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Environmental Physics, Institute of Biogeochemistry and Pollutant Dynamics, ETH Zurich, Zurich, Switzerland
Corresponding author: O. Eugster, Environmental Physics, Institute of Biogeochemistry and Pollutant Dynamics, ETH Zurich, CHN E27, Universitätstr. 16, CH-8092 Zürich, Switzerland. (firstname.lastname@example.org)
 We determine the global rates of marine N-fixation and denitrification and their associated uncertainties by combining marine geochemical and physical data with a new two-dimensional box model that separates the Atlantic from the IndoPacific basins. The uncertainties are estimated using a probabilistic approach on the basis of a suite of 2500 circulation configurations of this box model. N-fixation and denitrification are diagnosed in an inverse manner for each of these configurations usingN*, P*, and the stable nitrogen isotope composition of nitrate as data constraints. Our approach yields a median water column denitrification rate of 52 TgN yr−1 (39 to 66 TgN yr−1, 5th to 95th percentile) and a median benthic denitrification rate of 93 TgN yr−1 (68 to 122 TgN yr−1). The resulting benthic-to-water column denitrification ratio of 1.8 confirms that the isotopic signature of water column denitrification has a limited influence on the global mean stable isotopic value of nitrate due to the dilution of the waters with a denitrification signal with the remainder of the ocean's nitrate pool. On the basis of two different approaches, we diagnose a global N-fixation rate of between 94 TgN yr−1 and 175 TgN yr−1, with a best estimate of 131 TgN yr−1 and 134 TgN yr−1, respectively. Most of the N-fixation occurs in the IndoPacific suggesting a relative close spatial coupling between sources and sinks in the ocean. Our N-fixation and denitrification estimates plus updated estimates of atmospheric deposition and riverine input yield a pre-industrial marine N cycle that is balanced to within 3 TgN yr−1 (−38 to 40 TgN yr−1). Our budget implies a median residence time for fixed N of 4,200 yr (3,500 to 5,000 yr).
 Dinitrogen (N)-fixation and water column and benthic denitrification are the main source and sinks of biologically available nitrogen (fixed N) in the marine environment, yet estimates of the global rates of these processes differ widely (Table 1). These processes occur in distinct marine environments. Water column denitrification is confined to suboxic waters, located primarily in the Arabian Sea [e.g., Naqvi, 1987] and the Eastern Tropical Pacific [e.g., Brandhorst, 1959]. Benthic denitrification occurs in most sediments of the world's oceans, with highest rates found in regions of high organic matter sedimentation and low oxygen concentrations in the overlying waters, i.e., particularly in the sediments of the continental margins [Middelburg et al., 1996; Devol, 2008]. In contrast, N-fixation tends to be restricted to oligotrophic conditions as found in the warm surface waters of the low latitudes [Karl et al., 2002; Carpenter and Capone, 2008].
Table 1. Non-exhaustive Literature Compilation of Pre-industrial or Modern Estimated Sources and Sinks in the Global Marine Nitrogen Budgeta
We give the median, and the 5th and 95th percentile range, computed across 2500 circulation configurations, for N-fixation and water column and benthic denitrification. Residence time computed on the basis of all N sinks. We show the conservative estimates of N-fixation and denitrification proposed byGalloway et al. . Our N-fixation rate computed using the restoring approach does not include N-fixation diagnosed in the Southern Ocean.
125 ± 41
135 ± 50
131 (94 to 175)
134 (117 to 150)
15 ± 5
50 ± 20
41 ± 14
80 ± 15
181 ± 44
265 ± 55
85 ± 20
180 ± 50
93 (68 to 122)
Wat. col. denit.
80 ± 20
65 ± 20
52 (39 to 66)
15 ± 5
25 ± 10
4 ± 2
4 ± 2
184 ± 29
275 ± 55
Resid. time (yr)
4,200 (3,500 to 5,000)
3 (−38 to 40)
 The spatiotemporal variability of these processes, the relative paucity of direct rate measurements, as well as the many methodological difficulties in measuring such biological rates have resulted in widely different direct assessments of denitrification and N-fixation (Table 1) [see also Mahaffey et al., 2005]. Geochemical approaches on the basis of the distribution of nutrients and N isotopes [e.g., Michaels et al., 1996; Gruber and Sarmiento, 1997] have helped to overcome the sampling bias thanks to the tracer's property of integrating the signal in time and space, but leave room for interpretation due to their indirect nature.
 The large spread of estimates led to distinctly diverging views on whether the marine N budget is balanced. On the one hand, Codispoti et al.  and Codispoti  argued that the sinks of fixed N strongly exceed the sources (Table 1) causing the fixed N budget to be out of balance by several hundred TgN yr−1 (1 Tg = 1012 g). On the other hand, Gruber and Sarmiento  and later Gruber  proposed a fixed N budget in approximate balance, albeit with considerable uncertainties.
 In these discussions, relative little consideration has been given to the large uncertainties associated with the rate estimates. In most studies, no quantitative error assessment was conducted at all and thus no uncertainty estimates are usually provided. Gruber and Sarmiento  and Gruber  reported uncertainties with their global fixed N budgets, but these error estimates were largely based on subjective assessments rather than a thorough analysis of the sources of uncertainty and the propagation of these uncertainties to the global value. Therefore, the question of whether the fixed N budget of the ocean is balanced or not cannot be answered unless the errors associated with the individual source and sink terms are truly quantified.
 Our study aims to address these open issues, i.e., i) magnitude of rates and ii) magnitude of the associated uncertainties. To this end, we use a new multibasin geochemical model constrained with a large number of data, including anomalies in the nutrient distributions and information contained in the stable isotopic ratio of nitrate. This permits us to infer the global and regional rates of N-fixation and denitrification in the water column and sediments. We adopt a probabilistic approach to determine the uncertainties.
 In the next section, we provide some additional background on the specific geochemical constraints that we will make use of in our study. After the method section, we first discuss our global-scale estimates of denitrification (section 4.1) and N-fixation (section 4.2), and then combine them to assess the question of how far from balance the pre-industrial marine N cycle might have been (section 4.3). We then investigate the robustness of these results to additional sources of uncertainty that were not considered in the probabilistic estimates (section 4.4). Finally, we discuss the N-fixation rates (section 4.5) and budgets at the basin-scale and the implied lateral transports (section 4.6). We finish with a conclusion section (section 5).
2. Geochemical Constraints on the Marine N Cycle
 Geochemical tracers such as anomalies in the stoichiometric relationship of nutrients (e.g. N*), the isotopic composition of the different N compounds, or anomalies in the dissolved concentrations of N2 to argon [Codispoti et al., 2001; Devol et al., 2006; Chang et al., 2010] have played an important role in constraining the marine N cycle, mostly because direct rate measurements remain sparse. The geochemical approaches integrate in space and time, and hence offer the ability to overcome this undersampling problem. However, they tend to be indirect and often multiple assumptions have to be made in order to convert the tracer signals into nitrogen specific rates.
This tracer is built on the premise that regular phytoplankton consume nitrate ( ) and phosphate ( ) in the classical Redfield ratio of 16 to 1, and that these two nutrients are also released with this ratio when the resulting organic matter is further processed within the food chain and during bacterial degradation (see e.g., Weber and Deutsch for limitations). If this assumption is met, any non-conservative behavior ofN* is a quantitative indication of a net addition or removal of fixed N. An alternative means to express the same concept is the quasi-conservative tracerP* [Deutsch et al., 2007]:
which is related to N* through P* = (−N* + 2.9 mmol m−3)/16.
 The stable isotope ratio of 15N over 14N provides a second important avenue into the study of the sources and sinks of marine fixed N [Montoya, 2008]. This is because most relevant processes of the marine N cycle fractionate, i.e., one isotope (usually the lighter) reacts faster than the other one, leading to changes in the stable isotope ratio of the substrate and product pools. The nitrogen isotopic composition of a given sample is expressed as:
where (15N/14N)sample is the isotopic ratio of the sample under consideration, and (15N/14N)air is the isotopic ratio of atmospheric N, which is commonly used as the reference. The isotopic preference of a process for the light isotope is often expressed by the fractionation factor (α) or by the isotopic enrichment ε, which in very good approximation is equal to the difference in the δ15N value of the product and the substrate:
 Marine N cycle processes have varying degrees of isotopic fractionation. assimilation by phytoplankton occurs with a light isotopic enrichment of −5‰ [Sigman et al.,1999; DiFiore et al., 2006]. N-fixation exhibits very little to no fractionation [Carpenter et al., 1997]. Similarly, benthic denitrification has almost no effective isotopic fractionation as local is usually completely consumed [Brandes and Devol, 2002]. In contrast, water column denitrification is a key fractionating process that preferentially consumes 14 N with a high isotopic enrichment εwcd = − 25‰ [Brandes et al., 1998; Sigman et al., 2003]. Since this estimate of the isotopic enrichment comes from field data, we interpret it to reflect also the possible contribution of fixed N removal by the anammox process. Sediment N burial occurs with ε = 0‰ (sensitivity of the marine N cycle to the isotopic enrichment for organic matter burial is displayed in Figure S7 in the auxiliary material) [Brandes and Devol, 2002]. In addition, the isotopic composition of a pool can also be altered by the addition of/mixing with another nitrogen pool that has another δ15N, as is the case for the atmospheric deposition of fixed N onto the ocean's surface (δ15N of −4 ± 5‰ [Brandes and Devol, 2002]), riverine input of fixed N (δ15N of 4 ± 4‰ [Brandes and Devol, 2002]), or the addition of newly fixed atmospheric N into the oceanic fixed N pool (δ15N of 0‰).
 Given the strong fractionation associated with water column denitrification, the absence of fractionation during benthic denitrification, and the small difference between N-fixation derived fixed N and theδ15N of the mean ocean, the mean ocean δ15N is very sensitive to the benthic-to-water column denitrification ratio [Brandes and Devol, 2002]. This high sensitivity makes this value a possible important constraint for relative importance of water column versus benthic denitrification. However, Deutsch et al.  pointed out that this constraint is weakened by the fact that the strong regional localization of water column denitrification leads to a dilution effect, as the isotopic signal in generated in that region will be diluted as these waters are mixed with the remainder of the ocean.
 We determine the global and regional rates of N-fixation and denitrification in the water column and sediments in an inverse manner, i.e., by combining information contained in physical and biogeochemical tracers with a newly developed box model that describes the rates and pattern of ocean transport and mixing. We thereby adopt a probabilistic approach, permitting us to estimate the entire empirical probability density function (PDF) of N-fixation and denitrification. Two major sources of uncertainty are considered: uncertainty in the data constraining the marine N cycle and uncertainty in the rates and pattern of ocean transport and mixing.
 We address these two sources of uncertainty by following a two-step process: First, we determine the transport and mixing terms of the box model by optimizing the model with primarily physical observations, taking into consideration the uncertainties in the observations using a Monte Carlo approach. This results in the generation of a suite of 2500 circulation configurations, each of which is optimally consistent with the observational constraints. In the second step, we use this suite of circulation configurations and determine the rates of the N cycle again by optimally combining nutrient and isotopic observations and these models. This permits us to generate PDFs that contain not only the errors that come from the propagation of uncertainties in the data used to constrain the N cycle, but also the errors that come from the circulation.
 We follow two different strategies for determining the rates of N-fixation and denitrification in the water column and sediment. The denitrification rates are determined by inverting observations of nutrients and N isotopes coming from the whole water column. In contrast, N-fixation is estimated by using nutrient observations from the near surface ocean in a restoring approach. Since the inversion used to determine denitrification requires the assumption of a balanced marine N cycle, it gives us a second estimate of N-fixation, which we then use to assess the robustness of the restoring method.
 Our approach does not consider all sources of uncertainty explicitly. Namely the uncertainties associated with the geochemical assumptions underlying the data analyses, in particular the assumption of a constant stoichiometric ratio, are not systematically investigated. We will address their impact through sensitivity analyses.
3.2. Model Architecture and Circulation
 We constructed a new 14-box model of the global ocean consisting of an Atlantic, a Southern Ocean, and of the joint Indian and Pacific Ocean (IndoPacific) (Figure 1). The Atlantic basin is divided into a northern and a low-latitude part, whereas the IndoPacific is divided into an oxic and a suboxic part. In the vertical, each (sub)basin is separated into 2 to 4 depth layers, resulting in a total of 14 boxes. The suboxic lower thermocline box represents the regions where water column denitrification occurs i.e., the Arabian Sea and the Eastern Tropical Pacific. This arrangement of boxes essentially extends the 8 box model ofDeutsch et al.  and combines it with elements of the Cyclops box model of Keir .
 We determined the water mass transport (one-way fluxes) and mixing (two-way fluxes) terms by inverting three tracers, i.e., , as defined by Broecker et al. : , and natural radiocarbon Δ14C. Mean values and variances for each tracer and box were determined by depth and geographic-averaging climatological data from the World Ocean Atlas (WOA) (nutrients, O2) [Conkright et al., 2002] and from the gridded GLODAP product (natural Δ14C) [Key et al., 2004].
 A simple description of the cycling of was added, consisting of surface production of organic phosphorus, export and remineralization. Production and export was fixed for each region on the basis of the estimates provided by Dunne et al. , which gives a global carbon export flux of 11.3 PgC yr−1, i.e., 8.9 TmolP yr−1. In the ocean interior, organic P is remineralized according to a power law function [Martin et al., 1987]. Following Deutsch et al.  different exponents are used in the suboxic vs oxic regions (b = 0.400 and 0.858, respectively). O2 is not simulated, even though its distribution was used to construct the architecture of the model. Specifically, the volume of the suboxic box was calculated from WOA's climatological O2 distribution by integrating all waters with concentrations lower than 10 μmol kg−1.
 The inversion of the water circulations was performed by minimizing a least squares type cost function that included a Bayesian component. The initially estimated vertical mixing terms were adjusted so that the inverted water circulations produce a realistic global carbon export flux [Laws et al., 2000; Najjar et al., 2007] (see also discussion section). This was obtained by upscaling the prior values of the mixing fluxes by a factor of 4 to 6. A Markov Chain Monte Carlo (MCMC) method was used to investigate the sensitivity of the posterior transport and mixing terms toward , Δ14C, and export production. The MCMC was repeated 2500 times, which resulted in the generation of 2500 circulation configurations, each of which was then used to optimize the box model. The auxiliary material provides a detailed description of the inversion scheme for the ocean's circulation.
 In the subsequent investigations, all configurations were considered equally, i.e., no weighting was performed according to the value of their a posteriori cost function or any other criteria. However, we sometimes compare all 2500 circulation configurations with a suite of 100 configurations that have the smallest a posteriori cost function. For some specific investigations, the circulation setup with the smallest cost function was selected (displayed in Figure S1 in the auxiliary material).
3.3. Water Column and Benthic Denitrification
 We determined water column and benthic denitrification rates by considering the full marine N budget and then adjusting these rates in such a manner that the modeled distribution of N* and δ15N are optimally consistent with the observations. This required a number of a-priori simplifications. First we assumed that water column denitrification occurs only in the suboxic box within the thermocline of the IndoPacific. Additionally, since the current state of knowledge about anammox does not allow our geochemical approach to estimate the rates of anammox and canonical denitrification separately, anammox is implicitly included in our denitrification estimate. Second, we prescribed the relative distribution of benthic denitrification between the different boxes of our model, while keeping the global total adjustable. Third, for the purpose of this approach only, we imposed a steady state on the marine N and P budgets. We ensured this by forcing global N-fixation to balance the global marine N budget. However, we kept its regional distribution adjustable, i.e., the amount of N-fixation occurring in the Atlantic relative to that in the IndoPacific. This left us with three unknowns that we solved for, i.e., the global magnitudes of water column and benthic denitrification, and the relative spatial distribution of N-fixation.
 The starting points for determining these unknowns are the global marine budgets of N and P, for which we considered the following processes: Riverine input of both N and P, atmospheric deposition of N, N-fixation and denitrification for N, and finally burial at the seafloor of N and P. We considered here primarily the budget of the open ocean, for which we assume that the human footprint has remained small. This is supported by recent modeling studies that showed relatively small changes in open ocean biogeochemistry resulting from the anthropogenic imprint [Krishnamurthy et al., 2007, 2009]. Consequently, we will be using pre-industrial flux estimates for the budget.
 The pre-industrial input by riverine N and P discharge is based on the estimates from the Global Nutrient Export from WaterSheds (NEWS) model [Seitzinger and Mayorga, 2008], but scaled down to account for the significant loses of nutrients occurring in river mouths before reaching the coastal ocean. The global total N input is assumed to amount to 14 TgN yr−1 and that of P to 2 TgN yr−1. There is no river input into the Southern Ocean and inputs into the suboxic and oxic IndoPacific are calculated on a per-surface area basis given the integrated N and P discharge into the Indian and Pacific Oceans.
 The pre-industrial N input via atmospheric deposition is prescribed based onDuce et al. . Given the negligible source of P from the atmosphere [Baturin, 2003], atmospheric P deposition is neglected. We prescribed the loss of P by burial or organic matter to exactly balance the global river input of P in order to satisfy the steady state assumption. The spatial distribution of organic P burial in sediments is set to follow that of benthic denitrification.
 The relative spatial distribution of benthic denitrification is prescribed as 23% Atlantic, 69% IndoPacific, and 8% Southern Ocean [Christensen et al., 1987; Devol, 1991; Middelburg et al., 1996]. The fraction of benthic denitrification in each water column is defined on a per surface area, while within each water column benthic denitrification is vertically distributed based on Middelburg et al. . This gives the following relative vertical distribution (from surface box to bottom): 30%/30%/30%/10% (suboxic IndoPacific), 40%/50%/10% (oxic IndoPacific), 40%/60% (Southern Ocean), 40%/50%/10% (Low-latitude Atlantic), and 40%/60% (North Atlantic).
 The cycling of and associated with the biological loop is modeled as before, except that export production is now interactively modeled by restoring surface to observations. The cycling of is then linked to that of following the C:N:P Redfield ratio of 106:16:1 [Redfield et al., 1963]. A few additional assumptions had to be made for N-fixation: While the relative distribution between the Atlantic and the IndoPacific was left as an unknown, four times more N-fixation per surface area was prescribed in the suboxic column (same assumption thanDeutsch et al. ). In addition, 7% of the global N-fixation rate was set to occur in the Southern Ocean reflecting its contribution to the global ocean surface area. This spatial assignment is relatively ad hoc, but has only a limited impact on the global results. In the vertical, 90% of the newly fixed N is released in the surface box, while the remaining is exported as particulate organic matter to depth where it is subject to the same remineralization rates as standard organic matter.
 The cycling of 15N was implemented to follow the cycling of total nitrogen (15N + 14N), with proper consideration of the isotopic fractionations and the different isotopic values of the external sources. The values for these fractionations and source compositions are given in section 2.
 The three unknowns, i.e., the global rates of water column and benthic denitrification, and the fraction of N-fixation occurring in the Atlantic, were determined on the basis of a standard least squares method for each of the 2500 circulation configurations. Systematic scans over the ranges of the three parameters were done for each circulation configuration, and the parameter combination that matched best the observedN* at each box and the observed mean ocean δ15N in the least squares sense was extracted. Observed N* was computed for each box from the WOA [Conkright et al., 2002], except for the suboxic box, where we used a N* value of −13.0 mmol m−3 computed from the World Ocean Database, instead of the N* value of −10.6 mmol m−3 from WOA. The discrepancy comes from the smoothing performed to generate the gridded WOA product. For the mean ocean δ15N, we adopted a value of 4.8‰ [Liu and Kaplan, 1989; Sigman et al., 2000]. Due to the relatively sparse δ15N measurements, we decided to use the spatial distribution of the observed δ15N only as a validation for the posteriori solutions, rather than using it for the optimization. The auxiliary material provides a discussion of the misfits.
3.4. Nitrogen Fixation
 The primary means we use to estimate global and regional N-fixation is by diagnosing it from restoring excess relative to in surface waters [Deutsch et al., 2007]. We will later compare the results of this approach to the N-fixation rates implied by the budget approach used above to estimate denitrification. This restoring approach uses the quasi conservative tracerP* (see equation (2)), whose variations in the surface ocean primarily reflect the balance between N-fixation that consumesP* and the transport convergence of P* that tends to increase P*. Assuming that the N cycle is in steady state locally, i.e., within each surface box, the rate of N-fixation,JFIX(N)i, in box i can then be diagnosed from the transport convergence :
where λis a non-dimensional parameter andγe, prescribed to 0.1, corrects for the fraction of organic matter that sinks as particulate organic matter. rfis the N:P ratio of N-fixers, taken as 40 [Letelier and Karl, 1998; Krauk et al., 2006; Knapp et al., 2012]. The term summarizes a number of additional processes that occur with non-Redfieldian stoichiometry and thus contribute to sources or sinks ofP*. The only ocean internal source of P* is benthic denitrification (B). The only external source of P* is the river input of P (RIP), while the atmospheric deposition of N (AD), and the river input of N (RIN) represent external sinks of P*. Since water column denitrification is confined to a lower thermocline box that does not exchange directly with a surface box, we do not have to consider it here. Organic matter burial occurs with Redfield stoichiometry and thus is not included in . This gives for :
 All terms of were prescribed using the same rates and patterns as in the budget approach (see there for details). Atmospheric deposition of N was set to 14 TgN yr−1, a value of 14 TgN yr−1, and 2 TgP yr−1 was chosen for the river inputs of N and P, respectively. P* was estimated by first computing it for each grid-box of WOA using annual mean and and then averaging it over each box of the model. If the diagnosed rate of N-fixation (equation (5)) is negative in a basin, the rate is set to zero.
 We disregard the diagnosed N-fixation rates in the Southern Ocean based on the rationale that no N-fixation is expected to occur there [Deutsch et al., 2007]. Nevertheless, substantial transport convergences of P* exist in this ocean basin. We interpret this to be primarily the result of non-Redfield utilization of N and P by non-diazotrophic organisms, which have a significant impact on the upper ocean distribution of N and P in this ocean basin [Arrigo et al., 1999; Weber and Deutsch, 2010; Mills and Arrigo, 2010].
4. Results and Discussion
4.1. Global Denitrification
 Our budget approach yields an empirical probability density function (PDF) of the global rates of water column and benthic denitrification (includes both canonical denitrification and anammox) with a median of 52 TgN yr−1 and 93 TgN yr−1, respectively (Figures 2a and 2b). The 5th to 95th percentile range for water column denitrification goes from 39 to 66 TgN yr−1, while that for benthic denitrification goes from 68 to 122 TgN yr−1 (Table 1). Since the PDFs of the rates do not deviate too strongly from a normal distribution, the 5th to 95th percentile ranges are very similar to the ranges described by the mean ± two standard deviations. We regard our estimates to reflect the pre-industrial N cycle, as we assume that the anthropogenic perturbation has not yet significantly altered the open-ocean data that we employ to diagnose the rates.
 Our probabilistic estimates of the total N loss by denitrification of 145 (107 to 188) TgN yr−1 clearly refute the high rates proposed by Codispoti et al.  which are in excess of 400 TgN yr−1 (Table 1). They are also lower by nearly a factor of two in comparison to several other recent estimates [Gruber, 2004; Deutsch et al., 2004; Galloway et al., 2004]. Although these estimates pertain to different time periods, i.e., pre-industrial or present-day, the human perturbation is too small to explain the difference (maximally about 20 TgN yr−1 [Galloway et al., 2004; Gruber and Galloway, 2008]). Our low denitrification rates are in line with those suggested by Gruber and Sarmiento  and the recent estimate of Sigman et al. . However, Sigman et al.  noted that their model diagnosed denitrification rate may be biased low because of their unrealistically low simulated export production. Although our approach shares some similarities with that employed by Sigman et al. , our median diagnosed global C export is consistent with observationally based estimates, i.e., our relatively low denitrification rates cannot be related back to such a bias.
 Comparing our water column and benthic denitrification rates to the published estimates separately, it turns out that the water column denitrification rates tend to be more consistent among each other (with the notable exception of Codispoti et al.  and Codispoti ), and that the largest differences occur with the benthic rates. Nevertheless, also our water column denitrification rate of 52 (39 to 66) TgN yr−1 is at the lower end of most recent estimates.
 Our water column denitrification rate depends sensitively on the size of the suboxic lower thermocline box in the IndoPacific, which constitutes the only place where this sink of N occurs in our model. The larger the volume of this suboxic box, the more water column denitrification is diagnosed in our model in order to match the observed mean ocean δ15N and the low N* value in this box. The size of our suboxic box was estimated by considering the oceanic volume that has O2 < 10μmol kg−1. Since this threshold is higher than that normally associated with the onset of water column denitrification (5μmol kg−1) [Goering, 1968] we consider our estimate more likely to be biased high rather than biased low. Thus, this argument does not explain our relatively low water column denitrification rate.
Codispoti  suggested that his large modern water column denitrification estimate, in contrast to Gruber and our new estimates, could reflect the anthropogenic perturbation. His global estimate comes from a few in-situ observations extrapolated to the global ocean, which make them sensitive to recent perturbations. However, if modern water column denitrification were as high as suggested byCodispoti , i.e., above 150 TgN yr−1 and had been operating for at least a few decades, then this should have left an imprint on the tracers in the main denitrification zones and hence should have been detected by our approach. In addition, all modeling studies conducted so far to investigate the possible effect of the anthropogenic perturbation on the marine N cycle identified only small changes [Krishnamurthy et al., 2007 , 2009]. Thus, while we can clearly refute the very high water column denitrification rates suggested by Codispoti , our rate is at the low end, but not clearly inconsistent with most recent estimates that suggest fixed N loss rates of the order of 60 to 80 TgN yr−1.
 Our globally integrated rate of benthic denitrification of 93 (68 to 122) TgN yr−1 is considerably smaller than any other recent estimate (Table 1). It is about three times smaller than the value suggested by Codispoti et al. , but it is also smaller by a factor of about two compared to the estimates provided by Gruber , Galloway et al.  and Deutsch et al.  (Table 1). Most of these estimates are based on scaling the water column denitrification rate with the ratio of benthic-to-water column denitrification. Thus, an overly large water column denitrification rate would immediately lead to an overestimation of benthic denitrification. This is clearly the case withCodispoti et al.'s  estimate, but not for the others. In addition, a more direct estimate of benthic denitrification obtained by using the parameterizations of Middelburg et al.  and export production estimates following the particle export database of Dunne et al.  gives a global benthic denitrification rate close to 200 TgN yr−1, suggesting that our rate is rather on the low end. Our low rate is primarily driven by the need of the model to fit the observed global mean δ15N of , which puts strong constraints on the ratio between benthic-to-water column denitrification. With our water column denitrification being on the low end compared to recent estimates, this ratio demands also a relatively low benthic denitrification rate. It turns out, however, that also this ratio is relatively low compared to other estimates.
 The median benthic-to-water column denitrification ratio computed from all inverted configurations is 1.80 (1.63 to 2.01), (Figure 2c, lower left PDF). This ratio is lower than the value of 2.7 found by Deutsch et al.  and much lower than the originally proposed value of 4 [Brandes and Devol, 2002]. Our models estimate this low ratio while maintaining a mean ocean δ15N of 4.8‰, which means that in our models, the signal of water column denitrification is only partially successful in imprinting itself on the global mean δ15N of as a result of a strong dilution effect. This effect, introduced by Deutsch et al. , postulates that as water column denitrification takes place in a very limited ocean volume (Arabian Sea and Eastern Tropical Pacific) with high degrees of loss, denitrification causes less 15N enrichment than would arise if this process was homogeneously distributed throughout the ocean. If the latter was the case, the benthic-to-water column denitrification ratio would be 4 in order to match a mean oceanδ15N of 5‰ [Brandes and Devol, 2002]. This is because water column denitrification has an expressed isotope effect of 25‰, while benthic denitrification leads to no fractionation. If water column denitrification had an expressed isotopic fractionation of only 15‰, as recently suggested by Kritee et al. , the benthic-to-water column ratio would also be lower, even in a well mixed ocean. In fact,Kritee et al.  suggested a ratio of 1.6, very close to our estimate. The underlying reasons are very different, however. Our low value is a result of a strong dilution effect, while theirs is a result of a weaker effective fractionation.
 A possibly important determinant of the magnitude of the dilution effect is the fractional loss of fixed N by water column denitrification in the suboxic box. The larger this loss, the smaller the resulting N concentration and the lesser impact this N with its high isotopic signature can have on the global mean δ15N of . However, we find only a weak tendency for our simulations with a higher fractional loss to identify a higher dilution effect, i.e., a smaller benthic-to-water column denitrification ratio. Also the fractional losses tend to be similar to that diagnosed byDeutsch et al. . Thus, this process cannot be the most important control on the dilution effect. Rather, we hypothesize that our strong dilution effect and the thus inferred low benthic-to-water column denitrification ratio is due to a larger degree of spatial separation of suboxic waters in our model. Compared to all configurations, the suite of 100 circulation setups with the smallestcost functions have a distribution slightly shifted toward a higher ratio as a consequence of higher benthic denitrification. Nevertheless, all configurations have a ratio below 2.2.δ15N within each box provide some confidence of this low estimate, since modeled δ15N successfully reproduce the data (see auxiliary material). This validation is possible because δ15N within each box is not used to constrain the model.
4.2. Global N-fixation
 The global N-fixation rate estimated by restoring surfaceP* toward climatological data yields a median of 134 TgN yr−1 with a 5th to 95th percentile range of 117 TgN yr−1 to 150 TgN yr−1 (Figure 2e). If we also considered the diagnosed N-fixation in the Southern Ocean, the global fixation rate would increase by 21 TgN yr−1 to 155 TgN yr−1 (138 to 171 TgN yr−1). The global N-fixation rate estimated by restoringP* tends to be somewhat, but not significantly, higher than that implied from the budget approach, which yields a median rate of 131 TgN yr−1 (94 to 175 TgN yr−1) (Figure 2d). Among all 2500 circulation setups, there is no correlation between the global N-fixation rates estimated from the restoring and the budget approaches (not shown). This lack of correlation is interpreted as evidence that the two approaches are based on independent geochemical constraints. The budget approach aims to fit the mean oceanδ15N and N* within each box, while the restoring approach assimilates P* mainly in the surface and thermocline boxes.
 Our P*-inferred global N-fixation rate of 134 (117 to 150) TgN yr−1 is consistent with most recent estimates, such as those by Gruber , Galloway et al.  and Deutsch et al.  (Table 1). The latter estimate of 130 TgN yr−1 is largely based on the same methodology and the same data, i.e., the analysis of the transport convergence of P*, but used a full three-dimensional general circulation model coupled to a simple ecosystem model to compute this convergence. The close agreement indicates that our large set of circulation configurations captures the three-dimensional transport convergence well, yet also provides us with the capability to estimate the associated uncertainties.
 Our global N-fixation is, however, substantially smaller than the estimate put forward byDeutsch et al. . The latter is based on a similar box model as employed here, but did not include a separation of the ocean basins into an Atlantic and an IndoPacific region. In the budget approach, the most important difference comes from the spatial separation of the ocean into different basins. For the restoring approach, which Deutsch et al.  did not use, it is interesting to note that our estimate values are very comparable to those of the budget approach and are also very similar to those provided by Deutsch et al. , which was computed by applying the restoring approach in a three-dimensional general circulation model. A small part of the difference can also be explained by invoking thatDeutsch et al. did not consider the input of fixed N into the ocean by atmospheric deposition and rivers. Since global N-fixation is estimated by difference in this approach, the lack of consideration of this source biases their estimate to be too large by ∼30 TgN yr−1.
 The restoring-based estimate of the rate of N-fixation depends sensitively on the assumed N:P ratio of the diazotrophic organisms. Our value,rf = 40, stems largely from observations of the growth of Trichodesmium. Recent discoveries point toward a substantially greater diversity of diazotrophs that thrive under different environmental conditions [Zehr et al., 2001; Montoya et al., 2004; Moisander et al., 2010; Hamersley et al., 2011] and possibly have different N:P ratios. We cannot assess the implications of such variations well at this time, but note that recent measurements of the N:P ratio in the unicellular diazotroph Crocosphaera support our chosen value [Knapp et al., 2012]. In addition, the two independent geochemical approaches we used here estimate similar global fixation rates. This suggests that our rates reflect the global N-fixation by all diazotrophs, i.e., the sum of the contribution from bothTrichodesmium and unicellular diazotrophs.
4.3. State of the Pre-Industrial Marine N Cycle
 Our rates of N-fixation and denitrification and the literature-based estimates of the other source and sink terms indicate that the pre-industrial N cycle was balanced or close to being balanced (Figure 3). The median of the N budget imbalance is a small excess of 3 TgN yr−1 with a large range (−38 to 40 TgN yr−1), implying that the Nullhypothesis of a balanced N cycle cannot be rejected. This conclusion hinges critically on the assumption that the different rate estimates are independent. This is indeed the case, since (i) the data constraints used to determine the different rates are of different nature, and (ii) there exist no correlation in a plot of the global sources versus global sinks across all 2500 circulation setups (Figure 3).
 Our balanced budget for the pre-industrial N cycle clearly contrasts with Codispoti's proposition of a modern budget with a substantial imbalance, but corroborates evidences from geological records [Kienast, 2000] that indicate essentially a steady marine N cycle throughout the Holocene. Although we interpret our estimates to reflect largely the pre-industrial situation, i.e., a budget without anthropogenic influences, the data underlying our results were collected in the last few decades and therefore possibly could include an anthropogenic influence. The human alteration of the marine N cycle consists mainly of a substantial increase of atmospheric deposition and river discharge of N [Duce et al., 2008; Seitzinger and Mayorga, 2008], amounting to an increase in the inputs of about 50 TgN yr−1 since 1860 [Galloway et al., 2004; Gruber and Galloway, 2008]. Also the sinks could have increased, in part in response to the increased input of fixed N, but perhaps mostly in response to an increase in the regions with hypoxic to anoxic conditions [Diaz and Rosenberg, 2008]. Thus, most of the additional input and losses of fixed N in the ocean occurred along the continental margins, and thus they are not expected to have altered substantially the open and deep ocean data that largely underlie our estimate. Nevertheless, this adds further uncertainty to our estimates, but we consider this additional contribution to be rather small, i.e., likely less than 10 TgN yr−1.
 Although our estimates are limited to pre-industrial times, it is nevertheless tempting to investigate the consequences of our finding for the likelihood of a present imbalance in the marine N budget exceeding 100 TgN yr−1. One important argument speaks against this, i.e., the magnitude of the human perturbation is likely not large enough. With the anthropogenic increase in the sources amounting to about 50 TgN yr−1, the sinks would have had to increase by about 150 TgN yr−1since pre-industrial times, which essentially requires a doubling of total denitrification. This largely would have to be accomplished by benthic denitrification, since the observed expansion of the oxygen minimum zones over the last 50 years [Stramma et al., 2008] is too small to have increased water column denitrification substantially. Thus, benthic denitrification would have had to triple. While oxygen minimum zones along the continental margins have increased [Diaz and Rosenberg, 2008], it is difficult to conceive such a large increase since pre-industrial times. Thus, given our refined estimate of the pre-industrial fixed N budget, it is hard to justify the strong modern imbalance suggested byCodispoti et al. .
 Our pre-industrial budget implies a residence time of fixed N of 4,200 yr (3,500 yr to 5,000 yr) assuming an oceanic fixed N inventory of 660,000 Tg N [Gruber, 2008]. Our residence time is at the high end of the values published in the literature (Table 1), but still shorter than the time it took for Earth to transition from the last glacial maximum into the Holocene, which took about 10,000 years [Petit et al., 1999]. Thus, our longer residence times do not refute the hypotheses that have been put forward to explain part of the atmospheric CO2changes across glacial-interglacial transitions through transient source/sink imbalances that may have caused changes in the fixed N inventory [McElroy, 1983; Broecker and Henderson, 1998].
4.4. Sensitivity Analyses
 While our probabilistic approach explores the uncertainties associated with our estimates already in substantial depth, there exist several additional sources of uncertainty, such as (i) so far neglected processes potentially contributing to deviations from the assumed N:P Redfield stoichiometry of non-diazotrophic phytoplankton and organic matter, (ii) the magnitude of vertical mixing, which we upscaled by a factor of about 4 relative to the initial first guesses, (iii) the value ofN* in the suboxic box, (iv) the isotopic enrichment associated with water column denitrification (εwcd), and (v) the two vertical mixing fluxes exchanging water to the suboxic box. We explore the impact of these sources of uncertainty through sensitivity experiments. We do not investigate the sensitivity of the N-fixation rates to atmospheric deposition and riverine inputs as their rates are so small that even if their relative uncertainties were large, their impact on the results would be small.
 Phytoplankton community composition [Arrigo et al., 1999; Weber and Deutsch, 2010], growth rate induced variations within a particular phytoplankton group [Mills and Arrigo, 2010], and preferential remineralization of P relative to N [Monteiro et al., 2011] can also generate deviations from the N:P Redfield stoichiometry and thus lead to biased rates estimates in our data inverse geochemical approach. We consider the potential contribution of preferential remineralization to be of minor importance. First, it would generate distinct N* gradients in the vertical that are only seen in the North Atlantic but not elsewhere, and second, the vast majority of the available measurements show that the N:P ratio of remineralization is relatively constant and perhaps only slightly smaller than 16:1 [Deutsch and Weber, 2012]. This also implies that the budget approach is relatively robust to the assumption of a constant N:P ratio of 16 for the non-diazotrophic organisms. This is because the results of the budget approach are primarily driven by the ocean's interior N* distribution, where variations induced by phytoplankton community composition and variations in growth rate matter little.
 This does not apply for the restoring approach, as it makes an assumption about the N:P ratio of non-diazotrophic organisms in the upper ocean. We investigate the sensitivity of the restoring approach to such possible N:P variations by diagnosing N-fixation for two cases where we used basin specific N:P ratios, determined on the basis of a compilation of in-situ measurements [Deutsch and Weber, 2012]. In the first case, a simulation was run with specific N:P ratios assigned to the Southern Ocean (N:P = 15.2) versus the rest of the ocean (16.8). In the second case, the Southern Ocean N:P ratio was kept at 15.2, but the IndoPacific (18.2), and the Atlantic (15.1) had different ratios. The diagnosed rates of N-fixation turn out not to be very sensitive to these changes in the N:P ratios, with rates at most ∼15% larger in the variable stoichiometric ratio simulations (Figure S4 in theauxiliary material). We thus conclude that although variations in the stoichiometric ratio add uncertainty to our restoring-based estimates of N-fixation, this additional uncertainty is likely smaller than the uncertainty stemming from the data and the circulation. This conclusion is supported by our finding of a high degree of consistency between the global rates of N-fixation computed using the budget approach and that computed using the restoring approach.
 To determine the sensitivity of our results to vertical mixing, we re-determined N-fixation and denitrification using the suite of 100 circulation setups with the smallest cost functions, but imposed a different value of the upscaling factor. We varied this factor between 0.5 and nearly 5, resulting in an integrated vertical exchange flux ranging from 50 Sv to 450 Sv (standard value is 300 Sv) and then diagnosed for each factor the median of the different processes. Denitrification rates are hardly sensitive to subsurface vertical mixing fluxes (Figure 4, green and blue curves), because these rates are determined on the basis of N* at each box, mean ocean δ15N and the circulation and mixing of the entire ocean. On the other hand, the N-fixation rate diagnosed fromP* in the surface and thermocline strongly depends on subsurface vertical mixing fluxes since water masses carry the high P* concentration in the thermocline to the surface (Figure 4, red curve). Thus, stronger subsurface vertical mixing fluxes bring more high P* into surface waters, generating higher rate of N-fixation in order to restoreP* to its observed value. As a result of this differential behavior between the main sources and sinks of fixed N, the global marine N imbalance is strongly affected by the magnitude of vertical mixing in the models. Low vertical mixing (50 Sv) causes a deficit of ∼50 TgN yr−1, while high vertical mixing (450 Sv) increases N-fixation without affecting denitrification resulting in a surplus of nearly 50 TgN yr−1.
 We can use the diagnosed biological productivity as an indicator for a realistic value of this mixing flux. Since productivity is diagnosed in our model from the transport convergence of , which is largely controlled by the magnitude of vertical mixing, the production and export of organic matter (carbon) increases nearly proportionally with the changes in vertical mixing (Figure 4, bottom). We had used this constraint already to upscale the mixing fluxes from the initial first guess of 110 Sv to our standard case of 300 Sv, as a mixing flux of 110 Sv results in a too small C export flux of ∼5 PgC yr−1, while 300 Sv yields an export flux of ∼10 PgC yr−1, consistent with the most recent estimates [Najjar et al., 2007; Dunne et al., 2007]. This value of the vertical mixing flux yields our standard imbalance of 3 TgN yr−1 (−38 to 40 TgN yr−1). If we used the C export constraint less vigorously, the imbalance could be larger or smaller, but the median of the absolute imbalance will unlikely exceed 50 TgN yr−1.
 To investigate the sensitivity of the global N imbalance to the three parameters associated with water column denitrification, i.e., N* assigned to the suboxic box, the isotopic enrichment associated with water column denitrification, and the two vertical mixing fluxes of the suboxic box, we use the circulation setup with the smallest cost function. We investigate the co-influence by varying two parameters simultaneously (Figure S5 in theauxiliary material). Varying N* in the suboxic box between −16 to −10 mmol m−3 changes the N imbalance between −40 and 0 TgN yr−1 (Figures S4b and S4d). The uncertainty range of this N* concentration is difficult to estimate exactly, but we note that the standard value of N* (−13.6 mmol m−3 according to the World Ocean Database) implies a better match to the data than when the N* value computed from the WOA (−10.6 mmol m−3) is used (Figures S4a and S4c). Varying εwcd in the literature range from −30‰ to −20‰ [Altabet et al., 1999; Brandes et al., 1998; Sigman et al., 2003] yield imbalances ranging from −60 to 20 TgN yr−1 (Figure S4d). A doubling of the magnitudes of the two vertical mixing fluxes alters the imbalance by about 40 TgN yr−1 (Figure S4b). In all these cases, the primary driver for the changes in the imbalance are changes in denitrification, since N-fixation determined using the restoring approach does not depend on these values.
 In summary, these sensitivity analyses performed on several key parameters confirm that the pre-industrial N cycle was balanced within the uncertainties. They also demonstrate a relatively large robustness of the global rates of N-fixation and denitrification with changes that are smaller than the uncertainty ranges determined using the probabilistic approach.
4.5. Basin-Scale N-Fixation Rates
 The highest N-fixation rates estimated using the restoring approach are found in the IndoPacific, whereas essentially no fixation is diagnosed in the Atlantic (Table S1 (in the Text S1 file) and Figure S6 in theauxiliary material). The median rate of N-fixation in the oxic IndoPacific is 86 TgN yr−1 (78 to 95 TgN yr−1), followed by the suboxic IndoPacific with a median rate of 47 TgN yr−1 (31 to 61 TgN yr−1). In contrast, diagnosed fixation in the Atlantic ranges only from 0 to 3 TgN yr−1, with a median of 0 TgN yr−1. The restoring approach diagnoses a substantial amount of N-fixation in the Southern Ocean with a median rate of 21 TgN yr−1 (20 to 22 TgN yr−1). As discussed above, we disregard this rate, as we consider it to be caused by non-Redfieldian uptake by non-N-fixing organisms.
 The high N-fixation rate in the IndoPacific is consistent with the findings ofDeutsch et al. who suggested a relatively close coupling between the regions of denitrification and N-fixation. They diagnosed a N-fixation rate of 117 TgN yr−1 for the IndoPacific, close to our rate of 133 TgN yr−1 (116 to 149 TgN yr−1). If we assume that the Indian Ocean has a similar areal fixation rate as the Pacific, we can scale up the Pacific only rate of Deutsch et al.  of 59 ± 15 TgN yr−1 to about 100 TgN yr−1, again within the range of our estimate.
 But the absence of N-fixation diagnosed in the low-latitude Atlantic challenges the canonical view of a basin with substantial N-fixation as a result of high airborne rich-iron dust deposition [Michaels et al., 1996; Falkowski, 1997; Moore et al., 2009]. Gruber and Sarmiento calculated a N-fixation rate of 28 TgN yr−1 north of the equator and up to 45°N using N*. More recently Hansell et al.  computed a 60% lower estimate, but still substantially larger than our restoring based estimate. Isotopic analyses of suggested an Atlantic N-fixation rate of 15 to 24 TgN yr−1 [Knapp et al., 2008] and the P* restoring approach of Deutsch et al.  yielded a rate of 20 TgN yr−1. A similar rate, at least 20 TgN yr−1, has been inferred by direct measurements of N-fixation rates byTrichodesmium [Capone et al., 2005].
 Several reasons could lead to this discrepancy between the literature based values and those from our restoring approach: (i) the coarse vertical resolution leads to the computation of too small gradients in P*, and hence to a too small transport convergence, (ii) the vertical mixing is too small, or (iii) the vertical gradients in P* are too small due to either uncertainties in the data or excess smoothing in the horizontal due to the coarse horizontal resolution.
 In the auxiliary material, we demonstrate that the most likely cause of our estimates being low is the coarse horizontal resolution of our model, which causes the vertical gradients in P* to be too weak as a result of our model's inability to correctly reflect the important horizontal gradients. An increase of P* by one standard deviation in the thermocline box of the low-latitude Atlantic increases the diagnosed N-fixation in this basin to 30 TgN yr−1bringing our diagnosed rates in line with literature estimates of N-fixation rate in the Atlantic [Gruber and Sarmiento, 1997; Capone et al., 2005; Knapp et al., 2008].
 The budget approach reveals overall a similar spatial pattern as the restoring approach, with a substantially larger fixation occurring in the IndoPacific compared to the Atlantic. At the same time, the budget approach assigns a much larger fraction to the Atlantic, i.e., about 23 % of the global rate (median 30 TgN yr−1), which implies similar rates on a per surface area basis in each basin (26.13 mmol N/m2 yr−1 in the Atlantic and 26.05 mmol N/m2 yr−1in the oxic IndoPacific). Given the very high sensitivity of N-fixation in the low latitude Atlantic region to the rather uncertain gradient between the subsurface and surfaceP*, we are slightly more confident in the N-fixation estimate computed using the budget approach, as this value is less sensitive to this gradient, and since it incorporates more the large-scale data constraints. However, the large discrepancy between the two approaches in this ocean basin is clearly an issue that remains to be resolved.
4.6. Basin-Scale Budgets and N Transport
 The spatial separation of sources and sinks of N in the ocean leads to basin-scale budget imbalances even in a situation where the global N budget is balanced. This requires a net lateral transport from one basin to another. In order to arrive at these basin-scale budgets and the corresponding fluxes, we summed all N fluxes diagnosed using the budget approach for each ocean (sub) basin. We used the N-fixation results from the budget approach rather than those from the restoring approach in order to guarantee a globally balanced budget required to compute lateral fluxes. A second reason is our slightly higher confidence in the budget approach-derived values of N-fixation in the low-latitude Atlantic.
 We find the Atlantic to generate a small excess of 16 (12 to 20) TgN yr−1, while the IndoPacific has a small deficit of the same magnitude (Figure 5). This small deficit within the IndoPacific is actually the sum of a very large deficit of 41 (31 to52) TgN yr−1 in the suboxic part and a surplus of 24 (11 to 37) TgN yr−1in the oxic part. This distribution is primarily a consequence of water column denitrification only occurring in the suboxic IndoPacific, since benthic denitrification, N-fixation, and the other N sources and sinks largely tend to cancel each other in each (sub)basin.
 These basin-scale imbalances imply a net lateral transport of fixed N from the Atlantic, through the Southern Ocean and oxic IndoPacific into the suboxic IndoPacific (Figure 5), consistent with the large scale distribution of N* [Gruber and Sarmiento, 1997; Gruber, 2004]. The excess of 16 (12 to 20) TgN yr−1 in the Atlantic flows through the Southern Ocean, a basin with only a very small N imbalance, and enters the oxic IndoPacific, where an additional excess of 24 (11 to 37) TgN yr−1 is added. This results in the transport of about 41 (31 to 52) TgN yr−1 into the suboxic part of the IndoPacific. Considering the IndoPacific in a whole, the transport of fixed N entering the suboxic part of the basin mainly comes from the oxic part, while only one third of the fixed N comes from the Atlantic. This implies a relative close spatial coupling of the sources and sinks of fixed N in the marine environment, supporting the conclusions of Deutsch et al. .
5. Summary and Conclusion
 We developed a new geochemical box model to determine the global rates of N-fixation and denitrification in the water column and sediments by assimilating a large range of oceanic data. A special focus of our work was on the thorough assessment of the sensitivity of the global and basin-scale rates of the N sources and sinks to the uncertainties stemming from the data and ocean transport and mixing. To this end, we employed a suite of 2500 circulation configurations permitting us to determine the N-fixation and denitrification rates for the first time in a probabilistic manner.
 Our global rate of N-fixation is broadly consistent with literature estimates, while our denitrification rates are at the lower end compared to those reported in most recent studies. We have some confidence in our estimates, as they are consistent with a large number of data constraints, including nutrient anomalies (N* and P*) and δ15N. This is not the case for many of the previous studies, as they are largely based on a limited set of observations and a substantial amount of upscaling.
 On a basin-scale, the magnitude of N-fixation occurring in the Atlantic remains an unresolved issue, as the two approaches we employed do not agree. However, they both indicate a small to modest contribution of this ocean basin to global N-fixation, making the IndoPacific the key source of fixed N on a global basis. There, the close spatial coupling of this most important source of fixed N with the most important sink by denitrification, suggests that the N deficits generated in denitrification regions are an important controlling factor for balancing the global N budget [Gruber, 2004; Deutsch et al., 2007].
 Our finding of a largely balanced marine N-budget clearly argues against the proposition ofCodispoti et al. of a large imbalance in the current budget, even though our budget is strictly speaking applicable only for the pre-industrial period. The largest difference to Codispoti's budget is our much smaller denitrification estimate. Although our denitrification has a considerable uncertainty (∼30%), a substantially larger denitrification can be quite firmly excluded, as this would violate several important observational constraints, such as the large-scale distribution ofN* and δ15N.
 Our N budget implies a residence time of marine fixed N in the range 3,500 to 5,000 yr. This is at the high end compared to most recent literature estimates, but still within the range of the timescale of the glacial/deglacial transition, leaving open the question whether and how much the marine N cycle has contributed to the atmospheric CO2 variations over these transitions.
 We are indebted to Curtis Deutsch for sharing the code of his geochemical box model and for his help and many fruitful discussions. We thank Samuel Jaccard and Xavier Giraud for helpful discussions throughout this work. The constructive comments of two anonymous reviewers that greatly improved this submission were greatly appreciated. This work was supported by funds from ETH Zurich.