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

  • Full or part time
  • Application Deadline
    Monday, January 06, 2020
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

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

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].

Funding Notes

NERC GW4+ funded studentship available for September 2020 entry. For eligible students, the studentship will provide funding of fees and a stipend which is currently £15,009 per annum for 2019-20.


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.

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