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2010/1 Module Catalogue
 Module Code: MAT3013 Module Title: MATHEMATICS OF WEATHER
Module Provider: Mathematics Short Name: MS316
Level: HE3 Module Co-ordinator: ROULSTONE I Prof (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Assessment Pattern

Unit(s) of Assessment


Weighting Towards Module Mark( %)


Coursework: Assignments and Test




Exam: Written examination (2 hours).




Qualifying Condition(s) 


An overall aggregate mark of 40% for the module is required to pass the module.



Module Overview
This module uses applied mathematics to describe the fluid mechanics of the atmosphere.
MAT2007 ODEs, MAT2011 (Linear PDEs); Desirable – MAT2010 (Fluid Dynamics). (A good knowledge of Level 1 vector algebra and calculus will be assumed.)

Module Aims
The aim of this module is to introduce the student to the relevant topics in dynamical meteorology, and to the basics of the numerical modelling that underpins modern numerical weather prediction.
Learning Outcomes

By the end of the course students should 

           Understand the basic equations of fluid motion as used in weather prediction.

Understand the basic approximate models based on balance: quasi-geostrophic theory and semi-geostrophic theory;

Understand the basics of barotropic and baroclinic waves and their stability.

Module Content
The module starts with an overview of the weather prediction as it is done today at the

Mathematics plays a central role in the development and analysis of models for weather prediction, and this module will introduce the student to a range of mathematical topics including



·         The Lagrangian and Eulerian descriptions of fluid motion and their application to the analysis of weather systems;


·         Governing equations, including the effects of rotation and stratification, geostrophic and hydrostatic balance;


·         The role of quasi-geostrophic theory in meteorology;


·         Vorticity dynamics, potential vorticity;


·         Linear barotropic waves (Kelvin, inertia-gravity and Rossby waves);
·         Barotropic and baroclinic instability.

  • Semi-geostrophic theory
Methods of Teaching/Learning
Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises, coursework and background reading. 3 lecture/tutorial hours per week for 10 weeks.
Selected Texts/Journals



B. Cushman-Roisin (1994)  Introduction to Geophysical Fluid Dynamics, Prentice-Hall: New York .


J.R. Holton (1992) An Introduction to Dynamic Meteorology, Academic Press


E. Kalnay (2003) Atmospheric Modelling, Data Assimilation and Predictability, Cambridge University Press.
Last Updated

September 10