Applicability criteria of the variable parameter Muskingum stage and discharge routing methods

Abstract

The applicability criteria of the variable parameter Muskingum stage hydrograph (VPMS) and the variable parameter Muskingum discharge hydrograph (VPMD) routing methods are assessed and quantified. The assessment is made 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 the VPMS and the VPMD methods, respectively, in comparison with the propagation characteristics of the respective hydrographs simulated by solving the Saint‐Venant equations, which form the benchmark model. For each of the uniform rectangular and trapezoidal shape channel categories, a total of 2880 numerical experiments covering various combinations of Manning's roughness coefficient, channel bed slope, peak stage and respective time to peak, and shape factors of the stage hydrographs were conducted for each of these VPMS and VPMD methods, respectively, by routing the hypothetical stage and the respective discharge hydrographs for a reach length of 40 km. The routed stage and discharge hydrographs were compared with the corresponding Saint‐Venant solutions using four performance measures, namely, percentage variance explained, percentage error in volume, percentage error in peak, and percentage error in time to peak. Considering a maximum error of 5% of these measures, the experiments indicate that the applicability limit of the VPMS method for stage routing is (1/So)(∂y/∂x)max ≤ 0.79, while for the simultaneous computation of the discharge hydrograph corresponding to the routed stage hydrograph this method can be applied up to (1/So)(∂y/∂x)max ≤ 0.63 (where So is the channel slope and ∂y/∂x is the water profile gradient). The VPMD method is applicable up to (1/So)(∂y/∂x)max ≤ 0.43 for both discharge routing and the corresponding stage computation. The applicability of the VPMD method is compared with the variable parameter Muskingum‐Cunge (VPMC) method, an alternative method for discharge hydrograph routing, and it is found that for the same 5% error criteria of the VPMD method, the VPMC method is applicable only up to (1/So)(∂y/∂x)max ≤ 0.11. Thus it is seen that the VPMD method has an improved performance and wider applicability range than the VPMC method.