Water Resources Management

, Volume 33, Issue 2, pp 739–755 | Cite as

Pattern Detection and Scaling Laws of Daily Water Demand by SOM: an Application to the WDN of Naples, Italy

  • Roberta PadulanoEmail author
  • Giuseppe Del Giudice


In the present paper, a novel method is provided to detect significant daily consumption patterns and to obtain scaling laws to predict consumption patterns for groups of homogeneous users. The first issue relies on the use of Self-Organizing Map to gain insights about the initial assumption of distinct homogeneous consumption groups and to find additional clusters based on calendar dates. Non-dimensional pattern detection is performed on both residential and non-residential connections, with data provided by one-year measurements of a large-size smart water network placed in Naples (Italy). The second issue relies on the use of the variance function to explain the dependence of aggregated variance on the mean and on the number of aggregated users. Equations and related parameters’ values are provided to predict mean dimensional daily patterns and variation bands describing water consumption of a generic set of aggregated users.


Pattern detection Scaling laws Self-organizing map Variance function Water demand patterns 



The Authors would like to thank ABC Acqua Bene Comune – Napoli, who installed the telemetry system and provided for consumption data.

Compliance with Ethical Standards

Conflict of interests

There is no conflict of interest.


  1. Adamowski J, Fung Chan H, Prasher SO, Ozga-Zielinski B, Sliusarieva A (2012) Comparison of multiple linear and nonlinear regression, autoregressive integrated moving average, artificial neural network, and wavelet artificial neural network methods for urban water demand forecasting in Montreal, Canada. Water Resour Res 48(1):W01528CrossRefGoogle Scholar
  2. Alvisi S, Franchini M, Marinelli A (2007) A short-term, pattern-based model for water-demand forecasting. J Hydroinformatics 9(1):39–50CrossRefGoogle Scholar
  3. Alvisi S, Ansaloni N, Franchini M (2015) Five variants of a procedure for spatial aggregation of synthetic water demand time series. J Water Supply Res Technol 64(5):629–639CrossRefGoogle Scholar
  4. Bennett C, Stewart RA, Beal CD (2013) ANN-based residential water end-use demand forecasting model. Expert Syst Appl 40(4):1014–1023CrossRefGoogle Scholar
  5. Buchberger SG, Nadimpalli G (2004) Leak estimation in water distribution systems by statistical analysis of flow readings. J Water Resour Plan Manag 130(4):321–329CrossRefGoogle Scholar
  6. Buchberger SG, Wu L (1995) Model for instantaneous residential water demands. J Hydraul Eng 121(3):232–246CrossRefGoogle Scholar
  7. Cardell-Oliver R (2013) Water use signature patterns for analyzing household consumption using medium resolution meter data. Water Resour Res 49(12):8589–8599CrossRefGoogle Scholar
  8. Cheifetz N, Noumir Z, Samé A, Sandraz AC, Féliers C, Heim V (2017) Modeling and clustering water demand patterns from real-world smart meter data. Drinking Water Engineering and Science 10(2):75–82CrossRefGoogle Scholar
  9. Chen J, Boccelli D (2014) Demand forecasting for water distribution systems. Procedia Engineering 70:339–342CrossRefGoogle Scholar
  10. Cole G, Stewart RA (2013) Smart meter enabled disaggregation of urban peak water demand: precursor to effective urban water planning. Urban Water J 10(3):174–194CrossRefGoogle Scholar
  11. Cominola A, Giuliani M, Piga D, Castelletti A, Rizzoli AE (2015) Benefits and challenges of using smart meters for advancing residential water demand modeling and management: a review. Environ Model Softw 72:198–214CrossRefGoogle Scholar
  12. Davidian M, Carroll RJ (1987) Variance function estimation. J Am Stat Assoc 82(400):1079–1091CrossRefGoogle Scholar
  13. Firat M, Turan ME, Yurdusev MA (2010) Comparative analysis of neural network techniques for predicting water consumption time series. J Hydrol 384(1–2):46–51CrossRefGoogle Scholar
  14. Fontanazza CM, Notaro V, Puleo V, Freni G (2016) Multivariate statistical analysis for water demand modelling: implementation, performance analysis, and comparison with the PRP model. J Hydroinformatics 18(1):4–22CrossRefGoogle Scholar
  15. Gargano R, Tricarico C, Del Giudice G, Granata F (2016) A stochastic model for daily residential water demand. Water Sci Technol Water Supply 16(6):1753–1767CrossRefGoogle Scholar
  16. Ghavidelfar S, Shamseldin AY, Melville BW (2017) A multi-scale analysis of single-unit housing water demand through integration of water consumption, land use and demographic data. Water Resour Manag 31(7):2173–2186CrossRefGoogle Scholar
  17. Haque MM, de Souza A, Rahman A (2017) Water demand modelling using independent component regression technique. Water Resour Manag 31(1):299–312CrossRefGoogle Scholar
  18. House-Peters LA, Chang H (2011) Urban water demand modeling: review of concepts, methods, and organizing principles. Water Resour Res 47(5):W05401CrossRefGoogle Scholar
  19. Hutton CJ, Kapelan Z (2015) A probabilistic methodology for quantifying, diagnosing and reducing model structural and predictive errors in short term water demand forecasting. Environ Model Softw 66:87–97CrossRefGoogle Scholar
  20. Kalteh AM, Hjorth P, Berndtsson R (2008) Review of the self-organizing map (SOM) approach in water resources: analysis, modelling and application. Environ Model Softw 23(7):835–845CrossRefGoogle Scholar
  21. Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43(1):59–69CrossRefGoogle Scholar
  22. Kottegoda NT, Rosso R (2008) Applied statistics for civil and environmental engineers, 2nd edn. Wiley, UKGoogle Scholar
  23. Loureiro D, Mamade A, Cabral M, Amado C, Covas D (2016) A comprehensive approach for spatial and temporal water demand profiling to improve management in network areas. Water Resour Manag 30(10):3443–3457CrossRefGoogle Scholar
  24. Madsen H, Thyregod P (2010) Introduction to general and generalized linear models. Chapman & hall/CRC texts in statistical science. CRC Press, Boca RatonCrossRefGoogle Scholar
  25. Magini R, Pallavicini I, Guercio R (2008) Spatial and temporal scaling properties of water demand. J Water Resour Plan Manag 134(3):276–284CrossRefGoogle Scholar
  26. Magini R, Capannolo F, Ridolfi E, Guercio R (2017) Demand uncertainty in modelling WDS: scaling laws and scenario generation. WIT Trans Ecol Environ 210:735–746Google Scholar
  27. Mamade A, Loureiro D, Covas D, Coelho ST, Amado C (2014) Spatial and temporal forecasting of water consumption at the dma level using extensive measurements. Procedia Engineering 70:1063–1073CrossRefGoogle Scholar
  28. McCullagh P, Nelder J (1989) Generalized linear models. Chapman & hall/CRC monographs on statistics and applied probability. CRC Press, Boca RatonGoogle Scholar
  29. Nasseri M, Moeini A, Tabesh M (2011) Forecasting monthly urban water demand using extended Kalman filter and genetic programming. Expert Syst Appl 38 (6):7387–7395CrossRefGoogle Scholar
  30. Padulano R, Del Giudice G (2018) A mixed strategy based on Self-Organizing Map for water demand pattern profiling of large-size smart water grid data. Water Resour Manag 32(11):3671–3685CrossRefGoogle Scholar
  31. Quevedo J, Puig V, Cembrano G, Blanch J, Aguilar J, Saporta D, Benito G, Hedo M, Molina A (2010) Validation and reconstruction of flow meter data in the Barcelona water distribution network. Control Eng Pract 18(6):640–651CrossRefGoogle Scholar
  32. Tricarico C, De Marinis G, Gargano R, Leopardi A (2007) Peak residential water demand. In: Proceedings of the institution of civil engineers–water management, vol 160. Thomas Telford Ltd, pp 115–121Google Scholar
  33. Verdú SV, García MO, Senabre C, Marín AG, Franco FG (2006) Classification, filtering, and identification of electrical customer load patterns through the use of self-organizing maps. IEEE Trans Power Syst 21(4):1672–1682CrossRefGoogle Scholar
  34. Vertommen I, Magini R, da Conceição Cunha M (2015) Scaling water consumption statistics. J Water Resour Plan Manag 141(5):04014072CrossRefGoogle Scholar
  35. Wa’el AH, Memon FA, Savic DA (2016) Assessing and modelling the influence of household characteristics on per capita water consumption. Water Resour Manag 30 (9):2931–2955CrossRefGoogle Scholar
  36. Wong JS, Zhang Q, Chen YD (2010) Statistical modeling of daily urban water consumption in Hong Kong: Trend, changing patterns, and forecast. Water Resour Res 46(3):W03506CrossRefGoogle Scholar
  37. Zhou S, McMahon T, Walton A, Lewis J (2002) Forecasting operational demand for an urban water supply zone. J Hydrol 259(1–4):189–202CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil, Architectural and Environmental EngineeringUniversità degli Studi di Napoli Federico IINaplesItaly

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