Extreme temperature scenarios in Mexicali,Mexico under climate change conditions

Extreme weather events can have severe consequences for the population and the environment. Therefore, in this study a temporal trend of annual temperatures was built with a time series from 1950 to 2010 for Mexicali, Mexico, and estimates of 5- to 100-year return periods are provided by modeling of summer maximum and winter minimum temperatures. A non-parametric Kendall’s tau test and the Sen’s slope estimator were used to compute trends. The generalized extreme value (GEV) distribution was applied to the approximation of block maxima and the generalized Pareto distribution (GPD) to values over a predetermined threshold. Due to the non-stationary characteristic of the series of temperature values, the temporal trend was included as a covariable in the location parameter and substantial improvements were observed, particularly with the extreme minimum temperature, compared to that obtained with the GEV with no covariable and with the GPD. A positive and significant statistically trend in both summer maximum temperature and winter minimum temperature was found. By the end of 21st century the extreme maximum temperature could be 2 to 3 °C higher than current, and the winter could be less severe, as the probabilistic model suggests increases of 7 to 9 °C in the extreme minimum temperature with respect to the base period. The foreseeable consequences on Mexicali city are discussed.     

Estimating storm surge intensity with Poisson bivariate maximum entropy distributions based on copulas

This paper introduces four kinds of novel bivariate maximum entropy distributions based on bivariate normal copula, Gumbel–Hougaard copula, Clayton copula and Frank copula. These joint distributions consist of two marginal univariate maximum entropy distributions. Four types of Poisson bivariate compound maximum entropy distributions are developed, based on the occurrence frequency of typhoons, on these novel bivariate maximum entropy distributions and on bivariate compound extreme value theory. Groups of disaster-induced typhoon processes since 1949–2001 in Qingdao area are selected, and the joint distribution of extreme water level and corresponding significant wave height in the same typhoon processes are established using the above Poisson bivariate compound maximum entropy distributions. The results show that all these four distributions are good enough to fit the original data. A novel grade of disaster-induced typhoon surges intensity is established based on the joint return period of extreme water level and corresponding significant wave height, and the disaster-induced typhoons in Qingdao verify this grade criterion.     

Flood estimation in Mahanadi river system,India using partial duration series

Flood frequency analysis is a pre-requisite for setting up and safeguarding of many hydraulic structures, such as dams, barrages, check-dams, culverts and urban drainage systems. In the flood frequency analysis, partial duration series (PDS) may be considered when dealing with values exceeding certain limits causing floods. In fact, the PDS is capable of getting more information about extreme events than the annual maximum series (AMS). Additionally, an assumption that, the magnitude of the extreme events of a PDS is best described by a generalized Pareto (GP) distribution. The present work investigates the at-site flood frequency analysis to find the average number of peaks (λ) for modelling the PDS on the basis of the PDS/GP assumption and variability in the GP parameters coupled with the quantile estimation with an increase in the value of average number of peaks (λ) each year in the Mahanadi river system, Odisha, India. Also, to verify the PDS/GP assumption we tested seven different frequency distributions (Exponential, Gumbel, logistics, generalized extreme value (GEV), Lognormal (LN), generalized logistics (GL) and Pearson Type 3). Extensive daily discharge data collected from 23 gauging sites were used for the analysis. The results indicate precision and stability of GP distribution parameters for λ?=?4 for almost all the discharge sites. The peak flood estimated for various return periods in the Mahanadi river system using GP distribution is endowed with high correlation statistics for this λ value.     

GEV干旱指数及其在气象干旱预测和监测中的应用和检验

介绍了一种新的基于广义极值分布(Generalized Extreme Value,GEV)的干旱指数的构建过程及其原理。并利用1951—2010年中国地区160个气象台站的逐月降水资料,选择6个代表台站,检验1951—2010年60年间预测的干旱和实际干旱事件发生的吻合程度;利用2009—2010年资料检验GEV指数和实际发生的干旱事件在月尺度上的监测效果。结果表明,利用GEV方法定义的干旱指数能较好地监测干旱事件的发生和发展,与目前广泛使用的Ci指数监测结果较为一致。同时这种指数也能用于某一地区干旱事件的预测和干旱等级的划分。对干旱业务监测和预测有重要的参考意义。但该指数对站点疏密有一定的依赖性,站点稀疏的区域存在着一些误差。     

Application of Weibull model for redefined significant wave height distributions

It is well accepted that the parent distribution for individual ocean wave heights follows the Weibull model. However this model does not simulate significant wave height which is the average of the highest one-third of some ‘n’ (n- varies) wave heights in a wave record. It is now proposed to redefine significant wave height as average of the highest one-third of a constant number (n-constant, say,n = 100) of consecutive individual wave heights. The Weibull model is suggested for simulating redefined significant wave height distribution by the method of characteristic function. An empirical support of 100.00% is established by Χ²-test at 0.05 level of significance for 3 sets of data at 0900, 1200 and 1500 hrs at Valiathura, Kerala coast. Parametric relations have been derived for the redefined significant wave height parameters such as mean, maximum one-third average, extreme wave heights, return periods of an extreme wave height and the probability of realising an extreme wave height in a time less than the designated return period.     

Flood frequency analysis of river swat using Log Pearson type 3, Generalized Extreme Value,Normal, and Gumbel Max distribution methods

In Pakistan, floods are among the most devastating and recurring natural hazards. Flood hazard assessment requires flood event magnitude and probability of occurrence. Flood frequency analysis is the most common technique used for the at-site estimation of flood recurrence magnitude. This paper evaluates four most commonly used distribution methods, i.e., Generalized Extreme Value (GEV), Log Pearson 3 (LP3), Gumbel Max, and Normal for the flood frequency and estimation of flood recurrence. Different hydrological stations data namely Khwazakhela, Chakdarra, Panjkora, and Munda Headwork located at Swat river was taken from Provincial Irrigation Department, Khyber Pakhtunkhwa. The analysis is done for 5-, 10-, 25-, 50-, and 100-year return periods by using annual maximum discharge data from 1980 to 2016 (37 yr). Three goodness-of-fit tests were applied to the fitted distributions, i.e., Kolmogorov–Smirnov, Anderson–Darling, and Chi-squared at 5% significance level. Results indicate that LP3 and GEV were ranked top two distributions at all locations while Gumbel Max and Normal were the least fitted having rank 3 and 4, respectively. Based on the goodness-of-fit ranking, LP3 was selected for the estimation of flood magnitude and return periods at Khwazakhela. Designed hydrographs based on probabilistic approach and flood 2010 hydrograph are presented for flood simulation.     

雅鲁藏布江流域极端降水模拟及预估

为了解雅鲁藏布江流域汛期极端降水的变化规律,推算一定重现期的极端降水量分位数,通过百分位法、Hill图法、年交叉率法选取阈值,借助广义帕累托分布函数（GPD）对流域极端降水频率进行了分析。结果表明：99百分位时的阈值为流域内各站点的最佳阈值,且各站点超阈值序列通过了M-K的平稳性检验,无明显突变。拟合效果通过K-S检验,各站点拟合的极端降水理论频数和实测频数基本相符。尺度参数的大值区位于流域下游,表明该地区的极值波动大;形状参数正值区位于流域中上游地区,说明发生破纪录降水事件的概率较大,拟合结果与实际观测一致。从5年一遇和10年一遇的极端降水值来看,雅江流域除拉孜站外,其他地区降水极值均超过30 mm,日喀则地区的降水极值达50 mm;各地区20年一遇和30年一遇的降水极值增长的非常缓慢。通过与实际极端降水值对比分析得出,GPD拟合计算出的重现期水平基本符合实际,即具有一定的合理性。     

Numerical hindcast of extreme waves

The cyclone wave parameters are predicted using Young’s parametric hurricane wave prediction model. The input cyclone tracks for this work are obtained from Fleet Naval Meteorology and Oceanography Center, USA. Extreme value analysis is carried out to obtain the wave heights and periods for 1 in 5, 10, 50 and 100 years return periods, respectively. The deep-water hindcast wave corresponding to 100 years from probable directions are allowed to propagate to Visakhapatnam coastal waters using nearshore spectral wind-wave mode. The offshore wave height for one in 100-year return period is 11.9 m, and the corresponding nearshore wave height at 10-m water depth varies between 4.6 and 5.6 m depending on the directional spreading. Weibull distribution is chosen to fit the 24 cyclonic data sets over a total period of 30 years (September 1972 to November 2002). This paper demonstrates usefulness of Young’s wave model for deep-water extreme wave hindcasting. Further, the results of the present study would be highly useful for assessing the design wave height for Visakhapatnam coast.     

Comparison of the performance of power law and probability distributions in the frequency analysis of flood in Dez Basin,Iran

Determination of the return period of design flood depends on the nature of the project and the consequences of the flood and is based on economic criteria, human casualties, and hydrological factors. Underestimation of flood might result in casualties and economic damages, while the overestimation leads to capital waste. Therefore, in this research, the flood frequency analysis of Dez Basin, Iran was conducted within the period of 1956–2012 using power law approach together with ordinary distributions, including normal, log normal, Pearson type III, exponential, gamma, generalized extreme value, Nakagami, Rayleigh, logistic, generalized logistic, generalized Pareto, and Weibull distributions. The power law comes from the fractal nature of earth science phenomena such as precipitation and runoff. Accordingly, in this research the partial duration flood series of five hydrometric stations in Dez Basin were extracted using power law with the intervals of 7, 14, 30, and 60 days and then compared with the annual maxima. The results indicated that the annual maxima were not suitable for frequency analysis of the flood in Dez Basin, and the 30-day partial duration series obtained from the power law has a better correspondence with the flow and properties of the Dez Basin. The independence and stationarity of the 30-day partial duration series were examined by Wald–Wolfowitz test, confirming the independence of the considered series. Next, the power distribution and the typical statistical distributions were fitted onto the data of the flood in Dez Basin, with the performance of each distribution being investigated using normalized root-mean-square error and Nash–Sutcliffe criteria. The results revealed that in the SDZ and TPB stations, power distribution had a better performance than other considered distributions. Moreover, in the SDS, TPS, and TZ stations the power distribution stood in the second rank in terms of the best distribution. As the performance of power distribution in the estimation of the flood in Dez Basin has been very satisfactory and calculation of its parameters and its application is easier than ordinary probability distributions, thus it can be suggested as the superior distribution for flood frequency analysis in Dez Basin.     

A probabilistic approach for estimating return period of extreme annual rainfall in different cities of Punjab

Multi-day rainfall events are an important cause of recent severe flooding in Pakistan, and any change in the magnitude of such events may have severe impact upon urban structures such as dams, urban drainage systems, and flood. This article uses statistical distributions to define extremes of annual rainfall of different cities of Punjab (Lahore, Murree, Sialkot, and Jhelum) with given return periods. Our calculations suggest that general extreme value is the best-fitted distribution for the extreme annual rainfall of different cities of Punjab. Our calculations show that different cities of Punjab have 5 years return period for receiving more than 100 mm daily rainfall. While they have 30 years return period for receiving more than 200 mm daily rainfall. This asks for construction of new dams in Pakistan.     

Preparing stream flow drought severity–duration–frequency curves using threshold level method

Drought is a natural phenomenon which occurs in different climate regimes. In the present study, hydrological drought of the Roud Zard basin has been investigated based on run theory. Daily runoff data of Mashin hydrometery station during 1970 to 2012 was assessed using 70 % of mean daily runoff as threshold level. Results showed that the maximum drought duration of 309 days occurred in 1998 and 1999 and max drought deficit of 117.217 million cubic meters per second in 1983 with 275 days duration. Time series of the annual maxima values of duration and volume deficit showed similar trend of increase and decreasing. Burr statistical distribution, as the most suitable one fitted to the drought duration data, forecasted 339 days duration for drought event with 20 years return period and generalized extreme value forecasted 37.9 million cubic meters of deficit volume for this return period. Severity-duration-frequency (SDF) curves were prepared, classifying drought durations to four intervals and fitting statistical distribution to each. Resulted SDF curves showed that, in each period, increase of duration resulted in increased value of the volume deficit with a non-linear trend, though predicted drought volume with 20 years return period was 2.1 million cubic meters for 1 to 10 days duration, 6.9 for 11 to 30 days, 34.5 for 31 to 120 days, and 79.1 for more than 120 days duration drought event. Drought deficit volume increasing rate was also different in each class of duration interval. Drought SDF curves derived in this study can be used to quantify water deficit for natural stream and reservoir. SDFs could also be extended to allow for drought regional frequency analysis to be used in ungauged sites.     

Multi-criteria decision-making analysis in selecting suitable plotting positions for IDF curves of storm events

Selecting suitable distributions for rainfall data is usually subjective and complex since it requires decision-makers to consider results from various measures of goodness-of-fit indices. In this study, the VIKOR method in multi-criteria decision-making analysis is modified to select the most suitable plotting positions to represent extreme storm intensities in order to build the intensity–duration–frequency (IDF) curves of storm events. This is done by considering the rankings provided by all goodness-of-fit indices used to obtain a compromise solution. Nine plotting positions are considered: Weibull (W), Adamowski (A), Gringorten (G), Hazen (H) and Gumbel (EV I) and two known plotting positions for generalized extreme value (GEV) distribution using Pearson’s skewness and another two using L-skewness. The IDF curves obtained are compared to a reference IDF curves which was found using the GEV distribution. The mean and median for three goodness-of-fit indices, the coefficient of variation of root mean square error, CV_RMSE, the mean percentage of difference, Δ, and the coefficient of determination, R ², are taken as the criteria for selection process. The results show that six plotting positions, A, H, W, G and the two plotting positions with L-skewness, are equally superior compared to the other three plotting positions.     

非平稳条件下北京市最大月降水量频率特征分析

为探究气候变化下极端降水的频率变化特征,基于北京市22个雨量站实测月降水量数据,以时间为协变量构建平稳和非平稳GEV模型,对北京市最大月降水量序列(极值降水序列)进行模拟和频率分析,并采用Bootstrap方法对频率分析结果的不确定性进行评价。结果表明:所有极值降水序列的最优概率分布模型均为非平稳GEV模型,该模型能够抓住序列随时间呈显著下降趋势的变化特征;由非平稳GEV模型估算得到的极值降水重现水平随时间呈减少趋势,这意味着未来极值降水导致洪涝灾害的风险在降低,但导致干旱的风险将增加;随着重现期的增加,极值降水重现水平估计值的不确定性也随之增大。     

A study on selection of probability distributions for at-site flood frequency analysis in Australia

The most direct method of design flood estimation is at-site flood frequency analysis, which relies on a relatively long period of recorded streamflow data at a given site. Selection of an appropriate probability distribution and associated parameter estimation procedure is of prime importance in at-site flood frequency analysis. The choice of the probability distribution for a given application is generally made arbitrarily as there is no sound physical basis to justify the selection. In this study, an attempt is made to investigate the suitability of as many as fifteen different probability distributions and three parameter estimation methods based on a large Australian annual maximum flood data set. A total of four goodness-of-fit tests are adopted, i.e., the Akaike information criterion, the Bayesian information criterion, Anderson–Darling test, and Kolmogorov–Smirnov test, to identify the best-fit probability distributions. Furthermore, the L-moments ratio diagram is used to make a visual assessment of the alternative distributions. It has been found that a single distribution cannot be specified as the best-fit distribution for all the Australian states as it was recommended in the Australian rainfall and runoff 1987. The log-Pearson 3, generalized extreme value, and generalized Pareto distributions have been identified as the top three best-fit distributions. It is thus recommended that these three distributions should be compared as a minimum in practical applications when making the final selection of the best-fit probability distribution in a given application in Australia.     

The probability distribution of extreme precipitation

On the basis of the negative binomial distribution of the duration of wet periods calculated per day, an asymptotic model is proposed for distributing the maximum daily rainfall volume during the wet period, having the form of a mixture of Frechet distributions and coinciding with the distribution of the positive degree of a random variable having the Fisher–Snedecor distribution. The method of proving the corresponding result is based on limit theorems for extreme order statistics in samples of a random volume with a mixed Poisson distribution. The adequacy of the models proposed and methods of their statistical analysis is demonstrated by the example of estimating the extreme distribution parameters based on real data.     

Maximum daily rainfall in South Korea

Annual maxima of daily rainfall for the years 1961–2001 are modeled for five locations in South Korea (chosen to give a good geographical representation of the country). The generalized extreme value distribution is fitted to data from each location to describe the extremes of rainfall and to predict its future behavior. We find evidence to suggest that the Gumbel distribution provides the most reasonable model for four of the five locations considered. We explore the possibility of trends in the data but find no evidence suggesting trends. We derive estimates of 10, 50, 100, 1000, 5000, 10,000, 50,000 and 100,000 year return levels for daily rainfall and describe how they vary with the locations. This paper provides the first application of extreme value distributions to rainfall data from South Korea.     

Quantifying uncertainties associated with depth duration frequency curves

Uncertainty in depth–duration–frequency (DDF) curves is usually disregarded in the view of difficulties associated in assigning a value to it. In central Iran, precipitation duration is often long and characterized with low intensity leading to a considerable uncertainty in the parameters of the probabilistic distributions describing rainfall depth. In this paper, the daily rainfall depths from 4 stations in the Zayanderood basin, Iran, were analysed, and a generalized extreme value distribution was fitted to the maximum yearly rainfall for durations of 1, 2, 3, 4 and 5 days. DDF curves were described as a function of rainfall duration (D) and return period (T). Uncertainties of the rainfall depth in the DDF curves were estimated with the bootstrap sampling method and were described by a normal probability density function. Standard deviations were modeled as a function of rainfall duration and rainfall depth using 10⁴ bootstrap samples for all the durations and return periods considered for each rainfall station.     

Analysis of a Long Record of Annual Maximum Rainfall in Athens,Greece, and Design Rainfall Inferences

An annual series of maximum dailyrainfall extending through 1860–1995, i.e., 136 years,was extracted from the archives of a meteorologicalstation in Athens. This is the longest rainfall recordavailable in Greece and its analysis is required forthe prediction of intense rainfall in Athens, wherecurrently major flood protection works are under way.Moreover, the statistical analysis of this long recordcan be useful for investigating more generalisedissues regarding the adequacy of extreme valuedistributions for extreme rainfall analysis and theeffect of sample size on design rainfall inferences.Statistical exploration and tests based on this longrecord indicate no statistically significant climaticchanges in extreme rainfall during the last 136 years.Furthermore, statistical analysis shows that theconventionally employed Extreme Value Type I (EV1 orGumbel) distribution is inappropriate for the examinedrecord (especially in its upper tail), whereas thisdistribution would seem as an appropriate model iffewer years of measurements were available (i.e., partof this sample were used). On the contrary, theGeneral Extreme Value (GEV) distribution appears to besuitable for the examined series and its predictionsfor large return periods agree with the probablemaximum precipitation estimated by the statistical(Hershfield's) method, when the latter is consideredfrom a probabilistic point of view. Thus, the resultsof the analysis of this record agree with a recently(and internationally) expressed scepticism about theEV1 distribution which tends to underestimate thelargest extreme rainfall amounts. It is demonstratedthat the underestimation is quite substantial (e.g.,1 : 2) for large return periods and this fact must beconsidered as a warning against the widespread use ofthe EV1 distribution for rainfall extremes.     

Joint return probability analysis of wind speed and rainfall intensity in typhoon-affected sea area

Strong wind and rainfall induced by extreme meteorological processes such as typhoons have a serious impact on the safety of bridges and offshore engineering structures. A new bivariate compound extreme value distribution is proposed to describe the probability dependency structure of annual extreme wind speed and concomitant process maximum rainfall intensity in typhoon-affected area. This probability model takes full account of the case that there may be no rainfall in a typhoon process. A case study based on the observation data of typhoon maximum wind speed and maximum rainfall intensity in Shanghai is conducted to testify the efficiency of the model. Weibull distributions with two parameters are applied to fit respective probability margins, and the joint probability distribution is constructed by Gumbel–Hougaard copula. The fitting results and K–S tests show that these models describe the original data well. The joint return periods are calculated by Poisson bivariate compound extreme value distribution we have proposed. They indicate that typhoons with no rain have smaller joint return periods, and wind speed is the main factor which impacts the change of the joint return periods.     

Assessing the copula selection for bivariate frequency analysis based on the tail dependence test

The flood characteristics, namely, peak, duration and volume provide important information for the design of hydraulic structures, water resources planning, reservoir management and flood hazard mapping. Flood is a complex phenomenon defined by strongly correlated characteristics such as peak, duration and volume. Therefore, it is necessary to study the simultaneous, multivariate, probabilistic behaviour of flood characteristics. Traditional multivariate parametric distributions have widely been applied for hydrological applications. However, this approach has some drawbacks such as the dependence structure between the variables, which depends on the marginal distributions or the flood variables that have the same type of marginal distributions. Copulas are applied to overcome the restriction of traditional bivariate frequency analysis by choosing the marginals from different families of the probability distribution for flood variables. The most important step in the modelling process using copula is the selection of copula function which is the best fit for the data sample. The choice of copula may significantly impact the bivariate quantiles. Indeed, this study indicates that there is a huge difference in the joint return period estimation using the families of extreme value copulas and no upper tail copulas (Frank, Clayton and Gaussian) if there exists asymptotic dependence in the flood characteristics. This study suggests that the copula function should be selected based on the dependence structure of the variables. From the results, it is observed that the result from tail dependence test is very useful in selecting the appropriate copula for modelling the joint dependence structure of flood variables. The extreme value copulas with upper tail dependence have proved that they are appropriate models for the dependence structure of the flood characteristics and Frank, Clayton and Gaussian copulas are the appropriate copula models in case of variables which are diagnosed as asymptotic independence.