# Mathematics

## MTH3001 - Theory of Weather and Climate (2019)

MODULE TITLE CREDIT VALUE Theory of Weather and Climate 15 MTH3001 Dr Tim Jupp (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
 Number of Students Taking Module (anticipated) 61
DESCRIPTION - summary of the module content

This module is designed to give you an overview of the key physical processes determining the behaviour of the Earth's atmosphere. An informative subtitle might be climate physics for the mathematically literate. Topics covered will include radiative energy transfer, the structure, motion and thermodynamics of the atmosphere, the surface energy balance, and the main components of the general circulation (Hadley cells, Walker cells, jet streams etc.). The emphasis, where possible, will be on simple analytical models for commonly observed phenomena and on the development of physical intuition.

Prerequisite module: MTH3007, or equivalent

AIMS - intentions of the module

By the end of this module, you will have an understanding of the basic physics of the Earth’s climate, and will comprehend the structure and principal circulations of the atmosphere and the ocean.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 Appreciate how mathematics can be used to understand the physics of weather and climate;

2 Comprehend the physics responsible for the general circulation;

3 Understand in detail radiation, dynamics and atmospheric thermodynamics;

4 Demonstrate a familiarity with the terminology and physical mechanisms of common meteorological phenomena;

Discipline Specific Skills and Knowledge:

5 Understand the role of mathematical modelling in real-life situations;

6 Recognise how many aspects of applied mathematics learned in earlier modules have practical issues;

7 Develop expertise in using analytical and numerical techniques to explore mathematical models;

8 Formulate simple models;

9 Study adeptly the resulting equations and draw conclusions about likely behaviours;

Personal and Key Transferable / Employment Skills and Knowledge:

10 Display enhanced numerical and computational skills via the suite of practical exercises that accompany the formal lecture work;

11 Show enhanced literature searching and library skills in order to investigate various phenomena discussed;

12 Demonstrate enhanced time management and organisational abilities.

SYLLABUS PLAN - summary of the structure and academic content of the module

- Motivation: the observed state of the atmosphere

- Planetary scale energy balance (for planets with and without atmospheres)

- Surface energy balance

- Vertical structure and thermodynamics (dry and moist) of the atmosphere

- Rotating fluid dynamics: (Geostrophic flow, the thermal wind, Ekman transport, Potential vorticity and quasi-geostrophic potential vorticity)

- Waves (Plane waves. Shallow water theory. Inertial, Kelvin, Rossby and buoyancy waves)

- Instability (barotropic via Rayleigh and Fjortoft theorems, baroclinic via the Eady model)

- Wind-driven circulation in the ocean (Ekman spirals, Ekman pumping)

- Recap of how the theory above explains surface pressure maps, the jet stream, frontogenesis, Hadley and Walker cells etc.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 33 117 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning and Teaching Activities 33 Lectures Guided Independent Study 117 Assessment preparation, wider reading

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Two Coursework Sheets 15 hours All Feedback sheet and oral feedback during lecturer office hour

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 20 80 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework – based on questions submitted for assessment 20 2 assignments, 30 hours total All Annotated script and written/verbal feedback
Written Exam - Closed Book 80 2 hours All Written/verbal on request, SRS

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
All above Written Exam (100%) All August Ref/Def Period

RE-ASSESSMENT NOTES
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener