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Latent Compositional Factors in The Llobregat River Basin (Spain) Hydrogeochemistry
Authors:R Tolosana-Delgado  N Otero  V Pawlowsky-Glahn and A Soler
Institution:(1) Department d'Informàtica i Matemàtica Aplicada, Universitat de Girona, Girona, Spain;(2) Department de Cristal⋅lografia, Mineralogia i Dipòsits Minerals, Facultat de Geologia Universitat de Barcelona, Barcelona, Spain
Abstract:The study of hydrogeochemical data sets frequently calls for statistical dimension reducing techniques. It is well known that hydrochemical parameters are compositions and, for this type of data, the direct application of classical statistical methods based on the correlation matrix yield spurious results. But new results on compositional data analysis have identified the sampling space, the simplex, with an Euclidean space, a fact that allows us to define a simplicial factor analysis strategy, thus overcoming the problem. For illustration, we use samples from the Llobregat River and its tributaries (NE Spain). Three unobservable or latent factorial components are extracted, which are identified with pristine waters, potash-mining influence and urban sewage influence. These three factorial components or compositional factors are plotted in a factorial ternary diagram, which reflects the relative influence of each one of these factors on each observation.
Keywords:biplot  isometric log-ratio coordinates  end-member  orthonormal basis  river pollution
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