南京过去100年极端日降水量模拟研究

A simulative study of extreme daily rainfall in Nanjing for the past 100 years

中文关键词:  极值理论, 极端日降水量, 广义极值， 阈值模型

英文关键词:Extreme value theory, Extreme daily rainfall, GEV, GPD

中文摘要:

      在南京过去100年日降水资料的基础上，利用极值理论中的区组模型和阈值模型分析了极端日降水分布特征。首先通过广义极值(GEV)模型模拟了日降水的年极值序列(AMDR)，用极大似然估计（MLE）方法计算了模型的参数，并借助轮廓似然函数估计出参数的精确误差区间，同时采用4种较直观的诊断图形对模型的合理性进行全面评估，结果表明Frechet是区组模型中最适合描述极端日降水分布特征的函数。其次，将日降水序列分3种情景构建极值分布的阈值模型(GPD)，考察了观测数据的规模对应用该模型的限制，重点讨论了如何针对给定观测样本选择合适的阈值收集极值信息。分析结果认为，长度不小于50年的气候序列，采用24 mm的日降水量作为临界阈值均能进行GPD分析。该阈值处于年降水序列第91个百分位附近，即对目前长度为50年左右的日观测资料，第91个百分位点以上的数据基本能满足GPD研究的需要。另外，根据GEV和GPD对未来极端降水重现水平的推断情况，GPD预测值的置信区间要比GEV的窄，极值推断的不确定性相对也较小，更适合用于研究中国目前规模不大的气候资料。最后，对GPD模型的形状参数和尺度参数进行变换，分别引入描述线性变化的动态变量，分析降水序列中潜在的变异行为对极值理论应用的影响。这种变异包括降水序列中长期的均值变化及百分位变化，从模拟结果看，暂未发现资料变异行为对极值分析产生显著干扰。

英文摘要:

      A daily precipitation dataset, for the period from 1905 to 2007 in Nanjing is constructed. Firstly, annual maximum of daily rainfall (AMDR) are modeled by using the generalized extreme value (GEV) distribution from the extreme value theory to describe and predict extreme value of future behavior. We estimate model parameters by the MLE method and evaluate the confidence level with the profile log likelihood function. Meanwhile, the diagnosis of model's rationality through 4 kinds of visual illustration is made with the result that the Frechet distribution of GEV fits the extreme daily precipitation best. Second, the scope of application of the generalized Pareto distribution (GPD) based on three time series scenarios is studied and a detailed approach how to gather useful extreme information for a given threshold is discussed emphatically. The results show that regardless of length of climate time series, the critical threshold of daily precipitation of 24 mm assumed is appropriate for GPD analysis. This threshold is lacated near the 91th percentile of annual precipitation series, i.e. above 91% of the sample capacity in the 50 years daily observational data is able to meet the requirenment to analyze extreme daily precipitation with the GPD. According to statistical inference of extreme values through the GEV and GPD, it is concluded that the confidence level of GPD is higher than that of the GEV, i.e. with less uncertainty and thus more suitable for climate time series analysis for China where the sample capacity of climate data is not large at the moment yet. We also set additional variables to replace shape and scale parameters in the GPD model and esp. introduce dynamic variables to describe the linear change in order to analyse the variation of precipitation series and its possible influence on the extreme value distribution. This kind of variation includes changes in the long range mean and the percentile of precipitation series. However, no distinct interfere caused by these variations is found with the analyses.