HYDRODYNAMIC DERIVATION OF A GENERALIZED VARIABLE PARAMETER MUSKINGUM METHOD

Abstract

A Generalized Variable Parameter Muskingum Discharge (GVPMD) routing method is a simplified hydraulic routing method based on the approximation of the St. Venant's equations, which describe the one-dimensional flow in a channel or a river reach. An approach is presented for directly deriving a generalized variable parameter Muskingum method from the St. Venant's equations for routing floods in channels of prismatic cross-sections of any shape, and flow following Manning's friction law. The approach also allows for the simultaneous computation of the stage hydrograph corresponding to a given inflow or the routed hydrograph, a feature which is generally absent in the simplified hydraulic routing methods. The routing equation of this method is the same as that of Muskingum flood routing method and it has been demonstrated that• this method can directly account for flood wave attenuation without attributing it to numerical property of the method as theorized in the Muskingum-Cunge method. The Muskingum parameters B and K, viz., the weighting parameter and the travel time respectively, have been related to the channel and flow characteristics. Using this method, the nonlinear behaviour of flood wave movement may be modelled by varying the parameters of B and K at every routing time level, but still adopting the linear form of the solution equation. A total number of `675' numerical experiments have been conducted to test the developed method for routing the flood waves in channels of prismatic trapezoidal, rectangular and triangular cross-sections, and each type of these channels are characterized by different bed slopes and Manning's roughness coefficients. The test results were compared with the results of the corresponding St.Venant's solutions arrived iv at by routing the same inflow hydrograph using the HEC-RAS model, which is considered as the benchmark model. To obtain the benchmark solutions, 75 number of runs have been conducted on HEC-RAS model. Using the proposed method, routing solutions in each of the test runs have been obtained for a reach length of 100 km, and by considering the entire 100 km length as a single reach, and 2, 3, 4, 5, 8, 10, 25, 50 equal sub-reaches. Routing solutions at the end 100 km of the reach is obtained by successively routing the flood waves through each of these sub-reaches. Routing through all these sub-reaches could be achieved successfully when the proposed method is found to be well within the applicability limits of the method imposed by the assumptions of the method. Under this condition, the method could reproduce the benchmark solutions very closely. A number of performance measures have been defined to measure the closeness or otherwise of the benchmark solutions reproductions by the proposed method. V