Uncertainty quantification for the linking of spatio-temporal output of computer model hierarchies and the real world

用计算机模型来研究复杂的物理系统所引入的不确定性的量化是现代科学的一个基本问题。虽然存在一种统计方法来执行不确定性量化（UQ），但该技术尚未达到高端用户使用非常缓慢和昂贵的计算机模型（如最新的气候模型）所要求的水平。拟议的研究将在两个关键领域提供方法发展，这将促进高端模型的UQ。首先是动态模拟计算机模型的时空输出的方法。所开发的方法将允许创建表示计算机模拟器的时空输出中的不确定性的统计模型，对于其输入参数的任何选择，当从中采样时，将允许建模的空间场以模仿模拟器的方式及时演变，并报告表示中的不确定性。这将代表着许多科学学科的研究人员向前迈出了重要的一步，例如气候，在这些学科中，空间场的时间演变是非常有趣的。拟议的工作将从申请人对单变量时间序列的研究方法发展而来，并将结合状态空间建模文献中对多时间序列的贝叶斯分析技术，以及利用高斯过程仿真探索空间场的基扩展的UQ方法，以取得方法学上的进步。第二种方法涉及使用第一种方法，以便开发方法，使用相关的层次结构，但较低分辨率的模型结合当前在高端，最先进的模拟器上运行的任何运行，来动态模拟高端模拟器的时空输出。这将通过调整和扩展目前用于统计连接两个分层模拟器的方法来实现。这项研究将把这些方法应用到欧洲海洋模型核心（NEMO）框架的海洋模型中。该框架包含四个海洋模型的层次结构，由于求解器的精细空间分辨率，高端模型需要在超级计算机上以单一参数设置运行数月，而最快的版本在台式计算机上快速运行，以便生成大型集合。被称为ORCA12的高端模型构成了英国当前气候模型HadGEM3-H的海洋部分。与国家海洋学中心（NOC）的合作者合作，这些方法将应用于层次结构中现有的和专门设计的集成，以便对ORCA12合作者感兴趣的关键时空场进行建模。这将有助于他们了解这一重要模式的产出的反应，并有助于其未来的发展。进一步的目标将是利用ORCA12的统计模型和标准UQ方法促进真实海洋中关键时空场的不确定性量化。

Quantification of uncertainty introduced by using computer models to study complex physical systems is a fundamental problem for modern science. Though a statistical methodology exists to perform the uncertainty quantification (UQ), the technology is not yet at the level required by high-end users with very slow and expensive computer models, such as the latest climate models. The research proposed will provide methodological developments in two key areas that will facilitate UQ for high-end models. The first is a methodology for modelling spatio-temporal output of computer models dynamically. The methods developed will allow statistical models that represent the uncertainty in the spatio-temporal output of a computer simulator, for any choice of its input parameters, to be created that, when sampled from, will allow the modelled spatial field to evolve in time in a way that mimics the simulator and that reports the uncertainty in the representation. This will represent an important step forward for researchers in a variety of scientific disciplines, such as climate, where the evolution of spatial fields in time is of great interest. The proposed work will be developed from methods that the applicant has worked on for univariate time series and will combine techniques for the Bayesian analysis of multiple time series from the literature of state space modelling, with UQ methods that have explored basis expansions of spatial fields with Gaussian process emulation in order to make methodological advances.The second involves using the first methodology in order to develop methods for using a hierarchy of related, but lower resolution models combined with whatever runs currently exist on the high-end, state of the art, simulator, to model spatio-temporal output of the high-end simulator dynamically. This will be done by adapting and extending current methods for linking two hierarchical simulators statistically.The research will apply these methods to the Nucleus for European Modelling of the Ocean (NEMO) framework of ocean models. This framework contains a hierarchy of four ocean models, with the high-end model taking months to run at a single setting of the parameters on a super-computer due to the fine spatial resolution of the solver, and the fastest version running quickly on a desktop computer so that large ensembles can be generated. The high-end model, known as ORCA12, forms the ocean component of the UK's current climate model, HadGEM3-H. Working with collaborators at the National Oceanography Centre (NOC), the methodologies will be applied to existing and specially designed ensembles within the hierarchy in order to model key spatio-temporal fields of interest to the collaborators in ORCA12. This will aid them in understanding the response of the outputs of this important model and assist in its future development.A further goal will be to facilitate uncertainty quantification for key spatio-temporal fields in the real ocean using the statistical model for ORCA12 and standard UQ methods.