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ThiÃ³ i FernÃ¡ndez de Henestrosa, Santiago
MartÃn FernÃ¡ndez, Josep Antoni 

Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Otero PÃ©rez, Neus
Tolosana Delgado, Raimon Soler i Gil, Albert 

2003 October 16  
Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing models
between endmembers. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the endmember problem in a compositional framework.
We present here a possible solution based on factor analysis of compositions illustrated with a case study.
We find two factors on the compositional biplot fitting two noncentered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables that
lay nearest to it. With each subcomposition a logcontrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric logratio coordinates (ilr) of three hidden
components, that can be plotted in a ternary diagram. These hidden components might be interpreted as endmembers.
We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a biplot with a 57% of explained total
variance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphical
representation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysis
of diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, except
fertilisers due to the heterogeneity of their composition.
This approach is a useful tool to distinguish endmembers, and characterise them, an issue generally difficult to solve. It is worth note that the endmember composition cannot be fully estimated but only characterised through logratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations are
intrinsic to the relative nature of compositional data Geologische Vereinigung; Universitat de Barcelona, Equip de Recerca ArqueomÃ¨trica; Institut dâ€™EstadÃstica de Catalunya; International Association for Mathematical Geology; Patronat de lâ€™Escola PolitÃ¨cnica Superior de la Universitat de Girona; FundaciÃ³ privada: Girona, Universitat i Futur. 

application/pdf  
Otero, O.; Tolosana Delgado, R.; Soler i Gil, A. â€™A factor analysis of hidrochemical composition of Llobregat river basinâ€™ a CODAWORKâ€™03. Girona: La Universitat, 2003 [consulta: maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/678  
848458111X  
http://hdl.handle.net/10256/678  
eng  
Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Tots els drets reservats  
Hidrogeologia  MÃ¨todes estadÃstics
Aigua  QuÃmica Llobregat (Catalunya : Curs dâ€™aigua) 

A Factor analysis of hidrochemical composition of Llobregat river basin  
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