Unit Hydrograph Theory: A 60-Year Unfulfilled Promise

In the procedure proposed by Sherman and hence the standard procedure for unit hydrograph derivation, observed rainfall and corresponding runoff data are utilized to deduce the unit hydrograph for a specified rain duration. This is a lumped system approach without considering the physical flow process inside the watershed. It has long been found that for a given rain duration the unit hydrographs derived from different rainfalls are not the same; usually the more the rain the higher the peak. Often these different unit hydrographs are averaged or weighted and combined to yield a single graph which is regarded as the unit hydrograph for that rain duration. It is obvious that the relation between watershed rainfall (the input) and runoff (the output) is not a linear function. The nonlinearity can be observed through watershed hydrologic records or by investigating flow equations such as: Manning, Darcy-Weisbach or Saint-Venant, for depth and velocity or discharge. In this study, the kinematic-wave based geomorphic IUH model (KW-GIUH) proposed by Lee and Yen was adopted for simulating watershed runoff and demonstrating the nonlinearity of the rainfall-runoff processes. The watershed runoff-response function is expressed as a set of instantaneous unit hydrographs to account for different rainfall input conditions. Hydrologic records from two watersheds in Taiwan were used to demonstrate the nonlinearity of the runoff process, and used as examples to show the capability of the KW-GIUH model to handle the nonlinearity. It is hope that the improvement of accounting for the nonlinear effect will help to make the unit hydrograph theory to fulfill its promise.