University of Exeter funding: NERC GW4+ DTP PhD studentship

Deep Learning and Bayesian Time Series Analysis for Probabilistic Post-Processing in Weather Forecasting. PhD in Mathematics (NERC GW4+ DTP) Ref: 3694

About the award


Lead Supervisor

Dr Saptarshi Das, Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter

Additional Supervisors

Dr Tim Hughes, Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter

Aaron Hopkinson, Verification, Impacts and Post-Processing, Met Office

Ken Mylne, Verification, Impacts and Post-Processing, Met Office

Location: University of Exeter, Penryn Campus, Penryn, Cornwall, TR10 9FE

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


Students who are resident in EU countries are eligible for the full award on the same basis as UK residents.  Applicants resident outside of the EU (classed as International for tuition fee purposes) are not eligible for DTP funding. Residency rules are complex and if you have not been resident in the UK or EU for the 3 years prior to the start of the studentship, please apply and we will check eligibility upon shortlisting.

Project Background 

Weather forecasting is one of the oldest big data analytics challenges, both in the context of UK and globally. This typically involves handling several terabytes of streaming data per day from multiple forecast models and ensembles. With various data processing chains involved, the final goal is to generate regularly updated probabilistic forecasts for temperature, rain, snow, cloud, visibility, wind etc. and to derive weather forecasts suitable for public presentation including visual symbols. The goal of the project is two-fold. Firstly, to improve the reliability of probabilistic forecasts with bias correction and calibration through improved Bayesian time series analysis techniques like Kalman filters and other sequential Monte Carlo methods relating model outputs to weather observations or analyses. Secondly, correctly classifying the forecast data to generate weather symbols using deep learning based classification algorithms to match weather observations.

Project Aims and Methods 

This project will develop deep learning methods for handling big datasets in numerical weather prediction to calibrate the probabilistic forecasts using observational or analysis data. Recent advances in fast sequential Monte Carlo or Kalman filter variants will be explored with non-traditional noise distributions for bias correction of single and multi-station weather forecast while also estimating the noise correlation structures between multiple stations using modern Bayesian time series modelling techniques. As deep machine learning is a new approach in post-processing, there will be opportunities for the PhD student, working with the Met Office team, to explore new areas for further development, either in enhancing and advancing the work on calibration, or into additional areas. Weather forecasting is often at its most important in situations where there is a risk of extreme weather, situations which have rarely been previously encountered in the data, so there is a particular need for calibration systems to learn from rare events but also to fail safe where few data are available. Exploiting the calibrated forecasts, one of the challenges for forecasters is to communicate the message to the public, for example through the use of symbols for display in web and app. Met Office staff are developing simple machine learning approaches to classifying forecasts, but there will be a good opportunity for the student to explore deep learning techniques to exploit the correlation information between variables to better define the risks of different outcomes. Another challenge is to produce a range of consistent weather scenarios within a calibrated forecast probability distribution. One idea would be to explore the use of variational autoencoders with the aim of generating new ensemble members from the distribution, building in, for example, something of the complex relationships between weather diagnostics and the orography.


Example map for probability of rainfall rate in UK



Example of high-resolution rainfall rate prediction

Candidate Requirements

The candidate will have a good undergraduate and/or master’s degree in any of the following disciplines – Mathematics/Statistics, Computer Science, Physics, Engineering, Meteorology, Environmental Sciences. Good analytical, computational skills and in particular, some prior experience in Python/ R/ Matlab programming is necessary. Some previous research experience in big data analytics, machine learning, mathematical, statistical computing is also desirable. Prior experience on high-performance computing will also be advantageous for this project.

CASE or Collaborative Partner

The student will be mainly based in the University of Exeter, Penryn Campus and will also closely collaborate with the Met Office. This will be in the form of sharing datasets, communicating the research findings with the researchers in Met Office, develop better understanding and interpretations of weather data analysis in a broader industrial and academic context, and writing joint collaborative publications.   


The student will receive the required training to pursue fundamental and applied research in this project and will have the opportunity to attend some of the departmental modules in Mathematics. The student will spend significant time working at the partner organisation (Met Office) to understand the weather forecasting problems and the data and methods for testing and verifying forecast performance. The student will exchange their research findings and methods with their peers and other researchers through regular presentations and conference attendance. The project is inter-disciplinary in nature, so the student will have the opportunity to learn and discuss with other researchers both from Mathematics/Statistics and Meteorology/Environmental Science. It is expected that the student will also strengthen the collaborations of the supervisors with the Met Office through exchange of academic ideas, software tool, data, methods and collaborative research publications.

References / Background reading list 

1. Goodfellow, I., Bengio, Y. and Courville, A., 2016. Deep learning. MIT press, URL:

2. Murphy, K.P., 2012. Machine learning: a probabilistic perspective. MIT press, URL: 

3. Vannitsem, S., Wilks, D.S. and Messner, J. eds., 2018. Statistical Postprocessing of Ensemble Forecasts. Elsevier, URL: 

4. Rasp, S. and Lerch, S., 2018. Neural Networks for Postprocessing Ensemble Weather Forecasts. Monthly Weather Review, 146(11), pp.3885-3900 url:

5. Wilks, D.S., 2011. Statistical methods in the atmospheric sciences (Vol. 100). Academic press, url:

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 1600 hours GMT Monday 6 January 2020.  Interviews will be held between 10 and 21 February 2020.  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:6th January 2020
Value:£15,009 per annum for 2019-20
Duration of award:per year
Contact: PGR Enquiries