Instantaneous physical rainfall–runoff prediction technique using a power–law relationship between time to peak and peak flow of an instantaneous unit hydrograph and the rainfall excess intensity

The traditional instantaneous unit hydrograph (IUH) is very useful for theoretical analysis and practical forecasting of floods owing to its linear assumptions. Although various revised methods to overcome the unphysical assumptions have been proposed, it is still difficult to obtain efficiently a nonlinear IUH of diverse rainfall excess intensities in a watershed. In this study, we proposed practical and physical interpolation techniques to derive new IUHs from at least two existing IUHs corresponding to diverse rainfall excess intensities in a watershed. To interpolate the new IUHs, mass conservation law and power–law relationships between rainfall excess intensities and the peak flow and time to peak of IUHs were used. By employing convolution integration, surface rainfall–runoff hydrographs for timely varying rainfall events were derived. For verification, we applied the proposed technique to three real watersheds with different sizes ranging from 0.036 to 1,047 km². All flood prediction procedures were completed instantly, stably and the prediction results showed the accuracy of Nash–Sutcliffe efficiency (NSE) ¼ 0.55–0.93 and coefficient of determination (R²) ¼ 0.72–0.94.