Etude de quelques problemes relies a l'estimation des debits de crue.

摘要

This thesis deals with the problem of flood quantiles estimation using statistical and stochastic approaches. Flood quantiles estimates are required for various types of activities related to civil engineering practice, such as the design and long-term management of hydropower reservoirs, or the safety assessment of existing structures such as dams or levees.Sound statistical inference on flood discharges distribution at a gauging site requires that a sufficient amount of flood records be available for that site. This makes that the flood quantiles estimation problem often turns out to be an information problem. As a matter of fact, many catchments for which flood quantile estimates are needed are insufficiently gauged or are merely ungauged. The common approach used by hydrologists to circumvent such problems of lack of information is called flood regionalization. The purpose of flood regionalization is primarily to relate characteristics of the population of flood discharges to physical characteristics of drainage areas. This makes it possible to estimate flood quantiles for ungauged basins. The gauged basins used to infer the relationship between physical drainage area characteristics and flood behavior characteristics are supposed to have similar standardized flood discharges frequency distribution, i.e. to be homogeneous. The set of gauged basins which provide relevant hydrological information for estimation of flood quantiles at an ungauged site constitutes its hydrological neighborhood.As a first result of our thesis research, we have proposed a simple methodology for the purpose of identifying hydrological neighborhoods. This methodology is based on canonical correlation analysis, and allows to identify hydrological neighborhoods for either gauged or ungauged basins. Important aspects of the methodology include a normality assumption for the sampling distribution of the vector of canonical variables, and the use of a chi-square type distance in the space of hydrological canonical variables for identifying neighborhoods. This is done by setting a type one error risk As a second aspect of our thesis research, a hierarchical and empirical Bayes methodology was proposed for regionalizing a Pearson type III flood model. The approach is hierarchical in that it assumes homogeneity in terms of skewness coefficient and nonhomogeneity in terms of coefficient of variation.The third and final aspect of our research concerned at-site estimation of flood discharges frequency distribution. A filtered Poisson process was used for modeling flow hydrographs, thus allowing to describe the sequence of peaks over threshold (POT) as a Markov process. The dependency among successive POTs is summarized by a conditional probability distribution function, which was derived. (Abstract shortened by UMI.)