Towards the Concept of Background/baseline Compositions: A Practicable Path?

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 187)


Water geochemistry is often investigated considering a large number of variables, including major, minor and trace elements. Some of these are usually well associated due to coherent geochemical behaviour, but the effect of anthropic factors tends to increase data variability, sometimes obscuring the natural laws governing their relationships. It may thus be difficult to identify geochemical features linked to natural phenomena, as well as to separate geogenic anomalies from the anthropogenic ones, or to define background or baseline concentrations for single chemical elements. This is particularly true at regional level, where numerous phenomena may interact and mix together, forming a complex pattern not easy to interpret. The identification of background or baseline values is particularly difficult due to the compositional nature of chemical variables, so that under the Compositional Data Analysis (CoDA) theory single background or baseline values lose their meaning. However, they are fundamental references for public institutions and government policies. In this contribution a new approach is proposed, aimed at investigating the regionalised structure of the geochemical data by considering the joint behaviour of several chemical elements. The approach is based on the robust CoDA theory, so that the proportionality features of abundance data are fully taken into account, enhancing their relative multivariate behaviour, as well as the influence of outliers. An application example is presented for the groundwater compositions in Tuscany Region, a surface of about 23,000 km\(^2\), where more than 6000 wells have been sampled and analysed. The mapping of robust Mahalanobis distance was able to indicate (1) in which part of the investigated area the pressure toward anomalous behaviour was higher, (2) where the compositions nearest to the barycentre were and (3) if spatial continuity was present in limited portions of the territory.


Water chemistry Compositional data analysis Baseline Fractals Dissipative structures 


  1. 1.
    Agterberg, F.P.: Geomathematics: Theoretical Foundations, Applications and Future Developments.Springer Series in Quantitative Geology and Geostatistics, vol. 18 (2014)Google Scholar
  2. 2.
    Agterberg, F.P.: Mixtures of multiplicative cascade models in geochemistry. Nonlinear Process. Geophys. 14, 201–209 (2007)CrossRefGoogle Scholar
  3. 3.
    Aitchison, J.: The Statistical Analysis of Compositional Data (Reprinted in 2003 by The Blackburn Press), p. 416. Chapman & Hall Ltd., London (UK) (1986)Google Scholar
  4. 4.
    Aitchison, J.: The statistical analysis of compositional data (with discussion). J. Roy. Stat. Soc. Ser. B-Stat. Methodol. 44(2), 139–177 (1982)Google Scholar
  5. 5.
    Buccianti, A., Egozcue, J.J., Pawlowsky-Glahn, V.: Variation diagrams to statistically model the behaviour of geochemical variables: theory and applications. J. Hydrol. 519(PA), 988–998 (2014)Google Scholar
  6. 6.
    Buccianti, A., Magli, R.: Metric concepts and implications in describing compositional changes for world rivers water chemistry. Comput. Geosci. 37(5), 670–676 (2011)Google Scholar
  7. 7.
    Buccianti, A.: Is compositional data analysis a way to see beyond the illusion?. Comput. Geosci. 50, 165–173 (2013)Google Scholar
  8. 8.
    Buccianti, A., Gallo, M.: Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy). Environmetrics 24, 269–277 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Buccianti, A., Grunsky, E.: Compositional data analysis in geochemistry: are we sure to see what really occurs during natural processes? J. Geochem. Explor. 14, 1–5 (2014)CrossRefGoogle Scholar
  10. 10.
    Carmignani L., Conti P., Cornamusini G., Meccheri M.: The internal northern Apennines, the northern tyrrhenian sea and the Sardinia-Corsica block. In: Geology of Italy. Italian Geological Society Bulletin IGC32 Florence-2004, pp. 59–77 (2004)Google Scholar
  11. 11.
    Daszykowski, M., Kaczmarek, K., Vander Heyden, Y., Walczak, B.: Robust statistic in data analysis. A review. Basic concept. Chemometr. Intell. Lab. Syst. 85, 203–219 (2007)CrossRefGoogle Scholar
  12. 12.
    De Caritat, P., Grunsky, E.: Defining element associations and inferring geological processes from total element concentrations in Australia catchment outlet sediments: Multivariate analysis of continental-scale geochemical data. Appl. Geochem. 33, 104–126 (2013)CrossRefGoogle Scholar
  13. 13.
    Egozcue, J.J., Pawlowsky-Glahn, V.: Simplicial geometry for compositional data. In: Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V. (eds.) Compositional Data Analysis in the Geosciences: From Theory to Practice. Special Publication, vol. 264, pp. 12–28. Geological Society, London (2006)Google Scholar
  14. 14.
    Egozcue, J.J., Pawlowsky-Glahn, V.: Groups of parts and their balances in compositional data analysis. Math. Geol. 37(7), 795–828 (2005)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barcelo-Vidal, C.: Isometric logratio transformations for compositional data analysis. Math. Geol. 35(3), 279–300 (2003)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Filzmoser, P., Hron, K., Reimann, C.: Interpretation of multivariate outliers for compositional data. Comput. Geosci. 39, 77–85 (2012)Google Scholar
  17. 17.
    Filzmoser, P., Hron, K.: Outlier detection for compositional data using robust methods. Math. Geosci. 40(3), 233–248 (2008)CrossRefMATHGoogle Scholar
  18. 18.
    Filzmoser, P., Hron, K., Reimann, C.: Univariate statistical analysis of environmental (compositional) data: problems and possibilities. Sci. Total Environ. 407, 6100–6108 (2009)CrossRefGoogle Scholar
  19. 19.
    Filzmoser, P., Hron, K., Reimann, C.: Principal component analysis for compositional data with outliers. Environmetrics 20(6), 621–632 (2009)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Galuszka, A.: A review of geochemical background concepts and an example using data from Poland. Environ. Geol. 52, 861–870 (2007)Google Scholar
  21. 21.
    Garrett, R.G.: The chi-square plot: a tool for multivariate outlier recognition. J. Geochem. Explor. 32, 319–341 (1989)CrossRefGoogle Scholar
  22. 22.
    Goncalves, M.A.: Characteriszation of geochemical distributions using multifractals models. Math. Geosci. 33, 41–61 (2001)Google Scholar
  23. 23.
    Hunt, A.G., Ghanbarian, B., Skinner, T.E., Ewing, R.P.: Scaling of geochemical reaction rates via advective solute transport. Chaos 25(075403), 1–15 (2015)Google Scholar
  24. 24.
    Kondepudi, D., Prigogine, I.: Modern Thermodynamics. From Heat Engines to Dissipative Structures. Wiley (1998)Google Scholar
  25. 25.
    Ma, T., Li, C., Lu, Z.: Estimating the average concentration of minor and trace elements in surficial sediments using fractal methods. J. Geochem. Explor. 139, 207–216 (2014)CrossRefGoogle Scholar
  26. 26.
    Maronna, R.A., Zamar, R.H.: Robust multivariate estimates for highdimensional datasets. Technometrics 44, 307–317 (2002)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Matschullat, J., Ottenstein, R., Reimann, C.: Geochemical background can we calculate it? Environ. Earth Sci. 39(9), 990–1000 (2000)Google Scholar
  28. 28.
    Nieto, P., Custodio, E., Manzano, M.: Baseline groundwater quality: a European approach. Environ. Sci. Policy 8, 399–409 (2005)Google Scholar
  29. 29.
    Nisi, B., Buccianti, A., Raco, B., Battaglini, R.: Analysis of complex regional databases and their support in the identification of background/baseline compositional facies in groundwater investigation: developments and application examples. J. Geochem. Explor. 164, 3–17 (2016)CrossRefGoogle Scholar
  30. 30.
    Nordstrom, D.K.: Baseline and premining geochemical characterization of mined sites. Appl. Geochem. 57, 17–34 (2015)Google Scholar
  31. 31.
    R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0 (2015).
  32. 32.
    Raco, B., Buccianti, A., Corongiu, M., Lavorini, G., Macera, P., Manetti, F., Mari, R., Masetti, G., Menichetti, S., Nisi, B., Protano, G., Romanelli, S.: The geochemical database of Tuscany Region (Italy). Ital. J. Groundwater AS12055, 007–018 (2015). doi:10.7343/AS-100-15-0127
  33. 33.
    Reimann, C., Garrett, R.G.: Geochemical background concept and reality. Sci. Total Environ. 350, 12–27 (2005)Google Scholar
  34. 34.
    Rousseeuw, P.J.: Least median of squares regression. J. Am. Stat. Assoc. 79, 871–880 (1984)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    UN-Water: Annual report: Available via DIALOG. (2011). Accessed 15 Jan 2016
  36. 36.
    Verboven, S., Hubert, M.: LIBRA: a MATLAB libray for robust analysis. Chemometr. Intell. Lab. Syst. 75, 127–136 (2005)CrossRefGoogle Scholar
  37. 37.
    West, L.J., Odling, N.E.: Groundwater. In: Holden, J. (ed.) Water Resources. An Integrated Approach. Routledge, Taylor & Francis Group (2014)Google Scholar
  38. 38.
    World Health Organisation (WHO): Our plane, our health. Report of WHO Commission on Health and Environment, Geneva, World Health Organisaton (1992)Google Scholar
  39. 39.
    Xu, W., Du, S.: Information entropy evolution for groundwater flow system: a case study of artificial recharge in Shijiazhuang city, China. Entropy 16, 4408–4419 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Earth SciencesUniversity of FlorenceFirenzeItaly
  2. 2.CNR-IGG (Institute of Geosciences and Earth Resources)PisaItaly

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