A measure of watershed nonlinearity: interpreting a variable instantaneous unit hydrograph model on two vastly different sized – watersheds

This paper reviews the use of an input-dependent kernel in a linear convolution integral as a quasi-nonlinear approach to unify nonlinear overland flow, channel routing and catchment runoff processes. The conceptual model of a variable kernel or instantaneous unit hydrograph (IUH) is characterized by a nonlinear storage-discharge 5 relation, q=cs , where the storage exponent N is an index or degree of watershed nonlinearity. When the causative rainfall excess intensity of a unit hydrograph is known, parameters N and c can be determined directly from its shape factor, the product of the unit peak ordinate and the time to peak. The model is calibrated by the shape factor and verified by convolution integral on two watersheds of vastly different sizes, each 10 having a family of four or five unit hydrographs, data of which were published by Childs in 1958 for the Naugatuck River and by Minshall in 1960 for the Edwardsville catchment. For an 11-hectare catchment near Edwardsville in southern Illinois, the US, four moderate storms show an average N value of 1.79, which is 7% higher than the theoretical value of 1.67 by Manning friction law, while the heaviest storm, which is three to 15 six times larger than the next two events in terms of the peak discharge and runoff volume, follows the Chezy law of 1.5. At the other end of scale, for the Naugatuck River at Thomaston in Connecticut, the US, having a drainage area of 186.2 km, the average N value of 2.28 varies from 1.92 for a minor flood to 2.68 for a hurricane-induced flood, all of which lie between the theoretical value of 1.67 for turbulent overland flow and that 20 of 3.0 for laminar overland flow. Short examples and a spreadsheet template are given to illustrate key steps in generating the direct runoff hydrograph by convolution integral with the 2-parameter variable IUH model.