An advective-dispersive transport model for residential water consumption

This work applies an advective-dispersive framework to simulate utility-wide residential water consumption using the analogy of a continuum transport process. In this context, the advective-dispersive process describes how changes in real water price and seasonal weather variability influence water consumption distribution, which ultimately governs mean and total water consumption values. Water consumption response is measured using histogram data optimally fit using parametric probability density functions (PDF) that have consistent parametrization over the entire observation period. Median statistic denotes advection and prescribes location of the measurement-space PDF, while standard deviation combined with standard-score PDF denotes dispersion which provides the measurement-space PDF with scale and shape. Combining location, scale, and shape components produces a measurement-space PDF that represents the solution to advective-dispersive transport phenomena. We use a Taylor series expansion of the statistics that define the PDF along with curvilinear regression to develop constitutive relationships that define how location, scale, and shape of the PDF respond to price and weather information. This results in a fully parametrizing advective-dispersive process represented by a partial differential equation that provides a tool for anticipating the probability that households will experience water poverty or use excess amounts as price, weather, and policy considerations change through time. This approach is conducive to automation when combined with smart water metering.