Spatial and Temporal Scaling Properties of Water Demand
Publication: Journal of Water Resources Planning and Management
Volume 134, Issue 3
Abstract
The stochastic modeling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal aggregations. The observation of real data has revealed the presence of a nontrivial scaling of the second-order moments with the number of customers. The main objective of this paper is to analyze the spatial and temporal features of the demand at different spatial aggregation scales and sampled with different temporal resolutions, deriving appropriate scaling laws for the first- and second-order moments. In this context the analytical expressions of the scaling laws are first derived, pointing out the role of the space–time correlation. Then the scaling laws are empirically derived for two data sets of real indoor water demand data of two different case studies, sampled with different metering techniques. This enables the evaluation of the relevance of this effect on real data. A further analysis is carried out to understand how the sampling time affects the scaling properties of water demand. Finally some examples are reported on the use of these findings in some practical applications.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers wish to thank Professor S. G. Buchberger who provided the data of the Cincinnati case study.
References
Alvisi, S., Franchini, M., and Marinelli, A. (2003). “A stochastic model for representing drinking water demand at residential level.” Water Resour. Manage., 17(3), 197–222.
Buchberger, S. G., and Nadimpalli, G. (2004). “Leak estimation in water distribution systems by statistical analysis of flow readings.” J. Water Resour. Plann. Manage., 130(4), 321–329.
Buchberger, S. G., and Wells, G. J. (1996). “Intensity, duration, and frequency of residential water demands.” J. Water Resour. Plann. Manage., 122(1), 11–19.
Buchberger, S. G., and Wu, L. (1995). “Model for instantaneous residential water demands.” J. Hydraul. Eng., 121(3), 232–246.
Clement, R. (1966). “Calcul des débits dans les réseaux d’irrigation fonctionnant a la demande.” Houille Blanche, 5, 553–575.
Guercio, R., Magini, R., and Pallavicini, I. (2001). “Instantaneous residential water demand as stochastic point process.” Water resources management, C. A. Brebbia et al. eds., WIT Press, Southampton, U.K., 129–138.
Guercio, R., Magini, R., and Pallavicini, I. (2003). “Temporal and spatial aggregation in modeling residential water demand.” Water resources management II, C. A. Brebbia, ed., WIT Press, Southampton, U.K., 151–160.
Johnson, E. H. (1999). “Degree of utilisation—The reciprocal of the peak factor. Its application in the operation of a water supply and distribution system.” Water SA, 25(19), 111–114.
Pallavicini, I., and Magini, R. (2007). “Experimental analysis of residential water demand data: Probabilistic estimation of peak coefficients at small time scales.” Proc., CCWI2007 and SUWM2007 Conf. Water Management Challenges in Global Change, Taylor & Francis, London, 379–384.
Rodriguez-Iturbe, I., Gupta, V. K., and Waymire, E. (1984). “Scale considerations in the modeling of temporal rainfall.” Water Resour. Res., 20(11), 1611–1619.
Rodriguez-Iturbe, I., Marani, M., D’Odorico, P., and Rinaldo, A. (1998). “On space-time scaling of cumulated rainfall fields.” Water Resour. Res., 34(12), 3461–3469.
Tessendorff, H. (1972). “Problems of peak demands and remedial measures.” Proc., 9th Congress of Int. Water Supply Association Int. Standing Committee on Distribution Problems: Subject n. 2, s10–s14.
Tricarico, C., De Marinis, G., Gargano, R., and Leopardi, A. (2005). “Peak water demand for small towns.” Proc., 8th Int. Conf. on Computing and Control for the Water Industry (CCWI), Exeter, U.K., 2, 113–118.
Zhang, X., and Buchberger, S. G. (2005). “A new look at peaking factors.” Proc., 8th Int. Conf. on Computing and Control for the Water Industry (CCWI), Exeter, U.K., 2, 107–112.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 134 • Issue 3 • May 2008
Pages: 276 - 284
Copyright
© 2008 ASCE.
History
Received: Jan 16, 2007
Accepted: Aug 20, 2007
Published online: May 1, 2008
Published in print: May 2008
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.