Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Ocean biogeochemical modelling

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.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

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.

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.

References

  1. Riley, G. A. Factors controlling phytoplankton population on George’s Bank. J. Mar. Res. 6, 54–73 (1946).

    Google Scholar 

  2. Evans, G. T. & Parslow, J. S. A model of annual plankton cycles. Biol. Oceanogr. 3, 327–347 (1985).

    Google Scholar 

  3. Fasham, M. J. R., Ducklow, H. W. & McKelvie, S. M. A nitrogen-based model of plankton dynamics in the oceanic mixed layer. J. Mar. Res. 48, 591–639 (1990). This work is a seminal early example of an OBM applied to time-series data.

    Google Scholar 

  4. Franks, P. J. S., Wroblewski, J. S. & Flierl, G. R. Behavior of a simple plankton model with food-level acclimation by herbivores. Mar. Biol. 91, 121–129 (1986).

    Google Scholar 

  5. Sarmiento, J. L. et al. A seasonal three-dimensional ecosystem model of nitrogen cycling in the North Atlantic Euphotic Zone. Glob. Biogeochem. Cycles 7, 417–450 (1993). This regional model of the North Atlantic is probably the first true OBM, that is, an ocean circulation model with explicit representation of plankton dynamics.

    ADS  Google Scholar 

  6. Revelle, R. & Suess, H. E. Carbon dioxide exchange between atmosphere and ocean and the question of an increase of atmospheric CO2 during the past decades. Tellus 9, 18–27 (1957).

    ADS  Google Scholar 

  7. Sarmiento, J. L. & Toggweiler, J. R. A new model for the role of the oceans in determining atmospheric pCO2. Nature 308, 621–624 (1984).

    ADS  Google Scholar 

  8. Siegenthaler, U. & Wenk, T. Rapid atmospheric CO2 variations and ocean circulation. Nature 308, 624–626 (1984).

    ADS  Google Scholar 

  9. Maier-Reimer, E. & Hasselmann, K. Transport and storage of CO2 in the ocean — an inorganic ocean-circulation carbon cycle model. Clim. Dyn. 2, 63–90 (1987).

    Google Scholar 

  10. Maier-Reimer, E. Geochemical cycles in an ocean general circulation model. Preindustrial tracer distributions. Glob. Biogeochem. Cycles 7, 645–677 (1993). This seminal paper describes one of the first marine biogeochemical models of the global ocean.

    ADS  Google Scholar 

  11. Six, K. D. & Maier-Reimer, E. Effects of plankton dynamics on seasonal carbon fluxes in an ocean general circulation model. Glob. Biogeochem. Cycles 10, 559–583 (1996).

    ADS  Google Scholar 

  12. Sarmiento, J. L. & Gruber, N. Ocean Biogeochemical Dynamics (Princeton Univ. Press, 2006).

  13. Glover, D. M., Jenkins, W. J. & Doney, S. C. Modeling Methods for Marine Science (Cambridge Univ. Press, 2011).

  14. Franks, P. J. S. NPZ models of plankton dynamics: their construction, coupling to physics, and application. J. Oceanogr. 58, 379–387 (2002).

    Google Scholar 

  15. Gentleman, W., Leising, A., Frost, B., Strom, S. & Murray, J. Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics. Deep. Sea Res. Part II Top. Stud. Oceanogr. 50, 2847–2875 (2003).

    ADS  Google Scholar 

  16. Le Quéré, C. et al. Ecosystem dynamics based on plankton functional types for global ocean biogeochemistry models. Glob. Chang. Biol. 11, 2016–2040 (2005).

    Google Scholar 

  17. Cullen, J. J. Subsurface chlorophyll maximum layers: enduring enigma or mystery solved? Ann. Rev. Mar. Sci. 7, 207–239 (2015).

    Google Scholar 

  18. Fennel, K. & Boss, E. Subsurface maxima of phytoplankton and chlorophyll: steady-state solutions from a simple model. Limnol. Oceanogr. 48, 1521–1534 (2003).

    ADS  Google Scholar 

  19. Geider, R. J., MacIntyre, H. L. & Kana, T. M. Dynamic model of phytoplankton growth and acclimation: responses of the balanced growth rate and the chlorophyll a: carbon ratio to light, nutrient-limitation and temperature. Mar. Ecol. Prog. Ser. 148, 187–200 (1997).

    ADS  Google Scholar 

  20. Orr, J. C. et al. Biogeochemical protocols and diagnostics for the CMIP6 Ocean Model Intercomparison Project (OMIP). Geosci. Model. Dev. 10, 2169–2199 (2017). This work presents a framework detailing common protocols for including ocean biogeochemistry and chemical tracers in ESMs.

    ADS  Google Scholar 

  21. Lam, P. & Kuypers, M. M. M. Microbial nitrogen cycling processes in oxygen minimum zones. Ann. Rev. Mar. Sci. 3, 317–345 (2011).

    Google Scholar 

  22. Follows, M. J., Dutkiewicz, S., Grant, S. & Chisholm, S. W. Emergent biogeography of microbial communities in a model ocean. Science 315, 1843–1846 (2007). This paper is the first to explore competition among a large number of phytoplankton groups within a global ocean model.

    ADS  Google Scholar 

  23. Dutkiewicz, S. et al. Dimensions of marine phytoplankton diversity. Biogeosciences 17, 609–634 (2020).

    ADS  Google Scholar 

  24. Armstrong, R. A. Grazing limitation and nutrient limitation in marine ecosystems: steady state solutions of an ecosystem model with multiple food chains. Limnol. Oceanogr. 39, 597–608 (1994).

    ADS  Google Scholar 

  25. Banas, N. S. Adding complex trophic interactions to a size-spectral plankton model: emergent diversity patterns and limits on predictability. Ecol. Modell. 222, 2663–2675 (2011).

    Google Scholar 

  26. Galbraith, E. D., Gnanadesikan, A., Dunne, J. P. & Hiscock, M. R. Regional impacts of iron–light colimitation in a global biogeochemical model. Biogeosciences 7, 1043–1064 (2010).

    ADS  Google Scholar 

  27. Denman, K. L. Modelling planktonic ecosystems: parameterizing complexity. Prog. Oceanogr. 57, 429–452 (2003).

    ADS  Google Scholar 

  28. Haidvogel, D. B. & Beckmann, A. Numerical Ocean Circulation Modeling (Imperial College Press, 1999).

  29. Haltiner, G. J. & Williams, R. T. Numerical Prediction and Dynamic Meteorology (Wiley, 1980).

  30. Roache, P. J. Fundamentals of Computational Fluid Dynamics (Hermosa, 1998).

  31. Foucart, C., Mirabito, C., Haley, P. J. & Lermusiaux, P. F. J. High-order discontinuous Galerkin methods for nonhydrostatic ocean processes with a free surface. OCEANS 2021: San Diego–Porto https://doi.org/10.23919/OCEANS44145.2021.9705767 (2021).

    Article  Google Scholar 

  32. Schourup-Kristensen, V., Wekerle, C., Wolf-Gladrow, D. A. & Völker, C. Arctic Ocean biogeochemistry in the high resolution FESOM 1.4-REcoM2 model. Prog. Oceanogr. 168, 65–81 (2018).

    ADS  Google Scholar 

  33. Zang, Z. et al. Spatially varying phytoplankton seasonality on the northwest Atlantic Shelf: a model-based assessment of patterns, drivers, and implications. ICES J. Mar. Sci. 78, 1920–1934 (2021).

    Google Scholar 

  34. Brennan, C. E., Blanchard, H. & Fennel, K. Putting temperature and oxygen thresholds of marine animals in context of environmental change: a regional perspective for the Scotian Shelf and Gulf of St. Lawrence. PLoS ONE 11, e0167411 (2016).

    Google Scholar 

  35. Claret, M. et al. Rapid coastal deoxygenation due to ocean circulation shift in the northwest Atlantic. Nat. Clim. Chang. 8, 868–872 (2018).

    ADS  Google Scholar 

  36. Rutherford, K. & Fennel, K. Diagnosing transit times on the northwestern North Atlantic continental shelf. Ocean. Sci. 14, 1207–1221 (2018).

    ADS  Google Scholar 

  37. Bourgeois, T. et al. Coastal-ocean uptake of anthropogenic carbon. Biogeosciences 13, 4167–4185 (2016).

    ADS  Google Scholar 

  38. Laurent, A., Fennel, K. & Kuhn, A. An observation-based evaluation and ranking of historical Earth system model simulations in the northwest North Atlantic Ocean. Biogeosciences 18, 1803–1822 (2021).

    ADS  Google Scholar 

  39. Rutherford, K. & Fennel, K. Elucidating coastal ocean carbon transport processes: a novel approach applied to the northwest North Atlantic Shelf. Geophys. Res. Lett. 49, e2021GL097614 (2022).

    ADS  Google Scholar 

  40. Saba, V. S. et al. Enhanced warming of the northwest Atlantic Ocean under climate change. J. Geophys. Res. Ocean. 121, 118–132 (2016).

    ADS  Google Scholar 

  41. Sweeney, C. et al. Impacts of shortwave penetration depth on large-scale ocean circulation and heat transport. J. Phys. Oceanogr. 35, 1103–1119 (2005).

    ADS  Google Scholar 

  42. Bonan, G. B. & Doney, S. C. Climate, ecosystems, and planetary futures: the challenge to predict life in Earth system models. Science 359, eaam8328 (2018).

    Google Scholar 

  43. Matear, R. J. Parameter optimization and analysis of ecosystem models using simulated annealing: a case study at Station P. J. Mar. Res. 53, 571–607 (1995).

    Google Scholar 

  44. Fennel, K., Losch, M., Schroter, J. & Wenzel, M. Testing a marine ecosystem model: sensitivity analysis and parameter optimization. J. Mar. Syst. 28, 45–63 (2001).

    Google Scholar 

  45. Friedrichs, M. A. M. et al. Assessment of skill and portability in regional marine biogeochemical models: role of multiple planktonic groups. J. Geophys. Res. 112, 1–22 (2007).

    Google Scholar 

  46. Mattern, J. P. & Edwards, C. A. Simple parameter estimation for complex models — testing evolutionary techniques on 3-dimensional biogeochemical ocean models. J. Mar. Syst. 165, 139–152 (2017).

    Google Scholar 

  47. Laurent, A., Fennel, K., Wilson, R., Lehrter, J. & Devereux, R. Parameterization of biogeochemical sediment–water fluxes using in situ measurements and a diagenetic model. Biogeosciences 13, 77–94 (2016).

    ADS  Google Scholar 

  48. Wilson, R. F., Fennel, K. & Paul Mattern, J. Simulating sediment–water exchange of nutrients and oxygen: a comparative assessment of models against mesocosm observations. Cont. Shelf Res. 63, 69–84 (2013).

    ADS  Google Scholar 

  49. Thacker, W. C. The role of the Hessian matrix in fitting models to measurements. J. Geophys. Res. Ocean. 94, 6177–6196 (1989).

    ADS  Google Scholar 

  50. Ward, B. A., Friedrichs, M. A. M., Anderson, T. R. & Oschlies, A. Parameter optimisation techniques and the problem of underdetermination in marine biogeochemical models. J. Mar. Syst. 81, 34–43 (2010).

    Google Scholar 

  51. Schartau, M. et al. Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling. Biogeosciences 14, 1647–1701 (2017).

    ADS  Google Scholar 

  52. Gregg, W. W. et al. Skill assessment in ocean biological data assimilation. J. Mar. Syst. 76, 16–33 (2009).

    Google Scholar 

  53. Bagniewski, W., Fennel, K., Perry, M. J. & D’Asaro, E. A. Optimizing models of the North Atlantic spring bloom using physical, chemical and bio-optical observations from a Lagrangian float. Biogeosciences 8, 1291–1307 (2011).

    ADS  Google Scholar 

  54. Kuhn, A. M., Fennel, K. & Berman-frank, I. Modelling the biogeochemical effects of heterotrophic and autotrophic N2 fixation in the Gulf of Aqaba (Israel), Red Sea. Biogeosciences 15, 7379–7401 (2018).

    ADS  Google Scholar 

  55. Mattern, J. P., Fennel, K. & Dowd, M. Periodic time-dependent parameters improving forecasting abilities of biological ocean models. Geophys. Res. Lett. 41, 6848–6854 (2014).

    ADS  Google Scholar 

  56. Kitagawa, G. A self-organizing state-space model. J. Am. Stat. Assoc. 93, 1203–1215 (1998).

    Google Scholar 

  57. Mattern, J. P. Visualizing parameter and state estimation for a zero-dimensional ocean biological model. GitHub https://doi.org/10.5281/zenodo.6994739 (2022).

    Article  Google Scholar 

  58. Evensen, G. The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean. Dyn. 53, 343–367 (2003). This influential paper proposes the now widely used EnKF.

    ADS  Google Scholar 

  59. Kalman, R. E. A new approach to linear filtering and prediction problems. J. Basic Eng. 82, 35–45 (1960).

    MathSciNet  Google Scholar 

  60. Humpherys, J., Redd, P. & West, J. A fresh look at the Kalman filter. SIAM Rev. 54, 801–823 (2012).

    MathSciNet  MATH  Google Scholar 

  61. Jazwinski, A. R. Stochastic Processes and Filtering Theory (Academic, 1970).

  62. Pham, D. T., Verron, J. & Roubaud, M. C. A singular evolutive extended Kalman filter for data assimilation in oceanography. J. Mar. Syst. 16, 323–340 (1998).

    Google Scholar 

  63. van Leeuwen, P. J. A consistent interpretation of the stochastic version of the ensemble Kalman filter. Q. J. R. Meteorol. Soc. 146, 2815–2825 (2020).

    ADS  Google Scholar 

  64. Yu, L. et al. Insights on multivariate updates of physical and biogeochemical ocean variables using an ensemble Kalman filter and an idealized model of upwelling. Ocean. Model. 126, 13–28 (2018).

    ADS  Google Scholar 

  65. Yu, L. et al. Evaluation of nonidentical versus identical twin approaches for observation impact assessments: an ensemble-Kalman-filter-based ocean assimilation application for the Gulf of Mexico. Ocean. Sci. 15, 1801–1814 (2019).

    ADS  Google Scholar 

  66. Wang, B., Fennel, K. & Yu, L. Can assimilation of satellite observations improve subsurface biological properties in a numerical model? A case study for the Gulf of Mexico. Ocean. Sci. 17, 1141–1156 (2021).

    ADS  Google Scholar 

  67. Sakov, P. & Oke, P. R. A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters. Tellus A Dyn. Meteorol. Oceanogr. 60, 361–371 (2008).

    Google Scholar 

  68. Houtekamer, P. L. & Zhang, F. Review of the ensemble Kalman filter for atmospheric data assimilation. Mon. Weather. Rev. 144, 4489–4532 (2016).

    ADS  Google Scholar 

  69. Mattern, J. P., Song, H., Edwards, C. A., Moore, A. M. & Fiechter, J. Data assimilation of physical and chlorophyll a observations in the California current system using two biogeochemical models. Ocean. Model. 109, 55–71 (2017).

    ADS  Google Scholar 

  70. Wang, B., Fennel, K., Yu, L. & Gordon, C. Assessing the value of biogeochemical Argo profiles versus ocean color observations for biogeochemical model optimization in the Gulf of Mexico. Biogeosciences 17, 4059–4074 (2020).

    ADS  Google Scholar 

  71. Fiechter, J., Broquet, G., Moore, A. M. & Arango, H. G. A data assimilative, coupled physical–biological model for the Coastal Gulf of Alaska. Dyn. Atmos. Ocean. 52, 95–118 (2011).

    ADS  Google Scholar 

  72. Moore, A. M. et al. The regional ocean modeling system (ROMS) 4-dimensional variational data assimilation systems: part III — observation impact and observation sensitivity in the California Current System. Prog. Oceanogr. 91, 74–94 (2011).

    ADS  Google Scholar 

  73. Fennel, K. et al. Advancing marine biogeochemical and ecosystem reanalyses and forecasts as tools for monitoring and managing ecosystem health. Front. Mar. Sci. 6, 89 (2019).

    Google Scholar 

  74. Teruzzi, A., Bolzon, G., Salon, S., Lazzari, P. & Solidoro, C. Assimilation of coastal and open sea biogeochemical data to improve phytoplankton simulation in the Mediterranean Sea. Ocean. Model. 132, 46–60 (2018).

    ADS  Google Scholar 

  75. Cossarini, G. et al. Towards operational 3D-Var assimilation of chlorophyll biogeochemical-Argo float data into a biogeochemical model of the Mediterranean Sea. Ocean. Model. 133, 112–128 (2019).

    ADS  Google Scholar 

  76. Ford, D. Assimilating synthetic biogeochemical-Argo and ocean colour observations into a global ocean model to inform observing system design. Biogeosciences 18, 509–534 (2021).

    ADS  Google Scholar 

  77. Song, H., Edwards, C. A., Moore, A. M. & Fiechter, J. Data assimilation in a coupled physical–biogeochemical model of the California current system using an incremental lognormal 4-dimensional variational approach: part 3 — assimilation in a realistic context using satellite and in situ observations. Ocean. Model. 106, 159–172 (2016).

    ADS  Google Scholar 

  78. Courtier, P., Thépaut, J.-N. & Hollingsworth, A. A strategy for operational implementation of 4D-Var, using an incremental approach. Q. J. R. Meteorol. Soc. 120, 1367–1387 (1994).

    ADS  Google Scholar 

  79. Gordon, N. J., Salmond, D. J. & Smith, A. F. M. in IEE Proc. F-radar and Signal Processing Vol. 140 107–113 (IET Digital Library, 1993).

  80. Mattern, J. P., Dowd, M. & Fennel, K. Particle filter-based data assimilation for a three-dimensional biological ocean model and satellite observations. J. Geophys. Res. Ocean. 118, 2746–2760 (2013).

    ADS  Google Scholar 

  81. Mattern, J. P., Yu, L., Wang, B. & Fennel, K. Ensemble Kalman filter application for an ocean biogeochemical model in an idealized 3-dimensional channel. GitHub https://doi.org/10.5281/zenodo.6974184 (2022).

    Article  Google Scholar 

  82. Rothstein, L. M. et al. Modeling ocean ecosystems: the PARADIGM program. Oceanography 19, 22–51 (2006).

    Google Scholar 

  83. Lehmann, M. K., Fennel, K. & He, R. Statistical validation of a 3-D bio-physical model of the western North Atlantic. Biogeosciences 6, 1961–1974 (2009).

    ADS  Google Scholar 

  84. Taylor, K. E. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos. 106, 7183–7192 (2001).

    ADS  Google Scholar 

  85. Jolliff, J. K. et al. Summary diagrams for coupled hydrodynamic–ecosystem model skill assessment. J. Mar. Syst. 76, 64–82 (2009).

    Google Scholar 

  86. Stow, C. A. et al. Skill assessment for coupled biological/physical models of marine systems. J. Mar. Syst. 76, 4–15 (2009). This paper presents a tutorial on common statistical approaches to model-data skill assessment for OBMs.

    Google Scholar 

  87. Doney, S. C. et al. Skill metrics for confronting global upper ocean ecosystem–biogeochemistry models against field and remote sensing data. J. Mar. Syst. 76, 95–112 (2009).

    Google Scholar 

  88. Mattern, J. P., Fennel, K. & Dowd, M. Introduction and assessment of measures for quantitative model-data comparison using satellite images. Remote. Sens. 2, 794–818 (2010).

    ADS  Google Scholar 

  89. Capotondi, A. et al. Observational needs supporting marine ecosystems modeling and forecasting: from the global ocean to regional and coastal systems. Front. Mar. Sci. https://doi.org/10.3389/fmars.2019.00623 (2019).

    Article  Google Scholar 

  90. Roemmich, D. et al. On the future of Argo: a global, full-depth, multi-disciplinary array. Front. Mar. Sci. 6, 439 (2019).

    Google Scholar 

  91. Chai, F. et al. Monitoring ocean biogeochemistry with autonomous platforms. Nat. Rev. Earth Environ. 1, 315–326 (2020). This work reviews autonomous approaches to measuring ocean biogeochemical properties, which will likely prove transformative for OBM validation and assimilation.

    ADS  Google Scholar 

  92. Johnson, K. S. et al. Biogeochemical sensor performance in the SOCCOM profiling float array. J. Geophys. Res. Ocean. 122, 6416–6436 (2017).

    ADS  Google Scholar 

  93. Tanhua, T. et al. Ocean FAIR data services. Front. Mar. Sci. 6, 440 (2019).

    Google Scholar 

  94. Révelard, A. et al. Ocean integration: the needs and challenges of effective coordination within the ocean observing system. Front. Mar. Sci. https://doi.org/10.3389/fmars.2021.737671 (2022).

    Article  Google Scholar 

  95. Friedlingstein, P. et al. Global Carbon Budget 2021. Earth Syst. Sci. Data 14, 1917–2005 (2022).

    ADS  Google Scholar 

  96. Khatiwala, S. et al. Global ocean storage of anthropogenic carbon. Biogeosciences 10, 2169–2191 (2013).

    ADS  Google Scholar 

  97. IPCC. Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge Univ. Press, 2021).

  98. Hauck, J. et al. Consistency and challenges in the ocean carbon sink estimate for the global carbon budget. Front. Mar. Sci. 7, 571720 (2020).

    Google Scholar 

  99. Crisp, D. et al. How well do we understand the land–ocean–atmosphere carbon cycle? Rev. Geophys. 60, e2021RG000736 (2022).

    ADS  Google Scholar 

  100. Ilyina, T. et al. Predictable variations of the carbon sinks and atmospheric CO2 growth in a multi-model framework. Geophys. Res. Lett. 48, e2020GL090695 (2021).

    ADS  Google Scholar 

  101. Gattuso, J.-P. et al. Ocean solutions to address climate change and its effects on marine ecosystems. Front. Mar. Sci. https://doi.org/10.3389/fmars.2018.00337 (2018).

    Article  Google Scholar 

  102. National Academies of Sciences, Engineering, and Medicine. A Research Strategy for Ocean-based Carbon Dioxide Removal and Sequestration (National Academies, 2022).

  103. Aumont, O. & Bopp, L. Globalizing results from ocean in situ iron fertilization studies. Glob. Biogeochem. Cycles https://doi.org/10.1029/2005GB002591 (2006).

    Article  Google Scholar 

  104. Jin, X., Gruber, N., Frenzel, H., Doney, S. C. & McWilliams, J. C. The impact on atmospheric CO2 of iron fertilization induced changes in the ocean’s biological pump. Biogeosciences 5, 385–406 (2008).

    ADS  Google Scholar 

  105. Oschlies, A., Koeve, W., Rickels, W. & Rehdanz, K. Side effects and accounting aspects of hypothetical large-scale Southern Ocean iron fertilization. Biogeosciences 7, 4017–4035 (2010).

    ADS  Google Scholar 

  106. Dutreuil, S., Bopp, L. & Tagliabue, A. Impact of enhanced vertical mixing on marine biogeochemistry: lessons for geo-engineering and natural variability. Biogeosciences 6, 901–912 (2009).

    ADS  Google Scholar 

  107. Bach, L. T. et al. Testing the climate intervention potential of ocean afforestation using the Great Atlantic Sargassum Belt. Nat. Commun. 12, 2556 (2021).

    ADS  Google Scholar 

  108. Ilyina, T., Wolf-Gladrow, D., Munhoven, G. & Heinze, C. Assessing the potential of calcium-based artificial ocean alkalinization to mitigate rising atmospheric CO2 and ocean acidification. Geophys. Res. Lett. 40, 5909–5914 (2013).

    ADS  Google Scholar 

  109. Feng, E. Y., Koeve, W., Keller, D. P. & Oschlies, A. Model-based assessment of the CO2 sequestration potential of coastal ocean alkalinization. Earth’s Futur. 5, 1252–1266 (2017).

    ADS  Google Scholar 

  110. Siegel, D. A., DeVries, T., Doney, S. C. & Bell, T. Assessing the sequestration time scales of some ocean-based carbon dioxide reduction strategies. Environ. Res. Lett. 16, 104003 (2021).

    ADS  Google Scholar 

  111. Schmidtko, S., Stramma, L. & Visbeck, M. Decline in global oceanic oxygen content during the past five decades. Nature 542, 335–339 (2017).

    ADS  Google Scholar 

  112. Doney, S. C., Bopp, L. & Long, M. C. Historical and future trends in ocean climate and biogeochemistry. Oceanography 27, 108–119 (2014).

    Google Scholar 

  113. Bopp, L., Resplandy, L., Untersee, A., Le Mezo, P. & Kageyama, M. Ocean (de)oxygenation from the Last Glacial Maximum to the twenty-first century: insights from Earth system models. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 375, 20160323 (2017).

    ADS  Google Scholar 

  114. Takano, Y., Ito, T. & Deutsch, C. Projected centennial oxygen trends and their attribution to distinct ocean climate forcings. Glob. Biogeochem. Cycles 32, 1329–1349 (2018).

    ADS  Google Scholar 

  115. Levin, L. A. Manifestation, drivers, and emergence of open ocean deoxygenation. Ann. Rev. Mar. Sci. 10, 229–260 (2018).

    Google Scholar 

  116. Oschlies, A., Brandt, P., Stramma, L. & Schmidtko, S. Drivers and mechanisms of ocean deoxygenation. Nat. Geosci. 11, 467–473 (2018).

    ADS  Google Scholar 

  117. Breitburg, D. et al. Declining oxygen in the global ocean and coastal waters. Science 359, eaam7240 (2018).

    Google Scholar 

  118. Rabalais, N. N. et al. Eutrophication-driven deoxygenation in the coastal ocean. Oceanography 27, 172–183 (2014).

    Google Scholar 

  119. Andrews, O., Buitenhuis, E., Le Quéré, C. & Suntharalingam, P. Biogeochemical modelling of dissolved oxygen in a changing ocean. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 375, 20160328 (2017).

    ADS  Google Scholar 

  120. Cocco, V. et al. Oxygen and indicators of stress for marine life in multi-model global warming projections. Biogeosciences 10, 1849–1868 (2013).

    ADS  Google Scholar 

  121. Bopp, L. et al. Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models. Biogeosciences 10, 6225–6245 (2013).

    ADS  Google Scholar 

  122. Couespel, D., Lévy, M. & Bopp, L. Oceanic primary production decline halved in eddy-resolving simulations of global warming. Biogeosciences 18, 4321–4349 (2021).

    ADS  Google Scholar 

  123. Bahl, A., Gnanadesikan, A. & Pradal, M.-A. Variations in ocean deoxygenation across earth system models: isolating the role of parameterized lateral mixing. Glob. Biogeochem. Cycles 33, 703–724 (2019).

    ADS  Google Scholar 

  124. Lévy, M., Resplandy, L., Palter, J. B., Couespel, D. & Lachkar, Z. in Ocean Mixing Ch. 13 (eds Meredith, M. & Naveira Garabato, A. B. T.-O. M.) 329–344 (Elsevier, 2022).

  125. Fennel, K. & Testa, J. M. Biogeochemical controls on coastal hypoxia. Ann. Rev. Mar. Sci. 11, 105–130 (2019). This review of coastal hypoxia puts forward a simple non-dimensional number to elucidate key factors controlling hypoxia in diverse coastal systems.

    Google Scholar 

  126. Peña, M. A., Katsev, S., Oguz, T. & Gilbert, D. Modeling dissolved oxygen dynamics and hypoxia. Biogeosciences 7, 933–957 (2010).

    ADS  Google Scholar 

  127. Irby, I. D. et al. Challenges associated with modeling low-oxygen waters in Chesapeake Bay: a multiple model comparison. Biogeosciences 13, 2011–2028 (2016).

    ADS  Google Scholar 

  128. Zhang, H., Fennel, K., Laurent, A. & Bian, C. A numerical model study of the main factors contributing to hypoxia and its interannual and short-term variability in the East China Sea. Biogeosciences 17, 5745–5761 (2020).

    ADS  Google Scholar 

  129. Li, Y., Li, M. & Kemp, W. M. A budget analysis of bottom-water dissolved oxygen in Chesapeake Bay. Estuaries Coasts 38, 2132–2148 (2015).

    Google Scholar 

  130. Yu, L., Fennel, K., Laurent, A., Murrell, M. C. & Lehrter, J. C. Numerical analysis of the primary processes controlling oxygen dynamics on the Louisiana shelf. Biogeosciences 12, 2063–2076 (2015).

    ADS  Google Scholar 

  131. Laurent, A., Fennel, K., Ko, D. & Lehrter, J. Climate change projected to exacerbate impacts of coastal eutrophication in the northern Gulf of Mexico. J. Geophys. Res. Ocean. 123, (2018).

  132. Ni, W., Li, M., Ross, A. C. & Najjar, R. G. Large projected decline in dissolved oxygen in a eutrophic estuary due to climate change. J. Geophys. Res. Ocean. 124, 8271–8289 (2019).

    ADS  Google Scholar 

  133. LaBone, E. D., Rose, K. A., Justic, D., Huang, H. & Wang, L. Effects of spatial variability on the exposure of fish to hypoxia: a modeling analysis for the Gulf of Mexico. Biogeosciences 18, 487–507 (2021).

    ADS  Google Scholar 

  134. de Mutsert, K., Steenbeek, J., Cowan, J. H. & Christensen, V. in Modeling Coastal Hypoxia (eds. Justic, D. et al.) 377–400 (Springer International, 2017).

  135. Fennel, K. & Laurent, A. N and P as ultimate and proximate limiting nutrients in the northern Gulf of Mexico: implications for hypoxia reduction strategies. Biogeosciences 15, 3121–3131 (2018).

    ADS  Google Scholar 

  136. Saraiva, S. et al. Baltic Sea ecosystem response to various nutrient load scenarios in present and future climates. Clim. Dyn. 52, 3369–3387 (2019).

    Google Scholar 

  137. Irby, I. D., Friedrichs, M. A. M., Da, F. & Hinson, K. E. The competing impacts of climate change and nutrient reductions on dissolved oxygen in Chesapeake Bay. Biogeosciences 15, 2649–2668 (2018).

    ADS  Google Scholar 

  138. Kessouri, F. et al. Coastal eutrophication drives acidification, oxygen loss, and ecosystem change in a major oceanic upwelling system. Proc. Natl Acad. Sci. USA 118, e2018856118 (2021).

    Google Scholar 

  139. Laurent, A. & Fennel, K. Time-evolving, spatially explicit forecasts of the northern Gulf of Mexico Hypoxic Zone. Environ. Sci. Technol. 53, 14449–14458 (2019).

    ADS  Google Scholar 

  140. Matli, V. R. R. et al. Fusion-based hypoxia estimates: combining geostatistical and mechanistic models of dissolved oxygen variability. Environ. Sci. Technol. 54, 13016–13025 (2020).

    ADS  Google Scholar 

  141. Yu, L. & Gan, J. Mitigation of eutrophication and hypoxia through oyster aquaculture: an ecosystem model evaluation off the Pearl River Estuary. Environ. Sci. Technol. 55, 5506–5514 (2021).

    ADS  Google Scholar 

  142. Feely, R. A., Doney, S. C. & Cooley, S. R. Ocean acidification: present conditions and future changes in a high-CO2 world. Oceanography 22, 36–47 (2009).

    Google Scholar 

  143. Licker, R. et al. Attributing ocean acidification to major carbon producers. Environ. Res. Lett. 14, 124060 (2019).

    ADS  Google Scholar 

  144. Doney, S. C., Busch, D. S., Cooley, S. R. & Kroeker, K. J. The impacts of ocean acidification on marine ecosystems and reliant human communities. Annu. Rev. Environ. Resour. 45, 83–112 (2020).

    Google Scholar 

  145. Gehlen, M. et al. The fate of pelagic CaCO3 production in a high CO2 ocean: a model study. Biogeosciences 4, 505–519 (2007).

    ADS  Google Scholar 

  146. Ilyina, T., Zeebe, R. E., Maier-Reimer, E. & Heinze, C. Early detection of ocean acidification effects on marine calcification. Glob. Biogeochem. Cycles https://doi.org/10.1029/2008GB003278 (2009).

    Article  Google Scholar 

  147. Krumhardt, K. M. et al. Coccolithophore growth and calcification in an acidified ocean: insights from community earth system model simulations. J. Adv. Model. Earth Syst. 11, 1418–1437 (2019).

    ADS  Google Scholar 

  148. Kwiatkowski, L. et al. Twenty-first century ocean warming, acidification, deoxygenation, and upper-ocean nutrient and primary production decline from CMIP6 model projections. Biogeosciences 17, 3439–3470 (2020). This work assesses the projected evolution of ocean biogeochemistry under twenty-first-century climate change across a suite of ESMs.

    ADS  Google Scholar 

  149. Brady, R. X., Lovenduski, N. S., Yeager, S. G., Long, M. C. & Lindsay, K. Skillful multiyear predictions of ocean acidification in the California Current System. Nat. Commun. 11, 2166 (2020).

    ADS  Google Scholar 

  150. Laurent, A. et al. Eutrophication-induced acidification of coastal waters in the northern Gulf of Mexico: insights into origin and processes from a coupled physical–biogeochemical model. Geophys. Res. Lett. 44, 946–956 (2017).

    ADS  Google Scholar 

  151. Hauri, C. et al. A regional hindcast model simulating ecosystem dynamics, inorganic carbon chemistry, and ocean acidification in the Gulf of Alaska. Biogeosciences 17, 3837–3857 (2020).

    ADS  Google Scholar 

  152. Rutherford, K., Fennel, K., Atamanchuk, D., Wallace, D. & Thomas, H. A modelling study of temporal and spatial pCO2 variability on the biologically active and temperature-dominated Scotian Shelf. Biogeosciences 18, 6271–6286 (2021).

    ADS  Google Scholar 

  153. Hauri, C. et al. Spatiotemporal variability and long-term trends of ocean acidification in the California Current System. Biogeosciences 10, 193–216 (2013).

    ADS  Google Scholar 

  154. Hauri, C. et al. Modulation of ocean acidification by decadal climate variability in the Gulf of Alaska. Commun. Earth Environ. 2, 191 (2021).

    ADS  Google Scholar 

  155. Gruber, N., Boyd, P. W., Frölicher, T. L. & Vogt, M. Biogeochemical extremes and compound events in the ocean. Nature 600, 395–407 (2021).

    ADS  Google Scholar 

  156. Dutkiewicz, S. et al. Impact of ocean acidification on the structure of future phytoplankton communities. Nat. Clim. Chang. 5, 1002–1006 (2015).

    ADS  Google Scholar 

  157. Pauly, D. & Christensen, V. Primary production required to sustain global fisheries. Nature 374, 255–257 (1995).

    ADS  Google Scholar 

  158. Loukos, H., Monfray, P., Bopp, L. & Lehodey, P. Potential changes in skipjack tuna (Katsuwonus pelamis) habitat from a global warming scenario: modelling approach and preliminary results. Fish. Oceanogr. 12, 474–482 (2003).

    Google Scholar 

  159. Stock, C. A. et al. On the use of IPCC-class models to assess the impact of climate on living marine resources. Prog. Oceanogr. 88, 1–27 (2011).

    ADS  Google Scholar 

  160. Tittensor, D. P. et al. A protocol for the intercomparison of marine fishery and ecosystem models: Fish-MIP v1.0. Geosci. Model. Dev. 11, 1421–1442 (2018).

    ADS  Google Scholar 

  161. Lotze, H. K. et al. Global ensemble projections reveal trophic amplification of ocean biomass declines with climate change. Proc. Natl Acad. Sci. USA 116, 12907–12912 (2019).

    Google Scholar 

  162. Tittensor, D. P. et al. Next-generation ensemble projections reveal higher climate risks for marine ecosystems. Nat. Clim. Chang. 11, 973–981 (2021).

    ADS  Google Scholar 

  163. Cheung, W. W. L. et al. Large-scale redistribution of maximum fisheries catch potential in the global ocean under climate change. Glob. Chang. Biol. 16, 24–35 (2010).

    ADS  Google Scholar 

  164. Lam, V. W. Y., Cheung, W. W. L., Reygondeau, G. & Sumaila, U. R. Projected change in global fisheries revenues under climate change. Sci. Rep. 6, 32607 (2016).

    ADS  Google Scholar 

  165. IPCC. IPCC Special Report on the Ocean and Cryosphere in a Changing Climate (Cambridge Univ. Press, 2019).

  166. IPBES. Global Assessment Report of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES Secretariat, 2019).

  167. Aumont, O., Maury, O., Lefort, S. & Bopp, L. Evaluating the potential impacts of the diurnal vertical migration by marine organisms on marine biogeochemistry. Glob. Biogeochem. Cycles 32, 1622–1643 (2018).

    ADS  Google Scholar 

  168. Archibald, K. M., Siegel, D. A. & Doney, S. C. Modeling the impact of zooplankton diel vertical migration on the carbon export flux of the biological pump. Glob. Biogeochem. Cycles 33, 181–199 (2019).

    ADS  Google Scholar 

  169. Arnold, C. P. & Dey, C. H. Observing-systems simulation experiments: past, present, and future. Bull. Am. Meteorol. Soc. 67, 687–695 (1986).

    ADS  Google Scholar 

  170. Halliwell, G. R. et al. Rigorous evaluation of a fraternal twin ocean OSSE system for the open Gulf of Mexico. J. Atmos. Ocean. Technol. 31, 105–130 (2014).

    ADS  Google Scholar 

  171. Griffies, S. M. et al. OMIP contribution to CMIP6: experimental and diagnostic protocol for the physical component of the ocean model intercomparison project. Geosci. Model. Dev. 9, 3231–3296 (2016).

    ADS  Google Scholar 

  172. Chassignet, E. P. et al. DAMÉE-NAB: the base experiments. Dyn. Atmos. Ocean. 32, 155–183 (2000).

    ADS  Google Scholar 

  173. Orr, J. C. On ocean carbon-cycle model comparison. Tellus B Chem. Phys. Meteorol. 51, 509–510 (1999).

    ADS  Google Scholar 

  174. Séférian, R. et al. Tracking improvement in simulated marine biogeochemistry between CMIP5 and CMIP6. Curr. Clim. Chang. Rep. 6, 95–119 (2020).

    Google Scholar 

  175. Canadell, J. G. et al. in Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge Univ. Press, 2021).

  176. Najjar, R. G. et al. Impact of circulation on export production, dissolved organic matter, and dissolved oxygen in the ocean: results from phase II of the Ocean Carbon-cycle Model Intercomparison Project (OCMIP-2). Global Biogeochem. Cycles https://doi.org/10.1029/2006GB002857 (2007).

    Article  Google Scholar 

  177. Matsumoto, K. et al. Evaluation of ocean carbon cycle models with data-based metrics. Geophys. Res. Lett. https://doi.org/10.1029/2003GL018970 (2004).

    Article  Google Scholar 

  178. Luettich, R. A. Jr et al. A test bed for coastal and ocean modeling. Eos https://doi.org/10.1029/2017EO078243 (2017).

    Article  Google Scholar 

  179. Yu, L., Fennel, K. & Laurent, A. A modeling study of physical controls on hypoxia generation in the northern Gulf of Mexico. J. Geophys. Res. Ocean. 120, 5019–5039 (2015).

    ADS  Google Scholar 

  180. Fennel, K. et al. Effects of model physics on hypoxia simulations for the northern Gulf of Mexico: a model intercomparison. J. Geophys. Res. Ocean. 121, 5731–5750 (2016).

    ADS  Google Scholar 

  181. Glover, D. M. et al. The US JGOFS data management experience. Deep Sea Res. Part II Top. Stud. Oceanogr. 53, 793–802 (2006).

    ADS  Google Scholar 

  182. Baker, K. S. & Chandler, C. L. Enabling long-term oceanographic research: changing data practices, information management strategies and informatics. Deep Sea Res. Part II Top. Stud. Oceanogr. 55, 2132–2142 (2008).

    ADS  Google Scholar 

  183. Boyer, T. et al. Objective analyses of annual, seasonal, and monthly temperature and salinity for the World Ocean on a 0.25° grid. Int. J. Climatol. 25, 931–945 (2005).

    Google Scholar 

  184. Garcia, H. E., Boyer, T. P., Baranova, O. K. & Locarnini, R. A. World Ocean Atlas 2018: Product Documentation (ed. Mishonov, A.) (NOAA, 2019).

  185. Key, R. M. et al. A global ocean carbon climatology: results from Global Data Analysis Project (GLODAP). Glob. Biogeochem. Cycles https://doi.org/10.1029/2004GB002247 (2004).

    Article  Google Scholar 

  186. Olsen, A. et al. An updated version of the global interior ocean biogeochemical data product, GLODAPv2.2020. Earth Syst. Sci. Data 12, 3653–3678 (2020).

    ADS  Google Scholar 

  187. Sloyan, B. M. et al. The Global Ocean Ship-based Hydrographic Investigations Program (GO-SHIP): a platform for integrated multidisciplinary ocean science. Front. Mar. Sci. 6, 445 (2019).

    Google Scholar 

  188. Wanninkhof, R. et al. A surface ocean CO2 reference network, SOCONET and associated marine boundary layer CO2 measurements. Front. Mar. Sci. 6, 400 (2019).

    Google Scholar 

  189. Benway, H. M. et al. Ocean time series observations of changing marine ecosystems: an era of integration, synthesis, and societal applications. Front. Mar. Sci. 6, 393 (2019).

    Google Scholar 

  190. Buitenhuis, E. T. et al. MAREDAT: towards a world atlas of MARine Ecosystem DATa. Earth Syst. Sci. Data 5, 227–239 (2013).

    ADS  Google Scholar 

  191. Lombard, F. et al. Globally consistent quantitative observations of planktonic ecosystems. Front. Mar. Sci. 6, 196 (2019).

    Google Scholar 

  192. Bittig, H. C. et al. A BGC-Argo guide: planning, deployment, data handling and usage. Front. Mar. Sci. https://doi.org/10.3389/fmars.2019.00502 (2019).

    Article  Google Scholar 

  193. Maurer, T. L., Plant, J. N. & Johnson, K. S. Delayed-mode quality control of oxygen, nitrate, and pH data on SOCCOM biogeochemical profiling floats. Front. Mar. Sci. 8, 683207 (2021).

    Google Scholar 

  194. Harrison, C. S., Long, M. C., Lovenduski, N. S. & Moore, J. K. Mesoscale effects on carbon export: a global perspective. Glob. Biogeochem. Cycles 32, 680–703 (2018).

    ADS  Google Scholar 

  195. Katavouta, A. & Thompson, K. R. Downscaling ocean conditions with application to the Gulf of Maine, Scotian Shelf and adjacent deep ocean. Ocean. Model. 104, 54–72 (2016).

    ADS  Google Scholar 

  196. Debreu, L., Marchesiello, P., Penven, P. & Cambon, G. Two-way nesting in split-explicit ocean models: algorithms, implementation and validation. Ocean. Model. 49–50, 1–21 (2012).

    ADS  Google Scholar 

  197. Löptien, U. & Dietze, H. Reciprocal bias compensation and ensuing uncertainties in model-based climate projections: pelagic biogeochemistry versus ocean mixing. Biogeosciences 16, 1865–1881 (2019).

    ADS  Google Scholar 

  198. Eyring, V. et al. Taking climate model evaluation to the next level. Nat. Clim. Chang. 9, 102–110 (2019).

    ADS  Google Scholar 

  199. Kwiatkowski, L. et al. Emergent constraints on projections of declining primary production in the tropical oceans. Nat. Clim. Chang. 7, 355–358 (2017).

    ADS  Google Scholar 

  200. Terhaar, J., Kwiatkowski, L. & Bopp, L. Emergent constraint on Arctic Ocean acidification in the twenty-first century. Nature 582, 379–383 (2020).

    ADS  Google Scholar 

  201. Fennel, K. A simple one-dimensional NPZD model with graphical user interface. GitHub https://doi.org/10.5281/zenodo.6993508 (2022).

    Article  Google Scholar 

  202. Kuhn, A. M., Fennel, K. & Mattern, J. P. Progress in oceanography model investigations of the North Atlantic spring bloom initiation. Prog. Oceanogr. 138, 176–193 (2015).

    ADS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

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.).

Corresponding author

Correspondence to Katja Fennel.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

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.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s43586-022-00154-2

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing