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Advancing weather and climate prediction: breaking the convergence barrier, NERC GW4+ DTP PhD studentship for 2023 Entry, PhD in Mathematics and Statistics.

   College of Engineering, Mathematics and Physical Sciences

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  Prof John Thuburn, Dr J Shipton  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

About the Partnership

This project is one of a number that are in competition for funding from the NERC Great Western Four+ Doctoral Training Partnership (GW4+ DTP). The GW4+ DTP consists of the Great Western Four alliance of the University of Bath, University of Bristol, Cardiff University and the University of Exeter plus five Research Organisation partners: British Antarctic Survey, British Geological Survey, Centre for Ecology and Hydrology, the Natural History Museum and Plymouth Marine Laboratory. The partnership aims to provide a broad training in earth and environmental sciences, designed to train tomorrow’s leaders in earth and environmental science.

Project Background

Computer models of the atmosphere are crucial tools, at centres like the Met Office, for understanding and predicting the changing climate, and for operational forecasting of all types of weather, including warnings of high-impact severe weather. Such models are run at a wide range of resolutions: horizontal grid spacing might be several tens of km for a climate change forecast, or around 1 km for a regional weather forecast. In most branches of computational fluid dynamics it is taken for granted that the solution will get more accurate as resolution gets finer - there will be numerical convergence. However, practical experience with weather and climate models often shows slow convergence. Doubling the resolution of an operational forecast requires around an order of magnitude more computing power, so it is essential that the barriers to faster convergence (and hence better forecasts) are understood and, where possible, removed. 

Possible reasons for slow convergence include (i) features in the mathematical equations used to represent processes such as turbulence near the Earth's surface, or cumulus convection, (ii) features in the numerical methods used to solve those equations, or (iii) the properties of the solution itself, such as the on-off nature of condensation, or a nearly singular logarithmic wind profile near the surface. 

Project Aims and Methods

The overall aims of the project are (i) to identify factors, within different components of an atmospheric model, that are barriers to convergence, (ii) to quantify their effect, e.g. in terms of rates of convergence, and (iii) to develop alternative models or methods that remove or mitigate these barriers. Good progress on the project could have significant impact on model development as the Met Office move towards operational sub-km-scale modelling.

The project will start by analysing idealised component models, for which there is a strong possibility to develop a quantitative mathematical understanding. Later, it will use the insights obtained to investigate components of the model used operationally or under development at the Met Office. The project will be jointly supervised by the Met Office. Within the project theme described above, there is considerable scope for the student to develop their own ideas and determine the direction of the project.

Candidate requirements

A strong mathematical background is essential. Knowledge of programming, numerical methods, and fluid dynamics would be an advantage.

Project partners 

The project builds on a long and successful collaboration between the Universities of Exeter and Bath and the Met Office on model development. It is an exciting opportunity for the student to influence future generations of forecast models.


The student will work with experts at the Universities of Exeter and Bath learning about the mathematical and numerical techniques used in weather and climate prediction. They will also spend time working with the Dynamics Research team at the Met Office and will gain hands-on experience running (and dissecting!) their model code.

For further information and to submit an application please visit -

Funding Notes

For eligible successful applicants, the studentships comprise: A stipend for 3.5 years (currently £17,668 p.a. for 2022-23) in line with UK Research and Innovation rates; Payment of university tuition fees; A research budget of £11,000 for an international conference, lab, field and research expenses; A training budget of £3,250 for specialist training courses and expenses.


The Met Office web site gives some useful background information on how computer models are used to make weather and climate predictions.
This research paper by D. L. Williamson (2008) nicely illustrates the convergence problem.
This research paper by D. R. E. Holdaway et al. (2008), from our previous collaboration, shows how careful study of simplified problems can improve our understanding.
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