Nonlinear stochastic water environmental risk model

On the basis of Shastry's nonlinear water quality model, the concept of stochastic force is introduced to establish the stochastic differential equation for water environment. The probability density distribution function is deduced by numerically solving the multi-dimension stochastic partial differential equation. The relationship between the risk and duration of pollution exceeding standard is established accordingly. The calculation of case study shows that the stochastic variation intensity affects the risk, and the reductions of BOD5 or initial concentration of DO result in remarkable reduction of risk. The explicit scheme and implicit scheme are applied to solve the nonlinear stochastic differential equation respectively. The result shows that the difference of risk variation tendency calculated by different scheme is not significant.