Scaling Water Consumption Statistics

Abstract

Water consumption is perhaps the main process governing water distribution systems. Because of its uncertain nature, water consumption should be modeled as a stochastic process or characterized using statistical tools. This paper presents a description of water consumption using statistics as the mean, variance, and correlation. The analytical equations expressing the dependency of these statistics on the number of served users, observation time, and sampling rate, namely, the scaling laws, are theoretically derived and discussed. Real residential water consumption data are used to assess the validity of these theoretical scaling laws. The results show a good agreement between the scaling laws and scaling behavior of real data statistics. The scaling laws represent an innovative and powerful tool allowing inference of the statistical features of overall water consumption at each node of a network from the process that describes the demand of a user unit without loss of information about its variability and correlation structure. This will further allow the accurate simulation of overall nodal consumptions, reducing the computational time when modeling networks.