Bottom-Up Generation of Water Demands to Preserve Basic Statistics and Rank Cross-Correlations of Measured Time Series
Publication: Journal of Water Resources Planning and Management
Volume 146, Issue 1
Abstract
This paper presents a novel methodology for the generation of demand time series at water distribution network (WDN) users. After subdividing the day into an integer number of time steps with order of magnitude of 1 h, the methodology is based on two phases. First, it generates, for each user and for each time step of the day, demand time series of the first attempt, which are consistent with the measured time series in terms of mean, standard deviation, and skewness. This is done with a beta probability distribution with tunable bounds or with a gamma distribution with shift parameter. In the refinement phase, rank cross-correlations between users and at all temporal lags are imposed on the generated demand time series through a single Copula-based re-sort. The effectiveness of the methodology is proven in two real case studies with different numbers of users—namely, the literature case study of Milford, Ohio, and a novel Italian site. The demand time series obtained from the spatial aggregation of the generated user demand time series preserves very well mean and standard deviation of the measured aggregated demand time series. The preservation of skewness and temporal cross-correlations at all lags is very satisfactory. A procedure is also presented to reconcile the generated demand time series with demand pulses generated at fine time step, thus enabling reconstruction of demand at any time step.
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Data Availability Statement
The software used for the calculations can be made available upon request by the authors of the paper. The authors do not have ownership of the data used in this analysis and therefore have restrictions on sharing them publicly. In fact, the data of the Milford households were made available by Professor Buchberger. Those of the Soccavo district were made available by Azienda Speciale Acqua Bene Comune Napoli (ABC).
References
Alvisi, S., N. Ansaloni, and M. Franchini. 2014. “Generation of synthetic water demand time series at different temporal and spatial aggregation levels” Urban Water J. 11 (4): 297–310. https://doi.org/10.1080/1573062X.2013.801499.
Blokker, E. J. M., J. H. G. Vreeburg, S. G. Buchberger, and J. C. van Dijk. 2008. “Importance of demand modelling in network water quality models” Drinking Water Eng. Sci. 1 (1): 27–38. https://doi.org/10.5194/dwes-1-27-2008.
Buchberger S. G., J. T. Carter, Y. Lee, and T. G. Schade. 2003. Random demands, travel times, and water quality in deadends, subject area: High-quality water. Denver: AwwaRF.
Creaco, E., M. Blokker, and S. Buchberger. 2017a. “Models for generating household water demand pulses: Literature review and comparison” J. Water Resour. Plann. Manage. 143 (6): 04017013. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000763.
Creaco, E., R. Farmani, Z. Kapelan, L. Vamvakeridou-Lyroudia, and D. Savic. 2015. “Considering the mutual dependence of pulse duration and intensity in models for generating residential water demand” J. Water Resour. Plann. Manage. 141 (11): 04015031. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000557.
Creaco, E., G. Pezzinga, and D. Savic. 2017b. “On the choice of the demand and hydraulic modeling approach to WDN real-time simulation” Water Resour. Res. 53 (7): 6159–6177. https://doi.org/10.1002/2016WR020104.
Filion, Y. R., B. Adams, and B. Karney. 2007. “Cross correlation of demands in water distribution network design” J. Water Resour. Plann. Manage. 133 (2): 137–144. https://doi.org/10.1061/(ASCE)0733-9496(2007)133:2(137).
Gargano, R., F. Di Palma, G. de Marinis, F. Granata, and R. Greco. 2016. “A stochastic approach for the water demand of residential end users.” Urban Water J. 13 (6): 569–582. https://doi.org/10.1080/1573062X.2015.1011666.
Iman, R. L., and W. J. Conover. 1982. “A distribution-free approach to inducing rank correlation among input variables” Commun. Stat.-Simul. Comput. 11 (3): 311–334. https://doi.org/10.1080/03610918208812265.
Johnson, N. L., S. Kotz, and N. Balakrishnan. 1995. Continuous univariate distributions. 2nd ed. Hoboken, NJ: Wiley.
Moughton, L. J., S. G. Buchberger, D. L. Boccelli, Y. R. Filion, and B. W. Karney. 2006. “Effect of time step and data aggregation on cross correlation of residential demands.” In Proc., 8th Annual Int. Symp. on Water Distribution Systems Analysis, 27–30. Cincinnati: Univ. of Cincinnati.
Nelsen, R. B. 1999. An introduction to copulas. New York: Springer.
Pearson, K. 1895. “Notes on regression and inheritance in the case of two parents.” Proc. R. Soc. London 58 (347–352): 240–242. https://doi.org/10.1098/rspl.1895.0041.
Spearman, C. 1904. “The proof and measurement of association between two things” Am. J. Psychol. 15 (1): 72–101. https://doi.org/10.2307/1412159.
Walski, T. M., D. V. Chase, D. A. Savic, W. Grayman, S. Beckwith, and E. Koelle. 2003. Advanced water distribution modeling and management. Waterbury, CT: Haestad Press.
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©2019 American Society of Civil Engineers.
History
Received: Jan 5, 2019
Accepted: May 10, 2019
Published online: Oct 17, 2019
Published in print: Jan 1, 2020
Discussion open until: Mar 17, 2020
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