Ferdowsi University of MashhadWater and Soil2008-475735620220220Development of Reverse Hydraulic Flood Routing Method in Ephemeral Rivers Considering Infiltration RateDevelopment of Reverse Hydraulic Flood Routing Method in Ephemeral Rivers Considering Infiltration Rate8228054161510.22067/jsw.2022.73670.1116FAA.A. KhosraviCandidate Department of Irrigation and Reclamation Engineering. College of Agriculture and Natural Resources. University of Tehran. Karaj, IranA. Parvaresh RiziAssociate Professor, Department of Irrigation and Reclamation Engineering, College of Agriculture and Natural Resources, University of TehranR. BaratiPh.D. in Civil Engineering, Head of Applied Research Group, Khorasan Razavi Water AuthorityJournal Article20211120<strong>Introduction:</strong> In many cases, after a flood, some information is needed about the flood characteristics at the upstream of a specific location where there is no hydrometric station on the river or flow discharge, and water surface level was not measured at the time of the flood. In reverse flood routing, calculations are performed from the downstream section step by step to the upstream section of the river and inlet hydrograph is produced based on river hydraulic characteristics and downstream hydrograph. During floods in rivers, the volume of floods gradually decreases due to infiltration into the bed and sides. This reduction in flood volume, called transmission losses, is significant in arid areas. Therefore, developed models for flood routing in seasonal rivers in arid and semi-arid regions should provide an appropriate estimate of transmission losses. In the routing process, the governing equations are combined with an equation to account for infiltration or seepage losses into the riverbed or canal. Then, by routing the flood along the interval and examining the resulting hydrographs at different points, the amount of transmission losses is determined. In the present study, which deals with the reverse hydraulic routing of floods in arid areas, the infiltration losses along the river estimated by the Green-Ampt relationship was considered in numerical models so as to perform reverse flood routing with appropriate accuracy and under hydraulic conditions of ephemeral rivers. To the best of our knowledge, so far no study has analyzed transmission losses in reverse hydraulic flood routing.<br /><strong>Materials and Methods:</strong> The equations governing gradual variable flows are known as the Saint-Venant equations, which include the continuity and the momentum equations. In hydraulic flow routing models, the complete form of the continuity equation is used, but the momentum equation is applied in various forms obtained by removing some components. The simplest hydraulic routing model is the kinematic wave model in which the components related to inertial forces and pressure force in the momentum equation are omitted. In the diffusion wave model, the components related to inertial forces are omitted, but the pressure force is taken into account and finally, in the dynamic wave model, the momentum equation is considered completely without simplification. In the present study, separate programs were prepared in MATLAB 2013 software for reverse hydraulic flood routing by Kinematic and dynamic wave methods. In these numerical models, by coupling the Green-Ampt infiltration equation with the continuity equation, the depth and flow rate in different places and times are calculated in the upstream direction of the flow.<br /><strong>Results and Discussion:</strong> In order to validate the results of the developed numerical models and to evaluate its applicability, a set of measured data known as Lane hydrograph and Bambeichi hydrograph was used. The results showed that both reverse hydraulic flood routing models produced the upstream hydrograph with appropriate accuracy. The results of the Bambeichi hydrograph data were more accurate than the Lane hydrograph due to its shorter length of the interval between upstream and downstream sections. For example, the peak discharge of inlet hydrograph calculated by the dynamic wave method for the Lane hydrograph data had an error of 7% compared to the observed value, while the error obtained for Bambeichi hydrograph data was 2%. Therefore, the accuracy of inverse routing models in estimating the volume of upstream hydrograph and consequently the amount of transmission losses was desirable especially for the Bambeichi hydrograph data. The highest error in estimating losses was 25% for the reverse kinematic model and the data related to the Lane hydrograph.<br />Between the two reverse hydraulic flood routing methods, the performance of the dynamic wave method was more accurate for the most numerical experiments, as the governing equations are completely solved in this method. This difference is more pronounced in the Lane hydrograph, which represents the actual conditions of an ephemeral river.<br /><strong>Conclusion: </strong>The accuracy of the developed numerical models was 90% in estimating the peak flow rate of the upstream hydrograph, and between 85% and 97% in estimating the time related to this discharge. The volume of the upstream hydrograph, which indicates the model performance in estimating the infiltration in the flow path, was also modeled with 75 to 98% accuracy. These results show that the numerical models simulate reverse flood routing with acceptable accuracy in ephemeral rivers, where transmission or seepage losses are significant. Due to different approaches in calculating infiltration losses, these methods can make differences for the hydrograph output of numerical models.<br /> <strong>Introduction:</strong> In many cases, after a flood, some information is needed about the flood characteristics at the upstream of a specific location where there is no hydrometric station on the river or flow discharge, and water surface level was not measured at the time of the flood. In reverse flood routing, calculations are performed from the downstream section step by step to the upstream section of the river and inlet hydrograph is produced based on river hydraulic characteristics and downstream hydrograph. During floods in rivers, the volume of floods gradually decreases due to infiltration into the bed and sides. This reduction in flood volume, called transmission losses, is significant in arid areas. Therefore, developed models for flood routing in seasonal rivers in arid and semi-arid regions should provide an appropriate estimate of transmission losses. In the routing process, the governing equations are combined with an equation to account for infiltration or seepage losses into the riverbed or canal. Then, by routing the flood along the interval and examining the resulting hydrographs at different points, the amount of transmission losses is determined. In the present study, which deals with the reverse hydraulic routing of floods in arid areas, the infiltration losses along the river estimated by the Green-Ampt relationship was considered in numerical models so as to perform reverse flood routing with appropriate accuracy and under hydraulic conditions of ephemeral rivers. To the best of our knowledge, so far no study has analyzed transmission losses in reverse hydraulic flood routing.<br /><strong>Materials and Methods:</strong> The equations governing gradual variable flows are known as the Saint-Venant equations, which include the continuity and the momentum equations. In hydraulic flow routing models, the complete form of the continuity equation is used, but the momentum equation is applied in various forms obtained by removing some components. The simplest hydraulic routing model is the kinematic wave model in which the components related to inertial forces and pressure force in the momentum equation are omitted. In the diffusion wave model, the components related to inertial forces are omitted, but the pressure force is taken into account and finally, in the dynamic wave model, the momentum equation is considered completely without simplification. In the present study, separate programs were prepared in MATLAB 2013 software for reverse hydraulic flood routing by Kinematic and dynamic wave methods. In these numerical models, by coupling the Green-Ampt infiltration equation with the continuity equation, the depth and flow rate in different places and times are calculated in the upstream direction of the flow.<br /><strong>Results and Discussion:</strong> In order to validate the results of the developed numerical models and to evaluate its applicability, a set of measured data known as Lane hydrograph and Bambeichi hydrograph was used. The results showed that both reverse hydraulic flood routing models produced the upstream hydrograph with appropriate accuracy. The results of the Bambeichi hydrograph data were more accurate than the Lane hydrograph due to its shorter length of the interval between upstream and downstream sections. For example, the peak discharge of inlet hydrograph calculated by the dynamic wave method for the Lane hydrograph data had an error of 7% compared to the observed value, while the error obtained for Bambeichi hydrograph data was 2%. Therefore, the accuracy of inverse routing models in estimating the volume of upstream hydrograph and consequently the amount of transmission losses was desirable especially for the Bambeichi hydrograph data. The highest error in estimating losses was 25% for the reverse kinematic model and the data related to the Lane hydrograph.<br />Between the two reverse hydraulic flood routing methods, the performance of the dynamic wave method was more accurate for the most numerical experiments, as the governing equations are completely solved in this method. This difference is more pronounced in the Lane hydrograph, which represents the actual conditions of an ephemeral river.<br /><strong>Conclusion: </strong>The accuracy of the developed numerical models was 90% in estimating the peak flow rate of the upstream hydrograph, and between 85% and 97% in estimating the time related to this discharge. The volume of the upstream hydrograph, which indicates the model performance in estimating the infiltration in the flow path, was also modeled with 75 to 98% accuracy. These results show that the numerical models simulate reverse flood routing with acceptable accuracy in ephemeral rivers, where transmission or seepage losses are significant. Due to different approaches in calculating infiltration losses, these methods can make differences for the hydrograph output of numerical models.<br /> https://jsw.um.ac.ir/article_41615_bdce89c2c776d313b20f94bab401f3a5.pdf