This research presents a new analytical prediction model to calculate Manning’s roughness coefficient (n) through utilizing relative submergence ( \(h/{D}_{50}\) ), Shields parameter ( \(\theta\) ), Froude number ( \(Fr\) ), and volumetric sediment concentration \(\left({S}_{v}\right)\) parameters. The proposed analytical equation took the form \(n=0.041{\left(\frac{h}{{D}_{50}}\right)}^{-0.18}{\theta }^{0.15}F{r}^{-0.28}{S}_{v}^{-0.10}\) to achieve performance achievements of 16.3% absolute relative error coupled with NA of 0.85 and R2 = 0.88 compared to five benchmarked models including Wu and Wang (J Hydraul Eng 125(12):1309–1312, 1999: ARE = 23.5%) and Deng et al. (J Sediment Res 5:24–29, 2007: R2 = 0.15). The analysis demonstrated that flow Froude number (Fr) maintained (−0.28) the strongest effect which decreased n by 32% when Fr at 1.2 reached supercritical conditions. Sediment concentration \({S}_{v}\) at 2000 ppm displayed (−0.10) dominant influence by dropping n by 25%. The model simulation applied with 10,000 iterations showed hydraulic radius (R) was the most responsive variable (total-order Sobol index = 0.50) based on uncertainty analysis through Monte Carlo simulations while Bayesian inference validated a 95% confidence interval spanning from 0.025 to 0.045 for n. When applied to changing bedforms with the \({\theta }^{0.15}\) parameter the prediction accuracy increased by 15% under conditions of mobile bed movement (θ > 0.06). The calculated models find practical use in adaptive flood prediction and sediment-charged channel constructions which lead to risk cuts of 15–25% in flood scenarios. The presented work combines empirical methods with data-based strategies to improve predictive capabilities for situations involving non-uniform unsteady fluid motions.
