| 30 Oct 2025
An Innovative Equivalent River Channel Method for Integrated Hydrologic–Hydrodynamic Modeling
Abstract. To address the lack of river cross-sectional data in hilly regions, this study proposes a novel method that transforms Muskingum parameters (K and X) into Conceptual Equivalent River Channel (CERC). By integrating linear or nonlinear Muskingum parameters with characteristic discharge, roughness, and other relevant inputs, this approach derives simplified yet hydraulically representative cross-sections. Two types of CERC models are introduced: single-layer and dual-layer. The single-layer CERC model includes rectangular, parabolic and triangular cross-sections, while the double-layer CERC builds upon these with an exponential shape. The proposed method was applied to two river reaches in China: the Chenggouwan–Linqing reach in the Haihe River Basin and the Huayuankou–Jiahetan reach in the Yellow River Basin. Using previously calibrated and validated Muskingum parameters, the resulting channel geometries were incorporated into a one-dimensional (1-D) hydrodynamic model. Results indicated that CERCs accurately replicated observed hydrographs, and the dual-layer approach improved performance in reaches with strong nonlinear characteristics. Furthermore, the model effectively captured changes in water level and flow velocity, confirming the suitability of CERC for hydrodynamic modeling. A sensitivity analysis examined the impact of variations in roughness (n) affected the Conceptual Equivalent River Channel Cross-sections (CERCXs) and discharge outcomes, demonstrating the robustness of the proposed method. While CERCs simplify the natural complexity of river channels, their parametric framework represents the channel’s storage capacity and allows flexible shape selection, enabling accurate simulations of water levels and flow velocities when adjusted to match measured cross-sections. This research provides a practical solution that bridges traditional hydrological and hydrodynamic routing methods in regions with limited data availability, especially in hilly areas.
The manuscript proposes a workflow that takes reach-scale Muskingum routing parameters (K and X), translates them into an “equivalent” one-dimensional channel geometry (choosing among simple parametric shapes), and then uses those inferred cross-sections in a 1-D Saint-Venant solver to simulate flood wave propagation along long river reaches. The authors calibrate Muskingum parameters to reproduce observed hydrographs, present algebraic relations that map routing quantities to width, depth, slope and roughness, and report that the resulting hydrodynamic model reproduces the calibrated discharge time series at downstream gauges.
However, there are several limitations that undermine the central claim that routing parameters can be interpreted as physical channel geometry.
First, the inversion is underdetermined: the method attempts to recover multiple geometric and roughness unknowns from a small set of lumped routing observables, so the chosen shape family effectively forces one of many possible solutions rather than revealing a unique physical cross-section. The manuscript defines to mean that the cross-sectional area depends only on water depth , but Eqs. (17-19) explicitly contain additional variables (e.g. slope, roughness, geometric parameters) so the area is treated as a function of more than .
Second, the validation is circular and insufficient: Muskingum parameters are calibrated to match hydrographs, the calibrated values are converted to cross-sections, and the hydrodynamic model unsurprisingly reproduces the same hydrographs—this does not demonstrate that inferred widths, depths or slopes correspond to measured channel form.
Third, key algebraic approximations and a kinematic celerity assumption are introduced but not benchmarked against analytical solutions, synthetic channels with known geometry, or higher-fidelity (2D) models, so the error and applicability bound of the derivation are unknown.
Fourth, important practical issues are unaddressed: some reported weighting values fall outside conventional bounds, there is no propagation of calibration uncertainty into the inferred geometry, and no identifiability or equifinality analysis to show that the geometry estimates are robust.
Finally, representing long heterogeneous reaches as a single uniform cross-section ignores spatial variability (width, slope, tributaries, controls and backwater effects) that one-dimensional hydrodynamics are typically meant to capture.
To improve the manuscript the authors should clearly frame the product as an “equivalent storage” representation unless and until independent geometric validation is provided, perform synthetic and 2-D benchmark tests to quantify the limits of the algebraic approximations, propagate parameter uncertainty through to geometric and hydraulic outputs, and supply systematic comparisons of inferred widths/depths/slopes against surveyed or remote-sensing data at multiple locations and flow stages. Those steps will show whether the method offers a pragmatic engineering approximation or is simply a re-packaged calibration exercise.