• Journal of Korea Water Resources Association
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• v.55 no.7
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• pp.545-556
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• 2022

It is recommended to use long-term hydrometeorological data for more than the service life of the hydraulic structures and water resource planning. For the purpose of expanding rainfall data, stochastic simulation models, such as Modified Bartlett-Lewis Rectangular Pulse (BLRP) and Neyman-Scott Rectangular Pulse (NSRP) models, have been widely used. The optimal parameters of the model can be estimated by repeatedly comparing the statistical moments defined through a combination of parameters of the probability distribution in the optimization context. However, parameter estimation using relatively small observed rainfall statistics corresponds to an ill-posed problem, leading to an increase in uncertainty in the parameter estimation process. In addition, as shown in previous studies, extreme values are underestimated because objective functions are typically defined by the first and second statistical moments (i.e., mean and variance). In this regard, this study estimated the parameters of the NSRP model using the objective function with the third moment and compared it with the existing approach based on the first and second moments in terms of estimation of extreme rainfall. It was found that the first and second moments did not show a significant difference depending on whether or not the skewness was considered in the objective function. However, the proposed model showed significantly improved performance in terms of estimation of design rainfalls.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2B
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• pp.141-153
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• 2009

The occurrence causes of the extreme rainfall to happen in Korea can be distinguished with the typhoons and local downpours. The typhoon events attacked irregularly to induce the heavy rainfall, and the local downpour events mean a seasonal rain front and a local rainfall. Almost every year, the typhoons and local downpours that induced a heavy precipitation be generated extreme disasters like a flooding. Consequently, in this research, There were distinguished the causes of heavy rainfall events with the typhoons and the local downpours at Korea. Also, probability precipitation was computed according to the causes of the local downpour events. An evaluation of local downpours can be used for analysis of heavy rainfall event in short period like a flash flood. The methods of calculation of probability precipitation used the parametric frequency analysis and the Empirical Simulation Technique (EST). The correlation analysis was computed between annual maximum precipitation by local downpour events and sea surface temperature, moisture index for composition of input vectors. At the results of correlation analysis, there were revealed that the relations closely between annual maximum precipitation and sea surface temperature. Also, probability precipitation using EST are bigger than probability precipitation of frequency analysis on west-middle areas in Korea. Therefore, region of west-middle in Korea should prepare the extreme precipitation by local downpour events.

• Journal of The Korean Society of Agricultural Engineers
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• v.58 no.3
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• pp.57-69
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• 2016

In this study, we analyzed the extreme rainfall distribution scenarios based on probable rainfall calculation and applying various time distribution models over the landslide high risk zones in urban areas. We used observed rainfall data form total 71 ASOS (Automated Synoptic Observing System) station and AWS (Automatic Weather Station) in KMA (Korea Meteorological Administration), and we analyzed the linear trends for 1-hr and 24-hr annual maximum rainfall series using simple linear regression method, which are identified their increasing trends with slopes of 0.035 and 0.660 during 1961-2014, respectively. The Gumbel distribution was applied to obtain the return period and probability precipitation for each duration. The IDF (Intensity-Duration-Frequency) curves for landslide high risk zones were derived by applying integrated probability precipitation intensity equation. Results from IDF analysis indicate that the probability precipitation varies from 31.4~38.3 % for 1 hr duration, and 33.0~47.9 % for 24 hr duration. It also showed different results for each area. The $Huff-4^{th}$ Quartile method as well as Mononobe distribution were selected as the rainfall distribution scenarios of landslide high risk zones. The results of this study can be used to provide boundary conditions for slope collapse analysis, to analyze sediment disaster risk, and to use as input data for risk prediction of debris flow.

• Journal of Korea Water Resources Association
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• v.45 no.3
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• pp.253-262
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• 2012

The objectives of this study are to suggest the method for estimation of sub-daily extreme rainfall under climate change using scale properties and to assess the application in the 6 major weather stations including Seoul site. First, the proposed method was assessed by past observations. As the results, absolute relative errors of probability rainfall quantiles estimated by frequency analysis and scale property method show approximately 10% in the all durations. And as the result of application climate scenario, absolute relative errors of rainfall quantiles between two method show approximately 20%. From the results, the scale property method on this study will be derive as the reliable results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.4B
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• pp.319-328
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• 2009

This study quantified the data by applying the EDA techniques considering the data structure, and the results were then used for the frequency analysis. Although traditional methods based on the method of moments provide very sensitive statistics to the extreme values, the EDA techniques have an advantage of providing very stable statistics with their small variation. For the application of the EDA techniques to the frequency analysis, it is necessary to normalization transform and inverse-transform to conserve the skewness of the raw data. That is, it is necessary to transform the raw data to make the data follow the normal distribution, to estimate the statistics by applying the EDA techniques, and then finally to inverse-transform the statistics of transformed data. These statistics decided are then applied for the frequency analysis with a given probability density function. This study analyzed the annual maxima one hour rainfall data at Seoul and Pohang stations. As a result, it was found that more stable rainfall quantiles, which were also less sensitive to extreme values, could be estimated by applying the EDA techniques. This methodology may be effectively used for the frequency analysis of rainfall at stations with especially high annual variations of rainfall due to climate change, etc.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.581-585
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• 2010

This study introduced a Bayesian based frequency analysis in which the statistical trend seasonal analysis for hydrologic extreme series is incorporated. The proposed model employed Gumbel and GEV extreme distribution to characterize extreme events and a fully coupled bayesian frequency model was finally utilized to estimate design rainfalls in Seoul. Posterior distributions of the model parameters in both trend and seasonal analysis were updated through Markov Chain Monte Carlo Simulation mainly utilizing Gibbs sampler. This study proposed a way to make use of nonstationary frequency model for dynamic risk analysis, and showed an increase of hydrologic risk with time varying probability density functions. In addition, full annual cycle of the design rainfall through seasonal model could be applied to annual control such as dam operation, flood control, irrigation water management, and so on. The proposed study showed advantage in assessing statistical significance of parameters associated with trend analysis through statistical inference utilizing derived posterior distributions.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.15-15
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• 2016

In South Korea, annual maximum precipitation often occurs in association with mature typhoons in the western Pacific and from summer monsoon rains. In addition, certain years have no significant typhoon activity. Therefore, the characteristics of frequency distributions differ between extreme typhoons and monsoon events. Those extremes are also influenced from climate conditions in a different way. Application of nonstationary frequency analysis to the AMP data combined with typhoon and monsoon events might not always be reasonable. Therefore, we propose a novel approach of nonstationary frequency analysis to integrate extreme events of AMP induced from two main sources such as typhoons and monsoon in the current study. In this way, we were able to model the nonstationarity of extreme events from tropical storms and monsoon separately.

• 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.55 no.3
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• pp.177-189
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• 2022

The purpose of this study is to apply the d4PDF (Data for Policy Decision Making for Future Change) constructed from a large-scale ensemble climate simulation to estimate the probable rainfall with low frequency and high intensity. In addition, this study analyzes the uncertainty caused by the application of the frequency analysis by comparing the probable rainfall estimated using the d4PDF with that estimated using the observed data and frequency analysis at Geunsam, Imsil, Jeonju, and Jangsu stations. The d4PDF data consists of a total of 50 ensembles, and one ensemble provides climate and weather data for 60 years such as rainfall and temperature. Thus, it was possible to collect 3,000 annual maximum daily rainfall for each station. By using these characteristics, this study does not apply the frequency analysis for estimating the probability rainfall, and we estimated the probability rainfall with a return period of 10 to 1000 years by distributing 3,000 rainfall by the magnitude based on a non-parametric approach. Then, the estimated probability rainfall using d4PDF was compared with those estimated using the Gumbel or GEV distribution and the observed rainfall, and the deviation between two probability rainfall was estimated. As a result, this deviation increased as the difference between the return period and the observation period increased. Meanwhile, the d4PDF reasonably suggested the probability rainfall with a low frequency and high intensity by minimizing the uncertainty occurred by applying the frequency analysis and the observed data with the short data period.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.15-27
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• 2018

Parametric method of flood frequency analysis involves fitting of a probability distribution to observed flood data. When record length at a given site is relatively shorter and hard to apply the asymptotic theory, an alternative distribution to the generalized extreme value (GEV) distribution is often used. In this study, we consider the beta-P distribution (BPD) as an alternative to the GEV and other well-known distributions for modeling extreme events of small or moderate samples as well as highly skewed or heavy tailed data. The L-moments ratio diagram shows that special cases of the BPD include the generalized logistic, three-parameter log-normal, and GEV distributions. To estimate the parameters in the distribution, the method of moments, L-moments, and maximum likelihood estimation methods are considered. A Monte-Carlo study is then conducted to compare these three estimation methods. Our result suggests that the L-moments estimator works better than the other estimators for this model of small or moderate samples. Two applications to the annual maximum stream flow of Colorado and the rainfall data from cloud seeding experiments in Southern Florida are reported to show the usefulness of the BPD for modeling hydrologic events. In these examples, BPD turns out to work better than $beta-{\kappa}$, Gumbel, and GEV distributions.