Skip to main content

Award details

University of Exeter funding: NERC GW4+ DTP PhD studentship

Inversion modelling for Air Quality and Emissions. Mathematics PhD Studentship (NERC GW4+ DTP funded) Ref: 4011

About the award


Lead Supervisor

Professor Gavin Shaddick, Department of Mathematics, University of Exeter

Additional Supervisors

Dr Benjamin Drummond, Met Office

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 £15,285 p.a. for 2020-21) 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.
  • Up to £750 for travel and accomodation for compulsory cohort events.

Project details

Project Background

Inversion modelling is an important technique in allowing atmospheric measurements, dispersion science and first-guess emission estimates to be integrated in order to provide estimates of emissions (of air pollutants) on a regional scale. There are a number of important applications for these type of models in relating air quality and sources of pollution. For example, agricultural emissions (e.g. Nitrous Oxide (N2O), Methane (CH4)), ozone baseline trends, and providing evidence of emissions of key pollutants instrumental in the formation of poor air quality episodes.  Within the Met Office applications have previously focused on the interpretation of high frequency observations of long-lived greenhouse gases (GHGs) and ozone depleting gases measured at Mace Head on the west coast of Ireland. In particular, this has contributed to the verification of GHG emissions inventories as contributions for the development of policies for the Dept. for Energy and Climate Change (DECC), now part of the Dept for Business, Energy & Industrial Strategy (BEIS).  A key aspect of this project is that it will be a first step in exploring using such inversion techniques within operational air quality forecasts, enabling informed adjustments to be made to the emissions in the air quality model and giving better agreement between forecasts and observations. As such, there will be a strong focus on implementation and the computational challenges that may arise when performing inference with complex models and high-dimensional data. 

Project Aims and Methods

The aim of inversion modelling in this setting is to integrate atmospheric measurements, modelling and prior estimates of emissions (which could in this context be an estimated emissions inventory) to provide estimates of emissions on a regional scale. The analysis process normally consists of i) analysis of the long-term trends in observed measurements and ii) inversion modelling to verify UK ad European emissions of long-lived trace gases In this project, inversion models will be set within a Bayesian hierarchical modelling framework used to incorporate data from multiple sources, including measurements of a range of pollutants, simulations from numerical models and others in a coherent framework. Constraints based on knowledge of dispersion science and the air mass origin will be incorporated through the structure of prior distributions and the choice of hyper-parameters. The structure of the observational and prior components of the Bayesian hierarchical models will have to reflect the complex, non-linear, dependencies associated with some secondary pollutant species. In addition, each of the data sources may represent fundamentally different quantities, for example measurements and gridded outputs from dispersion models, and each will have their own biases and uncertainties that may vary over both space and time.  The aim is to produce models that acknowledge the inherent uncertainties in both input data and the modelling process and to propagate these through to the measures (of uncertainty) that are associated with the outputs, i.e. emission estimates. Preliminary experiments with the developed modelling system will be conducted to investigate feasibility of the methods for future operational use. 

Candidate requirements

Mathematics / Statistics / Computing CASE partner The collaboration with the Met Office will offer unique access to data, computing and expertise in air quality and environmental modelling. The student will have the opportunity to engage fully with the Met Office throughout the project, both in short-term visits and in longer-term placements. Collaborative partner The student will have access to a wealth of on-going Met Office science activities, including seminar series, and will have the opportunity to be involved with other projects, closely linked to the PhD research, offering a unique opportunity to experience working in teams within a large scientific institution. 


The student will have full access to the training and activities offered by the CDT in Environmental Intelligence (, including specialist training in data science and statistical modelling applied to environmentally-related challenges.

Background reading and references

Arnold, T. et al (2018), Atmos. Chem. Phys., doi:10.5194/acp-18-13305-2018

Carruthers, D.; et al (2019), IJEP, doi: 10.1504/IJEP.2019.10026620 

Ganesan, A. L.; et al (2014), Atmos. Chem. Phys., doi:10.5194/acp-14-3855-2014

Gelman, A.; Carlin, J. B.; Stern, H. S. & Rubin, D. B. (2004), Bayesian Data Analysis 

Chapman and Hall/CRC . Manning, A. J.; et al (2011), J. Geophys. Res., doi:10.1029/2010JD014763 


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 2021 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.

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 Friday 8 January 2021 2359 GMT .  Interviews will be held between 8th and 19th February 2021.  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:8th January 2021
Value:£15,285 per annum for 2020-21
Duration of award:per year
Contact: PGR Enquiries