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  Ensemble modelling and uncertainty quantification for simulations of atmosphere and ocean dynamics


   School of Mathematics and Physics

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  Dr Werner Bauer, Dr N Santitissadeekorn  No more applications being accepted  Funded PhD Project (Students Worldwide)

About the Project

​​Computational modelling is increasingly important in planning and decision making in many areas of public and economic life. However, many aspects of the real-world problem to be simulated, here the dynamics of atmosphere and ocean, are not, or are erroneously, included in these models, while the numerical approximation of the underlying mathematical equations is an additional source of errors. These errors cause uncertainties in the numerical forecasts. A powerful tool to obtain estimates of the likelihood of simulated scenarios is the process of ensemble prediction. In the field of “uncertainty quantification”, we apply stochastic modelling in combination with data assimilation, which allows us to quantify the errors of a forecast via such ensemble runs. Although operationally applied, for example in weather forecasting, state-of-the art methods lack important features such as structure preservation (e.g. mass and energy conservation) or consistent stochastic parameterisations to model unresolved processes. Also, current models often do not fully benefit from massively parallel supercomputer architectures. 

​The aim of this project is to address these problems and to develop a new generation of a stochastic modelling framework for atmosphere and ocean dynamics that applies: (i) consistent stochastic equations to model unresolved processes and permit to estimate the resulting errors; (ii) physics-informed neural networks (NN) (or other NN architectures) to learn unresolved processes from measurement data; (iii) structure-preserving data assimilation techniques to smoothly blend models with data; (iv) (stochastic) analysis to better understand the interaction of small and large scale fluid motion. This project will help to provide both more accurate predictions and significantly improved uncertainty estimates. 

Supervisors: Dr Werner Bauer and Dr Naratip Santitissadeekorn.

Entry requirements

Open to any UK or international candidates. Up to 30% of our UKRI funded studentships can be awarded to candidates paying international rate fees. Find out more about eligibility. Starting in October 2024.

You will need to meet the minimum entry requirements for our Mathematics PhD programme.

​​Applicants should have a minimum of a first class honours degree in Mathematics, the Physical Sciences or Engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, through exceptional BSc students will be considered.​ 

How to apply

Applications should be submitted via the Mathematics PhD programme page. In place of a research proposal, you should upload a document stating the title of the project that you wish to apply for and the name of the relevant supervisor.


Engineering (12) Environmental Sciences (13) Mathematics (25)

Funding Notes

UKRI standard stipend (currently £18,622 p.a.) with an additional bursary of £1,700 p.a. (for the full 3.5 years) for exceptional candidates. Full home or overseas fees (as applicable) covered. A research, training and support grant of £3,000 over the project is offered. Open to any UK or international candidates. Up to 30% of our UKRI funded studentships can be awarded to candidates paying international rate fees.

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