Snyder-gamma synthetic unit hydrograph

Abstract

By equating the time to peak and the peak flow rate computed by the formulae of the Snyder method to the abscissa and the ordinate of the peak point of the analytically modified density function of the 2-parameter gamma distribution, it is shown on a few real-life cases that such formed Snyder-gamma synthetic unit hydrograph satisfies very closely the one-third and two-thirds rule for the widths of the Snyder synthetic unit hydrograph at 50% and 75% of its peak (W50, W75). With the objective of bringing further closer together the four points at the tips of W50 and W75 of the fitted gamma distribution to those four points by the Snyder method, the time to peak of the synthetic unit hydrograph is allowed to vary within 50% and 150% of that given by the Snyder formula. In quite a few real-life cases considered in this study, by shifting the time to peak of the gamma synthetic unit hydrograph 20~40% of the time to peak by the Snyder formula, only about a 2 % improvement in matching the W50 and W75 points is achieved. Therefore, the modified density function of the 2-parameter gamma distribution whose two parameters are computed by equating its mode to the peak point of the synthetic unit hydrograph provides a reasonable curve for the overall shape of it.