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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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.
The authors declare no competing interests.
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- 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.
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.
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.
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