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

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.

Uncertainty estimations for the predictions of ocean and climate model output are essential for planning and risk management, both on short to long time scales, including the development of appropriate climate change mitigation and/or adaptation strategies.

The NEMO modelling community, and operational agencies using NEMO such as the UK Met Office and the National Centre for Ocean Forecasting and a wide number of users across Europe will benefit from this research. It will give them new insights into the behaviour of ORCA12, the ocean component of the UK's climate model HadGEM3-H, at untried input settings and into the sensitivity of the model output to different settings of the inputs. This will assist them in model development and in making informed decisions as to where to spend their budget of super-computer time on runs of the current model. The planned analysis will provide a road map for future uncertainty analyses using the NEMO model.

The climate modelling community, including organisations that provide evidence to the IPCC that predicts the future impacts of climate change (e.g. the Met Office Hadley Centre), will benefit from this research. Spatio temporal models are ubiquitous in climate science and the highest resolution models can only be run on the most powerful computers in the world. The proposed research leading to a methodology designed to address these two issues and providing an illustration on a high-end ocean model, will enable climate modellers to address their own uncertainty questions using the proposed methodology as a tool and the proposed application as a road map. Climate modellers using NEMO, such as the UK Met Office, will benefit more directly in the same was as the NEMO community

There will be many downstream beneficiaries of the proposed methodologies and their application to ocean and climate models. These include any organisation or body that requires uncertainty on climate predictions in order to plan or manage risk. Examples include government agencies, research organisations, and environmental consultancies that compile information to provide advice to policy makers, industry and society on future climate change impacts, adaptation strategies and risk management; climate change adaption and risk management initiatives with links to the insurance industry; users of the IPCC reports. They will benefit due to the improvements in uncertainty quantification for climate and ocean models. Many of these will also benefit more directly from inferences about ocean quantities made as part of the proposed research.

There will be beneficiaries outside environment-related applications. Non environmental users of computer models are a very wide group including industrial communities such as oil and gas, aerospace and pharmaceuticals. Where these models are expensive and/or produce spatio-temporal output, their users will benefit directly from the new methodologies.