Articles | Volume 5-opsr
https://doi.org/10.5194/sp-5-opsr-10-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/sp-5-opsr-10-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Numerical models for simulating ocean physics
Michael J. Bell
CORRESPONDING AUTHOR
Met Office, Fitzroy Rd, Exeter, UK, UK
Andreas Schiller
CSIRO Environment, Castray Esplanade, Hobart, Tasmania, Australia
Stefania Ciliberti
Nologin Oceanic Weather Systems, Santiago de Compostela, Spain
Related authors
Ibrahim Hoteit, Eric Chassignet, and Mike Bell
State Planet, 5-opsr, 21, https://doi.org/10.5194/sp-5-opsr-21-2025, https://doi.org/10.5194/sp-5-opsr-21-2025, 2025
Short summary
Short summary
This paper explores how using multiple predictions instead of just one can improve ocean forecasts and help prepare for changes in ocean conditions. By combining different forecasts, scientists can better understand the uncertainty in predictions, leading to more reliable forecasts and better decision-making. This method is useful for responding to hazards like oil spills, improving climate forecasts, and supporting decision-making in fields like marine safety and resource management.
Liying Wan, Marcos Garcia Sotillo, Mike Bell, Yann Drillet, Roland Aznar, and Stefania Ciliberti
State Planet, 5-opsr, 15, https://doi.org/10.5194/sp-5-opsr-15-2025, https://doi.org/10.5194/sp-5-opsr-15-2025, 2025
Short summary
Short summary
Operating the ocean value chain requires the implementation of steps that must work systematically and automatically to generate ocean predictions and deliver this information. The paper illustrates the main challenges foreseen by operational chains in integrating complex numerical frameworks from the global to coastal scale and discusses existing tools that facilitate orchestration, including examples of existing systems and their capacity to provide high-quality and timely ocean forecasts.
Yann Drillet, Matthew Martin, Yosuke Fujii, Eric Chassignet, and Stefania Ciliberti
State Planet, 5-opsr, 2, https://doi.org/10.5194/sp-5-opsr-2-2025, https://doi.org/10.5194/sp-5-opsr-2-2025, 2025
Short summary
Short summary
This article describes the various stages of research and development that have been carried out over the last few decades to produce an operational reference service for global ocean monitoring and forecasting.
David Storkey, Pierre Mathiot, Michael J. Bell, Dan Copsey, Catherine Guiavarc'h, Helene T. Hewitt, Jeff Ridley, and Malcolm J. Roberts
Geosci. Model Dev., 18, 2725–2745, https://doi.org/10.5194/gmd-18-2725-2025, https://doi.org/10.5194/gmd-18-2725-2025, 2025
Short summary
Short summary
The Southern Ocean is a key region of the world ocean in the context of climate change studies. We show that the Met Office Hadley Centre coupled model with intermediate ocean resolution struggles to accurately simulate the Southern Ocean. Increasing the frictional drag that the seafloor exerts on ocean currents and introducing a representation of unresolved ocean eddies both appear to reduce the large-scale biases in this model.
Catherine Guiavarc'h, David Storkey, Adam T. Blaker, Ed Blockley, Alex Megann, Helene Hewitt, Michael J. Bell, Daley Calvert, Dan Copsey, Bablu Sinha, Sophia Moreton, Pierre Mathiot, and Bo An
Geosci. Model Dev., 18, 377–403, https://doi.org/10.5194/gmd-18-377-2025, https://doi.org/10.5194/gmd-18-377-2025, 2025
Short summary
Short summary
The Global Ocean and Sea Ice configuration version 9 (GOSI9) is the new UK hierarchy of model configurations based on the Nucleus for European Modelling of the Ocean (NEMO) and available at three resolutions. It will be used for various applications, e.g. weather forecasting and climate prediction. It improves upon the previous version by reducing global temperature and salinity biases and enhancing the representation of Arctic sea ice and the Antarctic Circumpolar Current.
Davi Mignac, Jennifer Waters, Daniel J. Lea, Matthew J. Martin, James While, Anthony T. Weaver, Arthur Vidard, Catherine Guiavarc’h, Dave Storkey, David Ford, Edward W. Blockley, Jonathan Baker, Keith Haines, Martin R. Price, Michael J. Bell, and Richard Renshaw
EGUsphere, https://doi.org/10.5194/egusphere-2024-3143, https://doi.org/10.5194/egusphere-2024-3143, 2024
Short summary
Short summary
We describe major improvements of the Met Office's global ocean-sea ice forecasting system. The models and the way observations are used to improve the forecasts were changed, which led to a significant error reduction of 1-day forecasts. The new system performance in past conditions, where sub-surface observations are scarce, was improved with more consistent ocean heat content estimates. The new system will be of better use for climate studies and will provide improved forecasts for end users.
Jozef Skakala, David Ford, Keith Haines, Amos Lawless, Matthew Martin, Philip Browne, Marcin Chrust, Stefano Ciavatta, Alison Fowler, Daniel Lea, Matthew Palmer, Andrea Rochner, Jennifer Waters, Hao Zuo, Mike Bell, Davi Carneiro, Yumeng Chen, Susan Kay, Dale Partridge, Martin Price, Richard Renshaw, Georgy Shapiro, and James While
EGUsphere, https://doi.org/10.5194/egusphere-2024-1737, https://doi.org/10.5194/egusphere-2024-1737, 2024
Short summary
Short summary
In this paper we review marine data assimilation (MDA) in the UK, its stakeholders, needs, past and present developments in different areas of UK MDA, and offer a vision for their longer future. The specific areas covered are ocean physics and sea ice, marine biogeochemistry, coupled MDA, MDA informing observing network design and MDA theory. We also discuss future vision for MDA resources: observations, software, hardware and people skills.
Stefania A. Ciliberti, Enrique Alvarez Fanjul, Jay Pearlman, Kirsten Wilmer-Becker, Pierre Bahurel, Fabrice Ardhuin, Alain Arnaud, Mike Bell, Segolene Berthou, Laurent Bertino, Arthur Capet, Eric Chassignet, Stefano Ciavatta, Mauro Cirano, Emanuela Clementi, Gianpiero Cossarini, Gianpaolo Coro, Stuart Corney, Fraser Davidson, Marie Drevillon, Yann Drillet, Renaud Dussurget, Ghada El Serafy, Katja Fennel, Marcos Garcia Sotillo, Patrick Heimbach, Fabrice Hernandez, Patrick Hogan, Ibrahim Hoteit, Sudheer Joseph, Simon Josey, Pierre-Yves Le Traon, Simone Libralato, Marco Mancini, Pascal Matte, Angelique Melet, Yasumasa Miyazawa, Andrew M. Moore, Antonio Novellino, Andrew Porter, Heather Regan, Laia Romero, Andreas Schiller, John Siddorn, Joanna Staneva, Cecile Thomas-Courcoux, Marina Tonani, Jose Maria Garcia-Valdecasas, Jennifer Veitch, Karina von Schuckmann, Liying Wan, John Wilkin, and Romane Zufic
State Planet, 1-osr7, 2, https://doi.org/10.5194/sp-1-osr7-2-2023, https://doi.org/10.5194/sp-1-osr7-2-2023, 2023
Ibrahim Hoteit, Eric Chassignet, and Mike Bell
State Planet, 5-opsr, 21, https://doi.org/10.5194/sp-5-opsr-21-2025, https://doi.org/10.5194/sp-5-opsr-21-2025, 2025
Short summary
Short summary
This paper explores how using multiple predictions instead of just one can improve ocean forecasts and help prepare for changes in ocean conditions. By combining different forecasts, scientists can better understand the uncertainty in predictions, leading to more reliable forecasts and better decision-making. This method is useful for responding to hazards like oil spills, improving climate forecasts, and supporting decision-making in fields like marine safety and resource management.
Andreas Schiller, Simon A. Josey, John Siddorn, and Ibrahim Hoteit
State Planet, 5-opsr, 18, https://doi.org/10.5194/sp-5-opsr-18-2025, https://doi.org/10.5194/sp-5-opsr-18-2025, 2025
Short summary
Short summary
The study illustrates the way atmospheric fields are used in ocean models as boundary conditions for the provisioning of the exchanges of heat, freshwater, and momentum fluxes. Such fluxes can be based on remote sensing instruments or provided directly by numerical weather prediction systems. Air–sea flux datasets are defined by their spatial and temporal resolutions and are limited by associated biases. Air–sea flux datasets for ocean models should be chosen with the applications in mind.
Liying Wan, Marcos Garcia Sotillo, Mike Bell, Yann Drillet, Roland Aznar, and Stefania Ciliberti
State Planet, 5-opsr, 15, https://doi.org/10.5194/sp-5-opsr-15-2025, https://doi.org/10.5194/sp-5-opsr-15-2025, 2025
Short summary
Short summary
Operating the ocean value chain requires the implementation of steps that must work systematically and automatically to generate ocean predictions and deliver this information. The paper illustrates the main challenges foreseen by operational chains in integrating complex numerical frameworks from the global to coastal scale and discusses existing tools that facilitate orchestration, including examples of existing systems and their capacity to provide high-quality and timely ocean forecasts.
Jennifer Veitch, Enrique Alvarez-Fanjul, Arthur Capet, Stefania Ciliberti, Mauro Cirano, Emanuela Clementi, Fraser Davidson, Ghada el Serafy, Guilherme Franz, Patrick Hogan, Sudheer Joseph, Svitlana Liubartseva, Yasumasa Miyazawa, Heather Regan, and Katerina Spanoudaki
State Planet, 5-opsr, 6, https://doi.org/10.5194/sp-5-opsr-6-2025, https://doi.org/10.5194/sp-5-opsr-6-2025, 2025
Short summary
Short summary
Ocean forecast systems provide information about a future state of the ocean. This information is provided in the form of decision support tools, or downstream applications, that can be accessed by various stakeholders to support livelihoods, coastal resilience and the good governance of the marine environment. This paper provides an overview of the various downstream applications of ocean forecast systems that are utilized around the world.
Antonio Novellino, Alain Arnaud, Andreas Schiller, and Liying Wan
State Planet, 5-opsr, 25, https://doi.org/10.5194/sp-5-opsr-25-2025, https://doi.org/10.5194/sp-5-opsr-25-2025, 2025
Short summary
Short summary
The paper describes the significant role that ocean forecasting systems play in the blue economy, demonstrating their direct benefits in improving prediction accuracy and downstream applications.
Mauro Cirano, Enrique Alvarez-Fanjul, Arthur Capet, Stefania Ciliberti, Emanuela Clementi, Boris Dewitte, Matias Dinápoli, Ghada El Serafy, Patrick Hogan, Sudheer Joseph, Yasumasa Miyazawa, Ivonne Montes, Diego A. Narvaez, Heather Regan, Claudia G. Simionato, Gregory C. Smith, Joanna Staneva, Clemente A. S. Tanajura, Pramod Thupaki, Claudia Urbano-Latorre, and Jennifer Veitch
State Planet, 5-opsr, 5, https://doi.org/10.5194/sp-5-opsr-5-2025, https://doi.org/10.5194/sp-5-opsr-5-2025, 2025
Short summary
Short summary
Operational ocean forecasting systems (OOFSs) are crucial for human activities, environmental monitoring, and policymaking. An assessment across eight key regions highlights strengths and gaps, particularly in coastal and biogeochemical forecasting. AI offers improvements, but collaboration, knowledge sharing, and initiatives like the OceanPrediction Decade Collaborative Centre (DCC) are key to enhancing accuracy, accessibility, and global forecasting capabilities.
Stefania Ciliberti and Gianpaolo Coro
State Planet, 5-opsr, 24, https://doi.org/10.5194/sp-5-opsr-24-2025, https://doi.org/10.5194/sp-5-opsr-24-2025, 2025
Short summary
Short summary
This review explores how cloud computing technology and its foundational concepts can enhance operational forecasting with scalable, flexible, and measurable resources. It highlights its benefits for the ocean value chain in support of ocean data management, forecasting system infrastructure, data analysis, visualization of ocean forecasts, dissemination, and outreach, showcasing real-world initiatives from the weather and ocean community.
Yann Drillet, Matthew Martin, Yosuke Fujii, Eric Chassignet, and Stefania Ciliberti
State Planet, 5-opsr, 2, https://doi.org/10.5194/sp-5-opsr-2-2025, https://doi.org/10.5194/sp-5-opsr-2-2025, 2025
Short summary
Short summary
This article describes the various stages of research and development that have been carried out over the last few decades to produce an operational reference service for global ocean monitoring and forecasting.
David Storkey, Pierre Mathiot, Michael J. Bell, Dan Copsey, Catherine Guiavarc'h, Helene T. Hewitt, Jeff Ridley, and Malcolm J. Roberts
Geosci. Model Dev., 18, 2725–2745, https://doi.org/10.5194/gmd-18-2725-2025, https://doi.org/10.5194/gmd-18-2725-2025, 2025
Short summary
Short summary
The Southern Ocean is a key region of the world ocean in the context of climate change studies. We show that the Met Office Hadley Centre coupled model with intermediate ocean resolution struggles to accurately simulate the Southern Ocean. Increasing the frictional drag that the seafloor exerts on ocean currents and introducing a representation of unresolved ocean eddies both appear to reduce the large-scale biases in this model.
Manuel García-León, José María García-Valdecasas, Lotfi Aouf, Alice Dalphinet, Juan Asensio, Stefania Angela Ciliberti, Breogán Gómez, Víctor Aquino, Roland Aznar, and Marcos Sotillo
EGUsphere, https://doi.org/10.5194/egusphere-2025-657, https://doi.org/10.5194/egusphere-2025-657, 2025
This preprint is open for discussion and under review for Ocean Science (OS).
Short summary
Short summary
Accurate short-term wave forecasts are key for coastal activities. These forecasts rely on wind and currents as forcing, which in this work were both enhanced using neural networks (NNs) trained with satellite and radar data. Tested at three European sites, the NN-corrected winds were 35 % more accurate, and currents also improved. This led to improved IBI wave model predictions of wave height and period by 10 % and 17 %, respectively; even correcting under extreme events.
Catherine Guiavarc'h, David Storkey, Adam T. Blaker, Ed Blockley, Alex Megann, Helene Hewitt, Michael J. Bell, Daley Calvert, Dan Copsey, Bablu Sinha, Sophia Moreton, Pierre Mathiot, and Bo An
Geosci. Model Dev., 18, 377–403, https://doi.org/10.5194/gmd-18-377-2025, https://doi.org/10.5194/gmd-18-377-2025, 2025
Short summary
Short summary
The Global Ocean and Sea Ice configuration version 9 (GOSI9) is the new UK hierarchy of model configurations based on the Nucleus for European Modelling of the Ocean (NEMO) and available at three resolutions. It will be used for various applications, e.g. weather forecasting and climate prediction. It improves upon the previous version by reducing global temperature and salinity biases and enhancing the representation of Arctic sea ice and the Antarctic Circumpolar Current.
Davi Mignac, Jennifer Waters, Daniel J. Lea, Matthew J. Martin, James While, Anthony T. Weaver, Arthur Vidard, Catherine Guiavarc’h, Dave Storkey, David Ford, Edward W. Blockley, Jonathan Baker, Keith Haines, Martin R. Price, Michael J. Bell, and Richard Renshaw
EGUsphere, https://doi.org/10.5194/egusphere-2024-3143, https://doi.org/10.5194/egusphere-2024-3143, 2024
Short summary
Short summary
We describe major improvements of the Met Office's global ocean-sea ice forecasting system. The models and the way observations are used to improve the forecasts were changed, which led to a significant error reduction of 1-day forecasts. The new system performance in past conditions, where sub-surface observations are scarce, was improved with more consistent ocean heat content estimates. The new system will be of better use for climate studies and will provide improved forecasts for end users.
Jozef Skakala, David Ford, Keith Haines, Amos Lawless, Matthew Martin, Philip Browne, Marcin Chrust, Stefano Ciavatta, Alison Fowler, Daniel Lea, Matthew Palmer, Andrea Rochner, Jennifer Waters, Hao Zuo, Mike Bell, Davi Carneiro, Yumeng Chen, Susan Kay, Dale Partridge, Martin Price, Richard Renshaw, Georgy Shapiro, and James While
EGUsphere, https://doi.org/10.5194/egusphere-2024-1737, https://doi.org/10.5194/egusphere-2024-1737, 2024
Short summary
Short summary
In this paper we review marine data assimilation (MDA) in the UK, its stakeholders, needs, past and present developments in different areas of UK MDA, and offer a vision for their longer future. The specific areas covered are ocean physics and sea ice, marine biogeochemistry, coupled MDA, MDA informing observing network design and MDA theory. We also discuss future vision for MDA resources: observations, software, hardware and people skills.
Stefania A. Ciliberti, Enrique Alvarez Fanjul, Jay Pearlman, Kirsten Wilmer-Becker, Pierre Bahurel, Fabrice Ardhuin, Alain Arnaud, Mike Bell, Segolene Berthou, Laurent Bertino, Arthur Capet, Eric Chassignet, Stefano Ciavatta, Mauro Cirano, Emanuela Clementi, Gianpiero Cossarini, Gianpaolo Coro, Stuart Corney, Fraser Davidson, Marie Drevillon, Yann Drillet, Renaud Dussurget, Ghada El Serafy, Katja Fennel, Marcos Garcia Sotillo, Patrick Heimbach, Fabrice Hernandez, Patrick Hogan, Ibrahim Hoteit, Sudheer Joseph, Simon Josey, Pierre-Yves Le Traon, Simone Libralato, Marco Mancini, Pascal Matte, Angelique Melet, Yasumasa Miyazawa, Andrew M. Moore, Antonio Novellino, Andrew Porter, Heather Regan, Laia Romero, Andreas Schiller, John Siddorn, Joanna Staneva, Cecile Thomas-Courcoux, Marina Tonani, Jose Maria Garcia-Valdecasas, Jennifer Veitch, Karina von Schuckmann, Liying Wan, John Wilkin, and Romane Zufic
State Planet, 1-osr7, 2, https://doi.org/10.5194/sp-1-osr7-2-2023, https://doi.org/10.5194/sp-1-osr7-2-2023, 2023
Giovanni Coppini, Palmalisa Marra, Rita Lecci, Nadia Pinardi, Sergio Cretì, Mario Scalas, Luca Tedesco, Alessandro D'Anca, Leopoldo Fazioli, Antonio Olita, Giuseppe Turrisi, Cosimo Palazzo, Giovanni Aloisio, Sandro Fiore, Antonio Bonaduce, Yogesh Vittal Kumkar, Stefania Angela Ciliberti, Ivan Federico, Gianandrea Mannarini, Paola Agostini, Roberto Bonarelli, Sara Martinelli, Giorgia Verri, Letizia Lusito, Davide Rollo, Arturo Cavallo, Antonio Tumolo, Tony Monacizzo, Marco Spagnulo, Rorberto Sorgente, Andrea Cucco, Giovanni Quattrocchi, Marina Tonani, Massimiliano Drudi, Paola Nassisi, Laura Conte, Laura Panzera, Antonio Navarra, and Giancarlo Negro
Nat. Hazards Earth Syst. Sci., 17, 533–547, https://doi.org/10.5194/nhess-17-533-2017, https://doi.org/10.5194/nhess-17-533-2017, 2017
Short summary
Short summary
SeaConditions aims to support the users by providing the environmental information in due time and with adequate accuracy in the marine and coastal environments, enforcing users' sea situational awareness. SeaConditions consists of a web and mobile application for the provision of meteorological and oceanographic observation and forecasting products. The iOS/Android apps were downloaded by more than 105 000 users and more than 100 000 users have visited the web version (www.sea-conditions.com).
Nadia Pinardi, Vladyslav Lyubartsev, Nicola Cardellicchio, Claudio Caporale, Stefania Ciliberti, Giovanni Coppini, Francesca De Pascalis, Lorenzo Dialti, Ivan Federico, Marco Filippone, Alessandro Grandi, Matteo Guideri, Rita Lecci, Lamberto Lamberti, Giuliano Lorenzetti, Paolo Lusiani, Cosimo Damiano Macripo, Francesco Maicu, Michele Mossa, Diego Tartarini, Francesco Trotta, Georg Umgiesser, and Luca Zaggia
Nat. Hazards Earth Syst. Sci., 16, 2623–2639, https://doi.org/10.5194/nhess-16-2623-2016, https://doi.org/10.5194/nhess-16-2623-2016, 2016
Short summary
Short summary
A multiscale sampling experiment was carried out in the Gulf of Taranto (eastern Mediterranean) providing the first synoptic evidence of the large-scale circulation structure and associated mesoscale variability. The circulation is shown to be dominated by an anticyclonic gyre and upwelling areas at the gyre periphery.
Cited articles
Adcroft, A.: Representation of topography by porous barriers and objective interpolation of topographic data, Ocean Model., 67, 13–27, https://doi.org/10.1016/j.ocemod.2013.03.002, 2013.
Alvarez Fanjul, E., Ciliberti, S., and Bahurel, P.: Implementing Operational Ocean Monitoring and Forecasting Systems, IOC-UNESCO, GOOS-275, https://doi.org/10.48670/ETOOFS, 2022.
Arakawa, A.: Finite-difference methods in climate modelling, in: Physically-Based Modelling and Simulation of Climate and Climatic Change – Part I, edited by: Schlesinger, M. E., Kluwer Academic Publishers, 79–168, ISBN-13: 978-94-010-7868-9, e-ISBN-13: 978-94-009-3043-8, https://doi.org/10.1007/978-94-009-3043-8, 1988.
Arakawa, A. and Moorthi, S.: Baroclinic instability in vertically discrete systems, J. Atmos. Sci., 45, 1688–1707, 1988.
Bachman, S. D.: Evaluation of scale-aware subgrid mesoscale eddy models in a global eddy-rich model, Ocean Model., 115, 42–58, https://doi.org/10.1016/j.ocemod.2017.05.007, 2017.
Batchelor, G. K.: An Introduction to Fluid Dynamics, Cambridge Mathematical Library, Cambridge monographs on mechanics and applied mathematics, Cambridge University Press, ISBN 0521663962, 9780521663960, 1967.
Bell, M. J. and White, A. A.: Analytical approximations to spurious short-wave baroclinic instabilities on the Lorenz grid, Ocean Model., 118, 31–40, https://doi.org/10.1016/j.ocemod.2017.08.001, 2017.
Bell, M. J., Schiller, A., Le Traon, P.-Y., Smith, N. R., Dombrowsky, E., and Wilmer-Becker, K.: An introduction to GODAE OceanView, J. Oper. Oceanogr., 8, s2–s11, https://doi.org/10.1080/1755876X.2015.1022041, 2015.
Bell, M. J., Peixoto, P S., and Thuburn, J.: Numerical instabilities of vector invariant momentum equations on rectangular C-grids, Q. J. Roy. Meteor. Soc., 143, 563–581, https://doi.org/10.1002/qj.2950, 2017.
Brasseur, G. P. and Jacob, D. J.: Numerical Methods for Advection, Chapter 7 in Modeling of Atmospheric Chemistry, Cambridge University Press, 275-341, https://doi.org/10.1017/9781316544754.008, 2017.
Cotter, C. J. and Shipton, J.: Mixed finite elements for numerical weather prediction, J. Comput. Phys., 231, 7076–7091, https://doi.org/10.1016/j.jcp.2012.05.020, 2012.
Chassignet, E. P., Le Sommer, J., and Wallcraft, A. J.: General Circulation Models, in: Encyclopedia of Ocean Sciences, 3rd edn., edited by: Cochran, J. K., Bokuniewicz, J. H., and Yager, L. P., vol. 5, Elsevier, 486–490, ISBN 978-0-12-813081-0, https://doi.org/10.1016/B978-0-12-409548-9.11410-1, 2019.
Danilov, S.: On utility of triangular C-grid type discretization for numerical modeling of large-scale ocean flows, Ocean Dynam., 60, 1361–1369, https://doi.org/10.1007/s10236-010-0339-6, 2010.
Debreu, L. and Blayo, E.: Two-way embedding algorithms: a review, Ocean Dynam., 58, 415–428, https://doi.org/10.1007/s10236-008-0150-9, 2008.
Debreu, L., Kevlahan, N. K.-R., and Marchesiello, P.: Brinkman volume penalization for bathymetry in three-dimensional ocean models, Ocean Model., 145, 101530, https://doi.org/10.1016/j.ocemod.2019.101530, 2020.
de Lavergne, C., Vic, C., Madec, G., Roquet, F., Waterhouse, A. F., Whalen, C. B., Cuypers, Y., Bouruet-Aubertot, P., Ferron, B., and Hibiya, T.: A parameterization of local and remote tidal mixing, J. Adv. Model. Earth Sy., 12, e2020MS002065, https://doi.org/10.1029/2020MS002065, 2020.
Demange, J., Debreu, L., Marchesiello, P., Lemarié, F., Blayo, E., and Eldred, C.: Stability analysis of split-explicit free surface ocean models: implication of the depth-independent barotropic mode approximation, J. Comput. Phys., 398, 108875, https://doi.org/10.1016/j.jcp.2019.108875, 2019.
Ducousso, N., Le Sommer, J., Molines, J.-M., and Bell, M.: Impact of the Symmetric Instability of the Computational Kind at meso and submesoscale permitting resolutions, Ocean Model., 120, 18–26, https://doi.org/10.1016/j.ocemod.2017.10.006, 2017.
Durran, D. R.: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Berlin, Springer-Verlag, 465 pp., ISBN 978-1-4419-3121-4, https://doi.org/10.1007/978-1-4757-3081-4, 1999.
Eyring, V., Collins, W. D., Gentine, P., Barnes, E. A., Barreiro, M., Beucler, T., Bocquet, M., Bretherton, C. S., Christensen, H. M., Dagon, K., Gagne, D. J., Hall, D., Hammerling, D., Hoyer, S., Iglesias-Suarez, F.,Lopez-Gomez, I., McGraw, M. C., Meehl, G. A., Molina, M. J., Monteleoni, C., Mueller, J., Pritchard, M. S., Rolnick, D., Runge, J., Stier, P., Watt-Meyer, O., Weigel, K., Yu, R., and Zanna, L.: Pushing the frontiers in climate modelling and analysis with machine learning, Nat. Clim. Change, 14, 916–928, https://doi.org/10.1038/s41558-024-02095-y, 2024.
Fofonoff, P. and Millard Jr., R. C.: UNESCO: Algorithms for computation of fundamental properties of seawater, UNESCO Technical Papers in Marine Science, No. 44, 53 pp., http://unesdoc.unesco.org/images/0005/000598/059832eb.pdf (last access: 14 February 2025), 1983.
Fox-Kemper, B., Adcroft, A., Böning, C. W., Chassignet, E. P., Curchitser, E., Danabasoglu, G., Eden, C., England, M. H., Gerdes, R., Greatbatch, R. J., Griffies, S. M., Hallberg, R. W., Hanert, E., Heimbach, P., Hewitt, H. T., Hill, C. N., Komuro, Y., Legg, S., Le Sommer, J., Masina, S., Marsland, S. J., Penny, S. G., Qiao, F., Ringler, T. D., Treguier, A. M., Tsujino, H., Uotila, P., and Yeager, S. G.: Challenges and Prospects in Ocean Circulation Models, Front. Mar. Sci., 6, 65, https://doi.org/10.3389/fmars.2019.00065, 2019.
Fox-Kemper, B., Danabasoglu, G., Ferrari, R., Griffies, S., Hallberg, R., Holland, M., Maltrud, M., Peacock, S., and Samuels, B.: Parameterization of mixed layer eddies. III: Implementation and impact in global ocean climate simulations, Ocean Model., 39, 61–78, https://doi.org/10.1016/j.ocemod.2010.09.002, 2011.
Gent, P. R. and McWilliams, J. C.: Isopycnal mixing in ocean circulation models, J. Phys. Oceanogr., 20, 150–155, https://doi.org/10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2, 1990.
Griffies, S. M.: Fundamentals of ocean climate models, Princeton University Press, https://doi.org/10.2307/j.ctv301gzg, 2004.
Griffies, S. M. and Adcroft, A. J.: Formulating the Equation of Ocean Models. In Eddy resolving ocean models, editors: Hecht, M. and Hasumi, H., Geophysical Monograph, 177, 281–317, https://doi.org/10.1029/177GM18, 2008.
Griffies, S. M., Adcroft, A., and Hallberg, R. W.: A primer on the vertical lagrangian-remap method in ocean models based on finite volume generalized vertical coordinates, J. Adv. Model. Earth Sy., 12, e2019MS001954, https://doi.org/10.1029/2019MS001954, 2020.
Hallberg, R.: Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effect, Ocean Model., 72, 92–103, https://doi.org/10.1016/j.ocemod.2013.08.007, 2013.
Hofmeister, R., Burchard, H., and Beckers, J. M.: Non-uniform adaptive vertical grids for 3D numerical ocean models, Ocean Model., 33, 70–86, https://doi.org/10.1016/j.ocemod.2009.12.003, 2010.
Hogg, N. G.: Quantification of the deep circulation, in: Ocean circulation and climate: observing and modelling the global ocean, International Geophysics Series, edited by: Siedler, G., Church, J., and Gould, J., vol. 77, 259–270, Academic Press, San Diego, ISBN 0-12-641351-7, https://nora.nerc.ac.uk/id/eprint/158878 (last access: 16 February 2025), 2001.
Hollingsworth, A., Kallberg, P., Renner, V., and Burridge, D. M.: An internal symmetric computational instability, Q. J. Roy. Meteor. Soc., 109, 417–428, 1983.
Ilicak, M., Adcroft, A. J., Griffies, S. M., and Hallberg, R. W.: Spurious dia-neutral mixing and the role of momentum closure, Ocean Model., 45–46, 37–58, https://doi.org/10.1016/j.ocemod.2011.10.003, 2012.
IOC, SCOR, and IAPSO: The international thermodynamic equation of seawater. 2010: Calculation and use of thermodynamic properties. Intergovernmental Oceanographic Commission, Manuals and Guides No. 56, UNESCO (English), 196 pp., https://www.teos-10.org/pubs/TEOS-10_Manual.pdf (last access: 14 February 2025), 2010.
Korn, P., Brüggemann, N., Jungclaus, J. H., Lorenz, S. J., Gutjahr, O., Haak, H., Linardakis, L., Mehlmann, C., Mikolajewicz, U., Notz, D., Putrasahan, D. A., Singh, V., von Storch, J.-S., Zhu, X., and Marotzke, J.: ICON-O: The ocean component of the ICON Earth system model – Global simulation characteristics and local telescoping capability, J. Adv. Model. Earth Sy., 14, e2021MS002952, https://doi.org/10.1029/2021MS002952, 2022.
Large, W. G., McWilliams, J. C., and Doney S. C.: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization, Rev. Geophys., 32, 363–403, https://doi.org/10.1029/94RG01872, 1994.
Lemarié, F., Kurian, J., Shchepetkin, A., Molemaker, M. J., Colas, F., and McWilliams, J. C.: Are There Inescapable Issues Prohibiting the Use of Terrain-Following Coordinates in Climate Models?, Ocean Model., 42, 57–79, https://doi.org/10.1016/j.ocemod.2011.11.007, 2011.
Lemarié, F., Debreu, L., Demange, J., Madec, G., Molines, J., and Honnorat, M.: Stability constraints for oceanic numerical models: Implications for the formulation of time and space discretizations, Ocean Model., 92, 124–148, https://doi.org/10.1016/j.ocemod.2015.06.006, 2015.
Le Roux, D., Staniforth, A., and Lin, C. A.: Finite elements for shallow-water equation ocean models, Mon. Weather Rev., 126, 1931–1951, https://doi.org/10.1175/1520-0493(1998)126<1931:FEFSWE>2.0.CO;2, 1998.
Lorrain, P. and Corson, D.: Electromagnetic fields and waves, W. H. Freeman & Company, USA, 706 pp., ISBN 0-7167-0331-9, 1970.
Madec, G. and Imbard, M.: A global ocean mesh to overcome the north pole singularity, Clim. Dynam., 12, 381–388, https://doi.org/10.1007/BF00211684, 1996.
Mak, J., Maddison, J. R., Marshall, D. P., and Munday, D. R.: Implementation of a Geometrically Informed and Energetically Constrained Mesoscale Eddy Parameterization in an Ocean Circulation Model, J. Phys. Oceanogr., 48, 2363–2382, https://doi.org/10.1175/JPO-D-18-0017.1, 2018.
Martin, M. J., Hoteit, I., Bertino, L., and Moore, A. M.: Data assimilation schemes for ocean forecasting: state of the art, in: Ocean prediction: present status and state of the art (OPSR), edited by: Álvarez Fanjul, E., Ciliberti, S. A., Pearlman, J., Wilmer-Becker, K., and Behera, S., Copernicus Publications, State Planet, 5-opsr, 9, https://doi.org/10.5194/sp-5-opsr-9-2025, 2025.
McWilliams, J. C.: Modeling the oceanic general circulation, Annu. Rev. Fluid Mech., 28, 215–248, https://doi.org/10.1146/annurev.fl.28.010196.001243, 1996.
Pedlosky, J.: Geophysical Fluid Dynamics New York, Springer-Verlag, 624 pp., ISBN 0-387-90368-2, 1982.
Petersen, M. R., Williams, S. J., Maltrud, M. E., Hecht, M. W., and Hamann, B.: Evaluation of the arbitrary Lagrangian-Eulerian vertical coordinate method in the MPAS-Ocean model, Ocean Model., 86, 93–113, https://doi.org/10.1016/j.ocemod.2014.12.004, 2015.
Porter, A. R. and Heimbach, P.: Unlocking the Power of Parallel Computing: GPU technologies for Ocean Forecasting, in: Ocean prediction: present status and state of the art (OPSR), edited by: Álvarez Fanjul, E., Ciliberti, S. A., Pearlman, J., Wilmer-Becker, K., and Behera, S., Copernicus Publications, State Planet, 5-opsr, 23, https://doi.org/10.5194/sp-5-opsr-23-2025, 2025.
Redi, M. H.: Oceanic isopycnal mixing by coordinate rotation, J. Phys. Oceanogr., 13, 1154–1158, https://doi.org/10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2, 1982.
Reichl, B. G., Wang, D., Hara, T., Ginis, I., and Kukulka, T.: Langmuir Turbulence Parameterization in Tropical Cyclone Conditions, J. Phys. Oceanogr., 46, 863–886, https://doi.org/10.1175/JPO-D-15-0106.1, 2016.
Ringler, T. D., Thuburn, J., Klemp, J. B., and Skamarock, W. C.: A unified approach to energy conservation and potential vorticity dynamics for arbitrarily structured C-grids, J. Comput. Phys., 229, 3065–3090, https://doi.org/10.1016/j.jcp.2009.12.007, 2010.
Robinson, A. R. (Ed.): Eddies in Marine Science, Berlin, Springer, https://doi.org/10.1007/978-3-642-69003-7, 1983.
Ronchi, C., Iacono, R., and Paolucci, P. S.: The cubed sphere: A new method for the solution of partial differential equations in spherical geometry, J. Comput. Phys., 124, 93–114, https://doi.org/10.1006/jcph.1996.0047, 1996.
Ross, A., Li, Z., Perezhogin, P.,Fernandez-Granda, C., and Zanna, L.: Benchmarking of machine learning ocean sub-grid parameterizations in an idealized model, J. Adv. Model. Earth Sy., 15, e2022MS003258, https://doi.org/10.1029/2022MS003258, 2023.
Shchepetkin, A. F. and McWilliams, J. C.: A method for computing horizontal pressure-gradient force in an oceanic model with a nonaligned vertical coordinate, J. Geophys. Res.-Oceans, 108, 3090, https://doi.org/10.1029/2001JC001047, 2003.
Silvestri, S., Wagner, G. L., Constantinou, N. C., Hill, C., Campin, J.-M., Souza, A., Bishnu, S., Churavy, V., Marshall, J., and Ferrari, R. A GPU-based ocean dynamical core for routine mesoscale-resolving climate simulations, ESS Open Archive [preprint], https://doi.org/10.22541/essoar.171708158.82342448/v1, 2024.
Smith, N. R.: Ocean and climate prediction – the WOCE legacy, in: Ocean circulation and climate: observing and modelling the global ocean, International Geophysics Series, vol. 77, edited by: Siedler, G., Church, J., and Gould, J., San Diego, Academic Press, 585–602, ISBN 0-12-641351-7, https://nora.nerc.ac.uk/id/eprint/158878 (last access: 16 February 2025), 2001.
Soufflet, Y., Marchesiello, P., Lemarie, F., Jouanno, J., Capet, X., Debreu, L., and Benshila, R.: On effective resolution in ocean models, Ocean Model., 98, 36–50, https://doi.org/10.1016/j.ocemod.2015.12.004, 2016.
Srokosz, M., Danabasoglu, G., and Patterson, M.: Atlantic Meridional Overturning Circulation: Reviews of observational and modeling advances – An introduction, J. Geophys. Res.-Oceans, 126, e2020JC016745, https://doi.org/10.1029/2020JC016745, 2021.
Staniforth, A.: Regional modeling: A theoretical discussion, Meteorol. Atmos. Phys., 63, 15–29, https://doi.org/10.1007/BF01025361, 1997.
Stewart, A. L., Klocker, A., and Menemenlis, D.: Circum-Antarctic shoreward heat transport derived from an eddy- and tide-resolving simulation, Geophys. Res. Lett., 45, 834–845, https://doi.org/10.1002/2017GL075677, 2018.
Storto, A., Frolov, S., Slivinski, L., and Yang, C.: Correction of Air-Sea Heat Fluxes in the NEMO Ocean General Circulation Model Using Neural Networks, Geosci. Model Dev. Discuss. [preprint], https://doi.org/10.5194/gmd-2024-185, in review, 2024.
Taylor, J. R. and Thompson, A. F.: Submesoscale Dynamics in the Upper Ocean, Annu. Rev. Fluid Mech., 55, 103–127, https://doi.org/10.1146/annurev-fluid-031422-095147, 2023.
Umlauf, L. and Burchard, H.: Second-order turbulence closure models for geophysical boundary layers. A review of recent work, Cont. Shelf Res., 25, 795–827, https://doi.org/10.1016/j.csr.2004.08.004, 2005.
Vallis, G. K.: Atmospheric and oceanic fluid dynamics. Fundamentals and large-scale circulation, 2nd edn., Cambridge University Press, https://doi.org/10.1017/9781107588417, 2017.
Visbeck, M., Marshall, J., Haine, T., and Spall, M.: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models, J. Phys. Oceanogr., 27, 381–402, https://doi.org/10.1175/1520-0485(1997)027<0381:SOETCI>2.0.CO;2, 1997.
Wan, L., Garcia Sotillo, M., Bell, M., Drillet, Y., Aznar, R., and Ciliberti, S.: An Introduction to Operational Chains in Ocean Forecasting, in: Ocean prediction: present status and state of the art (OPSR), edited by: Álvarez Fanjul, E., Ciliberti, S. A., Pearlman, J., Wilmer-Becker, K., and Behera, S., Copernicus Publications, State Planet, 5-opsr, 15, https://doi.org/10.5194/sp-5-opsr-15-2025, 2025.
White, A. A., Hoskins, B. J., Roulstone, I., and Staniforth, A.: Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic, Q. J. Roy. Meteor. Soc., 131, 2081–2107, https://doi.org/10.1256/qj.04.49, 2005.
Williams, R. G. and Follows, M. J.: Ocean Dynamics and the Carbon Cycle: Principles and Mechanisms, Cambridge University Press, ISBN 978-0-521-84369-0, 2011.
Yu, L.: Global Air–Sea Fluxes of Heat, Fresh Water, and Momentum: Energy Budget Closure and Unanswered Questions, Annu. Rev. Mar. Sci., 11, 227–48, 2019.
Zanna, L. and Bolton, T.: Data-driven equation discovery of ocean mesoscale closures, Geophys. Res. Lett., 47, e2020GL088376, https://doi.org/10.1029/2020GL088376, 2020.
Short summary
We provide an introduction to physical ocean models, at elementary and intermediate levels, describing the properties they represent, the principles and equations they use to evolve these properties, the physical phenomena they simulate, and the wider context and prospects for their further development. We also outline, at a more technical level, the methods and approximations that they use and the difficulties that limit their accuracy or reliability.
We provide an introduction to physical ocean models, at elementary and intermediate levels,...
Altmetrics
Final-revised paper
Preprint