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

摘要

The linear unit hydrograph used in hydrologic design analysis and floodforecasting is known as the transfer function and the kernel function intime series analysis and systems theory, respectively. This paper reviewsthe use of an input-dependent or variable kernel in a linear convolutionintegral as a quasi-nonlinear approach to unify nonlinear overland flow,channel routing and catchment runoff processes. The conceptual model of avariable instantaneous unit hydrograph (IUH) is characterized by a nonlinearstorage-discharge relation, q = cNsN, where the storage exponent N is anindex or degree of watershed nonlinearity, and the scale parameter c is adischarge coefficient. When the causative rainfall excess intensity of aunit hydrograph is known, parameters N and c can be determined directly fromits shape factor, which is the product of the unit peak ordinate and thetime to peak, an application of the statistical method of moments in itssimplest form. The 2-parameter variable IUH model is calibrated by the shapefactor method and verified by convolution integral using both the direct andinverse Bakhmeteff varied-flow functions on two watersheds of vastlydifferent sizes, each having a family of four or five unit hydrographs asreported by the well-known Minshall (1960) paper and the seldom-quotedChilds (1958) one, both located in the US. For an 11-hectare catchment nearEdwardsville in southern Illinois, calibration for four moderate stormsshows an average N value of 1.79, which is 7% higher than the theoreticalvalue of 1.67 by Manning friction law, while the heaviest storm, which isthree to six times larger than the next two events in terms of the peakdischarge and runoff volume, follows the Chezy law of 1.5. At the other endof scale, for the Naugatuck River at Thomaston in Connecticut having adrainage area of 186.2 km2, the average calibrated N value of 2.28varies 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 turbulentoverland flow and that of 3.0 for laminar overland flow. Based on analyticalresults from the small Edwardsville catchment, the 2-parameter variable IUHmodel is found to be defined by a quadruplet of parameters N, c, the stormduration or computational time step Δt, and the rainfall excess intensityi(0), and that it may be reduced to an 1-parameter one by defaulting thedegree of nonlinearity N to 1.67 by Manning friction. For short, intensestorms, the essence of the Childs – Minshall nonlinear unit hydrographphenomenon is encapsulated in a peak flow equation having a single (scale)parameter c, and in which the impact of the rainfall excess intensityincreases from the linear assumption by a power of 0.4. To illustrate keysteps in generating the direct runoff hydrograph by convolution integral,short examples are given.