Nonparametric analysis of high wind speed data

In this paper, nonparametric curve estimation methods are applied to analyze time series of wind speeds, focusing on the extreme events exceeding a chosen threshold. Classical parametric statistical approaches in this context consist in fitting a generalized Pareto distribution (GPD) to the tail of the empirical cumulative distribution, using maximum likelihood or the method of the moments to estimate the parameters of this distribution. Additionally, confidence intervals are usually computed to assess the uncertainty of the estimates. Nonparametric methods to estimate directly some quantities of interest, such as the probability of exceedance, the quantiles or return levels, or the return periods, are proposed. Moreover, bootstrap techniques are used to develop pointwise and simultaneous confidence intervals for these functions. The proposed models are applied to wind speed data in the Gulf Coast of US, comparing the results with those using the GPD approach, by means of a split-sample test. Results show that nonparametric methods are competitive with respect to the standard GPD approximations. The study is completed generating synthetic data sets and comparing the behavior of the parametric and the nonparametric estimates in this framework.     

PVA-maxima and their connection to cloud systems in satellite images and to precipitation

Summary PVA-maxima can be a contributor to upward motion; there-fore cloudiness and precipitation can be expected there. This is investigated from several viewpoints: grey shade evaluations of false colour satellite images are done, frequencies of precipitation events for PVA maxima and grey shade intervals are investigated, precipitation amounts within the PVA maxima path are compared to a surroundings and the predictability from the ECMWF model is proved. Several results could be derived: PVA maxima are accompanied by brighter grey shade intervals and a higher precipitation probability than surrounding areas; for the brightest grey shade intervals a probability for precipitation of 60–70% can be stated; the path of the PVA maxima is an area of more precipitation than in the surroundings; ECMWF forecasts are able to predict the PVA maxima and their location very well but tend to underestimate the precipitation amounts on the PVA maxima path.With 9 Figures     

Generalized extreme wind speed distributions in South America over the Atlantic Ocean region

Statistical analysis of extreme values is applied to wind data from National Centers for Environmental Prediction and National Center for Atmospheric Research reanalysis grid points over the ocean region bounded at 23°S and 40°W and 42°W towards the south and southeastern Brazilian coast. The period of analysis goes from 1975 to 2006. The generalized extreme value and generalized Pareto distributions are employed for annual and daily maxima, respectively. The Pareto?CPoisson point process characterization is also used to analyze peaks over threshold. Return levels for 10, 25, 50, and 100?years are calculated at each grid point. However, most of the reanalysis data fall within 1?C10-year return periods, suggesting that hazardous wind speed with low probability (return periods of 50?C100) have rarely measured in this period. Wide confidence intervals on these levels show that there is not enough information to make predictions with any degree of certainty to return periods over 100?years. Low extremal index (??) values are found for excess wind speeds over a high threshold, indicating the occurrence of consecutively high peaks. In order to obtain realistic uncertainty information concerning inferences associated with threshold excesses, a declustering method is performed, which separates the excesses into clusters, thereby rendering the extreme values more independent.     

Uncertainty in drought monitoring by the Standardized Precipitation Index: the case study of the Abruzzo region (central Italy)

As shown by several authors, drought monitoring by the Standardized Precipitation Index (SPI) presents some uncertainties, mainly dependent on the choice of the probability distribution used to describe the cumulative precipitation and on the characteristics (e.g., length and variability) of the dataset. In this paper, the uncertainty related to SPI estimates has been quantified and analyzed with regards to the case study of the Abruzzo region (Central Italy), by using monthly precipitation recorded at 75 stations during the period 1951–2009. First, a set of distributions suitable to describe the cumulative precipitation at the 3-, 6-, and 12-month time scales was identified by using L-moments ratio diagrams. The goodness-of-fit was evaluated by applying the Kolmogorov–Smirnov test, and the Normality test on the derived SPI series. Then the confidence intervals of SPI have been calculated by applying a bootstrap procedure. The size of the confidence intervals has been considered as a measure of uncertainty, and its dependence on several factors such as the distribution type, the time scale, the record length, and the season has been examined. Results show that the distributions Pearson type III (PE3), Weibull (WEI), Generalized Normal (GNO), Generalized Extreme Value (GEV), and Gamma (GA2) are all suitable to describe the cumulative precipitation, with a slightly better performance of the PE3 and GNO distributions. As expected, the uncertainty increases as the record length and time scale decrease. The leading source of uncertainty is the record length while the effects due to seasonality and time scale are negligible. Two-parameter distributions make it possible to obtain confidence intervals of SPI (particularly for extreme values) narrower than those obtained by three-parameter distributions. Nevertheless, due to a poorer goodness of fit, two-parameter distributions can provide less reliable estimates of the precipitation probability. In any event, independently of the type of distribution, the SPI estimates corresponding to extreme precipitation values are always characterized by a relevant uncertainty. This is due to the explosion of the probability variability that occurs when precipitation values approach the tails of the supposed distribution.     

The use of bootstrap confidence intervals for the correlation coefficient in climatology

Summary The importance of defining confidence intervals for sample statistics that are used to estimate characteristics of the parent population(s) is emphasised. Not all sample statistics are unbiased estimators or have normally distributed sampling distributions and so it is not always easy to reflect the reliability of the estimator. In such cases, Efron's bias corrected percentile method, which uses bootstrap samples to estimate the bias and makes no assumptions about the distribution of the sample statistic can be used to define confidence limits for the population parameter. The method is explained and the procedure for calculating the confidence limits is outlined.As an example, bootstrap confidence limits calculated for the maximum correlation between the Southern Oscillation Index and rainfall at South African stations over the period 1935–1983 suggest that the sample correlation is an unreliable measure of the true association. One possible reason for this is that the association is thought to have broken down during the 1940s. However, the reliability of the estimator does not seem to improve when confidence limits are calculated for the 30-year period 1954–1983. It is possible that the width of the confidence interval is an indication of more than one distinct statistical population.     

Variability of extreme events in the Colombian Pacific and Caribbean catchment basins

This paper analyses the behavior of extreme events of surface precipitation and temperature inside the Pacific and Caribbean Catchment Basins in Colombia using several datasets such as observations, reconstructed data, NCEP-NCAR and ERA-40 reanalyses and data from the regional model REMO. We use an extreme value method that selects the time series excesses over a nonstationary threshold and adjusts them to a generalized Pareto distribution. The goodness of fit is evaluated through a test that includes the Cramer–von Mises, Kolmogorov–Smirnov and Anderson–Darling statistics and the p values generated by parametric bootstrap resampling. The test not only evaluates the goodness of fit but also the threshold choice. The parameters are presented in maps that allow recognition of the features of the extreme behaviour inside the catchment basins, and differences and similarities between them. Maps of return periods for the maximum extreme events are also presented. A strong influence of the El Niño–Southern oscillation on the extreme events of both temperature and precipitation is found in the two catchment basins.     

广义极值分布理论在重现期计算的应用

在气候统计学上,常用Weibull、Gumbel、Frechet统计分布函数对极端气候要素的分布进行拟合,广义极值分布理论综合了以上三种极值分布模型,在气候分析中得到了广泛应用。以南昌市年汛期日最大降水量为例,利用广义极值分布理论对其分布进行拟合,并对重现值及其置信区间进行计算,为气候要素极值的统计分析提供了一种新的手段。     

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。     

Assessment of the impacts of climate change and brackish irrigation water on rice productivity and evaluation of adaptation measures in Ca Mau province,Vietnam

This paper presents applications of the peaks-over-threshold methodology for both the univariate and the recently introduced bivariate case, combined with a novel bootstrap approach. We compare the proposed bootstrap methods to the more traditional profile likelihood. We have investigated 63 years of the European Climate Assessment daily precipitation data for five Hungarian grid points, first separately for the summer and winter months, then aiming at the detection of possible changes by investigating 20 years moving windows. We show that significant changes can be observed both in the univariate and the bivariate cases, the most recent period being the most dangerous in several cases, as some return values have increased substantially. We illustrate these effects by bivariate coverage regions.     

Diurnal precipitation cycle in Austria

A back-trajectory clustering method was developed to identify synoptic patterns associated with heavy precipitation in Austria. Extending this work from daily precipitation sums to accumulation intervals from 12 to 48 hours, an unexpected problem was encountered related to the observation schedule of data. To modify available data to our specific needs, evening precipitation falling between 19 and 21 LT (Local Time) was studied. Hourly precipitation data for the period of 1950 to 2005 from 132 weather stations over Austria were used. It was found that the evening precipitation fraction has its maxima in the central Alps in all seasons, except in autumn when maxima shift more towards the south of the Alps. These results encouraged us to analyse the variation of diurnal precipitation for different seasons in Austria as well. A total of 119 stations with sixteen years (1990?C2005) of data were used for this purpose. Mean hourly precipitation values were calculated, which were then normalised, smoothed and were finally clustered to find regions with homogeneous diurnal cycles. The diurnal cycles of precipitation of the centres exhibit systematic patterns and seasonal cycles, reflecting intensity and timing of convective activity over these regions. The winter season is relatively dry and summer is associated with the highest precipitation. The areas inside the Alps receive higher amplitudes of precipitation in summer. Interesting features such as bimodal distributions, nocturnal maxima and early morning maxima were also observed in many regions.     

Probabilistic model of maximum precipitation depths for Kraków (southern Poland, 1886-2002)

This study was designed to empirically determine what relationships existed between three characteristics of precipitation: maximum depth, duration, and probability of exceedance. Annual maximum series for intervals of between one and 120 h were identified using the 1886-2002 pluviographic record from Kraków. The Gumbel distribution was selected from a group of four of the most popular theoretical maximum value distributions and identified as the optimum solution. Its parameters were determined. Confidence intervals for quantiles were obtained using the bootstrap method. Formulae were derived for the relationships between the Gumbel distribution parameters, i.e., the α location and β scale, depending on precipitation duration. These take the form of a polynomial of the second degree. The model developed was subjected to a two-step validation with a positive result.     

Mediterranean climate extremes in synoptic downscaling assessments

The behaviour of precipitation and maximum temperature extremes in the Mediterranean area under climate change conditions is analysed in the present study. In this context, the ability of synoptic downscaling techniques in combination with extreme value statistics for dealing with extremes is investigated. Analyses are based upon a set of long-term station time series in the whole Mediterranean area. At first, a station-specific ensemble approach for model validation was developed which includes (1) the downscaling of daily precipitation and maximum temperature values from the large-scale atmospheric circulation via analogue method and (2) the fitting of extremes by generalized Pareto distribution (GPD). Model uncertainties are quantified as confidence intervals derived from the ensemble distributions of GPD-related return values and described by a new metric called “ratio of overlapping”. Model performance for extreme precipitation is highest in winter, whereas the best models for maximum temperature extremes are set up in autumn. Valid models are applied to a 30-year period at the end of the twenty-first century (2070–2099) by means of ECHAM5/MPI-OM general circulation model data for IPCC SRES B1 scenario. The most distinctive future changes are observed in autumn in terms of a strong reduction of precipitation extremes in Northwest Iberia and the Northern Central Mediterranean area as well as a simultaneous distinct increase of maximum temperature extremes in Southwestern Iberia and the Central and Southeastern Mediterranean regions. These signals are checked for changes in the underlying dynamical processes using extreme-related circulation classifications. The most important finding connected to future changes of precipitation extremes in the Northwestern Mediterranean area is a reduction of southerly displaced deep North Atlantic cyclones in 2070–2099 as associated with a strengthened North Atlantic Oscillation. Thus, the here estimated future changes of extreme precipitation are in line with the discourse about the influence of North Atlantic circulation variability on the changing climate in Europe.     

Modelling Korean extreme rainfall using a Kappa distribution and maximum likelihood estimate

Summary Attempts to use the 4-parameter Kappa distribution (K4D) with the maximum likelihood estimates (MLE) on the summer extreme daily rainfall data at 61 gauging stations over South Korea have been made to obtain reliable quantile estimates for several return periods. A numerical algorithm for searching MLE of K4D by minimizing the negative log-likelihood function with penalty method has been described. The isopluvial maps of estimated design values corresponding to selected return periods have been presented. The highest return values are centered at sites in the south-western part of the Korean peninsula. The distribution of return values for annual maxima of 2-day precipitation (AMP2) is more similar to the climatological features of annual total precipitation of Korea than that of annual maxima of daily precipitation (AMP1). Our results of return values delineate well the horizontal patterns of the heavy precipitation over the Korean peninsula. Received January 15, 2001 Revised October 8, 2001     

Basic statistical characteristics of hourly rainfall amounts in Barcelona (Spain)

Summary In order to derive some statistical rainfall characteristics applicable to hydrology, data of continuous rainfall rate recordings of a Jardí gauge installed in Barcelona (Spain) have been converted to an hourly precipitation series. From these data, four useful distributions have been obtained and further compared with some theoretical models. It has been found that the duration of events is distributed exponentially. The duration of rainless intervals follow a generalized Pareto distribution, and the cumulative rainfall in the cumulative rain duration is beta distributed. Concerning the distribution of rain amounts, two models can be accepted, depending on the duration of the events. Comparison with a similar study carried out in Farnborough (United Kingdom) indicates that the events are shorter and that the amounts of rain collected in short events are larger in Barcelona.This work was supported by the DGICYT (Project NAT91-0596) and the CCE (Project PL 910104 Environment).With 7 Figures     

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.     

AN OBSERVATIONAL STUDY ON DISTRIBUTION OF PRECIPITATION ASSOCIATED WITH LANDFALLING TROPICAL CYCLONES AFFECTING CHINA

In order to provide an operational reference for tropical cyclone precipitation forecast,this study investigates the spatial distributions of precipitation associated with landfalling tropical cyclones(TCs) affecting China using Geostationary Meteorological Satellite 5(GMS5)-TBB dataset.All named TCs formed over the western North Pacific that made direct landfall over China during the period 2001-2009 are included in this study.Based on the GMS5-TBB data,this paper reveals that in general there are four types of distribution of precipitation related to landfalling TCs affecting China.(a) the South-West Type in which there is a precipitation maximum to the southwestern quadrant of TC;(b) the Symmetrical South Type in which the rainfall is more pronounced to the south side of TC in the inner core while there is a symmetrical rainfall distribution in the outer band region;(c) the South Type,in which the rainfall maxima is more pronounced to the south of TC;and(d) the North Type,in which the rainfall maxima is more pronounced to the north of TC.Analyses of the relationship between precipitation distributions and intensity of landfalling TCs show that for intensifying TCs,both the maximum and the coverage area of the precipitation in TCs increase with the increase of TC intensity over northern Jiangsu province and southern Taiwan Strait,while decreasing over Beibu Gulf and the sea area of Changjiang River estuary.For all TCs,the center of the torrential rain in TC shifts toward the TC center as the intensity of TC increases.This finding is consistent with many previous studies.The possible influences of storm motion and vertical wind shear on the observed precipitation asymmetries are also examined.Results show that the environmental vertical wind shear is an important factor contributing to the large downshear rainfall asymmetry,especially when a TC makes landfall on the south and east China coasts.These results are also consistent with previous observational and numerical studies.     

Multi-day rainfall trends over the Iberian Peninsula

In order to analyze the effects of the duration of precipitation events, trends in extreme rainfall over the Iberian Peninsula (IP) for multi-day extreme precipitation events (1 to 7?days) were evaluated from records of 52 observatories regularly distributed over Iberia with no missing data for the common period 1958–2004. Two approaches were used: first, the nonparametric Mann–Kendall test together with the Sen method, and second, a parametric test based on the statistical theory of extreme values, involving time-dependent parameters to account for possible temporal changes in the frequency distribution. It was found that, in winter, there were significant negative trends for a great part of the Iberian Peninsula, but significant positive trends for the southeast over areas that shrank as the number of days considered for the precipitation event increased. Spring also showed negative trends for a great part of the IP but with a major area of positive trend over the northeast that remained unchanged when considering the maxima of from 1 to 7?days of rainfall. Autumn showed a bipolar spatial pattern, with the west being positive and the east negative.     

Nonparametric kernel estimation of annual precipitation over Iran

In this paper, annual precipitation data sets from five old rain gauge stations (Bushehr, Isfahan, Meshed, Tehran, and Jask) in Iran were fitted to nonparametric kernel function by using rectangular, triangular, and Gaussian or normal as kernel functions. The smoothing parameter was calculated by four methods including rule of thumb, Adamowski criterion, least squares cross-validation, and Sheater and Jones plug-in. The Adamowski criterion showed a better performance compared to other methods due to goodness of fit tests. The results of these proposed nonparametric methods will be then compared to the results of the parametric density functions including normal, two and three parameter log-normal, two parameter gamma, Pearson and log-Pearson type 3, Gumbel or extreme value type 1 and also Fourier series method which were applied by a previous study for the same stations. It was concluded that the annual precipitation data were fitted to nonparametric methods better than parametric methods.     

Estimates of the maximum land-fast ice thickness probable once in 5, 10, 25, 50, and 100 years

Presented are the empirical, nonparametric (quantile), parametric, and randomized estimates of the maximum land-fast ice thickness in the Northern Caspian probable once in 5, 10, 25, 50, and 100 years. The annual maxima of the land-fast ice thickness for the 72-year period from 1937 to 2008 are computed using the one-dimensional thermodynamic model of the sea ice developed at Arctic and Antarctic Research Institute.     

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.