Analytical Solution of Nonlinear Kinematic Wave Model with Time-Varying Rainfall

An analytical solution of the nonlinear kinematic wave model of overland flow with time-varying rainfall on a sloping plane is presented by the characteristic equation. To obtain it in the closed form, we approximate discharge of Manning’s formula per unit width by a parabolic curve. It is compared with experimental data of rainfall and runoff process, and their agreement is satisfactory. It is also compared with the numerical result of the finite difference method, and their agreement is found to be good. When the rainfall is time-varying, the method of this study can derive the analytical solution. The analytical solution of the kinematic wave model with time-varying rainfalls is found to be suitable for estimating design flood from rainfall in a simple watershed. Floods in urban areas can be predicted by the kinematic wave model with given time-varying rainfalls when the urban areas consist of several simple watersheds.