基于复合概率函数的水文频率分析计算

Hydrological Frequency Analysis and Calculation Based on Compound Probability Function

针对传统的频率曲线适线方法对复杂形状经验频率曲线的拟合效果常较差问题,根据概率函数中的概率与变量为一一对应关系,通过概率变换推求经验频率下的分位数;采用多项式建立变量与分位数的拟合函数,由此构造符合连续性、单调性、归一性等概率特性的变量与频率的复合概率函数。采用P-Ⅲ型、多项式拟合、复合函数等3种方法对昌邑市地下水埋深误差序列进行频率曲线适线,结果表明,基于正态变换及3次多项式的复合函数的拟合精度较高,拟合曲线的中间段与经验点基本重合、首尾两端与经验点趋于一致。该函数能适用于形状为首部上翘、中部平坦、尾部下翘的复杂频率曲线适线。

Traditional frequency curve calculation method is usually unsatisfactory for complex empirical frequency curve. According to one-to-one correspondence between probability and variable, probability transform function is used to calculate quantile under certain empirical frequency. And then the fitting function between variable and quantile is established with polynomial. So, the compound probability function between variable and frequency is set up which satisfied probability characteristics, such as continuity, unity and monotonicity. Taking groundwater depth error series in Changyi City as empirical data, the fitting results of three methods including P-Ⅲ distribution, polynomial fitting and compound function show that compound function based on normal transform and cubic polynomial has higher fitting precision; middle segment of fitting curve basically coincides with empirical points while the header and tail tend to be consistent. The model adapts to fit complex empirical frequency curve with upward header, flat middle and down tail.