PhD-Project P6 by Jana Ulrich (FU Berlin): Linking occurrence probabilities to large scale flow

Timescale: Oct. 2018 – Sept. 2021

Supervisors:

Prof. Dr. Henning Rust, Freie Universität Berlin

Prof. Dr. Uwe Ulbrich, Freie Universität Berlin

Background

Exceedance probabilities for extremes are an important basis for risk assessment. Univariate extreme value statistics with spatial covariates are a useful basis to obtain maps of return levels for atmospheric parameters from station based observations. These maps can be obtained in a covariates approach by setting up (parametric) linear models for the parameters of the extreme value distribution, as suggested for precipitation in the project P3.

Aim of this project is the extension of this approach from daily sums of precipitation towards a simultaneous description of arbitrary aggregation times (e.g. 5 min to 3 days), so called Intensity-Duration-Frequency (IDF) curves. These curves are typically obtained by fitting a model to return-levels from extreme value statistics carried out successively on precipitation sums of various time scales. Here, we propose a consistent model for the simultaneous description of return-levels for all time scales. This model allows for the estimation of consistent IDF curves without crossing of return-levels. Additionally, a spatial description of these curves is sought which includes also information from neighbouring gauges and yields IDF-curves also at ungauged sites. The latter can be realized in a covariates framework (as in P3) but also using a Bayesian Hierarchical model together with the consistent IDF model. The latter forms the bottom layer and a description of the spatial variation of IDF parameters forms the top layer.

Objectives and Methods

• Obtain a consistent description for the intensity-duration-frequency relationship for precipitation using a duration-dependent general extreme value distribution.
• Set up a spatial model for the parameters of a) to include also information from neighbouring sites and obtain IDF curves also for ungauged site

The consistent IDF curves can be estimated in the frame of a covariates model but also using a Bayesian hierarchimal modelling approach. Ideally, both approaches will be compared keeping in mind their different interpretation.