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This article presents a novel method to identify geometric-hydraulic relationships–in terms of mathematical formulas—in the form of segment-averaged outputs and a function of depth in rivers. There are several methods for determining geometric-hydraulic relationships in rivers, including flow area, wetted perimeter, and the flow top width. Direct field surveying and using aerial and satellite sensor instruments are the most prevalent. The model presented here, however, is based on the inverse solution of the Saint-Venant equations without costly field-surveyed river geometry data. The relationships mentioned earlier can be easily used in various hydraulic models, such as flood routing, sediment transport, pollutant transport, and so on. Moreover, this method requires the lowest number of parameters as the input of the inverse model because by minimizing the corresponding objective function, the desired parameters are estimated in the whole studied segment. The proposed inverse model is validated using hypothetical and real test cases. In one of the test cases—as the most comprehensive and practical test case—the application of the presented inverse model was validated in a river network. The Manning roughness coefficient and geometric-hydraulic relationships for different segments were simultaneously estimated at an acceptable level of accuracy and computational costs in this river network. Ultimately, the real and identified geometric-hydraulic relationships are compared for each test case, and statistical indexes are demonstrated. Overall, the results and statistical indexes indicate that the model is more successful and also cheaper than costly conventional methods.

Estimation of Segment-Averaged Geometric-Hydraulic Relationships as a Function of Depth in Natural Rivers Using Inverse Modeling