MT2MMNU: Mathematical Methods for Weather and Climate Science

Module code: MT2MMNU

Module provider: Meteorology; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 2 (Intermediate)

When you'll be taught: Semester 1

Module convenor: Dr David Ferreira, email: d.g.ferreira@reading.ac.uk

NUIST module lead: Vahid Darvish, email: vdarvish@gmail.com

Pre-requisite module(s): A-level mathematics or equivalent (Open)BEFORE TAKING THIS MODULE YOU MUST TAKE MA1LANU AND TAKE MA1CANU (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded: IN TAKING THIS MODULE YOU CANNOT TAKE MA2DENU OR TAKE MA2VCNU (Compulsory)

Placement information: NA

Academic year: 2024/5

Available to visiting students: No

Talis reading list: No

Last updated: 9 July 2024

Overview

Module aims and purpose

The module aims to further develop mathematical skills for atmospheric physicists. The approach is focused on the practical use of mathematics in physics in general and weather/climate in particular. Purely mathematical topics and formal proofs will be left to more advanced courses.

The course will expand or introduce three essential tools for climate sciences:

• Vector analysis and vector calculus
• Ordinary and partial differential equations
• Mathematical methods for analysing observations

In this module the student will have the opportunity to carry out experimental work in the Fluid Dynamics lab, and enhance their team-working skills and writing skills.

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Acquire and apply the concepts of vector calculus to problems in physics.
2. Analyse measurements and compare to theoretical predictions (e.g., manipulation of error bars, linear regression, statistical tests).
3. Solve simple cases of Ordinary and Partial Differential Equations relevant to weather/climate problems.
4. Write and present mathematical developments in a physics context and write a lab report.

Module content

• Concepts of scalar and vector fields, functions of multiple variables 
• Dot product, cross product, graphical representation of vectors 
• Integration of function of multiple variables; line, surface and volume integrals; Gauss’ and Stoke’s theorems  
• Partial differentiation. Chain Rule. Gradient, divergence, and rotational operators and their physical interpretation 
• Reinforcing/revising ODEs 
• Simple cases of PDE such as diffusion, wave equations, and their solutions, including numerical solutions 
• Basics of Fourier decomposition 
• Standard deviation, standard error. Hypothesis tests for population means 
• Manipulation (estimation, propagation, combinations, etc) of error bars 
• Linear regression, fitting a straight line; testing the significance of a regression relationship  
• Basic statistical testing (Student’s t test) 
• Writing and presentation skills of mathematics, writing a lab report 

Structure

Teaching and learning methods

Lectures supported by tutorials where students develop problem solving skills and receive feedback (formative) on their work (6h lectures per week), plus 6 x 2h sessions in Fluid lab (first for formative assessment, other two for summative) 

Study hours

At least 84 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• 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 (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: https://www.reading.ac.uk/cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

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.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Weekly problems sets supported by tutorials 

Feedback on first lab report (other two lab sessions for summative) 

Reassessment

Additional costs