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.     

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。     

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.     

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.     

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。     

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。     

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.     

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.     

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。     

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。     

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.     

中国区域气候极值重现水平的非平稳模型及趋势分析

应用基于GEV(Generalized Extreme Value)分布的平稳/非平稳极值概率模型,拟合中国区域489站自建站至2013年极端最高、最低温度和日最大降水量的年极值序列,并导出极值的重现水平及其变率随重现期和时间变化的一般表达式。着重分析了气候极值的"常态"(重现期为2年)与"极端态"(重现期为50年)的变化趋势及其线性变率的空间格局。详细探讨了极值的常态与极端态变化趋势相反的原因以及可能的影响。结果表明,极端最高温度在东部季风区普遍适用平稳模型;在其他地区更适用非平稳模型,其常态和极端态都以增温为主。极端最低温度在全国范围内普遍适用非平稳模型,其常态和极端态也都以增温为主,但在东北局部地区极端态呈现与常态相反的降温趋势。日最大降水量则在全国范围内普遍适用平稳模型。当GEV分布的尺度参数随时间变化时,与极值的常态相比,极端态的变率范围要大得多,并可能导致两者的变率异号的情形;尤其是当气候极值的常态日趋平缓而极端态却日益极端时,可能导致更为剧烈的灾害性天气。     

Regional frequency analysis of extreme rainfalls using partial L moments method

An approach based on regional frequency analysis using L moments and LH moments are revisited in this study. Subsequently, an alternative regional frequency analysis using the partial L moments (PL moments) method is employed, and a new relationship for homogeneity analysis is developed. The results were then compared with those obtained using the method of L moments and LH moments of order two. The Selangor catchment, consisting of 37 sites and located on the west coast of Peninsular Malaysia, is chosen as a case study. PL moments for the generalized extreme value (GEV), generalized logistic (GLO), and generalized Pareto distributions were derived and used to develop the regional frequency analysis procedure. PL moment ratio diagram and Z test were employed in determining the best-fit distribution. Comparison between the three approaches showed that GLO and GEV distributions were identified as the suitable distributions for representing the statistical properties of extreme rainfall in Selangor. Monte Carlo simulation used for performance evaluation shows that the method of PL moments would outperform L and LH moments methods for estimation of large return period events.     

广义极值分布在重庆短历时极值降水中的应用

利用广义极值分布函数拟合1981—2016年重庆34个国家气象站短历时(1、3、6、12 h)极值降水序列,对拟合结果进行显著性水平检验,并给出不同重现期极值降水的空间分布。结果表明:广义极值分布函数能较好地拟合重庆地区的短历时极值降水。随着降水历时的延长,服从Weibull分布(Frechet分布)的站点数逐渐减少(增加)。各短历时不同重现期降水的空间分布具体表现为10 a以下及20 a以上基本相似,位于长江沿线以北的重庆西北部地区降水量明显大于重庆长江沿线以南地区,且渝东南降水的相对大值区位于彭水地区。随着重现期的增加,降水中心更加集中,渝东北的大值中心随着历时的延长向北移动。广义极值分布函数的形状参数的绝对值接近或超出0.5时,计算的高重现期(大于样本长度)极值降水存在较大偏差;当不同历时降水拟合的形状参数值具有明显差异时,高重现期降水可能出现与客观规律相悖的现象。     

Probability Distribution of Precipitation Extremes over the Yangtze River Basin

 Based on the daily observational precipitation data of 147 stations in the Yangtze River basin for 1960-2005, and the projected daily data of 79 grids from ECHAM5/MPI-OM in the 20th century, time series of precipitation extremes which contain annual maximum (AM) and Munger index (MI) were constructed. The distribution feature of precipitation extremes was analyzed based on the two index series. Research results show that (1) the intensity and probability of extreme heavy precipitation are higher in the middle Mintuo River sub-catchment, the Dongting Lake area, the mid-lower main stream section of the Yangtze River, and the southeastern Poyang Lake sub-catchment; whereas, the intensity and probability of drought events are higher in the mid-lower Jinsha River sub-catchment and the Jialing River sub-catchment; (2) compared with observational data, the averaged value of AM is higher but the deviation coefficient is lower in projected data, and the center of precipitation extremes moves northwards; (3) in spite of certain differences in the spatial distributions of observed and projected precipitation extremes, by applying General Extreme Value (GEV) and Wakeby (WAK) models with the method of L-Moment Estimator (LME) to the precipitation extremes, it is proved that WAK can simulate the probability distribution of precipitation extremes calculated from both observed and projected data quite well. The WAK could be an important function for estimating the precipitation extreme events in the Yangtze River basin under future climatic scenarios.     

1960-2005年长江流域降水极值概率分布特征

Based on the daily observational precipitation data of 147 stations in the Yangtze River basin for 1960-2005,and the projected daily data of 79 grids from ECHAM5/MPI-OM in the 20th century,time series of precipitation extremes which contain annual maximum(AM)and Munger index(MI)were constructed.The distribution feature of precipitation extremes was analyzed based on the two index series.Research results show that(1)the intensity and probability of extreme heavy precipitation are higher in the middle Mintuo River sub-catchment,the Dongting Lake area,the mid-lower main stream section of the Yangtze River,and the southeastern Poyang Lake sub-catchment;whereas,the intensity and probability of drought events are higher in the mid-lower Jinsha River sub-catchment and the Jialing River sub-catchment;(2)compared with observational data,the averaged value of AM is higher but the deviation coefficient is lower in projected data,and the center of precipitation extremes moves northwards;(3)in spite of certain differences in the spatial distributions of observed and projected precipitation extremes,by applying General Extreme Value(GEV)and Wakeby(WAK)models with the method of L-Moment Estimator(LME)to the precipitation extremes,it is proved that WAK can simulate the probability distribution of precipitation extremes calculated from both observed and projected data quite well.The WAK could be an important function for estimating the precipitation extreme events in the Yangtze River basin under future climatic scenarios.