基于滞后响应模型的三门峡水库冲淤计算方法

基于水库冲淤平衡纵剖面几何关系和机理分析，得到了潼关高程和库区累计淤积量平衡值的计算公式。进而考虑河道调整速率随冲淤状态及水沙条件变化，采用滞后响应模型单步模式建立了潼关高程和累计淤积量计算方法。结果表明，潼关高程计算值与实测值的决定系数R²在1975—2002年和2003—2018年分别为0.80和0.75，累计淤积量计算值与实测值的决定系数R²在1967—2002年和2003—2018年分别为0.95和0.84。利用准平衡时间与调整速率参数的关系，计算了潼关高程和累计淤积量达到准平衡态所需时间，结果显示，潼关高程达到准平衡态的时间约为10.2年，累计淤积量达到准平衡态的时间约为6.7年，表明潼关高程的变化滞后于累计淤积量的变化。此外，潼关高程和累计淤积量逐时段以平衡值为目标的调整过程体现了河床演变的自动调整与滞后响应特性。

Calculation method for erosion and deposition processes in the Sanmenxia reservoir based on delayed response model

Based on the geometric relationship of equilibrium profiles of reservoir deposition and mechanism analysis, the calculation formulas of equilibrium value of Tongguan''s elevation and accumulated deposition in the reservoir are obtained. Considering the fact that channel adjustment rate varies with erosion and deposition state and water and sediment conditions, the calculation methods of Tongguan''s elevation and accumulated deposition are established based on single-step mode of delayed response model. The results show that the coefficient of determination R² between the calculated and measured values of Tongguan''s elevation is 0.80 and 0.75 in 1975-2002 and 2003-2018 respectively, and the coefficient of determination R² between the calculated and measured values of accumulated deposition is 0.95 and 0.84 in 1967-2002 and 2003-2018 respectively. By using the relationship between quasi equilibrium state and decay rate, the relaxation time required for Tongguan''s elevation and accumulated deposition to reach quasi equilibrium state is calculated. The results show that the relaxation time for Tongguan''s elevation to reach quasi equilibrium state is about 10.2 years, the relaxation time for the accumulated deposition to reach quasi equilibrium state is about 6.7 years. It shows that the change of Tongguan''s elevation delayed behind the change of accumulated deposition. In addition, the period by period adjustment process of Tongguan''s elevation and accumulated deposition characterized by aiming at the equilibrium value reflects the automatic adjustment and delayed response characteristic of riverbed evolution.