General stochastic instantaneous unit hydrograph

This paper describes a stochastic analysis of the Nash cascade of identical reservoirs in which the storage coefficient is treated as a random variable. Based on the theory of stochastic differential equations, a new stochastic expression for the instantaneous unit hydrograph is obtained and recommended as an alternative to the existing equation. It is found that the sample function of the proposed stochastic instantaneous unit hydrograph takes the same form as the corresponding deterministic solution (Nash's equation). Moments of the proposed stochastic instantaneous unit hydrograph are derived. An application to a watershed has shown that the proposed stochastic instantaneous unit hydrograph can preserve the statistical properties of the observed data. The effect of the random coefficient on the stochastic instantaneous unit hydrograph is also discussed.