It has been recognised that a flood propagation routine that operates
within the framework of a real-time flood forecasting service should u
se hydraulic numerical models-simplified for steep reaches but based o
n the complete de Saint Venant equations when the free surface slope i
s small. Using as state variable the steady-state discharge, instead o
f the water level corresponding to it, the authors identify a 'homogen
eous set' of five flood routing models, going from complete to kinemat
ic. To choose the most accurate and economic model, the suggested crit
erion, based on the analysis of sinusoidal solutions of the linearised
wave propagation, is the ratio between the desired time resolution an
d a channel response time, which is correlated with the slope. Congrue
nce of spatial steps with the temporal ones is discussed; some numeric
al examples, illustrating accuracy and economy of the proposed numeric
al models, are presented.