Analytical Solutions of Nonlinear Kinematic Wave Model

An analytical solution of the nonlinear kinematic wave model of overland flow on a sloping plane for time-varying excess rainfalls of sinusoidal functions is presented by the method of characteristics. To obtain the closed form of the analytical solution, discharge per unit width in the expression of Manning’s formula is approximated by a parabolic curve. The analytical solution is also compared with the numerical one and their agreement is found to be good. The analytical solution is applied to rainfall and runoff processes with given hyetograph using Fourier series analysis. The computational results of the analytical solution are compared with the observed data. It explains the observation on an impermeable slope very well. It is found that the analytical solution is suitable for estimating design flood from excess rainfall in a simple watershed.