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Numerical methods in atmospheric sciences and oceanography

The basic numerical methods and shortcomings for solving the hydrodynamic equations, which are common for Numerical Weather Prediction Models, Ocean Circulation models and Climate Models.

CIVIS focus area
Climate, environment and energy
Open to
  • MA
Field of studies
  • Engineering & Technology
  • Environment & Agriculture
  • Natural Sciences and Mathematics
Course dates
30 August - 03 October 2021
Apply by
31 May 2021 Apply now

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. In this course, you will build a numerical shallow water equation model.

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 climate physicist.

The teaching consists of lectures, calculation exercises and computer labs.

Application: Contact

Duration of the course: 5 weeks

Course format: Blended*

Location: Stockholm, Sweden

Language: English (B2 required)

Nb of ECTS: 7.5 (depending on your home University) Nb of CIVIS scholarships offered: 30 

*Subject to review, depending on the development of the current global pandemic. If overseas travelling and in-person teaching are not advisable, the entire course may be transferred online. 

Main topics

  • finite differences in time and space for the hydrodynamic equations
  • analysis of the limitations of finite difference methods
  • semi-implicit and semi-Lagrangian schemes
  • iterative methods for solving the Laplace and Poisson equations
  • staggered grids for the shallow-water equations in two dimensions
  • nonlinear advection terms
  • spectral coordinates for global atmospheric circulation models

Learning outcomes

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


Written exam at the end of the course as well as a series of computer exercises, which are written as reports.

Additional information

Admission to the course requires knowledge equivalent to Atmospheric physics and chemistry, 30 ECTS or Meteorology I, 15 ECTS and Meteorology II, 7.5 ECTS.

Kristofer Döös is a professor of climate modelling. He holds a PhD in oceanography from Université de Pierre et Marie Curie in Paris.

He has previously worked at Southampton Oceanography Centre and at the Institute of Oceanographic Sciences in the U.K. His main research has been on ocean and climate numerical modelling with particular emphasis on the overturning circulation and the Lagrangian tracking of heat and water masses in both the ocean and the atmosphere.