The devil ’ s in the disequilibrium : sensitivity of ocean carbon storage to climate state and iron fertilization in a general circulation model

Ocean dissolved inorganic carbon (DIC) storage can be conceptualized as the sum of four components: saturation (DICsat), disequilibrium (DICdis), carbonate (DICcarb) and soft tissue (DICsoft). Among these, DICdis and DICsoft have the potential for large changes that are relatively difficult to predict. Here we explore changes in DICsoft and DICdis in a large suite of simulations with a complex coupled climate-biogeochemical model, driven by changes in orbital forcing, ice sheets and the radiative effect of CO2. Both DICdis and DICsoft vary over a range of 40 μmol/kg in response to the climate forcing, 5 equivalent to changes in atmospheric CO2 on the order of 50 ppm for each. We find that, despite the broad range of climate states represented, changes in global DICsoft can be well-approximated by the product of deep ocean ideal age and the global export production flux, while global DICdis is dominantly controlled by the fraction of the ocean filled by Antarctic Bottom Water (AABW). Because the AABW fraction and ideal age are inversely correlated between the simulations, DICdis and DICsoft are also inversely correlated. This inverse correlation could be decoupled if changes in deep ocean mixing were to alter ideal 10 age independently of AABW fraction, or if independent ecosystem changes were to alter export and remineralization, thereby modifying DICsoft. As an example of the latter, iron fertilization causes DICsoft to increase, and causes DICdis to also increase by a similar or greater amount, to a degree that depends on climate state. We propose a simple framework to consider the global contribution of DICsoft + DICdis to ocean carbon storage as a function of the surface preformed nitrate and DICdis of dense water formation regions, the global volume fractions ventilated by these regions, and the global nitrate inventory. More 15 extensive sea ice increases DICdis, and when sea ice becomes very extensive it also causes significant O2 disequilibrium, which may have contributed to reconstructions of low O2 in the Southern Ocean during the glacial. Global DICdis reaches a minimum near modern CO2 because the AABW fraction reaches a minimum, which may have contributed to preventing further CO2 rise during interglacial periods. Copyright statement. Both authors accept the licence and copyright agreement. 20 1 Biogeosciences Discuss., https://doi.org/10.5194/bg-2017-328 Manuscript under review for journal Biogeosciences Discussion started: 19 September 2017 c © Author(s) 2017. CC BY 4.0 License.


Introduction
The controls on ocean carbon storage are not yet fully understood.Although potentially very important, given the large inventory of dissolved inorganic carbon (DIC) the ocean contains (38,000 Pg C vs. 700 Pg C in the pre-industrial atmosphere), the nuances of carbon chemistry, the dependence of air-sea exchange on wind stress and sea ice cover, the intricacies of ocean circulation and the activity of the marine ecosystem all contribute to making it a very complex problem.The scale of the challenge is such that, despite decades of work, the scientific community has not yet been able to satisfactorily quantify the role of the ocean in the natural variations of CO 2 between 180 and 280 ppm that occurred over ice age cycles.This failure reflects persistent uncertainty that also impacts our ability to accurately forecast future ocean carbon uptake.
In order to help with process understanding, DIC can be theoretically divided among four components that, together, determine the air-sea partitioning of the "active" carbon inventory: DIC sat , DIC dis , DIC soft and DIC carb (Ito and Follows, 2013;Bernardello et al., 2014).The first two components are defined in the surface ocean and are carried passively by ocean circulation in the interior, while the latter two are equal to zero in the surface layer and accumulate in the interior due to biogeochemical activity.
Saturation DIC (DIC sat ) is simply determined by the atmospheric CO 2 concentration and its solubility in seawater, which is a function of ocean temperature, salinity, and alkalinity.For example, cooling the ocean will increase CO 2 solubility, thereby leading to an increase in DIC sat .Given known changes in temperature, salinity, alkalinity, and atmospheric CO 2 , the effective storage of DIC sat can be calculated precisely.
The soft tissue pump (see e.g.Toggweiler et al., 2003) has been defined in various ways, but universally involves the uptake of DIC in the surface ocean by marine primary producers.The organic carbon that is formed then sinks or is subducted (as dissolved or suspended organic matter) and is transformed into remineralized DIC within the water column (a small fraction is buried at depth).Here we define DIC soft as that accumulated by the net respiration of organic matter below the top layer of the ocean (in our model, the uppermost 10 m).Thus, DIC soft depends both on the export flux of organic matter, affected by surface ocean conditions including iron supply (Martin, 1990), and on the flushing rate of the deep ocean, which clears out accumulated DIC soft (Toggweiler et al., 2003).The Southern Ocean (SO) is thought to be an important region for such changes on glacial/interglacial timescales, as the ecosystem there is currently iron-limited, and it also plays a major role in deep ocean ventilation (Martin, 1990;Toggweiler et al., 2003;Jaccard et al., 2016); furthermore, the degree of stratification may have changed significantly on these timescales (François et al., 1997;Sigman et al., 2010).Assuming a constant global oceanic phosphate inventory and constant C:P ratio, DIC soft would be stoichiometrically related to the preformed PO 4 (PO 4pre ) inventory of the ocean, where PO 4pre is the concentration of PO 4 in newly-subducted waters, and a passive tracer in the interior.
The potential to use PO 4pre as a metric of DIC soft prompted significant efforts to understand how it could change over time (Ito and Follows, 2005;Marinov et al., 2008a;Goodwin et al., 2008), though it has been pointed out that the large variation in C:P of organic matter weakens the relationship between DIC soft and PO 4pre (Galbraith and Martiny, 2015).Dissolved O 2 can potentially serve as a better metric of DIC soft , given the relatively small variations in the O 2 :C of respiration compared to the relatively high variability in C:P (Martiny et al., 2013).But Apparent Oxygen Utilization (AOU), typically taken as a measure of accumulated respiration, can be misleading if the preformed O 2 concentration differed significantly from saturation (Ito et al., 2004;Duteil et al., 2013).Thus, despite being conceptually simple, DIC soft can be difficult to quantify observationally.
Similar to DIC soft , DIC carb is defined here as the DIC generated by the dissolution of calcium carbonate shells below the ocean surface layer.Note that this does not include the impact that shell production has at the surface; calcification causes alkalinity to decrease in the surface ocean, raising surface pCO 2 and shifting carbon to the atmosphere.Rather, within the framework used here, this effect on alkalinity distribution falls under DIC sat , since it alters the solubility of DIC.Changes in DIC carb on the timescales of interest are generally thought to be small compared to those of DIC sat and DIC soft .
Typically, only these three components are considered as the conceptual drivers behind changes in the air-sea partitioning of pCO 2 (e.g., IPCC, 2007;Kohfeld and Ridgwell, 2009;Marinov et al., 2008a;Goodwin et al., 2008).However, a fourth component, disequilibrium carbon (DIC dis ), is also potentially significant as discussed by Ito and Follows (2013).Defined as the difference between preformed DIC and DIC sat , DIC dis can be relatively large (Takahashi et al., 2009) because of the slow timescale of atmosphere-surface ocean equilibrium of carbon compared to other gases, caused by the buffering capacity of seawater (e.g., Zeebe and Wolf-Gladrow, 2001;Broecker and Peng, 1974).
Like DIC sat , DIC dis is a conservative tracer determined in the surface ocean, with no sources or sinks in the ocean interior.
Since the majority of the ocean is filled by water originating from small regions of the Southern Ocean and the North Atlantic, the net whole-ocean disequilibrium carbon is approximately determined by the DIC dis in these areas weighted by the fraction of the ocean volume filled from each of these sites.Unlike the other three components, DIC dis could contribute either additional oceanic carbon storage (DIC dis > 0) or reduced oceanic carbon storage (DIC dis < 0).Studies using preformed nutrients as a metric for biological carbon storage have often ignored the potential importance of DIC dis by assuming fast air-sea gas exchange (e.g., Marinov et al., 2008a;Ito and Follows, 2005).In the pre-industrial ocean this is of little importance, given that global DIC dis is small because the opposing effects of North Atlantic and Antarctic water masses largely cancel each other.
However, Ito and Follows (2013) showed that DIC dis can have a large impact by amplifying changes in DIC soft under constant pre-industrial ocean circulation, and the possibility that DIC dis varied in response to changes in ocean circulation states has not been thoroughly explored.
Here, we use a fully-coupled general circulation model (GCM) to investigate the potential importance of DIC dis in altering air-sea CO 2 partitioning on long timescales.We make use of a large number of equilibrium simulations, conducted over a wide range of CO 2 , orbital and ice sheet boundary conditions, as a "library" of contrasting ocean circulations in order to test the response of disequilibrium carbon storage to physically plausible changes in ocean circulation.We supplement these with a smaller number of iron fertilization experiments to examine the additional impact of ecosystem changes.In order to simplify the interpretation, we chose to prescribe a constant CO 2 for the air-sea exchange in all simulations.Thus, the changes in DIC sat reflect only changes in temperature, salinity, alkalinity and ocean circulation, and not changes in pCO 2 .Nor do they explicitly consider changes in the total carbon or alkalinity inventories, although these may have changed significantly due to changes in outgassing and/or burial (Roth et al., 2014;Tschumi et al., 2011).As such, the experiments here should be seen as idealized climate-driven changes, and should be further tested with more comprehensive models including interactive CO 2 .Biogeosciences Discuss., https://doi.org/10.5194/bg-2017-328Manuscript under review for journal Biogeosciences Discussion started: 19 September 2017 c Author(s) 2017.CC BY 4.0 License.

Model description
The GCM used in this study is CM2Mc, the Geophysical Fluid Dynamics Laboratory's Climate Model version 2 but at lower resolution (3 o ), described in more detail by Galbraith et al. (2011).This includes the Modular Ocean Model version 5, a sea ice module, static land and ice sheets, and a module of Biogeochemistry with Light, Iron, Nutrients and Gases (BLINGv1.5)(Galbraith et al., 2010).Unlike BLINGv0, BLINGv1.5 allows for variable stoichiometry and calculates the mass balance of phytoplankton in order to prevent unrealistic bloom magnitudes at high latitudes, reducing the magnitude of disequilibrium O 2 , which was very high in BLINGv0 (Duteil et al., 2013;Tagliabue et al., 2016).

Experimental design
The basic setup of all model runs is identical to Galbraith and de Lavergne (submitted).A control run was conducted with atmospheric CO 2 set to 270 ppm and the Earth's obliquity and precession set to modern values (23.4 o and 102.9 o , respectively).
Experimental simulations were run at values of obliquity (22 o , 24.5 o ) and precession (90 o , 270 o ) representing the astronomical extremes encountered over the last 5 My (Laskar et al., 2004).Solar radiation was varied at CO 2 levels equivalent to 180, 220, 270, 405, 607, and 911 ppm.The biologeochemical component of the model calculates air-sea carbon fluxes using a fixed atmospheric CO 2 of 270 ppm throughout all model runs, irrespective of the CO 2 used for radiative forcing.
Eight additional runs were conducted using Last Glacial Maximum (LGM) ice sheets with CO 2 of 180 and 220 ppm and the same orbital parameters.Iron fertilization simulations use the glacial atmospheric dust field of Nickelsen and Oschlies (2015) instead of the standard pre-industrial dust field.Four iron fertilization experiments were run at an atmospheric CO 2 of 180 ppm with LGM ice sheets, as well as one model run similar to the control run.Finally, two simulations were run that were identical to the pre-industrial setup, but the rate of remineralization of sinking organic matter is set to 75% of the default rate, approximately equivalent to the expected change due to a 5 o C ocean cooling (Matsumoto et al., 2007); one of these runs also includes iron fertilization.All simulations are summarized in Table 1.
The simulations were run for 2100 -6000 model years beginning with a pre-industrial spinup.While the model years presented here largely reflect runs after having reached steady state, it is important to note that the pre-industrial run (41 in Table 1) still has a drift of 1 µmol/kg over the 100 y shown here and thus may not yet be at steady state.

DIC decomposition
Following Ito and Follows (2013) and Bernardello et al. (2014) term, defined as the degree of under-or oversaturation (DIC dis ).Note that in all simulations, DIC sat is calculated using a CO 2 concentration of 270 ppm, as this was prescribed identically for the biogeochemical component in all simulations, as discussed above.The use of a constant CO 2 concentration for biogeochemistry is not consistent with the CO 2 used for radiative forcing, which changes between simulations, but it provides a relatively simple framework for comparison of this large suite of simulations.
Within the mixed layer, plankton take up DIC to produce organic matter or calcium carbonate shells, both of which sink or are subducted and are remineralized in the water column to inorganic carbon (DIC soft and DIC carb , respectively).
DIC sat , DIC soft , and DIC carb can be calculated explicitly from the model tracers (for more details, see the appendix), and DIC dis is then calculated as a residual.

Climate experiments
Total DIC generally decreases from cold to warm simulations, under the constant CO 2 of 270 ppm used for air-sea exchange.
Changes in DIC sat drive the largest portion of this trend, decreasing approximately linearly with ln(CO 2 ) due to the temperaturedependence of CO 2 solubility, resulting in a difference of 50 µmol/kg over this range (see fig. 1).DIC carb is small in magnitude with a standard deviation of only 4 µmol/kg over the entire range of CO 2 values, and we do not discuss it further.
In contrast to DIC sat , DIC dis and DIC soft vary nonlinearly with global temperatures, with a clear and shared turning point at a radiative forcing near a CO 2 concentration of about 400 ppm.Both DIC dis and DIC soft are strongly correlated with ocean ventilation, quantified here by the global average of the ideal age tracer (r 2 = 0.69 and 0.89, respectively), and thus with each other (r 2 = 0.74).However, in contrast to the findings of Ito and Follows (2013), who found a positive correlation of DIC soft and DIC dis under nutrient depletion experiments with constant climate, DIC soft and DIC dis are negatively correlated under the range of climate states under constant iron supply explored here.

Iron fertilization experiments
The impact of increasing the dust flux to the ocean on DIC soft depends strongly on the ocean circulation state (see fig. 2).In the pre-industrial climate state (middle panel), half of the total oceanic C inventory change (14.6 µmol/kg) is due to increased soft tissue pump storage (∆DIC soft = 7.3 µmol/kg).This is qualitatively the same in the case that the remineralization rate of given the dependence of the saturation concentration on pCO 2 , so this estimate should not be interpreted as a straightforward atmospheric CO 2 change.Nonetheless, while this is only a first-order approximation and the model biases are potentially large, it seems very likely that the desquilibrium carbon storage was a significant portion of the net 90 ppm difference.
Below, we discuss the changes in DIC soft and DIC dis that result from the CO 2 , orbital and ice-sheet driven climate changes.
We then discuss related changes in disequilibrium O 2 , implications for preformed nutrient theory, and propose a new mechanism that may have helped to prevent the Earth from warming its way out of the ice age cycle.

Climate-driven changes in DIC soft
The biogeochemical model used here is relatively complex, with limitation by three nutrients (N, P and Fe), denitrification and N 2 fixation, in addition to the temperature-and light-dependence typical of biogeochemical models.The climate model is also complex, including a full atmospheric model, a highly-resolved dynamic ocean mixed layer, and many nonlinear subgridscale parameterizations, and uses short (< 3 h) timesteps.The simulations we show span a wide range of behaviours, including major changes in ocean ventilation pathways and patterns of organic matter export.It is difficult to assess the likelihood that the real ocean follows this relationship to a similar degree.One reason it might differ is if remineralization rates vary spatially, or with climate state.In the model here, as in most biogeochemical models, organic matter is respired according to a globally-uniform power law relationship vs. depth (Martin et al., 1987).Kwon et al. (2009) showed that ocean carbon storage is sensitive to changes in these remineralization rates, and this would provide an additional degree of freedom.It is not currently known how much remineralization rates can vary naturally; they may vary as a function of temperature (Matsumoto et al., 2007) or ecosystem structure.As a result, the relationship between DIC soft and ideal ocean age multiplied by global export may be stronger in the model than in the real ocean.
Nonetheless, the results suggest that, as a useful first-order approximation, the global change in DIC soft between two states can be given by a simple linear regression: ) or in CO 2 terms and assuming a buffer factor of 10: where m = 0.065, 0.042, 0.029 for modern, pre-industrial and glacial conditions respectively.This simple meta-model may provide a useful substitute for full ocean-ecosystem calculations, and could be further tested against other ocean-ecosystem coupled models.Note that, as for the disequilibrium estimate above, the soft tissue pump CO 2 drawdown would be partially compensated by a decrease in saturation carbon storage, so this should not be interpreted as a net atmospheric effect.In addition, we have not accounted for consequent changes in the surface ocean carbonate chemistry (including changes in the buffer factor).It would be useful to check this relationship with models including interactive CO 2 .
It is important to point out that the simulated change in DIC soft between interglacial and glacial states is in conflict with reconstructions.Proxy records appear to show that LGM dissolved oxygen concentrations were lower throughout the global ocean, with the exception of the North Pacific, implying greater DIC soft concentrations during the glacial then during the Holocene (Galbraith and Martiny, 2015).In contrast, the model suggests that greater ocean ventilation rates in the glacial state would have led to reduced global DIC soft .As discussed by Galbraith and de Lavergne (submitted), radiocarbon observations imply that the model ideal age is approximately 200 y too young under glacial conditions, compared to the LGM, suggesting a circulation bias that may reflect incorrect diapycnal mixing or non-steady-state conditions.Whatever the cause, if we take this 200 y bias into account, the regression implies an additional 33 µmol kg −1 DIC soft were stored in the glacial ocean.This would bring the simulated glacial DIC soft close to, but still less than, the simulated pre-industrial value.We propose that the apparent remaining shortfall in simulated glacial DIC soft could reflect one or more of the following non-exclusive possibilities: 1. the model does not capture changes in remineralization rates caused by ecosystem changes; 2. the model underestimates the glacial increase in the nitrate inventory, perhaps due to changes in the iron cycle; 3. the ocean was not in steady state during the LGM, and therefore not directly comparable to the "glacial" simulation; 4. the inference of DIC soft from proxy oxygen records is incorrect due to significant changes in preformed oxygen disequilibrium (see below The ocean basins below 1 km depth are largely filled by surface waters subducted to depth in regions of deepwater formation (Gebbie and Huybers, 2011).In our simulations, water originating in the surface North Atlantic, termed NADW, and the Southern Ocean, termed AABW, make up 80-96% of this total deep ocean volume.Thus, to first order, the deep average DIC dis concentration can be approximated by a simple mass balance: Here, f AABW and f NADW represent the fraction of deepwater originating in the SO and North Atlantic and DIC disAABW,NADW the DIC dis concentration at the sites of deepwater formation (see fig. 4).North Atlantic deep waters form with negative DIC dis , reflecting surface undersaturation, while the Southern Ocean is supersaturated (DIC dis > 0), and these opposing tendencies between NADW and AABW cause a partial cancellation of DIC dis when globally averaged.Although the exact values of DIC dis in the two polar oceans vary over time in response to climate (the reasons for which are discussed in more detail below), these changes are small relative to the consistent large contrast between AABW and NADW, so that deep DIC dis is strongly controlled by the global balance of AABW vs. NADW in each simulation (see fig. 5).Global DIC dis becomes much larger when f AABW is larger, similar to the dynamic evoked by Skinner (2009).
In this model, both the cold and the hot climate states show increased AABW production, with a minimum at intermediate values.The AABW/NADW fractions are determined by the relative density of surface waters in the two polar ocean basins, as discussed in more detail by Galbraith and de Lavergne (submitted).The minimum in AABW is thus responsible for the minimum in global ocean DIC dis (fig.1).In addition, expanded terrestrial ice sheets shift the ratio of AABW to NADW to higher values, due to their impact on NADW temperature and downstream expansion of Southern Ocean sea ice (Galbraith and de Lavergne), further increasing DIC dis in glacial-like conditions.

Climate-driven changes in DIC dis : end members
Due to the general dominance of AABW in the deep ocean, the concentration of DIC dis in the regions of AABW formation, DIC disAABW , is another important factor determining global DIC dis .This varies less significantly than f AABW over the range of simulations, in part due to competing effects of different processes.Surface ocean DIC dis in the Southern Ocean grows in response to upwelling of deepwater, which brings DIC-charged waters to the surface, thus contributing to the carbon supersaturation.Thus, when deep convection is occurring, the rapid injection of carbon to the surface tends to inflate DIC dis .Like the f AABW , ventilation rates (as quantified by global ideal age) are high at both the cold and hot extremes (Galbraith and de Lavergne, submitted), also contributing to the intervening minimum in DIC dis in the AABW formation regions.
Sea ice in the Southern Ocean exerts a further control over DIC dis , as this reduces air-sea gas exchange, thus allowing carbon to accumulate beneath the ice.The total sea ice cover decreases continuously from the low to high CO 2 simulations (fig.6), but DIC dis is markedly higher in the glacial-like scenarios compared to CO 2 = 270 or 911 ppm (fig.7 and 8).In the glacial state, high DIC dis is a widespread characteristic of the sea surface, whereas in the 270 and 911 ppm simulations, high DIC dis

Disequilibrium O 2
O 2dis is also sensitive to sea ice cover, but with a pronounced difference from DIC dis .Because O 2 has a much shorter time scale of exchange at the ocean-atmosphere interface, equilibrating one order of magnitude faster than CO 2 , it is not sensitive to sea ice as long as there remains a fair degree of open water (Stephens and Keeling, 2000).But as the sea ice concentration approaches complete coverage, O 2 equilibration rapidly becomes quite sensitive to sea ice.If there is a significant undersaturation of O 2 in upwelling waters, the disequilibrium can become quite large (fig.9).
In the model simulations, the magnitude of O 2dis in the Southern Ocean is as high as 100 µmol/kg.Because the disequilibrium depends on the O 2 depletion of waters upwelling at the Southern Ocean surface, it could potentially be even higher, if upwelling waters had lower O 2 .This suggests the hypothesis that very extensive sea ice cover over most of the exposure pathway in the Southern Ocean might have made a significant contribution to the low O 2 concentrations reconstructed for the glacial (Jaccard et al., 2016;Lu et al., 2015).

Iron fertilization-driven changes in DIC soft and DIC dis
As expected, both the global export and DIC soft increase when dust deposition is increased.However, the DIC soft increase is significantly lower in the well-ventilated glacial-like simulations (2.9 µmol/kg) compared to the interglacial-like simulation (7.3 µmol/kg).This difference is qualitatively in accordance with the age multiplied by export relationship (fig.3), though with a smaller increase of DIC soft than would be expected from the export increase, compared to the broad spectrum of climatedriven changes.This reduced sensitivity to export can be attributed to the fact that the iron-enhanced export occurs in the Southern Ocean, where the remineralized carbon can be quickly returned to the surface by upwelling when ventilation is strong.Thus, the impact of iron fertilization on DIC soft is strongly dependent on Southern Ocean circulation.
The iron addition also causes an increase of DIC dis , of approximately equal magnitude to DIC soft in the interglacial-like simulation, and of relatively greater proportion in the glacial-like simulations.Because the ocean in the glacial-like simulations is strongly ventilated, with extensive sea ice cover in the Southern Ocean, the increase in export leads to an increase of DIC dis , as remineralized DIC soft is rapidly returned to the Southern Ocean surface, where it has a relatively short residence time and the extensive sea ice inhibits outgassing to the atmosphere.Thus, with rapid Southern Ocean circulation and extensive sea ice cover, a good deal of the DIC sequestered by iron fertilization ends up in the form of DIC dis , rather than DIC soft as frequently assumed.Furthermore, experiments in which the remineralization rate was reduced by 25% indicate that the effects of iron fertilization alone on both DIC soft and DIC dis are quite insensitive to the remineralization rate (see fig. 2) Thus, the effects of iron fertilization and changes in the remineralization rate can be well-approximated as being linearly additive.The tendency to sequester carbon as DIC dis vs. DIC soft can be quantified by the global ratio ∆DIC dis /∆DIC soft .Our experiments suggest that this ratio is 0.9 for the pre-industrial state and 3.3 for the glacial-like state.Because of the circulation dependence of this ratio, it is expected that there could be significant variation between models.It is worth noting that Parekh et al. (2006) found ∆DIC dis /∆DIC soft of 2 in response to iron fertilization, using a modern ocean circulation, as analyzed by Ito and Follows (2013).We also caution that the quantitative values of DIC soft and DIC dis resulting from the altered iron flux should be taken with a grain of salt, given the very large uncertainty in models of iron cycling (Tagliabue et al., 2016).

A unified framework for DIC dis and preformed nutrients
The concept of preformed nutrients allowed the production of a very useful body of work, striving for simple predictive principles.This work highlighted the importance of the nutrient concentrations in polar oceans where deep waters form (Sigman and Boyle, 2000;Ito and Follows, 2005;Marinov et al., 2008a) as well as changes in the ventilation fractions of AABW and NADW, given their very different preformed nutrient concentrations (Schmittner and Galbraith, 2008;Marinov et al., 2008b).
Although the variability of P:C ratios implies significant uncertainty for the utility of PO 4pre in the ocean, the relative constancy of N:C ratios suggests that NO 3pre is indeed linked to DIC soft , inasmuch as the global N inventory is fixed (Galbraith and Martiny, 2015).
However, as shown by the analyses here, DIC soft -reflected by the preformed nutrients -is only half the story.Changes in DIC dis can be of equivalent magnitude, and can vary independently of DIC soft as a result of changes in ocean circulation and sea ice.Nonetheless, we find that the same conceptual approach developed for DIC soft can be used to predict DIC dis from the end member DIC dis and the global volume fractions.The preformed relationships and DIC dis can therefore be unified as follows (see fig. 10): Remineralized nitrate can be expressed in terms of the global nitrate inventory and the accumulated nitrate loss due to pelagic and benthic denitrification, analagous to AOU: Above, for simplicity, we consider only the deep ocean DIC dis .Now, however, we would like to include the upper ocean (above 1 km) as well.Because there is production of intermediate water but no deep convection in the North Pacific, we calculate this mass balance for the upper ocean (above 1 km) and deep ocean separately, dropping the final term in Eq. 10 in the calculation below 1 km: Finally, the global average is computed by summing the volume-weighted values in the upper and deep ocean: Fully expanded, this yields: which can be generalized for any number n of ventilation regions i as: Thus, total carbon storage as soft and disequilibrium carbon (i.e.everything other than DIC sat and DIC carb ) varies with the global nitrate inventory, corrected for NO 3 loss to denitrification, and the difference between DIC dis and r C:N • NO 3pre in the polar oceans, modulated by their respective volume fractions.It is interesting that this relationship is more accurate than either DIC dis or DIC soft , among our suite of simulations, with an RMSE of 3.6, 7.0 and 5.2 µmol kg −1 for DIC dis + DIC soft , DIC dis and DIC soft , respectively.

DIC dis nadir and peak CO 2
The model simulations show a clear minimum of DIC dis at intermediate CO 2 (270 -405 ppm).As we have shown, this occurs as a result of the minimum contribution of AABW to the global ocean, and to a lesser extent, a minimum in the DIC dis of AABW.It is important to note that DIC dis is not just a function of ocean circulation, soft tissue pump and sea ice, which are simulated here, but also the CO 2 driving gas exchange due to its impacts on saturation CO * 2 and DIC sat , which here is held fixed at 270 ppm.Because DIC dis is calculated as the departure from equilibrium with atmospheric CO 2 at 270 ppm, we expect that the resulting changes in DIC dis under interactive CO 2 will differ only due to minor, non-linear effects.So, although this simplification (in combination with other model biases) prevents a strict interpretation of the CO 2 and orbital combination at which this nadir is likely to occur, its robust emergence from the relative density control on deep water ventilation volumes makes its existence appear reasonable (Galbraith and de Lavergne, submitted).A minimum global extent of AABW during interglacials has been documented from Nd (Piotrowski et al., 2005), and it has been shown that AABW likely ceased to form entirely for a brief portion of the last interglacial, marine isotope stage 5e (Hayes et al., 2014).We suggest that the minimum AABW extent produced a nadir of DIC dis that may have contributed to a "soft" upper limit on CO 2 during interglacials.Galbraith and Eggleston (2017) showed that the lower limit of CO 2 over glacial cycles is quite firm and that low CO 2 is very common.In addition, they showed that, although the peak values of CO 2 during interglacials vary significantly, interglacial CO 2 levels are relatively common, suggesting that they are also a preferred state.
We propose that the DIC dis nadir would have contributed to preventing a significant CO 2 rise above interglacial CO 2 , since a rise of temperatures above that which gives the DIC dis nadir will increase AABW formation and thereby draw down CO 2 as DIC dis .Of course this would be counteracted by an increase of DIC soft , if it were to behave opposite of DIC dis , as occurs in our simulations -whether or not this is true depends on unresolved climate dependencies in the marine ecosystem, which currently remains an open question.We do not claim that this soft upper limit was significant, but simply propose the possibility as a hypothesis that can be tested.

Conclusions
Carbon storage in the ocean can be quantified as the sum of the saturation, soft tissue, carbonate, and disequilibrium components.Our simulations indicate that the latter may play a very important role, which has been largely neglected in other studies.
Changes in the climate state tend to drive the soft tissue pump and the disequilibrium pump in opposite directions.However, this is not necessarily true in the real ocean, given that the simulated anticorrelation is not mechanistically required, but instead arises from the fact that f AABW and ideal age • export are anticorrelated in the simulations.There is plenty of scope for these to have varied in additional ways, not captured by our idealized simulations.
Iron fertilization experiments are a popular method of testing the sensitivity of pCO 2 to an increase in dust flux to the Southern Ocean; here, these simulations illustrate the non-linearity of the effects of circulation and increased primary productivity on DIC.At moderate ventilation rates (the pre-industrial control run), an increase in iron results in an increase both in DIC soft , due to higher biological export, and DIC dis , because of the upwelling of C-rich water resulting from higher remineralization.
However, under a "glacial" state, high ventilation in this model produces only a small increase in DIC soft in response to increased Fe in the surface ocean, as the remineralized carbon is quickly returned to the surface, thus producing a significant increase in DIC dis only.This also raises an important warning for iron fertilization studies: the CO 2 impact of Southern Ocean iron addition can actually be dominated by the DIC dis , so that the overall impact may be significantly larger than would be predicted from DIC soft and/or O 2 utilization.
The results presented here suggest that disequilibrium carbon should be considered as a major component of ocean carbon storage, linked to ocean circulation, sea ice and biological export in non-linear and interdepenent ways.Despite these nonlinearities, we suggest that the resulting global carbon storage can be well-approximated by a simple relationship including the global nitrate inventory, and the DIC dis and preformed CO 3 in ocean ventilation regions (eq. 15).The glacial simulations suggest that disequilibrium carbon may have been the dominant component of oceanic carbon uptake during cold phases of organic carbon is reduced by 25% (left panel).However, in the high-ventilation runs under glacial-like conditions (right panel), Biogeosciences Discuss., https://doi.org/10.5194/bg-2017-328Manuscript under review for journal Biogeosciences Discussion started: 19 September 2017 c Author(s) 2017.CC BY 4.0 License. the change in total DIC is somewhat reduced (11.1 µmol/kg) and ∆DIC soft is small (SO average 4.3 µmol/kg; global average 2.9 µmol/kg).DIC dis is also dependent on the ocean circulation, but in the opposite direction: the change is more significant (9.4 µmol/kg global average) in the glacial-like simulations compared to the pre-industrial simulation (6.4 µmol/kg).Each of these values rises when considering only the SO (13.4 and 9.0 µmol/kg, respectively).In both the pre-industrial and glaciallike simulations, changes in DIC dis constitute an important part of the total change.DIC carb is reduced to a small extent by iron fertilization, due to the reduced nutrient content of AAIW/SAMW and consequent decrease in low latitude carbonate production, which raises low latitude surface ocean alkalinity, causing an increase in DIC sat .4DiscussionSimulated changes in DIC dis are of the same magnitude as the DIC soft changes, to which much greater attention has been paid.For a global average buffer factor between 8 and 14(Zeebe and Wolf-Gladrow, 2001), a rough, back-of-the-envelope calculation shows that a 1 µmol/kg change in DIC corresponds to a 0.9 -1.6 ppm change in atmospheric pCO 2 based on a DIC concentration of 2300 µmol/kg and CO 2 of 270 ppm.Thus, the increase in the global average DIC dis in these simulations of 16 µmol/kg (pre-industrial control) to 62 µmol/kg (LGM-like conditions with Fe fertilization) could have contributed the equivalent of a 40 -70 ppm change in the atmospheric CO 2 stored in the ocean during the glacial compared to today.It is important to recognize that the drawdown of CO 2 by disequilibrium storage would have resulted in a decrease of DIC sat , Biogeosciences Discuss., https://doi.org/10.5194/bg-2017-328Manuscript under review for journal Biogeosciences Discussion started: 19 September 2017 c Author(s) 2017.CC BY 4.0 License.only occurs in regions of AABW formation during episodes of deep convection.Terrestrial ice sheets cause an increase in the magnitude of DIC dis both in the Southern Ocean and the North Atlantic.Due to the opposing signs in the two regions, these effects partially compensate each other, but the volumetric dominance of AABW causes its DIC dis increase to win out, raising global DIC dis .
Biogeosciences Discuss., https://doi.org/10.5194/bg-2017-328Manuscript under review for journal Biogeosciences Discussion started: 19 September 2017 c Author(s) 2017.CC BY 4.0 License. the ice age cycles.As this study represents the result of a single model, prone to bias, it would be very useful to test our results using other GCMs.It would also be useful to consider how disequilibrium carbon can change under future pCO 2 levels, including developing observational constraints on its past and present magnitude, and exploring the degree to which inter-model variations in DIC dis may contribute to uncertainty in climate projections.Biogeosciences Discuss., https://doi.org/10.5194/bg-2017-328Manuscript under review for journal Biogeosciences Discussion started: 19 September 2017 c Author(s) 2017.CC BY 4.0 License.

Figure 1 .
Figure 1.Global average DIC and separate components in simulations 1-36 as a function of CO2.Orange and blue represent high and low obliquity scenarios, respectively; triangles pointing upward and downward represent greater northern and southern hemisphere seasonality, respectively; outlines are scenarios with LGM ice sheets; light shading indicates scenarios with LGM ice sheet topography but PI albedo.

Figure 2 .
Figure 2. Changes in total global average DIC and each of the components (iron fertilization simulation minus associated control run).Simulations were either run under pre-industrial or glacial-like conditions (in the case of the latter, results represent the average of four runs at CO2 = 180 ppm with LGM ice sheets), as well as 100% and 75% of the default remineralization rate of organic matter.The close agreement of the left and middle panels indicates that the effects of iron fertilization and changes in the remineralization rate are linearly additive in this model.

Figure 3 .
Figure 3. Globally averaged DICsoft, or remineralized carbon from the soft tissue pump, can be approximated remarkably well by the global export flux at 100 m multiplied by the average age of the ocean.The latter is an ideal age tracer in the model that is set to 0 at the surface and ages by 1 y each model year in the ocean interior.Markers as in fig. 1 with the size of the symbols corresponding to the CO2 level.

Figure 4 .
Figure 4. (a) Global average fraction of northern-(reddish colors) and southern-sourced (bluish colors) water.(b) Average values of DICdis of these water masses determined at 100 m depth in the model where convection down to 200 m occurs.Markers are identical to fig. 1 with lighter colors representing high and darker colors low obliquity.

Figure 5 .
Figure 5. Global average DICdis as a function of the fraction of the ocean below 500 m derived from the surface Southern Ocean; symbols as in fig. 1 with the size of the symbols corresponding to the CO2 level.
Thus, it is perhaps surprising that the net global result of the biological pump, as quantified by DIC soft , has highly predictable behavior.As shown in fig.3, the global DIC soft varies closely with the product of the global sinking flux of organic matter at 100 m and the ideal age of the global ocean.Qualitatively this is not a surprise, given that greater export pumps more organic matter to depth, and a large age provides more time for respired carbon to accumulate within the ocean.But the quantitative strength of the relationship is striking.Biogeosciences Discuss., https://doi.org/10.5194/bg-2017-328Manuscript under review for journal Biogeosciences Discussion started: 19 September 2017 c Author(s) 2017.CC BY 4.0 License.

Table 1 .
A total of 44 simulations were analyzed with varying CO2, obliquity, precession, ice sheets (PI = pre-industrial; LGM = Last Glacial Maximum reconstruction; LGM* = topography of LGM ice sheets but with PI albedo), and with and without iron fertilization.Runs 43 and 44 and identical to 41 and 42 but the remineralization rate of sinking organic matter is reduced by 25%.