For various hydrological applications such as flood control projects, a knowledge of stage–discharge relationship is of particular interest to river engineers. Stage-discharge curves in compound channels cannot be easily predicted in comparison with single channels due to their 3D characteristics of flow. In this paper, the concept of cross-sectional isovel contours is used for estimation of stage-discharge curves in compound channels. The multivariate Newton’s method is applied to the difference between the observed and estimated data to optimize the exponent values of the governing parameters. The accuracy of the proposed model is tested successfully against available experimental results, which are taken from the FCF (Flood Channel Facility) laboratory. Then the results are compared with the Single and Divided Channel Methods (SCM and DCM, respectively), the Weighted Divided Channel Method (WDCM), the Exchange Discharge Method (EDM) and the Coherence Method (COHM). The average values of MAPE (Mean Absolute Percentage Error) and NRMSE (Normalized Root Mean Square Error) in discharge estimation based on each referenced section at any level for six sections of the experimental cases are within 3.1% and 0.023, respectively. The biggest advantage of the proposed method is its inherent simplicity which does not need any calibration.

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