Input detection by the discrete linear cascade model

Abstract

This paper discusses inverse hydrological forecasting. As opposed to output prediction from known inputs (and model parameters), the detection of inputs from known outputs (and model parameters) is considered. The model used is the recursive, deterministic, discrete linear cascade model (DLCM) derived from the one-dimensional continuous two-parameter Kalinin-Milyukov-Nash (KMN) cascade set up in linear space. Input detection requires determination of the unsteady initial conditions. This is done via observability analysis. It is shown that the DLCM is observable and the unsteady initial states of the n-dimensional DLCM are uniquely computed from the first n discrete input/output data pairs, the inverse of the observability matrix and the first n DLCM impulse-response ordinates. The initial state vector is used in the recursive deterministic input-detection algorithm. The first n detected input values are necessarily identical with the first n actual inputs. A case study is presented, using the input-detection algorithm to derive operational rules for flood-release basins.