Extreme value modelling of rainfall from high resolution radar data in a changing climate

Background

Extreme rainfall events that cause flooding vary in duration and magnitude, from extreme rainfall over a few hours to multiple days of seemingly average rainfall. Short-lived events, e.g. thunderstorms, might cover 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 sampling frequency. This project will use such data to understand future extreme rainfall. Modelling radar data is itself a challenge, let alone using it to understand future rainfall events. First, we must deal with extremes from data at differing resolution and many time points. Then we must relate such data to rainfall projections. Once developed this framework can improve our quantitative understanding of extreme rainfall events, especially intense localised rainfall, and how it is expected to change into the future. Such understanding helps infrastructure planning, e.g. flood defences.

PhD Opportunity

To capture radar data, this project will develop statistical models using extreme value theory. These will capture the variation in extreme rainfall between many grid cells over time and over large areas. The models will accommodate varying grid cell size, as cells increase in size with distance from radar site. This project will also build downscaling models, via geostatistics, that link radar data to climate model output. Climate model output is of insufficient resolution to resolve localised rainfall events, but may still hold valuable information for quantifying how localised extreme rainfall 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.

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.

Applicant Profile

Students with a strong background in mathematics and interest in programming and the statistical modelling of extreme weather.

Other information

https://byoungman.github.io/
Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values.