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

未来几年将出现百亿亿次计算。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，这一点尤其正确，因为传统的方法往往由于子午线在两极的汇聚而使各点过于接近。与气象局合作的LFRic项目（Adams, 2019）和剑桥大学的Girolami（2021）提出了替代方法。LFRic建议使用立方球网格，而Girolami在统计有限元方法方面做了大量工作。统计有限元方法提供了一种基于物理的方法来解决微分方程，它允许问题的物理动力学中的微小变化，在数据中有足够的证据。这有助于解释可能不合适的建模假设、材料缺陷和系统中不同的几何形状。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。研究还可能包括如何在不同的离散化方案下最好地解释这些事件。最后，通过开发与Ming和Guillas（2021）描述的方法类似的方法，将离散化方法整合成一个单一的多物理场模型，以便对大尺度气候模型进行不确定性量化，这将是博士学位的最终目标。这项研究对英国气象局和其他预报机构进行当地天气预报非常有用，特别是在极端天气事件多发的地区。这可能有助于影响决策，例如是否应该疏散一个城市，以防止在飓风/台风期间造成大规模人员伤亡。这项研究还可能减少旨在预测未来100年内气候变化影响的气候模式的不确定性。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的一个模块，但这是一个快速发展的领域，我还有很多东西要学。同样，我可能需要在pde和/或气候科学方面进行进一步的培训，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.