A caution about the multilinear discrete lag-cascade model for flood routing

SummaryInvestigation of the ability of the multilinear discrete lag-cascade model in reproducing hypothetical routing results obtained in rectangular channels using the Saint-Venant equations reveals that, in general, this method closely reproduces the Saint-Venant solutions of flood waves characterized by significant attenuation as compared with the corresponding solutions of the simpler two-parameter multilinear discrete cascade model on which it is based. However, adjusting the lag parameter at every routing time level, in terms of integer multiples of the routing time interval, introduces truncation error in the routing process resulting in stacking or separation of flow leading to abrupt falls or discontinuities in the routed hydrograph, thus rendering the multilinear discrete lag-cascade model unsuitable for flood routing and flood forecasting. To overcome this deficiency, the present authors suggest that the lag parameter be kept constant for the entire routing process of a given flood wave in the channel reach, while allowing other two parameters of the multilinear discrete lag-cascade model to vary as per the physical relationships established for this model. It is demonstrated that this constraint on the lag eliminates the deficiency in the model, albeit at some slight cost in fitting of the peak, and permits consideration of this model as being suitable model for flood routing and flood forecasting purposes. The study serves as a caution to flood modelers about the hitherto unrecognized pitfall of the multilinear discrete lag-cascade model for flood routing purposes and advocates its amendment by means of the lag constraint in order to overcome this deficiency.