In many hydrologic investigations concerning small watersheds, data and observations are totally inadequate to provide a basis for outflow hydrographs. Consequently, a variety of empirical approaches have been developed which have limited rational validity. Hydrograph synthesis offers a reasonable approach to predicting the outflow hydrograph characteristics. In order to synthesize a hydrograph, it is necessary to mathematically describe the physical behavior of the dynamic processes involved in the hydrologic phenomena. Hydrograph synthesis may be considered to comprise (a) hydrographs (actual or simulated) of precipitation, (b) hydrographs of abstractions such as interception, infiltration, and depressional storage, (c) routing or translating the net rainfall rate (rate of rainfall excess) in finite intervals of time and distances up to the outlet point. The complexities of this routing procedure are many, considering the variable factors such as the shape and size of watershed, soil and vegetative characteristics, nonuniform surface conditions, slopes, and channel geometry. This report is a review of the relationships developed for describing each hydrologic process from the design storm pattern to the final phase of the channel routing. Satisfactory simulation requires connecting all of these process descriptions in such a manner that they combine into a logical and compatible total dynamic system. Schematic diagrams are presented in the discussion and the various methods available for the different stages of hydrograph synthesis are indicated.
Narayana, V. V. Dhruva and Bagley, Jay M., "Mathematical Simulation of Small Watershed Hydrologic Phenomena" (1967). Reports. Paper 449.