A Primer on the Vertical Lagrangian‐Remap Method in Ocean Models Based on Finite Volume Generalized Vertical Coordinates

• Published in: Journal of advances in modeling earth systems 2020-10, Vol.12 (10), p.n/a
• Main Authors: Griffies, Stephen M., Adcroft, Alistair, Hallberg, Robert W.
• Format: Article
• Language: English
• Subjects: finite volume methods; fluid mechanics; generalized vertical coordinates; ocean model equations; oceanography; vertical Lagrangian remapping
• ISSN: 1942-2466; 1942-2466
• DOI: 10.1029/2019MS001954

This paper provides a primer on the mathematical, physical, and numerical foundations of ocean models that are formulated using finite volume generalized vertical coordinate equations and that use the vertical Lagrangian‐remap method to evolve the ocean state. We consider the mathematical structure of the governing ocean equations in both their strong formulation (partial differential equations) and weak formulation (finite volume integral equations), thus enabling an understanding of their physical content and providing a physical‐mathematical framework to develop numerical algorithms. A connection is made between the Lagrangian‐remap method and the ocean equations as written using finite volume generalized vertical budgets. Thought experiments are offered to exemplify the mechanics of the vertical Lagrangian‐remap method and to compare with other methods used for ocean model algorithms. Plain Language Summary Numerical ocean models are based on a variety of mathematical methods that provide the framework for developing computational algorithms suitable for solving the ocean equations on a computer. The vertical Lagrangian‐remap method is ideally suited for finite volume ocean models formulated using generalized vertical coordinates. It is gaining popularity among the ocean modeling community since it holds the potential to resolve longstanding limitations inherent with standard methods. However, there is some mystery surrounding the fundamentals of such ocean models. The goal of this paper is to dispel the mystery. We do so by providing a pedagogical treatment of the fluid mechanics that forms the basis for numerical ocean models formulated with finite volume generalized vertical coordinate equations and that use the vertical Lagrangian‐remap method. Key Points A pedagogical discussion is provided for ocean model dynamical cores that use the vertical Lagrangian‐remap method Mathematical physics is developed for finite volume ocean models that use generalized vertical coordinates A comparison is made between quasi‐Eulerian, Arbitrary Lagrangian‐Eulerian, and vertical Lagrangian remapping methods