Application of stochastic differential equations in risk assessment for flood releases

Abstract

After analysing the Wiener process characteristics of reservoir storage capacity in flood regulation, an Ito stochastic differential equation including a random input term is proposed to describe and estimate the stochastic reservoir level hydrograph in a flood routing process. An expression of risk for flood release is given and the probability density functions of the reservoir level hydrograph, which are related to the risk of overtopping failure, are computed using a Fokker-Planck equation. Analysed and calculated results indicate that, by using the stochastic differential equations, the uncertainty influence of various random factors on the reservoir level hydrograph can be taken into account in the flood routing process. Therefore, the procedure of evaluating the risk of dam overtopping failure developed in this paper provides an improvement over existing methods.