2 - A daily streamflow model based on a jump-diffusion process

Summary

ABSTRACT The objective of this paper is to describe daily discharge series by a stochastic differential equation which is based on the mass balance of a linear reservoir. The input consisting of a series of jumps reflects the rainfall while the output refers to the discharges of a river basin. To account for random phenoma such as evaporation during the transformation process a perturbation term was introduced. The point process describing the shots (jumps) is based on an intensity function alternating randomly between two levels. Thus clustering of shots can be incorporated into the model.

INTRODUCTION

Numerous stochastic models have been applied to streamflow series. They can be grouped, for instance, into ARMAtype models (Fiering, 1967; Hipel et al., 1917; Noakes et al 1985; Kottegoda & Horder, 1980; Salas & Smith, 1981), long term memory models such as fractional Gaussian noise models (Mandelbrot & van Ness, 1968; Mandelbrot & Wallis, 1969) and related broken line models (Meija et al., 1972). The third class of models refers to the transformation of an intermittent rainfall process into a continuous discharge series (Treiber & Plate, 1975; Weiss, 1973, 1977; Miller et al., 1981; Kavvas & Delleur, 1984; Koch, 1985; Bodo & Unny, 1987). In this paper daily streamflow series (Beard, 1967; Quimpo, 1967; Valencia & Schaake, 1973; Mejia & Rousselle, 1976; Yakowitz, 1979; Morris, 1984; Miller et al 1981; Weiss, 1977; O'Cornell, 1977) are being modelled.