广义帕雷托分布在重庆暴雨强降水研究中的应用

引进广义帕雷托分布(GPD),借助于现代L-矩估计方法,模拟重庆地区极端降水事件,推算一定重现期的极端降水量分位数。模拟试验表明,基于超门限峰值法(POT)的GPD不但计算简便,而且基本不受原始序列样本量的影响,具有全部取值域的高精度稳定拟合(包括高端厚尾部),与GEV模拟结果相比,GPD具有更高精度和稳定性,更为实用。     

极值统计理论的进展及其在气候变化研究中的应用

着重论述极值统计分布在极端天气气候事件和重大工程设计中的重要意义,综述该领域国内外研究进展。例如,基于超门限峰值法（POT）的广义帕累托分布（GPD)和基于单元极大值法（BM）的广义极值分布（GEV）及其参数间的理论关系;采用极值分布模型与多状态一阶Markov链相结合构建降尺度模型模拟局地极端降水事件,推算一定重现期的极端降水量的分位数;探讨极值分布模型分位数估计误差问题,多维极值分布理论及其应用等问题。     

南京过去100年极端日降水量模拟研究

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于扰.     

Statistical analysis of annual maximum rainfall in North-East India: an application of LH-moments

An attempt has been made to determine the best fitting distribution to describe the annual series of maximum daily rainfall data for the period 1966 to 2007 of nine distantly located stations in North East India. The LH-moments of order zero (L) to order four (L₄) are used to estimate the parameters of three extreme value distributions viz. generalized extreme value distribution (GEV), generalized logistic distribution (GLD), and generalized Pareto distribution (GPD). The performances of the distributions are assessed by evaluating the relative bias (RBIAS) and relative root mean square error (RRMSE) of quantile estimates through Monte Carlo simulations. Then, the boxplot is used to show the location of the median and the associated dispersion of the data. Finally, it can be revealed from the results of boxplots that zero level of LH-moments of the generalized Pareto distribution would be appropriate to the majority of the stations for describing the annual maximum rainfall series in North East India.     

江淮地区极端降水特征及其变化趋势的研究

利用1961~2011年江淮地区5~9月无缺测的71站逐日降水资料,做基于POT(Peaks-Over-Threshold)的广义Pareto分布(GPD),研究江淮地区极端降水的分布特征及其变化趋势。结果表明:(1)皖赣交界处阈值最大,西北和东南部较小,且江淮大部分地区阈值的线性趋势系数为正,其中湖北东部和江西北部的站点,趋势达0.8 mm(10 a)-1以上,并通过了显著性水平0.01的MK(Mann-Kendall)检验。(2)江淮地区中东部多存在连续性极端降水,因此文中采用基于极值指数的自动分串技术获得近似独立的极值样本。(3)尺度参数大值区位于江淮南部,西北、东南以及淮河以北较小,且线性趋势系数在大部分地区均表现为正值,表明出现降水极大值的概率增加。(4)皖赣鄂交界处是极端降水发生概率大值区,而西北、东南及安徽中部地区较小,且极端降水在大部分地区有增加的趋势,特别是在大别山附近及河南东部,2年和20年重现水平的趋势分别达6 mm(10 a)-1和20 mm(10 a)-1以上。     

导线覆冰极值的概率分布模拟及其应用试验

利用南方地区多个气象站和电力部门观冰站的导线覆冰逐日冰厚资料,将广义极值分布和广义帕雷托分布引入导线覆冰的概率模型研究中,通过超门限覆冰次数的泊松分布拟合检验,结合H ill图解,提出了基于超门限峰值法门限值的确定方法;对两种分布在导线覆冰极值模型拟合的适用性研究表明,广义帕雷托分布对各站覆冰冰厚极值的拟合精度最高;重现期冰厚极值估计随样本长度的变化分析表明,广义帕雷托分布模型极值估计的稳定性比广义极值分布强,一般样本容量达到25 a左右时,广义帕雷托分布重现期冰厚极值的估计趋于稳定,可以作为短序列下估计导线覆冰极值的较好方法。     

Stable estimations for extreme wind speeds. An application to Belgium

Generalized Pareto distributions (GPD) are frequently applied for the statistical analysis of extreme wind speeds. A central topic in extreme-value theory is the adaptive estimation of the extreme-value index ??. Several authors have demonstrated a high sensitivity of ?? against the threshold when analyzing extreme wind speeds. This undesirable effect introduces the difficulty to provide reliable quantile estimates. This paper aims to bring this problem to meteorologists and proposes a stable estimator (the Zipf estimator) for ??. This could allow a more objective prior identification of the sign and range of ??. The method is based on regression in the so-called generalized quantile plots. A comparative study with a classical estimator (the probability-weighted method) is made and it is shown that the Zipf estimator significantly decreases the variance in the calibration of the GPD to extreme wind gusts. Finally, the new methodology is applied to get improved prediction of extreme wind gusts in Belgium.     

未来情景下南水北调中线工程水源区极端降水分布特征

利用南水北调中线工程水源区9个气象站点1961-2008年的日降水资料和IPCC第四次评估报告多模式数据结果,抽取逐年的最大日降水量序列样本,运用广义极值分布（GEV）和广义帕累托分布 (GPD）两种极值统计模型对样本进行拟合,遴选出描述流域最大日降水量分布规律的最优概率模型,推算重现期对应的降水量值,并预估该流域极端降水事件在未来气候变化情景下的响应。研究表明：南水北调中线工程水源区降水极值均符合GEV和GPD分布,但GPD模型更适合用于描述该流域降水极值分布;未来气候变化情景下用GPD分布拟合的降水极值优于使用GEV分布;A2情景下极端降水事件的发生将更频繁、更强烈,A1B情景下次之,B1情景下相对较小,表明未来高排放气候情景对极端降水事件的影响比中、低排放情景大。     

Regional analysis of annual maximum rainfall using TL-moments method

Information related to distributions of rainfall amounts are of great importance for designs of water-related structures. One of the concerns of hydrologists and engineers is the probability distribution for modeling of regional data. In this study, a novel approach to regional frequency analysis using L-moments is revisited. Subsequently, an alternative regional frequency analysis using the TL-moments method is employed. The results from both methods were then compared. The analysis was based on daily annual maximum rainfall data from 40 stations in Selangor Malaysia. TL-moments for the generalized extreme value (GEV) and generalized logistic (GLO) distributions were derived and used to develop the regional frequency analysis procedure. TL-moment ratio diagram and Z-test were employed in determining the best-fit distribution. Comparison between the two approaches showed that the L-moments and TL-moments produced equivalent results. GLO and GEV distributions were identified as the most suitable distributions for representing the statistical properties of extreme rainfall in Selangor. Monte Carlo simulation was used for performance evaluation, and it showed that the method of TL-moments was more efficient for lower quantile estimation compared with the L-moments.     

Duration and Seasonality of Hourly Extreme Rainfall in the Central Eastern China

Compared with daily rainfall amount, hourly rainfall rate represents rainfall intensity and the rainfall process more accurately, and thus is more suitable for studies of extreme rainfall events. The distribution functions of annual maximum hourly rainfall amount at 321 stations in China are quantified by the Generalized Extreme Value（GEV） distribution, and the threshold values of hourly rainfall intensity for 5-yr return period are estimated. The spatial distributions of the threshold exhibit significant regional diferences, with low values in northwestern China and high values in northern China, the mid and lower reaches of the Yangtze River valley, the coastal areas of southern China, and the Sichuan basin. The duration and seasonality of the extreme precipitation with 5-yr return periods are further analyzed. The average duration of extreme precipitation events exceeds 12 h in the coastal regions, Yangtze River valley, and eastern slope of the Tibetan Plateau. The duration in northern China is relatively short. The extreme precipitation events develop more rapidly in mountain regions with large elevation diferences than those in the plain areas. There are records of extreme precipitation in as early as April in southern China while extreme rainfall in northern China will not occur until late June. At most stations in China, the latest extreme precipitation happens in August–September. The extreme rainfall later than October can be found only at a small portion of stations in the coastal regions, the southern end of the Asian continent, and the southern part of southwestern China.     

Risk assessment of precipitation extremes in northern Xinjiang,China

This study was conducted using daily precipitation records gathered at 37 meteorological stations in northern Xinjiang, China, from 1961 to 2010. We used the extreme value theory model, generalized extreme value (GEV) and generalized Pareto distribution (GPD), statistical distribution function to fit outputs of precipitation extremes with different return periods to estimate risks of precipitation extremes and diagnose aridity–humidity environmental variation and corresponding spatial patterns in northern Xinjiang. Spatiotemporal patterns of daily maximum precipitation showed that aridity–humidity conditions of northern Xinjiang could be well represented by the return periods of the precipitation data. Indices of daily maximum precipitation were effective in the prediction of floods in the study area. By analyzing future projections of daily maximum precipitation (2, 5, 10, 30, 50, and 100 years), we conclude that the flood risk will gradually increase in northern Xinjiang. GEV extreme value modeling yielded the best results, proving to be extremely valuable. Through example analysis for extreme precipitation models, the GEV statistical model was superior in terms of favorable analog extreme precipitation. The GPD model calculation results reflect annual precipitation. For most of the estimated sites’ 2 and 5-year T for precipitation levels, GPD results were slightly greater than GEV results. The study found that extreme precipitation reaching a certain limit value level will cause a flood disaster. Therefore, predicting future extreme precipitation may aid warnings of flood disaster. A suitable policy concerning effective water resource management is thus urgently required.     

基于动态重现期的极端高温气候评估方法研究

利用全国754站逐日最高气温观测序列,在论证极端温度概率分布与非平稳性关系的基础上,构建和比较了多种非平稳广义极值模型,定义了极端高温的动态重现期和重现水平,提出了一种极端高温事件的新型评估思想和方法,并将其应用于极端气候变化研究。通过该方法可以更好地解释极端事件的真实极端性,有效地增强极端事件之间的可比性,从而保留更多历史极端气候事件的信息。动态重现期的变换运用可对当前极端事件发生的真实状态和趋势提出更准确评估。该方法的提出可有效澄清学术领域和公共舆论对于多年一遇极端事件的理解上长期混淆重现期的绝对值和概率性这一分歧和谬误。     

我国南方冬季气候变暖前后极端降水事件分析

利用我国南方逐日降水资料及逐月温度资料,采用Mann-Kendall突变检验方法,并计算极端降水的GPD(Generalized Pareto Distribution)重现值,讨论了气候变暖前后我国南方冬季极端降水事件的变化。结果表明,我国南方冬季气候变暖的突变发生在1991年前后,且气候变暖后我国南方冬季的极端降水强度普遍有所增加。利用NCEP/NCAR再分析资料进一步分析气候变暖前后的环流场特征,发现东亚热带冬季风异常与我国华南、江南地区降水异常有显著的相关关系。东亚热带冬季风偏强(弱),华南、江南地区降水偏少(多)。气候变暖后中高纬度环流经向度加大,有利于北方的冷空气向南输送。此外,气候变暖后我国南方地面气温升高,海陆热力差异减小,东亚热带冬季风减弱,有利于西太平洋的暖湿气流向我国大陆东南部输送,并在东南部形成异常的水汽通量辐合,有利于形成强降水。气候变暖后,中高纬度与中低纬度异常环流系统的相互作用是我国东南部降水强度增加的主要原因。     

Future trend of extreme value distributions of wintertime surface air temperatures over Korea and the associated physical changes

Daily winter temperatures in Korea have been analyzed via CSEOF analysis. Then, each PC time series was detrended and was fitted to an AR (autoregressive) model. Based on the identified AR model, an artificial time series of arbitrary length can be generated by using an arbitrary white-noise time series. In this way, one hundred new sets of PC time series were generated over the period of 1973–2058. Then, the trend for each PC time series was added back to the artificial PC time series extending the trend until 2058. Ultimately, artificial daily winter temperatures in Korea have been constructed by using the artificial PC time series and the original loading vectors derived from the observational data. The 100 new data sets have been investigated in order to understand the winter temperature variability 50 years into the future. Regression analysis in CSEOF space shows that temperature increase in Korea is associated with increased 850-hPa air temperature over most of the Asian domain (97°-153°E × 22°-73°N) and increased 850-hPa geopotential height in the southern part of the domain. As a result, southerly and southeasterly wind anomalies develop carrying positive temperature anomalies northward and northwestward. Both the 200-hPa air temperature and geopotential height changes indicate that there will be fairly significant northward shift of the jet stream in future. The standard deviation of the 200-hPa potential vorticity increases implying that shortwave trough and henceforth baroclinic instability will increase in future. Finally, GEV (Generalized Extreme Value) distribution and GPD (Generalized Pareto distribution) distribution have been compared between the observational records and the future records of the same length. The extreme value distributions based on the synthetic datasets show that warm extreme events will be more extreme in future and cold extreme events, on the other hand, will be less extreme. This study provides an estimate of future temperatures based on the observational data and serves as an independent baseline solution for comparisons with numerical model solutions.     

气候极值推断的不确定性及其置信区间初步探讨

提出了气候极值推断的不确定性问题.并以中国156个测站为例着重探讨了广义极值(GEV)分布模式的分位数估计的标准误差对气候极值不确定性的重要影响,评估了极值分位数的置信区间及其在地域上的分布特征.数值试验表明,样本容量(n)大小是影响广义极值的分位数标准误差的最主要因素,而随着重现期加长(概率愈小)其分位数的标准误差必然增大,因此,直接影响了置信区间——即估计的可信度.     

基于Copula函数的北京强降水频率及危险性分析

客观分析强降水事件的发生频率及其致灾因子危险性,能为局地洪涝灾害的防灾、减灾规划及灾害预警提供科学依据。探讨了基于二元Copula函数的强降水致灾变量联合分布及其在强降水危险性分析中的应用。利用北京地区2005-2014年逐时降水资料提取强降水事件案例,通过建立能反映两个主要致灾因素--降水持续时间和过程降水量依存关系的二元联合分布模型,计算了北京地区强降水事件条件重现期,并以此为基础开展危险性分析。研究表明,北京地区强降水事件的持续时间多小于24 h,且主要服从广义极值和对数正态分布,而过程降水量则更适用于广义极值分布;通过Gumbel Copula函数能较好刻画过程降水量与持续时间的相互依存关系。北京地区短时强降水重现期受持续时间影响明显,仅基于降水量的重现期估算会低估其致灾危险性,利用基于Copula函数的条件重现期能更合理描述不同强降水情景致灾因子的危险性特征及其空间差异性特征。北京地区持续时间小于12 h、过程降水量在50 mm以上的强降水事件多呈东北-西南走向,而持续时间在6 h以内的50 mm以上强降水则在北京城区及东北部地区更加频繁。     

Extreme daily precipitation in Belgrade and their links with the prevailing directions of the air trajectories

The main goal of this study was to present the statistical analysis of the daily precipitation exceeding 20 mm in Belgrade and their links with the prevailing directions of the air trajectories at 500, 1,500 and 5,000 m. For the extreme precipitation analysis, the generalised extreme value (GEV) distribution and generalised Pareto distribution (GPD) were used. The estimated return levels for 100- and 10-year return periods using GEV and GPD were obtained. Four-day backward trajectory simulations were conducted for days with precipitation exceeding 20 mm to investigate the regional transport of the air moisture towards Belgrade using the hybrid single-particle Lagrangian integrated trajectory model. The air trajectories were classified into 13 trajectory categories by the origin and direction of their approach to Belgrade. Three of the most frequent categories of air flow from south-west, south-east and north-west contributed to more than a half of the observed precipitation. Almost 74.5 % of precipitation totals in Belgrade fell during the warmer part of the year. These were directly connected with the intensive convection of colder and humid, usually maritime, air masses.     

Extremes of Daily Rainfall in West Central Florida

Annual maxima of daily rainfall data dating from 1901 to 2003 are modeled for fourteen locations in West Central Florida. The generalized extreme value (GEV) distribution is fitted to data from each location. The location parameter of the GEV is formulated as a function of time to adequately describe the extremes of rainfall and to predict their future behavior. We find evidence of non-stationarity in the form of trends for eight of the fourteen locations considered. We quantify the change in extreme rainfall for each location and provide return levels for the years 2010, 2020, 2050 and 2100. We also derive estimates of return levels for daily rainfall and provide a classification of the fourteen locations based on the degree of severity of these estimates. This paper provides the first application of extreme value distributions to rainfall data specifically from Florida.     

Effects of Urbanization on Extreme Warmest Night Temperatures During Summer near Bohai

Many previous studies have focused on the impacts of urbanization on regional mean temperatures. Relatively few have analyzed changes in extreme temperatures. Here, we examine the impact of urbanization on extreme warmest night temperatures from 33 stations in the Bohai area between 1958 and 2009. We compute the Generalized Extreme Value（GEV） distribution of extreme warmest night temperatures and analyze long-term variations in its characteristic parameters. A new classification method based on the factor analysis of changes in extreme night temperatures is developed to detect the efects of urbanization in diferent cities. Of the three parameters that characterize the GEV distribution, the position parameter is the most representative of long-term changes in extreme warmest night temperatures. During the period of rapid urbanization（i.e., after 1978）, all three parameters of the GEV distribution are larger for the urban station group than for the reference station group, so are the magnitudes of their variations, and the urban areas have been experiencing higher extreme warmest night temperatures with larger variability. Diferent types of cities in the Bohai area have all experienced an urban heat island efect, with an average urbanization efect of approximately 0.3 per decade.     

Experimental Simulations of Extreme Precipitation Based on the Multi-Status Markov Chain Model

A multi-status Markov chain model is proposed to produce daily rainfall, and based on which extreme rainfall is simulated with the generalized Pareto distribution (GPD). The simulated daily rainfall shows high precision at most stations, especially in pluvial regions of East China. The analysis reveals that the multistatus Markov chain model excels the bi-status Markov chain model in simulating climatic features of extreme rainfall. Results from the selected six stations demonstrate excellent simulations in the following aspects:standard deviation of monthly precipitation,daily maximum precipitation,the monthly mean rainfall days,standard deviation of daily precipitation and mean daily precipitation, which are proved to be consistent with the observations. A comparative study involving 78 stations in East China also reveals good consistency in monthly mean rainfall days and mean daily maximum rainfall, except mean daily rainfall. Simulation results at the above 6 stations have shown satisfactory fitting capability of the extreme precipitation GPD method. Good analogy is also found between simulation and observation in threshold and return values. As the errors of the threshold decrease, so do the di?erences between the return and real values. All the above demonstrates the applicability of the Markov chain model to extreme rainfall simulations.