**Study programme:** Geophysics

**Study cycle:** Master (second)

**Module:** Meteorology

**Core of the programme:** Mandatory for Meteorology module

**Year:** 2

**Semester:** 3

**Lectures:** 60 hours

**Exercises:** 15 hours

**Seminar:** 15 hours

**No. of ECTS credits:** 7

**Language:** Slovenian

**Specifics:** Additional 15 hours for homework assignments

# Numerical Methods in Meteorology

## Objectives of the course and intended learning outcomes (competences)

The purpose of the course is to introduce principles of numerical discretization of the equations for atmospheric motions. Students will learn how the typical meteorological equations are solved numerically and develop ability to independently apply numerical methods to solve simplified problems.## Contents (Syllabus outline)

- 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 the linear equations: 1-D and 2-D shallow-water equations, wave equation, (non)staggered grids, dispersion equation on various grids.
- Advection equation.
- Spatial discretization of the non-linear shallow-water equations.
- Scheme for the lateral boundary conditions.
- 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: the ALADIN model.

## Basic literature

- 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. Available at http://kiwi.atmos.colostate.edu/group/dave/at604.html.
- James R. Holton: An Introduction to Dynamic Meteorology, Academic Press; 1992 (III edition), 2004 (IV edition).

## Expected achievements

**Knowledge and understanding**

Discretization of atmospheric equations, numerical methods for solving problems in meteorology.

**Apllicability
**Planning, development and application of numerical models of atmospheric processes.

**Reflection
**Understanding the difference between the process and its numerical representation, understanding complexity.

**Transferable skills
**Numerical solution of partical differential equations.

## Teaching methods

Lectures, exercises, seminars; home assignments, students projects.## Prerequisites

Completed 1 level of Meteorology with Geophysics. Completed exam of Dynamical meteorology I. Oral exam only after successful completion of written exam.## Assesment methods

The assessment consists of two parts, a theoretical exam and a practical exercises exam. The practical exercises exam (50 % of final grade) can be completed with 2 half-term exams or 1 half-term exam together with a project assignment. A perquisite for theoretical exam is a successfully finished seminar. The theoretical exam together with the seminar is 50 % of final grade. The candidate successfully completes the assessment by obtaining a grade 6 (pass) to 10 (excellent) in both parts.## Methods of quality assessment

Self-evaluation, anonymous student questionnaire.## Course coodinator and his references

- Nedjeljka Žagar, assistant professor.