Stochastic water quality models: Solution, calibration and application

Stochastic water quality models attempt to describe the observed variability of pollutant concentrations in water bodies by estimating the probability distributions of those concentrations. In this research stochastic water quality models were developed, calibrated, solved and used to evaluate water quality management policies.;Parameter value and model uncertainties were analyzed with Monte Carlo simulation methods and stochastic differential equation models. The results were compared to deterministic model solutions. The means of the concentration distributions derived from stochastic models equal those of deterministic models evaluated at the mean parameter values. The variances of the constituent concentrations converge over time to constant values.;Calibrating stochastic models requires comparing estimated and observed probability distributions. The calibration procedure developed in this research uses least-squares estimation obtained from a genetic algorithm and a numerical method. The procedure was tested against two sets of synthetic data: one with and the other without assumed measurement errors. The calibration procedure increases the parameter value variances to account for the errors (higher variability) in the measured data. Calibration with actual data obtained for deterministic models demonstrates that the sampling effort needed for deterministic modeling can also be used for stochastic model calibration.;Two mutually exclusive water quality control policies for water quality management in a river were analyzed to determine which policy should be implemented and when. The river serves as the discharge site for industrial effluent and as the source for drinking water downstream. The stochastic water quality model identified the relationship between the increasing and uncertain effluent discharge characteristics and the stochastic evolution of the instream concentrations downstream. The analysis permitted one to determine when one policy would dominate the other. Policy domination depends upon the treatment costs, rate of discount, damages and the stochastic evolution of the concentrations.