Variable Parameter Muskingum Routing Considering Downstream Effects

摘要

Using a variable parameter Muskingum method, a procedure for discharge hydrograph routing in prismatic channels considering downstream effects is presented. The method involves a two step process: (1) a given routing reach is divided into a number of subreaches with each subreach having a representative unique stage-discharge relationship established by using a gradually varied flow profile estimation technique; and (2) the routing of a given inflow hydrograph through these subreaches successively using the variable parameter Muskingum method with parameter variation achieved using the established stage-discharge relationships pertinent to the subreaches and the assumptions of the routing method. The ability of this procedure to route floods accounting for downstream effects is demonstrated by routing a given hypothetical inflow hydrograph in three rectangular channels each with a reach length of 40 km, and for two different scenarios of downstream boundary conditions, one resulting in an M1 profile and another in an M2 profile with the control at the end of the 40 km reach. The M1 profile is formed due to the prescribed boundary condition at the outlet of the reach that the flow depth at that section is equal to twice the normal depth in the channel reach. The M2 profile is formed due to a free fall located at the outlet of the reach. The routing results obtained using this procedure are compared with the corresponding Saint-Venant solutions arrived at using the U.S. National Weather Service's DAMBRK model, which is used as a benchmark. The performance of this discharge routing procedure compares well with the corresponding DAMBRK model solutions subject to the criterion │(1/S_0)partial deriv y/partial deriv x│ < 1 being satisfied.