Analytical Solution of Kinematic Wave Time of Concentration for Overland Flow under Green-Ampt Infiltration

Abstract

In this paper the well-known kinematic wave equation for computing the time of concentration for impervious surfaces has been extended to the case of pervious hillslopes, accounting for infiltration. An analytical solution for the time of concentration for overland flow on a rectangular plane surface is derived using the kinematic wave equation under the Green-Ampt infiltration. The relative time of concentration is defined as the ratio between the time of concentration of an infiltrating plane and the soil sorptivity time scale, depending on the normalized rainfall intensity and a parameter synthesizing the soil and hillslope characteristics. It is shown that for a more complex case (corresponding to the second domain of solution domain), the time of concentration can also be estimated by two simplified approximate procedures. An error analysis for the time of concentration computed for constant and time-varying infiltration is carried out. Finally, for a hillslope under the Green-Ampt infiltration, the time of concentration obtained by the kinematic wave equation is compared with that computed by a nonlinear storage model. An application of the proposed method for two different soils is shown and discussed.