The conversion of dissolved nutrients and carbon to organic matter by phytoplankton in the surface ocean, and its downward transport by sinking particles, produces a “biological pump” that reduces the concentration of atmospheric CO2. Global rates of organic matter export are a poor indicator of biological carbon storage however, because organic matter gets distributed across water masses with diverse pathways and timescales of return to the surface. Here we show that organic matter export and carbon storage can be related through a sequestration efficiency, which measures how long regenerated nutrients and carbon will be stored in the interior ocean before being returned to the surface. For the first time, we derive global maps of the sequestration efficiency of the biological pump at different residence time horizons. These maps reveal how regional patterns of organic matter export contribute to the biological pump, and how the biological pump responds to changes in biological productivity driven by climate change.
 The ocean's carbon reservoir exceeds chemical equilibrium with the atmosphere because the deep ocean is a repository for CO2 and nutrients released during the decomposition of organic matter falling from the surface ocean. Diagnostic calculations [e.g., Ito and Follows, 2005] reveal that while deep ocean nutrients are partly derived from regenerated organic matter, a comparable fraction is transported from surface waters where limitations on plankton growth prevent complete nutrient consumption. These “preformed” nutrients do not contribute to biological carbon storage, implying that the biological pump is not operating at maximum efficiency. Changes in the efficiency of the biological pump, as measured by the fraction of nutrients in the regenerated pool, therefore have the potential to alter ocean carbon storage and atmospheric CO2 over time [Sigman and Boyle, 2000; Ito and Follows, 2005; Marinov et al., 2008a, 2008b].
 The fact that no quantitative relationship has been demonstrated between the rate of organic matter export and the efficiency of the biological pump represents a significant shortcoming in our understanding of the global carbon cycle, and our ability to link changes in ocean productivity and atmospheric CO2. Indeed, it is often noted that global rates of organic matter export can increase even while the efficiency of the biological pump decreases [Matsumoto, 2007; Marinov et al., 2008a; Kwon et al., 2011]. This ambiguity stems from the fact that organic matter settling out of the euphotic zone may be stored for as little as months or as long as a millennium before returning to the surface, depending on where the export occurs and the depth at which it is regenerated.
 Here we show that the strength of the biological pump can be related directly to the rate of organic matter export, Φex, by considering the sequestration efficiency(τ|r) of regenerated nutrients. (τ|r) is equal to the proportion of nutrients regenerated from organic matter exported out of the euphotic zone below point r that remain sequestered below the surface for a period τ or longer (see methods and Figure S1 in the auxiliary material). The inventory of regenerated nutrients can be expressed as a convolution of with Φex, allowing the biological pump efficiency Ebio to be expressed as
where Itot is the ocean's nutrient inventory, a is the ocean surface area and t is calendar time. Ebio varies between 0 (no biological pump) and 1 (perfectly efficient biological pump). Equation (1)is strictly valid for the case of steady circulation but can be generalized to the case of non-stationary flow. The advantage of expressingEbio, a globally integrated metric, using equation (1)is that it provides a direct connection to the time-dependent export production on regional scales.
2. Temporal and Spatial Dependence of the Sequestration Efficiency
 We estimated using a data-constrained ocean circulation and biogeochemistry model (seeAppendix A). By construction, = 1 everywhere at τ = 0. As τincreases, upwelling and eddy-diffusion return nutrients to the surface where they are removed from the regenerated pool (seeAppendix B), so that → 0 as τ → ∞. At τ = 1 year, some regions have lost as much as 50% of the initial pool of regenerated nutrients (Figure 1). Such low sequestration efficiencies are associated with regions of persistent upwelling or rapid vertical exchange, for example, along the northern flank of the Gulf Stream, in the Peru and Benguela upwelling systems, and in some parts of the Southern Ocean. By τ = 10 years the highest sequestration efficiencies are found in subtropical gyre regions where remineralized nutrients are downwelled by Ekman convergence. At τ = 100 years, the areas which feed the deep ocean circulation increasingly stand out, with exceeding 50% in areas where North Atlantic Deep Water and Antarctic Bottom Water are produced. Sequestration efficiencies over most of the rest of the ocean have dropped to around 10–30% after 100 years. By τ= 1000 years, only small amounts of regenerated nutrients remain, mainly originating from regions of deep convection in the Labrador Sea and Greenland-Iceland-Norwegian seas in the North Atlantic, and from the Weddell Sea in the Southern Ocean. A small proportion of the regenerated nutrients derived from organic matter exported from these regions is transported into the deep limb of the global overturning circulation, where it is sequestered for more than a thousand years.
3. Mean Sequestration Time and Regional Biological Pump Efficiencies
where is the mean sequestration time of regenerated nutrients originating from organic matter sinking out of the euphotic zone below r. Figure 2 shows estimated using our data-constrained model, revealing a structure similar to that shown in the longer timescales ofFigure 1. Maximum mean sequestration times of 400+ years are found in the high-latitude deep-water formation regions of the North Atlantic and Southern Ocean. Mean sequestration times generally decrease away from these regions. In the North Atlantic, there is a gradual transition from regions of high sequestration efficiency in the polar regions to regions of low sequestration efficiency in the tropics (except near the Gulf Stream region where the transition is abrupt) (Figure 2b). By contrast, the transition between regions of high- and low-sequestration times in the Southern Ocean is well-defined and abrupt. Waters along the Antarctic coast in the Weddell Sea (Figure 2c), and to a lesser extent the Ross Sea, have very high sequestration times, while elsewhere Southern Ocean waters have some of the lowest sequestration times of any open ocean waters (<100 years). Short sequestration times in the Southern Ocean are associated with strong Ekman upwelling that returns deep waters to the surface [Toggweiler and Russell, 2008], while the long sequestration times are associated with deep convection along the Antarctic margin [Marinov et al., 2006]. Deep convection does not occur in the Pacific and Indian Oceans, so mean sequestration times in these ocean basins are relatively uniform at ∼100–200 years, with longer sequestration times associated with areas of sub-tropical mode water formation and the poorly-ventilated shadow zone in the Arabian Sea.
 In the contemporary ocean, the distribution of mean sequestration times (Figure 2) and organic matter export rates is such that regenerated nutrients are supplied mainly by organic matter exported from the sub-polar and tropical regions (Figure 3a) (see Appendix B). However, these regions only export enough organic matter to account for about half of the total nutrient inventory, such that Ebio= 0.5 in the data-constrained model. The remaining 50% of nutrients are preformed nutrients supplied by waters ventilated primarily in the Southern Ocean, and to a lesser extent the North Atlantic (Figure 3a).
 The efficiency of the biological pump for a particular oceanic region can be expressed as the ratio of the total amount of regenerated nutrients supplied to the interior ocean by organic matter export within that region, to the sum of the regenerated and preformed nutrients delivered to the interior ocean from that region. This calculation reveals that the biological pump is inefficient at high latitudes, with efficiencies of 0.1–0.4 in polar regions, and that efficiencies increase to near 1 in the tropics (Figure 3b). The global efficiency of the biological pump (0.5) reflects a balance between nutrients supplied from high-efficiency regions (mainly the tropics) and nutrients supplied from low-efficiency regions (primarily the Southern Ocean). Sub-polar regions also supply significant amounts of nutrients (Figure 3a), with biological pump efficiencies near the global mean (Figure 3b).
 The view of regional biological pump efficiency derived here is different from that derived using interior distributions of regenerated nutrients [e.g., Williams and Follows, 2011]. Because nutrients are transported and mixed within the ocean, interior nutrient distributions reflect non-local biological processes, and therefore do not reflect the efficiency of the biological pump acting in surface waters in that region. This can be seen by comparing the efficiencies calculated here with those calculated from the ratio of regenerated to total nutrients in the model (Figure 3b). In regions where a single locally-ventilated water mass dominates, such as near the Antarctic margin or in the North Atlantic, the two approaches give approximately the same efficiency. But in regions where water masses mix, such as the equatorial regions, the regional efficiencies inferred from the two approaches diverge (Figure 3b). Efficiencies calculated using interior nutrient distributions tend to reflect the basin-scale average efficiency (around 0.4 in the Atlantic and 0.6 in the Pacific), while efficiencies calculated using organic matter export rates and sequestration efficiencies reflect local surface biological efficiency.
 At the global scale the two approaches should in principle yield the same biological pump efficiency, since all regenerated nutrients in the interior ocean are derived from organic matter exported from the surface ocean. In practice, interior distributions of regenerated nutrients are often calculated from the observed apparent oxygen utilization (AOU) using constant stoichiometries [e.g., Ito and Follows, 2005]. Thus the difference between the globally-integrated biological pump efficiency estimated here (Ebio = 0.5) and a previous estimate (Ebio = 0.36) based on AOU [Ito and Follows, 2005] is due to errors in the estimation of regenerated nutrients by the two methods, including uncertain stoichiometry of organic matter in the case of estimates based on AOU, and errors in the circulation and remineralization rates in the case of the model-based estimate (see discussion in theauxiliary material).
4. Biological Pump Response to Long-Term Changes in Organic Matter Export
 On long time horizons the strength of the biological pump, as measured by the inventory of regenerated nutrients [Ito and Follows, 2005; Marinov et al., 2008a, 2008b], is governed by the mean sequestration time of regenerated nutrients, and the mean rate of organic matter export (see equation (2)). Over glacial-interglacial cycles, variability in organic matter export rates may be driven by variability in aeolian iron deposition [Martin, 1990; Wolff et al., 2006] or by variability in the ocean's total nutrient inventory [Ganeshram et al., 1995; Falkowski, 1997; Ganeshram et al., 2000, 2002]. Here we explore how the strength of the biological pump responds to changes in organic matter export rates in a series of idealized simulations (see Appendix C). We maintain a constant circulation and therefore constant sequestration efficiency, although this is also likely to change over time due to changes in surface winds and buoyancy forcing.
 An idealized simulation of the effects of iron deposition is obtained by depleting surface nutrients to varying levels (Figure 4a). For slow nutrient uptake rates (τb= 5 years) associated with strong iron limitation, the biological pump is inefficient and the delivery of regenerated nutrients is relatively constant by latitude. As nutrient uptake rates increase, more regenerated nutrients are delivered by organic matter exported from the Southern Ocean, the tropics, and the sub-Arctic regions. Forτb≲ 45 days, surface nutrients are completely consumed and the biological pump reaches maximum efficiency. In this case nutrients are consumed directly where they are upwelled, showing that the majority of ocean waters upwell in the Southern Ocean, the tropics, and in the sub-Arctic (mainly the North Pacific) [DeVries and Primeau, 2011]. The biological pump response to variations in total nutrient inventory is somewhat different (Figure 4b). As in the nutrient depletion scenario (Figure 4a), the response is most pronounced in the Southern Ocean. However, the response is also significant in the tropics and the sub-Arctic, suggesting that these regions may be important drivers of variability in the biological pump over glacial-interglacial cycles if the cycles are accompanied by large changes in the ocean's nutrient inventory.
 A traditional paradigm holds that the efficiency of the biological pump is controlled by the preformed nutrient content of the ocean [Sigman and Boyle, 2000; Ito and Follows, 2005; Marinov et al., 2008a, 2008b]. This view is useful for quantifying how bulk changes in oceanic nutrient concentrations affect atmospheric CO2 concentrations [Ito and Follows, 2005; Marinov et al., 2008a, 2008b], but cannot be used to describe how the biological pump responds to regional changes in the rate of organic matter export. Here we proposed an alternate view based on the idea that the inventory of regenerated nutrients in the ocean can be expressed as the convolution of the organic matter export rate with a sequestration efficiency function . This sequestration efficiency is spatially variable, reaching maximum values in areas of deep convection where the densest water masses are formed. For the contemporary ocean, we find that biological pump efficiencies are highest in the tropics and lowest in the polar regions, with intermediate efficiencies in the sub-polar regions. Assuming modern-day sequestration efficiency patterns continue to hold, the response of the biological pump to changes in organic matter export is likely to be dominated by the Southern Ocean, with secondary contributions from the tropical and sub-Arctic regions.
Appendix A:: Data-Constrained Circulation and Biogeochemistry Model
 The model resolution is 2 degrees in the horizontal with 24 vertical levels. The circulation is steady-state and is meant to represent a climatological mean ocean circulation [DeVries and Primeau, 2011]. The model has been fit to climatological temperature, salinity, and natural radiocarbon distributions using an adjoint method as described elsewhere [DeVries and Primeau, 2011]. We have extended this work to include a simple biogeochemistry model for the production and remineralization of particulate organic phosphate, and adding the 2009 World Ocean Atlas gridded phosphate concentrations [Garcia et al., 2010] as an additional observational constraint. Export production is modeled by restoring to observed phosphate in the top two model layers wherever modeled PO4 is greater than observed PO4 with a timescale τb = 30 days,
Organic matter exported out of the euphotic zone is assumed to remineralize in the interior ocean following a power-law relationship [Martin et al., 1987],
where the compensation depth zc = 73 m, which corresponds to the top two layers of the model. The attenuation coefficient b is determined as part of the solution to the inverse model, and b = 0.82 at the optimal solution. The globally integrated rate of export production in the model is 9.4 × 1012 mol P yr−1. Comparison between model-simulated and observed PO4 is given in the auxiliary material (Figure S2).
Appendix B:: Preformed and Regenerated Nutrients
 For purposes of this study all nutrients in the production zone above the compensation depth zc (hereafter, “surface nutrients”) are considered preformed nutrients. At steady state, the inventory Ipref of preformed nutrients in the ocean can be expressed as the convolution of the surface nutrient concentration and the boundary propagator Green function (r),
where c is a generic nutrient (phosphate in our model). represents the volume of the interior ocean (below the euphotic zone) ventilated per unit surface area at point r, and has units of meters [Primeau, 2005]. The total amount of nutrients in the ocean is the sum of the preformed and regenerated components, , where the regenerated nutrient inventory at steady state is given by the numerator in equation (2)
Changing the limits of integration in (B1) and (B2) from the whole ocean to an arbitrary region of the surface ocean yields the total amount of preformed or regenerated nutrients delivered to the interior ocean from that particular region, as in Figure 3.
Appendix C:: Production Scenarios
 Nutrient depletion experiments (Figure 4a) were performed by setting PO4obs(r) = 0 in equation (A1) and varying the biological uptake timescale τb from 5 years to 45 days. The total amount of nutrients in the ocean was kept constant at modern levels for these experiments. To simulate the effect of adding or removing nutrients from the ocean (Figure 4b) we retained the production parameterization of equation (A1) but varied the total phosphate inventory from 50% to 150% of the modern inventory.
 Constructive comments from two anonymous reviewers helped improve the paper. Funding for this research was provided by NSF grant OCE-1131548 and NSF grant OCE-1131768.
 The Editor thanks two anonymous reviewers for assisting in the evaluation of this paper.