Stochastic Response of Storage Function Model

Non-Stationary and Mutually Dependent Rainfall Input and Its Stochastic Response

“…However, observed rainfall that causes¯oods is a non-stationary and mutually dependant random variable. Therefore, the results obtained by Fujita et al [1] and Tanaka et al [2] donot provide sucient solutions. In this paper, we assume that observed rainfall belongs to the ®rst-order auto-regressive process, AR (1).…”

“…Therefore, the results obtained by Fujita et al [1] and Tanaka et al [2] donot provide sucient solutions. In this paper, we assume that observed rainfall belongs to the ®rst-order auto-regressive process, AR (1). This assumption is veri®ed by statistical analysis of observed rainfall data.…”

“…In order to estimate the design¯ood, it is necessary that we provide the probability density function (PDF) of discharge of time change. Fujita et al [1] used the simplest storage function runo model and proposed a method for estimating the PDF by calculating the ®rst four moments of discharge on the condition that rainfall inputs were mutually independent. By applying the new method proposed by * Fujita et al [1], Tanaka et al [2] estimated the ®rst four moments of discharge from several runo models, such as the Kinematic wave model and two types of storage function runo model obtained from lumping the Kinematic wave model.…”

Application of the Equivalent Frequency Response Method to Nonlinear Runoff System

“…x, r: space and time coordinates h, u, q : depth, velocity, and discharge at (x, t) 1: length of the plane r : rainfall intensity g : acceleration due to gravity so : slope of the plane s f : friction slope defined by Chezy equation 3C: Chezy roughness of the plane These equations can be written in non-dimensional form by introducing the following normalizing quantities, denoted by the subscript (*) (4) The capital letters (such as x) denote non-dimensional quantities corresponding to dimensional quantities (such as h). The following two conditions were adopted.…”

“…Originally, the EFRM was first used in control engineering for analyzing nonlinear elements such as threshold and saturation. The notion of EFRM had already been used by Fujita and Kudo (1995) 4, and Fujita (1998, 1999) 5,6) to describe the characteristics of runoff models. These studies focused only on the gain characteristics of storage function model and kinematic wave model.…”