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

  • Full or part time
  • Application Deadline
    Monday, January 06, 2020
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

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:

- 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

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.

Funding Notes

NERC GW4+ funded studentship available for September 2020 entry. For eligible students, the studentship will provide funding of fees and a stipend which is currently £15,009 per annum for 2019-20.


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:

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