The Gumbel mixed model for flood frequency analysis

• Published in: Journal of hydrology (Amsterdam) Vol. 226; no. 1; pp. 88 - 100
• Main Authors: Yue, S, Ouarda, T.B.M.J, Bobée, B, Legendre, P, Bruneau, P
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 20.12.1999; Elsevier Science
• Subjects: Bivariate extreme distribution; Earth sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Exact sciences and technology; Flood duration; Flood peak; Flood volume; Gumbel distribution; Hydrology; Hydrology. Hydrogeology; Joint probability distribution; Natural hazards: prediction, damages, etc; Canada; Quebec; Eastern Canada; Flood duration; Gumbel distribution; Flood peak; Bivariate extreme distribution; Joint probability distribution; Flood volume; volume; floods; models; statistical distribution; probability; North America; frequency
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/S0022-1694(99)00168-7

Many hydrological engineering planning, design, and management problems require a detailed 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 flood peaks and volumes, and the joint probability distribution of correlated flood 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 flood peaks and volumes, as well as flood volumes and durations.