Tackling Sparse High‑Resolution Data in Extreme‑Value Statistics: A Spatial Multi‑source Approach

Intensity-duration-frequency (IDF) relations describe the major statistical characteristics of extreme precipitation events (return level, return period, time scale). These IDF relations help to visualize either how extreme (in terms of probability/frequency/return period) a specific event is or which intensity is expected for a given probability. We model the distribution of annual precipitation maxima in an extreme-value-statistics setting for the study region Berlin, Germany. To increase model efficiency, we include the accumulation duration and model a duration-dependent GEV. The durations range from 5 minutes to days and are modeled in one single model in order to prevent quantile-crossing. Latitude and longitude are considered as covariates for the GEV parameters.

A major challenge is the need for long precipitation records in order to reliably estimate return levels of long return periods. Especially for short durations (minutes to hours), long records are rare. Therefore, we pool 3 data sources: radar-based Radklim (5-minute) and spatially-interpolated HYRAS (daily) and station-based measurements (minutely). This way, data from sources with daily resolution can borrow information from sources with minutely resolution at nearby locations. This is possible because we assume a functional relationship between short and long durations. Also we assume similar characteristics between nearby stations. This requires a spatial model since different data sources are not collocated. IDF relations will be estimated for any given point in space by using all available multi-source data in a radius of a few kilometers. Two different models are compared to do that: (1) A parametric model is using latitude and longitude as covariates. (2) We plan to create and show a non-parametric Bayesian Hierarchical Model (BHM), including a Gaussian process which models the spatial dependence between locations. The quality of estimated IDF relations will be assessed in terms of a cross-validated quantile score.