University of Exeter funding: NERC GW4+ DTP PhD studentship

Next generation time stepping schemes for weather and climate prediction. PhD in Mathematics (NERC GW4+ DTP) Ref: 3695

About the award


Lead Supervisor

Dr Jemma Shipton, Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter

Additional Supervisors

Prof Beth Wingate, Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter

Dr Ben Shipway, Met Office

Location:  University of Exeter, Streatham Campus, Exeter, EX4 4QJ

This project is one of a number that are in competition for funding from the NERC GW4+ Doctoral Training Partnership (GW4+ DTP).  The GW4+ DTP consists of the GW4 Alliance of research-intensive universities: the University of Bath, University of Bristol, Cardiff University and the University of Exeter plus five unique and prestigious Research Organisation partners: British Antarctic Survey, British Geological Survey, Centre for Ecology & Hydrology, the Natural History Museum and Plymouth Marine Laboratory.  The partnership aims to provide a broad training in the Earth, Environmental and Life sciences, designed to train tomorrow’s leaders in scientific research, business, technology and policy-making. For further details about the programme please see

For eligible successful applicants, the studentships comprises:

  • A stipend for 3.5 years (currently £15,009 p.a. for 2019/20) 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.
  • Travel and accommodation is covered for all compulsory DTP cohort events
  • No course fees for courses run by the DTP

We are currently advertising projects for a total of 10 studentships at the University of Exeter


Students who are resident in EU countries are eligible for the full award on the same basis as UK residents.  Applicants resident outside of the EU (classed as International for tuition fee purposes) are not eligible for DTP funding. Residency rules are complex and if you have not been resident in the UK or EU for the 3 years prior to the start of the studentship, please apply and we will check eligibility upon shortlisting.

Project Background 

Accurate, timely weather and climate forecasting strongly relies on the design of the mathematical and numerical algorithms underpinning the forecast model and the efficiency with which they exploit supercomputer hardware.  Supercomputer design is undergoing a revolution driven by physical limitations on the size, and therefore speed, of processor components.  This opens a `chasm' between the forecast simulations we need to run and what is possible to run on the hardware [5].  Future hardware will consist of vastly more, but less powerful, processers meaning that we must distribute calculations across the processors so they can be computed simultaneously, or `in parallel'.  This requires revolutionary redesign of the mathematical and numerical algorithms.  An example of this is the recent UK Met Office GungHo project, motivated by parallel communication bottlenecks related to the geometry of the grid.  The outcome was a new spatial discretisation using compatible finite element methods which preserve underlying properties of the equations of motion without imposing restrictions on grid geometry [1, 2].  However, this does not solve the parallel scalability problem inherent in spatial domain decomposition: we must find a way perform parallel calculations in the time domain.

Project Aims and Methods 

While time-parallel methods sound counterintuitive since we expect the future state of the atmosphere to depend sequentially on its past state, schemes based on exponential integrators offer potential for larger timesteps and time-parallel computation. Of particular interest is the parareal method, which uses an accurate scheme to iteratively refine, in parallel, the output of a computationally cheap ‘coarse propagator’ that can take large timesteps. Atmospheric flows are challenging to model in this way due to fast waves which limit the timestep of the coarse propagator. The solution, proposed in [4], is to include the effects of near resonant waves. This algorithm has demonstrated substantial parallel speedup when applied to idealised configurations.

This project will continue the work of Wingate and Shipton in developing 1) time-parallel integration schemes for the rotating shallow water equations and 2) new test cases which focus on the situation where there is no timescale separation in the dynamics. Initially simulations will be run using the Gusto dynamical core toolkit - a compatible finite element model built on top of the Firedrake library - which enables rapid prototyping of new schemes which are directly relevant to the Met Office.

Further research depends on the interests of the student but could include investigating the impact of non-continuous physics parameterisation schemes on convergence. This would involve implementing a moist shallow water model as in [3]. 


Atmospheric vortices forming in the wake of the Canary Islands, visible due to the cloud layer.



An ‘aquaplanet’ simulation of the prototype Met Office next generation atmospheric model

Candidate Requirements

Ideally candidates will hold a first or upper second class honours degree, or equivalent, in mathematics or a closely related subject, including courses in fluid dynamics and numerical analysis. Experience in computer programming, particularly using Python, would be advantageous.

CASE or Collaborative Partner

In addition to regular visits throughout the project, the student will spend a minimum of three months on a placement at the Met Office – working alongside internationally recognized experts in the development of operational and next generation modelling systems.  During this period, the student will benefit from first-hand experience of how numerical methods pull through from research to operations and ultimately have a significant impact on people’s lives and wellbeing and influence government policy. There will be opportunity for the student to interact more widely across the scientific disciplines at the Met Office and to present their research.  


In addition to cohort training as part of the DTP, the student will have access to bespoke training at the Met Office and at workshops run by the Firedrake team (  The student will also be strongly encouraged to visit our international collaborators at Lawrence Livermore National Laboratory in California and/or the Technical University of Hamburg.  Results from project will be presented at the Parallel in Time workshops (  There will also be opportunities to disseminate results to the wider geophysical modelling community at prestigious international conferences such as SIAM Computational Science and Engineering or the annual meetings of the American or European Geophysical Unions.

References / Background reading list

  1. Adams, Samantha V., et al. "LFRic: Meeting the challenges of scalability and performance portability in Weather and Climate models." Journal of Parallel and Distributed Computing (2019).
  2. Cotter, Colin J., and Jemma Shipton. "Mixed finite elements for numerical weather prediction." Journal of Computational Physics 231.21 (2012): 7076-7091.
  3. Ferguson, Jared O., Christiane Jablonowski, and Hans Johansen. "Assessing Adaptive Mesh Refinement (AMR) in a Forced Shallow-Water Model with Moisture." Monthly Weather Review (2019).
  4. Haut, Terry, and Beth Wingate. "An asymptotic parallel-in-time method for highly oscillatory PDEs." SIAM Journal on Scientific Computing 36.2 (2014): A693-A713.
  5. Lawrence, Bryan N., et al. "Crossing the chasm: how to develop weather and climate models for next generation computers." Geoscientific Model Development 11.5 (2018): 1799-1821.

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

How to apply

In 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.

Reference information
You will be asked to name 2 referees as part of the application process, however we will not expect receipt of references until after the shortlisting stage. Your referees should not be from the prospective supervisory team.

If you are shortlisted for interview, please ensure that your two academic referees email their references to the, 7 days prior to the interview dates.  Please note that we will not be contacting referees to request references, you must arrange for them to be submitted to us by the deadline.

References should be submitted by your referees to us directly in the form of a letter. Referees must email their references to us from their institutional email accounts. We cannot accept references from personal/private email accounts, unless it is a scanned document on institutional headed paper and signed by the referee.

All application documents must be submitted in English. Certified translated copies of academic qualifications must also be provided.

The closing date for applications is 1600 hours GMT Monday 6 January 2020.  Interviews will be held between 10 and 21 February 2020.  For more information about the NERC GW4+ DPT please visit

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

Data Sharing
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.


Application deadline:6th January 2020
Value:£15,009 per annum for 2019-20
Duration of award:per year
Contact: PGR Enquiries