MTMW12-Introduction to Numerical Modelling

Module Provider: Meteorology
Number of credits: 10 [5 ECTS credits]
Terms in which taught: Autumn term module
Non-modular pre-requisites: A-level mathematics and modules in mathematics in undergraduate degree.
Modules excluded:
Current from: 2020/1

Module Convenor: Dr Hilary Weller


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.


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.  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 sources of numerical error and derive and measure order of accuracy; Use Fourier series for analysing both numerical methods an d 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:

The practical classes cover:

  • Introduction to Python;

  • Implementation of numerical schemes and demonstration of their behaviour.

Brief description of teaching and learning methods:

Lectures, computing practical classes, written reports on practicals and peer instruction.  A list of background reading is supplied with the lecture notes.

Contact hours:
  Autumn Spring Summer
Lectures 14
Practicals classes and workshops 18
Guided independent study: 68
Total hours by term 0 0
Total hours for module 100

Summative Assessment Methods:
Method Percentage
Report 60
Class test administered by School 40

Summative assessment- Examinations:
1 hour 50 minute class test at the end of the module during the Autumn term. Answer all 4 questions.

Summative assessment- Coursework and in-class tests:
Written exam worth 40%. 55% is made up of 2 assignments involving programming and report writing worth 20% and 35%. The 35% assignment will involve team work.

Formative assessment methods:
Students receive 5% of the final module total for participating in a peer assessed assignment.

Penalties for late submission:
Penalties for late submission on this module are in accordance with the University policy. Please refer to page 5 of the Postgraduate Guide to Assessment for further information:

Assessment requirements for a pass:

A mark of 50% overall.

Reassessment arrangements:
For candidates who have failed, an opportunity to take a resit examination will be provided within the lifetime of the course.

Additional Costs (specified where applicable):

1) Required text books: 2) Specialist equipment or materials: 3) Specialist clothing, footwear or headgear: 4) Printing and binding: 5) Computers and devices with a particular specification: 6) Travel, accommodation and subsistence:

Last updated: 4 April 2020


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