Bypassing Determination of Time of Concentration

Abstract

Reanalysis of the records, upon which the 120-year-old Rational Formula is based, reveals that the published linear relationship between rainfall duration and the ratio of peak discharge to the product of rainfall intensity and watershed area can also be replaced by a logarithmic regression. Such a regression is found, with reasonable correlation, suitable for two-dimensional laboratory watersheds, for four experimental urban watersheds, and for five small watersheds in Israel. Combining this regression with a power-law regression between rainfall intensity and duration, associated with any given recurrence interval, yields a general relationship between the variables. From this and through simple mathematical operations, the maximum discharge associated with that recurrence interval is determined. The variables in the new equation are watershed area and the empirical parameters of the regressions. Application of this equation bypasses determination of the highly influential time of concentration, which is an immeasurable variable and for which varied surrogates are used. It also saves determination of the coefficient