A statistically coherent robust multidimensional classification scheme for water

Serious limitations of the existing water classification schemes prompted us to propose a new statistically coherent water nomenclature system. An extensive database of ionic charge-balanced concentrations of 8 elements (4 cations Ca, Mg, Na, and K; and 4 anions SO₄, Cl, HCO₃, and CO₃), in 46,292 multivariate outlier-free simulated samples, was used for training the multidimensional classification system. The initial assignment for 16 classes was achieved from the greater molar concentration concept of each cation and anion, called the Greater molar conc model. Seven hybrid log-ratios (hlr) from 8 elemental concentrations were used for linear discriminant analysis (LDA) and canonical analysis to propose 16 multidimensional discriminant functions from the 7 hlr model. The LDA and canonical analysis were also performed on the initial molar concentrations of 7 elements, without any log-transformation, which was designated as the 7 M conc model. The robustness of these three classification systems (7 hlr, 7 M conc, and Greater molar conc) was tested against analytical uncertainty propagation and mineral-water interaction effects. The 7 hlr model, due to its higher robustness, was considered as the best option for the nomenclature of the 16 types of water. From the probability concept, it was possible to identify hybrid water types, along with the basic or primary types of water. Our water classification scheme (7 hlr model under the "basic+hybrid" option) can classify as many as 256 different classes of water. Due to the clearly high complexity of the proposed classification scheme, we developed a new online computer program WaterMClaSys_LDA (Water Molar Classification System from Linear Discriminant Analysis) available at our web portal http://tlaloc.ier.unam.mx, for use by anyone after registration and log-in. The usefulness of the new classification scheme is illustrated by applications to groundwater, lake water, and geothermal water samples from South India, Mongolia, and western Turkey, respectively.