Return Period vs. Probability of Failure: Which Concept to Choose for Decision-Making in Flood Risk Management

Typically, a hydraulic flood risk management structure is designed to handle a centennial hydrometeorological event. Usually, designers present this centennial return period as corresponding to the highest probable rainfall/flood in a hundred years. This tends to reassure public authorities about the resilience of the infrastructure in place. However, if the designer completes his initial statement by associating the lifetime of the structure, for example 50 years and the corresponding probability of failure is 40%, this may lead to further reflection on the choice of design return periods. Thus, basing the design on the probability of failure associating lifetime and return period seems to be a safer choice. The probability of failure, also defined as the predictive distribution, has an unknown mathematical formulation and density function. However, it can be estimated using numerical calculations. Indeed, a Bayesian statistical inferential process applied to a time series of observations can generate millions of values of a random hydrological variable and associate failure probabilities with them. The use of a Bayesian framework, allowing the integration of any historical information outside the observation series, reduces estimation uncertainties. Here, this approach is highlighted on observations of maximum annual daily flows recorded at the Carillon Dam station on the Ottawa River (Canada). The three largest floods of the Ottawa River in 1974, 2017 and 2019, where the last one was defined as centennial return period according to traditional frequency analysis approaches, are associated with a recurrence interval of less than 100 years through the Bayesian analysis proposed here. In addition, the centennial probability of failure results in an annual maximum daily flood discharge higher than what has been measured to date with a magnitude reasonably acceptable for flood risk management projects.

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