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Award details

Estimating radiological emissions through Bayesian source inversion techniques, NERC GW4+ DTP PhD studentship for 2022 Entry, PhD in Mathematics/Global System Ref: 4261

About the award


Lead Supervisor

Dr Helen Webster, Department of Mathematics, University of Exeter

Additional Supervisors

Dr Stefan Siegert, Department of Mathematics, University of Exeter 

Dr Luke Western, School of Chemistry, University of Bristol 

Sarah Millington, Met Office 

Mr Peter Bedwell, Public Health England 

Location: Streatham Campus, University of Exeter, Exeter, Devon

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. For further details about the programme please see

For eligible successful applicants, the studentships comprises:

  • An stipend for 3.5 years (currently £15,609 p.a. for 2021/22) 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

Project details

Project Background 

Atmospheric dispersion models are used to predict the transport and dispersion of potentially hazardous material in the atmosphere. Large uncertainties exist in the source term describing accidental emissions (e.g., release rate, release height) and this impacts on the accuracy of, and confidence in, predictions. Inverse modelling techniques can be used to constrain the uncertain source term, combining atmospheric dispersion modelling, observations and a first-guess estimate of the emissions. 

Source inversion work at the Met Office has largely focussed on estimating greenhouse gas and volcanic ash emissions, although there is interest in extending these techniques to other applications. The Met Office is keen to develop an operational source inversion capability for radiological releases, with potential to significantly improve the advice provided in the response to accidental releases of radioactivity into the environment. The project will draw upon established collaborations between the Met Office, the University of Bristol and Public Health England on modelling of radioactivity in the environment and previous source inversion studies, including determining the location of an unexpected release of ruthenium-106 in 2017. 

Project Aims and Methods 

The aim of the project is to explore the best way of combining a range of sparse radiological measurements and radiological expertise to constrain estimates of radionuclide emissions for different scenarios (e.g., an accident at a nuclear power plant or an unexpected detection of radioactivity from an unknown source). Radiological source inversion is a complex problem. Releases are often a cocktail of multiple radionuclides, which are subject to radioactive decay, and transformation into daughter decay products, and removal by dry and wet deposition processes. Furthermore, radiological observations may comprise of a range of measurements of different quantities (e.g., gamma dose, air activity or deposition), which may or may not be speciated, and which can span various timescales (e.g., weekly, daily, or hourly).  

Bayesian spatio-temporal modelling will be used to integrate radiological measurements, transport and dispersion modelling and initial (prior) estimates of radiological emissions. The relationships between emissions and the radiological measurement quantities are non-trivial, requiring suitable approximations such as Markov Chain Monte Carlo or history matching. Covariance matrices can be used to represent expert knowledge in terms of prior uncertainties and correlations. Uncertainties and spatio-temporal dependencies in observations and numerical model predictions can also be incorporated within error covariance matrices. The inversion problem is under-determined and hence prior assumptions, making use of expert radiological knowledge, are key. It is important, therefore, to construct a prior wisely and to understand the influence of the chosen prior on emissions estimates. The project will build on the current state-of-the-art, working with experts to develop techniques for different radiological release scenarios, incorporating additional types of measurements and expert knowledge, whilst overcoming limitations and reducing assumptions made. 

Candidate requirements 

Mathematics / Physics / Statistics / Computing 

Project partners  

The student will join an established and exciting collaboration between academia, the Met Office and Public Health England, offering the opportunity to develop new research for operational services. The collaboration with project partners will provide data, environmental models, and expertise, as well as access to a wealth of on-going science activities at partner organisations, including seminars and wider team involvement. 


The student will have access to training and activities in statistics and applications of statistical methods to environmental problems (for example, through the CDT in Environmental Intelligence ( The Met Office offers training on their atmospheric dispersion model, NAME, and their source inversion model, InTEM for volcanic ash. 

Background reading and references 

Saunier, O. et al (2013), Atmos. Chem. Phys., doi:10.5194/acp-13-11403-2013 

Stohl, A. et al (2012), Atmos. Chem. Phys., doi:10.5194/acp-12-2313-2012 

Western, L. M. et al (2020), J. Environ. Radioactiv., doi:10.1016/j.jenvrad.2020.106304 

Winiarek, V. (2014), Atmos. Environ., doi:10.1016/j.atmosenv.2013.10.017 

Useful links 

For information relating to the research project please contact the lead Supervisor via Dr Helen Webster (,


NERC GW4+ DTP studentships are open to UK and Irish nationals who, if successful in their applications, will receive a full studentship including payment of university tuition fees at the home fees rate.

A limited number of full studentships are also available to international students which are defined as EU (excluding Irish nationals), EEA, Swiss and all other non-UK nationals.  For further details please see the NERC GW4+ website.

Those not meeting the nationality and residency requirements to be treated as a ‘home’ student may apply for a limited number of full studentships for international students. Although international students are usually charged a higher tuition fee rate than ‘home’ students, those international students offered a NERC GW4+ Doctoral Training Partnership full studentship starting in 2022 will only be charged the ‘home’ tuition fee rate (which will be covered by the studentship). 

International applicants need to be aware that you will have to cover the cost of your student visa, healthcare surcharge and other costs of moving to the UK to do a PhD. More information on this is available from the universities you are applying to (contact details are provided in the project description that you are interested in.

The conditions for eligibility of home fees status are complex and you will need to seek advice if you have moved to or from the UK (or Republic of Ireland) within the past 3 years or have applied for settled status under the EU Settlement Scheme.


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, please see the entry requirements for details.
  • Two references

Reference information
You will be asked to submit two references as part of the application process.  If you are not able to upload  your reference documents with your application please ensure you provide details of your referees.  If you provide contact details of referees only, 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 Friday 10 January 2022. Interviews will be held between 28 February and 4 March 2022.  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:10th January 2022
Value:£15,609 per annum for 2021-2022
Duration of award:per year
Contact: PGR Enquiries