Abyssal Atlantic circulation during the Last Glacial Maximum: Constraining the ratio between transport and vertical mixing

Authors


Abstract

[1] The ocean's role in regulating atmospheric carbon dioxide on glacial-interglacial timescales remains an unresolved issue in paleoclimatology. Reduced mixing between deep water masses may have aided oceanic storage of atmospheric CO2 during the Last Glacial Maximum (LGM), but data supporting this idea have remained elusive. The δ13C of benthic foraminifera indicate the Atlantic Ocean was more chemically stratified during the LGM, but the nonconservative nature of δ13C complicates interpretation of the LGM signal. Here we use benthic foraminiferal δ18O as a conservative tracer to constrain the ratio of meridional transport to vertical diffusivity in the deep Atlantic. Our calculations suggest that the ratio was at least twice as large at the LGM. We speculate that the primary cause was reduced mixing between northern and southern component waters, associated with movement of this water mass boundary away from the zone of intense mixing near the seafloor. The shallower water mass boundary yields an order of magnitude increase in the volume of southern component water, suggesting its residence time may have increased substantially. Our analysis supports the idea that an expanded volume of Antarctic Bottom Water and limited vertical mixing enhanced the abyssal ocean's ability to trap carbon during glacial times.

1. Introduction

[2] 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 [1999] 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.

[3] 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.

Figure 1.

Contour map of benthic foraminiferal δ13C for the Western Atlantic during the Last Glacial Maximum [Curry and Oppo, 2005]. The strong vertical gradient in δ13C could be due to (1) enhanced remineralization of organic carbon at depth, (2) greater transport of AABW relative to northern component water, (3) reduced mixing between AABW and northern component water, or (4) some combination of these effects.

[4] 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.

[5] 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

[6] 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.

Figure 2.

(a) Brazil Margin Cibicidoides spp. δ18O (solid circles) [Curry and Oppo, 2005], outliers (open circles), and interpolated data points (crosses). Outliers are defined as those values which exceed the mean δ18O from adjacent water depths by more than ±0.3‰. Interpolated values are based on linear interpolation between data points at adjacent water depths. (b) Brazil Margin LGM-Holocene δ18O. (c) Blake Ridge Cibicidoides spp. δ18O (solid circles) [Keigwin, 2004], outliers (open circles), and interpolated data points (crosses). Also included are Uvigerina spp. δ18O (gray triangles) [Keigwin, 2004]. (d) Blake Ridge LGM-Holocene δ18O. Using a Student t test and assuming a threshold two-sided p value of 0.05, we are able to reject the null hypothesis that the shallow and deep LGM-Holocene δ18O data are sampled from the same population (p ≅ 0.005 for Brazil Margin Cibicidoides sp., p ≅ 0.0005 for Blake Ridge Cibicidoides sp., and p ≅ 0.02 for Blake Ridge Uvigerina sp.). This result is not surprising given that LGM-Holocene δ18O data above 2 km fall in the upper left-hand quadrant of each plot, while the deeper data fall in the lower right-hand quadrant.

1.2. Diagnosing the Transport to Mixing Ratio From Tracer Distributions

[7] 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.

[8] 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 [1996] 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 [2008] 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.

2. Methods

2.1. Tracer Budget for δ18O

[9] In this section, we provide an abbreviated description of the tracer budget for δ18O and δ13C. The full derivation is given in Appendix A. Our tracer budget encompasses the volume of water below a surface of constant tracer concentration, as shown in Figure 3, departing from the traditional approach that considers volumes below a fixed depth. The advantage is that the net amount of tracer flowing into such a volume from the south can only be balanced by mixing of tracer across the upper surface. By construction, the mean circulation advects tracer into the volume from the south, but it cannot flux tracer across a contour. Consider the conservative tracer δ18O. At the order of magnitude level, the transport of δ18O from the south is given by the maximum of the zonally averaged overturning circulation, Ψ (m3 s−1), multiplied by the difference in tracer at the top and bottom of our control volume, Δδ18O (‰). The transport of tracer into the South Atlantic is balanced by mixing with overlying waters giving

equation image

where the right hand side represents the diffusion of tracer expressed as a turbulent diffusivity, κ (m2 s−1), times the vertical tracer gradient at the upper boundary of AABW, δ18Oz (‰ m−1), and A is the area across which mixing occurs (m2). The scaling factor of 2/3 accounts for the fact that the top of our control volume corresponds to the maximum overturning stream function and therefore our budget does not include southward advection out of the Atlantic (see Appendix A). It is useful to rearrange the budget so that quantities that can be estimated from observations are on the right hand side and unknowns are on the left:

equation image

In other words, we can describe the ratio of tracer transport (Ψ) to vertical mixing of tracer (κ) using vertical gradients in the δ18O profiles, the vertical difference Δδ18O, and the area of the δ18O isosurface. By comparing the modern and LGM estimates of this ratio, we can evaluate the relative importance of transport to vertical mixing through time.

Figure 3.

Two-dimensional representation of the transport and mixing of a generic tracer (C) in the abyssal Atlantic. In reality, the tracer surface varies in three dimensions. The tracer budget is computed for volumes north of 27°S and below a constant tracer value. Cz is the vertical tracer gradient at the upper lid of AABW, and ΔC is the difference in C between the tracer surface and the seafloor. A conservative tracer like δ18O is affected by transport (Ψ) from the Southern Ocean (solid arrow) and vertical mixing (κ) with overlying waters. The horizontal dashed arrow represents transport of northern component water. A nonconservative tracer like δ13C is also affected by J, the remineralization of organic matter (dashed vertical arrow). Our approach depends on tracer distributions in the ocean interior (gray areas) distant from the water mass outcropping region near Antarctica.

[10] Our tracer budget approach is similar to W. Munk's local balance between upwelling and mixing in his classic paper “Abyssal Recipes” [Munk, 1966]. We differ from this approach by balancing the total transport of tracer within a water mass against mixing with other waters. In essence, we swap local upwelling (w, m/s) and mixing (κ, m2/s) for the integrated volume transport (Ψ, m3/s) and the mixing integrated over the whole upper ‘lid’ of the water mass (Aκ, m4/s). This difference is crucial, because a local vertical balance rarely holds in the ocean.

2.2. Tracer Budget for δ13C

[11] The budget describing the distribution of δ13C in the abyssal Atlantic (Figure 3) differs from that of δ18O in that it has the additional contribution of a biological remineralization term, J (‰ s−1), multiplied by the volume into which the remineralization occurs, V (m3):

equation image

where Δδ13C is the difference in δ13C between water entering the South Atlantic and δ13C of the upper ‘lid’ of AABW, defined as the maximum in the overturning stream function. δ13Cz is the gradient in δ13C at the upper boundary of AABW. In this equation, we place the sink terms on the left-hand side of the equation, and the source term on the right. Ψ is positive and acts as a sink of 13C/12C for the abyssal cell, because incoming AABW has a low 13C/12C ratio. J is also a sink, as organic matter is strongly depleted in 13C. The diffusive term is a source, since mixing with northern component water adds dissolved inorganic carbon with a higher 13C/12C ratio than AABW. Dividing through by the diffusive flux and rearranging the terms, we obtain:

equation image

where h is the vertical extent of the volume considered, that is, V = Ah. The first term is a bulk Peclet number, Pe, the nondimensional ratio of tracer transport to tracer diffusion. We use a bulk Pe because we focus on the zonally integrated advection (i.e., transport) of tracer. Pe can be estimated using Ψ/κ from the δ18O tracer budget and Δδ13C and δ13Cz derived from the δ13C profiles. With substitution we see that Pe is only dependent on the tracer distribution and not the volume or the area. The nonconservative term J can only make Pe smaller. In section 3, we evaluate modern and LGM δ18O and δ13C profiles that sample southern source water. We also check that our tracer balance for the modern ocean gives a value of Ψ that is consistent with other estimates. In section 4 we evaluate the Ψ/κ and Pe values implied by these results and comment on their implications.

3. Results

3.1. Modern δ18O Budget

[12] Does the δ18O tracer budget described above yield reasonable Ψ/κ values for the modern AABW circulation in the Atlantic? To answer this question, we first need to outline the δ18O domain for our analysis. Ideally, the δ18O surface that defines our control volume should coincide with the upper boundary of AABW. Here we define the upper boundary for AABW as the neutral density surface γ = 28.15 kg/m3, which ranges from 3000 to 4000 m water depth in the South Atlantic and corresponds to the maximum vertical salinity gradient (Figure 4). The γ = 28.15 kg/m3 surface coincides with the maximum overturning stream function in the abyssal South Atlantic; the net flow of water below γ = 28.15 kg/m3 is northward, while flow above γ = 28.15 kg/m3 is primarily southward [Lumpkin and Speer, 2007]. For consistency with the LGM budget, we set the southern edge of our domain at 27°S, the approximate latitude of the Brazil Margin cores [Curry and Oppo, 2005].

Figure 4.

(top) Salinity section along 30°W in the Atlantic Ocean. The contour interval is 0.02 salinity units. The largest vertical gradient in salinity in the deep Atlantic between 30°S and the equator exists from 3800 to 4300 m water depth, the approximate location of the upper boundary for AABW. (bottom) Neutral density section along 30°W in the Atlantic Ocean. The maximum vertical salinity gradient corresponds to a neutral density surface γ = 28.15 kg/m3 (dashed line), which also marks the maximum overturning stream function for the South Atlantic [Lumpkin and Speer, 2007]. Salinity and neutral density data are from the WOCE Global Hydrographic Climatology [Gouretski and Koltermann, 2004].

[13] Today, AABW sits below the deepest core sites at Brazil Margin. As a result, our modern δ18O budget must rely on estimates of the equilibrium δ18O of calcite calculated from temperature and seawater δ18O data. We created a data set of gridded calcite δ18O based on the δ18O of seawater database [LeGrande and Schmidt, 2006], in situ temperatures from the WOCE Global Hydrographic Climatology [Gouretski and Koltermann, 2004] and a paleotemperature equation [Kim and O'Neil, 1997] modified for an acid-fractionation factor of 1.0105. Sections of equilibrium δ18O of calcite for the western and eastern Atlantic are shown in Figure 5. The Atlantic AABW end-member has δ18O values ≥ 3.12‰ while the NADW end-member has δ18O values ≤ 3.00‰. Because δ18O is conservative, the maximum vertical gradient in δ18O (δ18Oz) should mark the approximate boundary between AABW and NADW.

Figure 5.

Contoured map of zonally averaged δ18O for the (top) eastern Atlantic and (bottom) western Atlantic. The gridded data set was created using a δ18O of seawater database [LeGrande and Schmidt, 2006], WOCE Global Hydrographic Climatology temperatures [Gouretski and Koltermann, 2004], and a paleotemperature equation [Kim and O'Neil, 1997] adjusted for an acid fractionation factor of 1.0105. Delta18O values exceeding 3.08‰ exist primarily in the southwestern Atlantic where the influence of AABW is most pronounced.

[14] We calculated δ18Oz for all grid points north of 27°S using δ18O estimates from immediately above and below a given δ18O horizon, over a span of 500 m water depth. A plot of δ18Oz across δ18O surfaces from 3.00‰ to 3.20‰ is shown in Figure 6. The maximum in δ18Oz occurs for values between 3.06‰ to 3.10‰. These δ18O surfaces track very closely the γ = 28.15 kg/m3 surface and provide an objective method to identify the upper boundary of AABW in the Atlantic from δ18O profiles. Figure 6 also shows the vertical gradient in potential temperature and salinity across the δ18O isosurfaces, calculated using the WOCE Global Hydrographic Climatology [Gouretski and Koltermann, 2004]. We take vertical differences across 250 m, the resolution of the climatology. The maximum vertical gradients in T and S correspond to the maximum in δ18Oz, confirming that δ18O acts as a conservative tracer that tracks the upper boundary of AABW. We choose δ18O = 3.08‰ to define our modern control volume for AABW. This δ18O surface has an average δ18Oz of (−3.1 ± 0.8) × 10−4‰ m−1 (±1σ) (Figure 7). The δ18O surfaces ranging from 3.06‰ to 3.11‰ have similar δ18Oz values (Figure 6).

Figure 6.

(top) The vertical gradient in δ18O, (middle) potential temperature, and (bottom) salinity across δ18O isosurfaces ranging from 3.00‰ to 3.20‰. One-sigma standard deviations are given as dashed lines. Temperature and salinity data are from the WOCE Global Hydrographic Climatology [Gouretski and Koltermann, 2004]. The maximum δ18Oz occurs between δ18O values of 3.06‰ and 3.11‰.

Figure 7.

(top) Contour map of the vertical δ18O gradient (δ18Oz) at δ18O = 3.08‰. This δ18O surface spans the southwestern Atlantic. (bottom) Histogram of δ18Oz values along the δ18O = 3.08‰ surface in the southwestern Atlantic. The mean δ18Oz value for this δ18O surface is −3.1 × 10−4 ‰ m−1.

[15] We calculated Δδ18O for the modern by subtracting the δ18O values nearest the seafloor at 27°S from the δ18O value = 3.08‰ chosen for the upper boundary of our control volume. A cross section of modern δ18O at 27°S, the southern limit of our circulation cell, is shown in Figure 8. At this latitude, there are 21 separate 1° longitude bins across the western Atlantic where the δ18O value at the seafloor exceeds 3.08‰. We calculated Δδ18O for each bin separately, and then took the average to calculate a Δδ18O of −0.09 ± 0.01‰. If instead we focus on the intense flow along the western boundary where most of the tracer flux occurs, Δδ18O = −0.15 ± 0.01‰. To cover these two different options, we use an intermediate Δδ18O value with an error that encompasses both (−0.12 ± 0.04‰).

Figure 8.

Contoured cross section of δ18O at 27.5°S in the southwest Atlantic. The δ18O values are contoured in 0.02‰ increments from 3.00 to 3.20‰. We calculated Δδ18O by subtracting the δ18O values nearest the seafloor from 3.08‰. Δδ18O is larger if the calculation is limited to the western boundary, where the majority of tracer fluxes into our control volume (see text for details).

[16] Using our estimates of δ18Oz and Δδ18O and the tracer budget for δ18O (equation (2)), we estimate Ψ/κ = (1.8 ± 0.8) × 1010 m for the modern δ18O surface = 3.08‰ (Table 1). We obtain similar Ψ/κ estimates for δ18O surfaces ranging from 3.06‰ to 3.11‰. Assuming a κ for the deep Atlantic of (3 ± 1.5) × 10−4 m2 s−1 [Ganachaud and Wunsch, 2000], then the tracer-derived AABW transport at 27°S is 5.5 ± 3.7 Sv (1Sv = 1 × 106 m3 s−1). We obtain a similar Ψ if we use an estimate of κ for the Brazil Basin at the approximate depth of the γ = 28.15 kg/m3 surface ((3.3 ± 2.4) × 10−4 m2 s−1) [Morris et al., 2001]. Our tracer-based estimates of Ψ agree with geostrophic estimates: 6.7 ± 0.5 Sv at 31°S and 5.0 ± 1.1 Sv at 24°S [Speer and Zenk, 1993]. Thus, the δ18O tracer budget provides a reasonable approximation of the modern Ψ for AABW in the Atlantic.

Table 1. Parameters for Modern Tracer Budget
Tracer SurfaceVertical Gradienta (×10−4 ‰ m−1)Vertical Differenceb (‰)Ratioc (m)Area (×1012 m2)Ψ/κ (×1010 m)Pe
  • a

    Vertical gradients are δ18Oz and δ13Cz.

  • b

    Vertical differences are Δδ18O and Δδ13C.

  • c

    Ratios are Δδ18O/δ18Oz and Δδ13C/δ13Cz.

δ18O = 3.08‰−3.1 ± 0.8−0.12 ± 0.04390 ± 1604.7 ± 0.51.8 ± 0.8 
δ13C = 0.70‰4.8 ± 1.00.24 ± 0.05510 ± 1504.7 ± 0.51.4 ± 0.41.3 ± 0.7

3.2. LGM δ18O Budget

[17] The first step in outlining the LGM tracer budget involves defining the domain for AABW in the Atlantic. We use three vertical profiles of δ18O for this task, one from the Brazil Margin [Curry and Oppo, 2005] and two from the Blake Ridge [Keigwin, 2004]. Similar to the modern, we can use δ18O to identify the upper boundary of AABW at the LGM. Cibicidoides data from above 2000 m water depth at the Blake Ridge suggest that the northern component end-member had a δ18O signature of ≤4.0‰ (Figure 2a). Data from below 2000 m water depth at the Brazil Margin indicate that the southern component end-member had a δ18O signature of ≥4.5‰ (Figure 2c). Given that δ18O is a conservative tracer, the maximum in δ18Oz should mark the boundary between northern and southern component waters during the LGM.

[18] Our estimates of δ18Oz are based on a Monte Carlo approach. We first assign a 1σ calibration error of ±0.18‰ to each LGM data point to account for the scatter observed in regressions between core top foraminiferal δ18O and predicted δ18O based on in situ temperature and seawater δ18O [Marchal and Curry, 2008]. This is likely a conservative error given that field-based calibrations reflect not only vital effects, but also the use of nonmodern core tops and spatial and temporal variability in water column properties. We generate 1000 surrogate vertical profiles where every δ18O value is sampled from a Gaussian distribution with the observed mean value and a standard deviation of 0.18‰. For each profile, we calculate δ18Oz by fitting a line to data spanning an 800 m water depth range, and vary the center point of the range from 1500 m to 2700 m. The depth spacing of deep cores at the Blake Ridge precludes use of a water depth range less than 800 m.

[19] The maximum δ18Oz occurs at δ18O values of 4.4‰ for the Cibicidoides sp. data at both the Brazil Margin and the Blake Ridge, suggesting that the upper boundary of AABW in the Atlantic was defined by this value (Figure 9). A similar structure is observed for the Uvigerina sp. data at Blake Margin, but with an offset in absolute δ18O which is likely due to vital effects [Keigwin, 2004]. Thus, the basic structure of the LGM water column profiles is resilient to the large scatter induced by a ±0.18‰ calibration error for δ18O. This result strongly suggests there was a water mass boundary near 2 km water depth at the LGM, and that this boundary was defined by a δ18O of 4.4 ± 0.1‰. The medians of each δ18Oz distribution overlap at 1σ: (−0.9 ± 0.2) × 10−3, (−1.0 ± 0.3) × 10−3, and (−1.0 ± 0.3) × 10−3 ‰/m for Brazil Cibicidoides, Blake Cibicidoides, and Blake Uvigerina, respectively (Table 2). We use an average of all three (Figure 10, top) in our calculation of Ψ/κ for the LGM.

Figure 9.

Probability density functions from the Monte Carlo results of δ18Oz as a function of δ18O for the LGM data. These contour plots show that the water mass boundary at ∼4.4‰ between northern and southern source waters at the LGM is a robust feature of the data even when an error of 0.18‰ is added to each data point. Cibicidoides sp. data at (top) the Brazil Margin and (middle) the Blake Ridge is shown with each peak at ∼4.4‰. (bottom) Uvigerina sp. data at the Blake Ridge and peak at ∼4.9‰. The offset in δ18O between the species is most likely due to vital effects.

Figure 10.

(top) Probability density function of the average δ18Oz for the three LGM δ18O profiles. (middle) Probability density function of Δδ18O at the Brazil Margin. (bottom) Probability density function of Δδ18O/δ18Oz for the LGM data. We plot Δδ18O/δ18Oz instead of δ18Ozδ18O because division by Δδ18O values close to zero creates infinitely large ratios. The peak in the Δδ18O/δ18Oz PDF overlaps with the average of Δδ18O/δ18Oz for the modern δ18O surface of 3.08‰ (solid vertical line; 390 ± 160 m).

Table 2. Parameters for LGM Tracer Budgeta
 Vertical Gradientb (×10−4‰ m−1)Vertical Differencec (‰)Ratiod (m)Area (×1012 m2)Ψ/κ (×1010 m)Pe
  • a

    Domain of AABW at LGM spanned from 27°S to 60°N and from the 2000 m isobath to the seafloor, a volume of ∼1 × 1017 m3. For the modern, AABW spans from 27°S to the equator and from 4000 m to the seafloor, a volume of ∼5 × 1015 m3.

  • b

    Vertical gradients are δ18Oz and δ13Cz.

  • c

    Vertical differences are Δδ18O and Δδ13C.

  • d

    Ratios are Δδ18O/δ18Oz and Δδ13C/δ13Cz.

δ18O = 4.4‰
Brazil (Cib)−8.7 ± 2.4−0.46 ± 0.23530 ± 25045 ± 913 ± 7 
Blake (Cib)−9.9 ± 3.1     
Blake (Uvi)−10.2 ± 3.1     
Average−10.0 ± 1.7−0.46 ± 0.23440 ± 23045 ± 916 ± 9 
 
δ13C = 0.6‰
Brazil (Cib)10.0 ± 2.01.14 ± 0.251140 ± 34045 ± 96 ± 22.2 ± 1.2
Blake (Cib)14.0 ± 3.2     
Average12.0 ± 2.01.14 ± 0.25930 ± 25045 ± 97 ± 32.1 ± 1.3

[20] The difference in δ18O between water entering the South Atlantic and the upper boundary of AABW at 27°S (Δδ18O) is the largest source of uncertainty in calculating Ψ/κ for the LGM. Although the upper value is well constrained, there are no δ18O data below 3000 m water depth at the Brazil Margin. To estimate δ18O of AABW entering the Atlantic, we extrapolate the linear trend in δ18O from 2000 to 3000 m water depth to 4500 m, yielding a bottom value of 5.0 ± 0.2‰. In the modern South Atlantic, δ18O increases linearly all the way to seafloor, supporting our assumption for the LGM. If instead abyssal δ18O was nearly constant below 3000 m (δ18O ∼ 4.6‰), our estimate of Ψ/κ for the LGM would increase.

[21] We calculated Δδ18O as linear regressions between the midpoint of the maximum δ18Oz (i.e., the water mass boundary) and the bottom of the ocean at 4500 m for each of the 1000 randomly generated profiles. The median Δδ18O is −0.46 ± 0.23‰ (Figure 10, middle), and the Δδ18O/δ18Oz ratio peaks at 440 ± 230 m (Figure 10, bottom). The LGM Δδ18O/δ18Oz ratio is statistically indistinguishable from the modern ratio (390 ± 160 m; Table 1). We plot Δδ18O/δ18Oz instead of δ18Ozδ18O because division by Δδ18O values close to zero creates infinitely large ratios.

3.3. Modern δ13C Budget

[22] To evaluate Pe for the modern Atlantic it is necessary to calculate δ13Cz and Δδ13C. Our estimates of these parameters are derived from WOCE and Ocean-Atmosphere Carbon Exchange Study (OACES) δ13C profiles (Figure 11). We estimate the budget for δ13C = 0.70‰ which approximately follows the δ18O = 3.08‰ surface. We calculated Δδ13C at 30°S using δ13C of the isosurface minus δ13C near the seafloor. Because there were no water column δ13C data below 4000 m near the Brazil site, data from 45°S to 35°S were used to estimate an abyssal δ13C value of 0.46‰ (water depths >4200 m). Together, these data yield a Δδ13C of 0.24 ± 0.05‰ (Table 1).

Figure 11.

Water column δ13C of DIC values for the western Atlantic Ocean, partitioned into 10° latitude bins. Data from 35°S to 5°N are from the Ocean Atmosphere Carbon Exchange Study (OACES; http://cdiac3.ornl.gov/las/servlets/dataset) and data from 5°N to 45°N are from World Ocean Circulation Experiment (WOCE) lines AR01, A20, and A22 (http://cchdo.ucsd.edu/atlantic.html). The influence of AABW is most prominent in the South Atlantic, where δ18C values below 4000 m approach −0.5‰. North of 15°N, the influence of AABW is barely perceptible.

[23] We calculated the gradient in δ13C (δ13Cz) across each isosurface for the latitude bins presented in Figure 11, using data from 300 m above and below the designated δ13C surface, similar to the water depth range used to calculate δ18Oz for modern AABW. We estimate a δ13Cz for the upper “lid” of AABW of (4.8 ± 1.0) × 10−4 ‰ m−1 (Table 1). The δ13Cz estimates are largest in the South Atlantic where the presence of nutrient-enriched (13C depleted) AABW is the most obvious. Our estimate of the Δδ13C/δ13Cz ratio (510 ± 150 m) is within one sigma error of the Δδ18O/δ18Oz ratio for the modern Atlantic (390 ± 160 m) (Table 1).

3.4. LGM δ13C Budget

[24] Our constraints for the LGM δ13C budget come from the Cibicidoides δ13C profiles at the Brazil Margin and Blake Ridge. As with the δ18O data, we use a Monte Carlo technique to test the robustness of our tracer budget calculation to uncertainty in the δ13C data. We estimate an RMS error of 0.14‰ for the regression between Holocene Cibicidoides δ13C and δ13C of dissolved inorganic carbon from Duplessy et al. [1984] (Figure 12). This calibration error is likely a maximum estimate, because (1) the sediment cores used in the regression lack good chronological control, meaning that the regression between dissolved inorganic carbon δ13C and benthic foraminiferal δ13C includes error associated with the unknown time offset between sediment and hydrographic data, and (2) the hydrographic data used by Duplessy et al. [1984] were sparse and required interpolation to match core locations.

Figure 12.

Scatterplot of dissolved inorganic carbon δ13C versus Holocene Cibicidoides δ13C data from Duplessy et al. [1984]. We estimate an RMS error of 0.14‰ for the regression between the two parameters. Inset shows a histogram of residual values (i.e., foraminiferal δ13C values predicted by the regression minus observed foraminiferal δ13C).

[25] Assuming a 0.14‰ uncertainty for individual δ13C points, we randomly generate 1000 δ13C profiles from these distributions. We calculate δ13Cz by fitting a line to data spanning an 800 m water depth range, and vary the center point of the range from 1500 m to 2700 m. Figure 13 shows a 2-D histogram of the vertical δ13C gradient (δ13Cz) and its corresponding δ13C for these 1000 profiles. The largest gradient occurs at similar δ13C values for each site, although the PDF is shifted toward lower δ13C at the Brazil Margin. The two sites also have similar δ13Cz values, but the pdf is shifted toward slightly higher δ13Cz at Blake Ridge. The steeper tracer gradient at Blake Ridge may reflect the greater influence of 13C-enriched northern component water at this latitude. To obtain the area averaged δ13Cz for our budget, we averaged the δ13Cz estimates from each location. The resulting values have a wide distribution with a median δ13Cz of 1.2 × 10−3‰ m−1 (Figure 14, top).

Figure 13.

Probability density function of the vertical gradient in δ13C (δ13Cz) versus δ13C where the maximum in δ13Cz occurs. At Brazil Margin, the maximum in δ13Cz occurs at δ13C values between 0.3‰ and 0.8‰. At Blake Ridge, the range is from 0.5‰ to 1.0‰. The maximum δ13Cz values are generally higher at Blake Ridge, with a median of 1.4 × 10−3‰/m, while at Brazil Margin the median is 1.0 × 10−3‰/m.

Figure 14.

(top) Average LGM δ13Cz for the Brazil Margin and Blake Ridge from Figure 13. (middle) LGM Δδ13C for the Brazil Margin based on 1000 randomly generated profiles, a calibration error of ±0.14‰, and a value at 4500 m water depth of −0.8‰ (see text). (bottom) Probability density function of Δδ13C/δ13Cz for the LGM data. The median for the LGM is 930 ± 250 m, larger than that for the modern (510 ± 150 m).

[26] The broad histogram of mean δ13Cz values can be combined with the Δδ13C data from Brazil Margin (defined as before for Δδ18O) to calculate the Δδ13C/δ13Cz ratio. We estimate a δ13C at 4500 m of −0.8 ± 0.2‰, based on linear extrapolation of the δ13C trend in shallower water. This value is in good agreement with δ13C for the abyssal southwest Atlantic [Ninnemann and Charles, 2002]. The median of the difference between δ13C at the seafloor and the top of our control volume (Δδ13C) for the LGM is 1.2‰ (Figure 14, middle). In combination with δ13Cz, this yields a median Δδ13C/δ13Cz of 930 ± 250 m (Figure 14, bottom). Although this distribution overlaps with the distribution of Δδ13C/δ13Cz for the modern, the agreement is not as good as that between the modern and LGM distributions of Δδ18O/δ18Oz (Figure 10).

4. Discussion

4.1. Modern Versus LGM Ψ/κ and Pe

[27] Our estimates of δ18Oz and Δδ18O for the LGM yield a Δδ18O/δ18Oz distribution that overlaps with modern values. However, to calculate Ψ/κ we must also account for the larger surface area over which tracer diffused into and out of AABW during the LGM (see equation (2)). The maximum in δ18Oz at δ18O ∼ 4.4‰ indicates the upper lid of AABW spanned 27°S to at least 30°N and was located at a water depth of ∼2000 m. The δ13C tracer field suggests that AABW reached 60°N in the Atlantic and encompassed both the western and eastern basins [Duplessy et al., 1988; Oppo and Lehman, 1993; Curry and Oppo, 2005]. The area of the horizontal surface in the Atlantic Ocean from 27°S to 60°N along the 2000 m isobath is approximately 4.5 × 1013 m2 (Table 2). If AABW reached to only 50°N during the LGM, its area would have been 4.3 × 1013 m2, about 10% lower. By comparison, the area of the upper lid of AABW in the modern Atlantic is (4.7 ± 0.5) × 1012 m2. Therefore, the area of AABW was about an order of magnitude larger at the LGM. Accounting for the difference in surface area, we estimate that Ψ/κ was approximately eight times larger at the LGM.

[28] The considerable errors for both our Ψ/κ estimates make it difficult to precisely determine the change in Ψ/κ from LGM to modern. We can, however, estimate the minimum difference between the two climate states. The smallest possible Ψ/κ for the LGM is set by the largest possible Δδ18O/δ18Oz ratio, or 1200 m (Figure 10, bottom). Using this value yields a minimum Ψ/κ for the LGM of 5.7 × 1010 m. Because the minimum estimate of the LGM Ψ/κ is at least two times the modern value, either the LGM transport was larger than today, the vertical mixing less, or some combination of the two. We explore the likelihood of these scenarios below. Given that the Δδ18O/δ18Oz histogram also includes values near zero, the upper limit for Ψ/κ during the LGM is unconstrained by the available data.

[29] By adding δ13C to the tracer budget we can assess how the larger Ψ/κ ratio affected the bulk Pe defined in equation (4). One of the long standing issues in paleoceanography is whether the glacial δ13C tracer field primarily reflects the biological remineralizaton of organic matter or the physical circulation of the ocean. In principle, we should be able to partition the influences of remineralization and circulation on δ13C using the tracer budget. As outlined in the methods, we can estimate a Peclet number for δ13C (the ratio of δ13C transport to δ13C diffusion) using parameters from the δ13C profiles (Δδ13C and δ13Cz) and Ψ/κ derived from the δ18O tracer budget. If Pe = 1, then the diffusive and transport fluxes balance, and the remineralization flux is negligible. When Pe < 1, the tracer displays nonconservative behavior because remineralization influences the budget. For example, a Pe of 0.5 would indicate that ∼50% of the diffusive flux is balanced by remineralization. Pe values above 1 indicate the tracer inventory is out of balance.

[30] Using our estimates of δ13Cz, Δδ13C, and the Ψ/κ from the δ18O budget, we calculate a Pe of 1.3 ± 0.7 for modern AABW (Table 1). The advective flux of δ13C appears to be largely balanced by the diffusive flux. If this is correct, δ13C is essentially conservative and it can be used to independently estimate Ψ/κ. Our δ13C-based Ψ/κ estimate of 1.4 ± 0.4 × 1010 m is very similar to the δ18O-dervived value (Table 1). However, at 1σ the minimum Pe also suggests that remineralization may account for up to 40% of the δ13C sink for the abyssal Atlantic. Our results also includes Pe values >1, which would indicate the tracer inventory is out of balance and that we have not accounted for all of the important fluxes.

[31] For the LGM, our estimates of Δδ18O/δ18Oz and Δδ13C/δ13Cz yield a Pe of 2.1 ± 1.3 (Table 2). Similar to the modern, Pe spans a range of values above and below 1. Assuming a Pe ∼ 1, the δ13C-derived Ψ/κ would be (7.3 ± 2.5) × 1010 m, within error of the δ18O-derived value of (16 ± 9) × 1010 m. The agreement is not as good as for the modern, however. Overall, the LGM Pe estimates span over a higher range of values, suggesting the LGM budget may be imbalanced. Given that Pe values >1 imply we have not fully accounted for all the fluxes of tracer, it is important to ask where there are likely sources of error in our analysis. In section 4.2 we consider the uncertainties in the tracer balances.

4.2. Sources of Error in the Tracer Budgets

4.2.1. Along Isopycnal Mixing Into the Control Volumes

[32] The full budget for δ18O outlined in Appendix A includes contributions from mixing both across (κ) and along isopycnal surfaces (κiso). Our tracer budget includes only cross-isopycnal mixing in the estimate of the Ψ/κ ratio, an acceptable approximation if isolines of δ18O are parallel to lines of constant density. The additional along isopycnal mixing that arises if the isosurfaces are not parallel is negligible only if

equation image

where sc is the slope of the tracer surface (sc = horizontal δ18O gradient/vertical δ18O gradient) and sρ is the slope of the density surface at the same point. The difference ∣scsρ∣ is approximately equal to the along isopycnal tracer gradient divided by the vertical tracer gradient. In the modern Atlantic, we define the upper boundary of AABW using the neutral density surface γ ∼ 28.15 kg/m3 or equivalently the δ18O = 3.08‰ surface. The median δ18Oz across this surface is −2.9 × 10−4‰ m−1 (Figure 15, top). We estimate δ18Oy at each grid point using δ18O values immediately to the north and south (given a grid spacing of 1°, δ18Oy is calculated over 2° latitude). The median along isopycnal gradient is 1.5 × 10−8‰ m−1 (Figure 15, bottom). Together these yield ∣scsρ∣ ≈ 5 × 10−5. Using equation (5) and typical diffusivities, κiso = O(1000) m2/s and κ = O(10−4) m2/s [Stammer, 1998; Ledwell et al., 1998], we find that the along-density diffusion of δ18O is ∼40 times smaller than the cross-density diffusion and can be neglected for the modern case.

Figure 15.

(top) Histogram of the vertical gradient in δ18O (δ18Oz) across the neutral density surface γ = 28.15 kg/m3 in the modern Atlantic. Nearly all of the values are negative, meaning δ18O increases with depth. The median δ18Oz is 2.9 × 10−4‰ m−1. (bottom) Histogram of the along isopycnal gradient in δ18O (δ18Oy) where γ = 28.15 kg/m3. Values are both positive and negative, meaning fluxes are into and out of the control volume. We use the median (1.5 × 10−8‰ m−1) to yield the largest tracer slope (sc) for evaluating along versus across isopycnal diffusion of δ18O (see text).

[33] Given that we have no direct constraints on the abyssal density field in the geologic past, we can only speculate about along isopycnal mixing of δ18O and δ13C at the LGM. We assume that isopyncals in the deep Atlantic were nearly horizontal north of 30°S, as they are today (Figure 4). Available stable isotope data for the LGM suggest the δ18O isolines were nearly horizontal as well. The LGM boundary between southern and northern component waters occurred at 4.4 ± 0.1‰, or 2000 ± 200 m water depth at the Brazil Margin (∼30°S) and Blake Ridge (∼30°N). Today, δ18O surfaces that bound the upper lid of AABW (3.05–3.10‰) vary by up to 1 km over the same latitude range (Figure 5). It is therefore plausible that both sc and sρ were small at the LGM and along isopycnal diffusion of δ18O played a negligible role in the tracer budget. For both today and the LGM, along-isopycnal diffusion of δ18O into AABW appears to be important only in the Southern Ocean, where AABW comes to the surface and tracer and density slopes become very steep. The Southern Ocean, however, is south of our tracer budget domain.

[34] While along isopycnal mixing is not important for δ18O, it may be an issue for δ13C because it has a different spatial distribution. Using δ13C values at the approximate depths of the neutral density surface γ ∼ 28.15 in the modern ocean, we estimate a δ13Cz of ∼5 × 10−4‰ m−1 (Table 1) and an along-isopycnal δ13C gradient of ∼5 × 10−8‰ m−1 (a 0.2‰ increase over 60° latitude; Figure 16). Together, this yields ∣scsρ∣ ≈ 1 × 10−4. These values suggest the along-isopycnal diffusion of δ13C is ∼10% of the diapycnal diffusion in the modern Atlantic. Therefore, along-isopycnal mixing seems to be a minor term in the modern δ13C tracer budget.

Figure 16.

Plot of δ18O (circles) and δ13C (crosses) versus latitude along the neutral density surface γ = 28.15. To estimate the δ13C values, we determined the approximate depth of γ = 28.15 in each latitude bin of Figure 11 and used the δ13C at that water depth. We estimate an along isopycnal gradient of 5 × 10−8‰ m−1 for δ13C, approximately twice the horizontal gradient for δ18O.

[35] Along isopycnal mixing may play a more significant role in the budget for δ13C at the LGM. The contrast in δ13C between northern and southern component waters at the LGM (∼2.5‰) was more than twice the δ18O contrast (∼1‰) (Figure 17). As a result, along isopycnal mixing likely played a more important role in the tracer budget for δ13C than δ18O. Indeed, our estimate of Pe for the LGM includes values greater than 1. If in reality Pe was this large, it would indicate that we underestimated the 13C flux into our control volume. A likely candidate for this missing flux is along isopycnal mixing.

Figure 17.

(left) Water depth versus benthic foraminiferal δ13C at the LGM for the Brazil Margin (solid line) [Curry and Oppo, 2005] and Blake Ridge (dashed blue) [Keigwin, 2004]. At the Brazil Margin, we estimated δ13C below 3000 m by linear extrapolation of the 2000–3000 m trend to 4500 m. The resulting value of −0.8‰ is consistent with values of −0.8‰ from the southeast Atlantic [Ninnemann and Charles, 2002]. The maximum vertical gradient in δ13C (δ13Cz) occurs between 2500 m and 3000 m water depth. (right) Water depth versus benthic foraminiferal δ18O at the LGM for the Brazil Margin (solid line) and Blake Ridge (dashed line). At the Brazil Margin, we estimated δ18O below 3000 m by linear extrapolation of the 2000–3000 m trend to 4500 m. A lower δ18O value at 4500 m decreases Δδ18O and therefore increases Ψ/κ for the LGM. The maximum vertical gradient in δ18O (δ18Oz) occurs at ∼2000 m water depth (horizontal gray bar).

4.2.2. Other Possible Errors in the δ18O Budget

[36] In the preceding discussion, we referred to δ18O as a conservative tracer. Because benthic foraminiferal δ18O reflects in situ rather than potential temperature, it is not strictly conservative. The effect of compressive heating on the Ψ/κ estimates is small, however. In the case of the modern AABW, the pressure effect makes water entering the South Atlantic at 4500 m about 0.1°C warmer than water leaving the South Atlantic at 3500 m. Given a δ18O-T relationship of 0.2‰ per °C, the implication is that the deep δ18O value is reduced by about 0.02‰. If we adjust Δδ18O for this effect, the modern Ψ/κ estimate decreases by 11%. During the LGM, the correction is larger (0.05‰) because the upper boundary of southern component water was near 2000 m water depth. If we increase the LGM Δδ18O by 0.05‰, Ψ/κ decreases by 13%. While significant, the Δδ18O adjustments do not change our result that Ψ/κ was larger at the LGM.

[37] Our LGM budget is based on three vertical δ18O profiles, one from the Brazil Margin and two from the Blake Ridge. This is a small data set for analyzing the LGM southern source water mass, especially given that much more δ13C data has been used to make tracer maps like Figure 1. We use these locations because they are the only LGM δ18O profiles in the Atlantic which meet the following criteria: (1) the cores used to create each depth profile are from tightly constrained geographic regions, (2) the sedimentation rates in the cores are high (generally >5 cm kyr−1), (3) the core depths span most of the water depth range relevant to AABW, and (4) the stable isotope data used to create each profile was run within an individual laboratory. Running in a single laboratory is particularly important for creating high-fidelity profiles of δ18O versus water depth. Interlaboratory offsets of ∼0.3‰ for benthic δ18O [Ostermann and Curry, 2000; Hodell et al., 2003] are similar to the total range of δ18O variability in the abyssal Atlantic during the LGM. As a result, it is very difficult to make coherent maps of benthic δ18O similar to those that exist for δ13C [Zahn and Mix, 1991]. As laboratory intercalibration improves and additional depth transects from high sedimentation rate sites become available, it will be possible to test whether the few available profiles provide a reliable picture of the abyssal Atlantic δ18O tracer field at the LGM.

4.3. Comparing the δ13C and δ18O Results

[38] The discussion above makes two important points. First, the ratio of Ψ/κ at the LGM was approximately eight times larger than it is today. Second, the difference in Pe values was not nearly as large, though uncertainties in the δ13C budget make it difficult to quantify the ratio of δ13C transport to tracer diffusion. Given this analysis, it is instructive to consider the LGM stable isotope profiles (Figure 17). At 27°S, δ18O increases monotonically below the boundary between northern and southern source waters. This shape is to be expected if dense, cold, and salty waters are transported into the Brazil Basin at the LGM. By the time this water mass reaches the Blake Ridge in the Northern Hemisphere vertical diffusion has worked to homogenize the vertical δ18O profile.

[39] The structure of the δ13C profiles is fundamentally different than those for δ18O. First, the slope of the δ13C profiles is opposite that for the δ18O profiles, because the southern end-member has lower δ13C than the northern end-member. Second, the slope of the Blake and Brazil profiles is essentially identical (Figure 17). An extra flux of low δ13C works against the tendency of vertical mixing to homogenize the profile. A likely candidate for this extra flux is biological remineralization. By adding isotopically depleted DIC to the water mass continuously along its flow path, this nonconservative term has the opposite effect than diffusive mixing of isotopically enriched northern source water. That these two processes would leave the δ13C profiles roughly parallel seems like a coincidence as there is no a priori reason that mixing and remineralization should be of nearly the same size.

4.4. The Combined Roles of Transport and Vertical Mixing

[40] Our analysis of the available LGM δ18O profiles in the Atlantic shows that Ψ/κ for AABW was larger than today. Similar to the local balance between upwelling and diffusion postulated for the modern North Pacific by W. Munk (his “z*” is analogous to our Ψ/κ) [Munk, 1966], a conservative tracer can tell you the ratio of advection to diffusion, but it cannot constrain the two independently. However, we speculate that higher Ψ/κ during the LGM was due to reduced mixing between northern and southern component waters, associated with movement of this water mass boundary away from the seafloor. Today, the upper boundary of AABW sits near 4 km water depth, whereas at the LGM it was at approximately 2 km. In the modern ocean, vertical diffusivities decrease away from bottom topography [Kunze et al., 2006]. Averaged over the Atlantic, vertical mixing is approximately three times lower above 4 km water depth than below [Ganachaud and Wunsch, 2000]. In the Brazil Basin, vertical diffusivities over rough topography are an order of magnitude lower at 2 km than at the seafloor [Polzin et al., 1997]. Reduced mixing due to upward migration of the water mass boundary at the LGM is therefore consistent with the vertical profile of κ in the modern ocean, in both sign and magnitude. Our budget results suggest that reduced vertical mixing across the upper boundary of AABW may play a primary role in setting the Atlantic δ18O tracer field during the LGM. Although we cannot rule out an increase in Ψ, our point is that such an increase is not necessary to explain the tracer distribution in the abyssal Atlantic.

[41] In contrast to our mixing-based interpretation of the δ18O profiles, the large vertical gradient in δ13C at the LGM has been interpreted in terms of water mass transport alone [Duplessy et al., 1988; Curry and Oppo, 2005]. Curry and Oppo [2005] argued that steep gradients in δ13C are likely maintained by robust deep water flow, if vertical mixing was similar to or greater than today. If the increase in Ψ/κ during the LGM was entirely a function of transport, it would imply that Ψ increased by a factor of 8, a highly unlikely scenario. If instead we use the minimum Ψ/κ for the LGM, it would require a factor of 2 increase in transport. Although more feasible, this would also be a large change in the rate of AABW formation. By comparison, a factor of 2–8 reduction in vertical mixing is reasonable considering the profile of κ in the modern ocean. In reality, both vertical mixing and transport likely changed, but we believe that most of the increase in Ψ/κ at the LGM was due to decreased vertical mixing.

[42] It has been suggested that oceanic vertical mixing was enhanced at the LGM, due in part to exposure of continental shelves and greater tidal dissipation in the deep sea [Wunsch, 2003]. If tidal dissipation was confined primarily to water depths below 2 km, however, its effect on mixing across the upper boundary of AABW would have been minimal. Rather than speculate on how κ changed in the past, our scenario calls on the variability in κ with depth in the ocean. The overall shape of this profile must be similar in alternative circulation scenarios, due simply to the presence of rough topography at the bottom of the ocean.

[43] Our constraints on Ψ/κ have implications for the residence time of AABW in the Atlantic. The ∼2 km depth of the boundary between southern and northern component waters indicates the volume of AABW in the LGM Atlantic was very large. Assuming that AABW spanned from 27°S to 60°N and across the width of the Atlantic, we estimate its volume was (1 ± 0.2) × 1017 m3. For the modern δ18O surface = 3.08‰, the approximate volume of AABW is (4 ± 0.4) × 1015 m3, ∼20 times lower than our LGM estimate. If transport during the LGM was similar to the modern value, the residence time would have increased 20 times. If transport was twice that of today, the residence time for AABW would have increased by an order of magnitude. A greater residence time for AABW is consistent with glacial reconstructions of highly depleted radiocarbon values [Keigwin, 2004; Robinson et al., 2005] and low Pa/Th ratios in the abyssal North Atlantic [Gherardi et al., 2009].

[44] While our analysis of the δ18O tracer budget places new quantitative constraints on the LGM Ψ/κ ratio, we would also like to place the results in the context of glacial-interglacial CO2 variability. The Harvardton Bears box models highlighted the interdependence of nutrient utilization in the Southern Ocean and deep overturning rate in setting atmospheric pCO2 [Knox and McElroy, 1984; Sarmiento and Toggweiler, 1984; Siegenthaler and Wenk, 1984]. Less vigorous circulation and lower preformed nutrient concentrations for southern source deep water both work to lower atmospheric carbon dioxide levels. Toggweiler [1999] refined the Havardton Bears by parsing the deep ocean's role into overturning rate and the efficiency of mixing between southern and northern component deep waters. Slower overturning works to lower pCO2, but carbon and nutrients are brought into contact with the atmosphere if the two deep waters mix efficiently because northern component waters flow back to the North Atlantic via the shallow circulation (in his model at least). Reducing mixing between the deep water masses makes the southern cell a more efficient carbon trap. A lower κ allows for smaller changes in overturning strength and/or nutrient utilization to produce the same lowering of atmospheric pCO2. In this sense, the results from our δ18O budget may provide an important clue as to how the glacial deep ocean was involved in lowering atmospheric carbon dioxide levels.

5. Conclusions

[45] The δ18O of benthic foraminifera in the deep Atlantic show the presence of a water mass boundary at a depth of 2 km during the LGM, defined by a δ18O value of approximately 4.4‰. The boundary appears to outline the spatial domain of AABW and allows for the creation of a conservative tracer budget based on δ18O. Our approach accounts for transport of δ18O into the South Atlantic and vertical mixing of δ18O across the upper boundary of AABW. The δ18O budget yields reasonable estimates of AABW flow for the modern, giving us confidence that the budget captures the key factors that influence δ18O in the ocean interior, namely tracer transport and tracer diffusion. For the LGM, we find that the ratio of transport to vertical mixing (Ψ/κ) was at least twice as large as today. Either the transport was greater, the vertical mixing less, or some combination of these two factors. We suggest that the increase in Ψ/κ is most easily explained by reduced vertical mixing. Today, the water mass boundary between northern and southern component waters is located at approximately 4000 m water depth, whereas at the LGM the boundary was near 2000 m. The decrease in vertical mixing over this water depth range in the modern Atlantic (3–10 times) [Polzin et al., 1997; Ganachaud and Wunsch, 2000] is broadly consistent with the implied decrease during the LGM.

[46] Box-model experiments invoke limited AABW ventilation and vertical mixing to sequester atmospheric carbon dioxide during the LGM [Toggweiler, 1999]. In this scenario, reduced exchange between abyssal and deep water promotes the accumulation of respired CO2. If reduced vertical mixing at the upper lid of AABW sequestered significant quantities of carbon during glacial times, it should be observed outside the Atlantic Ocean as well. Preliminary δ18O evidence from the Indian [Kallel et al., 1988] and Pacific [Herguera et al., 1992] show an apparent water mass boundary at 2 km water depth, suggesting the vertical diffusivity may have been reduced on global basis. Sequestration in the abyssal ocean during glacial times also requires minimal leakage of carbon dioxide from the Southern Ocean to the atmosphere. Sea-ice coverage and stratification are other key factors that control Southern Ocean outgassing, yet there is little agreement on how the processes change on glacial-interglacial timescales [Sigman and Boyle, 2000; Keeling and Stephens, 2001].

[47] Our approach demonstrates that the abyssal Ψ/κ ratio can be constrained using a simple tracer budget and traditional oxygen stable isotope data. Because transport and vertical mixing also influence δ13C, it is likely that the strong δ13C gradient in the glacial Atlantic was driven in part by reduced mixing between northern and southern component waters. The δ13C data also suggest that remineralization may influence the evolution of the δ13C profiles from south to north. In theory, we can combine the δ13C and δ18O data to quantify the relative influence of transport, mixing, and remineralization in the abyssal Atlantic. Understanding these parameters is key to understanding the ocean's role in glacial-interglacial CO2 cycles, and will be a priority for future refinements to the tracer budget approach. In addition, it will be essential to construct new high-fidelity profiles of δ13C and δ18O to test whether the results we present here are representative of the Atlantic basin as a whole.

Appendix A:: Derivation of the Zonally Averaged Tracer Equation

[48] The evolution of the concentration of a generic tracer c released into the ocean is governed by the advection-diffusion equation,

equation image

where t is time, ∇c is the three dimensional tracer gradient, and equation image is the along density surface tracer gradient. This equation describes the evolution of c averaged over the space and timescales characteristic of ocean turbulence, that is, O(100 km) and O(1 week). At these large scales the tracer is advected by the averaged ocean circulation u and by an eddy-driven circulation ueddy: turbulent eddies result from instabilities of the mean ocean currents and their interactions produce a velocity equivalent to the Stokes drift resulting from surface gravity waves [Plumb and Ferrari, 2005]. In addition to a velocity, turbulent eddies drive diffusion of tracers along density surfaces, represented by an isopycnal eddy diffusivity κiso, and diffusion across density surfaces, represented by the diapycnal diffusivity κ. In the abyssal ocean, the isopycnal diffusivity is typically 7–8 orders of magnitude larger than the diapycnal diffusivity (103 m2/s versus 10−4 m2/s), because eddy fluxes are directed primarily along density surfaces. Fair-sea is the flux of tracer at the ocean surface and J includes any interior sources and sinks of nonconservative tracers. The tracer equation must be supplemented by boundary conditions. For the tracers considered in this paper the tracer flux across the solid boundaries is zero; the surface flux is represented explicitly by the Fair-sea term. Knowledge of a tracer concentration c, be it δ18O or δ13C, is generally not sufficient to infer the full ocean velocity field. But it can be used to infer some bulk properties of the ocean circulation, like the zonally averaged overturning.

[49] We can write an expression for the overturning circulation as a function of latitude and tracer concentration, much alike oceanographers do when they compute the overturning circulation as a function of latitude and density [Andrews, 1983; Nurser and Lee, 2004]. Consider a zonal slice of the ocean at a fixed latitude y, that is an xz section through the ocean. We define A(y, C, t) as the area of that section below a certain tracer concentration value C and we assume that the tracer is increasing toward the surface (otherwise the inequalities must be reversed),

equation image

The area A(y, C, t) can be changed either by horizontal advection of water with tracer concentration larger than C, or by nonconservative processes like diffusion, air-sea fluxes or interior sources and sinks,

equation image

and v and veddy are the meridional velocity and eddy-induced velocity. Equation (A3) can be simplified if we integrate between any latitude y and the northern or southern continental boundaries and assume steady state,

equation image

where Ψ(y, C) represents the mass meridional transport across the latitude y,

equation image

In deriving (A4), we assumed that Ψ(y, C) vanishes at the southern boundary around Antarctica.

[50] Integrating between the surface defined by the C contour and the ocean bottom, we obtain the fundamental equation for our analysis,

equation image

where n is unit vector normal to the bounding surface S, defined by the C contour. The equation can be further simplified because, in the ocean, horizontal tracer gradients are many orders of magnitude smaller than vertical gradients, that is, surfaces of constant tracer concentration are approximately flat. Expanding equation (A6) in the limit of small tracer slopes, one obtains,

equation image

where sc is the slope of the tracer surface and sρ is the slope of the density surface at the same point. Mixing of tracer across the C contour is achieved both by along- and across-density diffusion. Diapycnal diffusion dominates if

equation image

For the conservative tracer δ18O, the scsρ term is very small, as shown in the paper, and isopycnal mixing can be ignored. The situation is not as clear for δ13C.

[51] Consider now the circulation associated with AABW, that is, a circulation that does not outcrop at latitudes north of 60°S. Then the integral (A7) for latitudes north of 60°S reduces to,

equation image

For conservative tracers J = 0 and the equation has a simple interpretation. The left-hand side of (A9) represents the tracer transport across a latitude y, ΨΔC. Tracer transport can only be achieved for ΔC ≠ 0, that is, if the tracer concentration going north is different from the concentration returning south. In order for the tracer concentration to change as it goes around the overturning loop, there must be diffusion of tracer from above, the term in the right-hand side of (A9). At the order of magnitude level, equation (A9) states,

equation image

where A is the horizontal area span by the tracer surface C north of y. We dropped the along-density surface diffusion term, because in the region of interest diapycnal diffusion dominates (see section 4). The simple balance (A10) can be compared with the expression derived by W. Munk in the famous paper “Abyssal Recipes” [Munk, 1966],

equation image

This budget is consistent with (A10) if vertical upwelling is uniform and can be estimated as Ψ/A, that is, the mass flux across the surface A. However, our approach shows that the budget is not local. The balance is between lateral transports of tracer and global vertical fluxes, not between local vertical upwelling and local vertical fluxes.

[52] The budget described by equation (A9) includes tracer transport into and out of the deep South Atlantic. However, our tracer domain is specifically limited to water flowing into the South Atlantic. For the modern climate, we define this domain using the depth of the maximum overturning stream function, which corresponds to the neutral density surface γ = 28.15 kg/m3 [Lumpkin and Speer, 2007] and it is well tracked by a maximum in salinity vertical gradient (Figure 4). Paleoceanographic proxies are too sparse to fully evaluate the terms in (A9). We therefore make some simplifying assumptions about the vertical structure of Ψ and C. We assume C has a linear vertical gradient within the volume considered, that is,

equation image

where D is the thickness of AABW. The stream function is instead assumed to be quadratic in z:

equation image

where Ψ is the magnitude of the stream function (and hence of the transport) at the top of AABW and the ocean bottom is set at z = 0. This is the simplest vertical structure that gives a northward flow of AABW and a southward flow of NADW. Plugging these expressions in the first integral of equation (A9), we obtain,

equation image