Uncertainty Quantification Methods for new Discretisation methods for Exascale computer models in Climate Sciences

The next few years will bring about the advent of Exascale computing. That is 10 to the 18 calculations per second for the most powerful supercomputers. To harness this increased computing power, new approaches for implementing large scale models are required. This is particularly true regarding the discretisation of climate models as traditional methods often suffer from points being too close to each other due to the convergence of the meridians at the poles. Alternative methods have been proposed with leading ideas from the LFRic project (Adams, 2019) in partnership with the Met Office, and from Girolami (2021) at the University of Cambridge. LFRic proposes the use of a cubed-sphere mesh, while Girolami has worked extensively on statistical finite element methods.

Statistical finite element methods provide a physics-based approach to solving differential equations that allow for small changes in the physical dynamics of problem, given sufficient evidence in the data. This helps to account for potentially unsuitable modelling assumptions, material defects and varying geometries in the system in question.

I am interested in researching these implementations, and other approaches, to ascertain how best to quantify uncertainty regarding systems of interest in climate models. This could include modelling the effects of ice melting at the polar ice caps on ocean circulation, or on modelling the evolution and likelihoods of extreme weather events. The research could also include how best to account for such events given different discretisation schemes. Finally, combing the discretisation approaches into a single multiphysics model, by developing methods similar to those described by Ming and Guillas (2021), in order to perform uncertainty quantification on large scale climate models would be ultimate goal of the PhD.

This research would be useful to the Met Office and other forecasting institutions for local weather forecasts, particularly in areas where extreme weather events are more prevalent. This may help influence decisions such as whether a city should be evacuated to prevent large scale loss of human life during a hurricane/typhoon. This research may also reduce uncertainty in climate models that look to predict the effects of climate change within the next 100 years.
My academic background is mostly in statistical inference and some scientific computing including C++. I am currently taking a module in Uncertainty Quantification however this is a rapidly growing field and I have much more to learn. Similarly, I may need further training in PDEs and/or climate sciences as I have little experience in these fields, only a passion to learn.