Multivariate statistical approach to estimate mixing proportions for unknown end members

Abstract

Summary A multivariate statistical method is presented, which includes principal components analysis (PCA) and an end-member mixing model to estimate unknown end-member hydrochemical compositions and the relative mixing proportions of those end members in mixed waters. PCA, together with the Hotelling T 2 statistic and a conceptual model of groundwater flow and mixing, was used in selecting samples that best approximate end members, which then were used as initial values in optimization of the end-member mixing model. This method was tested on controlled datasets (i.e., true values of estimates were known a priori ) and found effective in estimating these end members and mixing proportions. The controlled datasets included synthetically generated hydrochemical data, synthetically generated mixing proportions, and laboratory analyses of sample mixtures, which were used in an evaluation of the effectiveness of this method for potential use in actual hydrological settings. For three different scenarios tested, correlation coefficients ( R 2 ) for linear regression between the estimated and known values ranged from 0.968 to 0.993 for mixing proportions and from 0.839 to 0.998 for end-member compositions. The method also was applied to field data from a study of end-member mixing in groundwater as a field example and partial method validation.