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

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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.