Outlier Detection using Nonparametric Depth-Based Techniques in Hydrology

Abstract

Several issues arise when extending the methods of outlier detection from a single dimension to a higher dimension. These issues include limited methods for visualization, marginal methods inadequacy, lacking a natural order and limitation in parametric modeling. The intension to overcome and address such limitations the nonparametric outlier identifier, based on depth functions, is introduced. These identifiers comprise of four threshold type outlyingness functions for outlier detection that are Mahalanobis distance, Tukey depth, spatial Mahalanobis depth, and projection depth. The object of the present research is the application of the proposed nonparametric technique in hydrology. The study is intended to be executed in two different frameworks that are multivariate hydrological data analysis and functional hydrological data analysis. The event of a flood is graphically represented by hydrograph whose components are used for computing flood characteristics that are peak(p) and volume(v). These characteristics are frequently employed for the various types of analysis in the multivariate study. Whereas, hydrograph is exhaustively employed in the analysis of functional data so that all the important information regarding flood event are not missed while analysis. The proposed technique in a multivariate framework is applied to the bivariate flood characteristics (p,v)while in functional framework proposed approach is applied to the initial two scores of principal components denoted as (z_1,z_2 ), since initial two principal components capture major variation of data employed for analysis.