University of Tehran Press Iranian Journal of Soil and Water Research 2008-479X 50 7 2019 11 22 Flood Routing using Muskingum Model with Fractional Derivative Flood Routing using Muskingum Model with Fractional Derivative 1667 1676 73891 10.22059/ijswr.2019.275566.668120 FA MirMohammad Bayrami PhD Candidate of Water Structures, Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, University College of Agriculture and Natural Resources, University of Tehran, Iran. Alireza Vatankhah Associate Professor, Department of Irrigation and Reclamation Engineering, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran Arezoo Nazi Ghameshlou Assistant Professor, Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran. Journal Article 2019 02 14 The existing Muskingum models vary only in the form of the storage equation. So far, for accounting the nonlinearity characteristic of flood wave, the form of the storage equation has been modified based on the experience and in a trial and error manner in order to capture the overall flood propagating characteristics more accurately. One of the theoretical based method for considering the nonlinear characteristics in Muskingum model is to use the fractional derivative in the continuity differential equation. This study presents a new Muskingum model in which the linear storage equation and the continuity equation with fractional derivative are used. As shown in this study, the new model can simulate flood waves with both linear and nonlinear behaviors. The proposed Muskingum model with fractional derivative order was implemented and tested on three different sets of flood data. The results of this study indicate that the proposed Muskingum model improves the results and estimates the flood wave characteristics more accurately than the traditional linear Muskingum models. The existing Muskingum models vary only in the form of the storage equation. So far, for accounting the nonlinearity characteristic of flood wave, the form of the storage equation has been modified based on the experience and in a trial and error manner in order to capture the overall flood propagating characteristics more accurately. One of the theoretical based method for considering the nonlinear characteristics in Muskingum model is to use the fractional derivative in the continuity differential equation. This study presents a new Muskingum model in which the linear storage equation and the continuity equation with fractional derivative are used. As shown in this study, the new model can simulate flood waves with both linear and nonlinear behaviors. The proposed Muskingum model with fractional derivative order was implemented and tested on three different sets of flood data. The results of this study indicate that the proposed Muskingum model improves the results and estimates the flood wave characteristics more accurately than the traditional linear Muskingum models. https://ijswr.ut.ac.ir/article_73891_5a70591240975326ab77effe5d1b1208.pdf