• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3B
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• pp.259-267
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• 2009

Generalized Extreme Value (GEV) distribution is recommended for flood frequency and extreme rainfall distribution in many country. L-moment method is the most common estimation procedure for the GEV distribution. In this study, the relationships between the cross-site correlations between extreme events and the cross-correlation of estimators of L-moment ratios (L-moment Coefficient of Variation (L-CV) and L-moment Coefficient of Skewness (L-CS)) for data generated from GEV distribution were derived by Monte Carlo simulation. Those relationships were fit to the simple power function. In this Monte Carlo simulation, GEV+ distribution were employed wherein unrealistic negative values were excluded. The simple power models provide accurate description of the relationships between cross-correlation of data and cross-correlation of L-moment ratios. Estimated parameters and accuracies of the power functions were reported for different GEV distribution parameters combinations. Moreover, this study provided a description about regional regression approach using Generalized Least Square (GLS) regression method which require the cross-site correlation among L-moment estimators. The relationships derived in this study allow regional GLS regression analyses of both L-CV and L-CS estimators that correctly incorporate the cross-correlation among GEV L-moment estimators.

• Wind and Structures
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• v.9 no.3
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• pp.179-191
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• 2006

Parent wind data are often acknowledged to fit a Weibull probability distribution, implying that wind epoch maxima should fall into the domain of attraction of the Gumbel (Type I) extreme value distribution. However, observations of wind epoch maxima are not fitted well by this distribution and a Generalised Extreme Value (GEV) analysis leading to a Type III fit empirically appears to be better. Thus there is an apparent paradox. The reasons why advocates of the GEV approach seem to prefer it are briefly summarised. This paper gives a detailed analysis of the errors involved when the GEV is fitted to epoch maxima of Weibull origin. It is shown that the results in terms of the shape parameter are an artefact of these errors. The errors are unavoidable with the present sample sizes. If proper significance tests are applied, then the null hypothesis of a Type I fit, as predicted by theory, will almost always be retained. The GEV leads to an unacceptable ambiguity in defining design loads. For these reasons, it is concluded that the GEV approach does not seem to be a sensible option.

• Magazine of the Korean Society of Agricultural Engineers
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• v.40 no.4
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• pp.45-57
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• 1998

This study was conducted to derive optimal design floods by Generalized Extreme Value (GEV) distribution for the annual maximum series at ten watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was established by the tests of Independence, Homogeneity, detection of Outliers. L-coefficient of variation, L-skewness and L-kurtosis were calculated by L-moment ratio respectively. Parameters were estimated by the Methods of Moments and L-Moments. Design floods obtained by Methods of Moments and L-Moments using different methods for plotting positions in GEV distribution were compared by the Relative Mean Errors(RME) and Relative Absolute Errors(RAE). The results were analyzed and summarized as follows. 1. Adequacy for the analysis of flood data was acknowledged by the tests of Independence, Homogeneity and detection of Outliers. 2. GEV distribution used in this study was found to be more suitable one than Pearson type 3 distribution by the goodness of fit test using Kolmogorov-Smirnov test and L-Moment ratios diagram in the applied watersheds. 3. Parameters for GEV distribution were estimated using Methods of Moments and L-Moments. 4. Design floods were calculated by Methods of Moments and L-Moments in GEV distribution. 5. It was found that design floods derived by the method of L-Moments using Weibull plotting position formula in GEV distribution are much closer to those of the observed data in comparison with those obtained by method of moments using different formulas for plotting positions from the viewpoint of Relative Mean Errors and Relative Absolute Errors.

• Journal of Korean Society of Water and Wastewater
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• v.30 no.1
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• pp.41-49
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• 2016

In this study, rainfall characteristics with stationary and non-stationary perspectives were analyzed using generalized extreme value (GEV) distribution and Gumbel distribution models with rainfall data collected in major cities of Korea to reevaluate the return period of sewer flooding in those cities. As a result, the probable rainfall for GEV and Gumbel distribution in non-stationary state both increased with time(t), compared to the stationary probable rainfall. Considering the reliability of ${\xi}_1$, a variable reflecting the increase of storm events due to climate change, the reliability of the rainfall duration for Seoul, Daegu, and Gwangju in the GEV distribution was over 90%, indicating that the probability of rainfall increase was high. As for the Gumbel distribution, Wonju, Daegu, and Gwangju showed the higher reliability while Daejeon showed the lower reliability than the other cities. In addition, application of the maximum annual rainfall change rate (${\xi}_1{\cdot}t$) to the location parameter made possible the prediction of return period by time, therefore leading to the evaluation of design recurrence interval.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2003.10a
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• pp.443-446
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• 2003

This study was conducted to draw design rainfall for the regional design rainfall derived by the optimal distribution and method of frequency analysis. The design rainfalls were calculated by the regional and at-site analysis for Log-Pearson type III and GEV distributions and were compared with Relative efficiency(RE) which is ratio of Relative root-mean-square error(RRMSE) by the regional and at-site analysis for Log-Pearson type III and GEV distributions. Consequently, optimal design rainfalls following the regions and consecutive durations were derived by the regional frequency analysis for GEV distribution and design rainfall maps were drawn by GIS techniques.

• Proceedings of the Korea Water Resources Association Conference
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• 2009.05a
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• pp.1321-1326
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• 2009

강우는 수자원 확보 측면에서 근원이 되는 요소이다. 그러므로 정확한 확률강우량 산정은 미래의 가용 수자원량을 예측하는데 있어 중요한 사항중 하나이며 무엇보다 신중한 결정이 요구된다. 또한 하천의 범람에 의한 침수를 예방하는 수공구조물 등의 설계에 있어서는 신뢰할 수 있는 확률강우량 산정이 선행되어야 한다. 본 연구에서는 최근 우리나라 극치강우확률분포로서 많은 연구가 이루어지고 있는 GEV 분포(GEV-O)를 기반으로 위치 매개변수에 시간의 함수를 고려한 개선된 GEV 분포(GEV-A)를 이용하여 서울지점에 적용함으로서 GEV-O 분포에 의한 확률강우량과 GEV-A 분포로 산정된 확률강우량을 비교 검토하였다. 먼저 임의의 난수 발생을 통해 최우도추정법과 확률가중모멘트법으로 매개변수를 추정한 GEV-O 분포와 최우도추정법으로 매개변수를 추정한 GEV-A 분포의 상대평균제곱근오차 (R-RMSE)를 계산하여 비교함으로서 GEV-A 분포의 효율성을 판단하였다. 사례연구는 1961년부터 2008년까지 서울강우관측소에서 측정된 연최대 1일 강우량으로 하였으며 $X^2$-검정, PPCC-검정으로 적합도 검정을 실시하였다. 강우빈도분석 결과 GEV-A 분포가 GEV-O 분포로 산정된 결과 보다 대체로 재현기간 200년 이상일 경우, 과다 산정되는 경향을 보였다. 추후 개선된 GEV 분포를 서울 인근 지점에 적용함으로서 지역빈도해석(Regional Frequency Analysis)을 실행하기 위한 연구가 진행되어야 할 것이다. 또한 확률홍수량 산정 등에도 개선된 GEV 분포를 이용함으로서 보다 정확하고 신뢰성 있는 확률수문량을 예측하여야 할 것이다.

• Journal of Wetlands Research
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• v.20 no.4
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• pp.338-344
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• 2018

In this study, the surface air temperature (SAT) and the dew-point temperature (DPT) are applied as the covariance of the location parameter among three parameters of GEV distribution to reflect the non-stationarity of extreme rainfall due to climate change. Busan station is selected as the study site and the monthly maximum daily rainfall depth from May to October is used for analysis. Various models are constructed to select the most appropriate co-variate(SAT and DPT) function for location parameter of GEV distribution, and the model with the smallest AIC(Akaike Information Criterion) is selected as the optimal model. As a result, it is found that the non-stationary GEV distribution with co-variate of exp(DPT) is the best. The selected model is used to analyze the effect of climate change scenarios on extreme rainfall quantile. It is confirmed that the design rainfall depth is highly likely to increase as the future DPT increases.

• Journal of Korea Water Resources Association
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• v.44 no.2
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• pp.85-96
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• 2011

Probability plotting position is generally used for the graphical analysis of the annual maximum quantile and the estimation of exceedance probability to display the fitness between sample and an appropriate probability distribution. In addition, it is used to apply a specific goodness of fit test. Plotting position formula to define the probability plotting position has been studied in many researches. Especially, the GEV distribution which is an important probability distribution to analyze the frequency of hydrologic data was popular. In this study, the theoretical reduced variates are derived using the mean value of order statistics to derived an appropriate plotting position formula for the GEV distribution. In addition, various forms of plotting position formula considering various sample sizes and coefficients of skewness related with shape parameters are applied. The parameters of plotting position formulas are estimated using the genetic algorithm. The accuracy of derived plotting position formula is estimated by the errors between the theoretical reduced variates and those by various plotting position formulas including the derived ones in this study. As a result, the errors by derived plotting position formula is the smallest at the range of shape parameter with -0.25~0.10.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.3
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• pp.41-50
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• 1999

Derivatio of reasonable design floods was attempted by comparative analysis of design floods derived by Generalized Extreme Value(GEV) distribution using methods of L-moments and LH-moments for the annual maximum series at ten watersheds along Han, Nagdong. Geum, Yeongsan and Seomjin river systems, LH-coefficient of variation, LH-skewness and Lh-kurtosis were calcualted by KH-moment ration respectively. Paramenters were estimated by the Method of LH-Moments, Design floods obtained by Method of LH-Moments using different methods for plotting positionsi n GEV distribution and design floods were compared with those obtained using the Method of L-Moments by the Relative Mean Errors(RME) and Relative Absolute Errors(RAE). The results was found that design floods derived by the method of L-Moments and LH-Moments using Cunnane plotting position formula in the GEV distribution are much closer to those of the observed data in comparison with those obtained by methods of L-moments and LH-moments using the other formula for plotting positions from the viewpoint of Relative Mean Errors and Relative Absolute Errors. In viewpoint of the fact that hydrqulic structures including dams and levees are genrally using design floods with the return period of two hundred years or so, design floods derived by LH-Moments are seemed to be more reasonable than those of L-Moments in the GEV distribution.