• Water for future
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• v.28 no.2
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• pp.145-154
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• 1995

The various analyses of the historical rainfall data need to be utilized in a hydraulic engineering project. The probability distributions of the rainfall events according to annual maximum continuous rainfall depths are studied for the hydrologic frequency analysis. The bivariate normal distribution, the bivariate lognormal distribution, and the bivariate gamma distribution are applied to the rainfall events composed of rainfall depths and its durations at Kangnung, Seoul, Incheon, Chupungnyung, Teagu, Jeonju, Kwangju, and Busan. These rainfall events are fitted to the the bivariate normal distribution and the bivariate lognormal distribution, but not fitted to the bivariate gamma distribution. Frequency curves of probability rainfall events are suggested from the probability distribution selected by the goodness-of-fit test.

• Journal of Environmental Science International
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• v.20 no.3
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• pp.329-340
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• 2011

The probability concepts mainly used for rainfall or flood frequency analysis in water resources planning are the frequentist viewpoint that defines the probability as the limit of relative frequency, and the unknown parameters in probability model are considered as fixed constant numbers. Thus the probability is objective and the parameters have fixed values so that it is very difficult to specify probabilistically the uncertianty of these parameters. This study constructs the uncertainty evaluation model using Bayesian MCMC and Metropolis -Hastings algorithm for the uncertainty quantification of parameters of probability distribution in rainfall frequency analysis, and then from the application of Bayesian MCMC and Metropolis- Hastings algorithm, the statistical properties and uncertainty intervals of parameters of probability distribution can be quantified in the estimation of probability rainfall so that the basis for the framework configuration can be provided that can specify the uncertainty and risk in flood risk assessment and decision-making process.

• Journal of The Korean Society of Agricultural Engineers
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• v.64 no.2
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• pp.47-55
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• 2022

The objective of this study was to analyze the effect of the duration and time distribution of probability rainfall on farmland inundation for the paddy fields in the drainage improvement project site. In this study, eight drainage improvement project sites were selected for inundation modeling. Hourly rainfall data were collected, and 20- and 30-year frequency probability rainfalls were estimated for 14 different durations. Probability rainfalls were distributed using Intensity-Duration-Frequency (IDF) and Huff time distribution methods. Design floods were calculated for 48 hr and critical duration, and IDF time distribution and Huff time distribution were used for 48 hr duration and critical duration, respectively. Inundation modeling was carried out for each study district using 48 hr and critical duration rainfalls. The result showed that six of the eight districts had a larger flood discharge using the method of applying critical duration and Huff distribution. The results of inundation depth analysis showed similar trends to those of design flood calculations. However, the inundation durations showed different tendencies from the inundation depth. The IDF time distribution is a distribution in which most of the rainfall is concentrated at the beginning of rainfall, and the theoretical background is unclear. It is considered desirable to apply critical duration and Huff time distribution to agricultural production infrastructure design standards in consideration of uniformity with other design standards such as flood calculation standard guidelines.

• Journal of Wetlands Research
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• v.2 no.1
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• pp.49-58
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• 2000

The frequency analysis of annual maximum rainfall data and the derivation of probable rainfall intensity formula at Masan station are performed in this study. Based on the eight different rainfall duration data from 10 minutes to 24 hours, eight types of probability distribution (Gamma, Lognormal, Log-Pearson type III, GEV, Gumbel, Log-Gumbel, Weibull, and Wakeby distributions), three types of parameter estimation scheme (moment, maximum likelihood and probability weighted methods) and three types of goodness-of-fit test (${\chi}^2$, Kolmogorov-Smirnov and Cramer von Mises tests) were considered to find an appropriate probability distribution at Masan station. The Lognormal-2 distribution was selected and the probable rainfall intensity formula was derived by regression analysis. The derived formula can be used for estimating rainfall quantiles of the Masan vicinity areas with convenience and reliability in practice.

• Journal of Environmental Science International
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• v.28 no.1
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• pp.19-35
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• 2019

This study investigates the performance of four Bayesian methods, Random Walk Metropolis (RWM), Hit-And-Run Metropolis (HARM), Adaptive Mixture Metropolis (AMM), and Population Monte Carlo (PMC), for estimating the parameters and uncertainties of probability rainfall distribution, and the results are compared with those of conventional parameter estimation methods; namely, the Method Of Moment (MOM), Maximum Likelihood Method (MLM), and Probability Weighted Method (PWM). As a result, Bayesian methods yield similar or slightly better results in parameter estimations compared with conventional methods. In particular, PMC can reduce parameter uncertainty greatly compared with RWM, HARM, and AMM methods although the Bayesian methods produce similar results in parameter estimations. Overall, the Bayesian methods produce better accuracy for scale parameters compared with the conventional methods and this characteristic improves the accuracy of probability rainfall. Therefore, Bayesian methods can be effective tools for estimating the parameters and uncertainties of probability rainfall distribution in hydrological practices, flood risk assessment, and decision-making support.

• Journal of Korea Water Resources Association
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• v.51 no.7
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• pp.599-606
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• 2018

Most hydrological analysis such as probability rainfall and rainfall time distributions have typically carried out based on hourly rainfall and rainfall - runoff analysis have carried out by applying different periods of rainfall time distribution and probability rainfall. In this study, to quantify the change of design flood due to the data type (hourly and minutely rainfall data) and the probability rainfall and application of different data period to the rainfall time distribution, probability rainfall is calculated by point frequency analysis according to data type and period and rainfall time distribution was calculated by Huff's quartile distributions. In addition, the change analysis of design flood was carried out by rainfall - runoff analysis applying different data periods of design rainfall time distribution. and probability rainfall. As a result, rainfall analysis using minute rainfall data was more accurate and effective than using hourly rainfall data. And the design flood calculated by applying different data period of rainfall time distribution and probability rainfall made a large difference than by applying different data type. It is expected that this will contribute to the hydrological analysis using minutely rainfall.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.595-598
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• 2004

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.3
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• pp.31-42
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• 2004

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.1103-1106
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• 2004

The objective of this study is to induce the design drought rainfall by the methodology of L-moment including testing homogeneity, independence and outlier of the data of annual minimum monthly rainfall in 57 rainfall stations in Korea in terms of consecutive duration for 1, 2, 4, 6, 9 and 12 months. To select appropriate distribution of the data for annual minimum monthy rainfall by rainfall station, the distribution of generalized extreme value (GEV), generalized logistic (GLO) as well as that of generalized pareto (GPA) are applied and the appropriateness of the applied GEV, GLO, and GPA distribution is judged by L-moment ratio diagram and Kolmogorov-Smirnov (K-S) test. As for the annual minimum monthly rainfall measured by rainfall station and that stimulated by Monte Carlo techniques, the parameters of the appropriately selected GEV and GPA distributions are calculated by the methodology of L-moment and the design drought rainfall is induced. Through the comparative analysis of design drought rainfall induced by GEV and GPA distribution by rainfall station, the optimal design drought rainfall by rainfall station is provided.

• Journal of Korea Water Resources Association
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• v.32 no.4
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• pp.403-415
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• 1999

This study is to derive the rainfall intensity formula based on the representative probability distribution in Korea. The 11 probability distributions which has been widely used in hydrologic frequency analysis are applied to the annual maximum rainfall. The parameters of each probability distribution are estimated by method of moments, maximum likelihood method and method of probability weighted moments. Four tests such as $x^2$-test, Kolmogorv-Smirnov test, difference test and modified difference test are used to determine the goodness of fit of the distributions. The homogeneous tests (Mann-Whitney U test, Kruskal-Wallis one-way analysis of variance of nonparametric test) are applied to find the stations with rainfall homogeneity. The results of homogeneous tests show that there is no representative appropriate distribution for the whole duration in Korea. The whole region could be divided into five zones for 12-durations. The representative probability distribution of each divided zone for 12-durations was determined. The GEV distribution for I,II,V zones and the 3-parameter Weibull distribution for III,IV zones were determined as the representative probability distribution. The rainfall were obtained from representative probability distribution for the selected return periods. Rainfall intensity formula was determined by linearization technique for the rainfall.