Abstract
Abstract. The rainfall–runoff conceptual model as a cascade of submerged linear reservoirs with particular outflows depending on storages of adjoining reservoirs is developed. The model output contains different exponential functions with roots of Chebyshev polynomials of the first kind as exponents. The model is applied to instantaneous unit hydrograph (IUH) and recession curve problems and compared with the analogous results of the Nash cascade. A case study is performed on a basis of 46 recession periods. Obtained results show the usefulness of the model as an alternative concept to the Nash cascade.
Highlights
The significance of the rainfall–runoff relation conceptual model introduced by Nash as a linear cascade of reservoirs (Nash, 1957) and developed later as parallel cascades (Wittenberg, 1975; Oben-Nyarko, 1976) known nowadays as the Diskin model (Diskin et al, 1978; Diskin, 1980) cannot be overestimated
instantaneous unit hydrograph (IUH) and recession curves yielded by SC2 were compared with analogous Nash model results
0.90 (c) of equations describing water flow throughout the cascade, the value of the storage coefficient k for the last reservoir in the chain is doubled in relation to the previous reservoirs, which allows determination of the eigenvalues of the equations set as roots of successive Chebyshev polynomials of the first kind
Summary
The significance of the rainfall–runoff relation conceptual model introduced by Nash as a linear cascade of reservoirs (Nash, 1957) and developed later as parallel cascades (Wittenberg, 1975; Oben-Nyarko, 1976) known nowadays as the Diskin model (Diskin et al, 1978; Diskin, 1980) cannot be overestimated. Bárdossy (2007) noticed the great uncertainty of the identified cascade parameters and related difficulties in the determination of the optimum parameters set for a particular catchment. These problems, together considered with the high diversity of real hydrographs shapes in-
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