Clark's and Espey's unit hydrographs vs the gamma unit hydrograph / Les hydrogrammes unitaires de Clark et de Espey vs l'hydrogramme unitaire de forme loi gamma

Abstract

A two-parameter gamma distribution for synthetic unit hydrographs (SUH) is compared with the Clark's and Espey's SUHs. A critical comparison of Clark's and gamma UHs, in terms of recession characteristics and time–area curve, is presented. It is observed that, in principle, a gamma UH can represent the hydrograph recession better than the Clark's UH does. Selection of a time–area curve is needed for obtaining the Clark's UH. The main problem in developing a SUH using the Clark's method is identified as the non-availability of a parametric form of the time–area curve. The time–area curve as represented in the hydrological model HEC-1, for the use in Clark's method, is found inadequate and unjustified. Gamma UHs obtained without optimization, for several examples, are found consistent with their physical meanings and better than the respective Clark's UH in reproducing runoff obtained with optimization. The parameters of Clark's UH (i.e. time of concentration and recession constant), as optimized through the HEC-1 program, are found inconsistent with their empirical origins and physical meanings; these lose their physical meaning and serve only as fitting parameters. This is due to the inappropriate time–area curve. A gamma UH has also the advantage of having fewer parameters than Clark's UH, which makes it more identifiable while still maintaining a connection with the physics of the problem. Espey's SUH for urban watersheds is transmuted to a gamma distribution using the empirical equations for the peak and time to peak of the UH. A numerical UH for a gauged catchment, generally obtained through linear programming or a least-squares approach, can be easily transmuted to a gamma UH and, hence, can be given a conceptual interpretation. Thus, these can also be used for developing a SUH.