Understanding Extremes in Low Dimensional Dynamical System Weather Models - Mathematics - EPSRC DTP funded PhD Studentship

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide 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.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Location: Streatham Campus, Exeter

Project Description

This PhD studentship project will determine the statistics of extremes for low dimensional dynamical system weather models, such as the Lorenz equations or Charney de Vore model. The project will determine the probabilistic distributions governing the extremes using geometrical features of the dynamical system, and regularity properties of the underlying ergodic invariant measure. The project will study the rate of convergence to the limit distribution, and develop methods to improve the accuracy of corresponding statistical estimation schemes such as the Block-Maxima method.

A key challenge is to determine the probability distribution that governs the extremes in a dynamical system, including finding the analytic form given a specific observation on the phase space. There has been recent progress on this, but the analytic form depends on the long time limit behaviour of the dynamical system, and is described in terms of the ergodic invariant measure. Hence both from a theoretical and practical standpoint it is relevant to ask how well this limit distribution approximates the extreme statistics given finite time information. This leads us to study the convergence rate to the limit distribution. This project aims to optimize bounds for the fastest convergence rate possible given information on the statistical properties of the dynamical system, such as the regularity of the ergodic invariant measure. This optimization method will be of direct benefit to those using the Block-Maxima approach to fit an extreme value distribution to time series data. This will be achieved by determining the optimal block sizes and block lengths within this statistical estimation scheme.

Given good progress, an ambitious approach would be to implement the Block-Maxima method on systems where less (analytic) information is available on the extreme statistics, and then determine the optimal block decomposition. We will apply this method to dynamical system case studies within weather modelling, such as the Lorenz equations.

This project will use approaches in mathematical analysis of dynamical systems, and will be of benefit to those seeking to work in pure or applied mathematics, or to those working within statistical modelling of extremes for weather/climate.

Entry Requirements

You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in Mathematics. Experience in probability, dynamical systems is desirable.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes. If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.