We use the model cGENIE, an Earth system model of intermediate complexity (EMIC), which is a computationally efficient model developed for studying the ocean carbon cycle on timescales of 100–100 000 years. cGENIE is higher in complexity than box models, but is still efficient enough to allow for the running of a large ensemble to equilibrium for the carbon system. In terms of ocean carbon system tracers, the minimum required for this type of study is P, DIC, O2 and AT. cGENIE includes many additional tracers, out of which only some are used in this study. For example, particulate (POC) and dissolved organic carbon (DOC) are included in the calculations of model carbon inventory (see Appendix ). Of particular importance for this study is the possibility to run with preformed tracers (Ppre, Cpre, O2pre, Apre; see Sect. ). Model characteristics are described in , and .

The physical ocean is modelled using a frictional geostrophic 3-D model on a 36 × 36 equal area grid in the horizontal and 16 depth levels. The atmospheric model is an energy–moisture balance model (EMBM) with prescribed climatological wind fields . Ocean biogeochemistry and atmospheric chemistry are treated by separate modules that are coupled to the physical models and to each other . The biogeochemical module is based on a phosphate-only nutrient scheme. Hence, phosphate (P) is the limiting nutrient. The model description of the export flux of organic matter is based on available surface nutrients seeEqs. 1–4, and instead of having a “standing plankton biomass” in the model, the export of particulate organic matter is derived directly from the uptake of P. Remineralisation in cGENIE primarily depends on oxygen availability . POC is modelled as two fractions: one more easily degradable (labile) fraction, which undergoes an exponential decay with depth, and one fraction that is more resistant to degradation, which remineralises at the ocean floor. In the drawdown experiment (Sect. ), the length scale of the exponential decay is adjusted. The remineralisation of CaCO3 in the water column is treated in a similar manner to POC. The carbonate precipitation rate is thermodynamically based and relates the export flux of CaCO3 to the flux of POC seeEq. 8. As an investigation of carbonate system feedbacks is not the purpose of this study, interactive sediments are not used, and in terms of carbon cycling, the atmosphere–ocean is studied as a closed system.

As our control state, we use the pre-industrial equilibrium state described in . During the spin-up (10 000 years) to this equilibrium state, pCO2atm is restored to 278 µatm (≈278 ppm), while the inventory of carbon in the model is allowed to change. Henceforth, this pre-industrial equilibrium state will be referred to as PIES278.

The inventory of total carbon, TC [mol], in the equilibrium state can be described by TC=MapCO2atm+Mo(Csat‾+Csoft‾+Ccarb‾+Cres‾).

Equation () sums the contributions to TC. Changes in e.g. land carbon are not modelled and therefore not included in this equation. The atmospheric carbon content is given by the partial pressure of CO2 times the number of moles of gas in the atmosphere, Ma. Mo is the mass of the ocean (in kilograms). Csat is the concentration [mol kg-1] of carbon an individual water parcel would have had if it were in equilibrium with the atmosphere at the ambient temperature, salinity, alkalinity and concentration of PO4. Csoft originates from remineralisation of the soft tissue of biogenic material that has entered the water parcel. Carbon from biogenic hard tissue is denoted Ccarb. Cres is the residual needed to get the actual carbon concentration in the water parcel. Cres contains three components: (1) the disequilibrium component Cdis, which we will quantify in Sect. , (2) carbon in the form of particulate and dissolved organic matter and (3) errors associated with any imperfect assumptions in the theory used for calculating Csat, Csoft and Ccarb. The overbars represent global averages. The concentration Cpre in the water parcel consists of Csat+Cdis, whereas Csoft+Ccarb gives regenerated carbon, Creg. We calculate the contributions to Eq. () and any changes to this inventory (see Eq. ) using the methods of and , when necessary solving the carbon system equations using the solver of . More details about the calculations of the contributions to TC are given in Appendix .

Initialising from our pre-industrial equilibrium state PIES278, we perform 12 different equilibrium experiments in which one or two physical tuning parameters have been changed compared to the control (Fig. ). The parameters and their ranges are further described in Sect.  and listed in Table . The experiments are run for 10 000 years, which is enough to reach a new equilibrium state. These 12 sensitivity experiment equilibrium states (SE1–SE12) are given descriptive notations listed in Table . These modifications of physical tuning parameters will cause the ocean circulation to change relative to PIES278; the circulation gets weaker or stronger and overturning cells change their latitudinal extent, for example. During the spin-up phase, pCO2atm is still restored to 278 µatm (Fig. ). The ocean reservoir of nutrients (in this case, PO4) is the same as in PIES278, but the partitioning between Preg and Ppre is changed and thereby the strength of the biological pump. Likewise, the mean temperature of the ocean changes and thereby the strength of the solubility pump. Hence, while the atmospheric carbon inventory is the same in all ensemble members as in PIES278, the ocean carbon inventory and the TC of these 12 ensemble members is different. We aim at comparing the drawdown potential of models that have the same pCO2atm in their initial equilibrium state, but different oceanic carbon distributions and inventories, which is usually the case in model inter-comparison projects. For example, the instructions for the LGM simulations within the framework of the current PMIP3–CMIP5 project specify the LGM pCO2atm to be set to 185 ppm, whereas there are no specifications for the ocean carbon inventory (see https://pmip3.lsce.ipsl.fr/).

The change in the total carbon inventory, ΔTC [mol], between PIES278 and some equilibrium state SE(n), where n=(1,…,12), can be described by ΔTC=Mo(ΔCsat‾+ΔCsoft‾+ΔCcarb‾+ΔCres‾).

The contributions by Csoft, Ccarb and Csat to this observed change in TC in Eq. () are then evaluated as described in Sects.  and . The change in Cres will simply be the residual between the observed change in TC and the sum of the contributions by Csoft, Ccarb and Csat. pCO2atm is restored and thus the atmospheric carbon reservoir does not contribute to ΔTC.

The changes in the inventories of TC, Csat, Csoft, Ccarb and Cres are translated into the equivalent change in pCO2atm that would occur if we were not restoring it to pre-industrial levels, but instead kept TC constant in the ensemble cf. methods of. This translation is performed as described in detail in Appendix . This translation allows us to test the validity of the equation describing the effect on global ocean mean temperature effect on pCO2atm suggested by (see Appendix ).

Finally, starting from each state SE1–SE12 and from PIES278, we run experiments in which the NUE of biology is maximised (100 % efficiency; Fig. ) and again allow the model to run for 10 000 years to new equilibrium states (DE1–DE12). This reveals the differences in drawdown potential between ensemble members with different ocean circulation characteristics. Note that in this step, pCO2atm is not restored, and thus TC is held constant between SE(n) and DE(n) and carbon is only redistributed between reservoirs (see Eq. ). Equation () is not applicable in this step because it assumes constant pCO2atm. Maximum NUE, i.e. P*‾=1 (see Eq. ), is achieved by changing the remineralisation length scale in the model (Sect. ). It is made deep enough (10 000 m) for any carbon that is taken up in biogenic material to be highly efficiently trapped in the deep ocean and not undergo any significant remineralisation. The concentration of dissolved P (at the surface and as a global annual mean) being reduced by 2 orders of magnitude in all DEs due to P being bound in organic material confirms that this effect is achieved. However, due to convection, mixing and local remineralisation of dissolved organic matter, the surface concentration of P does not go to zero. Note that the contribution of biogenic material to the carbon inventory TC is substantial in this step. Thus, quantifying ΔCsoft and ΔCcarb for this step is not useful unless the carbon contained in biogenic material is also considered to contribute to these reservoirs. However, the very deep remineralisation length scale is a highly hypothetical case and we therefore choose not to separate the contributions by the different carbon reservoirs to the drawdown of pCO2atm.

The physical tuning parameters that we change are atmospheric heat diffusivity, wind stress and ocean vertical and isopycnal diffusivity. They are selected because they are common tuning parameters e.g., which influence the ocean circulation.

For this study, our intention is for the ensemble to be representative of a wide range of plausible ocean circulation states. The chosen parameter ranges correspond to a halving and doubling of the values used in the control simulation. Our chosen values are within the parameter space explored for a predecessor to the GENIE model by , except the low wind stress simulation (see below). Similar parameter ranges are also explored for GENIE by e.g. . For the most part, our selected values are within the parameter ranges that generate the subset refer to as low-error simulations. In the Bern3D model, with physics based on and thus similar to GENIE, doubled the observed wind stress (W=2) to get a more realistic gyre circulation. used the Geophysical Fluid Dynamics Laboratory Modular Ocean Model version 3, which has the same default value for isopycnal diffusivity (1500 m2 s-1) as our model. explore a range of 1000–2000 m2 s-1 (cf. our range of 750–3000 m2 s-1).

When comparing with models that have different available tuning parameters, diagnostic variables such as temperature, salinity and AMOC volume transport can indicate whether our achieved states are within the common tuning range for ocean circulation. The IPCC AR5 WG1 report shows temperature and salinity ranges in two selected deep ocean grid points, in the North and South Atlantic respectively, of the ensemble of pre-industrial control states (PIC) of PMPI2 and CMIP5–PMIP3 (see grid point positions and data in Table ). We compare those ranges to the corresponding grid cell ranges of our equilibrium states SE1–SE12. In these selected grid cells, we cover a similar span in salinity and an equally broad range in temperatures as the PMIP ensemble, though the temperatures in our ensemble are higher (range shifted by ∼ 1.5 ∘C). According to , the PMIP3 PIC AMOC range is 12.6–23.0 Sv (Table ). If we exclude the combined simulation with halved wind stress and halved diapycnal (vertical) diffusivity (WS/2_DD/2), which has a very weak AMOC (2.0 Sv), the AMOC range for our equilibrium states is 8.3–18.0 Sv (Table ). Thus, there is a difference of ∼ 8–9 Sv between highest and lowest value, which is also the case for the PMIP3 PICs, but our ensemble does not cover the two highest PMIP3 AMOC values.

In a coarse-resolution model like cGENIE, the overturning circulation, which transports carbon to the deep ocean and back up to the surface again , is one of the most sensitive circulation components. We diagnose an overturning circulation strength (henceforth denoted OVT) by taking the difference between the maximum and minimum of the zonal average overturning stream function, ψ, below 556 m of depth (excluding the uppermost five grid boxes), as shown in Eq. (). The subscript gr in Eq. () denotes the geographical region. OVT is diagnosed for the Atlantic basin and the Pacific basin separately. A global measure of OVT is calculated by taking the difference between the Northern Hemisphere maximum and the Southern Hemisphere minimum of ψ below 556 m of depth. OVTgr=ψmaxgr-ψmingr

The OVT measures the amount of flushing of the deep water, which is important for the carbon storage . Another important factor influencing the carbon pools is which overturning cell is dominating in terms of volume : the northern cell (producing North Atlantic Deep Water, NADW) or the southern cell (producing Antarctic Bottom Water, AABW, and Circumpolar Deep Water, CPDW). Since these water masses are of different origin, they will differ in properties, such as water temperature and nutrients, and will therefore have different capacities for holding Csat, Csoft and Cdis. However, the inter-member differences in this aspect are difficult to discern and we have therefore chosen to focus on the impacts of OVT described above, which are more clearly identifiable.

In this first step, we achieve a set of pre-industrial equilibrium states – all with pre-industrial pCO2atm of 278 ppm – in which, as a result of ocean circulation differences, the ensemble members have different carbon reservoirs.

In PIES278 and SE1–SE12, global average salinity, total alkalinity and PO4 are 34.90, 2363 and 2.15 µmol kg-1 respectively. These properties are conserved but redistributed, which gives some very small differences in the global averages between ensemble members. Global average temperature, Tavg, is 3.58 ∘C in PIES278, which is close to the modern day observational estimate of 3.49 ∘C . In the SEs, Tavg ranges between 2.31 and 4.91 ∘C. Sea ice cover ranges from 0.0 to 10.6 % in the SEs, with PIES278 in the centre of the interval (cf. observational estimates of sea ice cover, which range between 3 and 6 % due to seasonal variability; ). Diagnostic variables for all the individual SEs are given in Table .

The control PIES278 model total carbon inventory, TC, is 3×1018 mol (∼36 000 Pg C). ΔTC, and the contributions to ΔTC by the biological and the solubility pump and by Cres (Eq. ) in the SEs, which are effects of the changes in ocean circulation, are of the magnitude of a few percent (∼ 1016 mol; Fig. a–d). This corresponds to a range in pHavg between 7.80 and 7.97 (Table ), while pHsurf stays close to the observational estimate ∼ 8.2; see. For reference, Fig. e–h show the approximate differences in pCO2atm that would have occurred in the SEs if we were not restoring it to 278 ppm (see Sect.  and Appendix ). In this ensemble, these differences in pCO2atm stay at approximately ±50 ppm (Fig. e) because of the cancellation between the effects of the different carbon pumps. Note that the methods of Appendix  (used in Fig. e–h) are based on the assumption that changes in pCO2atm are small and are therefore less reliable for SEs with large changes, e.g. WS×2 and WS/2_DD/2. Because the computed changes in pCO2atm are approximate, the sum of the contributions from the different pumps do not exactly equal the ΔpCO2atm corresponding to ΔTC.

In this step, we use the set of equilibrium states (SEs and the control PIES278) from step 1 as initial states for determining the drawdown potential, DP (Fig. ). This reveals the dependence of the resulting equilibrium state DE1–DE12 on differences in the initial states SE1–SE12. The control drawdown equilibrium is denoted CDE. DP is computed as the difference in pCO2atm between 278 ppm and the drawdown equilibrium states.

The DP varies strongly between the ensemble members and is close to linearly related to the biological efficiency, in terms of P*‾, of the initial equilibrium state (Fig. c). The near-linear relationship between DP and P*‾ of the initial SE is expected see e.g.. If the biological efficiency in the SE is small, there is a larger pool of unused nutrients that can be used to capture carbon when biological efficiency is increased to 100 %. In this ensemble, an increase in biological efficiency manifested by an increase in P*‾ of 0.1 corresponds to a drawdown of CO2 from the atmosphere of about 20–30 ppm. This is similar to the theoretical prediction by of ∼ 30 ppm. However, the drawdown of atmospheric CO2 achieved during the drawdown experiments is not purely due to biology. There are also additional effects on pCO2atm due to changes in ocean temperature (caused by changes in radiative balance), circulation and disequilibrium and due to the climatic conditions of the initial state. Thus, the model results do not correspond exactly to the theoretical prediction in this case. The most prominent example is AD/2, which has a low initial P*‾, but still has a low DP. This is the coldest of all initial states, with very high ocean sea ice cover (Table ) compared to the other SEs, and the cold conditions are likely to be affecting the conditions for biological production and disequilibrium. Also note that the near-linear relationship between P*‾ and DP does not predict DP to be exactly zero for P*‾=1, as would have to be the case. When all climatic changes caused by the drawdown experiment itself are removed, DP is reduced by 4–7 ppm. This shows that the biological component is highly dominant in the total drawdown. However, the climatic differences between the initial states will still not allow the theoretical prediction to be exact.

Those experiments that have a lower Tavg (and thus a larger inventory of Csat) compared to PIES278 tend to have a smaller DP than those with higher temperatures, which is due to circulation changes acting in a predictable way. The circulation change that is causing a colder temperature is also causing the OVT to be weaker (Table ), and at the same time causing a more efficient biological pump (more Csoft; Fig. ), because there is more time for biology to take up nutrients. Hence, there are fewer preformed nutrients left at the surface, which means P*‾ is higher and the DP is smaller.

The effect on pCO2atm of a change in the solubility pump is approximately quantifiable from the change in global ocean average temperature, ΔTavg, between two simulations, as described by Eq. () and suggested by . According to this equation, the set of observed ΔTavg of our ensemble would correspond to 5.9 ± 5.0 ppm ∘C-1 (Fig. S1). Solving the carbon system for the same set of ΔTavg yields 7.3 ± 6.0 ppm ∘C-1 (Fig. S1). Here, the deviations from the straight line are caused by the temperature restriction on the solubility equation (Appendix ). The error in using the simplified equation seems to be on the order of 20 %. Depending on which process is causing the change in ocean circulation, the impact of changes in the solubility pump on pCO2atm can be almost as important as the impact of changes in the biological CO2 efficiency of carbon uptake. For changes in ocean isopycnal diffusivity, the solubility pump effect is even the dominant response. Due to the temperature restriction on the CO2 solubility constants, the effect of ΔCsat,T is likely to be underestimated by on average 56 ± 67 % in our results, further emphasising its importance. In previous studies, this has to some extent been disregarded when the response of the biological pump has been assumed to be the dominant response to the applied changes in circulation e.g..

The relationship between the changes in Tavg and ΔCsat,T is close to linear (Fig. ). Any deviation from a perfect straight line is again caused by the temperature restriction on the solubility equation (Appendix ). The slope of the line is ∂Csat∂T‾=-0.59×1016 mol ∘C-1. If the global ocean is cooled by ∼ 2.6 ∘C, as expected in a glacial state , the slope of the line suggests that the excursion in Csat would be ∼1.5×1016 mol. Note that this excursion is underestimated due to the restriction on the solubility equation. For a 2.6 ∘C cooling, the carbon system equations (see Appendix ) yield a corresponding decrease of about 30 ppm in pCO2atm. Here, we cannot use the simplified Eq. () because the buffered carbon inventory is unknown in this hypothetical case.

In a set of idealised GCM simulations, show that CO2 disequilibrium can be as important as Csoft. In our ensemble, the effects of Cdis appear to be particularly important in simulations with a lot of sea ice (e.g. AD/2; see Fig. d, h). This leads us to the conclusion that it may also be of importance in glacial simulations. A caveat to this finding is cGENIE's coarse resolution at high latitudes and its simplified representation of sea ice as a complete barrier to gas exchange. Assuming that ΔCres is mainly due to ΔCdis, the circulation changes we impose correspond to a change in pCO2atm of ∼ -30 to +10 ppm due to ΔCdis. This is comparable to the results of , while suggest as much as ∼40–70 ppm drawdown of CO2 due to increased Cdis in glacial-like simulations. This emphasises the need for further studies on the role of Cdis in glacial and other climate scenarios with changes in ocean circulation.

In experiments with stronger OVT (global and basin scale) than in PIES278, e.g. DD×2 (Figs. a and a), a water parcel will, on average, stay near the ocean surface for a shorter time (e.g. DD/2; see Figs. b and b). Hence, biology will have less time to use the available nutrients and this will give less Csoft, and thus ΔCsoft has a strong negative correlation with OVT (Fig. , Table ). Changes in OVT explain 75–80 % of the variance in Csoft in the SE ensemble, while the rest of the variance is likely explained by e.g. the redistribution of nutrients, light limitation regions or similar factors. Meanwhile, with stronger OVT there will be more mixing, leading to a deepening of the thermocline, and Tavg will increase (Fig. a, Tables  and ). Thus, the correlation with ΔCsat,T will also be negative, though weaker (43–64 %). The response of ΔCdis is more difficult to predict from the OVT due to competing changes in the temperature gradient (especially important in the North Atlantic), sea ice and outgassing (dominant in the Southern Ocean) resulting from a change in OVT. Interestingly, the total carbon inventory TC shows a closer correlation with the OVT than any of the individual ocean carbon components (Figs.  and , Table ). Thus, the inventories of the individual DIC components are affected by the choice of model tuning strategy, whereas the total carbon inventory is mainly a result of the strength of the circulation, i.e. the ventilation of the deep water. Similar results are found for Csoft and Cdis by , who describe the changes in ocean ventilation using an ideal age tracer. Here, we show that the correlation with ocean ventilation is even stronger for total carbon and is also present for Csat.

When comparing model studies, it is important to recognise differences in biological efficiency in their control states. The pre-industrial P*‾ of a model will determine its pre-industrial inventory of Csoft but also its drawdown potential. If the pre-industrial P*‾ is incorrect, the total carbon inventory in the model will adjust to compensate for this error in order to achieve equilibrium with pre-industrial pCO2atm. Hence, failing to tune the models for pre-industrial P*‾ will mean that they start from a non-representative state of the carbon system. Thus, models with different initial P*‾ will have different ΔpCO2 in response to similar circulation changes. This point was mentioned in and emphasised by , but does not seem to have been recognised in the model inter-comparison community, and models are still not tuned for P*‾. The range of P*‾ in our pre-industrial ensemble (SE1–SE12) is 0.32–0.59. This range includes the current estimate for the global ocean, which according to is 0.36. Our range in initial-state P*‾ corresponds to a range in drawdown potential of 94–139 ppm. While using a different model but a similar approach, we confirm the conclusion of and want to stress the importance of a similar initial efficiency of the biological pump in model inter-comparison studies in which CO2 drawdown is diagnosed.

Few studies have simultaneously diagnosed the individual contributions by the solubility and biological pumps and the effect of surface CO2 disequilibrium. Studies by , , and use a similar separation of the carbon storage processes as we do. For increases in wind stress, the sign of ΔTC (and thus of ΔpCO2atm) and the individual contributions by the carbon pumps and Cdis agree with those found by . In our ensemble, ΔTC does not fully reveal the magnitude of the differences in the individual carbon pumps between ensemble members because the changes to the individual pumps tend to be partially compensating for each other. We show that the differences in the equilibrium-state efficiency of the biological pump between SEs manifest themselves as differences in model sensitivity to the perturbation in biological pump efficiency, as predicted by . Our result can be important for future model inter-comparison studies and in explanations of results, but also in planning for common tuning strategies and experimental design. Compared to the scenario-specific results of , our results could be used more generally as a way of anticipating model behaviour based on the way in which the ocean circulation changes in a model study. Depending on the way in which we have changed the ocean forcing and what the resulting effect on ocean circulation is, the origin of the change in ocean carbon storage is different. When wind stress (WS) or ocean diapycnal diffusivity (DD) is changed, the response of the biological pump gives the most important effect on ocean carbon storage, whereas when atmospheric heat diffusivity (AD) or ocean isopycnal diffusivity (ID) is changed, the solubility pump and the disequilibrium component are also important and sometimes dominant. Our results give a first approximation of the effect of these ocean circulation changes on the ocean carbon storage, but it is important to keep in mind that the results of changes in individual parameters do not always combine linearly. For example, with doubled atmospheric heat diffusivity (AD×2) and doubled ocean diapycnal diffusivity (DD×2), the response of the solubility pump is very similar in both simulations. In the combined simulation (AD×2_DD×2), the response of the solubility pump is larger, but far from doubled, and the response of the soft-tissue pump is smaller than in DD×2 alone. In this particular case, it is difficult to discern which of these two parameters has the strongest impact on the system.

The four different preformed model tracers (Ppre, DICpre, O2pre, Apre) are shown to be useful for accurate determination of the initial-state carbon partitioning and nutrient utilisation efficiency, of which we demonstrate the importance for model drawdown potential. They eliminate errors associated with indirect methods used to determine AOU and Apre as described by e.g. and facilitate error estimates for the carbon partitioning methods. Some useful applications of preformed tracers have previously been presented by e.g. , and , but such extensive use of preformed tracers is, to our knowledge, unprecedented in studies of the ocean carbon system.

We have shown that when comparing model simulations with the same pCO2atm, but with differences in ocean circulation and overturning circulation strength (OVT; see Sect. ), the compared simulations will have different carbon inventories and different strengths of the ocean carbon pumps. In the PMIP3 inter-comparison project, in which glacial simulations with different models are compared, the models are forced with glacial pCO2atm to achieve the LGM state (https://pmip3.lsce.ipsl.fr/). The ocean circulation state is, however, not specified. showed that model simulations in the PMIP2 project developed very different LGM ocean circulation patterns and specifically large differences in AMOC strength, despite displaying similar ocean circulation patterns in pre-industrial simulations. Most models had been initiated with pre-industrial circulation and LGM boundary conditions according to the PMIP2 protocol. When run to quasi-equilibrium, some models would develop an LGM-like circulation, with a shallower boundary between NADW and AABW than today, as indicated by palaeo-nutrient tracers see e.g., and some would keep a more pre-industrial-like circulation. Since the ocean circulation patterns differ, the ocean carbon storage and thus the model carbon inventories of the compared PMIP simulations also differ. This will be important when comparing e.g. deglacial scenarios run with these different models e.g..

When attempting to simulate the glacial CO2 drawdown, it is crucial to critically evaluate the changes in forcing that need to be applied to achieve a glacial state in the model. Do these changes agree with what we believe actually happened in the climate system during a glacial? When applying PMIP3 boundary conditions for the LGM, the height of the ice sheet in the Northern Hemisphere will tend to intensify both the wind stress over the North Atlantic basin and as a result the AMOC . In a full glacial state, the associated deepening of the AMOC is, however, counteracted by the decrease in pCO2atm . Similar effects on the wind fields due to the Laurentide ice sheet are seen in e.g. . and suggest that Southern Hemisphere winds will also be stronger when applying LGM boundary conditions, though they emphasise that results from different palaeo-proxies and models disagree on this. In our simulation, we intensify the wind stress in both hemispheres and this leads to decreased capacity of both the biological and the solubility pump and effectively an increase in pCO2atm. showed similar results, but for increased Southern Ocean winds. Hence, the changes in wind fields achieved by the applied LGM boundary conditions in models may be contributing to the difficulties in simulating the glacial decrease in pCO2atm.

In our ensemble members for which ocean diapycnal (i.e. near vertical) diffusivity is halved, we achieve some glacial-like ocean characteristics: the circulation is weaker, the global ocean temperature is colder and the biological pump is stronger. However, it has been shown by that open ocean mixing is likely to have been intensified during glacials, when a lower sea level made shelf areas decrease and tidal mixing was shifted to the deep ocean. In their model, global ocean mean vertical diffusivity increased by more than a factor of 3, leading to an intensification of ocean overturning. In our experiments, a doubling of diapycnal diffusivity leads to a decrease in ocean carbon storage corresponding to an increase in pCO2atm of more than 20 ppm (see DD×2 in Fig. e). Hence, in a full glacial scenario, processes causing increased ocean carbon storage would have to offset this effect before causing any net decrease in pCO2atm. Other effects on glacial pCO2atm linked to lower sea level (reduced ocean volume) during glacials caused by higher salinity and a higher concentration of DIC, alkalinity and nutrients have been constrained to +12 to 16 ppm . In this process study we are not aiming to reproduce LGM conditions in the model and such effects of changes in ocean volume are beyond the scope of our investigations. Ocean volume and global averages of salinity, alkalinity and phosphate have thus been kept constant in our simulations.

Since numerous studies of proxy data indicate that the global ocean was in fact less ventilated during glacials e.g., it seems possible that the effect of increased mixing was indeed offset by some other process. One such factor could be that the global ocean was saltier and more stratified . In our simulations, weaker overturning circulation is also connected to colder temperatures. These cold simulations show a tendency towards lower drawdown potentials. It is likely that the more sluggish circulation is already allowing for a more efficient biological pump, leading to a higher P*‾ and thus a smaller drawdown potential. Another important mechanism for the global glacial deep ocean circulation is surface buoyancy loss around Antarctica driven by the brine rejection associated with sea ice formation . This effect is not explored in our simulations.

According to , the global average temperature of the glacial ocean was 2.6±0.6 ∘C colder than the modern day ocean. Since the ensemble member with the coldest ocean is only 1.3 ∘C colder than PIES278, the variations in Csat,T during the past glacial cycles were likely larger than in our set of experiments, allowing for a larger contribution by the solubility pump. Hence, the colder temperatures could play an important role in offsetting the effect of increased mixing. Figure 7 suggests that ΔCsat,T for a change in Tavg of -2.6 ∘C compared to pre-industrial would be approximately 1.5×1016 mol (180 GtC), whereas ΔCsat,T for the coldest of our simulations is only 0.58×1016 mol (70 GtC). If we account for a likely underestimation of ΔCsat,T of ∼50 % (see Sect.  and Appendix ) in Fig. , a simulation as cold as the LGM state suggested by would have an increase in strength of the solubility pump corresponding to ∼300 GtC.

In our ensemble of simulations, 100 % nutrient utilisation efficiency (NUE) causes more drawdown than is necessary to reach glacial values. Future efforts need to deduce how big an increase in NUE we could expect for a glacial when using proxy data for e.g. iron fertilisation e.g. and water mass properties e.g. as a constraint. By understanding how ocean circulation changes during the glacials may have contributed to altering the ocean NUE, it will be easier to quantify how much it may have increased due to e.g. fertilisation by the deposition of iron from dust. However, ongoing studies indicate that there may have been more, not less, preformed nutrients in the deep ocean during the last glacial and Arthur J. Spivack, personal communication, 2015, which implies less efficient nutrient utilisation by biology. One aspect that could explain how more carbon could still be trapped by biology in such a case is if the stoichiometric ratios in a glacial scenario no longer follow the averages described by . In most climate models, this is currently not taken into account. The implementation of variable stoichiometry in models could bring interesting insights in the future.