为了分析推理公式对代入数据误差的传递作用，应用数值分析中关于误差分析的原理和方法，推导了水科院推理公式在计算小流域设计洪峰流量过程的北京水科院推理公式中，其关于汇流参数、河流纵比降、损失参数和暴雨参数等的条件数。这些条件数的大小可以表征推理公式本身在计算洪峰流量过程中，对代入数据误差的传递作用的强弱。通过3个实际算例，分别计算并绘出了各个条件数随代入数据扰动幅度的变化曲线。分析可知：（1）暴雨参数n和汇流参数m的精度对于计算洪峰流量结果的精度影响较大；（2）损失参数μ和河流纵比降I的精度对洪峰流量计算结果的精度影响较小。

In order to analyze the transmission function of the rational formula on the substituting data error, the principles and methods of error analysis in numerical analysis were applied to derive the condition numbers of the confluence parameter, river longitudinal slope, loss parameter, and rainstorm parameter when the IWHR? rational formula was used to calculate the design peak flow of small watershed. The magnitudes of these condition numbers can characterize the intensity of transmission function of the rational formula on the data error in computing the design peak flow. In this paper, three practical examples were introduced to obtain the variation curves of each condition number with the disturbance of substituting data. The results showed that: 1) the accuracies of rainstorm parameter n and confluence parameter m have large effects on the accuracy of the results of peak flow; and 2) the accuracies of loss parameter μ and river longitudinal slope I have low impacts on the accuracy of the results of peak flow.

国家863计划课题项目“污灌农田及退化土壤修复关键技术”（2012AA101404）