基于水量平衡方程的水库调洪演算误差研究

Error Analysis of Reservoir Flood Regulating Calculation Based on Water Balance Equation

水库调洪需要采用水量平衡方程逐时段演算,通常采用梯形数值积分法计算逐时段的入库水量和出库水量,存在误差余项。梯形数值积分法具有一阶代数精度,可采用复化梯形求积公式等方法消除入库洪水的误差余项;时段内的出库流量过程无法获得,存在的误差余项会影响时段末的水位成果,并会向后续计算持续传播。利用计算时段库水位的上、下界,可以粗略确定最大可能误差余项,并进一步估计误差传播后的最大可能水位误差。

We usually use water balance equation to hourly compute reservoir flood regulating, and use trapezoidal numerical integration- to hourly compute inflow and outflow water of reservoir, though it must exist remainder errors during any computing period. Trapezoidal numerical integral method has a first order algebraic accuracy, so the method of compound trapezoid quadrature formula can be used to eliminate the remainder error of inflow flood. Because the process of outflow cannot be acquired during computing period, the existent remainder error of the calculation will affect the water level at the end, and will continue to the subsequent calculation. It can roughly determine the possible maximum remainder error and further estimate the possible maximum error of water level after being propagated by computing the periodical lower bound and upper bound of reservoir water level.