Statistical distributions of extreme dry spell in Peninsular Malaysia

Statistical distributions of annual extreme (AE) series and partial duration (PD) series for dry-spell event are analyzed for a database of daily rainfall records of 50 rain-gauge stations in Peninsular Malaysia, with recording period extending from 1975 to 2004. The three-parameter generalized extreme value (GEV) and generalized Pareto (GP) distributions are considered to model both series. In both cases, the parameters of these two distributions are fitted by means of the L-moments method, which provides a robust estimation of them. The goodness-of-fit (GOF) between empirical data and theoretical distributions are then evaluated by means of the L-moment ratio diagram and several goodness-of-fit tests for each of the 50 stations. It is found that for the majority of stations, the AE and PD series are well fitted by the GEV and GP models, respectively. Based on the models that have been identified, we can reasonably predict the risks associated with extreme dry spells for various return periods.     

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.     

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。     

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.     

Impacts of Anthropogenic Forcings and El Nio on Chinese Extreme Temperatures

This study investigates the potential influences of anthropogenic forcings and natural variability on the risk of summer extreme temperatures over China.We use three multi-thousand-member ensemble simulations with different forcings(with or without anthropogenic greenhouse gases and aerosol emissions) to evaluate the human impact,and with sea surface temperature patterns from three different years around the El Ni ?no–Southern Oscillation(ENSO) 2015/16 event(years 2014,2015 and 2016) to evaluate the impact of natural variability.A generalized extreme value(GEV) distribution is used to fit the ensemble results.Based on these model results,we find that,during the peak of ENSO(2015),daytime extreme temperatures are smaller over the central China region compared to a normal year(2014).During 2016,the risk of nighttime extreme temperatures is largely increased over the eastern coastal region.Both anomalies are of the same magnitude as the anthropogenic influence.Thus,ENSO can amplify or counterbalance(at a regional and annual scale) anthropogenic effects on extreme summer temperatures over China.Changes are mainly due to changes in the GEV location parameter.Thus,anomalies are due to a shift in the distributions and not to a change in temperature variability.     

浑太流域降水极值的统计分布特征

基于浑太流域1966-2006年73个雨量站的日降水资料,建立了逐站年最大日降水量(AnnualMaximum,AM)序列和汛期4-9月日降水量<1.27mm.d-1的最长持续干旱天数(Munger Index,MI)序列,并对其时空分布规律进行了分析。采用广义极值(General Extreme Value,GEV)分布、广义帕雷托(General Pareto,GP)分布、韦布尔(Weibull,WB)分布、约翰逊SB(Jonhson SB,J-SB)分布、Burr分布和对数逻辑(Log-Logistic,L-LG)分布等6种极值分布函数对AM和MI序列进行了逐站分布拟合,结果表明,广泛应用的GEV分布整体拟合程度最好,有50个测站的KS检验统计量Dn<0.09,而未曾推广使用的Burr分布的拟合效果也非常好,有36个测站Dn<0.09。用GEV分布对50年一遇的AM和MI进行了估算,发现流域中心地区极端强降水和极端干旱的程度较高,分别为>208mm.d-1和>47d。     

中国格点化日降水极值统计模型及阈值的选取

采用年最大值法（AM）及超阈值峰量法（POT）分别构建基于0.5°×0.5°网格的全国地面日降水极值序列,建立基于广义极值分布（GEV）和广义帕累托分布（GPD）的降水极值统计模型,通过K-S检验评估模型拟合效果,研究全国日降水极值的统计规律及其空间分布特征,提出适用于不同地区极端日降水的极值分布模型与阈值选取标准,结果表明：(1)POT序列比AM序列更符合降水极值序列的要求;(2)为便于比较并提高模型拟合效果,POT序列的阈值由百分位数法确定效果较好;(3)阈值方案优选结果在空间分布上与中国干湿区域的划分有很好的相关性,在湿润地区宜将第90～94百分位数作为阈值,在半湿润和半干旱地区宜将第94～97百分位数作为阈值,在干旱地区则使用第97～99百分位数较为合适。     

黔东南地区各季节极端干期日数的时空分布特征

利用1961—2009年黔东南地区16个地面气象站的逐日降水资料,分别统计了四季最大连续无雨日数(日降水量<0.1mm)的时间序列,采用正交函数分解、Mann-Kendall突变检验和线性倾向估计等方法,分析了各季节极端干期日数的空间结构和时间演变规律。结果表明,黔东南地区各季节极端干期日数的时空分布存在较大差异,极端干期日数最多出现在秋季,最少是春季;夏季黔东南北部的极端干期日数多,春、秋季南部多,冬季南、北部多,西部四季相对较少,年内非均匀性特征显著。在大尺度天气系统控制下,四季极端干期日数事件的步调基本一致,黔东南中东部发生异常的频次较高,不同季节的天气系统对黔东南各区域的影响具有明显的局地性和阶段性;近49年中各季节出现极端干期日数典型多的年份比典型少的年份多;进入21世纪以后,春、秋、冬季极端干期日数均呈显著的增多趋势,而夏季变化的特征不明显。     

干湿持续期随机模拟

该文应用数据建模技术, 实现干湿期随机建模。主要包括:利用历史气象资料, 从中采集干湿期数据; 应用实测数据, 创建干湿期经验分布函数; 应用Monte Carlo方法和经验分布参数, 随机生成干湿期序列, 通过和Markov链模型输出的对比分析, 讨论生成序列的统计误差, 测试结果显示, 与两状态Markov链方法相比, 所建模型性能更好。     

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。     

汉江流域极端水文事件时空分布特征

利用1960-2012年汉江流域15个气象站点的日降雨资料和3个水文站同时期日径流资料,分析了9个极端降雨指数的空间分布规律,运用广义极值分布（GEV）、Gamma分布两种极值统计模型对各站点的最大1 d降雨、最大3 d降雨极值样本进行拟合,遴选描述降雨极值分布规律最优概率模型,进而推算给定重现期下的降雨设计值,并分析其空间分布规律;选用Gumbel、Clayton和Frank这3种Copula函数建立降雨-洪量极值联合分布模型,优选最合适的Copula函数,由此计算给定重现期下的洪量设计值。结果表明：GEV分布模型能更好地模拟降雨极值序列,不同重现期下的降雨极值在空间上均呈西低东高的特征;3种Copula函数中,Frank Copula函数能更好地拟合降雨-洪量相关关系,由此推求的洪量设计值大于单变量拟合设计值。     

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.     

Extreme value analysis in the Danube lower basin discharge time series in the twentieth century

The daily discharge time series in the lower Danube basin (Orsova) have been considered for the 1900–2005 period. The extreme value theory (EVT) is applied for the study of daily discharges incorporating some covariates. Two methods are applied for fitting the data to an extreme value distribution: block maxima and peaks over thresholds (POT). Using the block maxima approach associated with the use of the generalised extreme value (GEV) distribution, monthly and seasonal maxima of daily discharge for 1900–2005 have been analysed. Separately the monthly maxima of daily discharge for the 1958–2001 was analysed in order to be compatible with atmospheric circulation available from ERA-40. For performing parameter estimation, the maximum likelihood estimation (MLE) method was used. From the three possible types of GEV distribution, a Weibull distribution fits both the monthly and seasonal maxima of the daily discharges very well. The North Atlantic Oscillation (NAO) and the first ten principal components (PC) of the decomposition in multi-variate empirical orthogonal functions (MEOF) of three atmospheric fields (sea level pressure, 500 hPa and 500–1000 hPa thickness) over the Atlantic-European region (ERA-40), have been introduced as covariates. An improvement over the model without the covariate is found by incorporating NAO as the covariate in location parameter, especially for the spring maxima having the NAO as predictor during the winter. Related to atmospheric circulation influence, the most significant results are obtained by incorporating the first 10 PCs of the MEOF in the location parameter of GEV distribution within a month before the month of the discharge level. Regarding the POT approach associated with generalised Pareto distribution (GPD), different thresholds have been tested for daily discharges in the period 1900–2005, where the maxima were fitted by a bounded (or beta) distribution.     

Analysis of precipitation extremes in an ensemble of transient regional climate model simulations for the Rhine basin

A non-stationary index-flood model was used to analyse the 1-day summer and 5-day winter precipitation maxima in the Rhine basin in an ensemble of 15 transient regional climate model (RCM) simulations. It is assumed that the seasonal precipitation maxima follow a generalized extreme value (GEV) distribution with time varying parameters. The index-flood assumption implies that the dispersion coefficient (the ratio of the scale and the location parameters) and the shape parameter are constant over predefined regions, while the location parameter varies within these regions. A comparison with the estimates from gridded observations shows that these GEV parameters are too large in the summer season, while there is a large overestimation of the location parameter and underestimation of the dispersion coefficient in winter. However, a large part of the biases in the summer season might be due to the low number of stations used for gridding the observations. Though there is considerable variation in the changes of the extreme value distributions among the RCM simulations, common tendencies can be identified. In summer, large quantiles increase as a consequence of an increase of the dispersion coefficient, while there is almost no change of low quantiles. In winter, low quantiles increase because of an increase of the location parameter. This effect is, however, counterbalanced by a decrease of the shape parameter in most RCM simulations, resulting in only a slight increase of large quantiles. Departures from the assumed index-flood model were observed in the Alpine region in the south of the basin. This is due to the strong spatial heterogeneity in the dispersion coefficient in a number of RCM simulations and a significant altitude dependence of the trend in the location parameter in winter in five RCM simulations.     

Temperature Extremes from Canadian Regional Climate Model (CRCM) Climate Change Projections

Future climate projections of extreme events can help forewarn society of high-impact events and allow the development of better adaptation strategies. In this study a non-stationary model for Generalized Extreme Value (GEV) distributions is used to analyze the trend in extreme temperatures in the context of a changing climate and compare it with the trend in average temperatures.

The analysis is performed using the climate projections of the Canadian Regional Climate Model (CRCM), under an IPCC SRES A2 greenhouse gas emissions scenario, over North America. Annual extremes in daily minimum and maximum temperatures are analyzed. Significant positive trends for the location parameter of the GEV distribution are found, indicating an expected increase in extreme temperature values. The scale parameter of the GEV distribution, on the other hand, reveals a decrease in the variability of temperature extremes in some continental regions. Trends in the annual minimum and maximum temperatures are compared with trends in average winter and summer temperatures, respectively. In some regions, extreme temperatures exhibit a significantly larger increase than the seasonal average temperatures.

The CRCM projections are compared with those of its driving model and framed in the context of the Coupled Model Intercomparison Project, phase 3 (CMIP3) Global Climate Model projections. This enables us to establish the CRCM position within the CMIP3 climate projection uncertainty range. The CRCM is validated against the HadEX2 dataset in order to assess the CRCM representation of temperature extremes in the present climate. The validation is also framed in the context of CMIP3 validation results. The CRCM cold extremes validate better and are closer to the driving model and CMIP3 projections than the hot extremes.     

European dry spell length distributions, years 1951–2000

Daily precipitation records of 267 European rain gauges are considered to obtain dry spell length (DSL) series along the second half of the twentieth century. A dry spell consists of consecutive days with daily rain amount below a given threshold, R ₀. Four DSL series are obtained for R ₀ values equal to 0.1, 1.0, 5.0, and 10.0 mm/day, and their empirical distributions are properly fitted to different statistical models: Pearson type III (PE3), Weibull (WEI), generalised Pareto, (GPA) and lognormal distributions. The parameters of every model are estimated by L-moments, and the goodness of fit is assessed by quantifying discrepancies between empirical and theoretical distributions in the L-skewness–kurtosis diagrams. The most common best-fitting model is PE3, especially for 0.1 and 1.0 mm/day. Nevertheless, a few stations in southern Europe are better modelled by the WEI distribution. For 5.0 and 10.0 mm/day, the spatial distribution of the best-fitting model is more heterogeneous than for the lowest thresholds. While PE3 is still the preferred model for Western Europe, some DSL series are better fitted to WEI or GPA models. Maps of DSL average and standard deviation and expected lengths for return periods of 2, 5, 10, 25, and 50 years show some common features. Whereas for thresholds of 0.1 and 1.0 mm/day, a N–S gradient is detected, especially in Mediterranean areas; for 5.0 and 10.0 mm/day, a NW–SE gradient is observed in the Iberian Peninsula and a SW–NE gradient in the Scandinavian Peninsula. Then, the vicinity to Atlantic and Arctic Oceans and the Mediterranean Sea, as well as orographic features, are more determining factors than the latitude in patterns associated with the highest R ₀ thresholds. Finally, a regional frequency analysis based on a clustering algorithm is attempted for the four thresholds R ₀, with the PE3 model as the parent distribution for the largest clusters.     

基于GEV分布的天山开都河洪水频率特征分析

本文选择天山开都河流域为研究区,基于巴音布鲁克和大山口2个水文站1957-2011年的日径流量观测资料,采用年最大值法（AM）抽取径流序列样本,用线性趋势法、Mann-Kendall趋势检验和Pettitt检验分析年最大日流量、春季最大日流量和夏季最大日流量序列的变化规律;并运用广义极值分布（GEV）对标准化的最大日流量序列进行拟合,分析洪水频率的变化特征。结果表明：提取的6个最大日流量序列均不存在明显的趋势性,且突变点不显著;其中巴音布鲁克站年最大日流量、春季最大日流量和大山口站年最大日流量序列近似服从Frechet分布,而大山口站春季最大日流量、夏季最大日流量和巴音布鲁克站夏季最大日流量序列则服从Gumbel分布。1980年代以来,开都河流域洪水的发生频次明显增加;巴音布鲁克站夏季洪水次数持续增加,大山口站春季和夏季洪水次数均呈增加趋势,且春季洪水出现时间均有所提前。春季显著升温与冬季降水增加,是春季融雪性洪水出现时间和水量变化的主要原因;而夏季降雨量和降雨频率显著增加,是夏季洪水形成与频率变化的主导因素。     

Regional intensity–duration–frequency analysis in the Eastern Black Sea Basin,Turkey, by using L-moments and regression analysis

The analysis of rainfall frequency is an important step in hydrology and water resources engineering. However, a lack of measuring stations, short duration of statistical periods, and unreliable outliers are among the most important problems when designing hydrology projects. In this study, regional rainfall analysis based on L-moments was used to overcome these problems in the Eastern Black Sea Basin (EBSB) of Turkey. The L-moments technique was applied at all stages of the regional analysis, including determining homogeneous regions, in addition to fitting and estimating parameters from appropriate distribution functions in each homogeneous region. We studied annual maximum rainfall height values of various durations (5 min to 24 h) from seven rain gauge stations located in the EBSB in Turkey, which have gauging periods of 39 to 70 years. Homogeneity of the region was evaluated by using L-moments. The goodness-of-fit criterion for each distribution was defined as the Z^DIST statistics, depending on various distributions, including generalized logistic (GLO), generalized extreme value (GEV), generalized normal (GNO), Pearson type 3 (PE3), and generalized Pareto (GPA). GLO and GEV determined the best distributions for short (5 to 30 min) and long (1 to 24 h) period data, respectively. Based on the distribution functions, the governing equations were extracted for calculation of intensities of 2, 5, 25, 50, 100, 250, and 500 years return periods (T). Subsequently, the T values for different rainfall intensities were estimated using data quantifying maximum amount of rainfall at different times. Using these T values, duration, altitude, latitude, and longitude values were used as independent variables in a regression model of the data. The determination coefficient (R ²) value indicated that the model yields suitable results for the regional relationship of intensity–duration–frequency (IDF), which is necessary for the design of hydraulic structures in small and medium sized catchments.     

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.