• Water for future
• /
• v.29 no.1
• /
• pp.129-139
• /
• 1996

It is very important to select appropriate distributions for hydrological data in planning and designing hydraulic structures. Also, it is necessary to check whether the selected distribution reproduces the statistical characteristics of the real data. In this study, the parameters of the two- and three-parameter gamma, two- and three-parameter lognormal, Gumbel, two- and three-parameter log-Gumbel, GEV, log-Pearsonn type III, two- and three-parameter Weibull, four- and five-parameter Wakeby distributions were estimated for the rainfall data of 22 sites in Korea with 7 different durations based on the methods of moments, probability weighted moments, and maximum likelihood. And the validity conditions were checked for the estimated parameters. The separation effect for each distribution was examined throught 10,000 simulations using the estimated parameters. As results, the separation effect was the smallest: log-Pearson type III for moment method, log-Pearson type III and GEV for probability weighted moment method, and GEV for maximum likelihood method. However, it is large for the two-parameter distributions.

• Water for future
• /
• v.26 no.4
• /
• pp.73-83
• /
• 1993

This study focuses on the separation effect analysis of rainfall data for 2-parameter log-normal, 3-parameter log-normal, type-extreme value, 2-parameter gamma, 3-parameter gamma, log-Pearson type-III, and general extreme value distribution functions. Difference in the relationship between the mean and standard deviation of skewness for historical data and relations derived from 7 distribution functions are analyzed suing the Monte Carlo experiment. The results show that rainfall data has the separation effect for 6 distribution functions except 3-parameter gamma distribution function.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.16 no.3
• /
• pp.130-141
• /
• 2004

For a coastal or harbor structure design, one of the most important environmental factors is the appropriate design wave condition. Especially, the information of deepwater wave height distribution is essential for reliability design. In this paper, a set of deep water wave data obtained from KORDI(2003) were analyzed for extreme wave heights. These wave data at 67 stations off the Korean coast from 1979 to 1998 were arranged in the 16 directions. The probability distributions considered in this research were the Weibull, the Gumbel, the Log-pearson Type-III, and Lognormal distribution. For each of these distributions, three parameter estimation methods, i.e. the method of moments, maximum likelihood and probability weighted moments, were applied. Chi-square and Kolmogorov-Smirnov goodness-of-fit tests were performed, and the assumed distribution was accepted at the confidence level 95%. Gumbel distribution which best fits to the 67 station was selected as the most probable parent distribution, and optimally estimated parameters and 50 year design wave heights were presented.

• Journal of Korea Water Resources Association
• /
• v.31 no.4
• /
• pp.469-481
• /
• 1998

A point frequency analysis is carried out for the Indogyo site at the Han river using 68 annual maximun flood data for the period of 1918-1992. Computed frequency discharges using the three parameter log-normal, type-I extreme value, type-III extreme value, and Pearson type-III computed as 35,500 m3/sec and 39,000 m3/sec, respectively, 33,500 m3/sec and 37,500 m3/sec of corresponding return periods are computed when the flood control effect of the dams are taken into account. The resulting flood discharge of 37,500 m3/sec is similar to the current design flood of 37,000 m3/sec in downstream reach of Han river, so, it could be desirable to keep the the current design flood, considering the increasing tendency of the flood due to the climate change. Keywords : frequency analysis, flood discharge, Han river.

• Korean Journal of Agricultural and Forest Meteorology
• /
• v.12 no.2
• /
• pp.83-94
• /
• 2010

The objective of this study was to determine the best probability distributions of annual, seasonal and monthly precipitation in Korea. Data observed at 32 stations in Korea were analyzed using the L-moment ratio diagram and the average weighted distance (AWD) to identify the best probability distributions of each precipitation. The probability distribution was best represented by 3-parameter Weibull distribution (W3) for the annual precipitation, 3-parameter lognormal distribution (LN3) for spring and autumn seasons, and generalized extreme value distribution (GEV) for summer and winter seasons. The best probability distribution models for monthly precipitation were LN3 for January, W3 for February and July, 2-parameter Weibull distribution (W2) for March, generalized Pareto distribution (GPA) for April, September, October and November, GEV for May and June, and log-Pearson type III (LP3) for August and December. However, from the goodness-of-fit test for the best probability distributions of the best fit, GPA for April, September, October and November, and LN3 for January showed considerably high reject rates due to computational errors in estimation of the probability distribution parameters and relatively higher AWD values. Meanwhile, analyses using data from 55 stations including additional 23 stations indicated insignificant differences to those using original data. Further studies using more long-term data are needed to identify more optimal probability distributions for each precipitation.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2008.05a
• /
• pp.209-213
• /
• 2008

재현기간이 수백년 이상인 이상홍수의 초과확률을 추정하기 위해서는 재현기간 이상의 홍수자료를 이용해 내삽(interpolation)을 해야 하지만 현재 우리나라의 체계적(systematic) 관측자료 기간은 이에 훨씬 미치지 못한다. 따라서, 역사 자료(historical data)를 이용해 자료 길이를 확장하는 방법, 홍수자료에 비해 비교적긴 강우자료와 유출 모형에 의한 합성자료를 이용하는 방법 등이 사용되어 왔다. 본 연구에서는 역사 자료와 체계적 관측자료를 효율적으로 결합할 수 있는 EMA(Expected Moment Algorithm) 기법을 연구하였다. EMA는 Cohn 등(1997)에 의해 제안된 방법으로 미국의 공식 분포인 LP3(Log-Pearson type 3) 분포를 대상으로 반복 계산을 통해 매개변수를 추정하는 기법으로서 본 연구에서는 LP3 분포 대신에 최근 국내 홍수빈도해석 시 많이 쓰이고 있는 GEV(Generalized Extreme Value) 분포를 대상으로 EMA 절차를 이론적으로 유도하였다.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2007.05a
• /
• pp.321-325
• /
• 2007

3개의 매개변수(location, scale, shape)로 이루어진 GEV와 GLO 분포는, 미국의 공식적인 홍수빈도 분포인 Log Pearson Type III와 함께 수문분야에서 중요한 위치를 차지하고 있다. 본 연구에서는 Monte Carlo 실험을 이용하여 GEV와 GLO 분포에서 서로 다른 두 지점의 유출량 자료를 생성하여 L-CV(L-moment Coefficient of Variation; $\tau_2$)와 L-CS(L-moment Coefficient of Skewness; $\tau_3$)를 추정하였으며, L-moment 추정값들 간의 교차상관$(\tau_2-\tau_2,\;\tau_3-\tau_3,\;\tau_2-\tau_3)$과 유출량 자료간의 교차상관의 관계를 Simple Power 함수를 이용하여 유도하였다. 실험 과정에서 GEV와 GLO 분포가 비현실적인 음수 유출량을 생성하여, 실험 결과에 큰 영향이 있음을 확인하여, 두 분포에서 생성된 유출량 자료에서 음수값을 제외한 GEV+와 GLO+ 분포를 이용하여 관계식을 유도하고 이를 GEV와 GLO 분포의 결과와도 비교하였다. 본 연구에서 도출된 관계식은 향후 Generalized Least Square 회귀식을 이용하여 홍수분포의 지역 매개변수를 추정하기 위해 활용성이 클 것으로 기대한다.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2017.05a
• /
• pp.349-349
• /
• 2017

표준강수지수(Standardized precipitation index, SPI)는 가장 널리 사용되고 있는 가뭄지수로, 우리나라 뿐만 아니라 세계기상기구(World Meteorological Organization)에서도 추천하고 있는 대표적인 기상학적 가뭄 지수라고 할 수 있다. 현재 표준강수지수는 2변수 gamma 분포를 적용하여 강수 부족 상황을 지수화하여 나타내고 있는데, 일부 연구에서는 다른 확률분포형의 적용하기도 하였다(Guttman, 1999; Lloyd-Hughes and Saunders, 2002; Stagge et al., 2015). 우리나라에서는 유원희(2000)에 의해 Pearson type 3, 2변수 gamma, generalized logistic, GEV, 3변수 log-normal 분포에 따른 SPI 산정 결과를 비교한 연구가 수행되었는데, SPI 산정에는 분포형별 차이가 뚜렷하지 않다는 결론을 얻었다. 그러나 이때 금강유역 내 지점에 국한하여 적용하였고, 분포형별 적합도 검정을 수행하지 않고 SPI 산정결과만을 비교하여 우리나라에 일반적으로 적용하기에는 어려움이 있다. 따라서 본 연구에서는 우리나라의 강우특성을 반영할 수 있도록 다양한 확률분포형을 고려하여 표준강수지수를 분석하고자 한다. 이를 위해 관측기간이 30년 이상인 기상관측소의 월단위 강우자료를 구축하고, 월단위 강우자료에 다양한 확률분포형을 적용하고자 한다. 이때 적용하는 확률분포형은 2변수 gamma, Gumbel, normal 분포이다. 적정 확률분포형 선정을 위해 적합도 검정을 수행하고자 한다. 또한 각 분포형별로 산정된 표준강수지수를 기존 표준강수지수와 비교검토하고자 한다.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.39 no.3
• /
• pp.83-95
• /
• 1997

This study was conducted to derive optimal design floods by Gamma distribution models of the annual maximum series at eight watersheds along Geum , Yeong San and Seom Jin river Systems, Design floods obtained by different methods for evaluation of parameters and for plotting positions in the Gamma distribution models were compared by the relative mean errors and graphical fit along with 95% confidence interval plotted on Gamma probability paper. The results were analyzed and summarized as follows. 1.Adequacy for the analysis of flood flow data used in this study was confirmed by the tests of Independence, Homogeneity and detection of Outliers. 2.Basic statistics and parameters were calculated by Gamma distribution models using Methods of Moments and Maximum Likelihood. 3.It was found that design floods derived by the method of maximum likelihood and Hazen plotting position formular of two parameter Gamma distribution are much closer to those of the observed data in comparison with those obtained by other methods for parameters and for plotting positions from the viewpoint of relative mean errors. 4.Reliability of derived design floods by both maximum likelihood and method of moments with two parameter Gamma distribution was acknowledged within 95% confidence interval.

• Proceedings of the Korean Society of Agricultural Engineers Conference
• /
• 2003.10a
• /
• pp.439-442
• /
• 2003

This study was conducted to choose optimal distribution and to estimate properly parameters for the derivation of design rainfall in Gamma Family. Design rainfall derived by Gamma Family Distributions were compared by the Relative Mean Errors(RME) and Relative Absolute Errors(RAE) for the consecutive durations of 1, 3, 6, 12, 24, 36, 48 and 72hr and 65 regions all over the regions except Cheju and Wulreung islands in Korea. Consequently, Design rainfall derived by Indirect Method of Moments in the Log-Pearson Type 3 distribution are seemed to be more reasonable than those of other distributions in Gamma Family.