Abstract
All real hydrologic processes are more or less stochastic. While the dynamics for a runoff process are described by differential equations, strictly speaking, runoff phenomena are best expressed by stochastic differential equations. In this paper, the differential equations whose solutions give the first four moments of discharge from storage function model are proposed under the condition that rainfall input from a random process is independently distributed. The validity of these equations is cross-checked by a simulation method. It is possible to estimate the probability density function of discharge by using the obtained first four moments.
