Generation of synthetic water demand time series at different temporal and spatial aggregation levels

This paper presents a procedure for the generation and spatial-temporal aggregation of synthetic water demand time series which reproduce the main statistics - mean, variance and (spatial and temporal) covariance - of the corresponding observed series. Starting from observed historical time series taken at low levels of temporal aggregation (e.g., one minute) and relating to individual users, the procedure enables a) the generation of synthetic water demand time series for every individual user with a time step of one minute, b) the temporal aggregation of these synthetic series in order to obtain synthetic water demand time series with a time step, for example, of one hour, and which are such as to reproduce the hourly mean, variance and temporal covariances of the corresponding temporally aggregated historical time series, and c) the spatial aggregation of the synthetic hourly water demand time series of every user in order to generate a synthetic water demand time series that is representative of the entire group of users considered, and is such as to reproduce the mean, variance and temporal covariance observed at that level of spatial aggregation; The entire procedure was parameterized and applied to a case study on the water demands of 21 users of the water distribution system of Milford (Ohio). The results obtained show that the temporal aggregation procedure is effective in generating hourly water demand time series that preserve the mean, variance and temporal correlation of the historical time series for every individual user, while the spatial aggregation method shows good level of effectiveness in preserving the statistics of the aggregated series. Overall, the proposed procedure is demonstrated to be a valid tool for the bottom-up generation of synthetic water demand time series at various levels of spatial-temporal aggregation which reproduce the mean, variance and covariance statistics of the historical time series.