Environmental and Ecological Statistics

, Volume 21, Issue 3, pp 565-581

First online:

Three-way compositional analysis of water quality monitoring data

  • Mark A. EngleAffiliated withUS Geological SurveyDepartment of Geological Sciences, University of Texas Email author 
  • , Michele GalloAffiliated withDepartment of Human and Social Sciences, University of Naples “L’Orientale”
  • , Karl T. SchroederAffiliated withNational Energy Technology Laboratory, US Department of Energy
  • , Nicholas J. GeboyAffiliated withUS Geological Survey
  • , John W. ZupancicAffiliated withBeneTerra, LLC

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Water quality monitoring data typically consist of \(J\) parameters and constituents measured at \(I\) number of static locations at \(K\) sets of seasonal occurrences. The resulting \(I \times J \times K\) three-way array can be difficult to interpret. Additionally, the constituent portion of the dataset (e.g., major ion and trace element concentration, pH, etc.) is compositional in that it sums to a constant (e.g., 1 kg/L) and is mathematically confined to the simplex, the sample space for compositional data. Here we apply a Tucker3 model on centered log-ratio data to find low dimensional representation of latent variables as a means to simplify data processing and interpretation of three years of seasonal compositional groundwater chemistry data for 14 wells at a study site in Wyoming, USA. The study site has been amended with treated coalbed methane produced water, using a subsurface drip irrigation system, to allow for irrigation of forage crops. Results from three-way compositional data analysis indicate that primary controls on water quality at the study site include: solutes concentration by evapotranspiration, cation exchange, and dissolution of native salts. These findings agree well with results from more detailed investigations of the site. In addition, the model identified Ba uptake during gypsum precipitation in some portions of the site during the final 6–9 months of investigation, a process for which the timing and extent had not previously been identified. These results suggest that multi-way compositional analyses hold promise as a means to more easily interpret water quality monitoring data.


Coalbed natural gas Log-ratio Multi-mode analysis Powder River Basin Produced waters Tucker3