OCG 694 Numerical Methods for Ocean and Atmospheric Modeling
3 hours/week (3 credits)
Course Description: The main focus of this course is on the various numerical methods applied for solving the fundamental hydrodynamic equations that govern atmospheric and oceanic motions. The discussion will range from very basic, simple methods to the ones that are currently used for weather prediction and ocean modeling.
Topics include:
- The basic mathematical concepts involved in the finite-difference methods of solving partial differential equations. Comparisons between analytical and numerical solutions (with particular emphasis on the phase and group velocities). Time integration methods (explicit, implicit, and semi-implicit). Computational stability and error estimates.
- Various grid systems (Arakawa A, B and C grids) to solve two-dimensional advection equation. The connection between a time integration scheme and spatial differencing.
- Numerical methods for solving parabolic equations illustrated with the help of the diffusion equation.
- Numerical methods for solving elliptic equations (known as diagnostic equations in meteorology and physical oceanography). Poisson and Helmholtz types of elliptic equations with Dirichlet, Neumann and mixture of the two boundary conditions.
- The basic concepts of Galerkin methods (spectral and finite element methods).
- Oceanic and atmospheric prediction models (quasi-geostrophic models, primitive equation models).
- Model initialization and verification. Data assimilation.
