A stochastic model for daily river flows in an arid region

We propose a model for daily river flow that differs from approaches (some of which are described herein) taken by other authors in that the flow on any day is a nonlinear function of previous flows plus a random component. Thus the theory of second-order time series analysis plays no role here. Additionally, ideas from meteorology are incorporated, and the random component is taken to be a Markov process (the transition matrix being dependent on the month of the year), arid thereby droughts, rainy periods, and seasonal variation are incorporated into simulated trajectories. In particular, by proper choice of the random component, sample trajectories exhibit episodes of zero flow such as those that characterize rivers in arid lands, drainage networks, and storm sewers. The statistical and computational properties of the model are explored as we estimate the parameters of the Rillito River and subsequently simulate flows. Then the simulated trajectories are compared to the actual Rillito River streamflow record.