TITLE: Computational methods for atmospheric and oceanic modeling

INSTRUCTOR: F. Baer

PURPOSE: This course is designed to give students the tools necessary for understanding and manipulating atmospheric and oceanographic models for their use in predicting the future state of these fluids on any space and time scale. In addition, the student will become familiar with a number of models used both currently and in the past.

COURSE CONTENT:

1. Numerical methods with linear systems:

• grid point methods;
• time differencing schemes;
• schemes for the advection equation;
• schemes for the gravity and gravity-inertia wave equation.

2. The splitting scheme for linear and nonlinear systems (Marchuk).

3. Vertical coordinates for models:

• generalized vertical coordinate;
• various coordinates with orography;
• energy considerations.

4. Finite difference approximations for global models:

• shallow water equations;
• conformal projections;
• nonconformal projections;
• spherical geodesic grids;
• latitude-longitude grids.

5. The spectral method:

• general principles;
• models in spherical geometry;
• transform method;
• pseudospectral method.

6. The finite element method:

• general considerations;
• some simple approximations;
• use in solving prediction type differential equations;
• analysis of method;
• practical applications in prediction.

7. The semi-implicit method:

• properties of explicit schemes;
• implicit schemes;
• semi-implicit algorithms;
• applications.

8. The Lagrangian method:

• general theory;
• semi-Lagrangian technique (mixed Eulerian/Lagrange methods)
• fully Lagrangian approach;
• applications.

9. The ETA model and its applications.