Estimating river flow is a critical step for planning and managing water resources. Since direct streamflow measurement is complex and time-consuming, managers rely on rating curves to estimate discharge. Due to this, it is crucial to develop accurate methods to estimate indirect streamflow. An estimated rating curve transforms recorded stages to discharge to obtain a streamflow time series. This study examines the estimation accuracy of the streamflow time series using the stage-discharge rating curve derived from geometric parameters and velocity parameter (U) based on inspiration from the Biot–Savart law. This model applies at least one year of measurement data for model training and the rest for model testing. Also, rolling cross-validation is performed to evaluate the trained model. The Markov Chain Monte Carlo method is used to calibrate and conduct the uncertainty analysis of the proposed model. Sensitivity analysis is also performed on model parameters (by the Sobol sensitivity indices) and Manning’s roughness coefficient. Comparisons are made between findings from the proposed model and two classic and flow-area rating curves. The classic rating curve produces the stage-discharge rating curve without requiring cross-section geometry by fitting the appropriate curve between discharge and stage. The flow-area model calculates the stage-discharge rating curve by combining the wetted-area/stage and the cross-sectionally averaged velocity/stage functions. The studied models are tested in two rivers, Colorado in the US and Severn in the UK. Before using the observational data, outliers are removed using the Kernel density estimation method. The results show that the proposed method better estimates the streamflow than classic and flow-area rating curves.

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