OMZ is well reproduced by the model. The forcings applied to GLcomb are not sufficient to reproduce a full glacial state. Still, we do get a vertical expansion of the OMZ in GLcombRED (Fig. 4h) compared to CtrlRED (Fig. 4c), in agreement with the findings of Hoogakker et al. (2018). In GLcombGAM, oxygen depletion is too extensive (see below), but the tendency of vertical expansion compared to the control state is present here as well.

In our glacial-like states, we see a significant reduction of O2 compared to the control state in both RED and GAM (Fig. d and e). This response is expected when we apply increased dust deposition and deeper remineralization , and the direction of the overall response of deep-ocean O2 to the glacial-like forcings is in line with observations. The reduction in O2 is stronger in GAM, due to the larger storage of respired carbon in this model version.

Finally, it should be noted that CtrlGAM (Fig. c) displays deeper oxygen minima in the oxygen minimum zones of both the Atlantic equatorial region and the North Pacific compared to what is seen in CtrlRED (Fig. b) and in climatological mean fields. In CtrlGAM, a large part of the interior North Pacific is anoxic (Fig. c), while the climatological mean fields (Fig. a) indicate very low oxygen levels, but not anoxia. As illustrated by simulations in , variable stoichiometry in itself is not always sufficient to achieve widespread deep-ocean de-oxygenation in a model under glacial-like climate change. Among other factors, model ocean oxygen conditions are also dependent on deep water formation characteristics of the model . The deep water formation characteristics of a model affect the amount of time available for remineralization and, consequently, the oxygen consumption. In addition, due to a lack of resolution deep water formation in climate models generally happens as open water convection, rather than as dense plumes along slopes . This may cause too much oxygen to be entrained into the deep ocean . In cGENIE, this effect is small enough not to cancel the increased O2 consumption caused by the higher average C/P in CtrlGAM compared to CtrlRED.

In summary, the GAM version of the model quantitatively reproduces the observed O2 patterns of both the LGM and the Holocene, but with too low concentrations. If this parametrization of variable stoichiometry is to be used in cGENIE in future studies, we suggest some retuning, for example by reducing the global average concentration of nutrients, to improve the representation of observed modern-day ocean O2 concentrations in the GAM control state.

Part of the observed difference in pCO2atm between GLcombRED and GLcombGAM results from a difference in global average C/P in the control states (CtrlRED and CtrlGAM). In CtrlGAM, the average C/P in the export production is close to 121/1, instead of 106/1 as in CtrlRED. We illustrate the consequences of this difference by running parallel simulations with fixed C/P of 121/1 (model version 121).

In a simulation with reduced wind stress (WNS ×0.5121), pCO2atm is reduced by -14.5 ppm compared to CtrlRED (Table S2). The corresponding pCO2atm drawdown in WNS ×0.5RED and WNS ×0.5GAM is -12.9 and -16.3 ppm respectively. This indicates that, for the reduced wind stress case, about half of the enhanced drawdown achieved by the flexible stoichiometry can be attributed to a difference in the mean C/P composition of the organic material between the control states CtrlRED and CtrlGAM. Similarly, for the enhanced dust deposition experiments, LGMdust121 explains about one-third of the difference in pCO2atm between LGMdustRED and LGMdustGAM (Table S2). In the combined experiment GLcomb, we can attribute about half (-8 ppm of -17 ppm) of the observed difference in drawdown between RED and GAM to the difference in control-state average C/P. In Acomb, the control-state difference in C/P accounts for about two-thirds of the difference between model versions (-5 ppm of -8 ppm). Evidently, the individual perturbation simulations and GLcomb have smaller fractions of the change in pCO2atm that are due to changed average C/P. As shown above, the simulations with 121 indicate that, depending on the change in forcing, between one-third and two-thirds of the difference in drawdown between RED and GAM is due to the difference in average C/P between the control states (Fig. , Table  S2). From this, we conclude that the effects of the perturbations do not add linearly.

As outlined in Sect. , an increase in C/P reduces deep-ocean O2 concentrations, through an increase in regenerated carbon. In this respect, the 121 experiments fall between the corresponding RED and GAM experiments. For example, the global ocean average O2 concentration, O2‾, in Ctrl121 is 152 µmolkg-1, which is lower than CtrlRED (166 µmolkg-1), but higher than CtrlGAM (144 µmolkg-1). Similarly, GLcomb121 has a lower O2‾ than GLcombRED (96 compared to 122 µmolkg-1), but higher than GLcombGAM (74 µmolkg-1).

The observed effects of modified average C/P could have implications for model intercomparison projects, if they compare results from models that use different versions of fixed stoichiometry (for example, or stoichiometries, compared to ). The problem with different stoichiometry assumptions in models is extensively discussed by . Our study shows a direct consequence of such differences, with a different model response to the same perturbation.

Proxy records of benthic δ13C indicate a change in ocean δ13C across the deglaciation. The whole ocean deglacial change has been estimated to ∼0.35 ‰ , and the surface-to-deep gradient weakened shown in numerous studies; see e.g.and references therein. Here we compare model ocean δ13C of our simulations to the benthic δ13C records, to see how well the simulations capture the observed patterns and whether there is a difference in model–data correlation between RED and GAM.

The model–data comparison in δ13C (Sect. ) suggests that the Ctrl simulations are overall well correlated with Holocene benthic δ13C data (HOL in Table S3). For the Atlantic, the correlation of the Ctrl simulations is higher with the LGM benthic δ13C (LGM in Table S3) than with HOL. However, the standard deviations (SDs) suggest that the Atlantic north–south gradient is not as strong as in an LGM ocean state and thus more similar to the modern ocean.

When we apply our combined forcings in the GLcomb simulations, we achieve a stronger δ13C gradient in the Atlantic, allowing for a closer match with LGM data in terms of SDs. A stronger gradient in δ13C and more depleted values suggest weaker ventilation of the deep ocean. The poor correlation in the Indo-Pacific, which may be partly due to sparse mid-ocean observations for almost 70 % of the ocean volume, makes the global statistics for LGM observations difficult to interpret. The forcings applied to GLcomb are factors that are likely to be important for the glacial ocean circulation and biogeochemistry. However, these forcings are not sufficient to reproduce a full glacial state (i.e. the use of the term glacial-like simulations rather than LGM simulation). Other forcings that have shown to be important for modelling of glacial δ13C are, for example, brine rejection , and freshwater forcing . The fact that some important forcings are missing is likely the main cause for the model–data discrepancy, and the reason for why we do not achieve a glacial Pacific Ocean circulation consistent with observed δ13C patterns.

Each of the two observational datasets (HOL and LGM) displays similar correlations across the two model simulations. The correlation of the HOL δ13C records with CtrlRED, CtrlGAM, GLcombRED, and GLcombGAM is in all cases between 0.76 and 0.78. Meanwhile, the correlation of LGM δ13C records with the same four simulations is in all cases between 0.55 and 0.58. That our GLcomb simulations still correlate so well with the HOL dataset suggests the applied forcings have not caused these simulations to be clearly different from Ctrl in terms of water mass distribution. For the same reason, the correlation with LGM δ13C records does not significantly improve from Ctrl to GLcomb. The water mass distribution in cGENIE is strongly constrained by the resolution of the model, especially in the vertical. Changes in temperature and salinity that should cause changes in water mass volume may not be sufficient to allow a water mass to extend to the next vertical level of the model. As a consequence, while the gradient between water masses may become more or less pronounced, the interface of water masses may still remain at the same depth. The applied changes affect the chemical and biological conditions for ocean carbon storage, such as CO2 solubility (temperature dependent) and nutrient availability, more than the physical conditions, such as water mass volume and turnover time. To achieve a full glacial state with cGENIE, with a more glacial-like water mass distribution, additional physical forcings (see above) are likely to be required.

How δ13C is represented in cGENIE is detailed in Appendix . The very small differences between RED and GAM suggests that using variable stoichiometry does not impact our ability to represent the δ13C patterns seen in observational data. However, we note that some retuning of the modern control state is recommended before cGENIE with variable stoichiometry is used in other studies.