A stochastic model for deriving the basic statistics of J‐day averaged streamflow

Abstract

This study provides the reader with a methodology for directly deriving basic streamflow statistics (mean, variance, and correlation coefficient) from long‐term recorded daily rainfall data. A daily streamflow sequence is considered as a filtered point process where the input is a storm time sequence that is assumed to be a marked point process. The mark is the storm magnitude that is constructed from a daily rainfall time series, and the correlation of the daily rainfall during the storm is considered. The number of storms is a counting process represented by either the binomial, the Poisson, or the negative binomial probability distribution, depending on its ratio of mean versus variance. As a pulse‐response function for a filtered point process, the model of three serial tanks with a parallel tank is adopted to describe the physical process of rainfall‐runoff. Thus the basic statistics (mean, variance, and covariance function) of J‐day averaged streamflows can be estimated in terms of the constants expressing stochastic properties of a rainfall time series and the tank model's parameters representing the causal relationship between rainfall and runoff. The method is used to derive the streamflow statistics of an actual dam basin, the Sameura Dam basin, located in Shikoku island, Japan. The resulting computed means and variances of 5‐day averaged streamflows show a good correspondence with observed ones.