Compatible finite element discretisations of neural network informed stochastic geophysical flow models and their evaluation with Bayesian data assimilation

Numerical weather predictions are subject to different sources of errors such as unknown processes or numerical inaccuracies. These errors lead to uncertainties in weather forecasts. Adding noise parametrization of unknown processes to the models and using them to run an ensemble of forecasts permits the estimation of uncertainties in weather forecasts. Current forecasting models often simply add white noise to the system, leading to inaccurate uncertainty estimates. Using operational models to explore physical meaningful noise representations is, however, difficult as the code of these models is usually not flexible enough to explore alternative equations or noise parametrisations such as neural networks (NN). This PhD project will overcome this challenge by developing a prototype of a numerical weather prediction model that allows us to explore a variety of equations, stochastic formulations, and the usage of NN. It will be based on a flexible-to-use software library (Firedrake/Gusto) to model weather phenomena which will be augmented with physically meaningful noise parametrisations, aiming at improving the match between model output and real-world data. This innovative new tool for data driven model design will help us to make weather predictions more accurate while providing a powerful measure to estimate the uncertainties of forecasts.

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

Additionally requirement:

• Mathematics, Physics and Engineering (or comparable) degrees are invited to apply
• The candidate should have a strong background in mathematics
• Experience in numerical methods and simulations is highly desired.

Open to candidates who pay UK/home rate fees. See UKCISA for further information.