Stochastic analysis of response functions in environmental modelling

This paper reports on the development of a new mathematical technique to include stochasticity in environmental models used for resource management and public health risk analysis.; The technique is based on the expansion of basic governing equations to include stochastic terms. The stochastic terms are then separated from the non-fluctuating terms, and the resulting set of equations solved simultaneously. The solutions of this set of equations are used to calculate the moments of the output variables. In addition, the moments are used in conjunction with the Fokker-Planck Equation to produce an analytical solution for the probability density functions of the dependent variables.; The technique is applied in two examples. The first example is an application to the Streeter-Phelps BOD-OD Equations. Results of the analysis are compared to field data as well as to results of a Monte Carlo model and to moments derived using a Stochastic Differential Equations approach. The second application involves analysis of health risks associated with waterborne diseases. The results of this analysis are compared to the results of a Monte Carlo simulation of a similar system of equations.; The technique presented in this dissertation represents a new and potentially powerful tool for extending the capabilities of computer models in management and decision analysis. The method can provide analytical solutions for the probability density functions and associated moments of important environmental variables. Furthermore, the technique gives the modeler the ability to perform a detailed quantitative examination of the sources and magnitudes of uncertainty, and may provide a means by which an "optimum" model could be selected, given a specific purpose for the model.