Bayesian temporal modeling of water demands at household level

This study is motivated by the need to develop stochastic models of water demand that can be applied to different scales of spatial and temporal aggregation to accurately represent hydraulics and water quality dynamics in water distribution systems. Previous work has produced models that were not used to represent spatial-temporal demands for extensive data sets, mainly due to limitations in collection of data necessary for testing and validation, in the mathematical structure of the models, and in the methods used for parameter estimation. The main goal of this work is to address such limitations by exploiting a unique opportunity to collect large volumes of data at the individual service connection (ISC) level and by introducing proposed enhancements to stochastic point process modeling methods. The methodology contemplates the implementation and testing of temporal models for single-site or ISC water demands, based on stochastic point processes. The Poisson Rectangular Pulses (PRP) and the Neyman-Scott Rectangular Pulses (NSRP) are the two point process models selected for representing the temporal variation of water demand. The model parameters account for the physical processes involved in water usage, namely, time dependent arrival rate, intensity, and duration of individual water usage events. A Bayesian parameter estimation methodology is proposed and is implemented using a Markov-Chain Monte Carlo (MCMC) method based on the Metropolis-Hastings algorithm. The MCMC approach produces samples from the posterior distribution of the model parameters providing more information than single point estimates.