This study addresses the evaluation of flow resistance in natural gravel‐bed rivers. Through a new data set collected on 136 reaches of 78 gravel‐bed rivers (Calabrian fiumare) in southern Italy, different conventional flow resistance equations to predict mean flow velocity in gravel‐bed rivers were tested in their original form. These equations have shown considerable disagreement with observed data, especially in river reaches characterized by high bed load conditions and for the domains of intermediate‐ and large‐scale roughness. This disagreement produced in almost all the cases an underestimation of the flow resistance, which can be corrected by introducing the Froude number and a particular form of the Shields sediment mobility parameter into the Manning, Chezy, and Darcy‐Weisbach equations. Through analyses carried out both on the whole data set and on its subsets, we propose a semiempirical approach with which, on the one hand, the tractive forces exerted by the flow on the bed are taken into account by considering the ratio between the sediment mobility parameter and its critical value, and on the other hand, water surface distortions are evaluated using the Froude number. This approach has been further validated using a literature‐based data set showing, even in this case, excellent performances. Finally, the literature‐based data set allowed us to improve the performances of the proposed approach in the field of large‐scale roughness. Efficiency tests indicate that the new equations can better reproduce the flow velocity in river reach where conventional flow resistance equations are not able to explain the entire dissipative process.
The Authors thank the Discussers for their interest in this article and for providing further opportunity to the Authors to clarify two fundamental aspects that in the last decades have significantly affected the development of the research concerning the role of the Froude number in the flow resistance estimation in gravel bed rivers and how the same number should be used within flow resistance equations. To that end, it is useful to remember the following main purposes of the paper of Mendicino and Colosimo (2019, https://doi.org/10.1029/2019WR024819): (1) providing the scientific community with a considerable new data set of field measurements carried out in 3 years on 136 reaches of 78 gravel bed rivers in southern Italy, covering a wide range of geometric, granulometric, hydraulic, and sediment parameters; (2) pointing out that the conventional flow resistance equations considered, when evaluated in their original form, were found to be reliable only for small‐scale roughness and absence of bedload transport; on the other hand, the same equations have to be used with extreme caution, both in the intermediate‐ and the large‐scale roughness domains and, especially, when river reaches characterized by very high values of bedload transport are analyzed; and (3) investigating the benefits produced by the Froude number and a particular form of the Shields sediment mobility parameter on the flow resistance estimation, suggesting corrective terms to add to the conventional flow resistance equations considered.
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