Estimating flood discharge in compound river channels using minimum gauging data

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 K_i=A_iR_i^2/3/n_i is computed for each water level. The river energy slope S_f=(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/(AR^2/3). 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.