大渡河流域超阈值降雨样本模拟及不确定性分析
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摘要
大渡河流域地形十分复杂,流域内气候随高程变化差异较大。通过超阈值模型模拟大渡河流域范围内9个雨量站的逐日降水资料序列,利用极大似然估计法计算模型参数,采用概率图、分位数图、重现水平图、密度函数图4种较直观的诊断图形对模型的合理性进行了全面评估,并借助轮廓似然方法估计模型关键参数及设计强降雨的置信区间。研究结果表明,各站点超阈值降雨样本均服从Pareto分布,可以选择GPD模型作为大渡河流域强降雨统计推断的分布函数类型,轮廓似然法能反映重现期长短对设计降雨置信区间的影响。可为大渡河流域降雨不确定性的定量评估及梯级水库群洪水预报提供依据。
The topography of Dadu River Basin is complicated,and its climate has a comparatively large difference with the elevation variation.Above-threshold model is used to fit the daily rainfall samples of nine rainfall stations in Dadu River Basin,based on this,the parameters of the model are estimated by maximum likelihood method and the fitting results are tested by probability plot,quantile plot,return level plot and density plot.Moreover,the profile likelihood function was used to estimate the key parameters of the model and the confidence interval of designed heavy rainfall.The results indicate that above-threshold precipitation samples of the 9 stations follow the Pareto distribution.The GPD model can be selected as the distribution function type of statistics inference of rainfall of Dadu River Basin.The Profile likelihood function method can reflect the effect of the length of return periods on confidence interval.The methods and results can help analyzing the uncertainty of extreme values of rainfall and flood forecast of cascade reservoirs of Dadu River Basin.
The topography of Dadu River Basin is complicated,and its climate has a comparatively large difference with the elevation variation.Above-threshold model is used to fit the daily rainfall samples of nine rainfall stations in Dadu River Basin,based on this,the parameters of the model are estimated by maximum likelihood method and the fitting results are tested by probability plot,quantile plot,return level plot and density plot.Moreover,the profile likelihood function was used to estimate the key parameters of the model and the confidence interval of designed heavy rainfall.The results indicate that above-threshold precipitation samples of the 9 stations follow the Pareto distribution.The GPD model can be selected as the distribution function type of statistics inference of rainfall of Dadu River Basin.The Profile likelihood function method can reflect the effect of the length of return periods on confidence interval.The methods and results can help analyzing the uncertainty of extreme values of rainfall and flood forecast of cascade reservoirs of Dadu River Basin.
引文
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[2]Coles S,Pericchi L R,Sisson S.A fully probabilistic approach to extreme rainfall modeling[J].Journal of Hydrology,2003,(273):35-50.
[3]董双林.水文气象极值统计推断的可靠性问题[J].水科学进展,2012,23(4):575-580.
[4]江志红,丁裕国,马婷婷,等.气候极值推断的不确定性及其置信区间初步探讨[J].气象学报,2012,70(6):1327-1333.
[5]鲁帆,严登华.基于广义极值分布和Metropolis-Hastings抽样算法的贝叶斯MCMC洪水频率分析方法[J].水利学报,2013,44(8):942-949.
[6]Lu Fan,Wang Hao,Yan Denghua,et al.Application of profile likelihood function to the uncertainty analysis of hydrometeorological extreme inference[J].Sci.China.Tech.Sci.,2013,(56):3151-3160.
[7]司波,余锦华,丁裕国.四川盆地短历时强降水极值分布的研究[J].气象科学,2012,32(4):403-410.
[8]陈子燊,路剑飞,刘曾美.广东极端降水的三参数概率分布模式对比[J].中山大学学报:自然科学版,2012,51(1):102-106.
[9]万仕全,周国华,潘柱,等.南京过去100年极端日降水量模拟研究[J].气象学报,2010,68(6):790-799.
[10]杜鸿,夏军,曾思栋,等.淮河流域极端径流的时空变化规律及统计模拟[J].地理学报,2012,67(3):398-409.
[11]史道济,实用极值统计方法[M].天津:天津科学技术出版社,2006.