Response Matrix Approach to River Water Quality Analysis

Document Type : Research Paper


1 M.Sc. Student of Civil Engineering College, IUST

2 (Prof.) Civil Engineering College, IUST


Every natural river has an capacity to assimilate wastes; this is referred to as the river's self purification capacity. DO content is usually an important water quality index. The water quality of a polluted river can be improved either by increasing the river's self purification capacity or by reducing the amount of waste loading the river receivers. Traditional physically based water quality models do not evaluate separately a receiving river's purification ability and the effect of waste loading; thus, these models are not ideal analytical tools for water quality management. This paper introduces and discusses an alternative river water quality modeling approach based on the linear systems theory. Steady-state-system response matrix is a means to summarize the interactions of loadings and responses for linear water quality models. BOD-DO variation in a receiving river has been investigated by following traditional physically based water quality models. A simple physically based river BOD-DO model was derived by Streeter and Phelps (1925) based on their Ohio River water pollution study. The Streeter-Phelps model has been used by sanitary/environmental engineers for many years to evaluate the waste assimilative capacity of a receiving river; it provides a basis on which the treatment requirement for wastewater discharged into the river can be determined. The BOD-DO variation in a time-variable river system with a dispersive effect is traditionally solved by numerical methods. In this study, physical parameterization method is used. Using this method, the system impulse response function of a receiving river can be determined by solving the governing equation of the corresponding physically based model with a Dirac delta function input. This modeling approach is an extension of Green's function techniques that solve a linear differential equation. In a linear systems model, a receiving river's patura-purification capacity is represented completely by the model's impulse response function, whereas the amount  of waste loading the river receives is represented by the model's input function. The Enhanced Stream Water Quality Model (QUAL2E) is a comprehensive and versatile stream water quality model. In this paper a river was simulated with QUAL2E. Then a response matrix was built for determination of  DO deficiency in any point of river.

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