General and Analytic Unit Hydrograph and Its Applications

Unit hydrograph (UH) is widely used for predictions of flood hydrograph from a known storm. Its concept and theory are simple and straightforward, but its practical applications are cumbersome because it is discrete and inflexible for different rainfall durations. An internet search indicates that though Nash's gamma function is widely accepted as a theoretical model, it is not a true form of instantaneous UH. Briefly, a simple, general, and analytic model for UH has not been found in the literature, which forms the objective of this research. To this end, we first make three hypotheses on instantaneous UH based on empirical observations; we next find a general unit-volume hydrograph for S-hydrograph that leads to analytic expressions for interval and instantaneous unit-volume hydrographs; we then apply the proposed method to simplify applications of the Soil Conservation Society (SCS) dimensionless UH. After that, we examine the proposed method with real-world data. We confirmed that the proposed general and analytic UH predicts flood hydrograph simply and accurately, and it agrees with data better than the classic Nash instantaneous UH model.