Rainfall-runoff phenomena generally belong to a random process. Thus, a rainfall runoff system is described by random differential equations. However, the stochastic response characteristics of rainfall runoff systems for a larger basin are not clear. In this paper, the Kinematic Wave model is used as a rainfall runoff system, derivation of theoretical differential equations to calculate the first-and second-order moments of discharge is shown. The validity of derived equations is shown by the results of simulation. By using a similar way, estimation of the higher-order moments of discharge output and its probability density function that change with time is possible. The results of this study can be applicable to the evaluation method of models based on their stochastic response characteristics.
