Mathematical Geosciences

, Volume 48, Issue 2, pp 163–186 | Cite as

Study of Water Quality in a Spanish River Based on Statistical Process Control and Functional Data Analysis

  • J. Sancho
  • C. IglesiasEmail author
  • J. Piñeiro
  • J. Martínez
  • J. J. Pastor
  • M. Araújo
  • J. Taboada
Special Issue


The control of chemical and physicochemical properties of water bodies is essential to guarantee a proper environment, not only for the species of a certain habitat, but also for human health. In this sense, the study of pollution and its variability can be assimilated to the detection of outliers (anomalous values that indicate the deviation of the measured variable compared to the defined objectives). In this paper, two methods have been used and compared for detecting outliers: statistical process control and functional data analysis (FDA). These techniques have been tested on three key water quality variables: turbidity, electrical conductivity and dissolved oxygen. Data were continuously recorded in 2008 using an automatic monitoring station located in the Ebro River (NE Spain). The results of the research show FDA as a powerful tool for this kind of study, since it takes into account the time correlation structure of the data. This research is focused on an essential natural resource, water. The study intends to provide analysts with a methodology for detecting anomalous values (possible pollution episodes) within a large dataset of measurements. The collection of information of natural resources is a basic task for their management and control, but the analysis of gathered data is frequently difficult due to the vast number of measurements taken in the field. This work is focused on water, but the methodologies presented here can be applied to other natural data. Thus, geoscientists and geoengineers might find this research useful for interpreting many kinds of data and detecting anomalous episodes among them with an objective approach.


Functional data analysis Statistical process control Water quality Outlier Water quality monitoring 



The authors would like to thank the Ebro Hydrographic Confederation for their collaboration in the study. C. Iglesias acknowledges the Spanish Ministry of Education, Culture and Sport for the FPU 12/02283 grant. J. Martínez acknowledges the Spanish Ministry of Economy and Competitiveness for the ECO 2011-22650 project. The University of Vigo supports J. Piñeiro’s research through a predoctoral contract (2014).


  1. Aitchison J (1986) The statistical analysis of compositional data. Chapman and Hall, London, New YorkCrossRefGoogle Scholar
  2. Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc Ser B Stat Methodol 26:211–252Google Scholar
  3. Camas-Anzueto JL, Gómez-Valdéz JA, Meza-Gordillo R et al (2015) Sensitive layer based on lophine and calcium hydroxide for detection of dissolved oxygen in water. Measurement. doi: 10.1016/j.measurement.2015.02.015
  4. Caulcutt R (2004) Control charts in practice. Significance 1:81–84CrossRefGoogle Scholar
  5. Champ CW, Woodall WH (1987) Exact results for Shewhart control charts with supplementary runs rules. Technometrics 29:393–399CrossRefGoogle Scholar
  6. Chen Y-K (2003) An evolutionary economic-statistical design for VSI X control charts under non-normality. Int J Adv Manuf Technol 22:602–610. doi: 10.1007/s00170-003-1612-3 CrossRefGoogle Scholar
  7. Chong CS, Colbow K (1976) Light scattering and turbidity measurements on lipid vesicles. Biochim Biophys Acta Biomembr 436:260–282. doi: 10.1016/0005-2736(76)90192-9 CrossRefGoogle Scholar
  8. Council of the European Union (1975) Council Directive 75/440/EEC of 16 June 1975 concerning the quality required of surface water intended for the abstraction of drinking water in the Member States. Off J Eur Commun L194:26–31Google Scholar
  9. Council of the European Union (1979) Council Directive 79/869/EEC of 9 October 1979 concerning the methods of measurement and frequencies of sampling and analysis of surface water intended for the abstraction of drinking water in the Member States. Off J Eur CommunL271:44–53Google Scholar
  10. Council of the European Union (1998) Council Directive 98/83/EC of 3 November 1998 on the quality of water intended for human consumption. Off J Eur Commun L330:32–54Google Scholar
  11. Crivineanu MF, Perju DS, Dumitrel GA (2012) Mathematical Models Describing the Relations between Surface Waters Parameters and Iron Concentration. Chem Bullet “Politehnica” Univ. (Timisoara) 57:23–28Google Scholar
  12. Cuevas A (2014) A partial overview of the theory of statistics with functional data. J Stat Plan Inference 147:1–23. doi: 10.1016/j.jspi.2013.04.002 CrossRefGoogle Scholar
  13. Cuevas A, Febrero M, Fraiman R (2006) On the use of the bootstrap for estimating functions with functional data. Comput Stat Data Anal 51:1063–1074. doi: 10.1016/j.csda.2005.10.012 CrossRefGoogle Scholar
  14. Cuevas A, Fraiman R (1997) A plug-in approach to support estimation. Ann Stat 25:2300–2312CrossRefGoogle Scholar
  15. Díaz Muñiz C, García-Nieto PJ, Alonso Fernández JR et al (2012) Detection of outliers in water quality monitoring samples using functional data analysis in San Esteban estuary (Northern Spain). Sci Total Environ 439:54–61CrossRefGoogle Scholar
  16. Ebro hydrological confederation (2008). Accessed 12 Jun 2014
  17. Egborge ABM, Benka-Coker J (1986) Water quality index: application in the Warri River, Nigeria. Environ Pollut Ser B Chem Phys 12:27–40. doi: 10.1016/0143-148X(86)90004-2 CrossRefGoogle Scholar
  18. Elskens M, de Brauwere A, Beucher C et al (2007) Statistical process control in assessing production and dissolution rates of biogenic silica in marine environments. Mar Chem 106:272–286. doi: 10.1016/j.marchem.2007.01.008 CrossRefGoogle Scholar
  19. European Parliament and the Council (2000) Directive 2000/60/EC of the European Parliament and of the Council of 23 October 2000 establishing a framework for Community action in the field of water policyGoogle Scholar
  20. Febrero M, Galeano P, González-Manteiga W (2008) Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels. Environmetrics 19:331–345. doi: 10.1002/env.878 CrossRefGoogle Scholar
  21. Fernández N, Ramírez A, Solano F (2004) Physico chemical water quality indices—a comparative review. Rev la Fac Ciencias Básicas 2:13Google Scholar
  22. Fraiman R, Muniz G (2001) Trimmed means for functional data. Test 10:419–440CrossRefGoogle Scholar
  23. Freeman J, Modarres R (2006) Inverse Box–Cox: the power-normal distribution. Stat Probab Lett 76:764–772. doi: 10.1016/j.spl.2005.10.036 CrossRefGoogle Scholar
  24. General Directorate of Urban Planning (2008) Land-use planning in Zaragoza, ZaragozaGoogle Scholar
  25. Grant EL, Leavenworth RS (1998) Statistical quality control. McGraw-Hill, New YorkGoogle Scholar
  26. Hofer V (2011) Functional methods for classification of different petrographic varieties by means of reflectance spectra. Math Geosci 43:165–181. doi: 10.1007/s11004-011-9317-x CrossRefGoogle Scholar
  27. Iglesias C, Sancho J, Piñeiro JI et al (2015) Shewhart-type control charts and functional data analysis for water quality analysis based on a global indicator. Desalin Water Treat 1–16: doi: 10.1080/19443994.2015.1029533
  28. Jethra R (1993) Turbidity measurement. ISA Trans 32:397–405. doi: 10.1016/0019-0578(93)90075-8 CrossRefGoogle Scholar
  29. Koutras MV, Bersimis S, Maravelakis PE (2007) Statistical process control using Shewhart control charts with supplementary runs rules. Methodol Comput Appl Probab 9:207–224. doi: 10.1007/s11009-007-9016-8 CrossRefGoogle Scholar
  30. Liou SM, Lo SL, Wang SH (2004) A generalized water quality index for Taiwan. Environ Monit Assess 96:35–52. doi: 10.1023/B:EMAS.0000031715.83752.a1 CrossRefGoogle Scholar
  31. Martínez J, Saavedra Á, García-Nieto PJ et al (2014) Air quality parameters outliers detection using functional data analysis in the Langreo urban area (Northern Spain). Appl Math Comput 241:1–10. doi: 10.1016/j.amc.2014.05.004 CrossRefGoogle Scholar
  32. Martínez J, Garcia-Nieto PJ, Alejano L, Reyes AN (2011) Detection of outliers in gas emissions from urban areas using functional data analysis. J Hazard Mater 186:144–149. doi: 10.1016/j.jhazmat.2010.10.091 CrossRefGoogle Scholar
  33. Montgomery D (2009) Introduction to statistical quality control, 6th edn. Wiley, New YorkGoogle Scholar
  34. Moore RD, Richards G, Story A (2008) Electrical conductivity as an indicator of water chemistry and hydrologic process. Streamline Watershed Manag Bull 11:25–29Google Scholar
  35. Ollero A, Sánchez M, Losada JA, Hernández C (2004) El comportamiento hídrico del río Ebro en su recorrido por Aragón. In: Peña JL, Longares LA, Sánchez M (eds) Geogr. Física Aragón. Asp. Gen. y temáticos. University of Zaragoza and Fernando El Católico Institution, Zaragoza, pp 243–252Google Scholar
  36. Pawlowsky-Glahn V, Buccianti A (2011) Compositional data analysis: theory and applications. Wiley, New YorkCrossRefGoogle Scholar
  37. Pawlowsky-Glahn V, Egozcue JJ, Tolosana-Delgado R (2015) Modeling and analysis of compositional data. Wiley, New YorkGoogle Scholar
  38. Pesce S, Wunderlin DA (2000) Use of water quality indices to verify the impact of Córdoba City (Argentina) on Suquía River. Water Res 34:2915–2926. doi: 10.1016/S0043-1354(00)00036-1 CrossRefGoogle Scholar
  39. Pyzdek T (2003) The Six Sigma handbook. Search. doi: 10.1036/0071415963 Google Scholar
  40. Quintela-del-Río A, Ferraty F, Vieu P(2011) Analysis of time of occurrence of earthquakes: a functional data approach. Math Geosci 43:695–719. doi: 10.1007/s11004-011-9349-2
  41. Ramsay JO, Silverman BW (2005) Functional data analysis. Spinger, New YorkCrossRefGoogle Scholar
  42. Sánchez E, Colmenarejo MF, Vicente J et al (2007) Use of the water quality index and dissolved oxygen deficit as simple indicators of watersheds pollution. Ecol Indic 7:315–328. doi: 10.1016/j.ecolind.2006.02.005 CrossRefGoogle Scholar
  43. Sancho J, Martínez J, Pastor JJ et al (2014a) New methodology to determine air quality in urban areas based on runs rules for functional data. Atmos Environ 83:185–192. doi: 10.1016/j.atmosenv.2013.11.010
  44. Sancho J, Pastor J, Martínez J, García MA (2014b) Variability analysis by statistical control process and functional data analysis—case of study applied to power system harmonics assessment. Key Eng Mater 615:118–123. doi: 10.4028/
  45. Sancho J, Pastor JJ, Martínez J, García MA (2013) Evaluation of harmonic variability in electrical power systems through statistical control of quality and functional data analysis. Procedia Eng 63:295–302. doi: 10.1016/j.proeng.2013.08.224 CrossRefGoogle Scholar
  46. Santoso S, Sabin DD, McGranaghan MF (2008) Evaluation of harmonic trends using statistical process control methods. In: 2008 IEEE/PES transmission and distribution conference and exposition. IEEE, pp 1–6Google Scholar
  47. Sarala Thambavani D, Uma Mageswari TSR (2013) Water quality indices as indicators for potable water. Desalin Water Treat 52:4772–4782. doi: 10.1080/19443994.2013.834517 CrossRefGoogle Scholar
  48. Shewhart WA (1931) Economic control of quality of manufactured product. Van Nostrand Company, New YorkGoogle Scholar
  49. Smith VH, Schindler DW (2009) Eutrophication science: where do we go from here? Trends Ecol Evol 24:201–7. doi: 10.1016/j.tree.2008.11.009 CrossRefGoogle Scholar
  50. Smith VH, Tilman GD, Nekola JC (1999) Eutrophication: impacts of excess nutrient inputs on freshwater, marine, and terrestrial ecosystems. Environ Pollut 100:179–196. doi: 10.1016/S0269-7491(99)00091-3 CrossRefGoogle Scholar
  51. Thomann M, Rieger L, Frommhold S et al (2002) An efficient monitoring concept with control charts for on-line sensors. Water Sci Technol 46(4–5):107–116Google Scholar
  52. Western Electric (1956) Statistical quality control handbook. Western Electric Corporation, IndianapolisGoogle Scholar
  53. Wheeler DJ, Chambers DS (1992) Understanding statistical process control, 2nd edn. SPC Press, KnoxvilleGoogle Scholar
  54. Woodall WH (2000) Controversies and contradictions in statistical process control—response. J Qual Technol 32:341–350Google Scholar
  55. Zhang S, Wu Z (2005) Designs of control charts with supplementary runs rules. Comput Ind Eng 49:76–97. doi: 10.1016/j.cie.2005.02.002 CrossRefGoogle Scholar
  56. Zimmerman SM, Brown LD, Brown SS (1992) Using the theory of runs in a biomedical application. In: Annual quality congress transactions. ASQC, pp 903–908Google Scholar
  57. Zuo Y, Serfling R (2000) General notions of statistical depth function. Ann Stat 28:461–482CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  1. 1.Centro Universitario de la Defensa, Zaragoza, Academia General MilitarZaragozaSpain
  2. 2.Department of Natural Resources and Environmental EngineeringUniversity of VigoVigoSpain

Personalised recommendations