In this course you will build a numerical shallow water equation model. By doing so you will learn the basic numerical methods that are common for Numerical Weather Prediction Models, Ocean Circulation models and Climate Models.
We start with a very simple model of the advection equation, which we use to study the shortcomings of the numerical methods, such as numerical instability, truncation errors, computational modes, computation phase speeds and groups velocities. We then continue with the shallow water equations, where you develop your own shallow water model. Finally, an introduction to 3D modelling will be given. You will acquire, in this course, a fundamental understanding of the very core of the numerics of the circulation models, which are used in both weather forecast models as well as Climate models. The course is in other words a must if you want to call yourself a meteorologist, oceanographer or a climate physicist.
The course deals with numerical methods for solving the hydrodynamic equations, which are common for Numerical Weather Prediction Models, Ocean Circulation models and Climate Models.
The course includes:
• finite differences in time and space of the hydrodynamic equations
• analysis of finite differential methods limitations
• semi-implicit and semi-Lagrangian schemes
• iterative methods for solving Laplace and Poisson equations
• alternating grid for shallow water equations in two dimensions
• nonlinear advection terms
• spectral coordinates for global atmospheric circulation models
Admission to the course requires knowledge equivalent to Atmospheric physics and chemistry, 30 ECTS credits (MO4000) or Meteorology I, 15 ECTS credits (MO8001) and Meteorology II, 7.5 ECTS credits (MO8002). Swedish Upper Secondary School Course English B/English 6 or equivalent. Information about entry requirements on universityadmissions.se
After taking this course the student is expected to be able to:
- discretise hydrodynamic equations
- explain the limitations caused by discretisation (precision, instability, numerical modes, phase velocity, resolution)
- implement a shallow-water model numerically
- solve the Laplace and Poisson equations numerically using three different methods