Values for the exponent of the storage-discharge equation in runoff-routing models

A storage-discharge equation: S = kQ^m is often used in runoff-routing models. The prediction by the models is highly sensitive to the value of exponent m used. A discharge-depth equation: q = Ky^αS ^{1 2}_e can be used to simulate overland and channel flows and the two equations considered here are shown to be similar and their parameters interrelated. Although the species of vegetative covers encountered in field data considered in the present study are probably not typical of those generally encountered on the catchments, their characteristics which influence overland and channel flows particularly on small catchments are of relevance here. The values of α obtained from shallow overland flow and channel flow studies suggest that the exponent m in the storage-discharge equation should be varied between 0.33 and 1.00 depending upon the regime of flow and degree of turbulence in the flow. While the study provides a further understanding of the variation of exponent m, more research is needed particularly in quantifying the degree of turbulence in the flow and developing a practical method of varying m in the runoff-routing model to account for flow conditions present over the catchment.