The Gumbel mixed model for flood frequency analysis

Many hydrological engineering planning, design, and management problems require a derailed knowledge of flood event characteristics, such as flood peak, volume and duration. Flood frequency analysis often focuses on flood peak values, and hence, provides a limited assessment of flood events. This paper proposes the use of the Gumbel mixed model, the bivariate extreme value distribution model with Gumbel marginals, to analyze the joint probability distribution of correlated hood peaks and volumes, and the joint probability distribution of correlated hood volumes and durations. Based on the marginal distributions of these random variables, the joint distributions, the conditional probability functions, and the associated return periods are derived. The model is tested and validated using observed flood data from the Ashuapmushuan river basin in the province of Quebec, Canada. Results indicate that the model is suitable for representing the joint distributions of hood peaks and volumes, as well as flood volumes and durations. (C) 1999 Elsevier Science B.V. All rights reserved.