Effects of Heavy-Tailed Demand Model Uncertainty on Water Distribution System Simulation

Abstract

Simulation of Water Distribution Systems (WDSs) is used to evaluate WDS management to ensure the security of water supply. Many such simulations rely on assumptions of demand uncertainty. In this paper, we investigate which probability distributions adequately describe demand uncertainty and how the choice of a distribution affects the simulation results. To identify distributions, we first decompose water demand data of District Metered Areas of a city into demand trends, daily patterns, and residual uncertainty using the LOESS algorithm. Residuals are heavy-tailed, typically fitting a local log-normal distribution, but occasionally aligning better with a log-t distribution. We then assess the operational impact of the identified demand uncertainty by simulating the L-Town benchmark network subject to log-normal and log-t-distributed uncertainty using the WNTR Python package. The simulation results are evaluated based on technical KPIs. The results show that log-t-distributed uncertainty leads to worse simulated WDS performance on these KPIs, indicating that the inadequate use of normal or log-normal distributions could overestimate the WDS performance. Our findings highlight the importance of selecting appropriate uncertainty distributions for stochastic WDS optimization.