The numerical methods, formulation and parameterizations used in models of the circulation of the atmosphere and ocean will be described in detail. Widely used numerical methods will be the focus but we will also review emerging concepts and new methods. The numerics underlying a hierarchy of models will be discussed, ranging from simple GFD models to the high-end GCMs. In the context of ocean GCMs, we will describe parameterization of geostrophic eddies, mixing and the surface and bottom boundary layers. The course will be graded for credit, based on problem sets and a project. These will entail hands-on use of the material covered in lectures.
Topics The finite difference method
Spatial discretization and numerical dispersion
Series expansion methods
Time-stepping methods
Space-time discretization
Discretization in more than one dimension
Shallow water dynamics and numerical dispersion
Barotropic models
Quasi-geostrophic equations
Quasi-geostrophic models
Eddy parameterization
The primitive equations
Vertical coordinates
Boundary layer parameterizations
Parameterizing geostrophic eddies
Overview and summary of GCM issues
Exams and grading: There will be no exams. Grading will be apportioned 50% problem sets and 50% project.