Rainfall-runoff phenomenon is more or less stochastic. From its stochastic viewpoint, runoff models are described by stochastic differential equations. We propose differential equations whose solutions estimate the first and second order central moments of discharge under the condition that the rainfall input, the storage coefficient and the initial condition of a storage function runoff model are treated as random variables respectively. The validity of these proposed differential equations

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... cross-checked by a simulation. The results in this study can be applicable to problems on the river engineering, such as the estimation of the design flood.