VARIABLE PARAMETER FLOOD ROUTING METHODS FOR HYDROLOGICAL ANALYSES OF UNGAUGED BASINS

Abstract

The major objective of the study is the development of extended variable parameter simplified flood routing methods for routing floods in channels, including the floodplain flow, required for the hydrological analyses of ungauged, scantly gauged, and gauged basins. The hydrological analyses deal with the discharge and stage hydrographs routing in both diagnostic and prognostic modes, development of rating curves, and establishment of wave speed-discharge relationships at any upstream and downstream gauged or ungauged sites of a river reach. The variable parameter flood routing methods developed in this study for incorporating floodplain flow in channels and river reaches are the extensions of the variable parameter Muskingum discharge hydrograph (VPMD) routing method advocated by Perumal in 1994, the variable parameter Muskingum stage hydrograph (VPMS) routing method developed by Perumal and Ranga Raju in 1998, and the multilinear Muskingum discharge (MMD) routing method developed by Perumal in 1992. Further, a new method of the multilinear Muskingum stage (MMS) routing method with and without considering the floodplain flow is also developed. All these methods have been studied herein for their strengths and weaknesses from the theoretical considerations in reproducing various characteristics of the solutions of the full Saint-Venant equations, and also by comparing among themselves. The present study is conducted with the following five objectives: 1) comparative evaluation of the variable parameter Muskingum-Cunge (VPMC) method, a well-known simplified routing method currently used in practice, and the VPMDmethod; 2) development of the applicability criteria for the variable parameter Muskingum discharge and stage routing methods; 3) extension of the VPMD and VPMS routing methods for incorporating floodplain flow; 4) development of the MMD and MMS routing methods accounting for floodplain flow; and 5) comparative study of these developed simplified flood routing methods. The VPMC method, since its evolution in 1978 by Ponce and Yevjevich, is widely used in flood hydrology. However, the VPMC method is susceptible to volume conservation error and, recently, many researchers such as Ponce and Chaganti in 1994, and Tang et al. in 1999 have advocated some remedial measures by modifying the routing parameter estimation methods to address the volume conservation problem in this method. This study evaluates these remedial measures by conducting a total of 6400 hypothetical routing experiments, 3200 experiments each in uniform rectangular and trapezoidal channel reaches. A parallel study was carried out using the VPMD routing method under the same routing conditions, and the ability of both the VPMC and VPMD methods to reproduce the benchmark Saint-Venant solutions was studied. It is brought out that within its applicability limits, the VPMD method is able to conserve mass accurately than the VPMC method. The reason for the better performance of the former over the latter method is attributed to the physical basis of its development. It is argued that adoption of artificial remedial measures as attempted by Tang et al. to overcome the volume conservation problem makes the VPMC method semi-empirical in nature, thereby, loosing the fully physically based characteristics of the method. Besides, the effect of incorporating the inertial terms in the estimation of Muskingum routing parameters and their impact on the overall Muskingum routing solutions is addressed by conducting another set of 6400 numerical experiments using both the VPMC and VPMD methods. Conclusively, it is surmised that consideration of the inertial terms in the VPMC routing solution, as attempted by Ponce and Lugo in 2001, does not improve the routing capability of this method, including the problem of volume conservation. With the availability of a vast number of simplified flood routing methods and their applicability criteria specified in the literature, the field hydrologists and river engineers face dilemma in selecting an appropriate routing method. Among all these applicability criteria, the criteria advocated by Ponce et al. in 1978 are widely used in practice. However, it is proved in this study that these criteria of Ponce et al., which were primarily developed using the linear stability theory, are not suitable for studying the nonlinear flood waves. Subsequently, this study proposes the applicability criteria for the selection of the VPMD, VPMS, VPMC, MMD, and MMS methods based on the maximum value of the nondimensional longitudinal water surface gradient, (l/S'0)(5y/&)max (where S0 = channel bed slope; y = flow depth; and x = space vector) while routing a given discharge/stage hydrograph. On the basis of these applicability criteria, the VPMD, VPMS, VPMC, and MMS routing methods were assessed by studying the propagation characteristics of hypothetical stage hydrographs of the form of a four parameter Pearson type III distribution and its corresponding discharge hydrographs in uniform rectangular and trapezoidal channels using these methods to reproduce the solutions of the full Saint-Venant equations. Similarly, the MMD routing method was assessed by studying the propagation characteristics of the Pearson type III distributed hypothetical discharge hydrographs using the same channel types to reproduce the benchmark Saint-Venant solutions. Considering a 95% level of model performance, the experiments reveal the following applicability criteria for different routing methods- i) VPMS method (for stage routing): (\/S0)(dy/dx)max < 0.79, ii ii) VPMS method (for discharge computation): (l/S0)(dy/dx)max < 0.63, iii) VPMD method (for discharge routing and stage computation): (l/50)(5y/ax)max < 0.43, iv) VPMC method (for discharge routing): (l/S0)(dy/8x)max < 0.11, v) MMD method (for discharge routing): {yS0\dy/dx)maK <0.17, and vi) MMS method (for stage routing): (l/S0\dy/8x)max <0.30. Thus it is surmised that the VPMD method has an improved performance and wider applicability range than the VPMC method. Hence, the VPMC method is not considered herein for its possible extension to account for the floodplain flow mainly because of its: i) volume conservation problem, ii) lower applicability range, and iii) the nonphysical basis for varying the parameters at every routing time interval. On the basis of the extension of the VPMD routing method, a routing method for discharge routing and corresponding stage estimation in channels with floodplains is proposed herein. In this study, a novel approach has been proposed to realistically estimate the wave celerity for a compound channel flow condition. The upstream discharge hydrograph is routed using the proposed extended VPMD method in different two-stage symmetrical trapezoidal compound cross section channel reaches, each having different size of floodplains. The performance of the proposed VPMD method extension is evaluated by conducting 72 systematically planned numerical experiments and comparing the results with the routing results obtained using the benchmark MIKE 11 hydraulic model. Further, the suitability of the proposed extended VPMD routing method is verified using six sets of field data of the upper Tiber River in central Italy. The methodology deals with calibrating the reach-averaged Manning's roughness coefficient to reproduce the upstream normal rating curve which is commonly available at an upstream gauged section and, using this roughness value, the routing in the downstream ungauged river reach can be performed. The routing results reveal that the proposed method is capable of accurately routing the discharge hydrographs, and for establishing the rating curves at downstream ungauged river sites which are not affected by any downstream effects. Furthermore, based on the analysis of the Tiber River data, the form of the wave speed-discharge relationship developed using the extended VPMD method is found to be in compliance with the earlier studies by Wong and Laurenson in 1983 and 1984, and Tang et al. in 2001. Similarly, another methodology for estimating discharges and development of rating curves at ungauged river sites is presented by employing a routing method, which is an extension of the VPMS routing method, for routing a given upstream stage hydrograph in a channel reach characterized by trapezoidal compound cross section to arrive at the stage in hydrograph at the downstream site. Further, the VPMS method enables one to estimate the discharge hydrographs at the upstream and downstream sites. The proposed approach of developing the rating curve using the extended VPMS method is verified for a number of hypothetical data sets as used for the extended VPMD method above. Furthermore, the appropriateness of the proposed extended VPMS routing method is verified using two sets of experimental data obtained from the study of unsteady flow in a laboratory channel with rectangular compound flow section, carried out by Rashid and Chaudhry in 1995. The methodology is also field tested using six sets of concurrent stage hydrographs data obtained at the upstream and downstream sites of a 15 km reach length of the Tiber River in central Italy, out of which only one set of data was used for calibrating the reach-averaged Manning's roughness coefficient. The close reproductions of the rating curves and discharge hydrographs recorded at the upstream and downstream sites demonstrate that the proposed methodology can be confidently used for rating curve development and discharge estimation at ungauged sites, thus avoiding the manual discharge measurement at any river site not subjected to backwater effects. The form of the wave speed-discharge relationship for the Tiber River established using the extended VPMS method is also found to be in agreement with the previous studies. Further, two alternative variable parameter hydrograph routing methods based on the improved time-distribution scheme of the multilinear modeling approach, namely, the MMD and MMS routing methods, are proposed for studying the flood wave propagation process in uniform rectangular and trapezoidal channels considering floodplain flow. In both the extended MMD and the MMS routing methods, the Muskingum-type scheme is used as the sub-model of the multilinear method, wherein the parameters of the Muskingum sub-model are related to the channel and flow characteristics by adopting the same relationships as established for the corresponding parameters of the extended VPMD and VPMS routing methods, respectively. The routing study reveals that the proposed MMD and MMS routing methods reproduce 95% of their respective benchmark Saint-Venant solutions when the rating curve corresponding to the input discharge or stage hydrograph is characterized by a narrow loop, with i}/St>){dy/dx)max < 0.17, and (l/S0)(dy/dx)m!a < 0.30, respectively. The routing capability of the extended MMD and the extended MMS methods was studied by using the same data sets as used for the extended VPMD and the extended VPMS methods, respectively. It is acknowledged that the estimation of the reference discharge and stage, respectively, required in the MMD and MMS methods under floodplain flow conditions is not realistic and, due to this reason, the benchmark solutions IV appropriately reproduced by the VPMD and VPMS methods were poorly reproduced by the MMD and MMS methods. Conclusively, it is surmised that the MMD and MMS routing methods may be used for flood forecasting in steep slope rivers of the ungauged or poorly gauged basins, whereas the VPMD and VPMS routing methods are more amenable for flood routing in moderate and steep slope rivers in both diagnostic and prognostic modes for hydrological analyses of ungauged or poorly gauged basins. Further, unlike the simplified flood routing methods available in the literature, the VPMD and VPMS methods have the capability to estimate both stage and discharge simultaneously at any section of a river reach, similar to the solutions of the full Saint-Venant equations. These two simplified hydraulic routing methods are advantageous over all other flood routing methods for their capability to establish the normal rating curves and wave speed-discharge relationships, commonly used bythe river engineers and field hydrologists in practice, at any ungauged or scantly gauged river reaches. .