Abstract
A weighting function model was developed to account for the relationship between flow unsteadiness and frictional resistance. The Manning equation cannot fully describe such processes, leading to deficiency in predictive capability under some conditions. Two fundamentally new contributions to our approach are the development of (1) an additional unsteady component using time derivatives of flow-state, and (2) an additional component that utilizes instantaneous and historical information to update the current system. Compared to the results from the Manning equation, the proposed model reduces the overall simulation error and also improves the accuracy in peak simulation. Furthermore, parameter values can be conveniently constrained for model prediction and show strong dependence with the friction coefficient n. However, the proposed model incorporates more parameters and is more complicated than the Manning equation. Further research is needed to explore specific physical meaning of the parameters, for its simplification, practical application, and parameter identification.
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