Background
Extreme rainfall events vary in duration and magnitude, from multiple days of fairly high rainfall to extreme rainfall over a few hours. Flooding results from either event type. Short-lived events, e.g. thunderstorms, can be limited to just a few kilometers, and if weather stations aren’t nearby, may lack measurements. Radar data bridge this gap with their high resolution, wide spatial coverage and high frequency of sampling. But statistical modelling of these data, and using them understand future rainfall events, is a challenge that involves modelling many different-sized grid cells of data at many time points, downscaling model output of too-low resolution to resolve local events, and developing software to fit models. Once developed, these models can improve our quantitative understanding of extreme rainfall events, offering better insight into the spatial dependence structure of extreme rainfall, how it changes between resolution and how local events may change into the future.
PhD opportunity
To capture radar data, this project will develop extreme value models for the variation in extreme rainfall from one grid cell to another over time, for many grid cells over large areas. Models will need to accommodate varying grid cell size, as cells increase in size with distance from radar sites. This project will also build downscaling models, via geostatistics, that link radar data to climate model output, the latter being of insufficient resolution to resolve localised rainfall events, but may still hold valuable information in their projections quantifying how such events may change into the future. With Met Office support we can employ best practice converting radar reflectivities to rain rates, which is a complex and involved process, due, e.g., to beam attenuation through intense rain.
First the conditional approach to extreme values (Heffernan and Tawn, 2004) will be used to capture these high-dimensional spatio-temporal data, by modelling extreme rainfall over regions and time; see Wadsworth and Tawn (2022). This model will allow for complex dependencies that exist between extreme rainfall at different locations and their spatially varying nature, such as frontal rainfall, which might affect the entire region, versus convective rainfall, such as a localised thunderstorm. The model will also capture how these evolve over time. Efficient methods will need to be developed to utilise the large amounts of radar data, such as low-rank representations and sparsity. Through a combination of a geostatistical downscaling and conditional extreme value models, historical relationships will be established between radar data and gridded climate model output. This will bring a high-resolution event simulation model that can be forced by data representing a changing climate. Its simulated events, will allow detailed study of features, such as dependencies between resolutions, and probabilistic summaries, such climate-dependent risk estimates.
Other information
Applicant profile: Students with a strong background in mathematics or statistics with particular interest in modelling of weather data and programming for statistical models.
- Wadsworth, JL and Tawn, JA. Higher-dimensional spatial extremes via single-site conditioning. Spatial Statistics 51, 100677 (2022) https://doi.org/10.1016/j.spasta.2022.100677
- Heffernan JE and Tawn JA. A conditional approach for multivariate extreme values (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol., 66 (3) (2004) https://doi.org/10.1111/j.1467-9868.2004.02050.x
