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Responses of a runoff system with slope-length distribution have been studied in detail by many researchers. In those studies, rainfall input to the runoff system was considered a deterministic variable. However, rainfall input should be treated as a random process.In this paper, the Kinematic Wave model is used as a runoff system, and differential equations whose solutions provide the first-to fourth-order moments of discharge outputs from the runoff system under the impact of mutually independent rainfall inputs and slope-length distribution are theoreticallyderived. The validity of the proposed differential equations is cross-checked by results of simulation. Estimation of the probability density function of discharge outputs is possible by using the first-to fourth-order moments presented in this paper.

STOCHASTIC RESPONSE CHARACTERISTICS OF A KINEMATIC WAVE MODEL UNDER THE IMPACT OF SLOPE-LENGTH DISTRIBUTION