Bayesian Storm-Water Quality Model and Its Application to Water Quality Monitoring

A Bayesian statistical approach for determining the parameter uncertainty of a storm-water treatment model is reported. The storm-water treatment technologies included a sand filter and a subsurface gravel wetland. The two field systems were loaded and monitored in a side-by-side fashion over a two-year period. The loading to each system was storm-water runoff generated by ambient rainfall on a commuter parking lot. Contaminant transport is simulated by using a one-dimensional advection-dispersion model. The unknown parameters of the model are the contaminant deposition rate and the hydrodynamic dispersion. The following contaminants are considered in the study: total suspended solids, total petroleum hydrocarbons–diesel range hydrocarbons, and zinc. Parameter uncertainties are addressed by estimating the posterior probability distributions through a conventional Metropolis-Hastings algorithm. Results indicate that the posterior distributions are unimodal and, in some instances, exhibit some level of skewness. The Bayesian approach allowed the estimation of the 10th, 25th, 50th, 75th, and 95th percentiles of the posterior probability distributions. The prediction capabilities of the model were explored by performing a Monte Carlo simulation using the calculated posterior distributions and two rainfall-runoff events not considered during the calibration phase. The objective is to estimate effluent concentrations from the treatment systems under different scenarios of flow and contaminant loads. In general, estimated effluent concentrations and the total estimated mass fell within the defined uncertainty limits.