Stochastic modeling of river flows

A family of linear stochastic difference equation models is proposed for monthly river flows, the variance of the disturbance in the model varying sinusoidally with time. The unknown parameters in the model are estimated by using the given data and an algorithm is given for the choice of the appropriate number and type of autoregressive terms, sinusoidal trend terms, etc., in the model. The method is used to construct a model for the flows in Wabash and other rivers. This model is useful not only for forecasting but also for generating "synthetic flows" since the various statistical characteristics of the output generated by the model such as power spectra, correlograms, monthly means, and variances, etc., are very close to the corresponding characteristics of the observed flows. The model presented in this paper is compared with other models in the literature. The models of the fiver flows constructed by using daily and yearly data and the relative capabilities of the aggregated and nonaggregated models for forecasting are also discussed.