UC Santa Barbara

Reverse stream flood routing determines the upstream hydrograph in a stream reach given the downstream hydrograph. The Muskingum model of flood routing involves parameters that govern the routed hydrograph. These parameters are herein estimated using simulation methods coupled with optimization tools to achieve optimized parameters. Different simulation methods are shown to perform unequally in the estimation of nonlinear Muskingum parameters. This paper presents two simulation methods for nonlinear Muskingum reverse flood routing: (1) Euler equations and (2) Runge-Kutta 4th order equations. Moreover, the generalized reduced gradient (GRG) is used as the optimization tool that minimized the sum of the squared deviations (SSQ) between observed and routed inflows in a benchmark flood routing problem. Results show the Runge-Kutta 4th order equations yield better routed hydrographs with smaller SSQ than obtained in previous research and with the first simulation method (Euler equations).