Depth-based multivariate descriptive statistics with hydrological applications

Abstract

[1] Hydrological events are often described through various characteristics which are generally correlated. To be realistic, these characteristics are required to be considered jointly. In multivariate hydrological frequency analysis, the focus has been made on modeling multivariate samples using copulas. However, prior to this step, data should be visualized and analyzed in a descriptive manner. This preliminary step is essential for all of the remaining analysis. It allows us to obtain information concerning the location, scale, skewness, and kurtosis of the sample as well as outlier detection. These features are useful to exclude some unusual data, to make different comparisons, and to guide the selection of the appropriate model. In the present paper we introduce methods measuring these features, which are mainly based on the notion of depth function. The application of these techniques is illustrated on two real-world streamflow data sets from Canada. In the Ashuapmushuan case study, there are no outliers and the bivariate data are likely to be elliptically symmetric and heavy-tailed. The Magpie case study contains a number of outliers, which are identified to be real observed data. These observations cannot be removed and should be accommodated by considering robust methods for further analysis. The presented depth-based techniques can be adapted to a variety of hydrological variables.