Clasification of partical differential equations, examples of typical PDEs in

meteorology.

Spatial finite differences: method, accuracy, stability analysis, computational dispersion.

Methods for time integration: overview of explicit and implicit methods, semi-implicit

and semi-Lagrangian methods.

Numerical discretization of linear equations: 1-D and 2-D shallow-water equations, wave equation, (non)staggered grids, dispersion equation on various grids.

Advection equation. Comparison of various nuemrical solutions with analytical tests.

Spatial discretization of the non-linear eqautions. Example of shallow-water equations.

Vertical discretization in numerical weather prediction models: choice of the vertical grid, generalized and specific vertical coordinate.

Finite differences on the sphere.

Spectral methods: general formulation, spectral method on the sphere.

Spectral modelling on the limited area.

Formulation of the ALADIN model.

Treatment of the lateral boundary conditions for mesoscale models. Example of ALADIN.

# Atmospheric numerical modelling

- E. Kalnay: Atmospheric modelling, data assimilation and predictability. Cambridge university press 2003.
- D. Randall: An introduction to atmospheric modelling. Department of Atmospheric Science, Colorado State University 2003. (http://kiwi.atmos.colostate.edu/group/ dave/at604.html)
- Različni strokovni članki.

The purpose of the course is to introduce

principles of numerical discretization of the

equations for atmospheric motions.

Students will learn to solve typical equations

numerically and develop ability to

independently apply numerical methods to

solve simplified problems. Understanding of

numerical aspects of NWP models.

Knowledge and understanding: Discretization of atmospheric equations, numerical methods for solving problems in atmospheric sciences, programming ability.

Application: Planning, development and application of numerical methods to solve problems associated with atmospheric processes.

Reflection: Understanding the physical process and its numerical representation, understanding complexity.

Transferable skills: Numerical solution of partical differential equations. Mathematical formulation and numerical solution of processes in nature. Programming ability.

Lectures, tutorials, discussion,

programming exercises, home assigments and projects.

oral exam (theory)

written exam (problem solving)The written exam consistsof project reports that haveproportional weights in thegrade.

Grades: 5 (fail), 6-10 (pass) (inagreement with the Statute of the University of Ljubljana)

- Žagar, N. et al., 2008: Impact assessment of simulated Doppler wind lidars with

multivariante variational assimilation of the tropics. Mon. Wea. Rev., 136,

2443-2459. - Žagar, N., 2004: Assimilation of equatorial waves by line-of-sight wind observations.

J. Atmos. Sci., 61, 1877-1893. - Žagar, N. et al., 2013: Balance properties of the short-range forecast errors in the

ECMWF 4D-Var ensemble. Q. J. R. Meteorol. Soc., 139, 1229-1238.