Module code: MAT3053

Module Overview

Understanding the motions in our atmosphere and oceans is key to understanding, and hence solving, the global climate crisis. By applying a range of mathematical techniques to the governing fluid flow equations we are able to consider simplified models of a hugely complex system which will allow us to gain a deeper understanding about the transports of energy and heat on our planet.

Module provider


Module Leader

GODOLPHIN Janet (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

Module cap (Maximum number of students): N/A

Overall student workload

Independent Learning Hours: 64

Lecture Hours: 33

Tutorial Hours: 5

Guided Learning: 15

Captured Content: 33

Module Availability

Semester 1

Prerequisites / Co-requisites


Module content

The module will cover the following content:


  • Derivation and understanding of the governing equations for atmospheric flows

  • Geostrophic wind, gradient wind, thermal wind, cyclostrophic flow

  • Vorticity and relative vorticity

  • Rossby waves


  • Derivation and understanding of governing equations for oceanographic flows

  • Ekman boundary layers

  • Gyre models

  • Coastal and equatorial Kelvin waves

Time permitting, additional topics will be considered, such as:

  • Effects of topography - Ertel's theorem

Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-Semester Test (50 mins) 20
Examination End-of-Semester Examination (2 hours) 80

Alternative Assessment


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate: 

  • Understanding of fundamental concepts in meteorology and oceanography and ability to develop and apply them in a new context.

  • Subject knowledge through recall of key definitions, formulae and derivations.

  • Analytical ability through the solution of unseen problems in the test and examination.

Thus, the summative assessment for this module consists of:

  • One in-semester test (50 minutes), worth 20% of the module mark, corresponding to Learning Outcomes 1 to 3.

  • A synoptic examination (2 hours), worth 80% of the module mark, corresponding to Learning Outcomes 1 to 5. 

Formative assessment
There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning. 

Students receive individual written feedback on the formative unassessed coursework and the in-semester test. The feedback is timed so that feedback from the first unassessed coursework assists students with preparation for the in-semester test. The feedback from both unassessed courseworks and the in-semester test assists students with preparation for the end-of-semester examination. This written feedback is complemented by verbal feedback given in lectures. Students also receive verbal feedback in office hours.

Module aims

  • The module aims to cover the range of mathematics required to understand the dynamics of fluid motion in the context of meteorology and oceanographic flows on planet earth.

Learning outcomes

Attributes Developed
001 Students will demonstrate understanding of the derivation and use of the governing fluid motion equations in both the atmosphere and the oceans. K
002 Students will understand the role of vorticity and relative vorticity in the atmosphere and will demonstrate their knowledge via the modelling of Rossby waves. KC
003 Students will show understanding of applications of the governing oceanographic equations by examining the boundary layer flow which forms at the ocean's surface. KC
004 Students will understand the significance of ocean gyres and their transport of heat and energy in the ocean. KCT
005 Students will apply the theory of oceanographic waves to examples such as coastal and Equatorial Kelvin waves. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to:  

Equip students with the knowledge, experience and confidence to apply the mathematical techniques of this module to practical meteorological and oceanographical problems.  

The learning and teaching methods include: 

  • Three one-hour lectures per week for eleven weeks, in which notes can be taken. Lectures are delivered using blackboards/whiteboards and/or visualizers for real-time presentation. The lectures provide a structured learning environment with opportunities for students to ask questions.  

  • Biweekly tutorials to give students opportunities to practice methods taught.  

  • There are two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.  

Lectures may be recorded. Lecture recordings are intended to give students the opportunity to review parts of the session that they might not have understood fully and should not be seen as an alternative to attendance at lectures.


Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list
Upon accessing the reading list, please search for the module using the module code: MAT3053

Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourcefulness and Resilience and Sustainability. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital Capabilities: The SurreyLearn page for MAT3053 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing.

Employability: Students are equipped to analyse fluid motion, a skill valued in various industries including: aerospace; environmental science; and energy.

Global and Cultural Capabilities: During tutorials, student engagement in discussions naturally cultivates the sharing of the different cultures from which the students originate.

Resourcefulness and Resilience: The problem-solving aspects of MAT3053 fosters resourcefulness. Through the often intricate scenarios of fluid dynamic problems, students develop resilience in tackling dynamic challenges.

Sustainability: Through MAT3053, students explore mathematical models for fluid motion, relevant to ecosystems and water resources. Thus MAT3053 contributes to sustainability by enabling students to analyse fluid behaviour in environmental contexts.

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Financial Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MSc 1 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.