MTMW12-Introduction to Numerical Modelling

Module Provider: Meteorology
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites:
Non-modular pre-requisites: A-level further mathematics or equivalent in modules in mathematics at undergraduate level.
Co-requisites:
Modules excluded:
Current from: 2023/4

Module Convenor: Dr Hilary Weller
Email: h.weller@reading.ac.uk

Type of module:

Summary module description:

We will derive and analyse a number of numerical methods for solving the type of equations used in atmosphere and ocean modelling. Students will implement some of these methods using the Python programming language, analyse the results and write reports.

Aims:

The aim of this module is to familiarise the students with a range of concepts and techniques used in the numerical modelling of atmospheric and oceanic fluid flows.Ìý This will include mathematical analysis, modelling and some good programming practices.

Assessable learning outcomes:

By the end of this module students should be able to:

• Derive finite difference approximations using Taylor series;


• Explain the concept of stability and perform a basic stability analysis;


• Implement and test the behaviour of numerical schemes using Python;


• Recognise sourcesof numerical error and derive and measure order of accuracy;


• Use Fourier series for analysing both numerical methods and climate data;


• Use functions and loops in Python and avoid code duplication;


• Describe various properties of numerical methods such as conservation and boundedness;


• Collaborate on writing code in groups;


• Design experiments to test the properties of numerical methods.

Additional outcomes:

Students will develop skills of working to deadlines and preparing clear, concise written reports.

Outline content:

The lecture content covers:

• Derive finite difference approximations using Taylor series;


• Differential equations with time and space derivatives;


• Techniques for solving the diffusion equation and the advection equation;


• Use of Fourier series:


• Python including use of functions and testing.

Brief description of teaching and learning methods:

Lectures, computing practical classes and written reports on practicals. Ìý