Bayesian estimation of rainfall intensity–duration–frequency relationships

Abstract

Summary Rainfall intensity–duration–frequency (IDF) curves are one of the most commonly used tools in water resources engineering. They give an idea of how return levels of extreme rainfall intensities vary with duration over a range of return periods. It is assumed that the annual maximum intensity follows the generalised extreme value (GEV) distribution. Conventional methods of estimating IDF relationships do not provide estimates of uncertainty. We propose a Bayesian framework for handling uncertainties in IDF models. Firstly, we collect annual maximum intensity data over a relevant range of rainfall durations. Secondly, we define an approximate likelihood, the “independence” likelihood, in which the correlations have been ignored between maximum intensity data of different durations. Finally, we apply Bayesian inference to obtain the adjusted posterior, which accounts for likelihood misspecification. A comparison with earlier methods, without any adjustment amongst others, shows that the adjusted posteriors are considerably wider.