Statistical models developed with extreme value theory as a basis allow us to use established mathematics to make probabilistic estimates about rare weather events. For example, we can take data and estimate 1-in-100 year events, and their uncertainty. This can even be done with fewer than 100 years worth of data. Fortunately, since they can cause considerable damage, such events are by definition rare. Unfortunately, from a statistical perspective, this means data quantifying them are inevitably scarce. This project aims to develop models that better use data so that we can make more accurate our understanding of extreme weather events.
Statistical modelling of extremes has recently seen a step change in methodology for representing spatial processes; see, e.g., Davison and Gholamrezaee (2012), for a review. The statistical importance of this is that we can pool data from multiple locations, which can partially compensate for data scarcity, when compared to considering each location on its own. Further recent developments, such as Engelke et al. (2018), allow us to model extreme events represented by finite-resolution data. This is important because numerical weather simulation models are a valuable source of such data and have now reached resolutions capable of capturing extreme meteorological phenomena that previously were previously unreliably modelled. If we can coherently link the statistical and numerical developments, we can improve risk estimation of extreme weather events. However, if we can also reliably incorporate climate projections and their uncertainty, then we can further - and perhaps dramatically - improve our understanding of future extreme weather risk.
Linking statistical and numerical developments will need a novel statistical framework that incorporates extreme value theory and spatial statistics; it must be capable of handling large quantities of aggregated data, avoiding excessive computational cost, and must explicitly recognise the discrepancies that are inevitable in model-generated data. Conventional approaches won’t suffice: they’re only feasible for small amounts of high-resolution data, which limits their applicability to very small regions, and they lack the robustness to readily incorporate climate projection uncertainty. However, we can now draw on developments for deep Gaussian processes and generalised additive models to build a framework that can applied in a valuable way to many more - and potentially all - extreme weather phenomena. This project will first develop such a framework, which will then be translated to efficient, user-friendly software. The proposed framework could benefit a considerable number of end-users, and ultimately bring new, quantitative understanding of risk for a variety of types of extreme weather.