What prevents nitrogen depletion in the oxygen minimum zone of the eastern tropical South Pacific ?

Local coupling between nitrogen fixation and denitrification in current biogeochemical models could result in runaway feedback in open-ocean oxygen minimum zones (OMZs), eventually stripping OMZ waters of all fixed nitrogen. This feedback does not seem to operate at full strength in the ocean, as nitrate does not generally become depleted in open-ocean OMZs. To explore in detail the possible mechanisms that prevent nitrogen depletion in the OMZ of the eastern tropical South Pacific (ETSP), we develop a box model with fully prognostic cycles of carbon, nutrients and oxygen in the upwelling region and its adjacent open ocean. Ocean circulation is calibrated with 1C data of the ETSP. The sensitivity of the simulated nitrogen cycle to nutrient and oxygen exchange and ventilation from outside the model domain and to remineralization scales inside an OMZ is analysed. For the entire range of model configurations explored, we find that the fixed-N inventory can be stabilized at nonzero levels in the ETSP OMZ only if the remineralization rate via denitrification is slower than that via aerobic respiration. In our optimum model configuration, lateral oxygen supply into the model domain is required at rates sufficient to oxidize at least about one fifth of the export production in the model domain to prevent anoxia in the deep ocean. Under these conditions, our model is in line with the view of phosphate as the ultimate limiting nutrient for phytoplankton, and implies that for the current notion of nitrogen fixation being favoured in N-deficit waters, the water column of the ETSP could even be a small net source of nitrate.


Introduction
The oceanic fixed nitrogen (fixed-N) budget is an essential control on the potential of the ocean to sequester atmospheric CO 2 via the marine biological pump.Denitrification is generally recognized as a major loss of fixed nitrogen, whereas the balance of the global oceanic nitrogen budget remains controversial.Accordingly, estimates derived from both field data and model analyses for the global oceanic fixed-N budget range from sources roughly balancing sinks (Gruber and Sarmiento, 1997;Gruber, 2004;Eugster and Gruber, 2012;DeVries et al., 2013) to a rather large net deficit between 140 and 234 Tg N yr −1 (Codispoti et al., 2001;Galloway et al., 2004;Codispoti, 2007).
One of the main uncertainties in the global marine nitrogen budget is the extent of nitrogen loss via denitrification and anaerobic ammonium oxidation (anammox) in oxygen minimum zones (OMZs), located in tropical coastal upwelling regions.Coastal upwelling zones are often associated with very high primary production.Subsequent decomposition of sinking organic matter leads to high levels of oxygen consumption in subsurface waters.Under conditions of sluggish circulation, oxygen-poor source waters, or lack of exchange with oxygenated surface waters, OMZs can develop, usually at intermediate depths of about 200-700 m (Bethoux, 1989;Capone and Knapp, 2007).An OMZ is commonly defined as a water body with an O 2 concentration below 20 µmol L −1 (Paulmier and Ruiz-Pino, 2009) be responsible for 30-50 % of the total fixed-N loss (Gruber and Sarmiento, 1997;Codispoti et al., 2001;Dalsgaard et al., 2005;Paulmier and Ruiz-Pino, 2009).Canfield (2006) used a simple steady-state box model of a coastal OMZ to show that a positive feedback between N 2 fixation and denitrification could strip the OMZ of all fixed nitrogen when N 2 fixation was permitted to restore the nitrate : phosphate ratio to Redfield proportions in the surface ocean.Observed concentrations of fixed-N (nitrate plus nitrite) in OMZ waters, however, typically range from about 15 to 40 µmol L −1 (Codispoti and Richards, 1976;Codispoti and Packard, 1980;Morrison et al., 1998;Voss et al., 2001).A possible explanation for the relatively high nitrate concentrations even in the suboxic core of open-ocean OMZs could be low levels of nitrogen fixation in the overlying surface waters (Landolfi et al., 2013).However, recent interpretations of observed fixed-N deficits relative to the Redfield equivalent of phosphorus point to high rates of nitrogen fixation closely related to the upwelling of nitrogen-deficit waters along the South American coast (Deutsch et al., 2007).Although alternative explanations for these nutrient patterns have been proposed in models (Mills and Arrigo, 2010), direct measurements have confirmed the occurrence of nitrogen fixation in and above the OMZ of the ETSP (Fernandez et al., 2011).Global biogeochemical models also generally predict substantial rates of N 2 fixation in the nitrate-deficit waters of the upwelling region of the ETSP that, if not compensated for by some ad hoc slow-down of remineralization in suboxic conditions, lead to a complete draw-down of nitrate in the OMZ (Moore and Doney, 2007;Schmittner et al., 2008).The question of how non-zero nitrate concentrations can be maintained in the OMZ thus still awaits a mechanistic answer.
The computational efficiency of box models makes them suitable for sensitivity analyses requiring thousands of model evaluations.In spite of its simplicity, Canfield's (2006) box model is also able to capture the most important first-order interactions among ocean circulation, nitrogen fixation, denitrification and OMZs.However, Canfield's model was limited in its power to investigate the influence of open ocean nutrients and oxygen conditions on the upwelling region, because its dynamics were restricted to the OMZ, where all biogeochemical tracers were prescribed in the surrounding waters.Based on Canfield's (2006) steady-state formulation with prescribed oxygen and nutrient concentrations at all depths outside the OMZ, we here present a fully prognostic box model of NO − 3 , PO 3− 4 and O 2 cycles in a coastal upwelling region and an adjacent ocean basin.We employ this model to examine under which conditions the observed situation of an essentially complete drawdown of subsurface oxygen and an incomplete drawdown of nitrate can be reproduced for the case of the ETSP.Sensitivity experiments explore how nutrient exchange and oxygen ventilation from the southern boundary influence the nitrogen budget within the model domain.
By including a prognostic description not only of conditions within the OMZ, but also in the water surrounding it, we aim to represent local as well as spatially separated feedbacks between the relatively small OMZ and the much larger open-ocean basin.The model describes net primary and export production by ordinary and N 2 -fixing phytoplankton, as well as aerobic and anaerobic remineralization.The latter is generally associated with nitrogen loss, commonly attributed to denitrification (Codispoti, 1995).Anammox has recently been reported as another major pathway for fixed-N removal (Kuypers et al., 2005;Hamersley et al., 2007;Molina and Farías, 2009), but the relative contributions of anammox and denitrification are still a matter of debate (Ward et al., 2009;Bulow et al., 2010).In our model, we do not explicitly resolve the different inorganic nitrogen species and pragmatically consider all loss of fixed-N via anaerobic remineralization as denitrification.In Canfield's (2006) model, most of the physical model parameters were constrained by observations from suboxic upwelling zones in the Arabian Sea and the eastern tropical North and South Pacific.The physical dynamics of our model system are governed by vertical and horizontal mixing and advection, which are calibrated with 14 C data of the ETSP from GLODAP (Global Ocean Data Analysis Project, Key et al., 2004).

Model description
Figure 1 shows the model structure, consisting of five boxes representing an upwelling region and an adjacent ocean basin.The U box represents the upper upwelling region.The UM box is the underlying OMZ, where suboxia is expected to develop.The S box represents the surface ocean away from the upwelling zone.Below the S box sits the I box, which represents water of intermediate depth and exchanges water with UM.D is the deep box, which represents water deeper than 500 m.When the UM, I or D boxes become suboxic, denitrification (Denif) will ensue to remineralize the exported organic matter, causing a loss of nitrate (the only form of fixed inorganic nitrogen in our model).
Prognostic tracers represent NO − 3 , PO 3− 4 , O 2 , 14 C and the biomass of ordinary and N 2 -fixing phytoplankton, respectively (Table 1).The rate of concentration change of a tracer, X i , in box i is composed of physical transport, Transport(X i ), and a sources-minus-sinks term, SMS(X i ), which represents the effects of biotic processes, air-sea gas exchange and, in the case of 14 C, radioactive decay on the tracer concentration (Eq.1).
where U, S, UM, I and D refer to the model boxes defined above and V i to the corresponding volumes (Fig. 1).and shallow (B) convection (thick grey lines).Mixing between boxes is implemented via mixing coefficients (K).Remineralization derived from net primary production by ordinary (Phy) and diazotrophic (NF) phytoplankton in the surface boxes consumes oxygen.Under anoxic conditions remineralization is fuelled by anaerobic remineralization (Denif).The model can be configured to exchange nutrients and oxygen with the southern subtropical ocean (right, denoted as "SO").See Table 3 for symbol definitions and text for details.

Transport model
Advection represents the large-scale circulation and is indicated in Fig. 1 by wide grey lines.L U and L S are the horizontal scales of the upwelling region and the open ocean, and H U , H UM and H D refer to the thickness of the respective boxes.The volumes V i of the boxes are defined in this 2-D model by V i = H i × L i .K US , K UM and K H are the coefficients of mixing between different boxes.A and B represent the deep and shallow large-scale circulation.The upwelling intensity into box U is given by A + B. The tracer transport equations for the standard configuration are given in Appendix A (Eqs.A1-A5).All parameters are defined in Tables 2 and 3.

Biogeochemical model
The ecological model is composed of two phytoplankton types, ordinary phytoplankton, Phy, and nitrogen fixers, NF.The SMS terms for phytoplankton are obtained as the difference between net primary production (NPP) and mortality (M): (2) Growth of ordinary phytoplankton is described by a Liebig-type dependence on the nitrate and phosphate limitation terms (Eq.4), where i is the model box, µ and µ NF are the maximum growth rates of Phy i and NF i , respectively.N i and P i are nitrate and phosphate concentrations, and N h and P h are halfsaturation concentrations for nitrate and phosphate.Considering possible viral lysis, phytoplankton aggregation, or a feedback between zooplankton grazing and phytoplankton concentration, a quadratic mortality term is adopted for both Phy and NF in all model configurations (Eq.6).
Both Phy and NF require phosphate, whereas nitrate is required in addition to phosphate only by Phy, and NF can fix N 2 as long as PO 3− 4 is available (Eqs. 4,5).While the ability to utilize organic P has been proposed as an advantage of diazotrophs (Houlton et al., 2008;Ye et al., 2012), ordinary phytoplankton can also use DOP (e.g.Chu, 1946;Cotner, Jr. and Wetzel, 1992) and a clear advantage of diazotrophs over ordinary phytoplankton in the presence of DOP has never been demonstrated.Thus, we treat all available P to phytoplankton operationally as PO 3−  4 and assume that all organic phosphate is remineralized to PO 3− 4 directly.N 2 fixers are given a lower maximum growth rate (µ NF , Eq. 5), which is 1/3 of the maximum growth rate of ordinary phytoplankton (µ), to account for the high cost of nitrogen fixation (La Roche and Breitbarth, 2005).The dependence of NF on iron is not explicitly considered in this model (Mills et al., 2004).Both types use nitrogen and phosphorus in the Redfield ratio of 16 : 1 (Redfield et al., 1963).
Sensitivity experiments are also performed with a configuration where nitrogen fixers preferentially use nitrate when available and cover only the residual nitrogen demand via N 2 fixation, denoted as facultative N 2 -fixation, but overall results are found to be virtually unchanged (Appendix B).
Dead phytoplankton is immediately remineralized in the surface layer and underlying boxes according to the respective remineralization fraction f i of box i. Remineralization occurs preferentially via aerobic respiration, with anaerobic remineralization and the associated nitrogen loss setting in only when all O 2 has been consumed by aerobic respiration.Phytoplankton growth and aerobic remineralization together with denitrification and, once all inorganic nitrogen is consumed, remineralization via sulfate reduction define the SMS terms of the nitrogen and phosphorus cycles: where the remineralization (Rem) and denitrification (Denif) terms are defined in Appendix C. O 2 is set constant in the surface ocean boxes U and S, which are in immediate contact with the atmosphere, but varies as a function of transport and respiration in the UM, I and D boxes.Thus, the aerobic respiration terms (Res i ) are only needed in the interior boxes UM, I and D: where Res is defined in Appendix C (Eq. C10).Note that aerobic respiration will, in general, also take place in anoxic model boxes, where it utilizes the O 2 transported from adjacent boxes, before anaerobic respiration starts.All model runs are initialized with O 2 , NO − 3 and PO 3− 4 annual data from the World Ocean Atlas 2009 (Garcia et al., 2010a, b), averaged over the regions indicated in Table 4.

Model calibration
In the present work, the prescribed transport among the different boxes in terms of advection and mixing was calibrated by fitting the modelled 14 C distribution to the GLODAP "pre-bomb" 14 C distribution of the eastern tropical South Pacific (Key et al., 2004;Table 4).The 13 C fractionationcorrected ratio of 14 C/ 12 C, 14 C, is commonly used in ocean modelling to evaluate and calibrate model physics b The fraction of regeneration above 500 m has been estimated between 92 % (Suess, 1980) and 97 % (Martin et al., 1987).According to Canfield (2006), most likely 60-70 % of the primary production is remineralized in the OMZ.Thus, we define 20 and 70 % of export production remineralized in the surface boxes and intermediate boxes, respectively.c Furnas (1990) d Robarts and Zohary (1987); Capone et al. (1997) e Temperature-corrected maximum growth rate of NF (Breitbarth et al., 2007 l These parameter values are defined in Table 2. (Toggweiler et al., 1989;Shaffer and Sarmiento, 1995) because it tends to cancel the effect of the biotic downward transport of14 C with the rain of organic particles produced by marine organisms.For practical reasons, we employ the arbitrary scale introduced by Shaffer and Sarmiento (1995) to represent 14 C, and define 14 C. 14 C can be converted to 14 C units as follows: The SMS term for 14 C is thus given by: where 14 C i is the value of 14 C in box i, 14 C a is the atmospheric 14 C, and g i is the gas exchange rate.For i ∈ [UM, I, D], g i = 0. We assume that the 14 C of the preindustrial atmosphere, 14 C a , is 0 ‰.Therefore, 14 C a is 1.Model configurations with an open southern boundary also include 14 C exchange with the adjacent subtropical ocean.
We also investigate how sensitive our main conclusions are to the uncertainty in the 14 C data.Table 4 shows the 14 C values used for the calibrations of the different model configurations.Transport and SMS terms for 14 C constitute a system of 5 linear equations with 7 parameters, including 5 transport parameters, A, B, K US , K UM , K H , and 2 air-sea 14 C exchange coefficients, g U and g S .After setting g U and g S , the 5 equations can be inverted to solve for the transport parameters.A detailed description of the inversion scheme is provided in Appendix D.

Model configurations
The above transport and biogeochemical formulations define the standard (STD) configuration, where the transport and biogeochemical models are applied without exchange with the southern boundary ("SO" in Fig. 1).Fixed fractions f i of net primary production in U and S are remineralized in the U, UM, S and I boxes, with the remainder being remineralized in D (Fig. 1).Nutrient regeneration is assumed to be instantaneous.
In order to investigate the relationships between the different biotic and physical processes and the nitrogen cycle in an OMZ, we introduce seven additional model configurations.The main differences to the STD configuration are shown in Table 5.
(1) In the Reduced-denitrification (RD) configuration, denitrification in the OMZ is reduced to 1/5 of the rate of the STD configuration following the procedure applied in the global biogeochemical circulation model by Schmittner et al. (2008).When oxygen is exhausted in the OMZ, denitrification within the UM box will be responsible for only 1/5 of the remaining organic matter remineralization and the remainder will be remineralized in the D box (Eqs.C7 and C8). ( 2) The Ventilation-D (VD) configuration modifies the STD configuration in that the southern boundary of the model domain is partially opened to allow ventilation of O 2 and 14 C (but not NO − 3 and PO3− 4 ) to the D box from the southern subtropical ocean (Eq.A7).The circulation parameters were recalibrated to account for ventilation of 14 C from the south.Ventilation is simulated by applying lateral mixing with the subtropical oligotrophic ocean tracer reservoirs with prescribed 14 C and O 2 concentrations inferred from observations.All other biogeochemical processes within the model domain are kept the same as in the STD configuration.(3) In the Ventilation-D + Reduced-denitrification (VDRD) configuration, the reduced denitrification rate is applied in the VD configuration.(4) In the Ventilation-ID (VID) configuration, the partially open southern boundary is extended to allow ventilation of O 2 and 14 C also into the I box from the subtropical ocean (Eq.A6).Again, circulation parameters are recalibrated against observed 14 C taking into account the 14 C exchange between the subtropical ocean and the I and D boxes.
(5) In the Ventilation-ID + Reduced-denitrification (VIDRD) configuration, the reduced denitrification rate is also applied in the VID configuration.(6) In the Open-boundary (OB) configuration, nutrient mixing is added to the VID configuration to allow for the exchange of nutrients between the I and D boxes and the subtropical ocean.(7) In the Openboundary + Reduced-denitrification (OBRD) configuration, the reduced-denitrification rate is again added to the OB configuration.The physical transports of NO − 3 and PO 3− 4 for the I and D boxes in the last six configurations are represented by Eqs.(A6) and (A7) in Appendix A.

Sensitivity experiments
Two sensitivity experiments are performed for each of the VID and OB configurations to explore the possibilities for preventing NO − 3 depletion in the OMZ: (a) different reduced remineralization rates (f UM ) and (b) facultative N 2 -fixation (see Appendix E).
For the OBRD configuration, three sensitivity experiments are performed to investigate our model sensitivity to variable physical transports and biogeochemical tracer concentrations: (1) the mixing rate with the southern boundary, K H , is reduced for individual tracers (nutrients, oxygen) or combinations thereof from full rates to zero.( 2    and O 2 concentrations in the OMZ to different physical parameters derived from variations of the 14 C data and O 2 concentrations in the U-box is also examined.
The literature ranges in Table 3 provide only a rough guide for the biogeochemical parameters.The sensitivity of r p , µ, µ NF , N h and P h is tested in the OBRD configuration by changing each of them according to the literature range.The effects of changing the remineralization fractions f U , f UM , f S , and f I are examined by redistributing remineralization between the U and UM, and S and I boxes.These sensitivity experiments will be discussed in Sect.3.3 below.

Results
The physical circulation parameters calibrated with 14 C are given in Table 2.The resulting circulation is comparable with our expectations for the upwelling region of the eastern tropical South Pacific.The parameters of the biogeochemical model are shown in Table 3.

Biogeochemical tracer concentrations
Nutrient and oxygen concentrations in the upwelling region (boxes U and UM) are influenced by physical exchange with regions outside the upwelling zone (boxes I and D) and subsequent remineralization of exported organic matter.The results for biogeochemical tracer concentrations of the STD, RD, VIDRD and OBRD configurations are shown in Fig. 2 and will be used to develop our main conclusions, whereas those of the VD, VDRD, VID and OB configurations are also included in Fig. 3 and described in Appendix E.
In the STD configuration, NO − 3 levels in the UM box are quickly exhausted by denitrification in the UM box (black bars in Fig. 2), where decomposition of exported organic matter consumes all O 2 entering the UM box via advection and diffusion, and all NO − 3 entering via physical transport and remineralization of exported organic matter.O 2 is also depleted in the D box, owing to weak ventilation.This results in over 90 % of the initial nitrate being lost from the model domain by denitrification once the model has reached steady state.The large nitrate deficit with respect to phosphate in the upwelling waters results in nitrogen fixers becoming dominant in the U box despite having a lower maximum growth rate than ordinary phytoplankton (black bars in Fig. 2a, c).
In the RD configuration, complete NO − 3 exhaustion in the UM box is prevented (grey bars in Fig. 2).There is some observational evidence for the efficiency of decomposition of organic matter driven by denitrification in some high-productivity areas being lower than for respiratory processes in the presence of sufficient dissolved oxygen (Liu and Kaplan, 1984;Devol and Hartnett, 2001;Van Mooy et al., 2002).In our model, this mechanism helps prevent NO − 3 depletion in the OMZ because less nitrate is consumed by denitrification during the passage of the particles through the OMZ.However, the NO − 3 concentration in the UM box is only 3.25 µmol kg −1 , far less than the literature range of about 15 to 40 µmol L −1 .The additional organic matter now passing through the OMZ must be remineralized in the D box, which still becomes anoxic in this configuration.Even though the RD configuration fails to simulate the realistic biogeochemical tracer concentrations in the OMZ and its ad-   5 and 2. NPP PhyU , NPP PhyS , NPP NFU and NPP NFS represent the net primary production rates of Phy U , Phy S , NF U and NF S , respectively.Denif UM indicates the nitrogen loss rate by anaerobic remineralization in the UM box.Export U and Export S represent the export production rate out of U and S.
Respiration UM represents aerobic respiration rate in the UM box.Note that all panels are in units of nitrogen except (h), which is in units of O 2 .Each panel uses a differrent linear scale for the y axis starting at zero.jacent ocean, it reveals a possible mechanism for preventing NO − 3 depletion in the OMZ.While a reduced remineralization rate under suboxic conditions appears to be a prerequisite for maintaining non-zero nitrate in the OMZ (Fig. 3), we find that ventilation of O 2 from the lateral subtropical ocean into the model domain is essential for preventing anoxic conditions in the D box.But even ventilation of O 2 into both I and D boxes fails to prevent NO − 3 depletion in the UM box in the VID configuration (Fig. 3i).After reducing the denitrification rate in the OMZ, which is the configuration denoted as VIDRD, NO − 3 depletion is prevented (bars with horizontal lines in Fig. 2).Compared to the RD configuration, NO − 3 concentration in the UM box is in a realistic range (15-40 µmol kg −1 ) for the OMZ, and O 2 concentrations in the I and D boxes are also closer to the WOA2009 data, but still about 15.0 and 22.7 % lower than the observations (blue dashed lines in Fig. 2).
In the OBRD configuration, nutrients are exchanged in addition to O 2 between the subtropical ocean and the I and D boxes, together with reducing the denitrification rate under suboxic conditions.N UM depletion is prevented and N UM approaches a concentration of 20 µmol kg −1 at steady state (bars with horizontal lines in Fig. 2).The UM box is suboxic and the O 2 concentrations in the I and D boxes agree very well with the WOA2009 data (blue dashed lines in Fig. 2).Overall, the tracer distributions simulated by the OBRD configuration agree best with the observations.
In the sensitivity configuration OB, where only nutrients are exchanged in addition to O 2 between the subtropical ocean and the I and D boxes, nitrate is still exhausted in the OMZ (Fig. 3m).

Biogeochemical fluxes
For the biogeochemical fluxes, we focus on the STD, RD, VIDRD and OBRD configurations (configurations in bold in Table 5), since they show most clearly the mechanisms responsible for preventing NO − 3 depletion in the OMZ (Fig. 4).Denitrification rates are much higher in the STD than in the RD configuration (black and grey bars in Fig. 4, respectively), even though the physical parameters are the same in the two configurations, leading to nitrate exhaustion in the UM box of the STD but not in the RD configuration.In both VIDRD and OBRD configurations, NO − 3 depletion is prevented (bars with horizontal and vertical lines in Fig. 2e).Denitrification is weaker in the OBRD than in the VIDRD configuration (bars with horizontal lines in Fig. 4), even though the physical parameters are the same in both, keeping more NO − 3 in the UM-box in the OBRD configuration.Aerobic respiration in the UM box continues even when the UM box is anoxic.It consumes all O 2 entering the UM box via the various physical transport processes and thereby oxidizes about 8.7, 64, 85 and 92 % of the organic matter remineralized (denitrification + aerobic respiration) in the UM box in all four configurations, STD, RD, VIDRD and OBRD, respectively.Aerobic respiration is increased in the OBRD configuration compared with the VIDRD configuration (92 % vs. 85 %) at the expense of denitrification.
Compared with the VIDRD configuration, total PO 3− 4 in the model domain decreases by about 28 % in the OBRD configuration at steady state, and the net PO 3− 4 flux out of the I box and the corresponding net flux of PO 3− 4 from the subtropical ocean into the D box causes a 9.6 % decrease in organic matter exported into the UM box.This explains why NO − 3 concentrations in the OMZ and O 2 concentrations in the I and D boxes are slightly higher (bars with vertical lines in Fig. 2).Restricting, in a hypothetical sensitivity experiment, exchange with the subtropical oligotrophic ocean to NO − 3 and O 2 does not result in higher O 2 concentrations in the I and D boxes, because PO 3− 4 is conserved and export production does not change substantially.Restricting, on the other hand, exchange to PO 3− 4 and O 2 depresses production and organic matter decomposition by almost the same amount as in the model run that exchanges NO − 3 , PO 3− 4 and O 2 , and succeeds in driving O 2I and O 2D concentrations closer to the observations (not shown).Thus, opening the model boundary to PO 3− 4 and O 2 helps to improve the model results with respect to those of the VIDRD configuration that do not exchange PO 3− 4 across the southern boundary.

Model sensitivity
In sensitivity experiments of the OBRD configurations, designed to elucidate the importance of the influence of the subtropical ocean on the model domain, we reduce the mixing rates (K H ) of O 2 , NO − 3 and PO 3− 4 across the southern boundary in different combinations (two of them are shown in Fig. 5).Total net primary production (NPP) is the same when varying the mixing rate of either only O 2 or O 2 together with NO − 3 , as long as the PO 3− 4 exchange rate with the subtropical ocean remains unchanged (dotted lines in Fig. 5b).The reason is that changes in nitrate exchange with the subtropical ocean are compensated for by changes in denitrifica- tion and nitrogen fixation.This implies that NPP is, at steady state, determined only by phosphate availability.Once the total NPP of NF and Phy is determined by PO 3− 4 supply, aerobic respiration will increase with increasing O 2 supply, while anaerobic remineralization will decrease (solid and dashed lines in Fig. 5c).Comparing simulations that vary the mix- not change the strength of our model domain as a net NO − 3 source.Increasing r p to 20 decreases N UM by about 18 %, but triples the strength of our model domain as a NO − 3 source.However, observations indicate that r p for the ETSP is more likely to be higher than lower compared to the Redfield N : P ratio of 16 (Franz et al., 2012).Increasing the maximum growth rate of NF, µ NF , to 1/2µ, the maximum growth rate of Phy, results in higher N UM concentrations and our model domain being a larger NO − 3 source.Intuitively, decreasing µ NF to 1/4µ results in lower N UM concentrations and our model domain becoming a smaller NO − 3 source.Varying the NO − 3 half saturation constant, N h , results in virtually unchanged results.N UM increases when changing remineralization fractions in the intermediate boxes (f UM and f I ) from 70 to 50 and 30 %, respectively, effectively lowering export production via lowering the export ratio.Nevertheless, the qualitative behaviour of the model remains the same in these sensitivity experiments.

Discussion and conclusions
Nitrogen is often considered to be the primary limiting nutrient in marine upwelling regions with OMZs (Cline and Richards, 1972;Codispoti and Christensen, 1985;Morrison et al., 1998;Voss et al., 2001), where denitrification rates can be high and are generally thought to cause a major loss of NO − 3 from the world's oceans.The nitrogen deficit is commonly assumed to stimulate N 2 fixation, both in observational estimates of N 2 fixation (Deutsch et al., 2007;Monteiro et al., 2010) and in current descriptions of N 2 fixation in biogeochemical models (Moore and Doney, 2007;Schmittner et al., 2008).However, if N 2 fixation is tightly linked to nitrogen loss processes, denitrification of organic matter derived from N 2 fixation can consume more nitrogen than was fixed via N 2 fixation and thereby lead to a vicious cycle of runaway nitrogen loss (Landolfi et al., 2013).This has been found to lead to total depletion of NO − 3 in the OMZ of box models (Canfield, 2006) and global biogeochemical circulation models (Moore and Doney, 2007;Schmittner et al., 2008).For our fully prognostic 5-box model, we have identified the mechanisms capable of arresting the runaway nitrogen loss that can result from a close coupling of nitrogen fixation and denitrification (Landolfi et al., 2013) and maintaining realistic non-zero NO − 3 concentrations in open-ocean OMZs of the ETSP: reduced NO − 3 consumption by denitrification owing to slower remineralization under suboxic compared to oxic conditions, coupled with lateral ventilation of oxygen and, to some extent, nutrients with the subtropics.
In this work, the model configuration with reduced denitrification rate, and lateral ventilation and nutrient exchange (OBRD configuration) performs best with respect to the observations, whereas reduced rates of denitrification alone lead to unrealistic O 2 depletion in the deep waters, and reduced rates of denitrification combined with only O 2 ventilation in the D, or both I and D boxes still underestimate the WOA2009 data for O 2 in the I and D boxes.By allowing for exchange of O 2 and nutrients with the subtropical ocean in the OBRD configuration, the delicate balance between sufficient O 2 supply required for maintaining high levels of aerobic respiration and sufficient PO 3− 4 loss through the open boundary appears fulfilled.Compared with other box models (Shaffer and Sarmiento, 1995;Tyrrell, 1999;Deutsch et al., 2004;Canfield, 2006;Mills and Arrigo, 2010;Eugster and Gruber, 2012;DeVries et al., 2012), the box model we use here explicitly employs both a reduced-denitrification rate and an open boundary condition, which seems to be a prerequisite for the ability to simulate realistic nitrate conditions in the OMZ and oxygen concentrations in the adjacent ocean.
The NO − 3 loss by denitrification in the OMZ of the OBRD configuration is compared with that of other model-based and observational estimates in Table 6.Our simulated denitrification is consistent with the results of Somes et al. (2010) and DeVries et al. (2013) for the ETSP, lower than the estimate of Bianchi et al. (2012) and Kalvelage et al. (2013), but higher than that of Mills and Arrigo (2010).However, the estimated denitrification by Bianchi et al. (2012) represents that of the entire South Pacific but not only the ETSP.The Kalvelage et al. (2013) model has much higher fixed-N influx into the OMZ via physical transport than our model, which could compensate for their more intense NO − 3 loss by denitrification.
Phosphate turns out to be the ultimate limiting nutrient in our model (Fig. 5), and hence determines the nitrogen content of the OMZ.This strong control of the N cycle by phosphate is similar to the findings of previous models (e.g.Lenton and Watson, 2000;Canfield, 2006), where the occurrence and extent of oceanic anoxia was also tightly linked to phosphate supply.These studies explicitly assumed that N 2 fixation acts to restore surface-oceanic dissolved inorganic N : P ratio towards the Redfield ratio.By contrast, we do not prescribe the effect of nitrogen fixation on surface inorganic nutrients, and the finding of phosphate as the ultimate limiting nutrient is obtained regardless of whether NF responds directly to the N : P ratio in the surface ocean or whether NF is inhibited by the presence of NO − 3 (see Appendix B).Even though our model indicates only a weak dependence of simulated NO − 3 concentrations in the OMZ on the lateral O 2 supply from the subtropical ocean, O 2 depletion in the adjacent ocean can be prevented only when the O 2 supply from the subtropical ocean accounts for more than 20 % of the O 2 required to oxidize export production from the surface ocean of our model domain (U and S boxes).This value only varies between about 17 and 23 %, when the size of the S box varies by ±50 %, indicating that our above conclusion is rather insensitive to our choice of model domain.The O 2 supply from the subtropical ocean might be also linked to the balance of the regional fixed-N cycle.In the most re-alistic (OBRD) configuration, the balance of water-column denitrification and nitrogen fixation is tightly linked to the nitrate concentration in the OMZ: if the model domain acts as a sink for NO − 3 , nitrate concentrations in the OMZ do not exceed about 15 µmol kg −1 , i.e. the lower limit of current observations, 15 to 40 µmol kg −1 (Codispoti and Richards, 1976;Codispoti and Packard, 1980;Morrison et al., 1998;Voss et al., 2001).Nitrate concentrations close to those commonly found in OMZs are predicted only when nitrogen fixation exceeds water-column denitrification and the ocean basin containing the OMZ becomes a net source of NO − 3 (Fig. 5a, f).There are no specific data or model results focusing on the water-column nitrogen balance of the ETSP.Our simulations using a parameterization where nitrogen fixation is inhibited by the presence of nitrate yield very similar results, only with slightly reduced nitrogen fixation resulting in a somewhat reduced (by ≤ 15 %) nitrogen source for strong enough lateral oxygen supply.Ganachaud and Wunsch (2002) estimated a net northward NO 3 transport of 270 ± 170 kmol s −1 (119.2 ± 75.1 Tg N yr −1 ) across 17 • S into the ETSP in a geostrophic inverse box model, which indicates that the ETSP is a net nitrogen sink, but their estimate included benthic denitrification, which is not accounted for in our current analysis.In a model-guided analysis, DeVries et al. ( 2012) predicted water-column denitrification rates of 21-33 Tg N yr −1 by simulating the distribution of observed dissolved N 2 gas produced by denitrifying bacteria.From an ocean circulation-biogeochemical modelbased analysis of nutrient concentrations and transport rates, Deutsch et al. (2007) estimated nitrogen fixation rates in the Pacific Ocean of about 95 Tg N yr −1 , half of which was speculated to occur in the ETSP.From these estimates, we cannot rule out that the water column of the ETSP is a net source of NO − 3 , which would be consistent with our results obtained in the OBRD configuration.More recently, Eugster and Gruber (2012) probabilistically estimated nitrogen fixation and water-column and benthic denitrification separately in their box model, which appears to be consistent with our results as their results also indicate that the water column of the Indo-Pacific is a large fixed-N source.
Based on our model results, we conclude that reduced NO − 3 consumption by denitrification owing to slower remineralization under suboxic conditions together with lateral transport is essential to arrest the vicious cycle of runaway fixed-N loss in the OMZ.More research is needed to better constrain the model parameters, in particular the upwelling transport and the difference between the organic matter remineralization rate via aerobic respiration and anaerobic denitrification.
For the VD, VDRD, VID, VIDRD, OB and OBRD configurations, Eqs.(A4) and (A5) are modified to read: The transport equations (Eqs.A1, A3) are modified for Phy and NF because Phy and NF are assumed to be capable of regulating their buoyancy and exist only in U and S without being transported vertically between the U and UM or the S and I boxes.

Appendix B
It is well known from laboratory studies that diazotrophic phytoplankton can also utilize nitrate for growth, denoted as facultative N 2 -fixation (e.g.Holl and Montoya, 2005).Schmittner et al. (2008) introduced a formulation where nitrogen fixers preferentially use nitrate when available and cover only the residual nitrogen demand via N 2 fixation.In order to examine the behaviour of our model when nitrogen fixers (NF) preferentially use nitrate, nitrogen fixation is separated from diazotroph growth, as in Schmittner et al. (2008): and Eq. ( 7) was modified to accommodate the additional nitrate uptake by NF as follows: SMS(N i ) = −NPP Phy i − NPP NF i − Nitrogen-fixation i After incorporating Eqs.B1 and B2 in our all configurations described in Sect.2.2, they behave very similarly compared to Fig. 2, except that Phy U and Phy S concentrations are somewhat lower because nitrogen fixers take up NO − 3 as well.Thus, we conclude that our results are robust with respect to assumptions about facultative N 2 -fixation by diazotrophs.
. The four major open-ocean OMZs are in the eastern North Pacific (ENP), the eastern tropical South Pacific (ETSP), the Arabian Sea, and the Bay of Bengal.OMZs currently account for only about 8 % of the global ocean area but observations of intense denitrification and anammox in the OMZs indicate that they could Published by Copernicus Publications on behalf of the European Geosciences Union.B. Su et al.: What prevents nitrogen depletion in the OMZ of the eastern tropical South Pacific?

Figure 1 .
Figure 1.Model structure and configurations.The model domain comprises five active boxes representing the top 100 m of an upwelling region (U), the underlying oxygen minimum zone (UM), and an adjacent open-ocean basin divided into a surface (S) and an intermediatedepth box (I).A deep box (D) underlies both the upwelling region and the open ocean.The large-scale circulation is represented by deep (A)and shallow (B) convection (thick grey lines).Mixing between boxes is implemented via mixing coefficients (K).Remineralization derived from net primary production by ordinary (Phy) and diazotrophic (NF) phytoplankton in the surface boxes consumes oxygen.Under anoxic conditions remineralization is fuelled by anaerobic remineralization (Denif).The model can be configured to exchange nutrients and oxygen with the southern subtropical ocean (right, denoted as "SO").See Table3for symbol definitions and text for details.

Figure 2 .
Figure 2. Simulated steady-state phytoplankton, nutrient and oxygen concentrations for the main model configurations defined in Tables 5and 2. Each panel uses a linear scale of the y axis starting at zero.Dashed blue lines represent the averages of the WOA2009 nitrate and oxygen data for the corresponding boxes, and the light blue shadings refer to the 95 % confidence intervals; however, there are no data for Phy U , Phy S , NF U and NF S .

Figure 3 .
Figure 3. NO − 3 concentration in the OMZ and O 2 concentration in the I box for all combinations of g U and g S resulting in all transport parameters being inside the literature range as given in Table 3.The x axis is the O 2 concentration in the D box.The red dot in each panel is the selected suite of physical transport parameters which fit the biogeochemical data best in each model configuration.The horizontal green dashed lines represent the averages of the WOA2009 data for N UM and O 2I , and the vertical green dashed lines denote the averages of the WOA2009 data for O 2D .The light green shadings show the 95 % confidence intervals of the WOA2009 data. 0 et al.: What prevents nitrogen depletion in the OMZ of the eastern tropical South Pacific?

Figure 5 .
Figure 5. Dependence of biogeochemical processes on the exchange of O 2 , NO − 3 and PO 3− 4 with the subtropical ocean through the southern boundaries of the I and D boxes.The x axes indicate the contribution of O 2 supplied from the subtropical ocean relative to that required to oxidize all export production from the surface ocean (boxes U and S).(a-e) only O 2 exchanged through the southern boundaries is reduced; (f-j) exchange of O 2 , NO − 3 and PO 3− 4 is reduced.N UM is NO − 3 concentration in the UM box and NO − 3 influx is the NO − 3 flux through the southern boundary (positive into model domain).NPP Phy , NPP NF and NPP NF+Phy are net primary production by ordinary phytoplankton, nitrogen fixers, and the sum of both in the surface ocean.Respiration and Denif (UM) represent O 2 consumption by aerobic remineralization and NO − 3 removal by anaerobic remineralization, respectively, in the UM box.N-inventory and P-inventory are the total nitrogen and phosphorus inventories in the model domain, including all organic and inorganic species.O 2D and Denif (D) represent O 2 concentration and NO − 3 removal by anaerobic remineralization in the D box.Units of all variables are 10 11 µmol yr −1 m −1 except for N UM and O 2D , which are given in µmol kg −1 , and N-inventory and P-inventory, which are 10 11 µmol m −1 .The shaded area denotes the parameter range for which the model domain is a net source of NO − 3 .

Figure 8 .a
Figure 8. NO − 3 and O 2 concentrations in the OBRD configuration for different physical parameters derived from variations of the 14 C data (a) and O 2 concentration in the U box (b).(a) Decrease and increase mean that 14 C values in all boxes are reduced or increased simultaneously.(b) Values of the x axis denote the variations of O 2 concentration in the U box relative to the standard.The standard run in each figure is the OBRD configuration with physical parameters defined in Table2.

B.
Su et al.: What prevents nitrogen depletion in the OMZ of the eastern tropical South Pacific?Appendix A Physical transports of a tracer X among the boxes U, UM, S, I and D are defined for the STD configuration as follows:Transport(X U ) = (X UM − X U )(A + B + K US ) • L U (A1) Transport(X UM ) = [AX D + BX I − X UM (A + B)

Table 1 .
Model variables. a

Table 2 .
Parameters of the physical model configurations.Detailed explanations for these parameters are given in Table3.
Canfield (2006)a , r c , r den , K US , K UM ,K H , A and B are the same as inCanfield (2006).

Table 4 .
14C (in ‰) data from GLODAP used for calibration of the model physical parameters.GLODAP natural 14 C data averaged over the respective regions.b SI and SD represent the southern boundary outside the I and D boxes, respectively. a ) Simulations are repeated with individual circulation parameters varied by ±50 % to explore the sensitivity with respect to the circulation parameters of the box model.(3) The sensitivity of NO −

Table 5 .
Summary of model configurations.+" means that the modification applies to this configuration.The configurations in bold are the main configurations in the text, while the others are the sensitivity configurations described in Appendix E. STD is defined in Sects.2.2 and 2.3; in RD, a reduced denitrification rate is applied; VD indicates that the southern boundary of the model domain is partially opened to allow ventilation of O 2 and 14 C (but not NO − 3 and PO 3− 4 ) to the D box; VDRD is the configuration when a reduced denitrification rate is applied in VD; VID differs from VD only in that the partially open southern boundary is extended to allow ventilation of O 2 and 14 C also into the I box; VIDRD is the configuration when a reduced denitrification rate is applied in VID; in OB, nutrient (NO − 3 and PO 3− 4 ) mixing is added to VID; OBRD is the configuration in which the reduced denitrification rate is added to OB. "