Simplified Use of Gamma-Distribution/Nash Model for Runoff Modeling

A simple method is suggested for computing the direct runoff hydrograph resulting from a complex storm using a two-parameter gamma distribution as the instantaneous unit hydrograph. The computation of the incomplete gamma function is accomplished indirectly, which requires evaluations of only simple functions that can be performed on a scientific calculator. In place of “unit hydrograph,” a “unit kernel” approach is suggested, which reduces the computational effort when dealing with any selected sampling interval because it implicitly accounts for the sampling interval. The use of the unit kernel renders the S-curve invariant with the sampling interval, as opposed to the conventional procedure. The new procedure enhances the applicability of the two-parameter gamma distribution or the Nash model for rainfall-runoff modeling, as the calculations can be performed using a spreadsheet, such as an Excel spreadsheet. Application of the new procedure on published data sets shows that the direct runoff obtained is almost the same as computed using either tabulated or computer-obtained values of the incomplete gamma function.