Considering the mutual dependence of the pulse intensity and duration in models for water demand generation.

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Enrico Creaco, Raziyeh Farmani, Zoran Kapelan, Lydia Vamvakeridou-Lyroudia, Dragan Savic

Thursday 2 july 2015

11:00 - 11:15h at North America (level 0)

Themes: (T) Special session, (ST) FP7 ICT and water

Parallel session: 11I. Special session: FP7 ICT and water

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In the last two decades various models (Buchberger and Wu, 1995; Buchberger and Wells, 1996; Alvisi et al., 2003; Garcia et al., 2004; Buchberger et al., 2005; Alcocer et al., 2006; Alcocer-Yamanaka and Tzatchkov, 2012) were proposed for the generation of the water demand at the scale of individual user. In these models the user’s demand is modelled by pulses, whose intensity and duration are considered to be independent random variables which follow prefixed probability distributions. Indeed, the assumption of mutual independence of intensity and durations, on the basis of which the previous models for pulses generation were developed, has never been analysed and verified thoroughly. The practical experience points out that a sort of positive correlation could exist between these variables for some kinds of consumption. As an example, in such a lengthy pulse as the bathtub filling, the user could tend to open the tap fully (and then to produce a high intensity pulse) in order to fill the bathtub in the shortest possible time. In such a brief pulse as hand washing, the user could, instead, tend to open the tap only partially. In the present work, a Poisson model for water demand generation at the scale of individual user is developed. Compared to the models previously proposed in the scientific literature, it features the novelty of considering a mutual dependence of pulse intensity and duration. To this end, it represents the two variables as dependent random variables following the bivariate lognormal distribution. The model is applied to the case study of the households in Milford, Ohio (Buchberger et al., 2003). The analysis of the results of the new model and the comparison with the results of a traditional model where the pulse intensity and duration are represented as independent random variables show that considering the mutual dependence of pulse intensity and duration helps obtaining water demand pulses which respect the statistical properties of the demand pulses observed experimentally, while obtaining consistent values of the overall daily water demand volume.