Instantaneous Water Demand Parameter Estimation from Coarse Meter Readings

On finer time scales, real residential water demand is a non steady stochastic process. The Poisson Rectangular Pulse (PRP) method can be used to model this process, provided the following basic parameters are given: intensity, duration and frequency of the demand pulses, each of them represented statistically by its mean value, variance and probability distribution. Known techniques for characterizing these parameters are based on registering the instantaneous water demand every second, separating the individual demand pulses, and processing statistically the resulting series of pulses. Unfortunately, that "direct" technique generates an enormous amount of data, and because of that is expensive and time-consuming. In this paper, a method for estimating the instantaneous water demand parameters from coarser time resolution (one minute or larger) demand readings is presented. The estimation is based on comparing the theoretical statistical moments of the demand series with the moments of the observed coarser time resolution demand data. The theoretical statistical moments are expressed by the Rodriguez-Iturbe's (Neyman-Scott process based) model for temporal rainfall processes. A least-squares objective function is then formulated for the differences between the theoretical and the observed statistical moments. The minimization of that objective function by a non linear programming technique provides the intensity, duration and frequency of the instantaneous demand pulses. Real residential water meter readings are used to validate the proposed method by comparing the observed water demand series with PRP model generated time series. This paper was presented at the 8th Annual Water Distribution Systems Analysis Symposium which was held with the generous support of Awwa Research Foundation (AwwaRF).