Simulation and application of hydrological frequency distribution with insufficient data

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．