3.1. Nutrient Distributions
 An example of the meridional and depth distribution of nutrients is illustrated in Figure 2, along the WOCE line P15 at 170°W in the Pacific Ocean (Figure 1). Nutrient concentrations are highest at depths of 2000–4000 m in the low-latitude South Pacific, from where they rise in Circumpolar Deep Water (CDW) centered on the neutral density surface 27.8 kg m−3 across the ACC [Pollard et al., 2002] to outcrop south of the Polar Front. CDW, easily recognized by its high nutrients and low oxygen values, is the source of nutrients to the Southern Ocean [Callahan, 1972], as is graphically shown by mapping nitrate on the 27.8 kg m−3 neutral density surface (Figure 3). Nitrate concentrations over 35 μmol kg−1 are confined to the deep Pacific and Indian Oceans, but can be seen rising southward along the west coast of South America, to be transported eastward across the South Atlantic sector of the Southern Ocean and onward by the ACC.
Figure 2. Sections of (a) nitrate and (b) silicate along 170°W are shown for the WOCE P15 section. Dots show all data points. Black lines are nutrient contours. These contours are at 2, 5, then in steps of 2.5 to 30, then in steps of 1 to 36 μmol kg−1 for nitrate and at 2, 5, then in steps of 5 to 25, then in steps of 25 to 125 μmol kg−1 for silicate. White lines are superimposed neutral density contours.
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 Let us first examine by how much nutrient concentrations vary on neutral density surfaces. For each conductivity-temperature-depth (CTD) profile along WOCE section P15 the oxygen and nutrient concentrations interpolated onto 27.4 kg m−3 are plotted on the side and bottom panels of Figure 4. For nitrate in particular, below 328 m (dashed line) the concentrations are remarkably constant (29.7–30.7 μmol kg−1) down to at least 1000 m and everywhere north of 60°S. Above 328 m, nitrate values drop to below 27 μmol kg−1. The rise in oxygen from 250 to 300 μmol kg−1 that accompanies this nitrate decrease shows that the decrease is the result of biological uptake of nutrients in the relatively recently ventilated surface layer. Just below this recently ventilated layer, between 56 and 60°S (Figure 4c), in the depth range 330 to 540 m, six out of seven values of nitrate lie between 29.6 and 30.0 μmol kg−1 with oxygen between 243 and 254 μmol kg−1. This indicates a water mass that has been influenced by surface drawdown at some time in the past more recent than all deeper (farther north) waters on the neutral density surface, whose nitrate and oxygen values are greater than 30.3 μmol kg−1 and less than 232 μmol kg−1 respectively.
Figure 4. (a) Potential temperature is contoured for the upper 1000 m of the WOCE P15 section south of 45°S with neutral density contours overlaid (white lines). Nitrate, silicate, and oxygen along the neutral density line (27.4) are plotted against (b) depth and (c) latitude. In 4c, potential temperature and salinity are also plotted.
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 Above 328 m, silicate values also fall, from 26.9 μmol kg−1 to under 23.1 μmol kg−1, but they rise again farther south. This rise is caused by winter mixing across neutral density surfaces (>27.4 kg m−3) that have much larger silicate values (Table 1). Below 328 m, silicate concentrations rise gradually with depth. Silicate lies in the range 26.6–26.9 μmol kg−1 between 56 and 60°S, jumps to 29.2–29.9 μmol kg−1 between 54 and 56°S (depths 530–630 m), then jumps to over 31.8 μmol kg−1 north of 54°S (and deeper than 800 m). This steplike structure indicates, as for nitrate, the influence of water masses with slightly different properties. Nevertheless, the variation of silicate below 328 m along the neutral density surface 27.4 kg m−3 is much less than the variation between neutral density surfaces. On the adjacent tabulated neutral density surface 27.6 kg m−3, for example, silicate is greater than 49 μmol kg−1 (Table 1).
 Structure similar to that just described is apparent along every neutral density surface for every section, so the nutrient values in Table 1 are those just below the tabulated depth above which oxygen rises and nutrients fall. We shall call this the surface-influenced depth (SID). Several striking conclusions can be drawn. First, below the SID there is remarkably little variation in nutrient concentrations on a given neutral density surface right around the Southern Ocean and over all depths below the SID. Variations along a neutral density surface (measured by the standard deviations in Table 1) are an order of magnitude less than variations between adjacent tabulated neutral density surfaces 0.2 kg m−3 apart, equivalent to a few hundred meters apart in the vertical (Figure 4a). We infer from this lack of variation that advection right around Antarctica and isopycnic stirring by mesoscale eddies homogenizes nutrient distributions on neutral density surfaces faster than they can be modified by diapycnic mixing with adjacent neutral density surfaces. Likewise, any signal of remineralization of nitrate or dissolution of silicate is greatly weakened by these physical processes, as we can find only weak hints of silicate or nitrate values slightly higher just below the SID than they are deeper on the upwelling neutral density surfaces. Finally, it is intriguing to note that the SID to which nutrient depletion extends is significantly deeper on all sections than the winter mixed layer depth, which can be identified in Figure 4a as the depth of the temperature minimum. This indicates that nutrient depletion in the surface layers is carried across the near-surface pycnocline by mesoscale isopycnic mixing (upwelling and downwelling along sloping neutral density surfaces), which can be large in small-scale ageostrophic motions [Hales and Takahashi, 2004; Pollard and Regier, 1990; Pollard and Regier, 1992]. These remarks all show that mesoscale eddies play a major role in setting nutrient distributions in the Southern Ocean.
3.2. Nutrient Supply
 Having established that nutrients are constant on neutral density surfaces below the SID, it is logical to use neutral density surfaces to calculate nutrient supply to the surface layer (Tables 2 and 3). The Ekman flux between pairs of neutral density surfaces has been previously calculated [Sloyan and Rintoul, 2001], but we have recalculated it using annual average winds from the ECMWF climatology combined with winter (July, August, and September) neutral densities from Levitus (1994, World Ocean Atlas 1994, available at http://ingrid.ldeo.columbia.edu/SOURCES/.LEVITUS94/). Table 2 shows that the Ekman flux is divergent for neutral densities greater than 27.0 kg m−3. The wind stress is nearly zero along neutral density 27.9 kg m−3 (mean latitude 67°S) and westward south of that. Thus water that upwells with neutral densities between 27.0 and 27.9 kg m−3 will be carried northward until it eventually crosses 27.0 kg m−3. The relationship between the wind stress maximum (south of which the Ekman flux will be divergent) and the winter neutral density surfaces is shown graphically in Figure 5. Around most of the Southern Ocean the wind stress maximum lies close to neutral density 27.2 kg m−3. The core of CDW lies along neutral density 27.8 kg m−3 (Figure 2) and CDW spans the range 27.4–28.0 kg m−3. Similarly, the low salinities identifying Antarctic Intermediate Water (AAIW) span the neutral density range 27.0–27.4 kg m−3 (Figure 2b) [Sloyan and Rintoul, 2001]. Table 3 confirms that it is CDW that is subject to the greatest upwelling, over 30 sverdrup (Sv; 1 sverdrup = 106m3s−1). However, we note in passing that AAIW is also upwelling (8 Sv) and it is Subantarctic Mode Water (SAMW) at neutral densities less than 27.0 kg m−3 which is downwelling, driven by Ekman convergence. Thus AAIW is actually an “old” water mass, as may be inferred from the gradients of oxygen and nutrients across the neutral density range 27.0–27.4 kg m−3 in Figure 2. This conclusion supports the hypothesis that AAIW is formed from SAMW [McCartney, 1977].
Figure 5. The annual mean wind stress amplitude (shaded) from the European Centre for Medium-Range Weather Forecasts (ECMWF) climatology highlights the wind stress maximum in the Southern Ocean. Winds are primarily eastward, and the Ekman divergence is positive south of the wind stress maximum, leading to upwelling. Lines of constant winter neutral density at 100 m are superimposed. Neutral density 27.2 kg m−3 (bold solid line) aligns reasonably closely with the path of the Subantarctic Front (SAF) (bold dashed line) [Orsi et al., 1995] and with the wind stress maximum.
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 During passage northward in the surface layer, which may take several years, the upwelled nutrients are taken up by phytoplankton growth in the surface layer, so that the nutrients remaining by the time the surface water leaves the Southern Ocean are much reduced. How do we define the "northern boundary of the Southern Ocean"? Strictly, in this analysis we mean the latitude of maximum wind stress, and Figure 5 shows that this is reasonably approximated by the 27.2 kg m−3 winter mixed layer isopycnal (at 52°S, Table 2) and by the Subantarctic Front (SAF). However, Table 2 shows the strongest zonally averaged Ekman flux at 27.0 kg m−3 (48.7°S). It is certainly north of the Antarctic Polar Front (APF) which lies close to the 27.4 kg m−3 isopycnal (at 56°S) and marks the transition from CDW to AAIW. Thus our calculations of nutrient supply (Table 3) include nutrients upwelling in AAIW as well as in CDW, although it makes little difference whether the cutoff is taken as 27.0 or 27.2 kg m−3 (say, 50°S).
 Maps of nutrients at 50 m depth (Figure 6) from the ODV database (nearly all summer stations in the Southern Ocean) show that silicate is reduced to about 5 μmol kg−1 and nitrate to 20 μmol kg−1 along neutral density 27.2 kg m−3, so we have used these values to determine the nutrients remaining when the Ekman transport crosses the Polar Front. The effect of varying these estimates is discussed in section 3.3, but we note that this work confirms that, despite the high-nutrient low-chlorophyll nature of the Southern Ocean, silicate is reduced to near limiting values for diatom growth by the time the upwelled water exits the Southern Ocean.
3.3. Sources of Error
 While our calculation of net nutrient supply to the surface layer does not suffer from errors resulting from extrapolation of local in situ measurements, there are still several possible sources of error. We consider variation of nutrients on density surfaces, reliability of neutral density distributions in the Levitus database, reliability of the wind climatology, the assumptions of nutrient drawdown, and the assumption that upwelling is balanced by divergence of the wind stress.
 We believe that negligible errors arise from the calculation of nutrient concentrations on neutral density surfaces because of the remarkable constancy shown in Table 1 for WOCE sections at longitudes right around the globe, each spanning a wide range of latitudes and depths. Isopycnic mixing in the Southern Ocean has homogenized nutrients on each density surface to a remarkable degree.
 To estimate sensitivity resulting from changes in the spatial distribution of neutral density surfaces, we compared nutrient fluxes calculated using the June and September positions of the Levitus neutral density surfaces with those in Table 3, calculated using the winter (July to September) mean. Between June and September the mean latitude of neutral density surfaces shifted northward by 0.4° (ND 27.9) to 3.9° (ND 26.8) and the resulting flux estimates increased from 47.8 to 53.5 Tmol Si yr−1 (compare with 50.8 Tmol Si yr−1 in Table 3) and from 12.8 to 13.8 Tmol N yr−1 (compare with 13.7 Tmol N yr−1 in Table 3). Thus our estimates are not seriously sensitive to changes of several degrees in the latitudes of the neutral density surfaces and we suggest that 51 ± 3 Tmol Si yr−1 and 14 ± 1 Tmol N yr−1 includes reasonable error bars.
 Initially we used a wind climatology based on in situ observations [Hellerman and Rosenstein, 1983] combined with published neutral density calculations [Sloyan and Rintoul, 2001]. This gave lower nutrient fluxes by a factor of 3 (15.6 Tmol Si yr−1 and 4.0 Tmol N yr−1). Thus our results are sensitive to the wind climatology. It is clear from Table 3 how the factor of 3 arises. The Hellerman and Rosenstein climatological wind stress peaks well north of the ECMWF climatology [Josey et al., 2002] so that contributions to the Ekman [Sloyan and Rintoul, 2001] and hence nutrient fluxes from the Hellerman and Rosenstein winds tail off rapidly for neutral densities greater than 27.6 kg m−3. For the ECMWF climatology (Table 3) in contrast, the Ekman divergence remains significant for the neutral density classes 27.6–27.8 and 27.8–27.9 kg m−3, so that the contributions to nutrient fluxes from those two classes are as large as for 27.4–27.6 kg m−3. Indeed they are larger, particularly for silicate, because of the substantial rise in silicate values with neutral density. Thus substantial contributions to the nutrient fluxes arise across the whole range of CDW densities (27.4–27.9 kg m−3).
 Having argued [Josey et al., 2002] that the Hellerman and Rosenstein climatology is particularly poor in the Southern Ocean, a more useful estimate of nutrient flux variability would be obtained by comparing results using the NCEP-NCAR climatology with the ECMWF results. We have not repeated the calculation, but note [Josey et al., 2002, Figure 5] that these two climatologies have very similar latitudinal dependence but the NCEP wind stresses are smaller by about 5%. A 5% reduction in the nutrient fluxes from the ECMWF winds is less than 3 Tmol Si yr−1 and 1 Tmol N yr−1, so less than half the range estimated above from latitudinal variations in the Levitus data.
 The net nutrient supply to the surface layer depends on how much residual nutrient leaves the Southern Ocean in the surface layer. We have used drawdown to 5 μmol kg−1 for silicate and 20 μmol kg−1 for nitrate in Table 3. From Figure 6, silicate may be even more reduced, to perhaps 2 μmol kg−1, and residual nitrate could be higher, say, 22 μmol kg−1, or possibly lower, say, 18 μmol kg−1. Lowering the residual silicate by 3 μmol kg−1 would increase the net silicate supply by 3.5 Tmol Si yr−1 to 54.3 Tmol Si yr−1. Changing the residual nitrate by 2 μmol kg−1 would change the net nitrate supply by 2.4 Tmol N yr−1.
 In a recent paper [Hoppema et al., 2003] it has been argued that a significant fraction of upwelled nutrients (in their case, iron) leaves the Southern Ocean in less than a year, before it can be taken up by phytoplankton. Our analysis shows that this is unlikely. Although the maximum Ekman flux is 39 Sv near 50°S (Table 2), recent wind climatologies indicate that the major upwelling is well south of that, in CDW between 56°S and 67°S, where the Ekman flux ranges from 0–30 Sv (Table 2). Hence the mean Ekman flux, and hence northward transport velocity, of much of the nutrient rich upwelled water is less than half the 34 Sv used by Hoppema et al. Thus water, once it has reached the surface, will likely take several years to advect out of the Southern Ocean across 50°S, giving more than one summer season in which nutrients, whether nitrate, silicate or iron, can be taken up by phytoplankton growth.
 Finally, the dynamical balance of the Southern Ocean is an active research area. For example, the eddy transports derived by Karsten and Marshall  would, if applied directly to the surface layer, reduce the upward mass divergence and hence the nutrient fluxes by 20–30%. The internal dynamics are still a matter of debate, and there is great uncertainty in Karsten and Marshall's estimates, but it is likely that our nutrients fluxes are upper limits, which will be somewhat reduced by eddy transports.
 In summary, we believe that our estimates of nutrient fluxes are robust, with a range estimate of ±6% for silicate and 20% for nitrate, thus 51 ± 3 Tmol Si yr−1 and 14 ± 3 Tmol N yr−1.