Modeling St. John River (N.B., Canada) incomplete hydrometric data using bivariate distributions

Abstract

This study deals with incomplete bivariate data in hydrology, where information contained in a hydrological series of relatively long length (X, the auxiliary variable) is utilized to enhance the quality of the quantile estimates for a series of shorter length (Y, the variable of main interest), when there is an association between X and Y. It is suggested that bivariate models for representing (X, Y) be constructed by means of copulas, which allows for flexibility in choosing both the marginals and the bivariate distributions. Parameter estimation is done by maximum likelihood (ML), where all the unknown parameters of the bivariate model are estimated simultaneously. A case study using flow records at three gauging stations on the St. John River (New Brunswick, Canada) is used to demonstrate the interest of using bivariate distributions for modeling incomplete data. By using (X, Y) bivariate data observed on the St. John River, the probability density function (pdf) obtained from a univariate frequency analysis of Y (Model A), is compared to the pdf constructed using a bivariate model relating X to Y (Model B). It is shown that Model B reduces the variability in the Y pdf as compared to the pdf obtained from Model A, and also corrects the quantile estimates for Y through a location shift.