At the Last Glacial Maximum (LGM; ∼20,000 years ago), atmospheric carbon dioxide levels were 80–90 ppm lower than preindustrial values [Neftel et al., 1982; Monnin et al., 2001]. Because more than 90% of the combined oceanic, atmospheric and terrestrial carbon resides in the deep ocean, this reservoir is believed to play a primary role in regulating atmospheric CO2 on glacial-interglacial timescales [Broecker, 1982; Sigman and Boyle, 2000]. Since publication of the “Harvardton Bears” box models, it was realized that nutrient utilization and overturning rate in Southern Ocean deep water are two of the key controls on atmospheric CO2 levels [Knox and McElroy, 1984; Sarmiento and Toggweiler, 1984; Siegenthaler and Wenk, 1984]. Toggweiler  refined this view when he speculated that reduced mixing between deep water masses formed in the Southern Ocean and the North Atlantic also helped sequester atmospheric CO2 during glacial times. Vertical mixing, overturning rate, nutrient status, and volume of the glacial southern source deep water are all thought to be important controls in regulating pCO2.
 Deep ocean nutrient tracers δ13C and Cd/Ca provide a relatively clear picture of the water mass distribution in the LGM Atlantic. Benthic δ13C shows that the deep ocean was more isotopically stratified during the LGM (Figure 1) [Boyle and Keigwin, 1982; Curry and Lohmann, 1982; Duplessy et al., 1988; Kallel et al., 1988; Herguera et al., 1992; Keigwin, 2004; Curry and Oppo, 2005; Oppo and Lehman, 1993]. The distribution of δ13C in the Atlantic has been explained by invoking changes in transport of Antarctic Bottom Water (AABW) relative to North Atlantic Deep Water (NADW) [Duplessy et al., 1988; Curry and Oppo, 2005]. However, tracers like δ13C also respond to variations in water mass mixing, variations in surface air-sea fluxes, and nonconservative behavior. In this paper, we use δ18O and δ13C data in an attempt to better quantify the relative roles of transport, vertical mixing, and remineralization in the abyssal Atlantic.
 Efforts to reconstruct the deep circulation using δ13C may be hindered by the fact that δ13C is a nonconservative tracer; its distribution is affected not only by the ocean circulation but also the biological remineralization of organic matter. Organic carbon created by phytoplankton in the surface ocean is depleted in its 13C/12C ratio relative to dissolved inorganic carbon (DIC). As organic matter falls through the water column, remineralization at depth produces 13C-depleted DIC that is incorporated in the shells of benthic foraminifera. This process masks the effect of circulation and mixing on the δ13C tracer field. A conservative tracer, that is, one which is influenced only by transport and mixing, is needed if one is to attempt a reconstruction of the deep ocean circulation from tracer profiles.
 The stable oxygen isotopic ratio of foraminifera (δ18Oc) varies as a function temperature and the δ18O of seawater, which is directly related to salinity. Because both temperature and salinity are conservative tracers, so too is δ18Oc. In the upper ocean, δ18Oc can be used as a proxy for seawater density because both parameters have a linear dependence on temperature and salinity [Lynch-Stieglitz et al., 1999]. In the deep ocean, however, this relationship breaks down because seawater density varies nonlinearly with temperature. Furthermore, the δ18O-seawater relationship can vary between water masses and on glacial-interglacial timescales [Zahn and Mix, 1991]. Instead of estimating paleo-densities for the abyss, here we simply exploit the conservative nature of δ18Oc. Once δ18Oc is set at the surface, the value is conserved by a water parcel as it moves into the ocean interior; δ18Oc can only be modified by mixing and transport. A minor caveat is that in situ temperature recorded by foraminifera is not truly conservative because it can be changed through compressive effects. However, this effect is negligible for the present study as we show below.
1.1. The δ18O Evidence for an Abyssal Water Mass Boundary
 The strong vertical gradient in North Atlantic Ocean benthic foraminiferal δ13C is a well-known feature of the LGM ocean. Less well recognized is that LGM benthic δ18O (we use δ18O as shorthand for δ18Oc for the remainder of the paper) profiles also have a larger gradient with water depth than today (Figure 2). At the Brazil Margin (30°S), the change in Cibicidoides δ18O between 1 and 3 km was approximately 0.3‰ larger during the LGM (Figure 2a) [Curry and Oppo, 2005]. The δ18O gradient is most easily observed in the difference between LGM and Holocene profiles (Figure 2b). The larger LGM gradient also exists in δ18O data from the Blake Ridge (30°N), where it is observed in two genera of benthic foraminifera, Cibicidoides and Uvigerina (Figure 2d). At each location, the LGM-Holocene δ18O pattern is driven by a larger increase in LGM δ18O below ∼2 km. Similar patterns have been observed in the Indian [Kallel et al., 1988] and Pacific Oceans [Herguera et al., 1992] suggesting the LGM “step” in δ18O may have been a global feature.
1.2. Diagnosing the Transport to Mixing Ratio From Tracer Distributions
 A detailed analysis of the processes that influence δ18O is necessary to identify what generates the observed differences in the LGM and modern data. The distributions of tracers in the ocean are set through a balance between advection (e.g., by the overturning circulation), air-sea fluxes at the surface, and mixing in the ocean interior. The overturning circulation of AABW in the Atlantic Ocean is associated with sinking of water through convection around Antarctica and a return flow at shallower levels. The properties of AABW are set by surface fluxes near Antarctica and mixing with overlying waters in the ocean interior. Air-sea fluxes have been used to estimate water mass transport in the present climate [Schlosser et al., 1991; Speer and Tziperman, 1992; Large and Nurser, 2001], but this type of data is lacking in the paleoclimate record. Instead, we infer the ratio between meridional transport and vertical diffusivity in the abyss from tracer distributions. AABW is uniquely suited to this approach because it does not outcrop north of Drake Passage and it is only modified through mixing with other water masses.
 Reconstructing the ocean circulation from tracer distributions is often necessary when tracer data are more readily available than velocity measurements. Using the inverse approach, Wunsch  shows how to combine tracer measurements to constrain ocean circulation with least square techniques: the larger the set of measurements, the smaller the uncertainty on the inferred circulations and fluxes. Inversions with available LGM data from the Atlantic have been used to evaluate whether the modern circulation is the same as the past [LeGrand and Wunsch, 1995; Gebbie and Huybers, 2006; Marchal and Curry, 2008]. Here we acknowledge that the data are too sparse to uniquely constrain the LGM circulation field and we set a more modest goal. We instead evaluate which transport to vertical mixing ratio for AABW is consistent with the available δ18O data. We assume that the few available profiles are representative of an entire basin and evaluate the implications. This exercise is informative because it highlights the key factors that influence δ18O and δ13C profiles in the modern and LGM Atlantic. The question of whether our results apply to the entire Atlantic Ocean will have to wait until more stable isotopic profiles are available. A recent inverse calculation for the LGM Atlantic by Marchal and Curry  focused on estimating the consistency of LGM data with the modern circulation. Our analysis differs from this work in two important ways. First, we only attempt to constrain the ratio of Ψ/κ for the glacial southern source water mass, not the circulation of the entire basin. Second, we explicitly consider vertical mixing in our analysis whereas the previous work treated this term implicitly as an error in the tracer budget. Overall our goal is less ambitious than a full tracer inversion, but our data set is also more limited. We see these two approaches as complimentary in the goal to better understand the role of the deep ocean in glacial-interglacial climate change.