Bayesian comparison of different rainfall depth-duration-frequency relationships

Depth-duration-frequency curves estimate the rainfall intensity patterns for various return periods and rainfall durations. An empirical model based on the generalized extreme value distribution is presented for hourly maximum rainfall, and improved by the inclusion of daily maximum rainfall, through the extremal indexes of 24 hourly and daily rainfall data. The model is then divided into two sub-models for the short and long rainfall durations. Three likelihood formulations are proposed to model and compare independence or dependence hypotheses between the different durations. Dependence is modelled using the bivariate extreme logistic distribution. The results are calculated in a Bayesian framework with a Markov Chain Monte Carlo algorithm. The application to a data series from Marseille shows an improvement of the hourly estimations thanks to the combination between hourly and daily data in the model. Moreover, results are significantly different with or without dependence hypotheses: the dependence between 24 and 72 h durations is significant, and the quantile estimates are more severe in the dependence case.