Pierre Bruneau

The Gumbel mixed model for flood frequency analysis

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.

Bivariate index-flood model: case study in Québec, Canada

Abstract Floods, as extreme hydrological phenomena, can be described by more than one correlated characteristic, such as peak, volume and duration. These characteristics should be jointly considered since they are generally not independent. For an ungauged site, univariate regional flood frequency analysis (FA) provides a limited assessment of flood events. A recent study proposed a procedure for regional FA in a multivariate framework. This procedure represents a multivariate version of the index-flood model and is based on copulas and multivariate quantiles. The performance of the proposed procedure was evaluated by simulation. However, the model was not tested on a real-world case study data. In the present paper, practical aspects are investigated jointly for flood peak (Q) and volume (V) of a dataset from the Côte-Nord region in the province of Quebec, Canada. The application of the proposed procedure requires the identification of the appropriate marginal distribution, the estimation of the index flood and the selection of an appropriate copula. The results of the case study show that the regional bivariate FA procedure performed well. This performance depends strongly on the performance of the two univariate models and, more specifically, the univariate model of Q. The results show also the impact of the homogeneity of the region on the performance of the univariate and bivariate models. Editor D. Koutsoyiannis

Rémus, Software for Missing Data Recovery

In order to manage adequately their water resources, Hydro-Quebec often uses simulation of energy at different points of the hydrological network. This simulation is based on monthly means computed from daily observed flows. However, it is possible that some daily values are missing. Hydro-Quebec will then reject the calculated monthly mean flow when four or more daily observations are not available or if they seem incorrect. Furthermore, the monthly means may be rejected for many consecutive months at certain sites. Also, when a basin is large, more than one station is needed to obtain a good estimation of flows at sites of reservoirs. As very few stations have complete series on a long period, it is therefore very important to be able to estimate these missing values in order to obtain reliable estimates from the energy production simulation models.