MTMFMD: Fundamentals of Modelling and Data Analysis

Module code: MTMFMD

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

Credits: 20

Level: Postgraduate Masters

When you'll be taught: Semester 1

Module convenor: Dr Hilary Weller, email: h.weller@reading.ac.uk

Module co-convenor: Professor Ted Shepherd, email: theodore.shepherd@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have Maths beyond A-Level in an UG degree including complex numbers, trigonometric identities, PDEs, and vector calculus. You need excellent recall of maths A-Level, and some programming experience would be helpful. (Open)

Co-requisite module(s):

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

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: No

Last updated: 21 May 2024

Overview

Module aims and purpose

The theory and practice of creating numerical and statistical models of the atmosphere and ocean. 

You will write Python code to analyse and display climate data, verify weather forecasts and solve simplified versions of the differential equations that govern the ocean and atmosphere and write reports on your findings. You will learn the underpinning theory enabling you to test hypotheses, quantify uncertainties, estimate parameters and design numerical methods.  

These skills are essential for weather and climate research, data analysis and model development. 

Module learning outcomes

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

1. Write flexible Python code to create reproducible science. 
2. Derive, analyse, implement and test numerical methods for solving partial differential equations. 
3. Describe the main concepts in statistical science and use statistical software. 
4. Critically analyse data and draw correct inferences using appropriate statistical methods 

Module content

1. Using Python to solve simple numerical and statistical problems and to display data. 
2. Probability theory, probability distributions and central limit theorem. 
3. Forecast skill scores. 
4. Regression, causal statistics and the physical interpretation of a statistical result. 
5. Cognitive biases related to statistics. 
6. Historical development and controversies in statistics. 
7. Parameter estimation. 
8. Hypothesis testing. 
9. Uncertainty quantification. 
10. Use of Taylor series to find finite difference approximations. 
11. Fourier analysis 
12. Terms of the Navier Stokes equations 
13. Numerical solution of the diffusion equations 
14. Stability analysis 
15. Numerical solution of the linear advection equation 
16. Waves, dispersion and numerical dispersion errors. 

Structure

Teaching and learning methods

1. Interactive lectures with quizzes and exercises. 
2. PC classes supporting writing code to solve statistical and numerical problems. 

Study hours

At least 67 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 50% 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: /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.

1. Using Python to solve simple numerical and statistical problems. 
2. Self assessment of statistics practicals. 
3. Report on statistics exercise (similar to the statistics summative coursework). 
4. Numerical solution of the diffusion equation – task similar to coursework 2. 

Reassessment

Additional costs