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

Abstract 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 overcome the unphysical assumptions have been proposed, it still difficult obtain efficiently a nonlinear IUH diverse rainfall excess intensities in watershed. In this study, we proposed physical interpolation techniques derive new IUHs from at least two existing corresponding To interpolate IUHs, mass conservation law power–law relationships between peak flow time were used. By employing convolution integration, surface rainfall–runoff hydrographs timely varying events derived. For verification, applied technique three real watersheds with different sizes ranging 0.036 1,047 km2. All flood prediction procedures completed instantly, stably results showed accuracy Nash–Sutcliffe efficiency (NSE) = 0.55–0.93 coefficient determination (R2) 0.72–0.94.