Consistent intensity-duration-frequency curves by post-processing of estimated Bayesian posterior quantiles

Abstract

As a warming climate leads to more frequent heavy rainfall, the importance of accurate rainfall statistics is increasing. Rainfall statistics are often presented as intensity-duration-frequency (IDF) curves showing the rainfall intensity (return level) that can be expected at a location for a duration, and the frequency of this intensity (return period). IDF curves are commonly constructed by fitting generalized extreme value (GEV) distributions to observed annual maximum rainfall for several target durations. As the estimation is performed independently across durations, the resulting IDF curves may be inconsistent across durations and return periods. This paper proposes to ensure consistency by post-processing the estimated IDF curves. Two post-processing approaches are considered, a quantile selection algorithm that searches for consistent return levels within the posterior quantiles of a Bayesian inference approach, and adjustments based on isotonic regression. The methods are evaluated for simulated data and for Norwegian rainfall data from 83 locations, for hourly and sub-hourly durations. The post-processing yields consistent estimates that are at least as accurate as the unadjusted, inconsistent estimates. We also demonstrate how our approach differs from d-GEV, a method that performs simultaneous estimation across durations. An R implementation for the post-processing methods is available athttps://github.com/ClimDesign/fixIDF.