Uncertainty Analysis of Stream Dissolved Oxygen Models (Reliability, Modeling, Wisconsin).

Abstract

Several dissolved oxygen models of differing complexity are analyzed, taking into consideration the stochastic nature of the models. The models are represented by stochastic differential equations. Uncertainty analysis is used to calculate the total uncertainty of each model and its two main components: (1) uncertainty due to propagated error from uncertain parameters such as model coefficients, loadings, initial and boundary conditions, and environmental conditions; and (2) uncertainty of the model due to structural inadequacy owing to incorrect determination of model structure. Reliability of the models is evaluated by calculating a reliability index. This factor indicates the degree of agreement between model calculations with system response data. This study also explores the effect of model complexity on both model accuracy and model reliability. The study can serve as a guide for designing water quality models within an optimum range of accuracy. This means that using the approach described in this study the engineer will be able to design his model at a level of complexity sufficient to provide optimum reliability and accuracy. This will save the effort and cost needed to design a very complex model, containing a large number of components and parameters, whose complexity might lead to a greater degree of uncertainty in model results. This study also enables engineers engaged in practical applications to choose an optimal model of low uncertainty from among different available models describing a given system under given conditions. The analysis is applied to Badfish Creek, Wisconsin, to determine the best model to describe the dissolved oxygen levels in Badfish Creek. The best model is validated against seven independent sets of water quality survey data. Such a validation assures the accuracy of the model for calculating Badfish water quality. The analysis utilizes Monte Carlo simulation where model parameters are r and omly generated from probability distributions representing these parameters and then substituted in the model equation. The repetition of this process results in a probability distribution for the dissolved oxygen level at various stations along the creek. The probability of violating the water quality st and ards is then determined. The study recommends aquatic weed control to prevent minimum dissolved oxygen violation in the creek.