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Emergent constraints on Earth’s future climate, NERC GW4+ DTP PhD studentship for 2023 Entry, PhD in Mathematics and Statistics

   College of Engineering, Mathematics and Physical Sciences

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  Dr Mark Williamson, Prof P M Cox  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

About the Partnership

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 five Research Organisation partners: British Antarctic Survey, British Geological Survey, Centre for Ecology and Hydrology, 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.

Project Background

The general circulation models (GCMs) used to make projections of future climate change are vitally important to inform climate mitigation and adaptation strategies, but are also invaluable tools for testing hypotheses about the functioning of the Earth System. Climate modelling centres around the world have devoted increasing effort to improving GCMs since the first IPCC report in 1990. As a result, they now provide a more complete representation of the myriad of interactions and feedbacks that determine how the climate will change in response to human and natural forcing factors. Unfortunately, the range of model projections has not significantly reduced despite this. It is critically important to reduce projection uncertainty so as to provide better information to impact national and global climate policy action (Cox et al., 2018, Nijsse et al., 2020). 

Project Aims and Methods

A promising method for reducing this uncertainty, the emergent constraint approach, combines empirical relationships found in model ensembles with observations to constrain an unknown sensitivity. The basic idea is to identify an element of the observable climate (𝑋) that varies significantly across the model ensemble, and which exhibits a statistically significant relationship, 𝑓, with variations in some important variable (𝑌) describing the simulated future climate. 

Unfortunately, the 𝑓 relationships are often little more than statistical fishing trips and may therefore occur by chance rather than from a deeper physical mechanism. In this project we will use a cross fertilization of ideas to guard against these chance correlations by putting model ensemble relationships on a sound, testable physical foundation thus providing much needed confidence in the constraints and insight into the most important physical processes involved. Depending on the skills and interests of the student, ideas from statistical thermodynamics, such as the fluctuation-dissipation theorem and maximum entropy production principle and from the theory of tipping point precursors, will be explored as sound theoretical bases for these model ensemble relationships.

Candidate requirements

We seek an enthusiastic student with broad interests in climate dynamics and climate change. A first degree in physics, maths, computer science, engineering or other quantitative subject is needed. The ideal candidate may have some experience, and/or an interest in both computational data analysis and modelling and analytical paper-and-pencil techniques. We value a diverse research environment, and you will join a vibrant team currently consisting of 3 other PhD students and 4 postdoctoral researchers.

Project partners 

Dr Chris Huntingford at CEH Wallingford, has substantial expertise in emergent constraints and all areas of climate change science. The CASE partner, Dr Chris Jones, is also an expert in a number of areas of climate change science, particularly climate carbon feedbacks. The student will have opportunities to spend significant time at both CEH Wallingford and at the Met Office’s world leading Hadley Centre. Both Chris Huntingford and Chris Jones are recognised as ISI Highly Cited Researchers.


The project will require coding and data analysis on large climate model and observational datasets. There will also be the opportunity to run and configure idealized and state-of-the-art climate models. Training in all the software and techniques needed to conduct this research will be provided. You will be encouraged to attend local and international workshops and conferences such as the European and American Geophysical Union meetings.

How to Apply

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

The closing date for applications is 2359 hours GMT Monday 9 January 2023. Interviews will be held between 22 February and 8 March 2023. For more information about the NERC GW4+ DPT please visit

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

For further information including entry requirements and academic qualifications, and to submit an application please visit -

Funding Notes

For eligible successful applicants, the studentships comprises:
A stipend for 3.5 years (currently £17,668 p.a. for 2022-23) 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


P. M. Cox, C. Huntingford and M. S. Williamson, Nature 553, 319-319 (2018).
F. J. M. M. Nijsse, P. M. Cox and M. S. Williamson, Earth Syst. Dynam. 11 (3), 737-750 (2020).
M. S. Williamson, C. W. Thackeray, P. M. Cox, A. Hall, C. Huntingford and F. J. M. M. Nijsse, Reviews of Modern Physics 93 (2), 025004 (2021).
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