Nash Cascade Research Articles

The discretization of the continuous linear cascade by means of state space analysis

In applying digital filtering techniques for hydrological forecasting by means of cascade models a discrete model of the continuous processes involved is necessary. The paper deals with the discretization of the continuous Nash cascade. The principles of state space modelling are used. The continuous state variable model of the Nash cascade together with the computation of the state transition matrix and the impulse response is given. A discrete state variable model is derived whose state and input transition matrices are in a dual relationship. Any different discrete state representations of the continuous Nash cascade are related to each other via a linear transformation. In the limit case the discrete state models are identical with the continuous Nash cascade. The discrete state models are discretely coincident with the continuous model but at the same time consider the dynamic changes in between the sampling points. A numerical example is presented.