Estimating demands with a Markov chain Monte Carlo approach

The use of drinking water distribution system models has been around for decades, and demand estimation has been a key component in the model development process. Existing techniques utilized by consultants/utilities have been capable of representing the general hydraulics for assessing typical objectives such as maintaining adequate pressure. However, these models are generally not appropriate, or simply do not work, when attempting to recreate the observed hydraulics and operational conditions associated with a specific time horizon. In general, these limitations in recreating demands have become even more important when attempting to assess the ability of models to represent complex water quality dynamics. In this paper, a Bayesian demand estimation algorithm is presented, and estimated water demand multipliers are compared with synthetically generated "observed" demand multipliers in a water distribution system network. Using two different data scenarios - an "ideal" case assuming all flow and pressure data are available for the estimation process and a more realistic "limited" case using only flow rates at the sources and tank levels - the Markov chain Monte Carlo (MCMC) method demonstrated an increase in demand estimate uncertainty for the "limited" data scenario. Using the "limited" data set only resulted in a moderate increase in the underlying flow rate uncertainty. These results demonstrate the potential feasibility of the MCMC algorithm for recreating adequate demand estimates that will provide an improved approach for evaluating water quality models.