A Stochastic Streamflow Model Based on Physical Principles

Based on hydrologic arguments, a stochastic model for discretized streamflow from rainfall is proposed in the form of an averaged filtered Poisson process (FPP). Using a two‐component description with excess precipitation and drainage as inputs to the surface and subsurface flow systems, simplified models are presented for the physical processes. The mean, variance, and covariance function of discretized streamflow are computed in terms of the first and second moments of excess precipitation and drainage which are derived analytically. The behavior of the stochastic properties of streamflow is evaluated for various soil types, basin travel times, and effective initial soil water contents. Where there is an intuitive, feeling for the interaction of physical characteristics and stochastic properties, such as the mean, the model appears to produce qualitatively correct results. Prediction of stochastic properties is limited by the selection of an effective initial soil moisture value.