Invers Flood Routing based on Diffusion Wave Model (A Case Study on Yuan River, China)

Document Type : Research Paper


Department of Water Science and Engineering, Faculty of Agriculture, University of Bu Ali Sina, Hamedan, iran


it is important to have a fast and accurate model for predicting incoming hydrographs in order to reduce the financial and life damage in flood forecasting systems as well as water allocation issues, especially high priority consumption. In this study, using diffusion wave model, inverse flood routing in Yuan River in China was performed using mixing cell and Crank Nicolson numerical method. These numerical methods were chosen because of their high computational speed and no need for river topographic and hydraulic information. For this purpose, Yuan River flood information data for five years were used, then the numerical simulation results were compared with observational data. Accordingly, the statistical indices of coefficient of determination, Nash-Sutcliffe index, Wilmot index and residual sum coefficient were determined. The results showed that both numerical methods have good accuracy. The maximum error for the observed and calculated maximum discharge in Crank-Nicolson and mixing cell methods were 0.22 and 0.59%, respectively. Based on the results obtained in the prediction of maximum discharge and inlet hydrograph, it was found that the Crank Nicolson method is more accurate than the mixing cell method.


Hoseini, M., and Abrishami, J., (2011). Hydraulics of open channel. Imam Reza University Press, Mashhad. (In Persian).
Koussis, A, D., Mazi, K., Lykodis, S., and Argirion, A. A., (2012). Reverse flood routing with the inverted Muskingum storage routing scheme. Journal of Natural Hazards on earth system science. 12. pp. 217-227.
Mahmoodian Shooshtari, M., (2010). Principles of flow in open channels. Shahid Chamran University Press, Ahvaz. (In Persian).
Ningning, L., Feng, J., and Jun, Z., (2012). Flood routing based on diffusion wave equation using Lattice Boltzman method. Journal of procedia engineering. 28. pp. 190-195.
Noye, J., (1982). Finite difference methods for partial differential equations, in Noye, J. (Ed.), Numerical Solutions of Partial Differential Equations. North-Holland, New York. 647 pp.
Oodi, SH. (2016). Inverse flood routing using diffusion wave model. M.S.C. dissertation, University of Bu Ali Sina, Hamadan.
Price, R. K., (1982). A nonlinear theory of flood wave propagation. Journal of Appl. Math. Modeling. Vol.6.
Singh, V.P., Wang, G-T. and Adrian, D.D., (1997). Flood routing based on diffusion wave Eq. using mixing cell method. Hydrological Process. 11, pp. 1881–1894.
Wang, G.T., Chen, S. and Boll, J., (2003a). A semi-analytical solution of the Saint-Venant Eqs. for channel flood routing. Water Resour.Res, 39 (4), pp. 1076.
Wang, G.T., Chen, S. and Boll, J., Singh, V.P., (2003b). Nonlinear convection-diffusion Eq. with mixing-cell method for channel flood routing. Journal of Hydraulic engineering, ASCE, 8 (5), pp. 259–265.
Wang, G.T., Chunmei Y., Cairo, O. and Chen, S., (2005). Point FDF of Muskingum method based on the complete St -Venant equations.
Yang, Y., Theodore, A. and Nowak, D. J., (2016). Application of advection-diffusion routing model to flood wave propagation, (A case study on big Piney River, Missouri USA). Journal of Earth science, 27 (1), pp. 009–014.