水文频率分析中修改双权函数法的研究与应用

Study On A Modified Double Weighted Function Method for Flood Frequency Analysis

修改的双权函数法(MDWF)是将两个负指数型函数之差所构成的函数类取作权函数,对于皮尔逊III型分布,它能使σ和Cs的估计由原权函数法的二阶加权中心矩降低为一阶加权中心矩估计。采用Monte-Carlo模拟分析技术,以设计值估计的不偏性和有效性为评价标准,将MDWF法与近年来在水文频率分析中得到广泛研究和应用的线性矩法(L-M)进行比较。统计试验结果表明,两种方法的无偏性、有效性均相当。采用全国范围内26个站点的洪水极值资料对MDWF方法的实际应用效果进行了验证,拟合结果表明,与L-M法相比,MDWF的整体拟合效果略优。

The modified double weight function method （MDWF） is to introduce new weight functions doing subtraction between two negative exponential-type functions. For a Pearson type three （P-Ⅲ） probability distribution, the MDWF is able to make estimations of the Standard Deviation （σ） and Coefficient of Skewness （Cs） from the second-order weighted central moments reduced to the first-order weighted central moment estimations. Monte-Carlo technique was adopted to evaluate statistical properties of the MDWF method with criteria of unbiasness and effectiveness of estimates on quantiles. Comparisons were conducted between the MDWF and the method of hnear moments （L-M） which has been widely applied recently in hydrological frequency analysis. Results indicate that in general the MDWF is comparable to L-M in both unbiasedness and efficiency for the studied cases. The MDWF method was also used to analyze flood extremes data collected at twenty-six gauges all over the country. It shows, from the view of point of goodness-of-fit, that MDWF is slightly better than L-M.