MTMNUM: Numerical Modelling for Weather and Climate Science

Module code: MTMNUM

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

Credits: 20

ECTS credits: 10

Level: 7

When you’ll be taught: Semester 2

Module convenor: Professor Pier Luigi Vidale, email: p.l.vidale@reading.ac.uk

Pre-requisite module(s):

Co-requisite module(s): IN THE SAME YEAR AS TAKING THIS MODULE YOU MUST TAKE MTMFMD (Compulsory)

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

Module(s) excluded:

Placement information: NA

Academic year: 2026/7

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 26 March 2026

Overview

Module aims and purpose

To show how numerical schemes can be designed to preserve fundamental properties of fluid flows. To bring you up to speed with the core components of state-of-the-art numerical models for the atmosphere and oceans and their use in predicting weather and climate. To bring you up to speed with experimental designs used in solving “Grand Challenge” problems with geoscientific modelling. 

Module learning outcomes

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

1. Recognise the strengths and weaknesses of the main numerical methods used to model the atmosphere and oceans and explain their derivation. 
2. Design numerical models to solve atmosphere/ocean problems, and 
3. Perform numerical analysis, prior to model implementation 
4. Implement idealised models by programming in Python, Julia, FORTRAN or C++, and
5. Evaluate models using benchmark problems and known properties of the system 
6. Understand complex model design and process-based assessment 

Module content

• History of numerical modelling: from first principles in the 1800s to today’s exascale challenges 
• Advanced time schemes: from explicit to implicit and iterative schemes 
• From Euler’s equations to the shallow water model 
• Chaos and predictability in weather and climate 
• Wave dispersion in finite difference models:
  • a refresher on advection, diffusion and CFL in 1-D and 2-D 
  • from 1D to 2D, to Arakawa grid staggering 
• Alternative numerical methods for transport by the flow: 
  • finite volumes, finite elements, spectral elements 
  • the spectral method 
  • the Semi-Lagrangian method 
• Parameterization of unresolved processes:
  • radiation and aerosols 
  • convective parametrisation and microphysics 
  • turbulence, orographic and gravity wave drag 
  • biophysics and carbon modelling on land and in the ocean 
  • New methods to represent unresolved processes: stochastic physics, artificial intelligence, reduced precision numerical schemes 
• Using complex nonlinear models:
  • experimental designs and injection of uncertainty by design 
  • coupling of multiple Earth System components
  • model hierarchies and experimental design for solving Earth System prediction problems 
• Supercomputing at the exascale:
  • parallelism,  scalability, new programming paradigms, Large Data strategies 
  • new dynamical cores, unstructured meshes.
• How to build an AI weather prediction model
  • framing the weather forecast problem for machine learning
  • understanding data, targets, and leakage
  • deterministic AIWP architectures (e.g., CNNs, transformers)
  • model evaluation and trustworthiness
  • probabilistic forecasting

Structure

Teaching and learning methods

The module counts on 15lectures which enable the students to tackle three practicals: 

1. On advanced time integration, starting with simple oscillation and going into the design and implementation of a simple model of ENSO, which includes ensemble prediction 
2. On simulation of an ocean gyre with a shallow water model, which teaches students about wave propagation in 2D and about coupled equations 
3. (Formative Practical): On designing and running a simple prediction problem with an idealised (simplified) version of a state-of-the-art numerical model.

Study hours

At least 47 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 a DAS-agreed extension as a reasonable adjustment indicated in your Individual Learning Plan): 10% of the total marks available for that piece of work will be deducted from the mark for each calendar day (or part thereof) following the deadline up to a total of three calendar days;
• where the piece of work is submitted up to three calendar days after the original deadline (or a DAS-agreed extension as a reasonable adjustment indicated in you Individual Learning Plan), 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 calendar days after the original deadline (or a DAS-agreed extension as a reasonable adjustment indicated in your Individual Learning Plan), no penalty shall be imposed;
• where the piece of work is submitted more than three calendar days after the original deadline (or a DAS-agreed extension as a reasonable adjustment indicated in your Individual Learning Plan): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three calendar days of the deadline (or a DAS-agreed extension as a reasonable adjustment indicated in your Individual Learning Plan): no penalty will be applied;
• where the piece of work is submitted more than three calendar days after the original deadline (or a DAS-agreed extension as a reasonable adjustment indicated in your Individual Learning Plan): a grade of Fail will be awarded.

Where a piece of work is submitted late after a deadline which has been revised owing to an extension granted through the Assessment Adjustments policy and process (self-certified or otherwise), it will be subject to the maximum penalty (i.e., considered to be more than three calendar days late). This will also apply when such an extension is used in conjunction with a DAS-agreed extension as a reasonable adjustment.

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.

Practical 

Reassessment

Additional costs