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

• Water for future
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• v.28 no.5
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• pp.191-203
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• 1995

In this study, the past flood levels of Goan station, which is one of major gaging stations and located at downstream of Paldang dam, were converted based on the 1994's cross section and the flood quantiles were estimated from flood frequency analysis. The recently established rating curve was used to convert flood levels. And the parameters of the several probability distributions commonly used in hydrologic analysis were estimated based on the method of probability weighted moments and the goodness of fit tests were applied to those distributions. As a result, the gamma-2 and gamma-3 distributions were selected as the appropriate models. The flood lovels and quantiles for selected return periods were calculated based on those distributions. Furthermore, frequency analysis using historical flood information was performed to overcome the misleading caused by missing data.

• Journal of Korea Water Resources Association
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• v.43 no.2
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• pp.187-199
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• 2010

This study evaluated applicability and confidence of probability rainfalls estimated by the non-stationary rainfall frequency analysis which was recently developed. Using rainfall data at 4 sites which have an obvious increasing trend in observations, we estimated 3 type probability rainfalls; probability rainfalls from stationary rainfall frequency analysis using data from 1973-1997, probability rainfalls from stationary rainfall frequency analysis using data from 1973-2006, probability rainfalls from non-stationary rainfall frequency analysis assuming that the current year is 1997 and the target year is 2006. Based on the comparison of residuals from 3 probability rainfalls, the non-stationary rainfall frequency analysis provided more effective and well-directed estimates of probability rainfalls in the target year. Using Bootstrap resampling, this study also evaluated the parameter estimation methods for the non-stationary rainfall frequency analysis based on confidence intervals. The confidence interval length estimated by the maximum likelihood estimation (MLE) is narrower than the probability weighted moments (PWM). The results indicated that MLE provides more proper confidence than PWM for non-stationary probability rainfalls.

• Wind and Structures
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• v.19 no.4
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• pp.371-387
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• 2014

Probability plotting positions are popular and used as the basis for distribution fitting and for inspecting the quality of the fit because of its simplicity. The plotting positions that lead to excellent approximation to the mean of the order statistics should be used if the objective of the fitting is to estimate quantiles. Since the mean depends on the sample size and is not amenable for simple to use closed form solution, many plotting positions have been presented in the literature, including a new plotting position that is derived based on the weighted least-squares method. In this study, the accuracy of using the new plotting position to fit the Gumbel distribution for estimating quantiles is assessed. Also, plotting positions derived by fitting the mean of the order statistics for all ranks is proposed, and an approximation to the covariance of the order statistics for the Gumbel (and Weibull) variate is given. Relative bias and root-mean-square-error of the estimated quantiles by using the proposed plotting position are shown. The use of the proposed plotting position to estimate the quantiles of annual maximum wind speed is illustrated.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.5
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• pp.482-490
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• 2008

For a coastal or harbor structure design, one of the most important environmental factors is the appropriate extreme highest tide level condition. Especially, the information of extreme highest tide level distribution is essential for reliability design. In this paper, 23 set of extreme highest tide level data obtained from National Oceanographic Research Institute(NORI) were analyzed for extreme highest tide levels. The probability distributions considered in this research were Generalized Extreme Value(GEV), Gumbel, and Weibull 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-offit tests were performed, and the assumed distribution was accepted at the confidence level 95%. Gumbel distribution which best fits to the 22 tidal station was selected as the most probable parent distribution, and optimally estimated parameters and extreme highest tide level with various return periods were presented. The extreme values of Incheon, Cheju, Yeosu, Pusan, and Mukho, which estimated by Shim et al.(1992) are lower than that of this result.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5B
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• pp.441-452
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• 2009

This paper describes the evaluation technique for climate change effect on daily precipitation frequency using daily precipitation generator that can use outputs of the climate model offered by IPCC DDC. Seoul station of KMA was selected as a study site. This study developed daily precipitation generation model based on two-state markov chain model which have transition probability, scale parameter, and shape parameter of Gamma-2 distribution. Each parameters were estimated from regression analysis between mentioned parameters and monthly total precipitation. Then the regression equations were applied for computing 4 parameters equal to monthly total precipitation downscaled by K-NN to generate daily precipitation considering climate change. A2 scenario of the BCM2 model was projected based on 20c3m(20th Century climate) scenario and difference of daily rainfall frequency was added to the observed rainfall frequency. Gumbel distribution function was used as a probability density function and parameters were estimated using probability weighted moments method for frequency analysis. As a result, there is a small decrease in 2020s and rainfall frequencies of 2050s, 2080s are little bit increased.

• Magazine of the Korean Society of Agricultural Engineers
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• v.43 no.4
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• pp.57-68
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• 2001

It is matter of common knowledge to give impetus to the water resources development to cope with increasing demand and supply for the water utilization project including agricultural living and industrial water owing to the economic and civilization development in recent years. Regional design rainfall is necessary or the design of the dam reservoir levee and drainage facilities for the development of various kinds of essential waters including agricultural water. For the estimation of the regional design rainfall classification of the climatologically an geographically homogeneous regions should be preceded preferentially This study was mainly conducted to derive the optimal regionalization of the precipitation data which can be classified by the climatologically and geographically homogeneous regions all over the regions except Cheju and Wulreung islands in Korea. A total of 65 rain gauges were used to regional analysis of precipitation. Annual maximum series for the consecutive durations of 1, 3, 6, 12, 24, 36, 48 and 72hr were used for various statistical analysis. Both K-means clustering and mean annual precipitation methods are used to identify homogeneous regions all over the regions. Nine and five homogeneous regions for the precipitation were classified by the K-means clustering and mean annual methods, respectively. Finally, Five homogeneous regions were established by the trial and error method with homogeneity test using statistics of $\chi$$^2$ distribution.

• Journal of Korea Water Resources Association
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• v.49 no.8
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• pp.645-656
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• 2016

The study performed a regional flood frequency analysis and proposed a regression equation to estimate design floods corresponding to return periods for ungauged basins in Geum-river basin. Five preliminary tests were employed to investigate hydrological independence and homogeneity of streamflow data, i.e. the lag-one autocorrelation test, time homogeneity test, Grubbs-Beck outlier test, discordancy measure test ($D_i$), and regional homogeneity measure (H). The test results showed that streamflow data were time-independent, discordant and homogeneous within the basin. Using five probability distributions (generalized extreme value (GEV), three-parameter log-normal (LN-III), Pearson type 3 (P-III), generalized logistic (GLO), generalized Pareto (GPA)), comparative regional flood frequency analyses were carried out for the region. Based on the L-moment ratio diagram, average weighted distance (AWD) and goodness-of-fit statistics ($Z^{DIST}$), the GLO distribution was selected as the best fit model for Geum-river basin. Using the GLO, a regression equation was developed for estimating regional design floods, and validated by comparing the estimated and observed streamflows at the Ganggyeong station.

• Journal of Korea Water Resources Association
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• v.45 no.4
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• pp.393-407
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• 2012

This study suggests the results of temporal and spatial variations for rainfall data in the Korean Peninsula. We got the index of the rainfall amount, frequency and extreme indices from 65 weather stations. The results could be easily understood by drawing the graph, and the Mann-Kendall trend analysis was also used to determine the tendency (up & downward/no trend) of rainfall and temperature where the trend could not be clear. Moreover, by using the FARD, frequency probability rainfalls could be calculated for 100 and 200 years and then compared each other value through the moment method, maximum likelihood method and probability weighted moments. The Average Rainfall Index (ARI) which is meant comprehensive rainfalls risk for the flood could be obtained from calculating an arithmetic mean of the RI for Amount (RIA), RI for Extreme (RIE), and RI for Frequency (RIF) and as well as the characteristics of rainfalls have been mainly classified into Amount, Extremes, and Frequency. As a result, these each Average Rainfall Indices could be increased respectively into 22.3%, 26.2%, and 5.1% for a recent decade. Since this study showed the recent climate change trend in detail, it will be useful data for the research of climate change adaptation.

• Journal of Korea Water Resources Association
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• v.45 no.8
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• pp.827-837
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• 2012

The estimation of the rainfall quantile is of great importance in designing hydrologic structures. Conventionally, the rainfall quantile is estimated by univariate frequency analysis with an appropriate probability distribution. There is a limitation in which duration of rainfall is restrictive. To overcome this limitation, bivariate frequency analysis by using 3 copula models is performed in this study. Annual maximum rainfall events in 5 stations are used for frequency analysis and rainfall depth and duration are used as random variables. Gumbel (GUM), generalized logistic (GLO) distributions are applied for rainfall depth and generalized extreme value (GEV), GUM, GLO distributions are applied for rainfall duration. Copula models used in this study are Frank, Joe, and Gumbel-Hougaard models. Maximum pseudo-likelihood estimation method is used to estimate the parameter of copula, and the method of probability weighted moments is used to estimate the parameters of marginal distributions. Rainfall quantile from this procedure is compared with various marginal distributions and copula models. As a result, in change of marginal distribution, distribution of duration does not significantly affect on rainfall quantile. There are slight differences depending on the distribution of rainfall depth. In the case which the marginal distribution of rainfall depth is GUM, there is more significantly increasing along the return period than GLO. Comparing with rainfall quantiles from each copula model, Joe and Gumbel-Hougaard models show similar trend while Frank model shows rapidly increasing trend with increment of return period.