极值统计模型在大渡河流域暴雨频率分析中的应用

发布时间：2018-12-26 07:08

【摘要】：暴雨和洪水是非常典型的极值事件,发生频率小,然而一旦发生却有巨大影响。相对于一般样本,它们的观测数据比较缺乏,这导致频率分析中分布参数和分位数的估计存在较大的不确定性。极值统计是专门研究很少发生,然而一旦发生却有巨大影响的随机变量极端变异性的建模及统计分析方法,它能够评估极值事件风险,在水文、气象、地震、保险和金融等领域有广泛的应用前景。与传统统计学研究相比,极值统计的发展历史相对较短,至今还在不断发展之中。大渡河是长江上游的主要支流之一,流经川西暴雨区,暴雨频繁。本文选择大渡河为典型流域,研究极值统计建模方法在暴雨频率分析中的应用效果。本文主要研究内容及结论如下:(1)根据大渡河气象站点降水资料,选取大渡河流域中下游龙头石-瀑布沟梯级水库间集水区域,运用不同的空间降水插值方法进行流域降水插值。在考虑高程及不同流域的情景下,在高程起伏变化大的地区,Kriging插值计算结果较大;而在高程变化小的地区,不同插值方法的插值结果由大到小的次序为:IDWLPGPKrigingRBF。综合不同插值比较,可以得出在大渡河中下游流域,IDW插值结果较符合实际降雨。(2)介绍了极值统计方法中的GEV分布和GPD分布模型,分别运用GEV分布和GPD分布模型分析极端降雨频率,计算不同重现水平的估计值及置信区间。GEV分布和GPD分布在大渡河中游流域都拥有较好的模拟。不同重现水平的GEV分布和GPD分布模型估计值始终位于对应的95%置信区间中,各站点估计值随重现水平的增加而变大;重现水平10年~50年估计的增加量比50年~100年的增加量大,且变化趋势相对稳定。由于GPD分布模型的样本较为全面,分析得GPD分布模型不同重现水平的估计值在暴雨集中站点基本均大于GEV分布模型,而降雨量较小的站点两者估计值相差不大。(3)运用Copula函数进行两集水区域暴雨联合概率分布的分析,通过不同的Copula函数构造变量间的联合分布,运用拟合优度评选方法分析得出Gumbel Copula可以较好的拟合两变量。根据Copula函数计算二维条件重现期,结果表明,用Copula函数构造的联合分布能够求得单区域一定暴雨面雨量值下的条件重现期,可以为流域内工程规划设计和风险评估工作提供参考依据。
[Abstract]:Torrential rain and flood are typical extreme events with small frequency, but once they occur, they have great influence. Compared with the general samples, their observation data are relatively scarce, which leads to the uncertainty of the estimation of distribution parameters and quantiles in frequency analysis. Extreme value statistics is a method of modeling and statistical analysis of extreme variability of random variables, which is rarely studied, but once it occurs, it can evaluate the risk of extreme events in hydrology, meteorology, earthquakes, Insurance and finance and other fields have a wide range of applications. Compared with the traditional statistical research, the development history of extreme value statistics is relatively short, and it is still developing up to now. The Dadu River is one of the main tributaries in the upper reaches of the Yangtze River. In this paper, Dadu River is selected as a typical watershed to study the application effect of extreme value statistical modeling method in rainstorm frequency analysis. The main contents and conclusions of this paper are as follows: (1) according to the precipitation data of the Dadu River meteorological station, the catchment area between the Longtoushi-Fudougou Cascade reservoirs in the middle and lower reaches of the Dadu River Basin is selected. Different spatial precipitation interpolation methods are used for watershed precipitation interpolation. In the scenario of considering elevation and different river basins, the results of Kriging interpolation are larger in areas with large elevation fluctuations, while in areas with small elevation changes, the order of interpolation results of different interpolation methods is: IDWLPGPKrigingRBF.. By synthesizing the different interpolation results, it can be concluded that in the middle and lower reaches of the Dadu River, the IDW interpolation results are in good agreement with the actual rainfall. (2) the GEV distribution and the GPD distribution model in the extreme value statistical method are introduced. GEV distribution and GPD distribution model are used to analyze the extreme rainfall frequency, and the estimated values and confidence intervals of different recurrence levels are calculated. GEV distribution and GPD distribution are all well simulated in the middle reaches of the Dadu River. The estimated values of GEV distribution and GPD distribution model with different reproducibility levels are always located in the corresponding 95% confidence interval, and the estimated values of each site increase with the increase of the reproducibility level. The estimated increase of 10 ~ 50 years is larger than that of 50 ~ 100 years, and the trend of variation is relatively stable. Because the sample of GPD distribution model is more comprehensive, it is found that the estimated values of different reproducibility levels of GPD distribution model are basically larger than that of GEV distribution model at rainstorm concentration stations. However, there is little difference between the estimated values of the two stations with less rainfall. (3) the Copula function is used to analyze the joint probability distribution of rainstorm in two catchment areas, and the joint distribution between variables is constructed by different Copula functions. It is concluded that Gumbel Copula can fit the two variables well by using the method of goodness of fit evaluation. According to the Copula function, the two-dimensional conditional recurrence period is calculated. The results show that the combined distribution constructed by the Copula function can obtain the conditional recurrence period under the rainfall value of a certain rainstorm area in a single area. It can provide reference for project planning and risk assessment in river basin.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P333.2

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