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

This project is one of a number that are in competition for funding from the NERC Great Western Four+ Doctoral Training Partnership (GW4+ DTP).

Supervisors:
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.

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
processes.

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.

Training:
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.

Entry requirements:
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.

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 (http://www.exeter.ac.uk/postgraduate/apply/english/). Applicants who are classed as International for tuition fee purposes are not eligible for funding.

Clicking the ’Apply online’ button below will take you to the Exeter application system.

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 [Email Address Removed]. Project-specific queries should be directed to the supervisor.