Muskingum river routing with dynamic bank storage

The Muskingum unsteady flow routing method is well established in the hydrological literature and its modest data requirements make it attractive for practical use. Muskingum routing is based on an assumed power relationship between channel storage and river stage, and consequently, it accounts for channel storage only and not bank storage. Routing parameters in the models are usually derived by calibration using measured discharge hydrographs. Bank storage is, therefore, implicitly accounted for, together with channel storage, but this may result in unrealistic parameter values. In this paper, Muskingum procedures are modified to explicitly account for the interaction between channel flow and bank storage in rivers with permeable river banks of varying hydraulic conductivity. The approach is verified by resynthesising a rating function used in rigorous routing in a hypothetical channel with permeable banks. The method is also applied to determine routing parameters for a reach along the Sabie River in South Africa by explicitly accounting for bank storage.

[1]  Vujica Yevjevich,et al.  Muskingum-Cunge Method with Variable Parameters , 1978 .

[2]  Vernon B. Sauer,et al.  Modification of routed streamflow by channel loss and base flow , 1974 .

[3]  Andrew Chadwick,et al.  Hydraulics in Civil and Environmental Engineering , 1993 .

[4]  G. Hornberger,et al.  Numerical Solution of the Boussinesq Equation for Aquifer‐Stream Interaction , 1970 .

[5]  Vijay P. Singh,et al.  Some notes on Muskingum method of flood routing , 1980 .

[6]  J. A. Cunge,et al.  On The Subject Of A Flood Propagation Computation Method (Musklngum Method) , 1969 .

[7]  Allen F. Moench,et al.  Application of the convolution equation to stream-aquifer relationships , 1972 .

[8]  Bernard Friedland,et al.  Linear Systems , 1965 .

[9]  M. A. Gill.  Flood routing by the Muskingum method , 1978 .

[10]  C. S. James,et al.  Synthesis of rating curves from local stage and remote discharge monitoring using nonlinear muskingum routing , 1998 .

[11]  Jaewan Yoon,et al.  Parameter Estimation of Linear and Nonlinear Muskingum Models , 1993 .

[12]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[13]  Victor Miguel Ponce.  Simplified Muskingum Routing Equation , 1979 .

[14]  Mohammad Akram Gill.  Numerical Solution of Muskingum Equation , 1992 .

[15]  Alvaro A. Aldama.  Least-Squares Parameter Estimation for Muskingum Flood Routing , 1990 .

[16]  C. Koutitas.  Elements of computational hydraulics , 1982 .

[17]  Y. Tung.  River flood routing by nonlinear muskingum method , 1985 .