Scaling properties of water demand in design and management of water distribution systems

Water demand, that is perhaps the main process governing Water Distribution Systems (WDS), is affected by natural variability. The inherent uncertainty of demand is not negligible. Thus, uncertain demand should be modelled as a stochastic process or characterized using statistical tools. The stochastic modelling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal scales. At this aim, this paper presents a stochastic description of demand and discusses in which measure its statistical properties depend on the level of spatial and temporal aggregation. The analytical equations, expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users, namely the scaling laws, are theoretically derived and discussed. Hereafter the scaling laws are validated using real water demand data of residential users and synthetic demand series generated by a non-homogeneous Poisson Rectangular Pulse (PRP) process. Through the scaling laws the statistical properties of the overall demand at each node of the WDS can be derived and the direct simulation of overall nodal demands can be done, reducing, among other things, the computational time in modelling these systems.