Time of Concentration Formula for Pervious Catchments

Abstract

An explicit formula is presented to determine the time of concentration of pervious, plane rectangular catchments. Unlike many existing empirical equations, the proposed formula expresses the time of concentration in terms of physically based catchment, soil, and rainfall characteristics. The length, slope, and surface roughness of the catchment are taken into account. The porosity, hydraulic conductivity, and a characteristic suction head of the underlying soil matrix are also considered. Moreover, the proposed formula takes into account the rate of rainfall, and the antecedent soil moisture content prior to the rain. The formula is based on the numerical results of a previously reported mathematical model, and it is derived using a curve-fitting technique. In the mathematical model, overland flow is represented by a kinematic wave, and the Green and Ampt formula is adopted to calculate losses from rainfall due to infiltration. It is shown that under special conditions of impervious catchments and initially saturated surface soil, for which analytical solutions are available, the proposed formula reduces to those obtained theoretically.