Estimating flood discharge in compound river channels using minimum gauging data

Document Type : Research/Original/Regular Article

Authors

1 Associate Professor, Water Engineering Department, Faculty of Water and Soil Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

2 Ph.D. Student of Water Science and Engineering, Water Engineering Department, Faculty of Water and Soil Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

Abstract

Extended Abstract
Introduction
Floods are among the most complex hydrological phenomena which are known to be the main factor of natural disasters and costs in many river basins, especially in regions with arid and semi-arid climate. Due to the nonlinear nature, high intensities and low durations of floods, there are large uncertainties in their predicting, forecasting, modeling, and managing. Therefore it is necessary to have measured characteristics of flood flows occurred in the river to calibrate and validate mathematical and hydraulic models. However, measuring river flow during floods and inundation of floodplains is very difficult, costly, and dangerous. For this reason, methods based on extrapolation of stage-discharge rating curve are usually used to estimate river flood discharge. Different methods can be used for this purpose, most of which require a lot of field data. For example, in most of these methods, the Manning roughness coefficients of the main channel and floodplains must be known, which has many limitations in this regard. In this study, a simple but practical method has been used to estimate flood discharge of compound river channels, which, while having appropriate accuracy, requires minimal gauging data. It only requires that the river channel geometry, flood stage, and the river stage-discharge rating curve be known.
 
Materials and Methods
To estimate flood discharges from stage–discharge curve, three methods were evaluated and compared. The first is the rating curve extension, which fits Q=a(h−h0​)b to non‑flood measurements data and then extrapolated to higher water levels. This method, introduces considerable error in rivers with wide and rough floodplains. The second method is the conveyance-slope approach, which is specifically developed for compound sections. The cross‑section is divided into the main channel and floodplains and then the conveyance factor Ki=AiRi2/3/ni is computed for each water level. The river energy slope Sf=(Q/K)2 is then derived and extrapolated to flood stages. A major limitation of this method is the need for reliable Manning’s roughness coefficients for both the main channel and the floodplains. To obtain these coefficients, the quasi‑2D model of Shiono and Knight (1991) was employed. The third method is the alpha (α) method, which combines energy slope and Manning’s n into one parameter as α=Q/(AR2/3). The Manning formula is usually face with many uncertainties in riverbed Manning roughness coefficient and energy slope, especially for compound channels with natural features or dense vegetation. This study discusses flood discharge estimation using a calibrated α parameter for alluvial rivers in Iran (Golestan province) and England. Parameter α accounts for the simultaneous effects of energy slope and Manning’s roughness. The method computes α from measured discharges and geometric properties (area A, hydraulic radius R), then fits a regression curve to α-R. From this curve, α is predicted for any flood stage, and flood discharge is subsequently calculated.
 
Results and Discussion
To evaluate three flood discharge extrapolation methods, some statistical metrics (RMSE, MAE, and R²) were used. For the new alpha method, the mean absolute errors were 7.4%, 12.4%, and 5.2% at Arazkooseh, Aghghala, and River Severn, respectively, which are quite acceptable for flood control engineering applications. The conveyance slope method yields MAE values of 20.7%, 42.1%, and 20.8%, while the stage-discharge curve extension method gives 26.3%, 6.0%, and 10.3% for these three river stations. The alpha coefficient method performs more accurately than the other two methods. Its superiority is confirmed by higher R² and lower RMSE error measure, demonstrating better reproduction of actual stage-discharge behavior under floods. The high errors of the conveyance slope method reflect its inability to capture nonlinearity during high flows and floodplain inundation. The rating curve extension method works acceptably only at some stations (e.g., Aghghala). From a hydraulic perspective view, the alpha parameter simultaneously considers variations in discharge (Q), cross-sectional area (A), and hydraulic radius (R), providing a more consistent physical description. Its superiority comes from incorporating concurrent changes in A, R and the nonlinear Q–h curve. When the floodplains become inundated, abrupt changes in velocity distribution and effective roughness occur. Methods relying on slope of rating curve or energy slope extension cannot fully represent this nonlinearity. The alpha parameter accounts for the rate of change of Q with respect to hydraulic cross-section characteristics, offering greater flexibility in modeling flow regime transitions. Therefore, the alpha-based method is proposed as a reliable framework for extrapolating stage-discharge curves, particularly for flood-prone rivers.
 
Conclusion
(1) In this study, a simple method proposed for flood discharge prediction in alluvial rivers with floodplains conveying flood flows which overtax the main river channel. The main reason behind the development of this method is its requirement for minimum river data recorded at the time of river flood flows, including river bathymetry (even before flood passage), flood stage and the common stage-discharge rating curve (and independent to riverbed Manning roughness coefficients of main channel and floodplains). (2) The obtained results of flood flow discharges based on the new developed method are quite satisfactory for all three selected gauge stations in comparison with the classic available methods for flood prediction.(3) The proposed method may faces with physical limitations or problem in rivers with prismatic or manmade main channel and in these cases, at least one data or record of flood flow (stage and discharge) should be given.(4) The implication of this new method is recommended for flood flow prediction in meandering compound river channels and also in multi-stage compound channels which have been recently become a topic of interest to researchers.  

Keywords

Main Subjects

References

منابع
باقری، علی (1402). ارزیابی روش­های محاسبه منحنی دبی-اشل بر اساس روابط مقاومت فرم بستر در ایستگاه هیدرومتری آبلو نکارود مازندران.  آبیاری و زهکشی ایران، (3)17: 503-493.
رجبی‌زاده، یوسف، ایوب‌زاده، سیدعلی، و ظهیری، عبدالرضا (1398). بررسی سیل استان گلستان در سال 1397ـ 1398 و ارائه راه‌کارهای کنترل و مدیریت آن در آینده. اکوهیدرولوژی، (4)6: 942-921.  doi:10.22059/IJE.2019.283004.1137
شجاعیان، زهرا. و حسین­زاده دلیر، علی (1389). واسنجی روش­های تجربی در برآورد رابطه دبی-اشل با توجه به فرم بستر (مطالعه موردی: ایستگاه هیدرومتری عبدالخان). پنجمین کنگره ملی مهندسی عمران، دانشگاه فردوسی مشهد.
قلی‌نژاد، جواد، ظهیری، عبدالرضا، و دهقانی، امیراحمد (1391). شبیه‌سازی یک و شبه‌دوبعدی جریان‌های سیلابی در رودخانه‌ها (مطالعه موردی: رودخانه گرگان‌رود ایستگاه هیدرومتری آق‌قلا).  پژوهش‌های حفاظت آب و خاک، (4)19: 119-103
ملکی، پری، کتابداری، محمدجواد،  صمدی،  حسین، و ملکی، داریوش (1394). ارزیابی روش‌های محاسبه منحنی دبی-اشل در رودخانه‌های با فرم بستر ریپل.  آب و خاک، (4)29: 819-810. doi: 10.22067/jsw. v0i0.30290
 
Alimenti, F., Bonafoni, S., Gallo, E., Palazzi, V., Gatti, R.V., Mezzanotte, P., Roselli, L., Zito, D., Barbetta, S., & Corradini, C. 2020. Noncontact measurement of river surface velocity and discharge estimation with a low-cost Doppler radar sensor. IEEE Transactions on Geoscience and Remote Sensing, 58(7), 5195-5207. doi:10.1109/TGRS.2020.2974184
Ammari, A., & Remini, B. (2010). Estimation of Algerian rivers discharges based one Chiu's equation. Arabian J. Geosciences, 3(1), 59-65. doi:10.1007/s12517-009-0056-y
Ardiclioglu, M., Genc, O., Kalin, L., & Agiralioglu, N. (2012). Investigation of flow properties in natural streams using the entropy concept. Water and Environment Journal, 26(2), 147-154. doi:10.1111/j.1747-6593.2011. 00273.x
Ardiçlioğlu, M., Kisi, O., Hadi, A. M.W., Kuriqi, A., & Kulls, C. (2023). Estimation of mean velocity upstream and downstream of a bridge model using metaheuristic regression methods. Water Resources Management, 37(11), 5559-5580. doi:10.1007/s11269-023-03504-4
Bagheri, A. (2023). Evaluation of stage-discharge curve calculation methods based on bed form resistance relations at Abloo hydrometric station of Nekarood, Mazandaran. Iranian Journal of Irrigation and Drainage, 17(3), 493-503[In Persian].
Bahmanpouri, F., Barbetta, S., Gualtieri, C., Ianniruberto, M., Filizola, N., Termini, D., & Moramarco, T. (2022). Prediction of river discharges at confluences based on Entropy theory and surface-velocity measurements. J. Hydrology, 606:127404. doi:10.1016/j.jhydrol.2021.127404
Barati, R., Akbari, G.H., & Rahimi, S. (2021). Performance evaluation of stage-discharge rating curve methods in compound channels with different floodplain width ratios. Flow Measurement and Instrumentation, 78: 101890.doi: 10.1016/j.flowmeasinst.2020.101890
Bjerklie, D.M., Dingman, S.L., Vorosmarty, C.J., Bolster, C.H., & Congalton, R.G. (2003). Evaluating the potential for measuring river discharge from space. J. Hydrology, 278(1-4), 17-38. doi:10.1016/S0022-1694(03)00129-3
Bolognesi, M., Farina, G., Alvisi, S., Franchini, M., Pellegrinelli, A., & Russo, P. (2017). Measurement of surface velocity in open channels using a lightweight remotely piloted aircraft system. Geomatics, Natural Hazards and Risk, 8(1), 73-86. doi:10.1080/19475705.2016.1184717
Chen, Y.‑C., & Hsu, E.O.Z. (2022). Streamflow measurement using mean surface velocity: A non‑contact approach. Water, 14(15), 2370. doi:10.3390/w14152370
Chen, Y-c.  (1998). An efficient method of discharge measurement. University of Pittsburgh.
Chimata, L.A., Venkata, A.S., Patlolla, S.B., Venkata, S.V.R., Kandrika, D.R., & Chauhan, P. (2025). Automated rapid estimation of flood depth using a digital elevation model and Earth Observation Satellite (EOS-04)-derived flood inundation. Natural Hazards and Earth System Sciences, 25(7), 2455–2470. doi:10.5194/nhess-25-2455-2025
Chimata, R., Srivastava, P.K., Pandey, A., & Mall, R.K. (2025). Flood inundation depth estimation using satellite remote sensing and digital elevation models under data-scarce conditions. Natural Hazards and Earth System Sciences, 25(5), 2455–2474. doi:10.5194/nhess-25-2455-2025
Cipolla, S., Nones, M., & Maglionico, M. (2018). Estimation of flow discharge using water surface velocity in reclamation canals: a case study. Proc. of the 5th IAHR Europe Congress-New Challenges in Hydraulic Research and Engineering, 623-624.
Corato, G., Ammari, A., & Moramarco, T. (2014). Conventional point-velocity records and surface velocity observations for estimating high flow discharge. Entropy, 16(10), 5546-5559. doi:10.3390/e16105546
Di Baldassarre, G., & Montanari, A. (2009). Uncertainty in river discharge observations: A quantitative analysis. Hydrology and Earth System Sciences, 13(6), 913–921. doi:10.5194/hess-13-913-2009
Di Baldassarre, G. (2013). Changes of stage–discharge rating curves. In Floods in a Changing Climate: Inundation     Modelling. Cambridge University Press. doi:10.1017/CBO9781139084244
Elmi, O., Gleeson, T., & Wagener, T. (2024). A global remote sensing–based monthly river discharge dataset with uncertainty estimates. Scientific Data, 11, 178. doi:10.1038/s41597-024-03001-3
Elmi, O., Tourian, M.J., Saemian, P., & Sneeuw, N. (2024). Remote sensing-based extension of GRDC discharge time series- A monthly product with uncertainty estimates. Scientific Data, 11(1), 1–12. doi:10.1038/s41597-024-04095-1
Ervine, D.A., Babaeyan-Koopaei, K., & Sellin, R.H.J. 2000. Two-dimensional solution for straight and meandering overbank flows. J. Hydraulic Engineering, ASCE, 126:9, 653-669. doi: 10.1061/(ASCE)0733-9429(2000)126:9(653)
Farooq, M., Shafique, M., & Khattak, M.S. (2022). Development of stage-discharge rating curves using limited data: A case study of Kabul River. Water Supply, 22(4), 4250–4263.doi: 10.2166/ws.2022.045
Genç, O., Ardıçlıoğlu, M., Ağıralioğlu, N. 2015. Calculation of mean velocity and discharge using water surface velocity in small streams. Flow Measurement and Instrumentation, 41, 115-120. doi: 10.1016/j.flowmeasinst.2014.10.009
Gholinejad, J., Zahiri, A., & Dehghani, A.A. (2012). One and quasi-two-dimensional simulation of flood flows in rivers (Case study: Gorganroud River at Agh-Qala hydrometric station). J. Water Soil Conserv., 19(4): 103-119[In Persian].
Hajikandi, H., and Hatami, M. 2010. Assessment of manning’s resistance coefficient in compound channels. J. Water Sciences Research, 2(1), 9-20.
Hampel, F., Krysanova, V., & Hattermann, F.F. (2022). Synthetic extension of rating curves using hydraulic models and uncertainty quantification for floodplain inundation mapping. J. Hydrol.: Reg. Stud., 39: 100984. doi: 10.1016/j.ejrh.2021.100984
Lee, M., Yoo, Y., Joo, H., Kim, K.T., Kim, H.S., & Kim, S. (2021). Construction of rating curve at high water level considering rainfall effect in a tidal river. J. Hydrology: Regional Studies, 37. doi:10.1016/j.ejrh.2021.100907
Lin, H., Cheng, X., Liu, J., Shi, Q., Li, T., Zheng, L., Hou, X., & Du, J. (2024). Estimating river discharge across scales with a novel regional gauging method driven by Sentinel satellite data. Remote Sensing of Environment, 311, 114266. doi:10.1016/j.rse.2024.114266
Lin, J-Y., Cheng, C-T., & Chau, K-W. (2006). Using support vector machines for long-term discharge prediction. Hydrological Sciences Journal, 51(4), 599-612. doi:10.1623/hysj.51.4.599
Lin, Y., Pavelsky, T.M., Allen, G.H., & Yang, X. (2024). Estimating river discharge using discharge-sensitive areas derived from Sentinel-1 and Sentinel-2 imagery. Remote Sensing of Environment, 306, 114152. doi:10.1016/j.rse.2024.114152
Liu, X., Liu, C., Shan, Y. Q., & Yang, K. J. (2021). Evaluation of energy slope methods in compound channels with         vegetated floodplains. Journal of Hydrology, 598, 126245. doi:10.1016/j.jhydrol.2021.126245
Maghrebi, M.F., & Ball, J.E. (2006). New method for estimation of discharge. J. Hhydraulic Engineering, 132 (10), 1044-1051. doi:10.1061/(ASCE)0733-9429(2006)132:10(1044)
Maleki, P., Ketabdari, M.J., Samadi, H., & Maleki, D. (2015). Evaluation of stage-discharge curve calculation methods in rivers with ripple bed form. Water and Soil, 29(4), 810-819. doi: 10.22067/jsw. v0i0.30290[In Persian].
Mansanarez, V., Westerberg, I.K., Lam, N., & Lyon, S.W. (2019). Rapid stage-discharge rating curve assessment using hydraulic modeling in an uncertainty framework. Water Resources Research, 55, 9765–9787. doi:10.1029/2018WR024176
Mc Gahey, C., Samuels, P.G., Knight, D.W., & O’Hare, M.T. (2008). Estimating river flow capacity in practice. J. Flood Risk Management, 1, 23-33. doi:10.1111/j.1753-318X.2008. 00004.x
Merz, R., & Blöschl, G. (2005). Flood frequency estimation from data of different length. Hydrology and Earth System Sciences, 9(5), 489–502. doi:10.5194/hess-9-489-2005
Moramarco, T., Alimenti, F., Zucco, G., Barbetta, S., Tarpanelli, A., Brocca, L., Mezzanotte, P., Rosselli, L., Orecchini, G., & Virili, M. (2015). A prototype of radar-drone system for measuring the surface flow velocity at river sites and discharge estimation. EGU General Assembly Conference Abstracts, 12853.
Moramarco, T., Barbetta, S., & Tarpanelli, A. (2017). From surface flow velocity measurements to discharge assessment by the entropy theory. Water, 9(2),120. doi:10.3390/w9020120
Moramarco, T., Barbetta, S., Bjerklie, D.M., Fulton, J.W., & Tarpanelli, A. (2019). River bathymetry estimate and discharge assessment from remote sensing. Water Resources Research, 55(8), 6692-6711. doi:10.3390/w9020120
Moramarco, T., Barbetta, S., & Tarpanelli, A. (2017). From surface flow velocity measurements to discharge assessment by the entropy theory. Water, 92-120. doi:10.1029/2018WR024220
Moramarco, T., & Singh, V.P. (2010). Formulation of the entropy parameter based on hydraulic and geometric characteristics of river cross sections. J. Hydrologic Engineering, 15(10), 852-858. doi:10.1061/(ASCE)HE.1943-5584.0000255
Omori, Y., Fujita, I., & Watanabe, K. (2021). Application of an entropic method coupled with STIV for discharge measurement in actual rivers. IOP Conference Series: Earth and Environmental Science, Vol. 1, IOP Publishing, 012036. doi:10.1088/1755-1315/712/1/012036
Paoletti, M., Pellegrini, M., Belli, A., Pierleoni, P., Sini, F., Pezzotta, N., & Palma, L. (2023). Discharge monitoring in open channels: an operational rating curve management tool. Sensors, 23(4), 2035.‏ doi:10.3390/s23042035
Paris, A., & Calmant, S. (2024). Monitoring river discharge from space: An optimization approach with uncertainty quantification for small ungauged rivers. Remote Sensing of Environment, 315, 114434. doi: 10.1016/j.rse.2024.114434
Paris, A., Biancamaria, S., & Durand, M. (2024). River discharge estimation for small ungauged rivers using satellite altimetry and uncertainty-aware optimization. Remote Sensing of Environment, 307, 114285. doi: 10.1016/j.rse.2024.114285
Perret, E., Le Coz, J., Renard, B., & Lang, M. (2019). Stage-discharge rating curve model includes the effect of seasonal aquatic vegetation. Geophysical Research Abstracts, 21, EGU2019-13956
Perroud, H., & Tygel, M. (2005). Velocity estimation by the common-reflection-surface (CRS) method: Using ground-penetrating radar data. Geophysics, 70(6), B43-B52. doi:10.1190/1.2122480
Rainville, F., Hutchinson, D., Stead, A., Moncur, D., & Elliott, D. (2016). Hydrometric manual- Data computations: Staged-discharge model development and maintenance. Water Survey of Canada.
Sivapragasam, C., & Muttil, N. (2005). Discharge rating curve extension–a new approach. Water Resources Management, 19(5), 505-520.‏ 10.1007/s11269-005-6811-2. doi:10.1007/s11269-005-6811-2
Stosic, B., Sacramento, V., Filho, M.C., Cantalice, J.R.B., & Singh, V.P. (2016). Computational approach to improving the efficiency of river discharge measurement. J. Hydrologic Engineering, 21(12), 04016049. doi:10.1061/(ASCE)HE.1943-5584.0001448
Tarpanelli, A., Barbetta, S., Brocca, L., & Moramarco, T. (2013). River discharge estimation by using altimetry data and simplified flood routing modeling. Remote Sensing, 5(9), 4145-4162. doi:10.3390/rs5094145
Torsten, D., Gerd, M., and Torsten, S. 2002. Extrapolating stage-discharge relationships by numerical modeling, Int. Conf. on Hydraulic Engineering, Warshaw, 1-8.
Wark, J.B., Samuels, P.G. & Ervine, D.A. (1990). A practical method of estimating velocity and discharge in compound channels. International Conference on River Flood Hydraulics, London, 163-172.
WMO (2018). Guide to Hydrological Practices (6th Ed.), Volume I: Hydrology – From Measurement to Hydrological Information. World Meteorological Organization, No. 168: 295-310.doi: 10.25607/OBP-1512.
Zakharova, E., Nielsen, K., Kamenev, G., & Kouraev, A. (2020). River discharge estimation from radar altimetry: Assessment of satellite performance, river scales and methods. J. Hydrology, 583, 124561.‏ doi:10.1016/j.jhydrol.2020.124561
Zakwan, M., Muzzammil, M., & Alam, J. (2017). Application of data driven techniques in discharge rating curve-an overview. Aquademia, 1(1), 02.‏ doi:10.20897/ aquademia.201702
 
 
Water and Soil Management and Modelling
Volume 6, Issue 3
August 2026
Pages 235-258

Files

History

  • Receive Date: 18 April 2026
  • Revise Date: 29 May 2026
  • Accept Date: 11 June 2026

Share

How to cite

Statistics