Improving moist thermodynamics in weather and climate models. Mathematics NERC GW4+ DTP PhD studentship Ref: 3129

About the award

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 six Research Organisation partners:  British Antarctic Survey, British Geological Survey, Centre for Ecology and Hydrology, the Met Office, 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. For further details about the programme please see

The Studentship will be awarded on the basis of merit and will commence in September 2018.  For eligible students the award will provide funding for a stipend which is currently £14,553 per annum (2017/2018), research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Main Supervisor: Prof. John Thuburn (Mathematics, University of Exeter)
Co-Supervisor: Dr Robert Beare (Mathematics, University of Exeter)
Co-Supervisor: Martin Willett (Met Office)

Project description:
The thermodynamics of moist processes is very complicated. All weather and climate models make a variety of simplifying approximations, for example to the specific heat capacities and latent heats, but these approximations are not always consistent between different parts of the model, and may be inconsistent with the laws of thermodynamics. These inconsistencies can result in significant energy budget errors, of order 1 Wm-2, and have other undesirable effects.
Thermodynamic consistency can be ensured by deriving all thermodynamic quantities from a potential such as the Gibbs function. A recent paper (Thuburn 2017) demonstrated the feasibility of this idea in a simplified model of the atmosphere based on similar governing equations and numerics to those in operation at the Met Office. The advantages that result
include better thermodynamic consistency, flexibility to modify the equation of state, and tighter coupling between phase changes and large-scale dynamics.


Shallow cumulus cloud over Exeter.


Vertical velocity field (colours) and region of liquid water (thick line) for a shallow cumulus
cloud simulated using the Gibbs function to represent moist thermodynamics.

Project aims and methods:
Thuburn's (2017) proof of concept assumed local thermodynamic equilibrium in every fluid parcel, in particular that liquid water and vapour are locally in equilibrium with each other. However, some important atmospheric processes are non-equilibrium, including evaporation of rain, freezing of supercooled water droplets in deep cumulus clouds, and surface moisture fluxes. To be of practical use, the Gibbs function approach must be extended to allow for nonequilibrium

The project will involve three stages.
1) Review and understand existing approaches to the representation of non-equilibrium processes in weather and climate models.
2) Determine how to reformulate these approaches in terms of the Gibbs function, with finite rates of approach towards equilibrium, respecting any constraints required by thermodynamic consistency, such as the Onsager reciprocal relations (e.g. de Groot and Mazur 1985).
3) Develop suitable numerical methods that can cope with both fast and slow thermodynamic processes, and implement them in an idealized atmospheric model. The approach will be tested and evaluated on simulations of precipitating clouds; special attention will be paid to the budgets of energy and entropy. The results will help inform future development of the Met
Office operational model.

The candidate should have excellent mathematical skills and a willingness to acquire new, interdisciplinary knowledge. They should be confident in working with complex computer codes. As the project will involve collaboration with the Met Office, excellent communication skills will be needed.

In addition to background reading and one-to-one sessions with the lead supervisor, depending on their prior knowledge, the student will take University of Exeter and/or MAGIC modules in fluid dynamics, thermal physics, and numerical methods.
The student will attend the NERC-NCAS climate modelling Summer School in 2019. If places are available they may also attend training courses in numerical modelling at the European Centre for Medium Range Weather Forecasts

de Groot, SR and Mazur P, 1985: Non-equilibrium Thermodynamics. Dover, 510pp.
Thuburn J, 2017: Use of the Gibbs thermodynamic potential to express the equation of state in
atmospheric models. Quart. J. Roy. Meteorol. Soc., 143, 1185-1196.

Entry requirements:       
Applicants should have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK.   Applicants with a Lower Second Class degree will be considered if they also have Master’s degree.  Applicants with a minimum of Upper Second Class degree and significant relevant non-academic experience are encouraged to apply.

All applicants would need to meet our English language requirements by the start of the  project

Applicants who are classed as International for tuition fee purposes are not eligible for funding.



Application deadline:8th May 2018
Value:£14,553 per annum for 2017-18
Duration of award:per year
Contact: PGR

How to apply

To apply for this funded studentship, please click and follow the 'Apply Now' button on this webpage.

During the application process you will be asked to upload several documents.  Please note our preferred format is PDF, each file named with your surname and the name of the document, eg. “Smith – CV.pdf”, “Smith – Cover Letter.pdf”, “Smith – Transcript.pdf”.
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim transcript
        if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.

You will be asked to name 2 referees as part of the application process however we will not contact these people until the shortlisting stage. Your referees should not be from the prospective supervisory team.

The closing date for applications is midnight on 8th May 2018.  Interviews will be held at the University of Exeter in the week commencing 21st May

If you have any general enquiries about the application process please email Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:
• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.
Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.