TR-147 : Stochastic modelling of water quality using data for river Yamuna

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.

Number of models have been proposed in recent years which treat water quality processes as stochastic. In the present study, a time series analysis approach was applied to model nine years of mean monthly dissolved oxygen data observedat U/S and DIG sections in river Yamuna at Delhi. The data was measured and compiled by Central water commission, New Delhi, in a form of status report on water quality survey for the Yamuna system.

The basic properties of the water quality data time series were determined, time and frequency-domain analysis were carried out, and the dependent stochastic component was represented by various stochastic models. The independent residual component was represented by probability distribution functions.