A STUDY ON PROPAGATION OF FLOOD WAVE IN A STREAM CONSIDERING STREAM-AQUIFER INTERACTION USING VARIABLE PARAMETER MUSKINGUM METHODS

Abstract

Stream aquifer interaction is one of the important components of the stream flow processes, especially in deserts and water deficient regions. Apart from the natural recharge which contributes to the groundwater storage due to rainfall-runoff process over a catchment, the stream-aquifer interaction process also contributes to this storage over the catchment and also sustains the flow in a river as baseflow. However, many a times this process is not given its due importance and consequently not taken into account in the water availability assessment of the catchment. The major objective of this study is to present different approaches of accounting this process during the passage of a flood wave in a stream, when stream-aquifer is enabled by the prevailing stream bed geological conditions of a stream, under the scenarios of stream fully or partially penetrating the adjoining aquifer. It is assumed that the flow in the stream is one-dimensional, but the flow in the aquifer can be one-dimensional or two-dimensional, depending on the existing flow scenarios in the aquifer and the data availability. With this background, the following related problems are investigated in this study. Stream-aquifer interaction process play a dominant role in the form of lateral flow which affects the flood wave transformation process in the considered study reach in the absence of runoff causing precipitation in the intervening catchment of the study reach. Tracking a flood wave along a stream requires the use of appropriate tools, like the flood routing model. The available literature in this regard reveal the use of a variant of the well-known Muskingum method, known as the nonlinear Muskingum method which routes the flood hydrograph considering non-linearity in the routing process by duly accounting for the river-aquifer interaction process in the study reach. However, this study uses the rating curve relevant to the study reach of the stream to convert the discharge to stage or flow depth at mid-section of the considered sub-reach of the study reach for using the governing equation of the stream-aquifer interaction process during the flood propagation study. Therefore, the use of rating curve for converting discharge of the nonlinear Muskingum method into the corresponding stage hydrograph required for considering stream-aquifer interaction process in the study reach restricts the application of the nonlinear rating method only to steep slope river reaches. iii To overcome such a limitation in the use of such simplified routing methods in streams of moderate bed slopes, this study proposes a better alternative simplified routing method which has the capability to route a flood hydrograph characterized by discharge variable, but capable of estimating the associated stage hydrograph required for accounting stream-aquifer interaction process in the study reach without the use of established rating curve of the study reach. This method known as the Variable Parameter Muskingum Method (VPMM) was proposed by Perumal and Price (2013). Alternatively, one can directly employ a stage hydrograph variable based simplified routing method for accounting stream-aquifer interaction process during the passage of a flood wave in a stream reach duly accounting for stream-aquifer interaction process in the study reach. This method known as the Variable Parameter Muskingum stage-hydrograph (VPMS) routing method was proposed by Perumal and Ranga Raju (1998) which is capable of estimating associated discharge hydrograph at the location of the study reach without using the established rating curve of the stream-reach. This study employs both these two routing methods for accounting stream-aquifer interaction process during the passage of a flood wave propagation in a stream reach, where this interaction process is conducive to take place. Different possible stream scenarios with reference to the surrounding aquifer environment are explored for accounting stream-aquifer interaction in a study reach of a stream, like the stream fully or partially penetrating the surrounding aquifer. Also, the flow scenarios of flow in aquifer being one-dimensional or two-dimensional can be considered in the study. A brief summary of the outcome of the investigations carried out in the study are presented herein. The present study is conducted with the following objectives: 1) Streamflow routing using the VPMM method and assuming one-dimensional flow in the aquifer perpendicular to the stream axis for the case of fully penetrating stream; 2) Streamflow routing using the VPMS method and assuming one-dimensional flow in the aquifer perpendicular to the stream axis for fully penetrating stream case. 3) Use of the VPMM and VPMS methods for streamflow routing and assuming twodimensional flow in the aquifer perpendicular to the stream axis as well as parallel to it for fully penetrating stream case. 4) Use of the VPMS and VPMM methods for streamflow routing and assuming two-dimensional flow in the aquifer for partially penetrating stream case. The streamaquifer model for fully penetrating stream has been developed for solving the one-dimensional aquifer flow, where the stream flow is also considered as one-dimensional. The VPMM and the VPMS methods considering stream-aquifer interaction have been verified using hypothetical data and their field applicability have been demonstrated in this study. The Nash-Sutcliffe Efficiency iv (NSE) estimate of the VPMM and VPMS methods for the hypothetical case studies are estimated to be 0.9979 and 0.9994 respectively and the respective Root-Mean Square (RMSE) estimates are found to be 0.84 and 0.43. The field application of the VPMM and VPMS show the NSE estimates with respect to the monitored data are found to be 0.9557 and 0.9304 respectively and the respective RMSE estimates of 0.0217 and 0.027, respectively. The routing model considering stream-aquifer interaction process for fully penetrating stream has been developed for solving the two-dimensional aquifer flow, where the stream flow is considered as one-dimensional. The validity of the proposed methods has been checked by applying these methods for the hypothetical case of step-rise input and by comparing the obtained bank storage with the same obtained using an analytical method available in the literature for the same step-rise input. The methods have also been applied on a hypothetical pulse input and the results show very close reproductions with the corresponding hypothetical analytical results. The stream-aquifer model for partially penetrating stream has been developed for solving the twodimensional aquifer flow. The lateral flow estimation of this model has been obtained using conformal mapping approach, which is based on the method developed by Aravin and Numerov (1965). The conformal mapping approach has been applied on the field data of the Platte River of Nebraska, USA using the VPMM method for streamflow routing. Results reveal that the VPMM method can closely reproduce the hydrograph recorded at the downstream of the considered routing reach. The NSE and RMSE estimates of the VPMM method are found to be 0.9922 and 10.26, respectively with reference to the available monitored data. The results reveal that with the moderate data requirements, the VPMM method can be chosen to evaluate the bank storage for a river segment. In the present study, two verification approaches have been employed for producing discharge hydrographs considering bank storage on both the sides of the channel cross-section. In the first verification case of the considered approach of modeling stream-aquifer interaction, the explicit finite difference method was used for the solution of the full Saint-Venant equations and the second using the VPMM method (Perumal and Price, 2013). Also, the hydrographs reproduced by the above-mentioned procedures have been compared with the explicit solution. Moreover, the VPMM method simultaneously computes the stage hydrograph corresponding to a given inflow or routed discharge hydrograph. Therefore, for the evaluation of bank storage, this method provides the values of hydraulic heads which are equal to the river stages at each river-section. Overall, the study shows the appropriateness of using the VPMM and VPMS methods accounting for stream-aquifer interaction can be very useful field applications while routing flood in streams where stream aquifer interaction process is dominant.