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 cross-correlated in space (between districts) and time. The procedure consists of two steps: 1) generation of hourly water demand coefficients which respect, for each hour of the day, pre-assigned means and variances and 2) introduction of the cross-correlation at different time lags through the application of a method which implies the reordering of the data generated at the step 1. The procedure was applied to a case study of the Ferrara water distribution system with the aim of generating cross correlated synthetic series of hourly water demand coefficients for the 19 water districts making it up. It was observed that the application of the method for introducing the cross correlation (step 2) causes numerical problems 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 an appropriate regularization of the observed cross-correlation matrix. 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.