An investigation of the relationship between the flood wave speed and parameters in runoff-routing models

An important aspect of flood management is the estimation of catchment response to storm events by simulation of flood wave propagation through the catchment storage. A derivation of the wave speed (c) is presented in terms of discharge (Q) and the exponent (m) in the storage (S)-discharge relationship S = kQm. The wave speed-discharge relationship has the form c = (αm c/m)Q1-m, where αc is a parameter in the kinematic wave model. The parameters in this relationship, however, change with flow conditions in the cross section, especially as flow leaves the main channel to inundate the floodplain. This finding confirms that the parameters in the single storage-discharge relationship do not have discrete values as used in many runoff-routing models, and hence the use of single parameter values is not suitable for estimating floods in many situations. It is shown that a more reasonable relationship is S = Sc + k1LQ1/b, where Sc is a threshold storage, and the other parameters are functions of the flow conditions. The parameters k, L, b and also the parameters in the wave speed-discharge relationship change between inbank, overbank, and fully developed floodplain flow situations. This paper investigates the relationship between the kinematic wave exponent (l/βc) and discharge that gives an estimate of (1/b) which is not provided by the wave speed-discharge relationship. This estimate is shown to be approximately equal to m, the exponent conventionally used in the storage-discharge relationship S = kQm. Further, the kinematic wave exponent (1/βc) can be approximated by the ratio between the water velocity and the flood wave speed. This analysis is used to explain the complicated behaviour of wave speed and water velocity in channel, overbank, and fully developed floodplain flows.