• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.443-451
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• 2005

The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.

• Journal of Korea Water Resources Association
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• v.43 no.8
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• pp.733-745
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• 2010

Seasonality of hydrologic extreme variable is a significant element from a water resources managemental point of view. It is closely related with various fields such as dam operation, flood control, irrigation water management, and so on. Hydrological frequency analysis conjunction with partial duration series rather than block maxima, offers benefits that include data expansion, analysis of seasonality and occurrence. In this study, nonstationary frequency analysis based on the Bayesian model has been suggested which effectively linked with advantage of POT (peaks over threshold) analysis that contains seasonality information. A selected threshold that the value of upper 98% among the 24 hours duration rainfall was applied to extract POT series at Seoul station, and goodness-fit-test of selected GEV distribution has been examined through graphical representation. Seasonal variation of location and scale parameter ($\mu$ and $\sigma$) of GEV distribution were represented by Fourier series, and the posterior distributions were estimated by Bayesian Markov Chain Monte Carlo simulation. The design rainfall estimated by GEV quantile function and derived posterior distribution for the Fourier coefficients, were illustrated with a wide range of return periods. The nonstationary frequency analysis considering seasonality can reasonably reproduce underlying extreme distribution and simultaneously provide a full annual cycle of the design rainfall as well.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.174-174
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• 2023

The impact of global warming on the south Asian summer monsoon is of critical importance for the large population of this region. This study aims to investigate the future changes of the precipitation extremes during pre-monsoon and monsoon, across this region in a more organized regional structure. The study area is divided into six major divisions based on the Köppen-Geiger's climate structure and 10 sub-divisions considering the geographical locations. The future changes of extreme precipitation indices are analyzed for each zone separately using five indices from ETCCDI (Expert Team on Climate Change Detection and Indices); R10mm, Rx1day, Rx5day, R95pTOT and PRCPTOT. 10 global climate model (GCM) outputs from the latest CMIP6 under four combinations of SSP-RCP scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) are used. The GCMs are bias corrected using nonparametric quantile transformation based on the smoothing spline method. The future period is divided into near future (2031-2065) and far future (2066-2100) and then the changes are compared based on the historical period (1980-2014). The analysis is carried out separately for pre-monsoon (March, April, May) and monsoon (June, July, August, September). The methodology used to compare the changes is probability distribution functions (PDF). Kernel density estimation is used to plot the PDFs. For this study we did not use a multi-model ensemble output and the changes in each extreme precipitation index are analyzed GCM wise. From the results it can be observed that the performance of the GCMs vary depending on the sub-zone as well as on the precipitation index. Final conclusions are made by removing the poor performing GCMs and by analyzing the overall changes in the PDFs of the remaining GCMs.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.183-183
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• 2015

수공구조물 설계 시 중요한 요소 중 하나인 확률강우량은 일반적으로 고정지속기간별 강우량에 대하여 일변량 빈도해석을 수행하고 가장 적절한 분포형을 선택하는 지점빈도해석의 과정을 거친다. 그러나 일변량 빈도해석을 수행하기 위해서는 지속시간을 고정하고 강우량의 변화로만 해석해야 단점이 있으며 이를 보완하기 위해 본 연구에서는 다변량 확률모형인 copula 모형을 이용하여 이변량 빈도해석을 수행하였다. 확률변수로는 강우량과 지속기간(hr)을 사용하였고, 주변분포형으로 강수량 - Gumbel (GUM), generalized logistic (GLO) 분포형, 지속기간(hr) - generalized extreme value (GEV), GUM, GLO 분포형을 사용하였으며, copula 모형은 Gumbel-Hougaard 모형을 이용하였다. 주변분포형의 매개변수는 일반적으로 가장 많이 사용하는 확률가중모멘트법을 이용하여 추정하였으며, copula 모형의 매개변수는 maximum pseudolikelihood(MPL) 방법을 사용하였다. 이를 통해 얻어진 이변량 빈도해석의 확률강우량 결과와 기존 지점빈도해석의 결과를 비교하였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.39 no.1
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• pp.165-174
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• 2019

As a nonstationarity is observed in hydrological data, various studies on nonstationary frequency analysis for hydraulic structure design have been actively conducted. Although the inherent diversity in the atmosphere-ocean system is known to be related to the nonstationary phenomena, a nonstationary frequency analysis is generally performed based on the linear trend. In this study, a nonstationary frequency analysis was performed using climate indices as covariates to consider the climate variability and the long-term trend of the extreme rainfall. For 11 weather stations where the trend was detected, the long-term trend within the annual maximum rainfall data was extracted using the ensemble empirical mode decomposition. Then the correlation between the extracted data and various climate indices was analyzed. As a result, autumn-averaged AMM, autumn-averaged AMO, and summer-averaged NINO4 in the previous year significantly influenced the long-term trend of the annual maximum rainfall data at almost all stations. The selected seasonal climate indices were applied to the generalized extreme value (GEV) model and the best model was selected using the AIC. Using the model diagnosis for the selected model and the nonstationary GEV model with the linear trend, we identified that the selected model could compensate the underestimation of the rainfall quantiles.

• Journal of Korean Society of Disaster and Security
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• v.8 no.1
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• pp.21-27
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• 2015

Recent researches show that climate change has impact on the rainfall process at different temporal and spatial scales. The present paper is focused on climate change impact on sub-daily rainfall quantile of Han River basin in South Korea. Climate change simulation outputs from ECHO-G GCM under the A2 scenario were used to estimate daily extreme rainfall. Sub-daily extreme rainfall was estimated using the scale invariance concept. In order to assess sub-daily extreme rainfall from climate change simulation outputs, precipitation time series were generated based on NSRPM (Neyman-Scott Rectangular Pulse Model) and modified using the ratio of rainfall over projection periods to historical one. Sub-daily extreme rainfall was then estimated from those series. It was found that sub-daily extreme rainfall in the future displayed increasing or decreasing trends for estimation methods and different periods.

• Journal of Korea Water Resources Association
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• v.41 no.5
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• pp.527-544
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• 2008

Generalized Pareto distribution (GPD) is frequently applied in hydrologic extreme value analysis. The main objective of statistics of extremes is the prediction of rare events, and the primary problem has been the estimation of the threshold and the exceedances which were difficult without an accurate method of calculation. In this paper, to obtain the threshold or the exceedances, four methods were considered. For this comparison a GPD model was used to estimate parameters and quantiles for the seven durations (1, 2, 3, 6, 12, 18 and 24 hours) and the ten return periods (2, 3, 5, 10, 20, 30, 50, 70, 80 and 100 years). The parameters and quantiles of the three-parameter generalized Pareto distribution were estimated with three methods (MOM, ML and PWM). To estimate the degree of fit, three methods (K-S, CVM and A-D test) were performed and the relative root mean squared error (RRMSE) was calculated for a Monte Carlo generated sample. Then the performance of these methods were compared with the objective of identifying the best method from their number.

• Journal of Environmental Science International
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• v.24 no.4
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• pp.383-391
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• 2015

As occurrence of gradually increasing extreme temperature events in Jeju Island, a hybrid downscaling technique that simultaneously applies by dynamical method and statistical method has implemented on design rainfall in order to reduce flood damages from severe storms and typhoons.As a result of computation, Case 1 shows a strong tendency to excessively compute rainfall, which is continuously increasing. While Case 2 showed similar trend as Case 1, low design rainfall has computed by rainfall in A1B scenario. Based on the design rainfall computation method mainly used in Preventive Disaster System through Pre-disaster Effect Examination System and Basic Plan for River of Jeju Island which are considering climatic change for selecting 50-year and 100-year frequencies. Case 3 selecting for Jeju rain gage station and Case 1 for Seogwipo rain gage station. The results were different for each rain gage station because of difference in rainfall characteristics according to recent climatic change, and the risk of currently known design rainfall can be increased in near future.

• Journal of The Korean Society of Agricultural Engineers
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• v.57 no.5
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• pp.139-152
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• 2015

Along with climate change, it is reported that the scale and frequency of extreme climate events show unstable tendency of increase. Thus, to comprehend the change characteristics of precipitation data, it is needed to consider non-stationary. The main objectives of this study were to estimate future design floods for Wonpyeongcheon watershed based on RCP (Representative Concentration Pathways) scenario. Wonpyeongcheon located in the Keum River watershed was selected as the study area. Historical precipitation data of the past 35 years (1976~2010) were collected from the Jeonju meteorological station. Future precipitation data based on RCP4.5 were also obtained for the period of 2011~2100. Systematic bias between observed and simulated data were corrected using the quantile mapping (QM) method. The parameters for the bias-correction were estimated by non-parametric method. A non-stationary frequency analysis was conducted with moving average method which derives change characteristics of generalized extreme value (GEV) distribution parameters. Design floods for different durations and frequencies were estimated using rational formula. As the result, the GEV parameters (location and scale) showed an upward tendency indicating the increase of quantity and fluctuation of an extreme precipitation in the future. The probable rainfall and design flood based on non-stationarity showed higher values than those of stationarity assumption by 1.2%~54.9% and 3.6%~54.9%, respectively, thus empathizing the necessity of non-stationary frequency analysis. The study findings are expected to be used as a basis to analyze the impacts of climate change and to reconsider the future design criteria of Wonpyeongcheon watershed.

• Journal of Korea Water Resources Association
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• v.43 no.9
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• pp.813-822
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• 2010

An important problem in frequency analysis is the estimation of the quantile for a certain return period. In frequency analysis an assumed probability distribution is fitted to the observed sample data to estimate the quantile at the upper tail corresponding to return periods which are usually much larger than the record length. In most cases, the selection of an appropriate probability distribution is based on goodness of fit tests. The goodness of fit test method can be described as a method for examining how well sample data agrees with an assumed probability distribution as its population. However it gives generally equal weight to differences between empirical and theoretical distribution functions corresponding to all the observations. In this study, the modified Anderson-Darling (AD) test statistics are provided using simulation and the power study are performed to compare the efficiency of other goodness of fit tests. The power test results indicate that the modified AD test has better rejection performances than the traditional tests. In addition, the applications to real world data are discussed and shows that the modified AD test may be a powerful test for selecting an appropriate distribution for frequency analysis when extreme cases are considered.