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 Using an ocean box model, we have studied the effect of altered circulation on the oceanic distributions of phosphate (PO4−3) and the 13C/12C and 14C/12C of dissolved inorganic carbon to evaluate competing hypotheses for the cause of observed nutrient depletion and 13C enrichment at intermediate depths of the Atlantic during the last ice age. Because of “nutrient trapping” and limited air-sea carbon isotopic equilibration, the simple imposition of an intense meridional overturning cell in the Atlantic fails to simultaneously lower nutrient concentrations and raise 13C/12C to observed glacial levels. Export of intermediate water out of the Atlantic causes a basin-to-basin nutrient transfer, thus providing a more efficient mechanism of intermediate-depth Atlantic nutrient depletion and improved carbon isotopic equilibration at low temperatures (i.e., 13C enrichment). Although this export adds nutrients to the intermediate depths of the Pacific and Indian Oceans, the simulated glacial intermediate-depth Indo-Pacific is nevertheless moderately depleted in PO4−3 relative to the model's interglacial control, in agreement with consensus paleoceanographic evidence. This Indo-Pacific PO4−3 depletion results from our use of a “glacial base case” in which nutrient-rich Antarctic Intermediate Water formation is absent as part of the elimination of the modern North-Atlantic-Deep-Water-based “conveyor” circulation.
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 The distributions of Cd and the 13C/12C of dissolved inorganic carbon, as recorded by the shell chemistry of benthic foraminifera, are established tools for the study of past ocean circulation. Because the Cd concentration of modern seawater is related to its phosphate concentration, the Cd content of benthic foraminifera provides a paleoceanographic proxy for oceanic phosphate concentration ([PO4−3]) [Boyle, 1988a]. In the deep ocean the 13C/12C of dissolved inorganic carbon also covaries with [PO4−3] due to the remineralization of low-13C/12C organic matter. In the modern deep ocean the δ13C of dissolved inorganic carbon (DIC) decreases by ∼1‰ for every 1 μM increase in [PO4−3] [Broecker and Peng, 1982] (δ13C = (13C/12Csample/13C/12Creference − 1) × 1000‰), where the reference is Pee Dee Bee Belemnite). However, atmospheric exchange also influences δ13C so that changes in the surface residence time and source region temperature can cause subsurface water δ13C to diverge from [PO4−3]-related behavior (i.e., from the −1‰/1 μM ratio of variation [Broecker and Maier-Reimer, 1992; Broecker and Peng, 1982; Lynch-Stieglitz et al., 1995; Oppo and Fairbanks, 1989]). Broecker and Maier-Reimer  and Lynch-Stieglitz and Fairbanks  formalized the paired use of Cd and δ13C in terms of “δ13Cas,” the δ13C of a water parcel normalized to its Cd content (a measure of its [PO4−3]), in an effort to recognize deviations from the remineralization-based δ13C/[PO4−3] relationship arising from air-sea gas exchange.
 A variety of hypotheses have been posed to explain intermediate-depth nutrient depletion during glacial times, including changes in ocean mixing, thermohaline circulation, and biogeochemical cycling [Boyle, 1988c]. Intermediate-depth δ13C tends to decrease from north to south in the Atlantic [Duplessy et al., 1988], suggesting the formation of nutrient-depleted glacial NAIW. While paired Cd/Ca and δ13C data indicate that glacial NAIW penetrated well into the subtropical South Atlantic [Oppo and Horowitz, 2000], its flow rate and downstream fate are not known. In addition, the role of NAIW formation in the apparent nutrient depletion and O2 enrichment of the intermediate-depth Indo-Pacific is unresolved [e.g., Lynch-Stieglitz and Fairbanks, 1994; Oppo and Horowitz, 2000; Yu et al., 1996].
 We use a geochemical box model to investigate the effect of altered circulation on the oceanic distributions of [PO4−3], δ13C, and Δ14C. Our goal is to complement other studies [e.g., Michel et al., 1995; Winguth et al., 1999] by adopting a process-based approach to several hypotheses regarding glacial circulation (Figure 2), with a focus on the potential constraints afforded by the pairing of foraminiferal Cd and δ13C data. Quantitative uncertainty in paleoceanographic studies of ocean circulation arises from both uncertainties in the observations and the paucity of constraints on the models that are used to interpret them [Legrand and Wunsch, 1995]. The study described here is motivated by our belief that progress can be made by developing a mechanistic understanding of how changes in circulation would affect the global distributions of observable tracers. Because intermediate-depth nutrient chemistry has been well documented in the glacial Atlantic, we have chosen to focus on the hypothesis of glacial NAIW formation (Figure 2). However, our results inevitably have implications for intermediate-depth nutrient chemistry in the other ocean basins.
 A set of three model experiments are carried out on the CYCLOPS ocean box model [Keir, 1988, 1995; Sigman et al., 1998]. The experiments are superimposed on a hypothetical “glacial base case” circulation, which differs from the standard interglacial circulation in that NADW formation and its downstream flows have been removed.
 In model experiment 1 (Figure 2c) we show that simple mixing with either low-latitude or high-latitude surface boxes fails to simultaneously produce both nutrient depletion and 13C enrichment in the intermediate-depth Atlantic. Rather, a circulation is required that not only extracts nutrients from the system but also forms new intermediate water in a cold source region. An intermediate-depth meridional overturning cell has both of these characteristics [Broecker, 1993].
 In model experiment 2 (Figure 2d) we find that the potential of a North-Atlantic-fed overturning cell to cause intermediate-depth nutrient depletion is substantially limited by “nutrient trapping,” that is, the sequestration of nutrients at intermediate depths by the regeneration of the biogenic flux under low-latitude regions of upwelling. Because of nutrient trapping, ≥20 sverdrups (Sv) (1 Sv = 106 m3 s−1) of overturning are required to approach the low nutrient concentrations apparently observed in the glacial intermediate-depth Atlantic. However, such high rates of overturning limit the residence time and isotopic equilibration of surface waters in the high-latitude North Atlantic. This causes intermediate-depth δ13C to underestimate the decrease in intermediate-depth [PO4−3], a model result that clearly disagrees with the sense of the paleoceanographic data [Lynch-Stieglitz and Fairbanks, 1994].
 In model experiment 3 (Figure 2d) we investigate the export of NAIW from the Atlantic basin as a means of circumventing nutrient trapping. This export causes a basin-to-basin transfer of nutrients, resulting in greater nutrient depletion of the intermediate Atlantic for a given rate of intermediate water formation. These results suggest that glacial nutrient depletion in the intermediate Atlantic could have been achieved with relatively low formation rates of intermediate water (as little as 5 Sv). At these low formation rates, δ13Cas remains high, in accordance with glacial observations.
 With NAIW export, intermediate Atlantic nutrient depletion is balanced by nutrient enrichment of the intermediate-depth North Pacific. However, for <7 Sv of NAIW export the net interglacial-to-glacial change is a decrease in intermediate Pacific [PO4−3]. This is because of a 0.6 μM [PO4−3] decrease, caused by the transition from standard interglacial conditions to the glacial base (NADW-off) case. This [PO4−3] decrease is due to the removal of Antarctic surface water as an intermediate water source to the Indo-Pacific; in the model, Antarctic Intermediate Water (AAIW) is a downstream component of the NADW-sourced overturning. This effect points to the consistency of the hypothesis of glacial Southern Ocean stratification and nutrient depletion with the observation of less nutrients and more dissolved O2 in the mid-depth glacial Indo-Pacific.
2. Model Description
 The model used in this study is a time-dependent geochemical box model, with architecture, circulation, and production/regeneration cycle after Keir . The model includes phosphate, DIC, alkalinity, and dissolved O2, 12C, 13C, and 14C as components. Model processes include biological cycling, circulation, gas exchange, and sedimentary CaCO3 dissolution [Sigman, 1997]. Biological cycling, air-sea CO2 exchange, and ocean circulation are summarized in sections 2.1'CO2 Exchange Between the Atmosphere and Surface Ocean'–2.3. Results of the model “interglacial” control simulation are compared with those of Keir  and with Geochemical Ocean Sections Study (GEOSECS) averages for [PO4−3], DIC, and alkalinity by Sigman et al. . Distributions of δ13C and Δ14C in our interglacial control are not significantly different from those of Keir ; this comparison and a comparison with GEOSECS averages are reported by Sigman . For convenience, “μM” is used to indicate to μmol kg−1 in seawater.
2.1. Biogeochemical Cycling
 Biological new production for the low-latitude (“warm”) surface ocean is calculated by allowing production to proceed until the PO4−3 supply is completely consumed (Figure 3). For all experiments but experiment 1, biological production in the high-latitude (“cold”) surface ocean boxes is varied to maintain a constant [PO4−3] of 0.55 and 1.62 μM for the surface North Atlantic and surface Antarctic, respectively, as per Keir . If the supply of PO4−3 to the high-latitude surface is too low to maintain the prescribed [PO4−3], the [PO4−3] is allowed to decrease to a new steady state value. The δ13C of the organic carbon rain is assumed in all cases to be 23‰ lower than that of the surface DIC pool. While this is simplistic and does not account for known isotopic variations in the δ13C of surface particulate matter, other assumptions have weaknesses of their own [Keller and Morel, 1999; Kienast et al., 2001; Popp et al., 1998].
 Of the organic C and P raining out of the model's warm surface ocean, 84% is degraded and regenerated at intermediate depths, and the remaining 16% is degraded and regenerated in the deep ocean [Betzer et al., 1984; Martin et al., 1987; Suess, 1980]. We address the effect of the prescribed organic P regeneration profiles in the context of model experiments 2 and 3.
2.2. CO2 Exchange Between the Atmosphere and Surface Ocean
 Gas exchange is similar to that in the model of Lynch-Stieglitz et al. , although it is of lower spatial and temporal resolution. The gross fluxes of CO2 into and out of the ocean are calculated, and the difference determines the net flux. The flux into the ocean is proportional to the temperature-dependent and salinity-dependent gas solubility, the fugacity of CO2 in the atmosphere, and the transfer velocity associated with gas exchange. Following Keir , gas transfer velocities are set at 1500 m yr−1 in the low latitudes and 1600 m yr−1 in the high latitudes. The flux out of the ocean is proportional to the surface aqueous CO2 activity and the gas transfer velocity. For the exchange of 13C the CO2 flux into the ocean is multiplied by the product of (1) the 13C/(12C + 13C) of atmospheric CO2, (2) the kinetic fractionation factor of gas exchange (0.9991 from Zhang et al. ), and (3) the temperature-dependent equilibrium isotope effects between aqueous CO2 and CO2 gas (equation from Mook ). The CO2 flux out of the ocean is multiplied by the product of (1) the 13C/(12C + 13C) of dissolved CO2 and (2) the kinetic fractionation factor. The net 13C flux is the difference in these gross fluxes. The exchange of 14C is analogous to that of 13C, with the kinetic and equilibrium isotope effects doubled in magnitude. Ten gas exchange steps are calculated each model year (whereas water is exchanged between boxes only once per year). Between each gas exchange step the distribution and isotopic compositions of the different dissolved inorganic carbon species (aqueous CO2, bicarbonate, and carbonate) are recalculated, reflecting the fact that CO2 hydration and acid-base chemistry occur much more rapidly than does CO2 diffusive transfer [Johnson, 1982]. The low-latitude surface boxes are held at 18.5°C and 35 ppm salinity, the high-latitude North Atlantic surface box is held at 4°C and 34.7 ppm salinity, and the Antarctic surface box is held at 0°C and 33.5 ppm salinity.
2.3. Circulation in the Interglacial Control and Glacial Base Case
 The interglacial control circulation is shown in Figure 4, with a view focused on the Atlantic in Figure 5a. Within the Atlantic basin, there is northward transport of both surface and intermediate-depth water. At high northern latitudes, these waters are converted into Northern Component Water, which flows southward through the deep Atlantic as NADW. NADW flows into the Antarctic Circumpolar box, where it mixes with water from other deep boxes and is upwelled into the surface Antarctic.
 The surface Antarctic is the sole source of intermediate-depth waters in the interglacial control. The 21.5 Sv of Antarctic upwelling, which is coupled to NADW formation, is exported from the surface Antarctic into the intermediate-depth boxes of all the ocean basins. Intermediate-depth water in the amount of 9.5 Sv upwells into the low-latitude surface ocean and returns via the surface to the high-latitude North Atlantic. The remaining 12 Sv of intermediate-depth water flows back to the North Atlantic at intermediate depths. These return flows complete the ocean “conveyor” associated with NADW formation [Broecker, 1991; Gordon, 1986]. In addition, the Antarctic surface box mixes vigorously with the Antarctic Circumpolar deep box, which mixes with the other deep boxes. As a result, deep water has effectively both North Atlantic and Southern Ocean sources.
 The hypothetical glacial experiments are performed on a “glacial base case” (Figure 5b). The glacial base case differs from the interglacial control in that NADW formation has been “shut off,” as have the downstream flows which complete the NADW conveyor circuit in the interglacial control, including AAIW formation. The [PO4−3], δ13C, and Δ14C distributions of the interglacial control and the glacial base case are compared in Figure 6. With the removal of NADW-associated advection in the glacial base case the [PO4−3] of the deep boxes is homogenized to 2.3 μM by mixing. While [PO4−3] in the high-latitude surface boxes is unchanged, δ13C increases dramatically in the high-latitude surface boxes and in Northern Component Water because of the increased residence time of this water in the cold polar surface and thus more complete air-sea isotopic exchange at low temperatures (Figure 6). Conversely, the δ13C of the intermediate-depth boxes is lower in the glacial base case because the removal of advection from the surface Antarctic has increased the mean temperature of the source water to the intermediate-depth boxes, resulting in a lower δ13Cas.
 The glacial base case is not in itself intended to be an adequate simulation of glacial circulation and geochemical distributions. Rather, its central characteristic, the removal of NADW, is necessary in order to isolate and evaluate circulation schemes that can produce intermediate-depth nutrient depletion and 13C enrichment. If NADW is kept on for the experiments that follow, it continues to sweep nutrients out of the Atlantic, and the entire Atlantic becomes extremely nutrient poor, a condition that can only be countered by a rapid supply of nutrient-rich Antarctic Bottom Water.
 While the initial goal of the glacial base case was simply to eliminate NADW formation, removal of the associated “return flows” for NADW formation had unanticipated consequences. In particular, the removal of AAIW formation caused the [PO4−3] of the intermediate-depth boxes in the Indo-Pacific to drop below that of the deep ocean, effectively causing “nutrient deepening” [Boyle, 1988c] by cutting off the influx of the nutrient-rich feed water from the Southern Ocean into the intermediate-depth global ocean. In the intermediate-depth Atlantic the effect on [PO4−3] is minor while the δ13C decreases significantly (0.7‰), so the shift to the glacial base case does not help to simulate glacial observations in the intermediate-depth Atlantic. However, as described in detail in section 3.3.2, the establishment of the glacial base case is found to be a necessary precondition for approaching glacial observations of global intermediate-depth nutrient chemistry with a circulation that includes NAIW formation.
3. Results and Interpretation
3.1. Model Experiment 1: Intermediate/Surface Mixing
 Experiment 1 demonstrates the fundamental requirements of the glacial observations that lead to our focus on the overturning cell geometry. In this experiment we consider two simple intermediate/surface exchanges: (1) between the intermediate-depth Atlantic and the low-latitude Atlantic surface ocean and (2) between the intermediate-depth Atlantic and the high-latitude North Atlantic (“boreal”) surface ocean (Figure 5c). We increase the surface/intermediate-depth exchange rate by 20 Sv in both cases. These experiments are carried out in the context of both the interglacial control (i.e., 21.5 Sv NADW formation) and the glacial base case (i.e., no NADW formation).
 As demonstrated by Boyle [1988b] and Keir , mixing with the low-latitude surface ocean provides a mechanism for intermediate-depth nutrient depletion due to the uptake of phosphate in the low-latitude surface ocean and the associated particle export. For a 20 Sv increase in the warm surface/intermediate-depth Atlantic mixing rate (to 24 Sv, or 6 times the standard interglacial mixing rate), intermediate-depth Atlantic [PO4−3] drops from 2.0 to 1.7 μM in the interglacial control and from 1.9 to 1.1 μM in the glacial base case (Figure 7a). The greater [PO4−3] decrease in the glacial base case is due to the removal of the buffering effect by advective input from the high-[PO4−3] surface Antarctic that exists in the interglacial control (compare Figures 5a and 5b). In either case the rate of intermediate-depth Atlantic/low-latitude surface Atlantic exchange required to lower intermediate-depth Atlantic [PO4−3] to near observed glacial levels (∼1 μM) is 5 times or more that of standard interglacial conditions.
 In both cases the δ13C increase is much less than would be expected from nutrient-related behavior. In addition, the glacial base case starts with a very low intermediate-depth Atlantic δ13C value of 0.1‰ so that the δ13C increase with increased mixing fails to return intermediate-depth Atlantic δ13C to the interglacial value. These δ13C results disagree with paleochemical data which suggest that the δ13C increase in the glacial intermediate-depth Atlantic was equivalent to or greater than expected from nutrient-related behavior [Lynch-Stieglitz and Fairbanks, 1994; Oppo and Lehman, 1993].
 The reason for the deviation of δ13C from nutrient-like behavior is that the effective gas equilibration temperature of the intermediate-depth Atlantic becomes higher (closer to that of low-latitude surface temperatures) as low-latitude surface/intermediate-depth Atlantic mixing is increased. Since intermediate-depth ventilation by isopycnal mixing is largely neglected in this model (and in other box models), it can be argued that intermediate-depth preformed δ13C is overly sensitive to the specified change in circulation. However, this isopycnal mixing would also import nutrients, requiring an even higher intermediate/low-latitude surface mixing rate to produce nutrient depletion. Our model does not attempt to balance the global heat budget so that it does not predict the cooling of the low-latitude surface Atlantic that would result from higher vertical mixing rates. However, given the range of estimates for the glacial/interglacial change in low-latitude surface temperature (≤5°C), including such glacial cooling does not greatly influence our results (results not shown). In addition, a sixfold increase in vertical mixing rates would have caused a threefold increase in basin-averaged biological new production, for which there is no paleoceanographic evidence [François et al., 1990; Ruhlemann et al., 1996, 1999]. Thus we consider the hypothesis of increased warm surface/intermediate-depth Atlantic mixing rates, when taken alone, to be untenable as an explanation for the observed changes in nutrient chemistry of the intermediate-depth Atlantic.
3.1.2. Intermediate-Depth Atlantic/High-Latitude Surface North Atlantic Mixing
 Mixing between the intermediate-depth Atlantic and the high-latitude surface ocean drives the δ13C (and the δ13Cas) of the intermediate-depth Atlantic to higher values (Figure 7b). However, this exchange does not in itself provide a mechanism for the removal of nutrients from intermediate depths. If we assume that biological export production for the high-latitude North Atlantic surface is constant (i.e., not higher during glacial times [Manighetti and McCave, 1995]), rapid exchange between the intermediate-depth Atlantic and the high-latitude North Atlantic does not reduce intermediate-depth Atlantic [PO4−3] in the glacial base case (Figure 7b). Instead, the [PO4−3] of the high-latitude North Atlantic surface increases to the intermediate-depth Atlantic value.
 If we allow high-latitude North Atlantic biological production to increase so as to maintain high North Atlantic surface [PO4−3] at 1 μM, then intermediate-depth Atlantic [PO4−3] will decrease toward this value, but this requires a large (sixfold) increase in the export production of the high-latitude North Atlantic, which has no basis in observations [Manighetti and McCave, 1995; Thomas et al., 1995]. In addition, this would lead to a very strong (∼1 μM) vertical [PO4−3] gradient in the upper water column of the high-latitude North Atlantic, with 1 μM surface water overlying subsurface water with a [PO4−3] of 2.3 μM. This conflicts with observations from the high-latitude North Atlantic of relatively constant (and low) nutrient concentrations above 2 km depth [Bertram et al., 1995]. If intermediate-depth Atlantic/high-latitude surface North Atlantic mixing played a role in glacial intermediate-depth nutrient depletion, then an additional process must have acted to export nutrients from the high-latitude region.
 Thus any hypothesized circulation scheme for the glacial Atlantic must involve both the low-latitude surface ocean (to remove nutrients) and the high-latitude surface ocean (to maintain a high δ13Cas). A meridional overturning cell represents one such circulation scheme (Figure 2d). The upwelling of water from the intermediate-depth ocean into the low-latitude surface layer strips nutrients from the overturning cell, while the routing of the upper limb through the high-latitude surface helps to maintain a high δ13Cas for the newly formed intermediate water.
3.2. Experiment 2: North Atlantic Intermediate Water (NAIW) Formation in a Closed-Basin Cell
 This experiment consists of an overturning cell, in which surface water sinks to intermediate depths in the high-latitude North Atlantic and upwells back into the surface Atlantic at low latitudes (Figure 5d) [Broecker, 1993]. Starting from the glacial base case, intermediate water formation is varied from 0 to 30 Sv.
 The formation and transport of intermediate water within a closed cell lowers the [PO4−3] of the intermediate-depth Atlantic box very gradually over the range of 0 to 30 Sv (Figure 8). Intermediate-depth Atlantic [PO4−3] does not drop below 1 μM until the rate of intermediate water formation exceeds 25 Sv, despite the fact that the [PO4−3] of the high-latitude North Atlantic boxes drops to 0 μM for any nonzero formation rate. The same formation rates reduce the Δ14C difference between the surface and intermediate-depth Atlantic to <50‰, compared to 95‰ in the interglacial control and 170‰ in the glacial base case.
 The very gradual nature of the decrease in intermediate-depth Atlantic [PO4−3] in response to the overturning cell is due to nutrient trapping. The input of phosphate to the intermediate-depth Atlantic, due solely to the 3.5 Sv mixing term with the deep Atlantic, is comparable to giving the intermediate water a “preformed” [PO4−3] of ∼0.3 μM. As described in Appendix A, with this PO4−3 burden, intermediate water formation is inefficient at lowering intermediate-depth [PO4−3]. The overturning rate required to reach 1 μM [PO4−3] in the intermediate-depth Atlantic would be still higher if even a small amount (e.g., 1–2 Sv) of AAIW with a preformed [PO4−3] of 1.6 μM were included as an input to the intermediate-depth Atlantic (“SAA-IA MIX” in Figure 5d, results not shown).
 As discussed in Appendix A, the magnitude of the [PO4−3] decrease associated with intermediate water formation is sensitive to the organic matter regeneration profile. Figure 9 compares the response of intermediate-depth Atlantic [PO4−3] to increasing rates of NAIW formation for both the standard regeneration profile of proportionality 0.84/0.16 (intermediate/deep) and for a deeper 0.6/0.4 regeneration profile. The intermediate-depth [PO4−3] for the deeper regeneration profile is consistently 0.4 μM lower than that of the standard profile. This permits simulation of glacial observations for intermediate-depth Atlantic [PO4−3] with lower overturning rates. However, nearly the same intermediate-depth Atlantic [PO4−3] difference for the two different regeneration profiles occurs in the interglacial control (Figure 9). Thus a deeper regeneration profile does not cause a major increase in the efficiency of nutrient depletion by the hypothesized meridional overturning cell.
 The intermediate-depth Atlantic [PO4−3] decrease to ∼1 μM for 30 Sv of intermediate water formation is associated with essentially no change in intermediate-depth Atlantic δ13C from its interglacial control value of 0.7‰ (Figure 10), signifying a δ13Cas decrease of ∼1‰. Without any overturning, the intermediate-depth Atlantic has a much lower δ13Cas in the glacial base case than in the interglacial control (lower δ13C despite similar [PO4−3], Figure 10). This is to be expected. The transition from the interglacial control to the glacial base case involves the removal of high-latitude advective inputs into the intermediate-depth Atlantic (Figure 5b) so that the Atlantic intermediate-depth box in the glacial base case is largely ventilated from the low-latitude Atlantic surface, which is warmer and thus has a lower δ13Cas. However, the δ13Cas of Atlantic intermediate water continues to decrease as the meridional overturning cell is spun up and the intermediate-depth Atlantic fills up with water from the (cold, 4°C) high-latitude North Atlantic. This can be seen from the ratio of δ13C: [PO4−3] change with increased overturning, which is roughly 0.5:1 (Figure 10 (solid squares)), rather than the 1:1 expected from nutrient-related behavior.
 This δ13Cas decrease relative to the interglacial control is mainly due to the limitation of gas exchange equilibration with rapid overturning (Figure 11). As the transport of water in the overturning cell increases, cold high-latitude North Atlantic surface waters have progressively less time to exchange carbon dioxide with the atmosphere. At 10 Sv of overturning the residence time of water in the high-latitude North Atlantic surface box is <6 years. For comparison, the results of Lynch-Stieglitz et al.  suggest a response time for surface ocean δ13C of 10 years for a surface layer that is only one third the thickness of our North Atlantic surface box (150 m). Thus it is not surprising that the δ13C of high-latitude North Atlantic surface water will decrease with increased overturning.
 The prescribed values for the areas, temperatures, and gas transfer velocities of the low-latitude and high-latitude Atlantic surface boxes affect the degree to which δ13C changes depart from nutrient-like behavior. For instance, if we assume a 4°C decrease in global surface ocean temperature (excluding the Antarctic surface box, which is already at 0°C) and twice the standard gas exchange rate for the high-latitude North Atlantic surface box, progressively increasing the cell overturning rate causes the δ13C of the intermediate-depth Atlantic to increase by 1.25‰, as its [PO4−3] decreases by 1 μM (Figure 10 (open squares)). However, because the intermediate-depth Atlantic has such a low δ13C in the glacial base case, the net intermediate Atlantic δ13C change from interglacial conditions to 30 Sv of intermediate-depth overturning is still ∼0.4‰ lower than expected for nutrient-like behavior (Figure 10).
 In summary, at the high rates of overturning required to produce the observed nutrient depletion in the intermediate-depth Atlantic, δ13C underestimates this nutrient decrease. This disagreement with observations [e.g., Lynch-Stieglitz and Fairbanks, 1994] suggests that nutrient depletion at intermediate depth in the Atlantic was not caused by the very rapid circulation (∼20 Sv) of an intermediate-depth cell within the Atlantic [Broecker, 1993]. In addition, such a rapid overturning rate for this intermediate-depth cell would require a tripling of low-latitude biological export production in the low-latitude Atlantic; again available paleoceanographic data do not support this prediction [François et al., 1990; Ruhlemann et al., 1996, 1999].
3.3. Experiment 3: NAIW Export
 In this experiment we consider an intermediate-depth circulation scheme with a source region in the North Atlantic, permitting the flow of varying proportions of total NAIW formation directly into the intermediate-depth boxes of the other basins (an intermediate-depth “conveyor”; Figures 2d (dashed lines) and 5e). Intermediate water formation (IWF in Figure 5) feeds both the intermediate-depth closed cell (ICC in Figure 5) and the intermediate-depth whole ocean conveyor (IOC in Figure 5). These changes are carried out on the glacial base case (i.e., no NADW formation). For the case where intermediate water export (IOC) is zero, this experiment is identical to experiment 2.
3.3.1. Effects on the Atlantic Basin
 While NAIW formation promotes a change in the intermediate-to-deep [PO4−3] gradient within the Atlantic, export of this intermediate water causes a basin-to-basin [PO4−3] gradient (Figures 12a–12c). This basin-to-basin gradient is driven by the export of phosphate at intermediate depths and its subsequent accumulation in the Indo-Pacific, where the water returns to the surface. NAIW export is highly efficient at lowering intermediate-depth Atlantic [PO4−3], allowing glacial observations for intermediate-depth Atlantic [PO4−3] (∼1 μM) to be met at total formation rates as low as 3 Sv (Figure 12a). This rate represents a lower estimate for NAIW export needed to drive nutrient depletion in that neither this experiment nor any of the experiments started from the glacial base case have any ventilation of the intermediate-depth Atlantic by AAIW; allowing for nutrient-rich AAIW to flow into the Atlantic increases the NAIW export rate required to lower intermediate-depth Atlantic [PO4−3] to 1 μM to 5 Sv or more (results not shown). Nevertheless, this is still dramatically lower than the rate of ≥20 Sv required by closed cell overturning alone (see experiment 2, section 3.2). While the amount of intermediate water export strongly controls the [PO4−3] of the Atlantic, the amount of intermediate water formation, not its downstream routing, determines the Δ14C of the intermediate-depth Atlantic (Figure 12b). This difference between [PO4−3] and Δ14C reminds us that intermediate-depth [PO4−3] is not a reliable indicator of ventilation rate.
 Whereas δ13C departs from nutrient-like behavior in response to intermediate water formation (see experiment 2, section 3.2), it conforms to nutrient-like behavior in response to intermediate water export (Figure 12d). At lower formation rates the δ13Cas of intermediate water reflects improved gas exchange equilibration in the high-latitude North Atlantic surface so that glacial intermediate-depth Atlantic δ13C more closely approximates nutrient-related behavior (Figure 3). Thus an overturning cell that exports water out of the Atlantic reproduces glacial δ13C observations much more readily than does a cell that is confined to the Atlantic. The export of NAIW can lower intermediate-depth Atlantic [PO4−3] to 1 μM with an order of magnitude lower formation rate than if no export is allowed (3 Sv versus 30 Sv; Figure 13 (solid and open squares, respectively)). Moreover, the δ13C: [PO4−3] ratio of change is much greater with NAIW export.
 While intermediate water export helps to raise the δ13C of the intermediate-depth Atlantic toward nutrient-like behavior, it is still not adequate in isolation. The δ13C of the intermediate-depth Atlantic can be further increased by (1) increasing the mixing between the intermediate-depth Atlantic and the high-latitude North Atlantic surface box (as in experiment 1.2; Figure 13 (diamonds)), (2) by cooling the global ocean surface (by 4°C in Figure 13 (triangles)), and (3) by increasing the gas exchange rate for the boreal surface (to twofold modern in Figure 13 (circles)), all of which lower the effective equilibration temperature of NAIW. These last steps are taken not because we attribute much significance to them but, rather, because they illustrate that the residual discrepancy between observations and simulated changes lies well within uncertainties pertaining to past physical conditions.
 Observations suggest that the deep Atlantic remained nutrient depleted relative to the deep Pacific during the last and preceding glacial periods [Boyle and Keigwin, 1982]. With only mixing fluxes between the Atlantic and the other basins (as in experiment 2) the deep Atlantic [PO4−3] is maintained very close the global deep ocean average of ∼2.3 μM. While the deep ocean gradient may have been maintained by some glacial NADW export, model experiment 3 demonstrates that intermediate water export also provides a mechanism for generating a deep Atlantic/Pacific nutrient gradient during the last ice age (Figures 12c). Thus the export of newly formed NAIW to other basins represents an efficient mechanism for both lowering intermediate-depth Atlantic nutrient concentrations and developing a deep Atlantic/Pacific nutrient gradient.
 The export of intermediate-depth Atlantic water to the Indo-Pacific works to enrich, not deplete, the intermediate-depth nutrient burden of the Pacific (Figure 12c). The [PO4−3] increase is due to nutrient trapping in the Pacific, where part of the exported water must upwell in order to return to the Atlantic as surface water (Figure 5e). It is not an artifact of an arbitrary choice among possible routes of Atlantic intermediate water export. For instance, if intermediate-depth Atlantic water export were routed through the deep Antarctic and/or through surface Antarctic boxes in order to feed intermediate-depth boxes in other basins, rather than bypassing these boxes as we do here, nutrient levels rise even more dramatically in the intermediate-depth Indo-Pacific as export increases (results not shown). Thus the export of intermediate-depth Atlantic waters to the Pacific, in its own right, is not a feasible explanation for global intermediate-depth nutrient depletion during the last ice age. Indeed, the Indo-Pacific constraint seems to limit the amount of allowable NAIW export to relatively low rates (∼7 Sv or less; Figure 12b). This rate is at the extreme lower end of the estimates from radionuclide data [Marchal et al., 2000; Yu et al., 1996] but fits very well with the geostrophy-based estimate [Lynch-Stieglitz et al., 1999a, 1999b].
 Despite the Indo-Pacific PO4−3 enrichment caused by NAIW export, with 3 Sv of NAIW formation and export the [PO4−3] of the intermediate-depth North Pacific is 2.5 μM, which is still slightly lower than the [PO4−3] of 2.7 μM in the model's interglacial control. This is due to the fact that the transition from the interglacial control to the glacial base case itself drove a significant Indo-Pacific intermediate-depth nutrient depletion, with the [PO4−3] of the intermediate-depth North Pacific dropping from 2.7 in the interglacial control to 2.1 μM in the glacial base case (Figure 6). What aspect of the circulation in the glacial base case is responsible for this nutrient depletion?
 Nutrients are constantly being lost from the upper and intermediate-depth ocean by the rain of organic detritus that survives into the abyss. In the modern ocean these nutrients are resupplied to the upper ocean by the conversion of nutrient-rich Antarctic surface water into AAIW and Subantarctic Mode Water, which in turn supply nutrients to the low-latitude surface. In the glacial base case this transport is shut off (Figure 5b), leading to a net depletion of nutrients in the global intermediate-depth ocean (Figure 6).
 While this change may, at first, appear to be an unwanted side effect of shutting off NADW-driven overturning, it may relate directly to actual conditions in the glacial ocean [Toggweiler and Carson, 1995]. It has been hypothesized that the Antarctic surface was more strongly stratified than it is today and that the concentration of nutrients in the glacial Antarctic surface was lower as a result [François et al., 1997; Sigman et al., 1999]. Such a condition might have involved a decrease in the Ekman circulation that today drives the conversion of Circumpolar Deep Water into Antarctic surface water and then of Antarctic surface water into intermediate water [Keeling and Visbeck, 2001; Sigman and Boyle, 2000, 2001; Toggweiler et al., 1999]. A decrease in the formation rate of AAIW (or Subantarctic Mode Water) and/or a decrease in the nutrient concentration of polar and subpolar Southern Hemisphere surface waters would have reduced the supply of nutrients to the intermediate-depth Indo-Pacific, leading to less nutrient trapping, a decrease in the nutrient concentration of the intermediate-depth Indo-Pacific, and an increase in its O2 content.
4. Summary and Concluding Remarks
 For glacial Atlantic intermediate water to have been low in [PO4−3] and high in δ13C a circulation scheme is required that includes communication of the intermediate depths with both the low-latitude surface (which strips out nutrients) and the high-latitude surface (which raises the δ13C of DIC by equilibration at low temperature). One circulation scheme that fits this requirement is an overturning cell composed of high-latitude intermediate water formation, equatorward advection, low-latitude upwelling, and a poleward return flow at the surface.
 However, nutrient trapping appears to limit the degree of intermediate-depth nutrient depletion that this type of overturning cell can cause. Because of nutrient trapping, if the cell circulates within the Atlantic alone, very high rates of intermediate water formation (≥20 Sv) appear to be required to cause the observed degree of nutrient depletion in the intermediate-depth glacial Atlantic.
 Glacial δ13C data may prohibit this “closed Atlantic cell” because a very high rate of intermediate water formation does not provide polar surface waters adequate time to equilibrate with the atmosphere at cold temperatures, which causes δ13C to substantially underestimate the degree of intermediate-depth nutrient depletion. This is contrary to comparisons of δ13C and Cd data for the glacial intermediate-depth Atlantic [Lynch-Stieglitz and Fairbanks, 1994; Marchitto et al., 1998]. An additional problem with a very rapidly spinning cell is that it would imply very high rates of nutrient-driven low-latitude biological production, which paleoceanographic data do not support [François et al., 1990; Ruhlemann et al., 1996, 1999].
 The export of newly formed North Atlantic Intermediate Water to other basins represents an efficient mechanism for lowering intermediate-depth Atlantic nutrient concentrations. At lower formation rates the δ13Cas of intermediate water reflects better gas exchange equilibration in the cold high-latitude North Atlantic surface so that glacial intermediate-depth Atlantic δ13C more closely approximates nutrient-related behavior and glacial observations.
 With North Atlantic Intermediate Water export, intermediate-depth Atlantic nutrient depletion is balanced by nutrient enrichment of the intermediate-depth Pacific. However, even with Atlantic intermediate water export sufficient to produce the observed nutrient depletion in the Atlantic, the intermediate-depth Pacific remains moderately depleted in PO4−3 relative to the model's interglacial control, in apparent agreement with paleoceanographic evidence [Altabet et al., 1995; Behl and Kennett, 1996; Boyle, 1992; Ganeshram et al., 1995; Herguera et al., 1992; Keigwin, 1998; Keigwin and Jones, 1990; Matsumoto, 2002; Pride et al., 1999]. In the model this PO4−3 depletion is due to the introduction of the glacial base case, in which the formation of Antarctic Intermediate Water is eliminated, as part of the elimination of the modern North-Atlantic-Deep-Water-based “conveyor”. Following Michel et al. , we suggest that nutrient depletion of the Southern Ocean surface in regions of intermediate water formation and/or a decrease in the formation rate of Southern-Ocean-derived intermediate water may have caused the apparent intermediate-depth nutrient depletion of the glacial Indo-Pacific [Sigman and Boyle, 2000, 2001; Spero and Lea, 2002].
 The hypothesis of intermediate-depth overturning cells during glacial times has been a popular idea [e.g., Broecker, 1993] and was the target of this study when we began it. However, it has become an increasingly common view that neither deep nor intermediate waters rise to the low-latitude surface at a significant rate [Schmitz, 1995]. Rather, it now seems more likely that waters of the cold sphere come to the surface largely in polar and subpolar regions. There, eddy mixing and warming can incorporate them into the warm sphere of the ocean [Gnanadesikan, 1999]. Our results essentially support this view, indicating that the previously hypothesized single-basin meridional overturning cell [e.g., Broecker, 1993] leads to anomalous relationships between [PO4−3] and δ13C that do not resemble apparent conditions in the glacial ocean. The North Atlantic Intermediate Water that fits glacial observations must be routed past the low-latitude Atlantic and into the Southern Ocean or beyond.
Appendix A:: Generalized Intermediate Water Formation
 Nutrient trapping is a generic consequence of the interaction between biological export production and the overturning circulation. In this Appendix we use a simplified four-box model of the ocean, composed of a low-latitude surface box maintained at 0 μM [PO4−3], a high-latitude surface box with a [PO4−3] that we prescribe, and intermediate-depth and deep boxes with [PO4−3] determined by the interplay of circulation and the production/regeneration cycle. Using this model, we simulate an intermediate-depth overturning cell with a source region in the high-latitude surface ocean (Figure A1). High-latitude surface water is allowed to sink and flow into the intermediate-depth box, where it upwells into the surface box and returns to high latitudes at the surface. The [PO4−3] of high-latitude surface water is controlled by allowing biological production to vary so as to maintain the prescribed concentration. For different values of preformed [PO4−3] we monitor intermediate-depth [PO4−3] as a function of the overturning rate (Figure A2). At high rates of flow through the overturning cell, high-latitude surface [PO4−3] may fall below the prescribed value because of large contributions of phosphate-free water from the low-latitude surface box. To prevent this from occurring, we maintain the phosphate supply by assigning a high deep/polar surface mixing rate (60 Sv). While this is clearly unrealistic, it allows us to focus on the specific effects of preformed [PO4−3] and the overturning rate on intermediate-depth [PO4−3].
 If the high-latitude surface is prescribed to be nearly phosphate free, intermediate-depth [PO4−3] decreases sharply over a 10 Sv increase in intermediate water formation (Figure A2). However, the nutrient depletion caused by a given amount of intermediate water formation weakens as the prescribed [PO4−3] of the high-latitude surface is increased. At a high-latitude surface with a prescribed [PO4−3] above 0.4 μM, intermediate-depth [PO4−3] actually increases with formation rate. This change in the nutrient impact of intermediate water formation from nutrient depletion to nutrient enrichment is a symptom of “nutrient trapping.” Nutrient trapping is the concentration of nutrients in the upwelling arm of intermediate-depth circulation by the coupling of nutrient-driven biological production in surface waters and by the regeneration of the biogenic flux in the shallow subsurface.
 The importance of nutrient trapping depends on the depth profile of organic matter regeneration in the subsurface. The degree of nutrient trapping decreases when we assume a “deeper” regeneration profile, for instance, in which 60% of export production is regenerated at intermediate depths as opposed to the standard case value of 84%. Under these conditions the switch to increasing intermediate-depth [PO4−3] associated with the increasing formation rate of intermediate water occurs at a higher prescribed high-latitude surface [PO4−3] of ∼0.9 μM (results not shown). By comparison, the standard interglacial values for [PO4−3] in the high-latitude North Atlantic surface and in the Antarctic surface are 0.55 μM and 1.62 μM, respectively [Bainbridge, 1976]. Thus nutrient trapping is a potentially important process, even under conditions that favor the loss of [PO4−3] from intermediate depths, so it cannot be dismissed as an artifact of the standard regeneration profile.
 These results show that vigorous intermediate water formation will not always produce nutrient depletion. An overturning cell of the above geometry could have driven nutrient depletion in the glacial intermediate-depth Atlantic only if its surface source region was nutrient poor. As described in experiment 2, even when the nutrient-poor high North Atlantic surface is the source for intermediate water formation, nutrient trapping limits the nutrient depletion caused by a meridional overturning cell.
 The experiment also offers perspective on the observation of higher mid-depth [O2] and lower nutrient content in the eastern Pacific Ocean [e.g., Behl and Kennett, 1996; Keigwin and Jones, 1990] and northern Indian Ocean [e.g., Altabet et al., 1995; Boyle et al., 1995] during glacial times. This change has previously been explained as the result of enhanced deep or intermediate water formation during cold periods [Behl and Kennett, 1996]. However, the model results indicate that enhanced formation of a water mass with significant preformed nutrients would have not effectively lowered mid-depth nutrient content or increased mid-depth [O2]. Alternatively, reduced coastal upwelling rates may have caused the apparent increase in mid-depth [O2] in the eastern tropical North Pacific [Ganeshram et al., 2000; Herbert et al., 2001]. However, the observation of higher mid-depth [O2] in all of the major zones of ocean suboxia during the last ice age (the eastern tropical North Pacific, the eastern tropical South Pacific, and the Arabian Sea [Altabet et al., 2002; Ganeshram et al., 2000]) suggest a global mechanism. This model experiment indicates that the preformed nutrient concentration of ventilating intermediate waters, rather than the ventilation rate, is the dominant control on intermediate-depth concentrations of nutrients and O2. Thus there should be a strong connection between the nutrient status of polar regions and the biogeochemistry of the lower-latitude intermediate-depth ocean [Sigman and Boyle, 2000]. For instance, the reduction in water column denitrification noted in the eastern tropical Pacific and Arabian Sea during glacial times [Altabet et al., 1995; Ganeshram et al., 2000] may have been driven, ultimately, by reduced nutrient concentrations in the Southern Ocean surface, where AAIW forms. The reduced nutrient content of the water feeding the intense upwellings in these regions would have reduced export production and the associated nutrient trapping, resulting in lower subsurface [PO4−3] and higher subsurface [O2].
 This work was supported by NSF grants OCE-9981479 and OCE-0081686 to D.M.S. and by British Petroleum and Ford Motor Company through the Princeton Carbon Mitigation Initiative.