Water demand uncertainty: the scaling law approach

The robust design of WDS has gained popularity over the last years. Researchers have been focusing on methods and algorithms to solve the stochastic optimization problems, and great improvements have been made in this aspect. However, the quantification of the uncertainty itself has not been addressed. Values for the variance and correlation of nodal demands are always assumed and no attention is being paid in properly quantifying these parameters. The optimization problems could be significantly improved if more realistic values for the uncertainty would be taken into account. This work addresses the need to understand in which measure the statistical parameters depend on the number of aggregated users and on the temporal resolution in which they are estimated. It intends to describe these dependencies through scaling laws, in order to derive the statistical properties of the total demand of a group of users from the features (mean, variance and correlation) of the demand process of a single-user. In future stages the results of this work will be incorporated in decision models for design purpose or scenario evaluation. Through this approach, we hope to develop more realistic and reliable WDS design and management solutions.