Generation of synthetic cross-correlated water demand time series

This paper presents a procedure for generating synthetic district-level series of hourly water demand coefficients which are cross-correlated in space (between districts) and time. The procedure consists of two steps: 1) generating hourly water demand coefficients which respect, for each hour of the day, pre-assigned means and variances and 2) introducing cross-correlation at different time lags through the application of a method based on reordering the data generated in step 1. The procedure was applied in a case study of the Ferrara water distribution system with the aim of generating synthetic series of hourly water demand coefficients for the 19 water districts making it up. It was observed that when the water demand coefficients are reordered to introduce cross-correlations (step 2), numerical problems can arise when a large number of water districts are involved and the cross-correlations are considered at many time lags; this problem is solved by carrying out a preliminary regularization of the cross-correlation matrix using a method available in the literature. The results obtained show that overall the proposed procedure constitutes a valid tool for generating synthetic water demand time series with pre-assigned characteristics in terms of means, variances and cross-correlation at different time lags.