Glacial – interglacial atmospheric CO 2 change : a possible “ standing volume ” e ff ect on deep-ocean carbon sequestration

Introduction Conclusions References Tables Figures


Explaining glacial-interglacial CO 2 change
Although it is clear that changes in atmospheric CO 2 have remained tightly coupled with global climate change throughout the past ∼730 000 years at least (Siegenthaler et al., 2005), the mechanisms responsible for pacing and moderating CO 2 change remain to be proven.The magnitude of the marine carbon reservoir, and its inevitable response to changes in atmospheric CO 2 (Broecker, 1982a), guarantees a significant role for the ocean in glacial-interglacial CO 2 change.Based on thermodynamic considerations, glacial atmospheric CO 2 would be reduced by ∼30 ppm simply due to the increased solubility of CO 2 in a colder glacial ocean (Sigman and Boyle, 2000); however this reduction would be counteracted by the reduced solubility of CO 2 in a more saline glacial ocean and by a large reduction in the terrestrial biosphere under glacial conditions (Broecker and Peng, 1989;Sigman and Boyle, 2000).The bulk of the glacial-interglacial CO 2 change therefore remains to be explained by more complex inter-reservoir exchange mechanisms, and the most viable proposals involve either the biological-or the physical "carbon pumps" of the ocean.On this basis, any mechanism that is invoked to explain glacialinterglacial CO 2 change must involve changes in the sequestration of CO 2 in the deepest marine reservoir (Broecker, 1982a;Boyle, 1988aBoyle, , 1992;;Broecker and Peng, 1989).
To date, three main types of conceptual model have been L. C. Skinner: Standing volume effects on CO 2 2001; Watson and Naveira Garabato, 2006); and (3) those involving changes in whole ocean chemistry and "carbonate compensation", possibly promoted by changes in the ratio of organic carbon and carbonate fluxes to the deep sea.(Archer and Maier-Reimer, 1994).Each of these conceptual models has its own set of difficulties in explaining the pattern and magnitude of past glacial-interglacial CO 2 change, and in fact none is likely to have operated in complete isolation (Archer et al., 2000;Sigman and Boyle, 2000).Nevertheless, one aspect of all of the proposed models that emerges as being fundamental to any mechanism proposing to explain glacial-interglacial CO 2 change is the balance between biological carbon export from the surface-ocean and the return of carbon to the surface by the ocean's overturning circulation.These two processes, one biological and one physical, essentially determine the balance of carbon input to and output from (and therefore the carbon content of) the deepest marine reservoirs (Toggweiler et al., 2003).
The regions of deep-water formation in the North Atlantic and especially in the Southern Ocean play a key role in setting the "physical side" of this balance.In the North Atlantic, carbon uptake via the "solubility pump" is enhanced by the large temperature change that surface water must undergo before being exported into the ocean interior.The formation of North Atlantic deep-water therefore represents an efficient mechanism for mixing CO 2 deep into the ocean interior (Sabine et al., 2004); though only to the extent that it is not completely compensated for (or indeed over-compensated for) by the eventual return flow of more carbon-enriched deep-water back to the surface (Toggweiler et al., 2003).Arguably, it is in controlling the extent to which the return flow of deep-water to the surface (which occurs primarily in the Southern Ocean) represents an effective 'reflux' of carbon to the atmosphere, acting against biological export, that the formation of deep-water in the Southern Ocean plays a pivotal role in controlling the partitioning of CO 2 between the surface-and the deep ocean.We might say that if the southern overturning loop "leaks" too much, it will be an efficient carbon source to the atmosphere (Toggweiler et al., 2003); and if it does not leak much, it will simply become a large standing carbon reservoir.The degree to which the southern overturning loop "leaks" depends on the efficiency of equilibration of up-welled Southern Ocean deep-water with the atmosphere, relative to the efficiency of carbon export (dissolved and particulate) from the surface Southern Ocean (Toggweiler, 1999;Gildor and Tziperman, 2001).
Today, a significant portion of the deep ocean (although not the deep Atlantic -"deep" meaning greater than ∼1 km in this context) is filled from the Southern Ocean by Lower Circumpolar Deep Water (LCDW) that is exported northwards into the various ocean basins from the eastward circulating Antarctic Circumpolar Current (ACC) (Orsi et al., 1999;Sloyan and Rintoul, 2001).This deep-water remains relatively poorly equilibrated with the atmosphere and is inefficiently stripped of its nutrients, thus maintaining an ele-vated "pre-formed" nutrient and dissolved inorganic carbon content.In part this is because of the very low temperature at which deep-water forms around Antarctica and because the rate of ocean -atmosphere CO 2 exchange cannot keep up with the rate of overturning in the uppermost Southern Ocean (Bard, 1988).However it is primarily because the bulk of southern sourced deep-and bottom-water is either produced via a combination of brine rejection below sea-ice and entrainment from the sub-surface, or converted from "aged" northern-sourced deep-waters that feed into the Southern Ocean via Upper Circumpolar Deep Water (UCDW) (Orsi et al., 1999;Speer et al., 2000;Webb and Suginohara, 2001;Sloyan and Rintoul, 2001).Intense turbulent mixing around topographic features in the deep Southern Ocean helps to enhance the amount of "carbon rich" subsurface water that is incorporated into LCDW (from UCDW above and from Antarctic Bottom Water, AABW, below), and that is subsequently exported northwards to the Atlantic and Indo-Pacific (Orsi et al., 1999;Naviera Garabato et al., 2004).The process of Lower Circumpolar Deep Water export in the deep Southern Ocean (as distinct from deep-water formation in the North Atlantic, and the vertical mixing in the uppermost Southern Ocean) can therefore be viewed as a mechanism that helps to "recycle" carbon-rich water within the ocean interior, circumventing ocean -atmosphere exchange, and eventual CO 2 leakage to the atmosphere.
It is notable that nearly all of the "physical pump" mechanisms that have been proposed as significant controls on glacial-interglacial CO 2 change have referred to dynamical (export-or mixing rate) or kinetic (ocean -atmosphere exchange rate) effects (e.g.Kohler et al., 2005;Toggweiler, 1999;Tziperman and Gildor, 2003;Brovkin et al., 2007;Peacock et al., 2006;Sigman and Haug, 2003).Consideration of the effect on atmospheric CO 2 of changes in the geometry, and therefore the volumes, of different intra-oceanic carbon reservoirs (i.e.different deep-water "masses") has largely escaped explicit treatment.This is surprising, given that the residence time of a reservoir will scale inversely to its renewal rate or positively to its volume.It is also surprising from an "experimental" perspective, given that most of the palaeoceanographic evidence available to us can tell us something about changes in water-mass distribution (hence volume), but usually cannot tell us much about changes in circulation or mixing rates.Furthermore, if we consider what controls the energy and buoyancy budgets of the ocean (and hence the capacity to maintain an overturning circulation), it is not obvious that the net overturning rate of the ocean must have been significantly different from modern over long time periods in the past (Gordon, 1996;Wunsch, 2003) even if it is true that the reconstructed hydrography of the glacial ocean is inconsistent with the modern circulation (especially in terms of vertical property distributions) (Marchal and Curry, 2008).The circulation rate (mass transport) of the glacial ocean therefore remains poorly constrained, despite well-defined property distribution (hence inventory) changes.
The purpose of the present study is to focus attention on the importance of distinguishing between past changes in the distribution of water-masses (which we can know something about) and past changes in their renewal rates (which we tend to know very little about), in particular when considering the role of the ocean circulation in setting the marine carbon inventory.By way of illustration, the simple hypothesis is advanced that the amount of carbon that can be "bottled up" in the deep ocean may be significantly affected by changes in the volumes of different glacial deep-water masses, prior to any imposed changes in overturning-, gas exchange-or biological export rates (but including the effects of any redistribution of temperature, salinity, and pre-formed/remineralised nutrients that is incurred).Of course, the suggestion is not that changes in circulation-or export rates are unimportant; but rather that they are not exclusively important.The distinction between these two aspects of the ocean circulation (i.e.water-mass distribution versus overturning rate), and the evaluation of their individual impacts on atmospheric CO 2 , could prove to be important in assessing the mechanisms of glacial-interglacial CO 2 change, in particular if it is possible for these two aspects of the ocean circulation to become decoupled, for example on long time-scales or for specific forcing.Put another way: if the mechanisms or time-scales required to alter the marine carbon inventory via changes in overturning rates and water-mass volumes differ, then they cannot be usefully conflated in the single term "ocean circulation" when considering the causes of glacial-interglacial CO 2 change.
In this paper additional emphasis is placed on how the hypsometry of the ocean basins (the area distribution at different water depths) may affect the efficiency of volumetric watermass changes that are caused by the shoaling/deepening of water-mass mixing boundaries.A notable fact in this regard is that ∼56% of the sea-floor lies between 6000 and 3000 m (Menard and Smith, 1966), thus accounting for a majority increment in the ocean's volume.If a water mass that once occupied the >5 km interval in the Atlantic comes to occupy the >2 km interval, it will have increased its volume in this basin almost four-fold.

A thought experiment: a "southern flavour ocean"
Arguably, one of the least ambiguous aspects of the palaeoclimate archive is the record of glacial-interglacial change in δ 13 C recorded by benthic foraminifera from the Atlantic Ocean (Curry and Oppo, 2005;Duplessy et al., 1988).The data suggest, at the Last Glacial Maximum, a more positive δ 13 C of DIC in the upper ∼2 km of the Atlantic, and a more negative δ 13 C of dissolved inorganic carbon (DIC) below this in the deepest Atlantic.These data do not appear to be consistent with the modern water-mass geometry/circulation (Marchal and Curry, 2008).The most widespread and wellsupported interpretation of these data is that they represent a redistribution of glacial northern-and southern-sourced deep and intermediate water-masses, including in particular an incursion of glacial southern-sourced deep water (rich in preformed and remineralised nutrients, and of low δ 13 C) into the deep North Atlantic, up to a water depth of ∼2-3 km (Curry et al., 1988;Duplessy et al., 1988;Oppo and Fairbanks, 1990;Oppo et al., 1990;Boyle, 1992;Curry and Oppo, 2005;Hodell et al., 2003).This interpretation is now strongly supported by glacial Atlantic benthic foraminiferal Cd/Ca, Zn/Ca and B/Ca ratios (Marchitto and Broecker, 2005;Boyle, 1992;Keigwin and Lehmann, 1994;Marchitto et al., 2002;Yu and Elderfield, 2007).Auxiliary support has been provided by benthic radiocarbon measurements from the North Atlantic (Robinson et al., 2005;Skinner and Shackleton, 2004;Keigwin, 2004), and neodymium isotope measurements (ε N d ) from the South Atlantic (Rutberg et al., 2000;Piotrowski et al., 2005Piotrowski et al., , 2004).An elegant box-model investigation of the possible causes of glacial deep-ocean chemistry (Michel et al., 1995) and coupled atmosphere-ocean general circulation model (AOGCM) simulations of the "last glacial maximum" circulation (e.g.Shin et al., 2003;Kim et al., 2003) have also added weight to this interpretation of glacial deep-water mass geometry.If we assume that the relationships between deep-water radiocarbon activity, carbonate ion concentration, δ 13 C of DIC and TCO 2 remained similar between glacial and interglacial (preindustrial) times, at least for deep-water exported northwards from the Southern Ocean, then we may also infer that the water that apparently replaced NADW in the Atlantic and dominated LCDW export to the Indo-Pacific basins was also of relatively high TCO 2 .Indeed, radiocarbon evidence (Marchitto et al., 2007), dissolution indices (Barker et al., 2009), benthic δ 13 C (Ninneman and Charles, 2002;Hodell et al., 2003) and pore-water temperature/salinity estimates (Adkins et al., 2002) all tend to suggest that deep-water exported from the Southern Ocean during the last glacial would have represented a concentrated and isolated carbon reservoir that was very poorly equilibrated with the atmosphere.
Given these constraints on the deep-water hydrography near the height of the last glaciation (Lynch-Steiglitz et al., 2007), one question immediately arises: how much must the volume of southern-sourced deep-water (LCDW) have increased, regardless of its export rate, in order to accomplish the observed change (i.e.filling the deep Atlantic, and dominating the deep-water export to the Indian and Pacific basins)?Further, and more importantly, what would have been the immediate effect on deep-water CO 2 sequestration, if any, of the resulting redistribution of dissolved inorganic carbon, nutrients and temperature/salinity? Answering the first question is straightforward enough: as noted above, based on the hypsometry of the Atlantic basin (Menard and Smith, 1966), raising the upper boundary of southernsourced deep-water (assumed for the sake of argument to be approximately flat) from 5 km to 2.5 km in the Atlantic requires this water-mass to increase its Atlantic volume from under 20 million km 3 to nearly 70 million km 3 (just under a 4-fold increase).In order to determine the eventual impact of this volumetric change on the carbon-storage capacity of the ocean we would obviously require knowledge of the changing chemistry of the various deep-water masses in the ocean as well as their turnover and "ventilation" (atmosphere equilibration) rates, and the flux of dissolved carbon that they eventually incorporate via biological export.However, if we assume simplistically that nothing in the ocean changes except the volume occupied by southern-sourced deep-water (i.e. the chemistry of all water-masses stays the same, but not their volumetric contribution to the ocean's total budget), then we can infer that for a 4-fold increase in the volume of AABW at the expense of NADW (having average total dissolved CO 2 concentrations of ∼2280 µmol kg −1 and ∼2180 µmol kg −1 , respectively, Broecker and Peng, 1989) the ocean would need to gain ∼63 Gt of carbon.If we assume that all this carbon must come from the atmosphere, then atmospheric pCO 2 would have to drop by ∼30 ppm, given 1 ppm change per 2.12 Gt carbon removed from the atmosphere (Denman et al., 2007).This is equivalent to ∼38% of the total observed glacial-interglacial CO 2 change (Siegenthaler et al., 2005), and is comparable to the magnitude of atmospheric CO 2 changes that are likely to have arisen from other viable mechanisms such as biological export increase, or carbonate compensation (Peacock et al., 2006).
Clearly many of the assumptions made in the above thought experiment might not be valid: the chemistry and dynamics, not to mention the character and rate of biological export, of the glacial ocean will probably not have remained constant.Nevertheless, palaeoceanographic proxy evidence holds that the basic premise of the thought experiment is valid: the volume of deep water closely resembling modern southern-sourced deep-water apparently increased significantly during the last glaciation.It seems warranted therefore to evaluate the impacts of this premise in a slightly more sophisticated way.The question to be answered is: does a deep ocean dominated by a LCDW-like water-mass hold more carbon at steady state (on time-scales longer than the mixing time of the ocean)?Below, a very simple box model is used as a first step toward answering this question.

Box-model description
Figure 1 illustrates a simple box-model that has been constructed in order to explore in more detail the implications of deep-water mass geometry (versus overturning rate) changes for glacial-interglacial CO 2 variability.This model comprises an atmosphere and six ocean boxes (Southern Ocean, low-latitude, North Atlantic, northern deep water, intermediate-water and southern deep water), and involves two coupled circulation cells with down welling in the southern and northern high latitudes.Geological exchange of minerals and nutrients (river alkalinity input, sedimentation, car-  Table 1).Table 1).bonate compensation) is not included in this model.Particle fluxes are treated as directly exported dissolved matter, with carbon and phosphate being exported in fixed proportions, as defined by modified Redfield Ratios (C:N:P:O 2 =130:16:1:-169) (Toggweiler and Sarmiento, 1985), and carbonate being exported in fixed proportion to the TCO 2 of the water.Particle fluxes are diagnosed for a baseline "pre-industrial" box-model scenario according to observed phosphate concentrations in the modern ocean (Najjar et al., 1992): where P is the instantaneous organic carbon flux, C * /P * is the ratio of organic carbon to phosphate in the particulate matter, V is the box volume, τ is the restoring time-scale (set to 0.1 year), and [PO 4 ] and [PO 4 ] mod are the instantaneous and restoring phosphate concentrations, respectively.In subsequent "altered" box-model scenarios, particle fluxes vary according to "Michaelis-Menton" type dynamics (Dugdale, 1967), with less export being supported by lower nutrient concentrations.This removes the possibility of unrealistically high/low export productivity for very low/high nutrient levels respectively: In the above equation, k m is set to 2.5 e −4 mol m −3 (Schulz et al., 2001), and ω (the biological uptake rate) is diagnosed from the equilibrium conditions for the "modern box-model scenario" (preceding equation).
The calculated components of the model include phosphate, alkalinity, total dissolved CO 2 (TCO 2 ), carbonate ion (CO 2− 3 ), pCO 2 , apparent oxygen utilisation (AOU) and normalised radiocarbon concentration ( 14 C).Because the modelled radiocarbon concentrations are not normalised with respect to δ 13 C, 14 C reported here is actually equivalent to d 14 C by definition (Stuiver and Polach, 1977).Idealised mass-balance equations for the evolution of box concentrations are of the form: C * P * (e.g.southern deep box) where C indicates the box concentration, F and f indicate water fluxes, P indicates particulate carbon fluxes (multiplied by chemical export/consumption ratios for different constituents, C * /P * ) and F AO indicates an air-sea exchange term (applicable to carbon dioxide and radiocarbon).The deep boxes receive particle fluxes from the high northern/southern latitude surface boxes as well as the intermediate box, through which one tenth of the low latitude particulate flux is transmitted.Each deep box receives particulate flux from the intermediate box in proportion to its relative volume (see Fig. 1).Surface boxes have AOU set to zero.
For the calculation of the TCO 2 of the surface boxes, an extra exchange term with the atmosphere must be included: The air-sea gas exchange ((CO 2 ) SOL ) is defined according to the thermodynamics of Millero (1995) (Eqs. 26,41 and 42 therein), and follows a similar scheme to that of Toggweiler and Sarmiento (1985), such that: where A s and g s are southern surface box area (m 2 ) and gas piston velocity (kg m −2 yr −1 ), respectively; (pCO 2 ) s and (pCO 2 ) atm are the partial pressures for CO 2 in the southern surface box and the atmosphere respectively, and where α s is the southern surface box solubility coefficient for CO 2 (Millero, 1995).
The carbonate system is treated using the C-SYS calculation scheme of (Zeebe and Wolf-Gladrow, 2001) given alkalinity, TCO 2 , pressure, temperature and salinity.The atmospheric pCO 2 is updated at each time step by integrating the air-sea CO 2 fluxes from each surface box: For radiocarbon, an extra term is included in the equations to account for radioactive decay.box, the mass balance equation for radiocarbon is: Here λ is the radiocarbon decay constant (1.2097 e −4 yr −1 ).
Radiocarbon is transported as a concentration (µmol kg −1 ), such that the ratio of radiocarbon to total carbon (R 14 C) is determined by dividing the radiocarbon concentration by the total carbon concentration of the relevant box at each timestep.The normalised radiocarbon concentration is then determined as: The radiocarbon concentrations of the various boxes are expressed relative to the pre-industrial standard 14 C/C ratio of 1.176 e −12 .Biological uptake/release of radiocarbon and cosmogenic radiocarbon production are not treated explicitly in this model.Instead these terms are diagnosed for an equilibrium atmospheric radiocarbon concentration equal to the pre-industrial standard ( 14 C/C=1.176e −12 ).Once diagnosed, both terms are kept constant for experiments that involve modifications in box-model geometry.The global radiocarbon inventory is also fixed at its pre-industrial value, and can be maintained at this constant level once a preindustrial equilibrium has been attained.Atmosphereocean exchange of radiocarbon is calculated as formulated for example by (Müller et al., 2006), such that: where F AO is the atmosphere to ocean radiocarbon flux, g is the gas piston velocity (fixed at 3 ms −1 ), A o is the exposed ocean box area, K h is the CO 2 solubility constant for the ocean surface and subscripts −atm and −o refer to atmospheric-and oceanic carbon concentrations or radiocarbon ratios.
A numerical integration method (ODE-45 in Matlab's Simulink) is used to update the box concentration at the end of each time step, until all boxes reach a steady equilibrium.In order for radiocarbon to reach equilibrium the model must be integrated for ∼20 000 model years.In the model, a correction scheme is used to check that the global inventories of phosphate, alkalinity and (radio-) carbon do not drift, and are all maintained at prescribed constant values.This correction scheme in fact only needs to be invoked for radiocarbon, since it is the only modelled species that includes diagnosed net input/output terms (production, decay and terrestrial biosphere uptake).Radiocarbon inventory correction factors thus differ from 1 during the "wind-up" to equilibrium, while the atmospheric input and output terms (cosmogenic production minus biosphere uptake) are being diagnosed.Note that box-volumes in the model do not change during simulations (dV /dt=0).It should also be noted that although the flow scheme of the box model essentially represents an Atlantic Ocean (i.e. it has two deep overturning "limbs"), it is scaled to global proportions so that the volumes and concentrations of the atmosphere and the ocean balance with global inventories (all of which are fixed input parameters).Nevertheless, the volumes of the two deepwater boxes are scaled relative to each other according to the hypothesised representation of North Atlantic and Antarctic deep-water end-members throughout the global ocean.
The model is initiated with the concentrations of all boxes set to the global average, except for the pCO 2 of the surface boxes and the atmosphere, which are set arbitrarily close to zero (this avoids singularities in the calculation of initial radiocarbon concentrations).Equilibrium outcomes were not found to be sensitive to changes in these initial concentration conditions, since global inventories are maintained.In all model runs temperatures and salinities are also kept constant, in order to investigate exclusively the effect of watermass geometry changes.

Model parameterisation and sensitivity
The parameterisation of the model's mass transport and mixing rate terms is outlined in Table 1.Circulation rates for the (modern) northern and southern overturning loops were initially set according to (Ganachaud and Wunsch, 2000).These export rates were then augmented in fixed proportion to each other (1:1.7) in order to achieve deep ocean radiocarbon concentrations that more closely matched the modern ocean (average deep-ocean age ∼1400 years) and such that atmospheric carbon dioxide reached an appropriate preindustrial value (∼ 280 ppm) when restoring to modern surface phosphate concentration estimates (see below).Mixing rates between boxes were set arbitrarily to 10 Sv in the high latitudes and 5 Sv for the deep-ocean and the low-latitude surface ocean, where it can be argued that up-welling should be small compared to high-latitude overturning (Gnanadesikan et al., 2007).The sensitivity of the variable biological export was diagnosed by restoring to prescribed surface phosphate concentrations, as described above, once appropriate mass transport rates were estimated (see Table 1).With the net biological export to the deep boxes estimated to be ∼10% of export production at 100 m (Martin et al., 1987), the total biological export at 100 m in the baseline model run is ∼20 PgC yr −1 .Although this value is rather high, there is ample scope for reducing it by prescribing a more sluggish net overturning rate in the model, while maintaining approximate pre-industrial atmospheric pCO 2 , and re-diagnosing (necessarily lower) biological uptake rates.As illustrated below, this can be done without significantly affecting the carbon and radiocarbon distributions in the model, and indeed without affecting the outcome of this study.Directly tuning the model to expected net biological export rates (closer to ∼10 PgC yr −1 , Kohler et al., 2005) can therefore be safely avoided.
Figure 2 illustrates the sensitivity of modelled atmospheric pCO 2 and deep-ocean radiocarbon ventilation with respect to changes in the physical transport and mixing rate parameters.As expected, the parameter that most strongly constrains both the ocean -atmosphere radiocarbon-and CO 2 partitioning is the net overturning transport rate (F n + F s , where F s = F n /1.7; see Fig. 1).In the majority of the sensitivity tests illustrated in Fig. 2 (solid lines), biological "uptake rates" (ω, the variable-export sensitivity) were maintained at the values diagnosed for the baseline "pre-industrial" scenario (i.e. for F n =28 Sv, F s =16.5 Sv, and for modern surfaceocean phosphate concentrations; see Table 1).However, when surface-ocean nutrient (phosphate) concentrations are restored to modern values while at the same time changing the mixing rate parameters, the impact of large changes in overturning rates on atmospheric pCO 2 is greatly reduced (crossed circles in Figure 2).This demonstrates how the balance between physical overturning and biological export effectively sets the carbon sequestration capacity of the deep ocean for a given deep-water geometry (e.g.Sarmiento and Toggweiler, 1984).It also illustrates that a lower net biological export could be obtained with a lower net overturning rate, while approximately maintaining pre-industrial pCO 2 and deep-ocean 14 C.
Clearly, a box-model like the one presented here represents a highly conceptualised system, though in this case only radiocarbon (as a ventilation time-scale indicator), surface-ocean phosphate concentration (as a biological export rate indicator), and atmospheric pCO 2 (as a carbon climatology indicator) are used to "tune" the model.The rest of the box-model equilibrium chemistry is determined by these conditions, and can therefore be used for a first-order evaluation of the model behaviour.The "realism" of the baseline pre-industrial model scenario is illustrated in Fig. 3 relative to modern/pre-industrial observations (Key et al., 2004;Broecker and Peng, 1982).The modern/pre-industrial "observations" should be seen merely as indications of what plausible box concentrations might be, since their counterparts in reality are difficult to assess.The concentrations, volumes and chemical inventories of the boxes for the baseline control scenario are listed in Table 2.As shown in Fig. 3, even this highly simplified model is capable of mimicking the chemical distribution of the modern ocean with adequate realism, without being explicitly tuned to do so.
The goal will be to explore differences in the equilibrium carbon-sequestration capacity of the box-model ocean for a series of different deep-water box geometries.In order to do this, the model is run to equilibrium after the relative volumes of the two deep-water boxes in the model are changed, while the total volume is of course maintained and while the global chemical inventories and all other model parameters are kept constant.1.The crossed circles indicate results experiments where both the total overturning strength (Fn+Fs) and the surface-box biological uptake rates (i.e.export efficiency) were varied in order to maintain prescribed modern surface box phosphate concentrations.

Model experiments
As noted above, the reconstruction of past changes in the dynamical structure (flow rates) of the ocean remains a major challenge (Wunsch, 2003;Lynch-Steiglitz et al., 2007).However, proxies for past deep-water composition, such as for example benthic foraminiferal Cd/Ca (Boyle, 1988b), δ 13 C (Duplessy et al., 1988;Curry and Oppo, 2005  shoaled to a depth of ∼1.8 to 2.5 km, and was replaced at greater depths by southern-sourced (or LCDW-like) deepwater (Lynch-Steiglitz et al., 2007;Marchitto and Broecker, 2005;Hodell et al., 2003).New ε N d evidence from the deep South Atlantic and Indian Ocean (Piotrowski et al., 2009;Piotrowski et al., 2008) also indicates a marked reduction in the contribution of NADW to LCDW exported to these basins.
If we take into account the hypsometry of the ocean floor (Menard and Smith, 1966), and if we assume that northern-sourced deep-water can account for up to 50% of the Lower Circumpolar Deep Water (LCDW) that is exported to the deep Indo-Pacific basins (Broecker and Peng, 1982;Matsumoto, 2007), then we can calculate the expected global volume ratio (R ns ) of "northern-sourced deep-water" (NDW) versus "southern-sourced deep-water" (SDW) given the depth of a presumed (horizontal) boundary between the two.The rationale behind this approach is that if NADW does not affect the Atlantic sector of the Southern Ocean below a given depth, then LCDW exported to the Indo-Pacific below this depth would also be without significant NADW influence.This is illustrated in Fig. 4, where a rise in the NDW/SDW boundary from 5 km to 2.5 km in the Atlantic is taken to imply a proportionate reduction of the amount of NDW mixed into the Indo-Pacific basins via CDW and hence a global reduction in the total volume ratio of northernto southern deep-water (R ns ) from 1.43 to 0.5 between the Holocene and the LGM.Using more sophisticated models of the ocean circulation it should be possible to determine this ratio more exactly for a "physically sensible" ocean circulation and water-mass geometry (e.g.Cox, 1989).This could eventually permit a "calibration" of simulated changes in atmospheric pCO 2 to simulated changes in R ns (including perhaps for different causes of R ns change).
In the box model described here, equilibrium atmospheric pCO 2 is found to drop consistently as the R ns value for the box-model geometry decreases (i.e.NDW gives way   to SDW).This is shown in Fig. 5, where a shift in the NDW/SDW water-mass boundary from 5 km to 2.5 km (or a change in R ns from 1.43 to 0.5) corresponds to a drop in equilibrium atmospheric pCO 2 of just over 25 ppm.The box model volumes and chemical inventories for the hypothesised "glacial" water-mass geometry (2.5 km NDW/SDW water-mass boundary, R ns =0.5) are summarised in Table 3.As expected, a "standing volume effect" such as described here is not going to account for the entirety of glacialinterglacial pCO 2 change.However, the important and perhaps surprising observation is that this mechanism might account for nearly as much of the glacial-interglacial atmospheric pCO 2 change as has been attributed to other fundamental mechanisms, such as sea-surface cooling, carbonate compensation, or ocean fertilisation (Sigman and Boyle, 2000;Peacock et al., 2006;Brovkin et al., 2007).The box model experiments illustrated in Fig. 5 appear to confirm the thought experiment described in Sect.2.0, whereby an ocean that is dominated by LCDW-like deep water holds more CO 2 .In order to operate effectively however, this sequestration mechanism requires three conditions: 1) there must be rather large changes in water-mass volumes (in the scenario envisaged here ∼60% of the Atlantic and ∼30% of the Indo-Pacific is affected by the reduced NADW contribution); 2) the expanding water-mass must have high TCO 2 relative to the water it effectively displaces; and 3) the expanding southern overturning loop must not "leak" CO 2 to the atmosphere very efficiently.These three conditions stem from the fact that the standing volume effect operates by causing an increase in the "efficiency" of the biological pump (via an increase in the deep sea nutrient pool), and by enhancing the solubility pump (via an expansion of a watermass that is colder and relatively poorly equilibrated with the atmosphere), in both cases for a given overturning flux and polar outcrop area.If combined with a lower global average temperature, the expansion of a colder deep watermass would further reduce the average ocean heat content.Once again, the key point is that a change in deep water-mass geometry could provide an effective means of keeping the ocean interior cold (against diffusive and geothermal warming from above and below), without any changes in overall overturning rates.This could be particularly important for enhancing the vertical abyssal temperature gradient if indeed the advection rate of cold deep-water from the poles was significantly reduced during the last glacial, relative to today.Because the proposed standing volume effect operates via modulations of the biological and solubility pumps, it should combine additively with other imposed changes in gas-exchange or nutrient utilisation in the Southern Ocean, due to sea-ice expansion, increased upper-ocean stratification or ocean fertilisation for example.This is shown in Fig. 6, which shows that independently imposed changes in Southern Ocean air-sea gas exchange do not attenuate the standing volume effect at all, while a completely depleted Southern Ocean nutrient pool only attenuates the standing volume effect by ∼50% (due to the near elimination of the surface nutrient pool that the expanding SDW can draw from).One implication of the results shown in Fig. 6 is that imposed changes in gas exchange or biological export will result in a greater change in atmospheric pCO 2 if they are accompanied by an increase in the volumetric dominance of southernsourced deep-water.
Previously, it has been suggested on the basis of first order principles and numerical modelling experiments that if global nutrient inventories are maintained while surface nutrients are depleted, either via reduced overturning rates or increased biological export rates, atmospheric pCO 2 will vary in proportion to the resulting average preformed nutrient concentration of the deep sea (Ito and Follows, 2005;Sigman and Haug, 2003;Toggweiler et al., 2003;Marinov et al., 2006).The average deep-sea preformed nutrient concentration is thus suggested to scale with atmospheic pCO 2 , with an estimated ∼130-170 ppm change in pCO 2 per 1 µmol kg −1 change in preformed phosphate (Ito and Follows, 2005;Sigman and Haug, 2003;Marinov et al., 2006).One way to explain the positive correlation is that any change that acts to reduce the mean nutrient (i.e.phosphate) concentration at the ocean surface (especially in regions of deepwater formation, Marinov et al., 2006) will result in: (1) a reduction of the advected nutrient flux into the ocean   interior (thus lowering the mean preformed nutrient concentration of deep sea); and (2) an increase in the total nutrient concentration of the deep-sea (due to the conservation of ocean nutrients), thus sequestering more carbon in the deep sea.
The proposed scaling between mean deep-sea preformed nutrient concentrations and atmospheric pCO 2 might be taken to imply that the domination of the deep sea by LCDWlike deep water (with a relatively high preformed nutrient concentration) would cause atmospheric pCO 2 to rise, contrary to the hypothesis presented here (Toggweiler et al., 2003;Sigman and Haug, 2003).This apparent contradiction can be clarified by considering a heterogeneous deep-sea with constant total volume despite variable deep-sea watermass volumes.The conservation of the global carbon inventory in this system can be stated as follows: where M is the total molar content of the atmosphere; V d , V sd , V nd and V surf are the volumes of the whole deep ocean, southern deep-water component, northern deep-water component, and surface ocean respectively; C d and C surf are the mean carbon concentrations in the deep-and surface ocean; C sd and C nd are the southern-and northern deep-water carbon concentrations; and B tot is the global carbon inventory.In this system, any perturbation to the carbon budget of the deep-sea must be balanced by a change in the atmospheric carbon content, which will remain in approximate equilibrium with the carbon content of the surface ocean.If we consider a perturbation to the system due only to changing V s at the expense of V n (i.e.δV sd =−δV nd ), where R C:P is the Redfield C:P ratio, then we find that (cf.Ito and Follows, 2005): where: In the above equation γ is a dimensionless parameter that accounts for the equilibration between the atmosphere and the surface ocean, and represents the relative magnitudes of the atmospheric and surface ocean carbon reservoirs, via the "Revelle factor" (buffer factor), γ DIC .Although this parameter may vary with physical/climatic conditions, it is assumed to be constant in the discussion that follows.This is justified on the grounds that during the last glacial any changes in γ are likely to have been negative rather than positive, as a result of decreased equilibration between the glacial ocean and the atmosphere, especially in the Southern Ocean as described in Sect. 2. This would only tend to exacerbate, rather than attenuate, the relationships described below.
The above relationships, which are drawn from the framework proposed by Ito and Follows (2005), confirm the intuitive expectation that changes in pCO 2 and the surface nutrient concentration ( P surf ) or TCO 2 should all be negative for increasing V s as long as the expanding southern deep-water mass has a higher nutrient content and TCO 2 than the watermass it replaces (C sd >C nd ).Otherwise, the opposite is true.
The mean preformed nutrient concentration of the deep sea can be defined as the total flux of dissolved nutrients into the sub-surface (i.e. the sum of the products of surface phosphate and their associated downward mass transport terms) divided by the net overturning circulation (e.g.Sigman and Haug, 2003).This means that mean preformed nutrients in the deep-sea must also decrease as V sd increases and pCO 2 decreases (again if C nd <C sd ).Hence as long as the postulated changes in deep water-mass volumes cause the surface TCO 2 and nutrient concentrations to drop (especially in regions of deep-water formation), we can expect them to cause a drop in atmospheric pCO 2 and a drop in mean deep-water preformed nutrient concentration, all because of an increase in the total deep-sea nutrient inventory.
In the box model experiments carried out here, the expected theoretical relationships based on the arguments presented above, and based on previous work (Ito and Follows, 2005;Sigman and Haug, 2003;Toggweiler et al., 2003;Marinov et al., 2006), are borne out: atmospheric pCO 2 drops by almost 100 ppm per 1 µmol kg −1 drop in the mean preformed nutrient concentration in the ocean interior boxes (calculated from Tables 1, 2 and 3).The proposed standing volume effect therefore appears to be consistent with previous conceptualisations of the biological pump and its variable efficiency, although it demonstrates that dissolved-or particulate export rates are not the only parameters controlling the mean surface-to-deep nutrient/carbon concentration gradient in a closed system.

Ocean circulation and the "CO 2 stew"
The main purpose of the present study is not to attempt a complete simulation or explanation of glacial-interglacial atmospheric CO 2 change, nor is it to suggest that ocean circulation rates and biological export rates are unimportant for glacial-interglacial CO 2 change.Rather, the goal here is to draw a distinction between two separate aspects of the "ocean circulation" (water-mass distribution versus water-mass renewal/overturning rates) in terms of their respective roles in glacial-interglacial CO 2 change.Based on a simple thought experiment and a set of box-model tests, it would appear that a surprisingly large portion of the glacial-interglacial CO 2 change might be explained simply by changes in the volumetric contribution of contrasting deep-water end-members to the deep sea, prior to any imposed changes in overturning-, gas exchange-or biological export rates.The proposed "standing volume effect" would arise due to substantial changes in the volume of relatively high-TCO 2 (LCDW-like) deep-water filling the ocean basins, and requires only that the expanding overturning loop does not "leak" excess CO 2 to the atmosphere as a result of countervailing changes in biological export rates or gas exchange rates for example.Indeed, the standing volume effect www.clim-past.net/5/537/2009/Clim.Past, 5, 537-550, 2009 will be additive with respect to accompanying changes in biological export or gas exchange around Antarctica.
Although previous studies that have simulated glacial atmospheric CO 2 using complex numerical models with accurate bathymetry (e.g.Heinze et al., 1991) may have already included the proposed standing volume effect implicitly, none so far have tried to identify or quantify its possible impact on glacial CO 2 draw-down.Although one recent exception (Brovkin et al., 2007) has suggested that the expansion of AABW at the expense of NADW in the glacial ocean might have caused atmospheric CO 2 to drop by as much as 43 ppm, this estimate includes the effects of changes in deep-water overturning rates (reduced NADW export rate by ∼20% and intensified AABW export rate).The proposed standing volume effect therefore remains to be tested adequately using complex numerical model simulations of the glacial ocean circulation.
If the simple standing volume mechanism proposed here for enhancing deep-sea carbon sequestration can be incorporated into the list of "ingredients" that have contributed to glacial-interglacial CO 2 change (Peacock et al., 2006;Kohler et al., 2005;Archer et al., 2000;Sigman and Boyle, 2000), it may help to reduce or eliminate the CO 2 deficit that remains to be explained by appealing to more equivocal or controversial processes.More importantly however, it may also help us to evaluate more explicitly the role of the 'ocean circulation' as an ingredient in the glacial-interglacial "CO 2 stew", as well as the triggers that repeatedly pushed the marine carbon cycle between glacial and interglacial modes (Paillard and Parrenin, 2004;Shackleton, 2000).This is especially true if the mechanisms or timescales for changing the vertical mass transport rate in the ocean differ from those for changing the (vertical) redistribution of contrasting deep-water end-members.Indeed, a de-convolution of the expected impacts of an altered "ocean circulation" into renewal-rate effects and standing-volume effects can only gain importance to the extent that proxy evidence for a large reduction in the net overturning rate of the glacial ocean remains equivocal (Lynch-Steiglitz et al., 2007), and/or theoretical support for such a change continues to be debated (Wunsch, 2003).

Fig. 1 .
Fig. 1.Box-model schematic (S, southern surface; L, low-latitude surface; N, northern surface; ND, north deep; Int, intermediate; SD, south deep).The vertical dashed line is intended to suggest an alternative hypothetical box geometry, where southern sourced water dominates the deep ocean.Heavy black lines indicate thermohaline circulation (Fn=northern overturning; Fs=southern overturning).Red arrows indicate two-way exchange (i.e.mixing) terms.Blue arrows indicate gas exchange.Grey arrows indicate particle fluxes.The particle fluxes Pi(sd) and Pi(nd) that by-pass the intermediate box from the low-latitude box are calculated in proportion to the volume of each deep box relative to the total deep ocean in the model, such that if Vnd/Vd=f, Pi(nd)=f×0.1×Pl and Pi(sd)=(1f)×0.1×Pl.Approximate box depths are indicated at left (surface areas are given inTable 1).

Fig. 2 .
Fig. 2. Sensitivity of modelled atmospheric pCO 2 (a) and average deep ocean 14C (b) to changes in the box-model physical mixing terms, expressed here as percentages relative to the baseline values given in Table1.The crossed circles indicate results experiments where both the total overturning strength (Fn+Fs) and the surface-box biological uptake rates (i.e.export efficiency) were varied in order to maintain prescribed modern surface box phosphate concentrations.
) and more recently dispersed ferromanganese oxide ε N d (Goldstein and Hemming, 2003), more readily allow us to infer past changes in water-mass distribution.Thus during the last glacial in the Atlantic and the Atlantic sector of the Southern Ocean it would appear that NADW-influenced deep-water www.clim-past.net/5/537/2009/Clim.Past, 5, 537-550, 2009 Figure 4.

Figure 4 .
Figure 4. Illustration of how the volume ratio (R ns ) of 'northern' (NDW) to 'southern' (SDW) water-masses is hypothesised to change based on water-mass boundary shoaling and given the hypsometry of the sea floor.The left hand panel shows changing water-mass ratio R ns versus the water depth of a presumed horizontal water-mass boundary.Solid dots indicate estimated values for 'modern' and last glacial maximum (LGM) hydrography.The right hand panel shows how the sea floor area varies with water depth in the Atlantic and Indo-Pacific basins.Shading illustrates how R ns is calculated, by assuming that SDW fills the abyssal ocean up to the presumed water-mass boundary, while NDW fills only half of the Indo-Pacific basin and all of the Atlantic basin above this.The volume ratio R ns for a given fill depth is thus estimated as the volume above the fill depth in the Atlantic, plus half the volume above the fill depth in the Indo-Pacific, divided by the volume below the fill depth in the Atlantic and the Indo-Pacific plus half the volume above the fill depth in the Indo-Pacific.This tempers the exaggeration in volume change that would otherwise result from treating the whole ocean as analogous to the Atlantic.

Fig. 4 .
Fig. 4. Illustration of how the volume ratio (R ns ) of "northern" (NDW) to "southern" (SDW) water-masses is hypothesised to change based on water-mass boundary shoaling and given the hypsometry of the sea floor.The left hand panel shows changing water-mass ratio R ns versus the water depth of a presumed horizontal water-mass boundary.Solid dots indicate estimated values for "modern" and last glacial maximum (LGM) hydrography.The right hand panel shows how the sea floor area varies with water depth in the Atlantic and Indo-Pacific basins.Shading illustrates how R ns is calculated, by assuming that SDW fills the abyssal ocean up to the presumed water-mass boundary, while NDW fills only half of the Indo-Pacific basin and all of the Atlantic basin above this.The volume ratio R ns for a given fill depth is thus estimated as the volume above the fill depth in the Atlantic, plus half the volume above the fill depth in the Indo-Pacific, divided by the volume below the fill depth in the Atlantic and the Indo-Pacific plus half the volume above the fill depth in the Indo-Pacific.This tempers the exaggeration in volume change that would otherwise result from treating the whole ocean as analogous to the Atlantic.

Fig. 5 .
Fig. 5. Sensitivity of modelled atmospheric pCO2 to changes in the NDW/SDW volume ratio (R ns ).As the water-mass boundary shoals from 5 km (modern baseline) to 2.5 km (last glacial), R ns is estimated to change from 1.43 to 0.5.This results in a 26 ppm drop in atmospheric pCO 2 in the box model.

Figure 6 .
Figure6.Sensitivity of the modelled change in atmospheric pCO 2 to changes in R ns when Southern Ocean gas exchange efficiency is enhanced/reduced and Southern Ocean biological export efficiency is enhanced to 100%.The sensitivity of ∆pCO 2 to R ns remains positive in each case, such that a reduction in pCO 2 driven by gas exchange or biological export change would be enhanced by a reduction in R ns .

Fig. 6 .
Fig.6.Sensitivity of the modelled change in atmospheric pCO 2 to changes in R ns when Southern Ocean gas exchange efficiency is enhanced/reduced and Southern Ocean biological export efficiency is enhanced to 100%.The sensitivity of pCO 2 to R ns remains positive in each case, such that a reduction in pCO 2 driven by gas exchange or biological export change would be enhanced by a reduction in R ns .

Table 1 .
Input parameterisation for "baseline" model run.Only R ns is varied in subsequent model runs.
axes; see text).The parameterisation used for the baseline model run is given in Table 1.Dotted lines indicate 1:1 relationship (i.e.equivalent modelled and expected values).