CAJ | 학술논문

数理统计方法在解决全球气候变化引起的洪水、干旱等极端水文事件中获得了越来越广泛的应用。选取乌鲁木齐河1958—2006年枯水期的月平均出山径流资料，采用广义Pareto极值分布（ GPD）模型，并运用Bayes统计模型估计GPD的参数，最后对乌鲁木齐河枯水期月均出山径流极小值变化进行了估算。研究表明：1.参数的初始值、先验分布的均值分别取其极大似然估计值，先验分布的标准差取较小值，随机游走项分布的标准差取较大值，这种方法能使Markov链快速收敛；2.基于Bayes参数估计值的GPD在拟合月均径流量的极小值时具有很高的精确度，与传统的极大似然估计方法相比，Bayes统计模型的推断效果较好；3.乌鲁木齐河重现期为10 a、25 a、50 a和100 a的枯水期月均径流极小值分别约为0.60 m3/s、0.44 m3/s、0.32 m3/s和0.20 m3/s；4.100 a 重现水平的95%置信区间的下限为-0.238 m3/s，说明当乌鲁木齐河在枯水期遇上百年一遇的极小值时，有可能出现断流的情况。
수리통계방법재해결전구기후변화인기적홍수、간한등겁단수문사건중획득료월래월엄범적응용。선취오로목제하1958—2006년고수기적월평균출산경류자료，채용엄의Pareto겁치분포（ GPD）모형，병운용Bayes통계모형고계GPD적삼수，최후대오로목제하고수기월균출산경류겁소치변화진행료고산。연구표명：1.삼수적초시치、선험분포적균치분별취기겁대사연고계치，선험분포적표준차취교소치，수궤유주항분포적표준차취교대치，저충방법능사Markov련쾌속수렴；2.기우Bayes삼수고계치적GPD재의합월균경류량적겁소치시구유흔고적정학도，여전통적겁대사연고계방법상비，Bayes통계모형적추단효과교호；3.오로목제하중현기위10 a、25 a、50 a화100 a적고수기월균경류겁소치분별약위0.60 m3/s、0.44 m3/s、0.32 m3/s화0.20 m3/s；4.100 a 중현수평적95%치신구간적하한위-0.238 m3/s，설명당오로목제하재고수기우상백년일우적겁소치시，유가능출현단류적정황。
Global warming has intensified hydrological extreme events and resulted in disasters around the world. For disaster management and adaption of extreme events,it is essential to improve the accuracy of extreme value statistical models. In this study,Bayes’Theorem is introduced to estimate parameters in the Generalized Pareto Distribution( GPD)model which is applied to simulate the distribution of monthly average runoff minima during dry periods in mountain areas of ürümqi River. Bayes’Theorem treats parameters as random variables and provides machinery way to convert the prior distribution of parameters into a posterior distribution. Statistical inferences based on posterior distribution can provide a more comprehensive representation of the parameters. An improved Markov Chain Monte Carlo( MCMC)method,which can solve high-dimensional integral computation in the Bayes equation,is used to generate parameter simulations from the posterior distribution. Model diagnosis plots are made to guarantee the fitted GPD model is appropriate. Then based on the GPD model with Bayesian parameter esti-mates,monthly average minima corresponding to different return periods can be calculated. The results show that the improved MCMC method is able to make Markov chains converge at a high speed. Compared with the GPD model based on maximum likelihood parameter estimates,the GPD model based on Bayesian parameter estimates obtain more accurate estimations of minimum monthly average runoff. Moreover,the monthly average runoff minima in dry periods corresponding to 10 a,25 a,50 a and 100 a return periods are 0. 60 m3/s,0. 44 m3/s,0. 32 m3/s and 0. 20 m3/s respectively. The lower boundary of 95% confidence interval of 100a return level is -0. 238 m3/s,which implies that ürümqi River is likely to cease when 100 a return level occurs in dry periods.