Bottom-Up Generation of Water Demands to Preserve Basic Statistics and Rank Cross-Correlations of Measured Time Series

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.