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

Abstract

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 min to 24 hr). The use of likelihood‐based Bayesian Markov chain Monte Carlo 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 data set of 48 rain gauge records, spread over the north central part of Algeria (25,000 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.

Climate change impact on short-duration extreme precipitation and intensity–duration–frequency curves over Europe

“…They, in turn, lead to cross-sectoral cascading infrastructure system failures because of extensive interdependencies in urban areas, threatening human health and local economies (Wilbanks and Fernandez, 2014;Penny et al, 2018). The design of flood control structures and urban water infrastructure is typically based on the statistical properties of extreme precipitation in the form of intensity-duration-frequency (IDF) curves, which quantify the frequency of occurrence of a given precipitation intensity over a range of time scales or temporal durations (Hosseinzadehtalaei et al, 2017(Hosseinzadehtalaei et al, , 2018Yan et al, 2018;Boukhelifa et al, 2018). The IDF curves also have important implications for other infrastructure vulnerable to heavy precipitation such as land-based transportation systems (e.g., streets and railways) (Kermanshah et al, 2017), electricity and telecommunication networks and those related to river floods and landslides (Nissen, and Ulbrich, 2017).…”

A note on statistical tests for homogeneities in multivariate extreme value models for block maxima

“…If such an assumption is met, one may ultimately estimate the marginal model at each specific site using observations from other homogeneous sites. A second example concerns model assumptions that link intensity and duration of extreme precipitation events to their frequency, see (Boukhelifa et al, 2018; Jurado et al, 2020; Koutsoyiannis et al, 1998), and Section 4.2 below.…”

“…We would like to point out that Bayesian (MCMC) methods provide yet another method to obtain parameter estimates. The approach has been widely applied in environmental extremes, see Boukhelifa et al (2018), Gaume et al (2010), Nguyen et al (2014), Renard et al (2006, Viglione et al (2013), among others, and yields the advantage of providing credibility intervals for the parameters when following the Bayesian paradigm. However, throughout this paper we follow the frequentist paradigm, and deriving respective limit results would require a frequentist evaluation of Bayesian methods (see, e.g., Section 10 in van der Vaart, 1998), which is beyond the scope of this paper.…”

Reply on RC1

“…Other solutions build also on the power law relationship between extremes and durations are for instance Bayesian distribution models (Boukhelifa et al, 2018;Lima et al, 2016;Roksvåg et al, 2021;Van de Vyver, 2018), marginal probabilities (Veneziano et al, 2007), and artificial intelligence (Cannon, 2018). An alternative approach for achieving a DDF based on data from example of such implementation in Germany was proposed by Fischer and Schumann (2018),…”