Multiscale Stochastic Characterisation of Residential Water Demand for Sustainable Network Design

Residential water demand exhibits marked variability over time and across users, with direct implications for the sustainable and robust design of water distribution networks. In this study, a high-resolution experimental dataset is analysed to characterise the statistical structure of hourly consumption, deriving mean and variance scaling laws, cross-correlations between user groups, and probability density functions (PDFs) of aggregated demand. The results show that demand does not behave as an independent process. During the morning peak (07:00–08:00), the distribution does not converge to a unimodal shape as aggregation increases, but exhibits a clear bimodality for aggregation levels larger than approximately N ≈ 400 users. This behaviour indicates the presence of two synchronised consumption regimes and a non-negligible average correlation. In contrast, during the evening and night slots, unimodal distributions (Gamma or Lognormal) emerge, consistent with largely independent contributions and limited synchronisation. For comparison, a simplified Poisson Rectangular Pulse (PRP) model is evaluated. While this model reproduces the mean flow rate, it does not capture the observed variance, underscoring the need for models that account for heterogeneity and user correlations. The scaling laws, correlations, and empirical PDFs derived in this study provide a quantitative basis for generating probabilistic demand scenarios, supporting the sustainable, resilient, and robust design of water distribution networks.