Scaling Approaches for Manning’s Roughness Coefficient in Reduced-Scale Hydrodynamic River Simulations With Delft3D

Abstract

Despite extensive theoretical work on Manning’s roughness coefficient (n) in hydraulic literature, its numerical validity across multiple scales in two-dimensional depth-averaged (2DH) frameworks remains poorly quantified. This study addresses this gap by developing a systematic multi-scale calibration protocol applied to a complex reach of a large alluvial river. The novelty lies in the simultaneous evaluation of three geometric ratios (1:10, 1:20, and 1:30) within a single modeling environment to derive an empirically grounded scaling relationship. Results demonstrate that prototype roughness is not directly transferable: unscaled parameters yield errors 25 to 50 times greater than optimal configurations. A non-linear power-law relationship is identified between the scale ratio and the required roughness reduction, achieving 98% mean agreement with classical Froude–Manning theory. Crucially, this research identifies the 1:20 scale as the optimal threshold for minimizing scale-induced numerical distortions. By quantifying the slight deviation from theoretical exponents caused by the numerical “absorption” of three-dimensional turbulent structures into two-dimensional parameters, this work provides a physics-based predictive tool that eliminates subjective trial-and-error calibration in downscaled river simulations.