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.     

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。     

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。     

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。     

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.     

Extreme daily precipitation: the case of Serbia in 2014

The extreme daily precipitation in Serbia was examined at 16 stations during the period 1961–2014. Two synoptic situations in May and September of 2014 were analysed, when extreme precipitation was recorded in western and eastern Serbia, respectively. The synoptic situation from 14 to 16 May 2014 remained nearly stationary over the western and central Serbia for the entire period. On 15 May 2014, the daily rainfall broke previous historical records in Belgrade (109.8 mm), Valjevo (108.2 mm) and Loznica (110 mm). Precipitation exceeded 200 mm in 72 h, producing the most catastrophic floods in the recent history of Serbia. In Negotin (eastern Serbia), daily precipitation of 161.3 mm was registered on 16 September 2014, which was the maximum value recorded during the period 1961–2014. The daily maximum in 2014 was registered at 6 out of 16 stations. The total annual precipitation for 2014 was the highest for the period 1961–2014 at almost all stations in Serbia. A non-significant positive trend was found for all precipitation indices: annual daily maximum precipitation, the total precipitation in consecutive 3 and 5 days, the total annual precipitation, and number of days with at least 10 and 20 mm of precipitation. The generalised extreme value distribution was fitted to the annual daily maximum precipitation. The estimated 100-year return levels were 123.4 and 147.4 mm for the annual daily maximum precipitation in Belgrade and Negotin, respectively.

     

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.     

A newly-discovered GPD-GEV relationship together with comparing their models of extreme precipitation in summer

It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （Generalized Extreme Values） distribution can be derived from GPD （Generalized Pareto Distribution）. Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT （Peaks Over Threshold）-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values （including the high-end heavy tailed）. In comparison, BM （Block Maximum）-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.     

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。     

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.     

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。     

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。     

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。     

Simulation of extreme precipitation over the Yangtze River Basin using Wakeby distribution

Based on the daily observational precipitation data at 147 stations in the Yangtze River Basin during 1960–2005 and projected daily data of 79 grid cells from the ECHAM5/ MPI-OM model in the 20th and 21st century, time series of precipitation extremes which contain AM (Annual Maximum) and MI (Munger Index) are constructed. The distribution feature of precipitation extremes is analyzed based on the two index series. Three principal results were obtained, as stated in the sequel. (i) In the past half century, the intensity of extreme heavy precipitation and drought events was higher in the mid-lower Yangtze than in the upper Yangtze reaches. Although the ECHAM5 model still can’t capture the precipitation extremes over the Yangtze River Basin satisfactorily, spatial pattern of the observed and the simulated precipitation extremes are much similar to each other. (ii) For quantifying the characteristics of extremely high and extremely low precipitation over the Yangtze River Basin, four probability distributions are used, namely: General Extreme Value (GEV), General Pareto (GPA), General Logistic (GLO), and Wakeby (WAK). It was found that WAK can adequately describe the probability distribution of precipitation extremes calculated from both observational and projected data. (iii) Return period of precipitation extremes show spatially different changes under three greenhouse gas emission scenarios. The 50-year heavy precipitation and drought events from simulated data during 1951–2000 will become more frequent, with return period below 25 years, for the most mid-lower Yangtze region in 2001–2050. The changing character of return periods of precipitation extremes should be taken into account for the hydrological design and future water resources management.     

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.     

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。     

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。     

1981～2010年北京地区极端降水变化特征

采用北京地区20个常规气象站1981~2010年逐日降水数据,对北京地区极端降水的空间分布特征进行了分析。得到以下主要结论:1981~2010年,北京地区极端降水百分位数(第90、95和99个百分位数)阈值表现出较一致的空间分布特征,以第95个百分位数阈值计算的极端降水日数与降水阈值和降水量的分布有较大差异,极端降水量对总降水量的贡献可达30%~37%,极端降水强度分布与极端降水阈值分布相似。近30年,北京地区多数站点的极端降水量、降水日数和降水强度呈下降趋势,极端降水量以上甸子、怀柔、平谷和观象台下降较为明显,可达到40 mm(10 a)–1以上,极端降水强度以顺义、海淀、观象台、大兴和上甸子等站下降较为显著,每10 a降水强度减小趋势可达4 mm d–1,极端降水日数变化分布与极端降水量变化分布类似,极端降水强度变化与降水量和降水日数变化的分布有明显不同。     

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.     

袁河流域极端降水事件成因分析

利用欧洲中期天气预报中心格点再分析资料和HYSPLIT模式对袁河流域5次极端降水天气过程的平均环流背景、主要影响系统、物理量场以及降水发生过程中的120 h气块后向轨迹特征进行分析。结果发现:(1)极端降水发生时,高层袁河流域处于南亚高压东侧辐散气流中,中层副热带高压位置适中,受584 dagpm线附近的西南气流控制,低层正好处于切变线上,且有强盛的西南气流向降水区输送能量和水汽。(2)物理量场上,袁河流域附近低层辐合、高层辐散,垂直速度场、水汽分布、水汽通量散度场都有利于该区域出现暴雨天气。(3)与袁河流域一般性暴雨的平均t-lnp图对比分析可见,极端暴雨的能量条件更好,降水对流性更强,水汽条件也更为充沛。(4)袁河流域极端降水上空的水汽路径总体上可以归纳为5条。来源于孟加拉湾附近、中南半岛南部和云南南部的西南水汽路径最多,占轨迹总数的59.5%;其次是来源于我国南海的南方路径,主要位于1 500 m以下,占轨迹总数的15.0%。