• Journal of the Korean Society of Hazard Mitigation
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• v.11 no.2
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• pp.137-146
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• 2011

In this study, annual maximum storm events are evaluated by applying the bivariate extremal distribution. Rainfall quantiles of probabilistic storm event are calculated using OR case joint return period, AND case joint return period and interval conditional joint return period. The difference between each of three joint return periods was explained by the quadrant which shows probability calculation concept in the bivariate frequency analysis. Rainfall quantiles under AND case joint return periods are similar to rainfall depths in the univariate frequency analysis. The probabilistic storm events overcome the primary limitation of conventional univariate frequency analysis. The application of these storm event analysis provides a simple, statistically efficient means of characterizing frequency of extreme storm event.

• Journal of Korean Foot and Ankle Society
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• v.16 no.1
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• pp.38-46
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• 2012

Purpose: This study was performed retrospectively to evaluate clinical outcomes of distal metatarsal osteotomy using bio-compression screw as the joint preservation method for advanced hallux rigidus. Materials and Methods: Eleven cases were followed up for more than 1 year after distal metatarsal dorsal wedge osteotomy for advanced hallux rigidus. The clinical evaluation was performed according to the American Orthopaedic Foot and Ankle Society (AOFAS) score and patient's satisfaction score. The range of motion, and the period to return to running exercise, tip-toeing gait, squatting, walking down the stairs were evaluated. As the radiographic evaluation, the interval of $1^{st}$ MTP (metatarsophalangeal) joint space and the period to union were measured. Results: The AOFAS hallux score had improved significantly from preoperative average 50.7 points to 87.6 points at the last follow-up (p=0.005). The subjective satisfaction score was average 90.6 points. There were no case of subsequent fusion or additional operation, and no complication associated with bio-compression screw. The period to return to running exercise, tip-toeing gait, squatting, walking down the stairs were average of 24.8 weeks, 20.4 weeks, 16.8 weeks, 18.5 weeks respectively. Dorsiflexion of $1^{st}$ MTP joint had improved significantly from preoperative average $17.5^{\circ}$ to $44^{\circ}$ (p<0.001). All cases achieved union of osteotomy site, and the period to union was average 10.4 weeks. The interval of $1^{st}$ MTP joint space had improved significantly from preoperative average 1.2 mm to 3.5 mm (p=0.014). Conclusion: Distal metatarsal osteotomy using bio-compression screw seems to be one of effective treatment methods for advanced hallux rigidus, because of restoration of the first MTP joint motion, and reliable pain relief, and needlessness of hardware removal.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.3B
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• pp.161-168
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• 2012

Drought is a normal and recurrent phenomenon. But, recurring prolonged droughts have caused consequences and diverse impacts on human system. Therefore, understanding drought characteristics is indispensable element in well-prepared drought management. This study aims to investigate the hydrological droughts of Pyongchang stream and Upstream of Namhan-river in Korean peninsula. For modelling of the joint distribution of drought duration and drought severity, the copula method is used to construct the bivariate drought distribution and return period from the predetermined marginal distributions of drought duration and drought severity. As the result, the most severed drought of the Pyongchang stream and Upstream of Namhan-river occuring during period 1967 to 2007 is the 1981 and 1973. Return period for this drought derived from copula is 550 and 110 years.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2B
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• pp.155-162
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• 2009

Univariate frequency analyses are widely used in practical hydrologic design. However, a storm event is usually characterized by amount, intensity, and duration of the storm. To fully understand these characteristics and to use them appropriately in hydrologic design, a multivariate statistical approach is necessary. This study applied a Gumbel mixed model to a bivariate storm frequency analysis using hourly rainfall data collected for 46 years at the Seoul rainfall gauge station in Korea. This study estimated bivariate return periods of a storm such as joint return periods and conditional return periods based on the estimation of joint cumulative distribution functions of storm characteristics. These information on statistical behaviors of a storm can be of great usefulness in the analysis and assessment of the risk associated with hydrologic design problems.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1996.10a
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• pp.42-44
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• 1996

Recently due to repeatedly occurrence of flood, a lot of Chinese cities accept new design criteria for their protective project Most of them calculated by a certain type of probability distribution. In order to meet the demand of development economy the return period of design criteria is changed more longer and longer even 1000years, but the data which the calculation dependent on is only about 30-40 years. (omitted)

• Journal of Korea Water Resources Association
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• v.46 no.8
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• pp.795-805
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• 2013

Drought is one of the severe natural disasters and it can profoundly affect our society and ecosystem. Also, it is a very important variable for water resources planning and management. Therefore, the drought is analyzed in this study to understand the drought distribution and trend. The Standard Precipitation Index (SPI) is estimated using precipitation data obtained from 55 rain gauge stations in South Korea and the SPI based drought variables such as drought duration and drought severity were defined. Drought occurrence and joint probabilistic analysis for SPI based drought variables were performed with run theory and copula functions. And then the return period and spatial distribution of droughts on the South Korea was estimated. As the results, we have shown that Gongju and Chungju in Chungcheong-do and Wonju, Inje, Jeongseon, Taebeak in Gangwon-do have vulnerability to droughts.

• Wind and Structures
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• v.30 no.2
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• pp.141-153
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• 2020

Probabilistic information regarding directional extreme wind speeds is important for the precise estimation of the design wind loads on structures. A joint probability distribution model of directional extreme typhoon wind speeds is established using Monte Carlo simulation and empirical copula function to fully consider the correlations of extreme typhoon wind speeds among the different directions. With this model, a procedure for estimating directional extreme wind speeds for given return periods, which ensures that the overall risk is distributed uniformly by direction, is established. Taking 5 typhoon-prone cities in China as examples, the directional extreme typhoon wind speeds for given return periods estimated by the present method are compared with those estimated by the method proposed by Cook and Miller (1999). Two types of directional factors are obtained based on Cook and Miller (1999) and the UK standard's drafting committee (Standard B, 1997), and the directional risks for the given overall risks are discussed. The influences of the extreme wind speed correlations in the different directions and the simulated typhoon wind speed sample sizes on the estimated extreme wind speeds for a given return period are also discussed.

• Journal of Korea Water Resources Association
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• v.56 no.2
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• pp.151-163
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• 2023

This study explored the 2022 drought over the Nakdong River watershed. Here, we developed a bivariate regional frequency analysis method to evaluate the risk of hydrological drought. Currently, natural streamflow data are generally limited to accurately estimating the drought frequency. Under this circumstance, the existing at site frequency analysis can be problematic in estimating the drought risk. On the other hand, a regional frequency analysis could provide a more reliable estimation of the joint return periods of drought variables by pooling available streamflow data over the entire watershed. More specifically, the Copula-based regional frequency analysis model was proposed to effectively take into account the tail dependencies between drought variables. The results confirmed that the regional frequency analysis model showed better performance in model fit by comparing the goodness-of-fit measures with the at-site frequency analysis model. We find that the estimated joint return period of the 2022 drought in the Nakdong River basin is about eight years. In the case of the Nam river Dam, the joint return period was approximately 20 years, which can be regarded as a relatively severe drought over the last three decades.

• Wind and Structures
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• v.25 no.3
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• pp.261-282
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• 2017

The probabilistic information of directional extreme wind speeds is important for precisely estimating the design wind loads on structures. A new joint probability distribution model of directional extreme wind speeds is established based on observed wind-speed data using multivariate extreme value theory with the t-Copula function in the present study. At first, the theoretical deficiencies of the Gaussian-Copula and Gumbel-Copula models proposed by previous researchers for the joint probability distribution of directional extreme wind speeds are analysed. Then, the t-Copula model is adopted to solve this deficiency. Next, these three types of Copula models are discussed and evaluated with Spearman's rho, the parametric bootstrap test and the selection criteria based on the empirical Copula. Finally, the extreme wind speeds for a given return period are predicted by the t-Copula model with observed wind-speed records from several areas and the influence of dependence among directional extreme wind speeds on the predicted results is discussed.

• Ocean Systems Engineering
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• v.9 no.3
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• pp.287-328
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• 2019

Comprehensive understanding of the flood risk assessments via frequency analysis often demands multivariate designs under the different notations of return periods. Flood is a tri-variate random consequence, which often pointing the unreliability of univariate return period and demands for the joint dependency construction by accounting its multiple intercorrelated flood vectors i.e., flood peak, volume & durations. Selecting the most parsimonious probability functions for demonstrating univariate flood marginals distributions is often a mandatory pre-processing desire before the establishment of joint dependency. Especially under copulas methodology, which often allows the practitioner to model univariate marginals separately from their joint constructions. Parametric density approximations often hypothesized that the random samples must follow some specific or predefine probability density functions, which usually defines different estimates especially in the tail of distributions. Concentrations of the upper tail often seem interesting during flood modelling also, no evidence exhibited in favours of any fixed distributions, which often characterized through the trial and error procedure based on goodness-of-fit measures. On another side, model performance evaluations and selections of best-fitted distributions often demand precise investigations via comparing the relative sample reproducing capabilities otherwise, inconsistencies might reveal uncertainty. Also, the strength & weakness of different fitness statistics usually vary and having different extent during demonstrating gaps and dispensary among fitted distributions. In this literature, selections efforts of marginal distributions of flood variables are incorporated by employing an interactive set of parametric functions for event-based (or Block annual maxima) samples over the 50-years continuously-distributed streamflow characteristics for the Kelantan River basin at Gulliemard Bridge, Malaysia. Model fitness criteria are examined based on the degree of agreements between cumulative empirical and theoretical probabilities. Both the analytical as well as graphically visual inspections are undertaken to strengthen much decisive evidence in favour of best-fitted probability density.