AN INVESTIGATION OF THE RELATIONSHIP BETWEEN THE FLOOD WAVE SPEED ANDPARAMETERS 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 thro ugh the catchment storage. A derivation of the wave speed (c) is prese nted in terms of discharge (Q) and the exponent (m) in the storage (S) -discharge relationship S = kQ(m). The wave speed-discharge relationsh ip has the form c = (alpha(c)(m)/m)Q(1-m), where alpha(c) is a paramet er in the kinematic wave model. The parameters in this relationship, h owever, change with flow conditions in the cross section, especially a s flow leaves the main channel to inundate the floodplain. This findin g confirms that the parameters in the single storage-discharge relatio nship do not have discrete values as used in many runoff-routing model s, and hence the use of single parameter values is not suitable for es timating floods in many situations. It is shown that a more reasonable relationship is S = S-c + k(1)LQ(1/b), where S-c is a threshold stora ge, and the other parameters are functions of the flow conditions. The parameters k(1), L, b and also the parameters in the wave speed-disch arge relationship change between inbank, overbank, and fully developed floodplain flow situations. This paper investigates the relationship between the kinematic wave exponent (1/beta(c)) and discharge that giv es an estimate of (lib) which is not provided by the wave speed-discha rge relationship. This estimate is shown to be approximately equal to m, the exponent conventionally used in the storage-discharge relations hip S = kQ(m). Further, the kinematic wave exponent (1/beta(c)) can be approximated by the ratio between the water velocity and the flood wa ve speed. This analysis is used to explain the complicated behaviour o f wave speed and water velocity in channel, overbank, and fully develo ped floodplain flows.