Integrated Bayesian Estimation of Intensity-Duration-Frequency Curves: Consolidation and Extensive Testing of a Method

Intensity-duration-frequency (IDF) curves are one of the most common rainfall statistical models used in hydrologic design and analysis projects. The uncertainties related to the elaboration of these IDF curves have nevertheless seldom been evaluated in the past. The article will recall the existing link between the IDF formulation and some properties of the rainfall series such as simple scaling and multifractal structure. Assuming that these properties are valid, the IDF curves formulation is then the product of a dimensionless (i.e. reduced) distribution function for the annual maximum rainfall intensities/depths and a duration-dependent scaling factor. Its parameters can be evaluated in an integrated way (i.e. based on a unique pooled sample of peak intensities over a range of durations: from 15 minutes to 24 hours). The use of likelihood-based Bayesian Monte-Carlo Markov Chain (MCMC) statistical inference methods for this evaluation provides consistent uncertainties for all the parameters of the IDF relation and for the corresponding rainfall quantiles. This methodology has been tested, via a local analysis, on a large dataset of 48 rain-gauge records, spread over the North Central part of Algeria (25000 km²), under various climatic regimes. The integrated approach is undoubtedly consistent with estimates from annual maximum rainfall fitted to single durations. Furthermore, credibility intervals are significantly reduced. Also, this integrated approach appears to be robust: unlike the traditional method based single durations, it generally provides rational quantile estimates, even when short observed series are available. This is a significant advantage for engineering applications.