Development and Verification of an Analytical Solution for Forecasting Nonlinear Kinematic Flood Waves
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VIEW THE REPLYPublication: Journal of Hydrologic Engineering
Volume 11, Issue 4
Abstract
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 simple to apply and permits the efficient forecast of nonlinear kinematic flood waves without the usual stability restrictions of numerical models. The new formula also permits the analysis of the effect of nonlinear parameters in the area-discharge relationship on hydrograph characteristics. The hydrograph peak time appears to be very sensitive to the magnitude of the nonlinear exponent . For values of , the peak flow occurs at a time earlier than that predicted by a linear hydrograph . For values of , the peak flow occurs at a time later than that predicted by a linear hydrograph.
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Acknowledgments
Streamflow data for the present study was provided online by the U.S. Geological Survey. Rainfall information for the present study was provided online by the U.S. National Oceanic and Atmospheric Administration.
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© 2006 ASCE.
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Received: Feb 8, 2005
Accepted: Aug 29, 2005
Published online: Jul 1, 2006
Published in print: Jul 2006
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