Bayesian estimation of intensity–duration–frequency curves and of the return period associated to a given rainfall event

  • David Huard
  • Alain Mailhot
  • Sophie Duchesne
Original Paper


Intensity–duration–frequency (IDF) curves are used extensively in engineering to assess the return periods of rainfall events and often steer decisions in urban water structures such as sewers, pipes and retention basins. In the province of Québec, precipitation time series are often short, leading to a considerable uncertainty on the parameters of the probabilistic distributions describing rainfall intensity. In this paper, we apply Bayesian analysis to the estimation of IDF curves. The results show the extent of uncertainties in IDF curves and the ensuing risk of their misinterpretation. This uncertainty is even more problematic when IDF curves are used to estimate the return period of a given event. Indeed, standard methods provide overly large return period estimates, leading to a false sense of security. Comparison of the Bayesian and classical approaches is made using different prior assumptions for the return period and different estimation methods. A new prior distribution is also proposed based on subjective appraisal by witnesses of the extreme character of the event.


Urban drainage Extreme hydrological event Annual maximum Rainfall Bayesian statistic Return period 



David Huard is grateful for the financial support of the Natural Sciences and Engineering Research Council of Canada. David Huard is also thankful to the community developping the open source scientific computing environment used for this project (Oliphant 2007; Jones et al. 2001; Hunter 2007; Perez and Granger 2007).


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Atmospheric and Oceanic SciencesMcGill UniversityMontrealCanada
  2. 2.Institut National de la Recherche ScientifiqueCentre Eau, Terre et EnvironnementQuebecCanada

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