The Gumbel mixed model for flood frequency analysis
ABSTRACT 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.
- Water Resources Research 04/2001; 37(4):1107-1110. · 3.15 Impact Factor
- Water Resources Research 01/2001; 37(4). · 3.15 Impact Factor
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ABSTRACT: Copula dependence functions have shown their usefulness to environmental hydrological applications such as rainfall frequency analysis. In this paper we illustrate the utility of the Generalized Diagonal Band copula with two-sided power generating densities (GDB-TSP) in modeling rainfall return periods. Using QQ plots, in addition to, the Cramer-von Misés and Kolmogorov-Smirnov test statistics we show an improvement in using the GDB-TSP model over a traditional distribution approach using the Gumbel mixed model. A comparison of both models produces different results depending on the rainfall regime and returns period under consideration.