To investigate the non-Redfield N/P depletion ratio in the Polar Frontal Zone (PFZ) of the Southern Ocean, we simulated the seasonal nitrate, phosphate, and silicate cycle in the upper ocean with a biophysical model. Total phytoplankton biomass was prescribed from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) estimates, and we included two phytoplankton types, diatoms and nondiatoms. We set the nondiatoms N/P uptake ratio to 16 while the diatoms N/P and N/Si ratios were determined by fitting the observed seasonal nitrate, phosphate, and silicate cycle in the mixed layer. The best model fit to the observations required an annual N/P utilization ratio of 13.2, but this low N/P ratio still overestimated the nitrate utilization during the summer. We considered three mechanisms for improving the simulated nitrate cycle: (1) seasonal variation in the N/P ratio of the horizontal nutrient supply to the PFZ, (2) different remineralization length scales for particulate organic nitrogen (PON) and particulate organic phosphorus (POP), and (3) seasonal accumulation and decomposition of labile dissolved and suspended organic matter (OM). Model simulations showed that the seasonal variability in the N/P ratio of horizontal supply failed to reduce the simulated excess nitrate utilization in summer. Preferential recycling of PON compared to POP below the mixed layer degrades the simulation and cannot produce results that satisfy both the observed seasonal nitrate and phosphate cycle in the mixed layer. The most realistic model simulation was obtained with preferential recycling of POP over PON, but this mechanism alone was incapable of satisfying the summer nitrate and phosphate data. With the inclusion of an OM pool in our model we were able to reproduce the observed seasonal mixed layer nitrate and phosphate cycles. Satisfactory results can be achieved through various combinations of the N/P ratio of OM and the lifetime of the OM. Seasonal observations of dissolved and suspended organic phosphorus, nitrogen and carbon are needed to confirm their role. The important conclusion of our model study is that in the PFZ the annual nutrient utilization ratio of nitrate to phosphate is considerably less than the classical Redfield value of 16.
 In the Southern Ocean, surface phosphate and nitrate are never completely consumed. This feature prompted Martin  to hypothesize that enhanced oceanic uptake of CO2 may occur with enhanced nutrient utilization. Model studies do show that increased nutrient utilization in the Southern Ocean could explain a large portion of the observed CO2 decrease during the Last Glacial Maximum [Sigman and Boyle, 2000; Watson et al., 2000; Keeling and Visbeck, 2001]. Simulations of future climate change predict a continued slowdown in thermohaline overtuning in the Southern Ocean producing a net storage of carbon and nutrients in the interior of the Southern Ocean [Sarmiento et al., 1998; Matear and Hirst, 1999; Bopp et al., 2001]. A fundamental assumption in these models of past and future conditions is that the export of particulate organic matter (POM) from the euphotic zone and its subsequent remineralization in the ocean interior occurs with a constant C/N/P ratio (e.g., the classical Redfield ratio of 106/16/1) [Redfield et al., 1963]. As discussed by Denman et al. , the modeled air-sea carbon fluxes are sensitive to the C/N/P ratio and the potential for the marine biota to alter this ratio either spatially or temporally could significantly impact these fluxes. A recent study documented a decadal trend in these ratios in the Northern Hemisphere [Pahlow and Riebesell, 2000]. Therefore, it is important to determine the stoichiometry of the exported material to accurately model the regional CO2 uptake.
 Oceanwide estimates of the stoichiometry of POM as derived from either averaged phytoplankton assemblages [Redfield et al., 1963] or changes in C, N, and P along isopycnal surfaces [Takahashi et al., 1985; Anderson and Sarmiento, 1994] are consistent with the constant “Redfield” stoichiometry. The latter studies yield basinwide estimates, but the method is not suitable for regional investigation because of the limited accuracy of the data, the small change in C, N, and P from the remineralization of POM, and the potential influence of diapycnal mixing.
 Recent observations from the Southern Ocean document N/P utilization ratios in the euphotic zone that are less than the classical Redfield value of 16 [Lourey and Trull, 2001]. Observations show that Southern Ocean diatoms can produce N/P utilization ratios between 4 and 10 [de Baar et al., 1997; Arrigo et al., 2000; Sweeney et al., 2000]. The low N/P utilization ratio for diatom usually occurs during spring diatom blooms. Observations also show that N/P uptake ratio in diatoms decreases under Fe limited condition [Takeda, 1998; Boyd et al., 1999]. The observed non-Redfield nutrient utilization ratio may reflect the Southern Ocean's unique phytoplankton community and the low iron concentrations in the upper ocean which limits biological production [Sedwick et al., 1999; Boyd et al., 2000].
 Our study investigates the non Redfield N/P utilization ratios observed in the euphotic zone of the Polar Front Zone (PFZ) [Lourey and Trull, 2001]. We use model simulations and seasonal observations to close the annual budgets of nitrate, phosphate, and silicate in the upper ocean of the PFZ and determine the nutrient utilization of nitrate, phosphate, and silicate. Our one-dimensional biophysical model couples a vertical mixing model with a parameterization of horizontal advective supply [Wang and Matear, 2001; Wang et al., 2001] to a two-functional group phytoplankton model (diatoms and nondiatoms). In the phytoplankton model, the nondiatom phytoplankton satisfy the classical N/P uptake ratio of 16 but the diatoms are permitted to have a varying N/P and N/Si uptake ratios. We include silicate in the model to provide additional constraints on the diatom production. To close the annual nitrate, phosphate, and silicate budgets requires the annual export from the euphotic zone to equal the supply. The N/P ratio of the annual export may be less than 16, but this requires at least one of the following possibilities: (1) advective supply of N/P is less than 16; (2) there is preferential regeneration of particulate organic nitrogen (PON) into nitrate relative to particulate organic phosphorus (POP) into phosphate; or (3) the dissolved and suspended organic materials (OM) accumulate nitrogen and phosphorus in non-Redfield proportions. The final possibility is that the Redfield N/P uptake only applies on a seasonal to annual timescale and non-Redfield uptake is a short-period event, which, averaged over the seasonal cycle, does not drive the N/P uptake ratio far from the classical Redfield value of 16 [Hoppema and Goeyens, 1999].
 In this study we simulate the daily nutrient utilization ratios in the euphotic zone and investigate the relationships between the observed low N/P depletion ratio in the upper ocean and the proposed mechanisms for closing the annual nutrient budgets. Our simulations do not support the hypothesis that the observed low N/P utilization ratio in PFZ is a transient feature, which does not represent the seasonal nitrate and phosphate uptake.
2. Hydrographic Setting and Distribution of Nutrients
 South of Tasmania several prominent ocean fronts (Figure 1), the Sub-Antarctic Front (SAF), the Polar Front-North (PF-N), the Polar Front-South (PF-S), and the Southern Antarctic Circumpolar Current Front (SACCF) separate the region into four distinct zones, the Sub-Antarctic Zone (SAZ), the PFZ, the Inter-Polar Frontal Zone (IPFZ), and the Antarctic Zone-South (AZ-S) [Rintoul and Bullister, 1999; Trull et al., 2001]. The biophysical behavior in these zones differs substantially, changing from deep winter mixed layers (600 m) and nearly complete silicate depletion in summer (∼1 μmol/L) in the SAZ to shallow winter mixed layers (less than 150 m) and high silicate concentrations (greater than 30 μmol/L) in the AZ-S. Because there is no significant difference in the biogeochemical field between the PFZ and IPFZ, these two zones are often combined and referred as the PFZ (see Figure 2).
 Several repeat hydrographic and biogeochemical measurements have been made along ∼140°E south of Tasmania in the 1990s [see Griffiths et al., 1999; Lourey and Trull, 2001; Trull et al., 2001; Rintoul and Trull, 2001, and references therein]. Figure 2 shows the meridional nutrient distributions south of Tasmania and the nutrient ratios in the mixed layer in both the early winter (July, AU9501) and the late summer (March, AU9309). In the PFZ, the winter mixed layer phosphate, nitrate, and silicate concentrations are high. In the summer, nutrient concentrations decline with silicate nearly completely depleted. At the SAF, there is a large meridional gradient in nitrate and phosphate that is slightly greater in the summer than in the winter. At the PF-S, there is a prominent meridional silicate gradient in both the summer and winter.
 The nitrate/phosphate ratio in the mixed layer of the PFZ displays weak seasonality increasing from ∼14.5 in winter to ∼16 in summer (Figure 2). In the winter, the nitrate/phosphate ratio in the mixed layer shows no prominent gradient across the SAF, but in the summer, the ratio from south of the front exceeds the value from north of the front. In the mixed layer of the PFZ, the Si/N and Si/P ratios display clear seasonal changes (Figure 2). The ratios are high in winter and decline towards zero as the silicate is nearly completely consumed during the spring-summer growing season.
3. Model Description
 To describe the evolution of phosphate, nitrate, and silicate concentrations in the euphotic zone we use the following equations:
 Vertical, horizontal, and biological processes affect the evolutions of the nutrient concentrations. For the vertical process, the vertical mixing coefficient, Kz, is calculated by our one-dimensional upper ocean model forced by 6-hourly heat fluxes, freshwater flux, and wind-stresses from the Nation Center for Environmental Prediction (NCEP) data set. The model and forcing fields are identical to what was used at the PFZ site in the Wang and Matear  study. The biological processes that affect the nutrient concentrations are the accumulation and remineralization of dissolved and suspended organic phosphorus (OP) and nitrogen (ON), QOP and QON, and export of POP, PON, and biogenic silica (the first biological terms in equations (1), (2), and (3), respectively). For simulations without ON and OP pools, QOP and QON are set equal to zero.
 Below the euphotic zone we model the evolution of the phosphate concentrations as
where EP is the export of POP from the euphotic zone and RP is the remineralization profile for POP. Similar equations apply for nitrate and silicate where EN and ESi are the export of PON and opal, respectively, and RN and RSi are the remineralization profiles for PON and opal, respectively. In the model, we assume that POP, PON and opal produced in the euphotic zone are instantaneously exported and remineralized according to prescribed remineralization profiles.
 In the following sections we will describe the parameterization of the horizontal and biological processes. For reference, the model parameters and their values are summarized in Table 1.
where τx(t) is the eastward wind stress at time t, x is the 4-year (1995–1998) averaged eastward wind stress, Py(t) is the meridional gradient of the phosphate at time t, and y is the annual mean meridional phosphate gradient. The term P is the annual mean horizontal transport of phosphate necessary to close the annual phosphate budget. The horizontal supply of nitrate and silicate is treated in the same way with N and Si as the two parameters used to close the annual mixed layer cycle of nitrate and silicate, respectively.
 The meridional gradient of nitrate and phosphate displays weak seasonality south of the SAF and in the PFZ. The corresponding N/P ratio of the mixed layer nutrients is also nearly uniform (∼14.5 in the winter and ∼16 in the summer, Figure 2). Hence, we initially use no seasonal variability in the meridional gradient of phosphate and nitrate (i.e., Py(t) = y and Ny(t) = y) and we set N = 14.5 P. For silicate, the meridional gradient is largest in the winter and smallest in the summer (Figure 2). Based on the observations, Siy(t) is calculated from silicate concentration (Si), Siy(t) = λ(Si(t) − 0.5), where λ is a constant (1 m−1). Our formulation produces a winter meridional gradient that is approximately 6 times the summer gradient, which is consistent with the observed seasonal changes in gradient at the PFZ site.
3.2. Biological Model
 The biological model parameterizes the biological uptake of phosphate, nitrate, and silicate and the export of particulate organic matter from the euphotic zone and the accumulation and remineralization of labile OM.
3.2.1. Phytoplankton Growth Model
 Our model includes two phytoplankton types, diatoms (Phy1) and nondiatoms (Phy2). In equations (1) to (3), Q1 and Q2 denote the growth rate in moles phosphate per m3 per day of diatoms and nondiatoms, respectively, and they are set to
where Phy1 and Phy2 are the concentration of diatoms and nondiatoms in moles phosphate per m3. The algal growth rate, σ, is given by [Clementson et al., 1998]
where I is light intensity, T is temperature (°C), V(T) is the maximum growth rate given by V(T) = 0.6(1.066)T [Eppley, 1972], and α is the initial slope of the P-I curve. Light intensity is a function of depth and it is given by
where PAR is the photosynthetically active fraction of total insolation, and kw and kc are the light attenuation constants for water and phytoplankton. The solar insolation at the surface, I(t, 0), was obtained from NCEP data [Kalnay et al., 1996].
 In equations (6) and (7), and are the nutrient limiting factors controlling the growth rate of diatoms and nondiatoms, respectively, with KμSi and KμP as the half-saturation constants. For both diatoms and nondiatoms, the phosphate concentrations are always high enough in the euphotic zone that phosphate never limits growth and this limiting term never drops below 0.9. For diatoms, silicate limitation is always more restrictive than phosphate limitation; hence we only retain the former term in the growth rate of diatoms. We are aware that iron may limit growth of the both diatoms and nondiatoms. The availability of only limited data on the seasonal iron distribution and algal iron requirements makes it very difficult to explicitly model the iron cycle in this region, but we will explore how iron may alter diatoms ability to utilize nitrate.
18.104.22.168. Prescription of the Biomass of Diatoms and Nondiatoms
 Total biomass in moles phosphate per m3 (Po) was estimated from the monthly chlorophyll a (chl a) derived from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) using
where C/chl is the carbon to chl a mass ratio, and C/P is the ratio of carbon to phosphate. We assume that chl a concentration is uniform within the mixed layer. To approximate the observed subsurface chl a maximum (SCM) between the base of the mixed layer and base of the euphotic zone, we took an ad hoc approach and linearly increased biomass to 2.5Po at the middle of this layer and then linearly decreased it to Po at the base of the euphotic zone.
Parslow et al.  showed that in the mixed layer, diatoms dominated the phytoplankton biomass in the early spring but accounted for less than ∼30% of the phytoplankton biomass in late summer. In the SCM, diatoms always dominated and they represented between 70 and 80% of the phytoplankton biomass. To satisfy these observations, we compute the diatoms' phosphate concentration in the mixed layer (Phy1) as follows:
 Below the mixed layer, we set Phy1 to 75% of the total phytoplankton phosphate concentration. The phosphate concentration of the nondiatom phytoplankton is simply prescribed as Phy2 = P0 − Phy1. Figure 3 shows the seasonal evolution of the concentration of diatoms and nondiatoms in the mixed layer and the SCM.
22.214.171.124. Diatom Uptake of Silicate
Pondaven et al.  summarized the published Ks values for silicate uptake by diatoms, and the values varied between 3 and 30 μM. Recent Southern Ocean studies give a similar large range in Ks of 4 to 50 μM [Franck et al., 2000; Quéguiner, 2001]. To set the Ks for our simulations, we compared the simulated opal export production for a range of Ks values (2–6 μM). The simulations showed that with Ks = 6 μM, a short and early October peak in export occurred, while with Ks = 2 μM, there was no spring peak and high export occurred throughout the October to December period. Comparison of the seasonal changes in the simulated opal export with sediment trap data suggests that the best agreement occurred for a Ks value of 3.6 μM, and hence we used this value for our reference simulation.
126.96.36.199. Diatom Uptake of Nitrate
 The availability of iron plays a role in nitrate assimilation because iron is an essential element to the enzymes use in nitrate and nitrite reductase. Shipboard experiments in the PFZ suggest diatoms are more iron stressed than nondiatoms and Fe additions preferentially stimulate diatoms growth in comparison to nondiatoms [de Baar et al., 1997; Franck et al., 2000]. To account for different responses of diatoms and nondiatoms, we multiply Q1 in equation (2) by to account for the influence of iron on the diatoms uptake of nitrate. In this term, Fe is the dissolved iron concentration and Kf is the half saturation constant for nitrate uptake with respect to iron (it differs from the half saturation constant for iron uptake). An estimated Kf value for diatoms in the PFZ is 0.09 nM [Blain et al., 2002]. We cannot explicitly model Fe concentrations because we lack data on the seasonal evolution of Fe in the upper ocean in the PFZ. However, the available observations show that in winter dissolved Fe is 0.3–0.4 nM and in summer it is less than 0.1 nM (P. Sedwick, personal communication, 2001). To obtain a seasonal cycle of Fe in the upper ocean, we assumed that it has the same seasonal cycle as silicate and set Fe = 0.04 Si in the upper ocean. This gives a seasonal change of Fe from 0.36 nM to 0.08 nM, which is similar to the limited observations, but it assumes that diatoms drive the seasonal depletion of iron.
3.2.2. Export production
 To convert the phytoplankton uptake of phosphate to the export of POP, we use the scaling factors, r1P and r2P, for diatoms and nondiatoms, respectively. Based on the observation that diatoms have much higher f ratio than nondiatoms, due to their faster sinking rate [Boyd and Newton, 1999], we set r1P = 3r2P. With this assumption, the averaged fraction of export for phosphate is ∼0.75 and ∼0.25 for the diatoms and nondiatoms, respectively, in this study. The simulated f ratio in community (ratio of export to total production for phosphate) is ∼0.6 in the spring and ∼0.3 in the summer, and thus is consistent with the observations in the PFZ [Mengesha et al., 1998; Cailliau et al., 1999; Sambrotto and Mace, 2000].
 For nondiatoms, we assume that the uptake of nitrate and phosphate satisfies the Redfield ratio (N/P = 16); therefore we have the relationship r2N = 16r2P. For diatoms, the conversion of nitrate and silicate uptake to the export of PON and opal, r1N and r1Si, respectively, are determined by trying to reproduce the observed seasonal cycle of nutrients in the upper ocean.
3.2.3. OM Accumulation and Remineralization
 We investigated the potential role of OM on the seasonal nutrient cycle by adding terms to represent the accumulation and remineralization of OP and ON, QOP and QON, in equations (1) and (2), respectively. To maintain the same export of phosphorus and nitrogen as in the simulation without the OM pool, we imposed the condition that any accumulation of OP and ON requires a corresponding reduction of POP and PON export. In the simulations with OM that are discussed in the next section we prescribed the time period over which OM is either accumulating or remineralizing OP and ON. We investigate different ratios of OP to ON to assess model sensitivity.
3.2.4. Parameterization of the Remineralization of POM
 In our model, we assumed that the export of POP, PON, and biogenic silica is instantaneously remineralized below the euphotic zone (ze) according to prescribed profiles. We used the following remineralization profile for phosphate [Williams and Follows, 1998]:
where zLP is the scale length for remineralization for POP. Similar equations were applied for the remineralization of PON and opal with zLN and zLSi as the remineralization length scales of PON and opal, respectively. To determine zLN and zLSi we used the simulated export production and Trull et al.  sediment trap measurements of PON and opal fluxes. We set zLN = 180 m and zLSi = 450 m. Since we have no sediment trap observations of POP, we assume zLN = zLP.
3.3. Model Setup
Wang and Matear  and Wang et al.  described the model setup in detail. In brief, the model was forced with the surface fluxes of heat and fresh water and the wind stress from the NCEP (September 1997 to September 1998) and initialized with observed winter profiles of temperature and salinity from the Aurora Australis cruise AU9501. The initial profiles of nitrate, phosphate, and silicate were taken from Niskin bottle data from the same cruise [Rosenberg et al., 1997]. The model domain was 0–1000 m, with a uniform vertical grid spacing of 5 m. The model bottom boundary was closed so that diffusive fluxes through the bottom were zero. The location of the simulation site is 54°S 140°E in the PFZ, which corresponds to the location of the PFZ sediment trap mooring of Trull et al. .
 As presented above and summarized in Table 1, the biophysical model given in equations (1) to (3) had five unknown variables (P, Si, r2P, r1N, and r1Si) which need to be determined. In a steady state ocean, the annual consumption and export of nutrients in the euphotic zone must balance the vertical and horizontal nutrient supply. By closing the annual budget for phosphate and silicate in the euphotic zone and by reproducing the observed winter-summer silicate and phosphate depletion, we iteratively solved for P, Si, r2P, and r1Si. The observed seasonal nutrient cycle was obtained from bottle data collected on Aurora Australis and Southern Survey cruises during the 1991–1998 period [see Griffiths et al., 1999; Lourey and Trull, 2001, and references therein]. For the PFZ, the solution for P, Si, r2P, and r1Si was unique because the seasonal cycle of export production differs from that of horizontal supply which decouples two unknowns for each nutrient. Export production primarily occurs in the spring-summer period while horizontal supply is nearly constant throughout the year for phosphate and is greatest in winter for silicate. To test the uniqueness of our solution, we fitted the observations using various initial guesses of the model parameters and still obtained the same solution. Once P and r2P were determined, the unknown r1N was determined by closing the annual nitrate budget. Hence, nitrate depletion was not tuned to match the observations, which allowed us to use the nitrate cycle to identify the potential limitations of the model and investigate different mechanisms for reproducing the observed seasonal cycle of nitrate.
4. Model Results
 The reference simulation used the previously described model and parameters (Table 1) but did not include an OM pool. In the mixed layer, the reference simulation reproduced the seasonal phosphate and silicate concentrations and the Si/N ratio (Figure 4). The reference simulation overestimated seasonal nitrate depletion in the mixed layer and underestimated mixed layer nitrate concentrations in March (Figure 4c). The simulated nitrate/phosphate ratios in the mixed layer (14.3–14.7) were generally less than the observed values (Figure 4b). The simulations had nearly a constant vertical Si/N utilization profile which was high (∼3) during September–December (data not shown) but low (∼1) during January–April. In the mixed layer, the simulated Si/N utilization ratio in March agrees with the limited observations (∼1) [Parslow et al., 2001].
 The initial simulation failed to reproduce the seasonal nitrate depletion in the mixed layer. In the following sections, we attempt to remedy these defects. First, we test the impact of changing the diatom uptake dependency on iron by altering the half saturation uptake constant, Kf, in equation (2). Second, we use different remineralization length scales for PON and POP. Third, we add an OM pool to account for seasonal accumulation and remineralization of labile OM and nitrogen pool other than nitrate.
4.1. Iron Limitation
 Shipboard and in situ experiments demonstrate that iron addition to the PFZ stimulates phytoplankton growth [Sedwick et al., 1999; Boyd et al., 2000]. However, there is limited quantitative information to relate the iron concentrations to the nitrate uptake rate. We parameterize this relationship for diatoms using with Kf = 0.09 nM [Blain et al., 2002]. As discussed by Blain et al. , there are large variations in Kf. In particular, their study indicated a Kf value of ∼0.4 nM Fe for the PFZ in the Indian sector. Here we explore the sensitivity of our model simulation to the Kf value.
 For a range of Kf values between 0.03 nM and 0.4 nM, the simulations produced similar seasonal patterns of nitrate depletion to that of the reference simulation. While variations in Kf can not fix the overestimate of nitrate depletion, it influences the Si/N utilization ratio in the mixed layer. Figure 5a shows that in the mixed layer the simulation with the highest Kf (0.4 nM) produced the greatest diatom Si/N utilization ratio. During the growing season, the Si/N utilization ratio for the diatoms is ∼0.6 greater using the largest Kf value than using the smallest Kf value. However, the difference of Si/N utilization ratio in the community with different Kf value is much smaller, in particular during the period of January–April (Figure 5b). Unfortunately, there is only one measurement of Si/N uptake in the PFZ Australian sector, and it shows that in March, Si/N uptake ratio was ∼1 in the mixed layer [Parslow et al., 2001]. It is important to note that the Si/N utilization ratio from the model represents the Si/N ratio of the material exported from the upper ocean and may not be comparable observation of the Si/N uptake. Our simulations show that the seasonality of the Si/N utilization is insensitive to the Kf value, and we use a value of 0.09 in our subsequent simulations.
4.2. Remineralization of PON and POP
 There is large uncertainty in estimating the remineralization length scale of POM from the modeled export production and deep sediment trap data. Here, we are not interested in the absolute values of the POP and PON remineralization length scales but in how differing length scales for POP and PON would impact the N/P utilization ratio and the simulated seasonal nutrient cycles. For convenience we keep the length scale of POP constant (180 m) and perform two additional simulations with the remineralization length of PON set to 125 m and 250 m. Assuming a euphotic depth of 100 m, a remineralization length scale of 125 m, 180 m, and 250 m would enable only 4%, 11%, and 20% POM, respectively, to sink below 500 m. In comparison, using the classical Martin curve ([z/100]−0.858), 25% of the POM would sink below 500 m.
 With a shallower remineralization of PON than POP (125 m versus 180 m, respectively), one further overestimates the summer nitrate depletion in the mixed layer from the reference run (Figure 6). This appears to contradict the intuition that preferential recycling of PON relative to POP should increase the supply of nitrate to the mixed layer and reduce the seasonal depletion of nitrate. However, in the PFZ the seasonal nutrient uptake is largely decoupled from the resupply, because most of the uptake occurs during the spring-summer when the mixed layer is shoaling and most of the resupply occurs during the fall and winter when the mixed layer is deepening. Therefore, increasing the nitrate supply in the fall-winter period by reducing the remineralization length scale of PON requires increased nitrate uptake in the spring-summer period to close the annual nitrate budget. The increased spring-summer uptake increases the summer depletion of nitrate and worsens the agreement with the observations. The seasonal nitrate and phosphate budgets are summarized in Table 2, which shows how changes in vertical resupply arising from differing remineralization length-scales alter simulated export of PON.
Table 2. Nitrate and Phosphate Fluxes in Relation to Remineralization Length Scale During September–March (S–M) and March–September (M–S)a
 Our simulations show that preferential recycling of POP compared to PON improved the agreement with the observations from either equal or preferential recycling of PON. Although preferential recycling of POP over PON improved the simulation, this process alone cannot enable the model to reproduce the observed late summer nitrate concentrations. Between late January and late March the observed nitrate concentrations increase slightly and modifications to the PON recycling cannot remedy this situation because there is little vertical resupply of nitrate to the mixed layer during this period to offset the biological uptake of nitrate.
4.3. OM Pool
 The seasonal depletion of nutrients in the euphotic zone may inaccurately represent seasonal nutrient utilization if there is a seasonal accumulation of organic matter (OM) as either dissolved and suspended particulate organic matter or dissolved inorganic nitrogen other than nitrate (ODIN). To quantify the seasonal change in the OM pool, we use seasonal observations from the PFZ. For phosphate, we define the organic phosphorus (OP) pool as the sum of dissolved organic phosphorus (DOP) and the suspended POP. For nitrogen, we define the organic nitrogen (ON) pool as the sum of dissolved organic nitrogen (DON), suspended PON and ODIN.
 In the Australian sector of the PFZ, neither DON nor DOP measurements are available, but dissolved organic carbon (DOC) measurements show a winter to summer accumulation of DOC that varies between 5 and 15 μM in the upper 50 m (T. Trull, unpublished data, 2001). Assuming a DOC/DOP ratio of 106 for the labile dissolved organic matter (DOM) pool, the estimated seasonal accumulation of DOP in the mixed layer is approximately 0.14 μM. The ratio of either DOC/DON or DON/DOP in the labile DOM is uncertain. Measured ratios of labile DON to DOP in the PFZ (54°S, 176°W) were approximately 16 in the euphotic zone [Loh and Bauer, 2000]. However, others have observed DOC/DON ratios that are greater than 106/16 in the PFZ [Ogawa et al., 1999] and in the DOM produced by diatoms [Biddanda and Benner, 1997]. To deal with the uncertainty in specifying the DON/DOP ratio of labile DOM, we consider two different ratios, 16 and 6.
 The abundance of PON in the surface water of the upper PFZ varied between a minimum winter value of 0.2 μM and a maximum summer value of 0.7 μM [Lourey and Trull, 2001]. Hence we assign a seasonal accumulation of 0.5 μM for the PON. POP was 0.02 μM in the PFZ in March 1998 [Cardinal et al., 2001]. Without winter data, we assume that half of this value represents the seasonal POP accumulation. Observations of the ODIN are also sparse. Seasonal accumulation of ammonium (A. J. Watson, unpublished data, 2001), nitrite (T. Trull, unpublished data, 2001), and urea (F. Dehairs, unpublished data, 2001) are estimated to be ∼1.0 μmol N in the mixed layer in mid-March.
 We investigated the potential role of OM pool on the seasonal nutrient cycle by prescribing the temporal pattern of accumulation and remineralization of OM. We set the seasonal accumulation of OP in the mixed layer to 0.15 μM, and the seasonal ON to
where r* is the N/P ratio in the seasonal accumulation of labile DOM and ΔDON is the seasonal accumulation of DON. For all the simulations, we assumed ΔODIN and ΔPON accumulated at a constant rate during the September–March period and was converted to nitrate at a constant rate during the March 1 to August 1 period. For the first two simulations, we assumed that ΔDON and ΔDOP accumulated at a constant rate from September 1 to early January 1 and then were remineralized at a constant rate from January 1 to March 31 (referred as fast remineralization). For comparison, we also performed two additional simulations: ΔDON and ΔDOP accumulating from September 1 to March 1 and remineralizing from March 1 to September 1 (referred as slow remineralization).
 Adding the OM pool greatly improved the simulations (Figure 7). With the OM pool it is possible to reproduce the observed seasonal cycles of phosphate and nitrate by varying the combination of OM remineralization and the value of r*. The solution does not appear unique, and various combinations of remineralization and r* would be able to reproduce the nitrate and phosphate observations. More observations of DOM stoichiometry and seasonality are required to verify the role of the DOM pool.
4.4. Seasonal Export Production and Nutrient Export Ratio
 Using the model run with ΔDON/ΔDOP = 16 and fast remineralization, we get an annual export production from the euphotic zone of ∼69 mmol P m−2, ∼762 mmol N m−2, and 1816 mmol Si m−2. Diatoms contribute ∼75% of the annual export production of phosphate and nitrate. Figure 8 shows that total export of PON and POP from the euphotic zone is greatest in December. Opal export from the euphotic zone was high between October and late December with a peak in early December, which may reflect high light intensity and high Si concentrations (>Ks) in the mixed layer. The simulated opal export production remains high for about 120 days (October to late December), which is roughly similar to the period of high biogenic silica collections found in the 800-m sediment trap [Trull et al., 2001], although those observations suggest two peaks of export rather than a single broad peak as in the model (Figure 8e). It is difficult to further assess temporal and amplitude differences between the modeled EP (at 120 m) and the deep sediment collection (at 800 m) because remineralization, differential settling of different components of the export materials, and ocean circulation can significantly alter the magnitude and timing of sedimentation. Interestingly, there are similar time lags between the onset of the simulated high export production in the model and the first peak of biogenic silica at 800 m, and between the first peaks of biogenic silica at 800 m and at 1500 m from the sediment trap collections.
 The N/P export ratio is higher during December–March than other seasons (Figure 8b), with a range of 8–15 in the diatoms and 10–15 in the community. The diatoms Si/N export ratio ranged from ∼5 in the spring to ∼2 in the summer (Figure 8d). For the community, the Si/N export ratio was high (3–4) during September–December but low (∼1) during January–April. The simulated decrease in the Si/N export ratio from spring to summer reflects the impact of silicate limitation. Data from the Antarctic Environment Southern Ocean Process Study supports our silicate response with high Si/N depletion ratio (3–4) in high Si water and a low ratio (1–2) in low Si water (X. Wang et al., manuscript in preparation, 2002). In our model, silicate limitation on diatom growth is more restrictive than iron limitation on the uptake of nitrate by diatoms. Hence, as the seasons progress from spring to summer, the dominance of the silicate limitation causes the Si/N ratio to decline. This model response occurs for Kf values between 0.03 and 0.4 nM (Figure 5). Shipboard incubations produce large ranges in the Si/N utilization (1–8) during spring-summer in the PFZ waters in the Pacific Sector [Franck et al., 2000]. They obtained the highest ratio in the summer, which may reflect the higher silicate concentration (5 μM) and lower nitrate concentration (2.5 μM) at their site relative to those at our site. Our simulated Si/N export ratio for diatoms was greater than the measured uptake ratio for diatoms (2.3–3) from incubation experiments under iron deficit condition [Takeda, 1998; Hutchins and Bruland, 1998]. Part of the difference between the model and observations may reflect the fact that the model is providing the Si/N ratio of the export material, which is not a direct measure of the Si/N uptake ratio of phytoplankton. Another explanation for the difference is that our PFZ site has lower iron concentrations than water used in the incubation experiments.
5. Discussion and Conclusion
 Summer observations in the PFZ show that the N/P depletion ratio in the mixed layer is less than the classical Redfield value of 16. To address the question of the non-Redfield N/P utilization, we use a biophysical model to simulate the seasonal nitrate, phosphate, and silicate cycle. Our biophysical model included two phytoplankton types, diatoms, and nondiatoms. We used SeaWiFS derived estimates of the seasonal phytoplankton biomass to prescribe the biomass of diatoms and nondiatoms. We assumed that the nondiatoms N/P utilization ratio is 16 while the diatoms N/P ratio is determined by trying to reproduce the seasonal nitrate, phosphate, and silicate cycle.
 Our study estimates a N/P utilization ratio of 8–15 for diatoms and 10–15 for the combined diatoms and nondiatoms (Figure 8). Our simulations do not support the hypothesis that the observed low N/P utilization ratio is a transient feature which does not represent the seasonal nitrate and phosphate uptake. Our estimated annual N/P utilization ratio (∼12) is similar to the observed spring N/P utilization ratio of 8.3 ± 5.4 in the Polar Frontal zone at 140°E [Lourey and Trull, 2001], to water along 6°W [De Baar et al., 1997], and to the ratio measured in January 1995 at 64°S, 141°E [Takeda, 1998]. Assuming a C/P utilization ratio of 106, our estimated C/N utilization ratio is ∼10.5 in the spring and ∼6.5 in the summer. These values are similar to the spring and summer POC/PON ratios of 9–10 and 6.8, respectively, which were measured in the sediment traps at our simulation site [Trull et al., 2001].
 To close the annual nitrate and phosphate budgets in the upper ocean and explain the observed non-Redfield N/P depletion ratio in the mixed layer during the spring-summer period requires that the export or the resupply of nitrate and phosphate is also non-Redfield. Three mechanisms are proposed for closing the annual nitrogen and phosphate budgets: (1) the horizontal transports supplying nutrients with a low N/P ratio, (2) the preferential recycling of PON relative to POP below the euphotic zone, and (3) the accumulation of OM during the spring-summer period and subsequent remineralization of the OM during the late summer-winter period.
 Observations show that the horizontal gradient of nitrate/phosphate in the PFZ has a weak seasonality, ∼14.5 in the winter and ∼16 in the late summer (Figure 2). For our model simulations, we set the nitrate/phosphate ratio for horizontal supply to 14.5, which may underestimate the horizontal supply of nitrate in the late summer and winter. However, if we increase nitrate supply during this period, additional nitrate export is needed to close the annual nitrate budget. The increase in export production will further increase nitrate utilization during the spring-summer period the mixed layer. Therefore, horizontal supply is ruled out of as a possible mechanism for satisfying the observed nitrate/phosphate depletion ratio.
 Our simulations showed that preferential recycling of PON over POP degrades the simulation and cannot satisfy both the observed seasonal nitrate and phosphate cycle. A more realistic simulation is obtained with preferential recycling of POP over PON but again this mechanism is incapable of satisfying the observed nitrate and phosphate data from the mixed layer.
 The simulations with the OM pool enable us to satisfy the seasonal cycle of N/P depletion in the mixed layer. Through a combination ΔDON/ΔDOP ratio and accumulation/remineralization period, one is capable of producing results consistent with observations. We postulate that DOM is an important component to the seasonal nutrient budget. We expect that DOC will also play a role in the seasonal evolution of the fCO2. Seasonal observations of DOP, DON, and DOC are needed to confirm this hypothesis. These observations need to be supplemented with better seasonal observations of nitrate, phosphate, and silicate. While these details will be clarified further by additional observation, in the PFZ of the Australian sector, diatoms utilize nitrate and phosphate in a ratio considerably lower than the classical Redfield value and the net annual community export also has a N/P ratio that is lower than the Redfield value of 16.
 The NCEP Reanalysis data were provided by the NOAA-CIRES Climate Diagnostics Center, Boulder, Colorado, from the Web site at http://www.cdc.noaa.gov. NASA provided the SeaWiFS Chl a data, at http://SeaWiFS.gsfc.nasa.gov/SEAWIFS.html via the Hobart local receiving station (John Parslow and Chris Rathbone, CSIRO). Funding support from the Environment Australia Climate Change Research Program was provided to R.J.M. This work was partially supported by an Antarctic CRC Ph.D. scholarship to X. Wang and by Australian Antarctic Division grants.