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.

开发了一个加权函数模型来解释流动不稳定和摩擦阻力之间的关系。曼宁方程不能完全描述这些过程，导致在某些条件下预测能力不足。对我们的方法的两个根本性的新贡献是开发（1）使用流动状态的时间导数的附加非稳态组件，以及（2）利用瞬时和历史信息更新当前系统的附加组件。与曼宁方程的结果相比，所提出的模型减少了整体模拟误差，也提高了峰值模拟的准确性。此外，参数值可以方便地约束模型预测，并显示出与摩擦系数n的强相关性. 然而，所提出的模型包含更多参数并且比曼宁方程更复杂。需要进一步的研究来探索参数的具体物理意义，以便其简化、实际应用和参数识别。