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.     

An analysis of annual maximum streamflows in Terengganu, Malaysia using TL-moments approach

TL-moments approach has been used in an analysis to determine the best-fitting distributions to represent the annual series of maximum streamflow data over 12 stations in Terengganu, Malaysia. The TL-moments with different trimming values are used to estimate the parameter of the selected distributions namely: generalized pareto (GPA), generalized logistic, and generalized extreme value distribution. The influence of TL-moments on estimated probability distribution functions are examined by evaluating the relative root mean square error and relative bias of quantile estimates through Monte Carlo simulations. The boxplot is used to show the location of the median and the dispersion of the data, which helps in reaching the decisive conclusions. For most of the cases, the results show that TL-moments with one smallest value was trimmed from the conceptual sample (TL-moments (1,0)), of GPA distribution was the most appropriate in majority of the stations for describing the annual maximum streamflow series in Terengganu, Malaysia.     

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.     

Observed Changes in One-in-20 Year Extremes of Canadian Surface Air Temperatures

Weather and climate extremes are often associated with substantial adverse impacts on society and the environment. Assessment of changes in extremes is of great and broad interest. This study first homogenizes daily minimum and maximum surface air temperatures recorded at 146 stations in Canada. In order to assess changes in one-in-20 year extremes (i.e., extremes with a 20-year return period) in temperature, annual maxima and minima of both daily minimum temperatures and daily maximum temperatures are derived from the homogenized daily temperature series and analyzed with a recently developed extreme value analysis approach based on a tree of generalized extreme value distributions (including stationary and non-stationary cases). The procedure is applied to estimate the changes over the period 1911 to 2010 at 115 stations, located mainly in southern Canada, and over the period 1961 to 2010 at 146 stations across Canada (including 37 stations in the North). The results show that warming is strongest for extreme low temperature and weakest for extreme high temperature and is much stronger in the Canadian Arctic than in southern Canada. Warming is stronger in winter than in summer and stronger during nighttime than daytime of the same season.     

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.     

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.     

年最大日雨量极值分布拟合与推算

采用红河州12个站近48～58年的年最大日雨量资料,用PearsonⅢ型分布、耿贝尔分布、对数正态分布等3种概率分布模型分别进行了拟合,选择拟合最好的分布模型来估算最大给定重现期极值.结果表明:3种分布均能较好地拟合年最大日雨量的分布,在红河州12个站的拟合中,有7个站用耿贝尔分布,4个站用Pearson-Ⅲ分布,1个...     

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.     

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。     

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 Frequency Analysis of Observed Sub-Daily Rainfall Maxima over Eastern China

Based on hourly rainfall observational data from 442 stations during 1960–2014, a regional frequency analysis of the annual maxima(AM) sub-daily rainfall series(1-, 2-, 3-, 6-, 12-, and 24-h rainfall, using a moving window approach) for eastern China was conducted. Eastern China was divided into 13 homogeneous regions: Northeast(NE1, NE2), Central(C), Central North(CN1, CN2), Central East(CE1, CE2, CE3), Southeast(SE1, SE2, SE3, SE4), and Southwest(SW).The generalized extreme value performed best for the AM series in regions NE, C, CN2, CE1, CE2, SE2, and SW, and the generalized logistic distribution was appropriate in the other regions. Maximum return levels were in the SE4 region, with value ranges of 80–270 mm(1-h to 24-h rainfall) and 108–390 mm(1-h to 24-h rainfall) for 20- and 100 yr, respectively.Minimum return levels were in the CN1 and NE1 regions, with values of 37–104 mm and 53–140 mm for 20 and 100 yr,respectively. Comparing return levels using the optimal and commonly used Pearson-III distribution, the mean return-level differences in eastern China for 1–24-h rainfall varied from-3–4 mm to-23–11 mm(-10%–10%) for 20-yr events, reaching-6–26 mm(-10%–30%) and-10–133 mm(-10%–90%) for 100-yr events. In view of the large differences in estimated return levels, more attention should be given to frequency analysis of sub-daily rainfall over China, for improved water management and disaster reduction.     

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。     

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.     

华北中部近45a极端降水事件变化特征

利用华北中部41个气象台站1961—2005年逐日降水资料,采用通用的极端气候指数,分析了近45a来华北中部极端降水事件频率变化的时空特征。结果表明：华北中部平均年最大日降水量呈下降趋势,南部平原地区一般减少,北部山地区域多有增加,降水日数有较明显减少,强降水日数和暴雨日数变化趋势不明显,降水日数的减少主要是中、小雨（雪）日数减少造成的。暴雨日数和强度在20世纪90年代中后期显著增加。华北中部强降水日数和暴雨日数在降水日数中的比重有增大趋势,强降水量和暴雨降水量在总降水量中的比重可能也增加了。这种相对增加趋势主要发生在20世纪90年代中期以后。     

新、旧气候态差异及对中国地区气候和极端事件评估业务的影响

利用1961—2020年中国区域2089个地面观测站资料,分析了1991—2020年和1981—2010年新、旧气候态下,平均气温、最高气温、最低气温和降水量等变量的空间变化特征,探讨对气候距平值、极端事件等评估结果的影响。结果表明：新气候态下,全国三类气温年和季节平均均一致升高,年降水增加,空间上气温偏高（低）、降水偏多（少）的特征将弱（强）化;华北东部、华东中部和北部以及青海西南部的年平均风速和日照时数距平增加;极端高温年减少,低温年增多,其中平均气温和最低气温受到的影响较最高气温更大;夏季南北方两条雨带极端强降水年的发生概率降低,冬季东北中部和南部、华北、华东北部、西北东部极端弱降水年概率显著增加;全国超过一半的站点极端日高温、低温和强降水事件的历史频次发生改变;新气候态还减弱了极端日高温事件的增速,加快了极端日低温事件的降速。     

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.     

华北地区小时极端降水的非稳态研究

本文以华北五省为研究区，基于1960—2014年小时降水数据建立1、2、3、6、12和24 h极端降水序列，对比分析稳态和非稳态假设下极端降水重现期估计的差异。研究表明：1960―2014年华北不同时间极端降水的变化趋势略有不同，时间越短呈上升趋势的站点越多，1~3 h的极端降水呈上升趋势的站点较多，稳态和非稳态假设下的20~100 a一遇重现期平均差异较大，其中，1 h极端降水的显著上升站点中，二者的平均相对误差达30%~43%；而6~24 h极端降水中，呈下降趋势的站点增多，其中，24 h极端降水显著下降站点中，二者的平均相对误差达-43%~-32%；无显著趋势站点，二者的平均相对误差大部分介于-10%~10%。随着重现期增大，二者差异的不确定性区间增大，不同变化趋势站点表现一致。研究发现，华北地区短历时极端降水强度增加，稳态假设下极端降水的重现期会严重低估。因此，选用非稳态假设估计极端降水的重现期，将降低极端降水的灾害风险。     

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.     

Statistical modeling of CMIP5 projected changes in extreme wet spells over China in the late 21st century

The observed intensity, frequency, and duration (IFD) of summer wet spells, defined here as extreme events with one or more consecutive days in which daily precipitation exceeds a given threshold (the 95th percentile), and their future changes in RCP4.5 and RCP8.5 in the late 21st century over China, are investigated by using the wet spell model (WSM) and by extending the point process approach to extreme value analysis. Wet spell intensity is modeled by a conditional generalized Pareto distribution, frequency by a Poisson distribution, and duration by a geometric distribution, respectively. The WSM is able to realistically model summer extreme rainfall spells during 1961–2005, as verified with observations at 553 stations throughout China. To minimize the impact of systematic biases over China in the global climate models (GCMs) of the Coupled Model Intercomparison Project Phase 5 (CMIP5), five best GCMs are selected based on their performance to reproduce observed wet spell IFD and average precipitation during the historical period. Furthermore, a quantile–quantile scaling correction procedure is proposed and applied to produce ensemble projections of wet spell IFD and corresponding probability distributions. The results show that in the late 21st century, most of China will experience more extreme rainfall and less low-intensity rainfall. The intensity and frequency of wet spells are projected to increase considerably, while the duration of wet spells will increase but to a much less extent. The IFD changes in RCP8.5 are in general much larger than those in RCP4.5.     

从小时尺度考察中国中东部极端降水的持续性和季节特征

相对于日降水量,小时尺度降水资料可以更准确地反映降水强度并描述降水过程,因而更适用于极端降水阈值确定及其特性研究.利用广义极值分布估计中国321个站最大小时降水量的分布函数,确定了5a重现期的小时降水强度阈值.阈值的空间分布呈现出明显的地域差异,西北地区阈值偏低,华北地区、长江中下游地区、华南沿海地区和四川盆地西部地区为高阈值中心.取各站5a一遇极端降水事件对其持续性特征和季节特征进行分析,发现在沿海地区、长江流域和青藏高原东坡极端降水事件的平均持续时间较长(超过12h);中国北部地区持续时间较短.在具有较大海拔落差的复杂地形区,极端降水事件较平原地区更快地发展到峰值.华南地区4月就可有极端降水事件出现,而中国北方地区要到6月底才出现极端降水;全中国大部分地区的年最晚极端降水在8-9月,但沿海地区、大陆南端和西南地区南部的少数站点在10月以后仍有极端降水发生.