• Journal of Environmental Science International
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• v.20 no.12
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• pp.1541-1551
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• 2011

This study applied the Bayesian method for the quantification of the parameter uncertainty of spatial linear mixed model in the estimation of the spatial distribution of probability rainfall. In the application of Bayesian method, the prior sensitivity analysis was implemented by using the priors normally selected in the existing studies which applied the Bayesian method for the puppose of assessing the influence which the selection of the priors of model parameters had on posteriors. As a result, the posteriors of parameters were differently estimated which priors were selected, and then in the case of the prior combination, F-S-E, the sizes of uncertainty intervals were minimum and the modes, means and medians of the posteriors were similar to the estimates using the existing classical methods. From the comparitive analysis between Bayesian and plug-in spatial predictions, we could find that the uncertainty of plug-in prediction could be slightly underestimated than that of Bayesian prediction.

• Water for future
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• v.20 no.2
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• pp.139-150
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• 1987

The present study is to develop the hydrologic analysis procedure for the purpose of drawing the probable isohyetal charts in Korea. In the establishment of optimal distribution types, the eleven continuous probability distribution types included the transformed variable normal distribution (Y-k method) is applied to the annual maximum rainfall depth series in each duration. The optimal selection of distribution is done by Chi-square test and Kolmogorov-Smirnov test in the eui-class interval. The application of probability distribution is checked by the fitting on four durations of annual maximum rainfall data(10 min., 60 min., 6 hrs., and 24hrs.) at four meteorological stations in Korea (Seoul, In Cheon, Bu san, and Kwang Ju). The properties in hydrologic application of the considered distribution and the hydrologic characteristics of the applied rainfall data groups are investigated from the results of this study.

• Journal of Korean Society of Water and Wastewater
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• v.14 no.3
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• pp.251-259
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• 2000

In this study, the urban runoff models, ILLUDAS model and SWMM, are analyzed the probable peak discharge and discharge using rainfall distribution by Huff's method at Bum-uh chun area in Taegu city. The probability rainfall and intensity is analyzed by Pearson-III type. The rainfall duration, 90 minutes, is determined by the critical duration computed the maximun peak discharge for some rainfall durations. The peak discharge according to Huff's rainfall distribution types compute in order of type 3, type 4, type2, and type 1, so Huff's 3 type is selected as an adequate rainfall distribution in Bum-uh chun basin. ILLUDAS model and SWMM are shown as good models in Bum-uh chun, but SWMM is computed higher peak discharge than ILLUDAS model, so SWMM is shown as the adequate urban runoff model for the design of interior drainage in urban basin.

• Journal of Environmental Science International
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• v.23 no.11
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• pp.1775-1790
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• 2014

The regional rainfall intensity formula for Gimhae in Gyeongsangnam-do province is developed in this study. The nine points of rainfall observations were selected. In order to demonstrate the accuracy and the versatility of the proposed rainfall intensity formula, three regions under the jurisdiction of the Meteorological Agency near Gimhae, namely Busan, Changwon, Miryang observatories were selected. The present formula can be effectively employed for various design of hydraulic structures in Gimhae area since it is divided into several refined regions.

• Journal of Korea Water Resources Association
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• v.33 no.2
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• pp.263-276
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• 2000

This paper is to derive the probable rainfall depths and the probable rainfall intensity formulas for Inchon Metropolitan district. The annual maximum rainfall data from 10 min. to 6 hours have been collected from the Inchon weather station. Eleven types of probability distribution are considered to estimate probable rainfall depths for 12 different storm durations at the Inchon Metropolitan district. Three tests including Chi-square, Kolmogorov-Smimov and Cramer Von Mises with the graphical analysis are adopted to select the best probability distribution. The probable rainfall intensity formulas are then determined by the least squares method using the trial and error approach. Five types of Talbot type, Sherman type, Japanese type, Unified type I, and Unified type II are considered to determine the best type for the Inchon rainfall intensity. The root mean squared errors are computed to compare the accuracy from the derived formulas. It has been suggested that the probable rainfall intensities having Unified type I for the short term duration should be the most reliable formulas by considering the root mean squared errors and the difference between computed probable rainfall depth and estimated probable rainfall depth.

• Journal of Korean Society of Water and Wastewater
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• v.30 no.1
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• pp.51-58
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• 2016

On account of the increase in water demand and climate change, droughts are in great concern for water resources planning and management. In this study, rainfall characteristics with stationary and non-stationary perspectives were analyzed using Weibull distribution model with 40-year records of annual minimum rainfall depth collected in major cities of Korea. As a result, the non-stationary minimum probable rainfall was expected to decrease, compared with the stationary probable rainfall. The reliability of ${\xi}_1$, a variable reflecting the decrease of the minimum rainfall depth due to climate change, in Wonju, Daegu, and Busan was over 90%, indicating the probability that the minimal rainfall depths in those city decrease is high.

• 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.

• Journal of Korea Water Resources Association
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• v.50 no.3
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• pp.211-221
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• 2017

In statistical hydrology, various extreme distributions such as the generalized extreme value (GEV), generalized logistic (GLO) and Gumbel (GUM) models have been widely used to analyze the extreme events. In the case of rainfall events in South Korea, the GEV and Gumbel distributions are known to be appropriate among various extreme distribution models. However, the proper probability distribution model may be different depending on the type of extreme events, rainfall duration, region, and statistical characteristics of extreme events. In this regard, it is necessary to apply a wide range of statistical properties that can be represented by the distribution model because it has two shape parameters. In this study, the statistical applicability of rainfall data is analyzed using the Burr XII distribution and the dimensionless L-moment ratio for 620 stations in South Korea. For this purpose, L-skewness and L-kurtosis of the Burr XII distribution are derived and L-moment ratio diagram is drawn and then the applicability of 620 stations was analyzed. As a result, it is found that the Burr XII distribution for the stations of the Han River basin in which L-skewness is relatively larger than L-kurtosis is appropriate, It is possibility of replacing the distribution of commonly used Gumbel or GEV distributions. Therefore, the Burr XII model can be replaced as an appropriate probability model in this basin.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.627-636
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• 1999

In 60 years when the double $CO_2$concentration is anticipated the average annual rainfall depth is expected to be increased by 5 10% due to global warming. However, in the water resources area the frequency change of meteorological extremes such as droughts and floods attracts more interests than the increase of annual rainfall amount. Even though recent frequent occurrences of this kind of meteorological extremes are assumed as an indirect proof of global warming, the prediction of its overall tendency has not yet been made. Thus, in this research we propose a possible methodology to be used for its prediction. The methodology proposed is based on the frequency distribution of daily rainfall be Todorovie and Woolhiser(1975), and Katz(1977), where the input parameters are modified to consider the change of monthly or annual rainfall depth and, thus, to result in the change of frequency distribution. We adopt two values(10mm, 50mm) as thresholds and investigate the change of occurrence probability due to the change monthly and annual rainfall depth. these changes do not directly indicate the changes of occurrence probability of floods and droughts, but it may still be a very useful information for their prediction. Finally, the changes of occurrence probability were found to be greater when considering the monthly rainfall rather than the annual rainfall, and those in rainy season than those in dry season.

• Journal of Korea Water Resources Association
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• v.48 no.1
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• pp.37-44
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• 2015

A Bayesian nonstationary probability rainfall estimation model using the Grid method is developed. A hierarchical Bayesian framework is consisted with prior and hyper-prior distributions associated with parameters of the Gumbel distribution which is selected for rainfall extreme data. In this study, the Grid method is adopted instead of the Matropolis Hastings algorithm for random number generation since it has advantage that it can provide a thorough sampling of parameter space. This method is good for situations where the best-fit parameter values are not easily inferred a priori, and where there is a high probability of false minima. The developed model was applied to estimated target year probability rainfall using hourly rainfall data of Seoul station from 1973 to 2012. Results demonstrated that the target year estimate using nonstationary assumption is about 5~8% larger than the estimate using stationary assumption.