Analytically derived runoff models based on rainfall point processes

This paper presents four stochastic and lumped-in-space rainfall-runoff models. Rectangular pulses arriving according to some stochastic process represent rainfall while runoff is modeled by routing these pulses through linear reservoirs. Closed-form expressions for the mean and second-order properties of the rainfall and runoff processes are respectively reviewed and introduced. The reservoir coefficients are shown to be of major importance in the statistical behaviour of runoff, mainly influencing the scale on which the process varies. An outline is given of the statistical conditions which rainfall and runoff data must initially satisfy in order for the models to be applicable. -Authors