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 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.