Nitrogen (N) plays a central role in marine biogeochemistry by limiting biological productivity in the surface ocean; influencing the cycles of other nutrients, carbon, and oxygen; and controlling oceanic emissions of nitrous oxide (N

Nitrogen (N) limits phytoplankton production over large swathes of the ocean

Schematic of the main N cycle tracers and reactions represented by NitrOMZ. Tracers are shown in bold, ordered by the oxidation state of N, and consist of organic nitrogen (

The ocean's inventory of fixed N is dominated by

The emerging picture of the ocean's N cycle is that of a web of inter-dependent transformations that is particularly active in OMZs, where overlapping aerobic and anaerobic reactions exchange nitrogen metabolites and substrates

The ultimate goals of these models are multifold and include improving predictability of oceanic

The representation of N transformations in models often relies on crude assumptions that simplify the network of N reactions and their controls to simple empirical parameterizations. For example, models that include

The goal of this paper is to present a new model of the oceanic N cycle designed to be incorporated in current ocean biogeochemical models, with a particular focus on processes occurring within OMZs. We refer to this model as NitrOMZ (

The rest of the paper is organized as follows: Sect.

The NitrOMZ model is based on the current understanding of the N cycle in OMZs

A schematic of the model's tracers and transformation is shown in Fig.

The underlying assumption is that the occurrence and rates of N transformations are controlled by, and can be predicted from, the physical and chemical conditions of the oceanic environment. Implicitly, the model assumes that diverse populations of microbes are always present in the water column and that their activity (i.e., metabolic rate) is controlled by the abundance of substrates, analogous to chemical reactions, and dissolved

We assume that each reaction is implicitly mediated by specialized microorganism groups, each relying on a distinct metabolism

These assumptions are sufficient for providing a broad representation of microbial N transformations and their environmental expressions in the ocean, while limiting model complexity and the proliferation of poorly constrained parameters. They are also grounding steps toward models that explicitly represent microbial populations, including their diversity and dynamics in OMZs

The model focuses on microbial processes that take place below the euphotic zone, as driven by the flux of organic matter produced near the surface and exported into the ocean interior by the biological pump

Heterotrophic reactions resolved by the model (Fig.

We do not include an explicit representation of nitric oxide,

There are also several notable processes that are not represented in the current model formulation but could be introduced in future releases. Some of these processes (e.g., dissimilatory

Production of

DNRA, which can be dominant in anoxic sediment, has been sporadically observed in the water column of oxygen-deficient zones, where it may provide an additional source of

Recent tracer incubation studies show substantial and often dominant formation of

Other work suggests the occurrence of

Finally, the model could easily accommodate missing processes that couple the N cycle with other elemental cycles, in particular carbon and sulfur. These include formation of organic matter by chemolithotrophy; changes in inorganic carbon chemistry (e.g., pH) by anaerobic reactions

Heterotrophic reactions (i.e., organic matter remineralization) are parameterized as a function of the respective oxidants and organic matter concentration and expressed in carbon units per unit volume and time. Heterotrophic reaction rates are assumed to be on the first order in the concentration of organic matter and limited by the oxidant, following a Michaelis–Menten formulation

Chemolithotrophic reactions are proportional to the respective substrates. A maximum reaction rate is modulated by the concentration of oxidants and reductants, following Michelis–Menten dynamics. For anaerobic reactions (here, anammox), an

Equations for each of the heterotrophic and chemolithotrophic reactions are presented in Appendix

In the model, we assume that heterotrophic reactions are first-order to the concentration of organic matter; thus all organic matter can be utilized by microorganisms without saturation at high concentrations. Because of the low abundance of organic matter in seawater and extensive colonization of particles by heterotrophic bacteria, this is a reasonable first-order assumption. However, see

We do not explicitly model conversion of dissolved

The use of an exponential inhibition term for anaerobic reactions by

Parameter values for maximum reaction rates, half-saturation constants, and

Summary of the main NitrOMZ parameters, with any reported values from the literature (NA – not available).

We implement the model for a one-dimensional water column that includes physical transport by vertical advection and turbulent diffusion

In the one-dimensional framework, the conservation equation for the concentration

The lateral transport term LT can be included to parameterize horizontal circulation by advection and diffusion in the one-dimensional framework. Typically, these terms are simplified by a linear restoring to far-field tracer concentration profiles

In the one-dimensional model implementation, we represent organic matter (

Considering the flux of sinking

The advantage of Eq. (

For the purpose of testing and illustration, we implement NitrOMZ in a one-dimensional representation of the water column below the mixed layer, following previous work

As in

Under constant forcings and boundary conditions, the model tracers evolve towards steady state (

Figure

Example of spinup of the model. (top) Temporal evolution of

The model contains 23 major parameters that control the N cycle, some of which are relatively well constrained by observations, whereas others are poorly known and can plausibly span a broad range of values (Table

To conduct this optimization, we compile available tracer and biogeochemical rate observations for the ETSP OMZ from a July 2013 cruise aboard the R/V

The optimization is characterized by large dimensionality, strong non-linearity, a significant computational cost (requiring several 10 000 s model runs to converge), and inherent flexibility in the formulation of the cost function

The CMA-ES is a stochastic, population-based algorithm that seeks to minimize an objective cost function

The CMA-ES has been shown to be more efficient (i.e., requiring fewer objective function evaluations), accurate (i.e., able to approximate the global optimum when it is known to exist), and robust (i.e., not overly sensitive to the initial choice of parameters) compared to other optimization algorithms, when applied to multi-dimensional, non-linear optimization problems

Flowchart of the CMA-ES optimization algorithm used to constrain uncertain model parameters.

As an illustration of NitrOMZ, we perform a series of optimizations against ETSP OMZ observations. For this configuration, we set a constant upwelling velocity (

As a first step, we select parameters that control aerobic remineralization processes (

To optimize more uncertain parameters that control the anaerobic N cycle, we then conduct four sets of optimizations, with cost functions devised to match desired characteristics of tracer and rate profiles in the ETSP OMZ. Briefly, the cost function is calculated as the mean square of the difference between observations and model output profiles for a series of variables that include tracers and N transformation rates (listed in Table

The distributions of the parameter values from the 382 sets of optimizations (see Sect.

Pairwise correlations in Fig.

Pairwise correlations between model parameters for model solutions optimized for the ETSP OMZ. See Table

Considering the variability in the optimal parameter sets and the complexity of the cost function, which depends on observations for multiple variables at different depths, the resulting N cycle profiles show similar features across all optimal solutions (Fig.

N cycle transformation rates also show similar consistency in their vertical profiles, albeit with more notable discrepancies with observations, possibly reflecting the higher variability and more complex nature of these measurements. Lower rates than observed may also reflect the fact that incubation experiments provide potential rates rather than in situ rates. In general, the yield of

Results from the optimized ensemble of model solutions. (top) Tracer (

Several robust features emerge from the optimized parameter solutions, suggesting underlying mechanisms that need to be captured for a faithful representation of the OMZ N cycle. In particular, the differences in the exponential

Within the anoxic core of the OMZ (

Progressive

The vertical profile of the step-wise denitrification rates (

The processes responsible for fixed

Contribution of different reactions to organic matter remineralization and fixed

Among tracers,

Compared to the other parameter sets, Opt

As shown in Sect.

Sensitivity coefficient (

The results demonstrate high sensitivity to changes in the maximum rates for all reactions (Fig.

Figures

Model sensitivity to parameter values. Panels show

Notably, by increasing

Figures

Model sensitivity to parameter values. Panels show changes to

The main features of the OMZ simulated by the model are strongly dependent on environmental parameters such as upwelling and mixing; organic matter fluxes; and the model boundary conditions, including mixed-layer depth and

Figure

Opposite changes are observed for a reduction in both

Model sensitivity to physical drivers. (top) Sensitivity of the Opt

Because the supply of

Similar changes can also be driven by variations in the bottom-boundary

Model sensitivity to biogeochemical drivers. The same as in Fig.

We developed a model of the N cycle in low

The optimization indicates that multiple parameter sets can produce equally good fits to tracer and rate profiles (Fig.

A better characterization of environmental sensitivities to substrate concentrations (e.g., half-saturation constant for substrate uptake) and

Despite the variability in parameter values, analysis of the optimal ensemble reveals emerging features that appear robust across multiple optimizations and that compare well with observations. For example, the sensitivity of denitrification processes to

Because the model is based on a mechanistic representation of N transformations, it is suitable for investigating the response of the N cycle to environmental variability and other perturbations (Figs.

Because the model reflects an evolving understanding of the N cycle, its assumptions should be re-evaluated as new N transformation processes and aspects of microbial dynamics are uncovered. The model is built around two major simplifications: the modularity of the N cycle and the representation of microbial metabolisms as bulk chemical reactions that avoid explicitly tracking diverse microbial populations. Both are approximate views of the N cycle. For example, recent evidence suggests that microorganisms with the ability to carry out intracellular reduction of

Our bulk approach assumes that metabolic reaction rates are proportional to substrates following a Michaelis–Menten dependency. However, in reality, reaction rates also depend on the abundance of microorganisms present in the water column. If microorganism biomass is assumed to be proportional to substrates, then a higher-order dependency of reaction rates may be more appropriate, as adopted by some biogeochemical models (e.g.,

Indeed, previous modeling studies have pointed out the value of explicitly resolving the biomass of microbial populations

Based on its modular design, the model can be naturally expanded to represent new processes that, while thought to be relevant in OMZ, are still uncertain. These include (1) additional known N cycle pathways and their sensitivity to environmental variability, such as DNRA

Production of

The stoichiometry of heterotrophic redox reactions is based on an electron balance and follows the procedure outlined in

Based on the stoichiometry of

Finally, for anammox,

NitrOMZ nitrogen cycle parameters and CMA-ES optimization ranges. NA – not available.

ETSP configuration for optimization routines. NA – not available.

ETSP boundary conditions.

Optimized ETSP parameter sets.

Parameter distributions from the 382 CMA-ES-optimized ETSP solutions. Red markers denote Opt

The same as in Fig.

The current version of NitrOMZv1.0 is available from the project website:

DB conceptualized the formulation of the model; DB and SY developed the model code, including optimization procedures; DB and SY organized the validation data; DB and DM designed the analyses; DM prepared the tables and visualization of data; and DB and DM prepared the manuscript with contributions from SY.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Daniele Bianchi acknowledges support from the Alfred P. Sloan Foundation and computational support by the Extreme Science and Engineering Discovery Environment (XSEDE) through allocation TG-OCE17001. The authors wish to thank Andrew Babbin, Alyson Santoro, and Colette Kelly for helpful discussion.

This research has been supported by the Division of Ocean Sciences (grant no. 1847687).

This paper was edited by Heather Hyewon Kim and reviewed by Colette LaMonica Kelly and one anonymous referee.