Spatial and Temporal Scaling Properties of Water Demand

Abstract

The stochastic modeling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal aggregations. The observation of real data has revealed the presence of a nontrivial scaling of the second-order moments with the number of customers. The main objective of this paper is to analyze the spatial and temporal features of the demand at different spatial aggregation scales and sampled with different temporal resolutions, deriving appropriate scaling laws for the first- and second-order moments. In this context the analytical expressions of the scaling laws are first derived, pointing out the role of the space–time correlation. Then the scaling laws are empirically derived for two data sets of real indoor water demand data of two different case studies, sampled with different metering techniques. This enables the evaluation of the relevance of this effect on real data. A further analysis is carried out to understand how the sampling time affects the scaling properties of water demand. Finally some examples are reported on the use of these findings in some practical applications.