Development and Verification of an Analytical Solution for Forecasting Nonlinear Kinematic Flood Waves

A new approximate analytical solution to the nonlinear kinematic wave equation is proposed. The solution has been derived by combining an implicit solution obtained with the method of characteristics with analytical decomposition and successive approximation. The new solution was verified favorably with a finite-difference approximation. A field verification via a comparison with observed storm hydrographs from the Schuylkill River near Philadelphia indicated that with constant lateral flow the nonlinear model reasonably predicted the observed flow rates, except during periods of intense rainfall. An improved nonlinear model that accounts for variable lateral flow due to changing effective precipitation is proposed. Numerical measures of accuracy indicated that the new variable-rate nonlinear model performs better than the constant lateral flow and the linear kinematic wave model. The linear kinematic wave model produced poor forecasts, especially in the flow time and flood-peak time. The new solution is ...