Water and Irrigation Management

Water and Irrigation Management

Investigation of Unsteady Flow Dynamics in Rivers under the Influence of Cross-Sectional Uncertainty

Document Type : Research Paper

Authors
razieh Valizadeh
Mahdi Mazaheri
Jamal Mohammad Vali Samani
Department of Water Engineering and Management, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran.
10.22059/jwim.2026.405429.1273
Abstract
Rivers serve as a fundamental component of the hydrological cycle, exhibiting continuous and stable flow. However, river flow modeling is inherently associated with uncertainties in input data and geometric parameters, which make sensitivity analysis and the assessment of error sources a complex and challenging task. Among the most significant sources of uncertainty are measurement errors and inaccuracies in defining river cross-sections, which can directly influence the outcomes of hydrodynamic models. In this study, a Monte Carlo simulation framework was employed to investigate the propagation of uncertainty in hydraulic flow modeling. The uncertainties were analyzed through three case studies, including two real rivers and one hypothetical river. Simulation scenarios were constructed based on normal and uniform probability distributions, incorporating random errors of 10% and 20%, as well as systematic errors of 0% and ±3% in the cross-sectional data. The results demonstrated that random errors following a uniform distribution introduced the greatest variability in flow predictions, and an increase in the magnitude of geometric data errors directly led to higher variance in the model outputs. In contrast, the influence of systematic errors on the results was comparatively smaller, indicating the model’s greater sensitivity to stochastic variations in geometric input data. The findings of this study can contribute to enhancing the accuracy of hydrodynamic models and improving the interpretation of their results. Moreover, the outcomes provide practical implications for water resources management, hydraulic structure design, and risk-informed decision-making in the field of river engineering.
Keywords
Normal distribution
Uniform distribution
River cross-sections
Monte Carlo
Subjects
  1. Akan, A.O. (2011). Open Channel Hydraulics. Butterworth-Heinemann.
  2. Apel, H., Merz, B., & Thieken, A.H. (2008). Quantification of uncertainties in flood risk assessments. International Journal of River Basin Management, 6(2), 149-162.
  3. Badiger, G., Sonawane, P., Patil, N., Shelake, G., & Jadhav, S. (2025). Investigating the influence of nano coolant and cross-sectional variations on microchannel cooling for electronic devices. Materials Research Proceedings, 49, 338-349. https://doi.org/10.21741/9781644903438-34
  4. Castellarin, A., Di Baldassarre, G., Bates, P.D., & Brath, A. (2009). Optimal cross-sectional spacing in Preissmann scheme 1D hydrodynamic models. Journal of Hydraulic Engineering, 135(2), 96-105.
  5. Chaudhry, M.H. (2008). Open-channel flow. 2nd edn. New York: Springer.
  6. Chow, V.T. (1959). Open-channel hydraulics. New York: McGraw-Hill.
  7. Conner, J., & Tonina, D. (2014). Effect of cross section interpolated bathymetry on 2D hydrodynamic model results in a large river. Earth Surface Processes and Landforms, 39(4),463-475.
  8. Cunge, J.A., Holly, F.M., & Verwey, A. (1980). Practical aspects of computational river hydraulics. London: Pitman.
  9. Di Baldassarre, G., & Montanari, A. (2009). Uncertainty in river discharge observations: a quantitative analysis. Hydrology and Earth System Sciences, 13,913-921.
  10. Henderson, F. M. (1957).Open Channel Flow. Journal of Fluid Mechanics, 29(2), 414-415.
  11. Henderson, F.M. (1966). Open channel flow. New York: Macmillan.
  12. Jakeman, A.J., Letcher, R.A., & Norton, J.P. (2006). Ten iterative steps in development & evaluation of environmental models. Environmental Modelling & Software, 21(5),602-614.
  13. Jesna, I., Bhallamudi, S., & Sudheer, K. (2023). Impact of cross‐sectional orientation in one‐dimensional hydrodynamic modeling on flood inundation mapping. Journal of Flood Risk Management, 16(3), e12893.
  14. John Brackins, Moragoda, N., Rahman, A., Cohen, S., & Lowry, C. (2021). The role of realistic channel geometry representation in hydrological model predictions. JAWRA Journal of the American Water Resources Association, 57(2),222-240.
  15. Knapp, J.L., González‐Pinzón, R., Drummond, J.D., Larsen, L.G., Cirpka, O.A., & Harvey, J.W. (2017). Tracer-based characterization of hyporheic exchange and benthic biolayers in streams. Water Resources Research, 53(2),1575-1594.
  16. Knapp, J.L.A., & Kelleher, C. (2020). A perspective on the future of transient storage modeling: Let’s stop chasing our tails. Water Resources Research, 56(3), e2019WR026257.
  17. Lambert, R.J.W., Mytilinaios, I., Maitl&, L., & Brown, A.M. (2012). Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel. Computational Methods and Programs in Biomedicine, 107,155-163.
  18. Leong, T.Y. (2007). Monte Carlo spreadsheet simulation using resampling. INFORMS Transactions on Education, 7,188-200.
  19. Li, J., He, L., Lu, H.W., & Fan, X. (2014). Stochastic goal programming based groundwater remediation.
    Javernick, L., Brasington, J., & Caruso, B. (2014). Modelling the topography of shallow braided rivers using Structure from Motion photogrammetry. Geomorphology, 213,166-182. doi:10.1016/J.GEOMORPH.2014.01.006
  20. Li, T., Douglas, K.A., Le, H.P., Raz, A.K., Huang, W.J., & Fentiman, A.W. (2020). Applying Social Constructivism in Model-based Systems Engineering Online Instructional Module for Engineering Professionals. In: 2020 IEEE Frontiers in Education Conference (FIE), Uppsala, Sweden, 21-24 October 2020. IEEE. DOI: 10.1109/FIE44824.2020.9274251.
  21. Mahmood, K.M., & Mohammed-Ali, W.S. (2025). A hydraulic performance model of Khassa Chai River under varying flow conditions. Engineering, Technology & Applied Science Research, 15(2),20934-20940. https://doi.org/10.48084/etasr.9675
  22. Matott, L.S., Babendreier, J.E., & Purucker, S.T. (2009). Evaluating uncertainty in integrated environmental models: a review of concepts & tools. Water Resources Research, 45(6),1-14.
  23. Oakley, J.E., & O’Hagan, A. (2004). Probabilistic sensitivity analysis of complex models: a Bayesian approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(3),751-769.
  24. Pianosi, F., Beven, K., Freer, J., Hall, J.W., Rougier, J., Stephenson, D.B., & Wagener, T. (2016). Sensitivity analysis of environmental models: a systematic review with practical workflow. Environmental Modelling & Software, 79,214-232.
  25. Ren, L., He, L., Lu, H., & Chen, Y. (2016). Monte Carlo based interval transformation analysis for multi criteria decision analysis of groundwater management strategies under uncertain naphthalene concentrations and health risks. Journal of Hydrology, 539,468-477.
  26. Siedersleben, J., Jocham, S., Aufleger, M., & Klar, R. (2021). Morphodynamic modelling with uncertain geometry input. Water, 13(16), 2248.
  27. Tennakoon, T., Lai, T.W., Chan, K.C., Liu, C.-H., Leung, R.C.K., Chao, C.Y.H., & Fu, S.C. (2025). Leveraging microchannel cross-sectional geometry for acoustophoretic manipulation of submicron particles. Ultrasonics, 149, 107570.
  28. Tian, Q., & Boccelli, D.L. (2019). Estimating distribution system water demands using Markov chain Monte Carlo. Journal of Water Resources Planning and Management, 145(7), 04019023.
  29. Tian, H., Yao, C., Ren, Z., Zeng, Z., Guo, J., Yu, M., & Xia, C. (2025). Cross-sectional geometrical characteristic for the bends along the lower Jingjiang reach. Proceedings of the Institution of Civil Engineers - Water Management, 178(1),18-27.
  30. Vatanchi, S.M., & Maghrebi, M.F. (2024). Calibration and uncertainty analysis for isovel contours-based stage–discharge rating curve by sequential uncertainty fitting (SUFI-2) method. Water Resources Management, 39(4),1655-1676. https://doi.org/10.1007/s11269-024-04039-9
  31. Wagener, T., & Pianosi, F. (2019). What has Global Sensitivity Analysis ever done for us? A systematic review to support scientific advancement & to inform policy-making in earth system modelling. Earth Science Reviews, 194,1-18.
  32. Ward, A.S., & Packman, A.I. (2019). Advancing our predictive understanding of river corridor exchange. Water Resources Research, 6(1), e1327.
  33. Warmink, J.J., van der Klis, H., Booij, M.J., & Hulscher, S.J.M.H. (2011). Identification and quantification of uncertainties in a hydrodynamic river model using expert opinions. Water Resources Management, 25(2), 601-622.
  34. Wong, J.S., Freer, J., Bates, P., Warburton, J., & Coulthard, T. (2021). Assessing the hydrological and geomorphic behaviour of a landscape evolution model within a limits of acceptability uncertainty analysis framework. Earth Surface Processes and Landforms, 46(10),1981-2003.
  35. Yue, S., Chen, M., Song, J., Yuan, W., Chen, T., Lü, G., Chen, C., Ma, Z., Xu, K., Wen, Y., & Song, H. (2020). Participatory intercomparison strategy for terrestrial carbon cycle models based on a service-oriented architecture. Future Generation Computer Systems, 112,449-466.
  36.  
Water and Irrigation Management
Volume 16, Issue 1
Spring 2026
Pages 193-213