• Journal of Korea Water Resources Association
• /
• v.32 no.3
• /
• pp.265-279
• /
• 1999

In this study, one of the techniques on the extension of low flow series has been developed, in which the daily streamflows were simulated by the Tank model with the input of extended daily rainfall series which were stochastically generated by the Markov chain model. The annual lowest flow serried for each of the given durations were formulated form the simulated daily streamflow sequences. The frequency of the estimated annual lowest flow series was analyzed. The distribution types to be used for the frequency analysis were two-parameter and three-parameter log-normal distribution, two-parameter and three-parameter Gamma distribution, three-parameter log-Gamma distribution, Gumbel distribution, and Weibull distribution, of which parameters were estimated by the moment method and the maximum likelihood method. The goodness-of-fit test for probability distribution is evaluated by the Kolmogorov-Sminrov test. The fitted distribution function for each duration series is applied to frequency analysis for developing duration-low flow-frequency curves at Yongdam Dam station. It was shown that the purposed technique in this study is available to generate the daily streamflow series with fair accuracy and useful to determine the probabilistic low flow in the watersheds having the poor historic records of low flow series.

• Journal of The Korean Society of Agricultural Engineers
• /
• v.54 no.5
• /
• pp.141-153
• /
• 2012

In this study, we estimated probable precipitation amounts at the target year (2020, 2030, 2040) of 55 weather stations in Korea using the 24 hour annual maximum precipitation data from 1973 through 2009 which should be useful for management of agricultural reservoirs. Not only trend tests but also non-stationary tests were performed and non-stationary frequency analysis were conducted to all of 55 sites. Gumbel distribution was chosen and probability weighted moment method was used to estimate model parameters. The behavior of the mean of extreme precipitation data, scale parameter, and location parameter were analyzed. The probable precipitation amount at the target year was estimated by a non-stationary frequency analysis using the linear regression analysis for the mean of extreme precipitation data, scale parameter, and location parameter. Overall results demonstrated that the probable precipitation amounts using the non-stationary frequency analysis were overestimated. There were large increase of the probable precipitation amounts of middle part of Korea and decrease at several sites in Southern part. The non-stationary frequency analysis using a linear model should be applicable to relatively short projection periods.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.29 no.2B
• /
• pp.155-162
• /
• 2009

Univariate frequency analyses are widely used in practical hydrologic design. However, a storm event is usually characterized by amount, intensity, and duration of the storm. To fully understand these characteristics and to use them appropriately in hydrologic design, a multivariate statistical approach is necessary. This study applied a Gumbel mixed model to a bivariate storm frequency analysis using hourly rainfall data collected for 46 years at the Seoul rainfall gauge station in Korea. This study estimated bivariate return periods of a storm such as joint return periods and conditional return periods based on the estimation of joint cumulative distribution functions of storm characteristics. These information on statistical behaviors of a storm can be of great usefulness in the analysis and assessment of the risk associated with hydrologic design problems.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
• /
• v.29 no.1
• /
• pp.245-251
• /
• 2005

When we design coastal and harbol facilities deepwater design wave and wind speed are the important design parameters. Especially, the analysis of these informations is a vital step for the point of disaster prevention. In this study, we made and an extreme value analysis using a series of deep water significant wave data arranged in the 16 direction and supplied by KORDI real-time wave information system ,and the wind data gained from Wan-Do whether Station 1978-2003. The probability distributions considered in this characteristic analysis were the Weibull, the Gumbel, the Log-Pearson Type III, the Normal, the Lognormal, and the Gamma distribution. The parameter for each distribution was estimated by three methods, i.e. the method of moments, the maximum likelihood, and the method of probability weight moments. Furthermore, probability distributions for the extreme data had been selected by using Chi-square and Kolmogorov-Smirnov test within significant level of 5%, i,e. 95% reliance level. From this study we found that Gumbel distribution is the most proper model for the deep water design wave height off the southwest coast of Korea. However the result shows that the proper distribution made for the selected site is varied in each extreme data set.

• Wind and Structures
• /
• v.38 no.4
• /
• pp.309-323
• /
• 2024

The gust factor and turbulence intensity are two crucial parameters that characterize the properties of turbulence. In tropical cyclones (TCs), these parameters exhibit significant variability, yet there is a lack of established formulas to account for their probabilistic characteristics with consideration of their inherent connection. On this condition, a probabilistic analysis of gust factors and turbulence intensities of TCs is conducted based on fourteen sets of wind data collected at the Sutong Cable-stayed Bridge site. Initially, the turbulence intensities and gust factors of recorded data are computed, followed by an analysis of their probability densities across different ranges categorized by mean wind speed. The Gaussian, lognormal, and generalized extreme value (GEV) distributions are employed to fit the measured probability densities, with subsequent evaluation of their effectiveness. The Gumbel distribution, which is a specific instance of the GEV distribution, has been identified as an optimal choice for probabilistic characterizations of turbulence intensity and gust factor in TCs. The corresponding empirical models are then established through curve fitting. By utilizing the Gumbel distribution as a template, the nexus between the probability density functions of turbulence intensity and gust factor is built, leading to the development of a generalized probabilistic model that statistically describe turbulence intensity and gust factor in TCs. Finally, these empirical models are validated using measured data and compared with suggestions recommended by specifications.

• Journal of Korea Water Resources Association
• /
• v.43 no.4
• /
• pp.337-351
• /
• 2010

There is a growing dissatisfaction with use of conventional statistical methods for the prediction of extreme events. Conventional methodology for modeling extreme event consists of adopting an asymptotic model to describe stochastic variation. However asymptotically motivated models remain the centerpiece of our modeling strategy, since without such an asymptotic basis, models have no rational for extrapolation beyond the level of observed data. Also, this asymptotic models ignored or overestimate the uncertainty and finally decrease the reliability of uncertainty. Therefore this article provide the research example of the extreme rainfall event and the methodology to reduce the uncertainty. In this study, the Bayesian MCMC (Bayesian Markov Chain Monte Carlo) and the MLE (Maximum Likelihood Estimation) methods using a quadratic approximation are applied to perform the at-site rainfall frequency analysis. Especially, the GEV distribution and Gumbel distribution which frequently used distribution in the fields of rainfall frequency distribution are used and compared. Also, the results of two distribution are analyzed and compared in the aspect of uncertainty.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.2A
• /
• pp.197-205
• /
• 2008

In order to estimate mean wind speed in the Gwangyang-Myodo Region, the probability distribution model of extreme values has been used in the statistical analysis of joint distribution probability of daily maximum wind speed and corresponding direction in this paper. For this purpose frequency of daily maximum records at respective stations is inquired into and sample of largest yearly wind speed of sixteen compass direction and non-direction is extracted from daily data of maximum wind speed and appropriate direction of the meteorological observing stations nearby the bridge construction site. These extreme speed records are applied to Gumbel and Weibull distribution model and parameters are estimated through method of moment and method of least squares etc. And also, distribution and parameters are inquired into whether it is fitted through the probability plot correlation coefficient examination. From fitted parameters the largest yearly wind speed of sixteen compass direction and non-direction is extrapolated taking into account factors regarding sample size of data and distance from the bridge construction site according to the appropriate stations.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.3B
• /
• pp.257-267
• /
• 2010

A flood event can be characterized by three attributes such as peak discharge, total flood volume, and flood duration, which are correlated each other. However, the amount of peak discharge is only used to evaluate the flood events for the hydrological plan and design. The univariate analysis has a limitation in describing the complex probability behavior of flood events. Thus, the univariate analysis cannot derive satisfying results in flood frequency analysis. This study proposed bivariate flood frequency analysis methods for evaluating flood events considering correlations among attributes of flood events. Parametric distributions such as Gumbel mixed model and bivariate gamma distribution, and a non-parametric model using a bivariate kernel function were introduced in this study. A time series of annual flood events were extracted from observations of inflow to the Soyang River Dam and the Daechung Dam, respectively. The joint probability distributions and return periods were derived from the relationship between the amount of peak discharge and the total volume of flood runoff. Applicabilities of bivariate flood frequency analysis were examined by comparing the return period acquired from the proposed bivariate analyses and the conventional univariate analysis.

• International Journal of Reliability and Applications
• /
• v.11 no.2
• /
• pp.107-122
• /
• 2010

This paper deals with the reliability analysis of a complex system, which consists of two subsystems A and B connected in series. Subsystem A has only one unit and B has two units $B_1$ and $B_2$. Marked process has been applied to model the complex system. Present reliability model incorporated two repairmen: supervisor and novice to repair the failed units. Supervisor is always there and the novice remains in vacation and is called for repair as per demand. The repair rates for supervisor and novice follow general and exponential distributions respectively and the failure time for both the subsystems follows exponential distribution. The model is analyzed under "Head of line repair discipline". By employing supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula various transition state probabilities, reliability, availability and cost analysis have been obtained along with the steady state behaviour of the system. At the end some special cases of the system have been taken.

• Journal of Korean Society of Water and Wastewater
• /
• v.22 no.6
• /
• pp.609-617
• /
• 2008

Water pipes are supposed to deliver the predetermined demand safely to a certain point in water distribution system. However, pipe burst or crack can be happened due to so many reasons such as the water hammer, natural pipe ageing, external impact force, soil condition, and various environments of pipe installation. In the present study, the reliability model which can calculate the probability of pipe breakage was developed regarding unsteady effect such as water hammer. For the reliability model, reliability function was formulated by Barlow formula. AFDA method was applied to calculate the probability of pipe breakage. It was found that the statistical distribution for internal pressure among the random variables of reliability function has a good agreement with the Gumbel distribution after unsteady analysis was performed. Using the present model, the probability of pipe breakage was quantitatively calculated according to random variables such as the pipe diameter, thickness, allowable stress, and internal pressure. Furthermore, it was found that unsteady effect significantly increases the probability of pipe breakage. If this reliability model is used for the design of water distribution system, safe and economical design can be accomplished. And it also can be effectively used for the management and maintenance of water distribution system.