基于多项式正态变换的年径流频率计算研究

水文设计值精度直接影响到工程规模的确定。应用多项式正态变换（PNT）法推求给定频率的设计值（分位数），提高水文频率计算精度。采用蒙特卡洛法进行模拟试验，对比分析三阶多项式系数的矩（PM）法、L-阶线性矩（LM）法、最小二乘（LS）法和Fisher-Cornish（FC）不对称展开法的参数求解方法，并选用黄河流域五个测站天然年径流资料，开展三阶多项式正态变换法的年径流频率计算研究。结果表明：4种方法求解所得的多项式系数均能推求给定频率下的年径流设计值，且设计值序列整体与实测序列拟合效果良好，对数据的正态性转换和拟合效果排序结果为最小二乘法、L-阶线性矩法、Fisher-Cornish不对称展开法、矩法。

Investigation of annual runoff frequency calculation based on polynomial normal transformation

The accuracy of hydrological design values directly affects the engineering scale to be determined. A polynomial normal transformation (PNT) method is used in this study to estimate the design values (in quantile) of annual runoff at given frequencies to improve the accuracy of hydrological frequency calculations. We use a Monte Carlo method in numerical simulations and compare four calculation methods of third-order polynomial coefficients: product-moment (PM) method, L-moments (LM), least-square (LS) method, and Fisher-Cornish (FC) asymptotic expansion method . And a third-order polynomial normal transformation method is used to calculate the frequencies of the natural annual runoff at five stations in the Yellow River Basin. The results show that the polynomial coefficients obtained using the four methods give good estimates of the annual runoff design values at given frequencies, and the design value sequences fit well with the measured sequences. In the accuracy of normality conversion and data fitting, a list from high to low is LS method, LM method, FC method and PM method.