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  • Primer
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Ocean biogeochemical modelling

Nature Reviews Methods Primers volume 2, Article number: 76 (2022) Cite this article

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Abstract

Ocean biogeochemical models describe the ocean’s circulation, physical properties, biogeochemical properties and their transformations using coupled differential equations. Numerically approximating these equations enables simulation of the dynamic evolution of the ocean state in realistic global or regional spatial domains, across time spans from years to centuries. This Primer explains the process of model construction and the main characteristics, advantages and drawbacks of different model types, from the simplest nutrient–phytoplankton–zooplankton–detritus model to the complex biogeochemical models used in Earth system modelling and climate prediction. Commonly used metrics for model-data comparison are described, alongside a discussion of how models can be informed by observations via parameter optimization or state estimation, the two main methods of data assimilation. Examples illustrate how these models are used for various practical applications, ranging from carbon accounting, ocean acidification, ocean deoxygenation and fisheries to observing system design. Access points are provided, enabling readers to engage in biogeochemical modelling through practical code examples and a comprehensive list of publicly available models and observational data sets. Recommendations are given for best practices in model archiving. Lastly, current limitations and anticipated future developments and challenges of the models are discussed.

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Fig. 1: State variables and biogeochemical transformations across a range of OBMs.
Fig. 2: Typical horizontal resolutions and bathymetries in global and regional models.
Fig. 3: Representation of a two-dimensional cost function.
Fig. 4: Application of a stochastic ensemble Kalman filter for estimating three parameters of a zero-dimensional (single box) NPZD model in a twin experiment using example code57.
Fig. 5: Illustration of state estimation and parameter optimization.
Fig. 6: Application of ensemble-based state estimation for a three-dimensional model, using example code81.

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Code availability

Example code for a nutrient–phytoplankton–zooplankton–detritus (NPZD) model, parameter optimization and state estimation can be found in refs.57,81,201, respectively.

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Acknowledgements

K.F. and B.W. acknowledge support from the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Program (RGPIN-2014-03938), the Canada Foundation for Innovation (Innovation Fund 39902) and the Ocean Frontier Institute. J.P.M. was supported by the Simons Foundation (CBIOMES award ID: 549949). S.C.D. acknowledges support from the US National Science Foundation via the Center for Chemical Currencies of a Microbial Planet (National Science Foundation (NSF) 2019589). L.B. acknowledges support from the European Union’s Horizon 2020 research and innovation programmes COMFORT (grant agreement no. 820989) and ESM2025 (grant agreement no. 101003536). L.Y. acknowledges support from the Center for Ocean Research in Hong Kong and Macau.

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Authors and Affiliations

  1. Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

    Katja Fennel & Bin Wang

  2. Ocean Sciences Department, University of California Santa Cruz, Santa Cruz, CA, USA

    Jann Paul Mattern & Andrew M. Moore

  3. Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA

    Scott C. Doney

  4. Laboratoire de Météorologie Dynamique, Institut Pierre-Simon Laplace, CNRS, Ecole normale supérieure, Paris Sciences Lettres Université, Paris, France

    Laurent Bopp

  5. Earth, Ocean and Atmospheric Sciences Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China

    Liuqian Yu

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Contributions

Introduction (K.F. and L.B.); Experimentation (S.C.D., K.F., J.P.M., A.M.M. and B.W.); Results (K.F. and J.P.M.); Applications (S.C.D., L.Y., L.B., J.P.M. and K.F.); Reproducibility and data deposition (S.C.D. and K.F.); Limitations and optimizations (K.F. and S.C.D.); Outlook (K.F.); Overview of the Primer (K.F.).

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Correspondence to Katja Fennel.

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Nature Reviews Methods Primers thanks Yvette Spitz, Zhengui Wang, Peng Xiu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Glossary

Functional plankton groups

Groups of planktonic organisms that share similar traits, for example size, biogeochemical function or elemental requirements. These groups are defined to simplify the diversity of planktonic communities while capturing their essential biogeochemical functions in ocean biogeochemical models.

Initial condition

The complete set of state variables at one instant in time. Model integration starts from an initial condition.

State variables

A set of variables that fully characterize a model’s dynamical state such that its future behaviour can be calculated, provided any external inputs are known. Each variable that belongs to this set is a state variable.

External forcing

All prescribed inputs that are needed to determine the evolution of a model’s state and are not calculated internally by the model.

Projections

Simulations into the future that go significantly beyond the timescale for which models have demonstrated predictive or forecast skill, such as Earth system model (ESM) simulations to the end of the current century or longer.

Model parameters

Constants that are usually specified at the beginning of model integration and determine the dynamical behaviour of the model.

A priori knowledge

Assumptions about ocean processes, represented by the equations of an ocean model and its parameters and initial and boundary conditions, that are available before data assimilation is applied.

Parameter optimization

The determination of the most likely values of poorly known model parameters based on the agreement of model output with observations.

Integration time

The simulated length of model integration. It varies from months to decades in regional models and hundreds of years in Earth system models (ESMs).

Spin up

The initial period of a model simulation during which the model adjusts from its initial state to a new state according to the internal model dynamics and subject to external forcing. The spin up period ranges from a few months or years for regional models to one or a few hundred years for global models.

State estimation

A method to obtain the optimal model state by combining the information contained in the model equations and the available observations.

Variational methods

Methods aimed at obtaining the best fit, in a least-squares sense, between model and observations by minimizing a cost function. These can be applied to parameter and state estimation problems.

Sequential methods

The model state, and, sometimes, its parameters are updated through an alternating sequence of forecast steps when the model is integrated forward in time, and update or analysis steps when the model state and, if applicable, the parameters are updated using observations.

Cost function

A measure of the misfit between observations and their model counterparts in a least-squares sense.

Control vector

A vector containing all of the values to be optimized during data assimilation. It can include model parameters, the full model state, a subset thereof or a combination of both.

Optimal parameters

The results from parameter optimization; the parameter values that minimize the cost function in a parameter optimization problem.

A posteriori error

An estimate of the error in the solution of an optimization problem given the observations and numerical solution technique applied.

Least-squares

A measure of misfit between observations and the model equivalents of those observations that sums the squared distances between them.

Decorrelation scales

The e-folding scales of the autocorrelation function of the property under consideration; the distance or period over which the autocorrelation decreases by a factor of 1 / e.

Eutrophication

An excessive supply of plant nutrients to a body of water, often due to input from land.

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Fennel, K., Mattern, J.P., Doney, S.C. et al. Ocean biogeochemical modelling. Nat Rev Methods Primers 2, 76 (2022). https://doi.org/10.1038/s43586-022-00154-2

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