Reverse stream ﬂow routing by using Muskingum models
Reverse stream ﬂow routing is a procedure that determines the upstream hydrograph given the downstream hydrograph. This paper presents the development of methodology for Muskingum models parameter estimation for reverse stream ﬂow routing. The standard application of the Muskingum models involves calibration and prediction steps. The calibration step must be performed before the prediction step. The calibration step in a reverse stream ﬂow routing system uses the outﬂow hydrograph and the inﬂow at the end period of the inﬂow hydrograph as the known inputs and Muskingum model parameters are determined by minimizing the error between the remaining portion of the predicted and observed inﬂow hydrographs. In the present study, methodology for parameter estimation is developed which is based on the concept of minimizing the sum of squares of normalized difference between observed and computed inﬂows subject to the satisfaction of the routing equation. The parameter estimation problems are formulated as constrained nonlinear optimization problem, and a computational scheme is developed to solve the resulting nonlinear problem. The performance evaluation tests indicate that a fresh calibration is necessary to use the Muskingum models for reverse stream ﬂow routing.