Multilinear discrete cascade model for channel routing

Discrete state-space approximation of the continuous Kalinin–Milyukov–Nash cascade of noninteger storage elements

“…Camacho and Lees, 1999;Keefer and McQuivey, 1974;Kontur, 1977;Kundzewicz and Dooge, 1985;O'Connor, 1976;Perumal, 1994;Szolgay, 1991Szolgay, , 2004, the discrete linear cascade model (DLCM) (Szollosi-Nagy, 1982, 1989Szilagyi, 2003Szilagyi, , 2004Szilagyi et al, 2005) stands out for several reasons: (a) it is equivalent to the discretized form of the continuous, spatially discrete, kinematic wave equation (Szollosi-Nagy, 1989); (b) it is specifically formulated to deal with discrete data whether in a pulse-or sample-data system framework; (c) it is discretely coincident, which means that for identical inputs (as between the discrete and continuous models), it gives identical outputs at discrete time increments; (d) it does not require numerical iterations (so numerical stability is not an issue) because it is written in a state-space form with the state-and input-transition matrices given explicitly; (e) since it is in a state-space form, linear filtering techniques, such as the Kalman filter (1960), can directly be applied; and last but not the least, (f) with it, the inverse problem of finding the input sequence to a given output sequence (which often is needed to fill data gaps in a streamflow series) is a simple algebraic manipulation.…”

A caution about the multilinear discrete lag-cascade model for flood routing

“…The convenience of linear analysis can still be used for modeling the nonlinear flood movement process by working within the limitation imposed by the linearity assumption. Recognition of this concept has led to the development of multilinear flood routing methods (Keefer and McQuivey, 1974;Becker, 1976;Kundzewicz, 1984;Becker and Kundzewicz, 1987;Perumal, 1992Perumal, , 1994a and variable parameter flood routing methods (Ponce and Yevjevich, 1978;Perumal, 1994b).…”

Modular conceptual modelling approach and software for river hydraulic simulations

“…Several expansions and novel approaches are being proposed, such as multi-linear discrete (lag) channel routing methods (e.g. Perumal, 1994;Camacho and Lees, 1999) and straightforward raster-based flood inundation models, which use Cunge-type storage cells (Cunge, 1975) in combination with simple equations to calculate the intercell fluxes (e.g. Estrela and Quintas, 1994;Bechteler et al, 1994; and see Hunter et al (2007Hunter et al ( , 2008 and references therein).…”