No abstract

We derived differential equations whose solutions provide the first four moments of discharge under the condition that rainfall input is mutually dependent random variable using the storage function runoff model proposed by Hoshi et al.. In the concrete, we assumed that the deviation from average rainfall is described by AR(1) process based on the statistical analysis of observed rainfall. The validity of proposed theoretical equations was cross-checked by a simulation. It is possible to estimate the probability density function of discharge by the calculated first four moments of discharge. The results of this study can be applied to estimating the design flood.

Observed rainfall is a non-stationary and mutually dependant random variable. Based on the condition that the stochastic characteristics of rainfall are known, we derived dierential equations whose solutions provide the ®rst four moments of discharge output from a storage function runo model. The validity of the derived dierential equations was cross-checked by a simulation method. The results showed that it is possible to obtain the probability density function of discharge from the calculated ®rst four moments of discharge.