A discrete linear cascade model for hydrology

The discrete analogies of the classical Muskingum and the equal-reservoir cascade models are compared with the ARMA-type models used in the generation of synthetic time series. Applying the cascade concept to the ARMA-type difference equation and including a pure translation parameter, a family of discrete linear parametric models is developed. Expressions are derived for the direct estimation of model parameters by cumulants for the general input-output case and for the special case of a white-noise input. The family of models can be applied in unit-hydrograph analysis, in flood routing, and in the generation of synthetic time series.