Decomposition of Water Demand Patterns Using Skewed Gaussian Distributions for Behavioral Insights and Operational Planning

TL;DR

This paper introduces a Skewed Gaussian Distribution-based method to decompose urban water demand patterns, enabling better behavioral insights, anomaly detection, and operational planning with improved accuracy over traditional models.

Contribution

The study presents a novel SGD-based approach for detailed peak decomposition of water demand, capturing asymmetry and improving pattern reconstruction and interpretability.

Findings

SGD outperforms symmetric Gaussian models in accuracy by over 50%.

Method enables detection of behavioral shifts and anomalies.

Framework supports synthetic demand scenario creation.

Abstract

This study presents a novel approach for decomposing urban water demand patterns using Skewed Gaussian Distributions (SGD) to derive behavioral insights and support operational planning. Hourly demand profiles contain critical information for both long-term infrastructure design and daily operations, influencing network pressures, water quality, energy consumption, and overall reliability. By breaking down each daily demand curve into a baseline component and distinct peak components, the proposed SGD method characterizes each peak with interpretable parameters, including peak amplitude, timing (mean), spread (duration), and skewness (asymmetry), thereby reconstructing the observed pattern and uncovering latent usage dynamics. This detailed peak-level decomposition enables both operational applications, e.g. anomaly and leakage detection, real-time demand management, and strategic analyses, e.g. identifying behavioral shifts, seasonal influences, or policy impacts on consumption patterns. Unlike traditional symmetric Gaussian or purely statistical time-series models, SGDs explicitly capture asymmetric peak shapes such as sharp morning surges followed by gradual declines, improving the fidelity of synthetic pattern generation and enhancing the detection of irregular consumption behavior. The method is demonstrated on several real-world datasets, showing that SGD outperforms symmetric Gaussian models in reconstruction accuracy, reducing root-mean-square error by over 50% on average, while maintaining physical interpretability. The SGD framework can also be used to construct synthetic demand scenarios by designing daily peak profiles with chosen characteristics. All implementation code is publicly available at: https://github.com/Relkayam/water-demand-decomposition-sgd