MT24C-Numerical Methods for Environmental Science

Module Provider: Meteorology
Number of credits: 10 [5 ECTS credits]
Terms in which taught: Autumn term module
Non-modular pre-requisites:
Modules excluded:
Current from: 2020/1

Module Convenor: Prof Paul Williams


Type of module:

Summary module description:

A module based around computer practicals and lectures, introducing students to numerical algorithms for solving the equations relevant to environmental science.


To introduce students to the computational techniques needed to solve physical problems arising in environmental science and to develop the programming skills necessary to implement the techniques.

Assessable learning outcomes:
By the end of the module, the student should be able to: Develop numerical algorithms for solving basic differential equations commonly encountered in environmental science problems and implement them as computer programs. Use numerical analysis to evaluate the results produced by the programs and design ways to improve them. Relate the computational solutions to their anticipated nature from theory, including perturbation growth and propagation, and chaotic behaviour.

Additional outcomes:

Students will enhance their problem solving skills, general IT skills, the production of scientific figures and their inclusion in reports, and written presentation skills. Programming ability will enhance the quality of students’ dissertation projects and will be a key transferable skill from their degree.

Outline content:

  • Numerical solution of algebraic equations.

  • Numerical solution of ordinary and partial differential equations, especially finite difference methods.

  • Multi-dimensional systems and chaos theory.

  • The physical behaviour of solutions to common equations in environmental science, such as diffusion and advective transport by winds or curr ents.

  • Accuracy, stability, and convergence of numerical algorithms.  

Brief description of teaching and learning methods:

Lectures: Theory will be presented, reinforced by short exercises carried out by the students. Computing practicals: Students will develop programming skills using the Python language and apply the theory to problems set in assignments.

Contact hours:
  Autumn Spring Summer
Lectures 10
Practicals classes and workshops 20
Guided independent study: 70
Total hours by term 100
Total hours for module 100

Summative Assessment Methods:
Method Percentage
Report 30
Set exercise 50
Class test administered by School 20

Summative assessment- Examinations:

Summative assessment- Coursework and in-class tests:
The theory is assessed via a problem sheet.
The practical side is assessed via an in-class test plus a written report on a project.

Formative assessment methods:

Assignments in weekly practical classes, plus short exercises in the lectures.

Penalties for late submission:

The Module Convenor will apply the following penalties for work submitted late:

  • where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day[1] (or part thereof) following the deadline up to a total of five working days;
  • where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at:
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

40% overall.

Reassessment arrangements:
Resubmitted project report and alternative problem sheet.

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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