Application of Gamma functions to the determination of unit hydrographs

Abstract. There are many methods for calculating unit hydrograph, such as analysis method, trial algorithm and least squares method. But these methods have certain requirements for flood datas and the unit hydrograph may not be optimal. Based on the theory of composition, a hydrological system was viewed as a generalized collection in this study and Gamma functions were used to simulate the basin convergence process. At the same time, the Gamma function is parameterized and the parameters of Gamma function are optimized by genetic algorithm, which is based on the minimum error between the calculation of confluence process and the measurement process, before deriving the unit hydrograph. The Collins iteration method was used to compute the unit hydrograph. The results of actual calculated examples showe that this method is more precise than other methods, while it can also illustrate the law of runoff.