Title Page
Contents
ABSTRACT 9
Chapter 1. Introduction 11
Chapter 2. Literature Review 15
2.1. Bivariate frequency analysis with copula model 15
2.2. Non-stationary probability distribution 16
2.3. Extreme events selected by the POT 17
Chapter 3. Materials and Methods 20
3.1. Study stations 20
3.2. Generation of rainfall event from hourly rainfall data 23
3.3. Extraction of several extreme rainfall events per year 24
3.3.1. POT method 24
3.3.2. Threshold of POT 25
3.4. Adoption of the non-stationary probability distribution 28
3.4.1. Marginal distribution, GPD 28
3.4.2. Application of nonlinear regression in GPD 28
3.4.3. Joint distribution using Frank copula 32
3.4.4. Estimation of the joint return period 33
Chapter 4. Results and Discussion 34
4.1. Selection of extreme rainfall events using Tand[이미지참조] 34
4.2. Non-stationary GPD 37
4.2.1. Optimal nonlinear regression to represent non-stationarity 37
4.2.2. Fitness of stationary and non-stationary GPD 41
4.3. Return periods by Frank copula 45
4.3.1. Temporal return periods with the appropriate model 45
4.3.2. Efficiency of applying non-stationary models 50
4.4. Comparison with conventional frequency analysis 53
4.5. Influence of rainfall event intensity 58
Chapter 5. Conclusions 61
References 64
Appendices 70
[Appendix A] Joint return period estimation for stations that are stationary for rainfall volume and intensity 70
[Appendix B] Joint return period estimation for stations that are non-stationary for rainfall volume and stationary for rainfall intensity 77
[Appendix C] Joint return period estimation for stations that are stationary for rainfall volume and non-stationary for rainfall intensity 82
[Appendix D] Joint return period estimation for stations that are non-stationary for rainfall volume and intensity 84
[Appendix E] AIC values for 57 stations to compare the fit of stationary and non-stationary GPDs 86
Abstract (in Korean) 90
Table 2.1. The originality of this study by comparing existing studies 19
Table 3.1. Details of automated synoptic observing system stations in South Korea 21
Table 3.2. Nonlinear regression equations applied to time-varying scale parameters of non-stationary GPD model 31
Table 4.1. Average coefficient of determination (R²) of 57 stations in one regression equation 37
Table 4.2. Cumulative distribution function (CDF) of stationary and non-stationary generalized Pareto distribution (GPD) models 41
Figure 1.1. Study process 14
Figure 3.1. Study area 20
Figure 4.1. The number of extreme rainfall events in weather station S108 over different thresholds: (a) Number of rainfall events selected by Tand, (b) Number of rainfall events...[이미지참조] 35
Figure 4.2. Characteristics of extreme rainfall events extracted by the Peaks Over Threshold (POT) method: (a) Threshold, (b) Number of rainfall events 36
Figure 4.3. Taylor diagram of non-stationary GPD models using 28 nonlinear regression equations for rainfall volume and intensity: (a) Stationary for volume and intensity (S90),... 40
Figure 4.4. The most suitable model for stations by comparing stationary and non- stationary generalized Pareto distribution (GPD) models in South Korea 42
Figure 4.5. Time-varying scale parameters, a, and their tendencies with the fitted line for rainfall volume and intensity: (a) Stationary for volume and intensity (S90), (b) Non-... 44
Figure 4.6. Estimation of joint return period of stationary and non-stationary combinations for rainfall volume and intensity; for example: (a) Stationary for volume and intensity (S90), (b) Non-stationary for volume and stationary for intensity (S279), (c) Non-stationary for... 48
Figure 4.7. Variabilities of joint return periods across weather stations for the corresponding maximum rainfall events obtained from each station and time period, and... 49
Figure 4.8. Comparison of combinations of stationary and non-stationary models in station S108 (the station where the non-stationary model is suitable for rainfall volume and intensity): (a) Non-stationary model combination, (b) Stationary model combination 52
Figure 4.9. Return period estimation based on rainfall volume and intensity with three different approaches in 2020 to compare hypothetical rainfall events A and B at station S108: (a) Rainfall event-based bivariate non-stationary model, (b) Rainfall event-based bivariate stationary... 54
Figure 4.10. Joint return period estimation over three time periods with three different approaches for station S108 (Seoul) 55
Figure 4.11. Temporal change of joint return periods based on intensity and volume of rainfall events in station S108: (a) 3-dimensional return periods based on intensity and volume, (b) Return periods based on volume at constant intensities of 10, 30, and 50 mm/h 60