数据稀缺条件下水文频率分布模拟及应用  

Simulation and application of hydrological frequency distribution with insufficient data

作　　者：冯婧涵 钱龙霞 唐加山[1] 王红瑞[2] FENG Jinghan;QIAN Longxia;TANG Jiashan;WANG Hongrui(College of Science,Nanjing University of Posts and Telecommunications,210023,Nanjing,Jiangsu,China;College of Water Sciences,Beijing Normal University,100875,Beijing,China)

机构地区：[1]南京邮电大学理学院,江苏南京210023 [2]北京师范大学水科学研究院,北京100875

出　　处：《北京师范大学学报（自然科学版）》2023年第1期72-84,共13页Journal of Beijing Normal University(Natural Science)

基　　金：水文水资源与水利工程科学国家重点实验室“一带一路”水与可持续发展科技基金资助项目(2020nkms03);国家自然科学基金资助项目(51879010,41875061)。

摘　　要：传统水文频率分析往往需要大量样本以保证分布的拟合效果,而我国仍有部分站点水文数据记录较少,因此本文提出小样本算法:将Jackknife方法、Bootstrap方法与水文频率分析中传统参数估计方法相结合,得到新的参数估计值,以增强传统水文频率分布的拟合效果.为验证小样本算法的优越性,以泾河流域为例,将8个站点的年最大日降水量作为原样本,利用小样本算法对不同样本量的样本进行多次再抽样,将多组再抽样样本分别进行分布的拟合,得到小样本算法的参数估计值,并通过Kolmogorov-Smirnov检验和RMSE检验结果,验证小样本算法对传统参数估计方法的改进效果.结果表明:1)在小样本情况下,该算法明显优于传统方法的拟合效果,尤其部分站点的Bootstrap方法,使用较少样本量时达到了使用较多样本量的拟合效果;2)随着样本量的减少,某些站点的传统方法所求分布不能通过检验,而小样本算法可以得到较好的结果.Traditional hydrological frequency analysis often requires large numbers of samples to ensure good fitting of distribution,but few hydrological data records are available for some stations in China.This paper studies the small sample algorithm.The Jackknife method,Bootstrap method and traditional parameter estimation methods in hydrological frequency analysis are combined to obtain new parameter estimates to enhance fitting effect of traditional hydrological frequency distribution.The Jinghe River basin is taken as an example to verify advantages and disadvantages of this algorithm.Annual maximum daily precipitation data at 8 stations are selected as original sample.Small sample algorithm is used to re-sample the samples with different sample sizes multiple times,and the resampled samples are fitted with the distribution.Parameter estimation of small sample algorithm is obtained after parameter optimization.Kolmogorov-Smirnov(K-S)test and RMSE test are used to verify improvement of small sample algorithm upon traditional parameter estimation method.The fitting effect of small sample algorithm is markedly better than traditional algorithm in cases of small sample size.The fitting effect of Bootstrap for small samples is almost the same as traditional parameter estimation method using larger sample sizes.When the sample size at some stations is small,the distribution obtained by the traditional method cannot pass the K-S test,but the small sample algorithm can get better results.

关 键 词：Jackknife方法 BOOTSTRAP方法 小样本算法 年最大日降水量 

分 类 号：TV213[水利工程—水文学及水资源]