TR(BR)-127 : Uncertainty analysis of dissolved oxygen model

Abstract

In the past two decades, many mathematical water quality models have been developed to simulate physical, chemical, and biological processes occurring in river water. Their possible applications range from identifying in streaming processes affecting river water quality to forecasting the quality for operational purposes.

It was a common practice to describe problems related to chemical and biological processes in river waters through deterministic differential equations. Since the deterministic model provides a single response for each set of model parameters and initial conditions, there is always some uncertainty, both in the evaluation of field data and in the use of mathematical models to predict the outcome of natural processes. The full representation of the process responses is usually too complicated and may be too costly to develop. Due to inherent variability and randomness in natural processes and their measurements, all these sources of uncertainty could be represented as input forcing terms in the balance equations. The initial conditions may be random, either because of the imperfect real initial conditions or because of the biased measurements. The model coefficients (rate constants) may be random due to variations in measurements.

In this study, Monte Carlo simulation method is utilized in which water quality parameters of simplified Streeter-Phelps model ( 1 925) e.g. K , K , Lo, and D0, as well as the output critical DO deficit D , and its location x are treated as random variables.

The contribution to the uncertainty of reach maximum DO deficit and its location due to the uncertainty of a single parameter have been investigated by inducing uncertainty in a single parameter at a time and assuming others to be constant with their mean values. Further, considering the mean values as random, the simulation have been done by varying the mean values to both upper and lower side of mean values as quoted by Tung and Hathhorn ( 1988) for low velocity stream system. For each mean value, different level of uncerertainty have been induced by varying the coefficient of variation from 0.0 to 0.3.