This paper aims to fill a gap between present and past research approaches to modelling flow in open channels. In particular, a history of the analytical solutions of a linearized St. Venant equation is presented. A solution of the linearized St. Venant equation, describing the response of a river channel to a single impulse forcing, the so called Instantaneous Unit Hydrograph (IUH), can be described using cumulants, defined as the moments of a logarithm of a variable. A comparison of analytical and numerical solutions of flood wave propagation under various flow conditions is given. The river reach of Biała Tarnowska is used as an illustration of both approaches. A practical application of simplified solutions to the emulator of a flood wave propagation is suggested showing a link between theory and practice.
Castelletti A., Galelli S., Restelli M., Soncini-Sessa R., 2012, Data-driven dynamic emulation modelling for the optimal management of environmental systems, Environmental Modelling and Software 34, 30-43, DOI: 10.1016/j.envsoft.2011.09.003.
Cholet C., Charlier J.-B., Moussa R., Steinmann M., Denimal S., 2017, Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection-diffusion equation, Hydrology and Earth System Sciences, 21 (7), 3635-3653, DOI: 10.5194/hess-21-3635-2017.
Chow V.T., Maidment D.R., Mays L.W., 1988, Applied hydrology, McGraw Hill, 572 pp.
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