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This paper describes the development and application of a new mathematical technique to include stochasticity in environmental models. The techniques are studied to develop stochastic analysis model of the CBOD NBOD DO equations for predicting the river water quality. The CBOD NBOD DO equations are expanded to include stochastic terms. Stochastic terms are separated from non fluctuating terms, and the resulting set of equations is solved simultaneously. Solutions are used to calculating the integral solutions and the distribution moments of the state variables. 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. Because the approach produces analytical solutions, it offers greater flexibility than a Monte Carlo approach in treating complex environmental situations. The model is used to calculate water quality for the Qingao river. The calculated results are in good agreement with the Monte Carlo model and field data.
The paper describes the development and application of a new mathematical technique to include stochasticity in environmental models. The techniques are studied to develop stochastic analysis model of the CBOD NBOD DO equations for predicting the river water quality. Stochastic terms are separated from non-fluctuating terms, and the resulting set of equations is solved simultaneously. Solutions are used to calculating the integral solutions and the distribution moments of the state variables. 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. as the approach produces analytical solutions, it offers greater flexibility than a Monte Carlo approach in treating complex environmental situations. The model is used to calculate water quality for the Qingao river. The calculated results are in good agreement with the Monte Carlo model and field data.