• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.4B
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• pp.389-397
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• 2010

This study introduced a Bayesian based frequency analysis in which the statistical trend analysis for hydrologic extreme series is incorporated. The proposed model employed Gumbel 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 Gumbel distribution and trend 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. The proposed study showed advantage in assessing statistical significance of parameters associated with trend analysis through statistical inference utilizing derived posterior distributions.

• 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.

• Journal of Wetlands Research
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• v.13 no.3
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• pp.499-514
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• 2011

An underlying assumption of traditional hydrologic frequency analysis is that climate, and hence the frequency of hydrologic events, is stationary, or unchanging over time. Under stationary conditions, the distribution of the variable of interest is invariant to temporal translation. Water resources infrastructure planning and design, such as dams, levees, canals, bridges, and culverts, relies on an understanding of past conditions and projection of future conditions. But, Water managers have always known our world is inherently non-stationary, and they routinely deal with this in management and planning. The aim of this paper is to give a brief introduction to non-stationary extreme value analysis methods. In this paper, a non-stationary hydrologic frequency analysis approach is introduced in order to determine probability rainfall consider changing climate. The non-stationary statistical approach is based on the conditional Generalized Extreme Value(GEV) distribution and Maximum Likelihood parameter estimation. This method are applied to the annual maximum 24 hours-rainfall. The results show that the non-stationary GEV approach is suitable for determining probability rainfall for changing climate, sucha sa trend, Moreover, Non-stationary frequency analyzed using SOI(Southern Oscillation Index) of ENSO(El Nino Southern Oscillation).

• Journal of Korea Water Resources Association
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• v.45 no.8
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• pp.815-826
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• 2012

The underestimating trend using existing ordinary regression (OR) based trend analysis has been a well-known problem. The existing OR method based on least squares approximate the conditional mean of the response variable given certain values of the time t, and the usual assumption of the OR method is normality, that is the distribution of data are not dissimilar form a normal distribution. In this regard, this study proposed a quantile regression that aims at estimating either the conditional median or other quantiles of the response variable. This study assess trend in annual daily maximum rainfall series over 64 weather stations through both in OR and QR approach. The QR method indicates that 47 stations out of 67 weather stations are a strong upward trend at 5% significance level while OR method identifies a significant trend only at 13 stations. This is mainly because the OR method is estimating the condition mean of the response variable. Unlike the OR method, the QR method allows us flexibly to detect the trends since the OR is designed to estimate conditional quantiles of the response variable. The proposed QR method can be effectively applied to estimate hydrologic trend for either non-normal data or skewed data.