極值統(tǒng)計(jì)模型在大渡河流域暴雨頻率分析中的應(yīng)用
發(fā)布時(shí)間：2018-12-26 07:08
【摘要】：暴雨和洪水是非常典型的極值事件,發(fā)生頻率小,然而一旦發(fā)生卻有巨大影響。相對(duì)于一般樣本,它們的觀測(cè)數(shù)據(jù)比較缺乏,這導(dǎo)致頻率分析中分布參數(shù)和分位數(shù)的估計(jì)存在較大的不確定性。極值統(tǒng)計(jì)是專門研究很少發(fā)生,然而一旦發(fā)生卻有巨大影響的隨機(jī)變量極端變異性的建模及統(tǒng)計(jì)分析方法,它能夠評(píng)估極值事件風(fēng)險(xiǎn),在水文、氣象、地震、保險(xiǎn)和金融等領(lǐng)域有廣泛的應(yīng)用前景。與傳統(tǒng)統(tǒng)計(jì)學(xué)研究相比,極值統(tǒng)計(jì)的發(fā)展歷史相對(duì)較短,至今還在不斷發(fā)展之中。大渡河是長(zhǎng)江上游的主要支流之一,流經(jīng)川西暴雨區(qū),暴雨頻繁。本文選擇大渡河為典型流域,研究極值統(tǒng)計(jì)建模方法在暴雨頻率分析中的應(yīng)用效果。本文主要研究?jī)?nèi)容及結(jié)論如下:(1)根據(jù)大渡河氣象站點(diǎn)降水資料,選取大渡河流域中下游龍頭石-瀑布溝梯級(jí)水庫(kù)間集水區(qū)域,運(yùn)用不同的空間降水插值方法進(jìn)行流域降水插值。在考慮高程及不同流域的情景下,在高程起伏變化大的地區(qū),Kriging插值計(jì)算結(jié)果較大;而在高程變化小的地區(qū),不同插值方法的插值結(jié)果由大到小的次序?yàn)?IDWLPGPKrigingRBF。綜合不同插值比較,可以得出在大渡河中下游流域,IDW插值結(jié)果較符合實(shí)際降雨。(2)介紹了極值統(tǒng)計(jì)方法中的GEV分布和GPD分布模型,分別運(yùn)用GEV分布和GPD分布模型分析極端降雨頻率,計(jì)算不同重現(xiàn)水平的估計(jì)值及置信區(qū)間。GEV分布和GPD分布在大渡河中游流域都擁有較好的模擬。不同重現(xiàn)水平的GEV分布和GPD分布模型估計(jì)值始終位于對(duì)應(yīng)的95%置信區(qū)間中,各站點(diǎn)估計(jì)值隨重現(xiàn)水平的增加而變大;重現(xiàn)水平10年~50年估計(jì)的增加量比50年~100年的增加量大,且變化趨勢(shì)相對(duì)穩(wěn)定。由于GPD分布模型的樣本較為全面,分析得GPD分布模型不同重現(xiàn)水平的估計(jì)值在暴雨集中站點(diǎn)基本均大于GEV分布模型,而降雨量較小的站點(diǎn)兩者估計(jì)值相差不大。(3)運(yùn)用Copula函數(shù)進(jìn)行兩集水區(qū)域暴雨聯(lián)合概率分布的分析,通過(guò)不同的Copula函數(shù)構(gòu)造變量間的聯(lián)合分布,運(yùn)用擬合優(yōu)度評(píng)選方法分析得出Gumbel Copula可以較好的擬合兩變量。根據(jù)Copula函數(shù)計(jì)算二維條件重現(xiàn)期,結(jié)果表明,用Copula函數(shù)構(gòu)造的聯(lián)合分布能夠求得單區(qū)域一定暴雨面雨量值下的條件重現(xiàn)期,可以為流域內(nèi)工程規(guī)劃設(shè)計(jì)和風(fēng)險(xiǎn)評(píng)估工作提供參考依據(jù)。
[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.
【學(xué)位授予單位】：中國(guó)礦業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P333.2
本文編號(hào)：2391708
[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.
【學(xué)位授予單位】：中國(guó)礦業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P333.2
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