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Three-way compositional analysis of water quality monitoring data

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Abstract

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.

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References

  • Aitchison J (1982) The statistical analysis of compositional data. J R Stat Soc B Methodol 44:139–177

    Google Scholar 

  • Aitchison J (1986) The statistical analysis of compositional data. Chapman & Hall, London. Reprinted in 2003 with additional material by Blackburn Press

  • Aitchison J, Greenacre M (2002) Biplots of compositional data. J R Stat Soc C Appl Stat 51:375–392

    Article  Google Scholar 

  • Astel A, Simeonov V, Bauer H, Puxbaum H (2010) Multidimensional modeling of aerosol monitoring data. Environ Pollut 158:3201–3208

    Article  CAS  PubMed  Google Scholar 

  • Bern CR, Boehlke AR, Engle MA et al (2013a) Shallow groundwater and soil chemistry response to 3 years of subsurface drip irrigation using coalbed natural gas produced water. Hydrogeol J 21:1803–1820

    Google Scholar 

  • Bern CR, Breit GN, Healy RW et al (2013b) Deep subsurface drip irrigation using coal-bed sodic water: Part I. Water and solute movement. Agric Water Manag 118:122–134

    Article  Google Scholar 

  • Buccianti A, Pawlowsky-Glahn V (2005) New perspectives on water chemistry and compositional data analysis. Math Geol 37:703–727

    Article  CAS  Google Scholar 

  • Carroll JD, Chang J-J (1970) Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart–Young” decomposition. Psychometrika 35:283–319

    Article  Google Scholar 

  • Daunis-i-Estadella J, Thió-Henestrosa S, Mateu-Figueras G (2011) Including supplementary elements in a compositional biplot. Comput Geosci 37:696–701

    Article  CAS  Google Scholar 

  • Egozcue J, Pawlowsky-Glahn V, Mateu-Figueras G, Barceló-Vidal C (2003) Isometric logratio transformations for compositional data analysis. Math Geol 35:279–300

    Article  Google Scholar 

  • Engle MA, Bern CR, Healy RW et al (2011) Tracking solutes and water from subsurface drip irrigation application of coalbed methane-produced waters, Powder River Basin, Wyoming. Environ Geosci 18:169–187

    Article  Google Scholar 

  • Engle MA, Rowan EL (2013) Interpretation of Na–Cl–Br systematics in sedimentary basin brines: comparison of concentration, element ratio, and isometric log-ratio approaches. Math Geosci 45:87–101

    Article  CAS  Google Scholar 

  • Gallo M (2012) CoDa in three-way arrays and relative sample spaces. Electron J Appl Stat Anal 5:400–405

    Google Scholar 

  • Gallo M (2013a) Tucker3 analysis for compositional data. Commun Stat A Theor (in press)

  • Gallo M (2013b) Log-ratio and parallel factor analysis: an approach to analyze threeway compositional data. In: Proto AN, Squillante M, Kacpzyk J (eds) Advanced dynamic modeling of economic and social systems. Springer, Berlin, pp 209–221

    Chapter  Google Scholar 

  • Gallo M, Buccianti A (2013) Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy). Environmet 24:269–277

    Article  CAS  Google Scholar 

  • Ganjegunte GK, King LA, Vance GF (2008) Cumulative soil chemistry changes from land application of saline–sodic waters. J Environ Qual 37:S128–S138

    Article  PubMed  Google Scholar 

  • Geboy NJ, Engle MA, Schroeder KT, Zupancic JW (2011) Summary of inorganic compositional data for groundwater, soil-water, and surface-water samples at the Headgate Draw subsurface drip irrigation site, Johnson County. Wyoming. U.S. Geological Survey Data Series 619

  • Hanor JS (2000) Barite–celestine geochemistry and environments of formation. Rev Miner Geochem 40:193–275

    Article  CAS  Google Scholar 

  • Harshman RA (1970) Foundations of the PARAFAC procedure: models and conditions for an “explanatory” multimodal factor analysis. University of California at Los Angeles working papers in phonetics 16

  • Hirsch RM, Slack JR, Smith RA (1982) Techniques of trend analysis for monthly water quality data. Water Resour Res 18:107–121

    Article  Google Scholar 

  • Jackson RE, Reddy KJ (2007) Geochemistry of coalbed natural gas (CBNG) produced water in Powder River Basin, Wyoming: salinity and sodicity. Water Air Soil Pollut 184:49–61

    Article  CAS  Google Scholar 

  • Kroonenberg PM (2008) Applied multiway data analysis. Wiley-Interscience, London

    Book  Google Scholar 

  • Mateu-Figueras G, Pawlowsky-Glahn V, Egozcue JJ (2011) The principle of working on coordinates. In: Pawlowsky-Glahn V, Buccianti A (eds) Compositional data analysis: theory and applications. Wiley, London, pp 31–42

  • Minsley BJ, Smith BD, Hammack R et al (2012) Calibration and filtering strategies for frequency domain electromagnetic data. J Appl Geophys 80:56–66

    Article  Google Scholar 

  • Otero N, Tolosana-Delgado R, Soler A et al (2005) Relative vs. absolute statistical analysis of compositions: a comparative study of surface waters of a Mediterranean river. Water Res 39:1404–1414

    Article  CAS  PubMed  Google Scholar 

  • Pawlowsky-Glahn V, Egozcue JJ (2001) Geometric approach to statistical analysis on the simplex. Stoch Environ Res Risk A 15:384–398

    Article  Google Scholar 

  • Pawlowsky-Glahn V, Egozcue JJ (2006) Compositional data and their analysis: an introduction. Geol Soc Lond (special publications) 264:1–10

    Article  CAS  Google Scholar 

  • Reimann C, Filzmoser P, Garrett RG (2002) Factor analysis applied to regional geochemical data: problems and possibilities. Appl Geochem 17:185–206

    Article  CAS  Google Scholar 

  • Rice CA, Ellis M, Bullock J (2000), Water co-produced with coalbed methane in the Powder River Basin, Wyoming: preliminary compositional data. USGS open-file report 00-372

  • Sams JI, Smith BD, Veloski G, et al. (2010) Third year of subsurface drip irrigation monitoring using GEM2 electromagnetic surveys, Powder River Basin, Wyoming. In: Symposium on the application of geophysics to engineering and environmental problems (SAGEEP) 2010. Keystone, Colorado, p 9

  • Singh K, Malik A, Sinha S et al (2007) Exploring groundwater hydrochemistry of alluvial aquifers using multi-way modeling. Anal Chim Acta 596:171–182

    Article  CAS  PubMed  Google Scholar 

  • Smilde AK, Bro R, Geladi P (2004) Multi-way analysis with applications in the chemical sciences. Wiley, Chichester

    Book  Google Scholar 

  • Tucker L (1966) Some mathematical notes on three-mode factor analysis. Psychometrika 31:279–311

    Article  CAS  PubMed  Google Scholar 

  • Ward RC, Loftis JC, McBride GB (1986) The “data-rich but information-poor” syndrome in water quality monitoring. Environ Manag 10:291–297

    Google Scholar 

  • U.S. Energy, Information Administration (2012) Annual energy outlook 2012

  • Yli-Tuomi T, Hopke P, Paatero P et al (2003) Atmospheric aerosol over Finnish Arctic: source analysis by the multilinear engine and the potential source contribution function. Atmos Environ 37:4381–4392

    Article  CAS  Google Scholar 

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Acknowledgments

Funding for this project was provided by the U.S. Department of Energy (DOE), U.S. Geological Survey Energy Resources Program and by ex-60 % 2011 funds of the University of Naples—“L’Orientale” (I). Thoughtful review and comment on an earlier version of this paper were provided by Carl Bern (USGS). Assistance with sampling logistics and analytical results were provided by Adam Quist (BeneTerra), Carol Cardone (National Energy Technology Laboratory [NETL]), and Kristen Carlisle (NETL).

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Correspondence to Mark A. Engle.

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Handling Editor: Pierre Dutilleul.

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Engle, M.A., Gallo, M., Schroeder, K.T. et al. Three-way compositional analysis of water quality monitoring data. Environ Ecol Stat 21, 565–581 (2014). https://doi.org/10.1007/s10651-013-0268-x

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  • DOI: https://doi.org/10.1007/s10651-013-0268-x

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