Demand uncertainty in modelling 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 described 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. These relationships have reference to the mean-variance scaling or Taylor’s power law. The scaling laws are also validated using real water demand data of residential users. 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 or performing Monte Carlo Sampling of these systems.