Nash瞬时单位线推演河道汇流的完整公式

Nash瞬时单位线是基于零初始条件而得到的，没有反映河道汇流的完整过程。通过拉普拉斯变换和数学归纳，推导出了考虑初始槽蓄量退水过程的完整Nash河道汇流公式。分析讨论了公式各项的物理含义，出口断面的流量应是河槽初始槽蓄量的退水过程与上游入流演算结果的叠加，据此建立了一种具有物理概念的河道洪水演算实时校正模型，通过实例分析验证了公式的实用性和合理性。完整公式是更为一般情形下的Nash河道汇流模型，一定程度上丰富和发展了现有Nash汇流理论，并可适当提高河道洪水演算的精度。

Complete formula of river flow routing based on Nash instantaneous unit hydrograph

Nash Instantaneous Unit Hydrograph (NIUH) is based on the assumption of zero initial conditions which is unable to represent river flood routing in real situation. The complete formula of NIUH for river flood routing which includes initial channel storage recession flow was deduced by the Laplace transform and mathematical induction. The physical meaning of each item of the complete formula was analyzed and discussed. It is demonstrated that outflow is composed of two portions: One is the recession of the initial channel storage, the other is the inflow routed through the channel. A real-time updating approach of the river flood routing was proposed based on the complete formula. The practicability and rationality of the formula were verified through the case study. The complete formula can be considered to be a more general case of the Nash river flood routing model. It is a development of the existed NIUH theory and can adequately improve the accuracy of the river flood routing.