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MT2MM: Mathematical Methods for Weather and Climate Science

MT2MM: Mathematical Methods for Weather and Climate Science

Module code: MT2MM

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

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST TAKE MA1LA AND TAKE MA1CA (Compulsory)

Co-requisite module(s):

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

Module(s) excluded: IN TAKING THIS MODULE YOU CANNOT TAKE MA2DE OR TAKE MA2VC OR TAKE MA2MMP (Compulsory)

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 9 July 2024

Overview

Module aims and purpose

The module aims to further develop mathematical skills for 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 analyzing 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 test)
  3. Solve simple cases of Ordinary and partial Differential Equations relevant to weather/climate topics
  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 test (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 (2-hour lectures per week and 2-hour practical per week), plus 3 3-hour sessions in Fluid lab (first for formative assessment, other two for summative).

Study hours

At least 45 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.


 Scheduled teaching and learning activities  Semester 1  Semester 2  Summer
Lectures 18
Seminars
Tutorials 18
Project Supervision
Demonstrations
Practical classes and workshops 9
Supervised time in studio / workshop
Scheduled revision sessions
Feedback meetings with staff
Fieldwork
External visits
Work-based learning


 Self-scheduled teaching and learning activities  Semester 1  Semester 2  Summer
Directed viewing of video materials/screencasts
Participation in discussion boards/other discussions
Feedback meetings with staff
Other
Other (details)


 Placement and study abroad  Semester 1  Semester 2  Summer
Placement
Study abroad

Please note that the hours listed above are for guidance purposes only.

 Independent study hours  Semester 1  Semester 2  Summer
Independent study hours 155

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

Type of assessment Detail of assessment % contribution towards module mark Size of assessment Submission date Additional information
Set exercise Problem sheet 20 Semester 1, Teaching Week 7 Application of basic concepts explored in first part of term.
Written coursework assignment Lab assessment 30 Semester 1, Teaching Week 10 Adapting MT25F's model: 3 sessions in lab. First for formative feedback. Following 2 sessions for summative assessment: Student will choose which of these 2 lab sessions they submit for summative assessment
In-person written examination Exam 50 2 hours Semester 1 Assessment Period Final exam will focus on more complex ideas studied in second part of the term (but Maths works with building blocks, and so will reassess some of the basic concepts tested in coursework 1).

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

Type of reassessment Detail of reassessment % contribution towards module mark Size of reassessment Submission date Additional information
In-person written examination Exam 70 3 hours Will focus on higher level concepts of the module as for the normal final exam, but because of nature of Maths, this will effectively cover content of Coursework 1, hence the combined percentage.
Written coursework assignment Lab report 30 Resubmission of lab report accounting for feedbacks

Additional costs

Item Additional information Cost
Computers and devices with a particular specification
Required textbooks
Specialist equipment or materials
Specialist clothing, footwear, or headgear
Printing and binding
Travel, accommodation, and subsistence

THE INFORMATION CONTAINED IN THIS MODULE DESCRIPTION DOES NOT FORM ANY PART OF A STUDENT'S CONTRACT.

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