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.     

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.     

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.     

Spatio-temporal variation and statistical characteristic of extreme dry spell in Yellow River Basin, China

Drought is one of the most detrimental natural hazards in Yellow River Basin (YRB). In this research, spatio-temporal variation and statistical characteristic of drought in YRB is studied by using dry spell. Two extreme series, including annual maximum series (AMS) and partial duration series (PDS), are used and simulated with generalized extreme value (GEV), generalized Pareto (GP), and Pearson type III (PE3) distributions. The results show that the northern part is drier than the southern part of YRB. Besides, the maximum dry spell usually starts in October, November, and December. According to the trend analysis, mean maximum length of dry spell (MxDS) shows a negative trend in most stations. From the L-moments and Kolmogorov–Smirnov test method, it can be found that GEV model can better fit AMS while GP and PE3 can better fit PDS. Moreover, the quantiles from optimal model of AMS and PDS depict a similar distribution with values increases from south to north. The spatial distribution of scale and location parameters of GEV model for AMS shows a south-to-north gradient, while the distribution of shape parameter is a little irregularity. Furthermore, based on the linear correlation analysis, there is an evident linear relation between location and scale parameters with mean and standard variation of MxDS, respectively.     

淮河流域水文极值预测模型研究

为探索气候变化影响下水文极值的非平稳性和预测方法,建立了水文极值非平稳广义极值（GEV）分布的统计预测模型。利用1952-2010年淮河上游流域累计面雨量和流量年最大值资料、同期500 hPa环流特征量资料以及17个CMIP5模式对环流特征量的模拟结果,筛选出对水文极值影响显著的年平均北半球极涡强度指数作为GEV分布参数的预测因子。分析了在RCP2.6、RCP4.5和RCP8.5情景下2006-2050年淮河上游流域水文极值对气候变化的响应。结果表明,10年以下与10年以上重现期的水文极值在非平稳过程中呈现前者下降而后者上升的相反变化趋势;多模型预测的集合平均在未来情景中均呈现上升趋势,情景排放量越大增幅越大,重现期越长增幅也越大。与极值的常态相比,极值的极端态更易受气候变化影响。     

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.     

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。     

中国南方6省1月份降水和极端低温的分布特征

采用中国南方湖南、湖北、贵州、广西、江西和安徽6省近50 a 1月份降水和气温资料,运用正交函数分解法和SYM8小波分析了它们的时空分布特征,并对极端低温的区域均值进行了广义极值模型拟合,同时研究了降水与气温的相关性.结果表明,该地区1月份降水量主要有全区域分布型和南北分布型,极端低温主要有全区域分布型、南北分布型和东西分布型.1月份降水量的全区域总和以及南北部差值都有先增后减的趋势.全区域的极端低温缓慢增长,南北部的差值先减后增,东西部的差值在1975年以前递增,随后几乎趋于稳定.6省1月份极端低温区域均值服从Weibull分布,在95%置信水平下,预测50 a一遇和100 a一遇的极小值达-6.78 ℃和-7.41 ℃.1月份降水量与极端低温的相关不显著,与平均气温在局部地区为负相关.     

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.     

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.     

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.     

Precipitation extremes in the Yangtze River Basin,China: regional frequency and spatial–temporal patterns

Regional frequency analysis and spatial–temporal patterns of precipitation extremes are investigated based on daily precipitation data covering 1960–2009 using the index-flood L-moments method together with some advanced statistical tests and spatial analysis techniques. The results indicate that: (1) the entire Yangtze River basin can be divided into six homogeneous regions in terms of extreme daily precipitation index. Goodness-of-fit test indicates that Pearson type III (PE3, three parameters), general extreme-value (GEV, three parameters), and general normal (GNO, three parameters) perform well in fitting regional precipitation extremes; (2) the regional growth curves for each homogeneous region with 99 % error bands show that the quantile estimates are reliable enough and can be used when return periods are less than 100 years, and the results indicate that extreme precipitation events are highly probable to occur in regions V and VI, and hence higher risk of floods and droughts; and (3) spatial patterns of annual extreme daily precipitation with return period of 20 years indicate that precipitation amount increases gradually from the upper to the lower Yangtze River basin, showing higher risks of floods and droughts in the middle and lower Yangtze River basin, and this result is in good agreement with those derived from regional growth curves.     

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.     

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。     

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。     

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.     

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.     

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。     

Future regional projections of extreme temperatures in Europe: a nonstationary seasonal approach

This paper analyzes changes of maximum temperatures in Europe, which are evaluated using two state-of-the-art regional climate models from the EU ENSEMBLES project. Extremes are expressed in terms of return values using a time-dependent generalized extreme value (GEV) model fitted to monthly maxima. Unlike the standard GEV method, this approach allows analyzing return periods at different time scales (monthly, seasonal, annual, etc). The study focuses on the end of the 20th century (1961?C2000), used as a calibration/validation period, and assesses the changes projected for the period 2061?C2100 considering the A1B emission scenario. The performance of the regional models is evaluated for each season of the calibration period against the high-resolution gridded E-OBS dataset, showing a similar South-North gradient with larger values over the Mediterranean basin. The inter-RCM changes in the bias pattern with respect to the E-OBS are larger than the bias resulting from a change in the boundary conditions from ERA-40 to ECHAM5 20c3m. The maximum temperature response to increased green house gases, as projected by the A1B scenario, is consistent for both RCMs. Under that scenario, results indicate that the increments for extremes (e.g. 40-year return values) will be two or three times higher than those for the mean seasonal temperatures, particularly during Spring and Summer in Southern Europe.     

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。