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

未来几年将带来Exascale计算的出现。对于最强大的超级计算机来说，这是每秒10的18次方次计算。为了利用这种增加的计算能力，需要用于实现大规模模型的新方法。对于气候模型的离散化，这一点尤其如此，因为传统方法往往由于子午线在两极的收敛而受到点彼此太近的影响。替代方法已经提出了与气象局合作的LFRic项目（亚当斯，2019）和剑桥大学的Girolami（2021）的领先思想。LFRic建议使用立方体球网格，而Girolami则广泛研究统计有限元方法。统计有限元方法提供了一种基于物理的方法来求解微分方程，该方法允许问题的物理动力学发生微小变化，并在数据中提供足够的证据。这有助于解释潜在的不合适的建模假设、材料缺陷和所讨论的系统中的不同几何形状。我有兴趣研究这些实现和其他方法，以确定如何最好地量化气候模型中感兴趣的系统的不确定性。这可能包括模拟极地冰盖的冰融化对海洋环流的影响，或模拟极端天气事件的演变和可能性。该研究还可能包括如何最好地考虑到不同离散化方案的此类事件。最后，通过开发类似于Ming和Guillas（2021）所描述的方法，将离散化方法结合到一个单一的多物理场模型中，以便对大尺度气候模型进行不确定性量化，这将是博士的最终目标。特别是在极端天气事件较为普遍的地区。这可能有助于影响决策，例如是否应该疏散城市，以防止飓风/台风期间大规模的人员伤亡。这项研究还可以减少气候模型的不确定性，这些模型旨在预测未来100年内气候变化的影响。我的学术背景主要是统计推断和一些科学计算，包括C++。我目前正在学习不确定性量化模块，但这是一个快速发展的领域，我还有很多东西要学。同样，我可能需要进一步培训偏微分方程和/或气候科学，因为我在这些领域的经验很少，只有学习的热情。

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.