# Hydrologic Risk Assessment of Future Extreme Drought in South Korea Using Bivariate Frequency Analysis

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## Abstract

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## 1. Introduction

## 2. Study area and Data

## 3. Methodology

#### 3.1. Threshold Level Method

#### 3.2. Bivariate Frequency Analysis

_{DS}) is exceeded within the expected life (n) of the structure [49], as given by Equation (3).

## 4. Results

#### 4.1. Definition of a Drought Event

#### 4.2. Drought Risk Analysis Using Bivariate Frequency Analysis

^{2}goodness-of-fit test. Among the Archimedean copula functions such as Clayton, Frank and Gumbel, a suitable copula function was selected for observed data in individual watershed and applied to the future climate change scenario data to perform the bivariate frequency analysis. Consequently, the largest value of the bivariate return periods was chosen as the maximum drought event for a watershed and dataset. The characteristics of maximum drought events are shown in Figure 3 and Figure 4. Table 4 summaries the characteristics of maximum drought event.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Lee, J.H.; Kwon, H.H.; Jang, H.W.; Kim, T.W. Future changes in drought characteristics under extreme climate change over South Korea. Adv. Meteorol.
**2016**, 2016, 1–19. [Google Scholar] [CrossRef] - Kwon, H.-H.; Khalil, A.F.; Siegfried, T. Analysis of extreme summer rainfall using climate teleconnections and typhoon characteristics in South Korea. J. Am. Water Resour. Assoc.
**2008**, 44, 436–448. [Google Scholar] [CrossRef] - Kwon, H.-H.; Brown, C.; Lall, U. Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modeling. Geophys. Res. Lett.
**2008**, 35, 05404. [Google Scholar] [CrossRef] - Kwon, H.-H.; Sivakumar, B.; Moon, Y.-I.; Kim, B.-S. Assessment of change in design flood frequency under climate change using a multivariate downscaling model and a precipitation runoff model. Stoch. Environ. Res. Risk Assess.
**2011**, 25, 567–581. [Google Scholar] [CrossRef] - Janga, R.M.; Ganguli, P. Application of copulas for derivation of drought severity-duration-frequency curves. Hydrol. Process.
**2012**, 26, 1672–1685. [Google Scholar] [CrossRef] - Obasi, G.O.P. WMO’s role in the international decade for natural disaster reduction. Bull. Am. Meteorol. Soc.
**1994**, 75, 1655–1662. [Google Scholar] [CrossRef] - Lee, J.H.; Park, S.Y.; Kim, J.S.; Sur, C.; Chen, J. Extreme drought hotspot analysis for adaptation to a changing climate: Assessment of applicability to the five major river basins of the Korean Peninsula. Int. J. Climatol.
**2018**, 38, 4025–4032. [Google Scholar] [CrossRef] - Waseem, M.; Ajmal, M.; Kim, T.W. Development of a new composite drought index for multivariate drought assessment. J. Hydrol.
**2015**, 527, 30–37. [Google Scholar] [CrossRef] - Van Huijgevoort, M.H.J.; Hazenberg, P.; van Lanen, H.A.J.; Uijlenhoet, R. A generic method for hydrological drought identification across different climate regions. Hydrol. Earth Syst. Sci.
**2012**, 16, 2437–2451. [Google Scholar] [CrossRef] [Green Version] - Shiau, J.T.; Shen, H.W. Recurrence analysis of hydrologic droughts of differing severity. J. Water Resour. Plan. Manag.
**2001**, 127, 30–40. [Google Scholar] [CrossRef] - Mirakbari, M.; Ganji, A.; Fallah, S.R. Regional bivariate frequency analysis of meteorological droughts. J. Hydrol. Eng.
**2010**, 15, 985–1000. [Google Scholar] [CrossRef] - Yu, J.S.; Shin, J.Y.; Kwon, M.S.; Kim, T.W. Bivariate drought frequency analysis to evaluate water supply capacity of multi-purpose dams. J. Korean Soc. Civ. Eng.
**2017**, 37, 231–238. [Google Scholar] [CrossRef] - Kim, T.-W.; Valdés, J.B.; Yoo, C.S. Nonparametric approach for estimating return periods of droughts in arid regions. J. Hydrol. Eng.
**2003**, 8, 237–246. [Google Scholar] [CrossRef] - Mirabbasi, R.; Fakheri-Fard, A.; Dinpashoh, Y. Bivariate drought frequency analysis using the copula method. Theor. Appl. Climatol.
**2012**, 108, 191–206. [Google Scholar] [CrossRef] - Yoo, J.; Kim, D.; Kim, H.; Kim, T.W. Application of copula functions to construct confidence intervals of bivariate drought frequency curve. J. Hydrol. Environ. Res.
**2016**, 11, 113–122. [Google Scholar] [CrossRef] - Ganguli, P.; Reddy, M.J. Risk assessment of droughts in Gujarat using bivariate copulas. Water Resour. Manag.
**2012**, 26, 3301–3327. [Google Scholar] [CrossRef] - Yoo, J.Y.; Kwon, H.H.; Lee, J.H.; Kim, T.W. Influence of evapotranspiration of future drought risk using bivariate drought frequency curves. KSCE J. Civ. Eng.
**2016**, 20, 2059–2069. [Google Scholar] [CrossRef] - Kim, N.S.; Kim, J.S.; Jang, H.W.; Lee, J.H. Hydrologic risk analysis based on extreme drought over the Korean peninsula under climate change. J. Korea Soc. Hazard Mitig.
**2015**, 15, 45–52. [Google Scholar] [CrossRef] - Yu, J.S.; Yoo, J.Y.; Lee, J.H.; Kim, T.W. Estimation of drought risk through the bivariate drought frequency analysis using copula functions. J. Korea Water Resour. Assoc.
**2016**, 49, 217–225. [Google Scholar] [CrossRef] - Park, M.W.; Lee, O.J.; Park, Y.K.; Kim, S.D. Future drought projection In Korea under AR5 RCP climate change scenarios. J. Korea Soc. Hazard Mitig.
**2015**, 15, 423–433. [Google Scholar] [CrossRef] - Wood, A.W.; Leung, L.R.; Sridhar, V.; Lettenmaier, D.P. Hydrologic implications of dynamical and statistical approaches to downscaling climate model outputs. Clim. Chang.
**2004**, 62, 189–216. [Google Scholar] [CrossRef] - Bae, D.H.; Jung, I.W.; Lettenmaier, D.P. Hydrologic uncertainties in climate change from IPCC AR4 GCM simulations of the Chungju basin, Korea. J. Hydrol.
**2011**, 401, 90–105. [Google Scholar] [CrossRef] - Kwak, J.W.; Lee, S.D.; Kim, Y.S.; Kim, J.S. Return period estimation of droughts using drought variables from standardized precipitation index. J. Korea Water Resour. Assoc.
**2013**, 46, 795–805. [Google Scholar] [CrossRef] - Wada, Y.; van Beek, L.P.H.; Wanders, N.; Bierkens, M.F.P. Human water consumption intensifies hydrological drought worldwide. Environ. Res. Lett.
**2013**, 8, 034036. [Google Scholar] [CrossRef] [Green Version] - Yoo, J.Y.; Kim, T.W.; Kim, S.D. Drought frequency analysis using cluster analysis and bivariate probability distribution. J. Korea Water Resour. Assoc.
**2010**, 30, 599–606. [Google Scholar] [CrossRef] - Yoo, J.Y.; Kwon, H.H.; Kim, T.W.; Ahn, J.H. Drought frequency analysis using cluster analysis and bivariate probability distribution. J. Hydrol.
**2012**, 14, 102–111. [Google Scholar] [CrossRef] - Sung, J.H.; Chung, E.S. Proposal and application of water deficit-duration-frequency curve using threshold level method. J. Korea Water Resour. Assoc.
**2014**, 47, 997–1005. [Google Scholar] [CrossRef] - Carrão, H.; Singleton, A.; Naumann, G.; Barbosa, P.; Vogt, J. An optimized system for the classification of meteorological drought intensity with applications in frequency analysis. J. Appl. Meteor. Climatol.
**2014**, 53, 1943–1960. [Google Scholar] [CrossRef] - Van Loon, A.F. Hydrological drought explained. Wiley Interdiscip. Rev. Water
**2015**. [Google Scholar] [CrossRef] - Hisdal, H.; Tallaksen, T. Drought Event Definition; Technical Report; ARIDE Technical Report NO. 6; University of Oslo: Oslo, Norway, 2000. [Google Scholar]
- Karimi, M.; Shahedi, K. Hydrological drought analysis of Karkheh River basin in Iran using variable threshold level method. Curr. World Environ. J.
**2013**, 8, 419–428. [Google Scholar] [CrossRef] - Kim, T.-W.; Valdés, J.B.; Yoo, C.S. Nonparametric approach for bivariate drought characterization using Palmer drought index. J. Hydrol. Eng.
**2006**, 11, 134–143. [Google Scholar] [CrossRef] - De Michele, C.; Salvadori, G. A generalized pareto intensity-duration model of storm rainfall exploiting 2-copulas. J. Geophys. Res.
**2003**, 108, 4067. [Google Scholar] [CrossRef] - De Michele, C.; Salvadori, G.; Canossi, M.; Petaccia, A.; Rosso, R. Bivariate statistical approach to check adequacy of dam spillway. J. Hydrol. Eng.
**2005**, 10, 50–57. [Google Scholar] [CrossRef] - Favre, A.C.; Adlouni, S.E.; Perreault, L.; Thiemonge, N.; Bobbe, B. Multivariate hydrological frequency using copulas. Water Resour. Res.
**2004**, 40, 1–12. [Google Scholar] [CrossRef] - Salvadori, G.; De Michele, C. Analytical calculation of storm volume statistics with pareto-like intensity-duration marginals. Geophys. Res. Lett.
**2004**, 31, 1–4. [Google Scholar] [CrossRef] - Salvadori, G.; De Michele, C. Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water Resour. Res.
**2004**, 40, 1–17. [Google Scholar] [CrossRef] - Salvadori, G.; De Michele, C. Statistical characterization of temporal structure of storms. Adv. Water Resour.
**2006**, 29, 827–842. [Google Scholar] [CrossRef] - Salvadori, G.; De Michele, C. On the use of copulas in hydrology: Theory and practice. J. Hydrol. Eng.
**2007**, 12, 369–380. [Google Scholar] [CrossRef] - Wong, G. A comparison between the Gumbel-Hougaard and distorted Frank copulas for drought frequency analysis. Int. J. Hydrol. Sci. Technol.
**2013**, 3, 77–91. [Google Scholar] [CrossRef] - Wong, G.; Lambert, M.F.; Leonard, M.; Metcalfe, A.V. Drought analysis using trivariate copulas conditional on climate states. J. Hydrol. Eng.
**2010**, 15, 129–141. [Google Scholar] [CrossRef] - Lee, T.; Salas, J.D. Copula-based stochastic simulation of hydrological data applied to Nile River flows. Hydrol. Res.
**2011**, 42, 318–330. [Google Scholar] [CrossRef] - Yoo, J.Y.; Yu, J.S.; Kwon, H.H.; Kim, T.W. Determination of drought events considering the possibility of relieving drought and estimation of design drought severity. J. Korea Water Resour. Assoc.
**2016**, 49, 275–282. [Google Scholar] [CrossRef] [Green Version] - Shiau, J.-T.; Wang, H.-Y.; Tsai, C.-T. Bivariate frequency analysis of flood using copulas. J. Am. Water Resour. Assoc.
**2006**, 42, 1549–1564. [Google Scholar] [CrossRef] - Nelson, R.B. An Introduction to Copulas; Springer: New York, NY, USA, 1999. [Google Scholar]
- Zhang, L.; Singh, V.P. Bivariate flood frequency analysis using the copula method. J. Hydrol. Eng.
**2006**, 11, 150–164. [Google Scholar] [CrossRef] - Chen, L.; Sinngh, V.P.; Guo, S.; Mishra, A.K.; Guo, J. Drought analysis using copulas. J. Hydrol. Eng.
**2013**, 18, 797–808. [Google Scholar] [CrossRef] - Kwon, Y.-M.; Kim, T.-W. Derived I-D-F curve in Seoul using bivariate precipitation frequency analysis. J. Korean Soc. Civ. Eng.
**2009**, 29, 155–162. [Google Scholar] - Chow, V.T.; Maidment, D.R.; Mays, L. Applied Hydrology; McGraw-Hill: New York, NY, USA, 1988; p. 572. [Google Scholar]
- Park, B.S.; Lee, J.H.; Kim, C.J.; Jang, H.W. Projection of future drought of Korea based on probabilistic approach using multi-model and multi climate change scenarios. J. Korean Soc. Civ. Eng.
**2013**, 33, 1871–1885. [Google Scholar] [CrossRef]

Model | Institution |
---|---|

CanESM2 | Canadian Centre for Climate Modelling and Analysis |

CCSM4 | National Center for Atmospheric Research |

CESM1-BGC | National Center for Atmospheric Research |

CESM1-CAM5 | National Center for Atmospheric Research |

CMCC-CM | Centro Euro-Mediterraneo per I Cambiamenti Climatici |

CMCC-CMS | Centro Euro-Mediterraneo per I Cambiamenti Climatici |

CNRM-CM5 | Centre National de Recherches Meteorologiques |

GFDL-ESM2G | Geophysical Fluid Dynamics Laboratory |

GFDL-ESM2M | Geophysical Fluid Dynamics Laboratory |

HadGEM2-AO | Met Office Hadley Centre |

HadGEM2-ES | Met Office Hadley Centre |

INM-CM4 | Institute for Numerical Mathematics |

IPSL-CM5A-LR | Institut Pierre-Simon Laplace |

IPSL-CM5A-MR | Institut Pierre-Simon Laplace |

MIROC5 | Atmosphere and Ocean Research Institute |

MPI-ESM-LR | Max Planck Institute for Meteorology |

MPI-ESM-MR | Max Planck Institute for Meteorology |

MRI-CGCM3 | Meteorological Research Institute |

NorESM1-M | Norwegian Climate Centre |

Name | $\mathbf{Equation}\text{}\mathbf{C}\left(\mathbf{u},\mathbf{v}\right)$ | Note |
---|---|---|

Clayton | ${\left({\mathrm{u}}^{-\mathsf{\theta}}+{\mathrm{v}}^{-\mathsf{\theta}}-1\right)}^{-1/\mathsf{\theta}}$ | $\mathrm{u}$ and $\mathrm{v}$ denote random variates $\mathsf{\theta}$ is a parameter. |

Frank | $\frac{1}{\mathsf{\theta}}\mathrm{ln}\left[1+\frac{\left({\mathrm{e}}^{-\mathsf{\theta}\mathrm{u}}-1\right)\left({\mathrm{e}}^{-\mathsf{\theta}\mathrm{v}}-1\right)}{{\mathrm{e}}^{-\mathsf{\theta}}-1}\right]$ | |

Gumbel | $\mathrm{exp}\left[-{\left\{{\left(-\mathrm{ln}\mathrm{u}\right)}^{\mathsf{\theta}}+{\left(-\mathrm{ln}\mathrm{v}\right)}^{\mathsf{\theta}}\right\}}^{1/\mathsf{\theta}}\right]$ |

Characteristics | Dataset | Han River | Nakdong River | Geum River | Seomjin River | Yeongsan River | |
---|---|---|---|---|---|---|---|

Average Duration (mon) | Observed data | 3.42 | 3.56 | 3.41 | 3.47 | 3.43 | |

GCMs | Lowest | 3.18 (HadGEM2-AO) | 2.97 (HadGEM2-AO) | 3.19 (HadGEM2-AO) | 3.23 (IPSL-CM5A-MR) | 3.21 (HadGEM2-AO) | |

Highest | 3.73 (CFDL-ESM2M) | 3.83 (CMCC-CM) | 3.72 (CMCC-CM) | 3.73 (IPSL-CM5A-LR) | 3.87 (CFDL-ESM2M) | ||

Average | 3.44 | 3.51 | 3.50 | 3.51 | 3.47 | ||

Average Severity (mm) | Observed data | 660.8 | 600.3 | 601.8 | 711.2 | 630.9 | |

GCMs | Lowest | 599.9 (CESM1-BGC) | 503 (CESM1-BGC) | 558.5 (CESM1-BGC) | 654.7 (CESM1-BGC) | 579.2 (CESM1-BGC) | |

Highest | 804.1 (INM-CM4) | 725.4 (HadGEM2-AO) | 771.8 (HadGEM2-AO) | 832.7 (CNRM-CM5) | 742.3 (CFDL-ESM2M) | ||

Average | 685.73 | 6225.73 | 661.41 | 760.20 | 669.51 |

Characteristics | Dataset | Han River | Nakdong River | Geum River | Sumjin River | Yeongsan River | |
---|---|---|---|---|---|---|---|

Average Duration (mon) | Observed data | 12 | 14 | 14 | 14 | 14 | |

GCMs | Lowest | 8 (CESM1-BGC) | 7 (HadGEM2-AO) | 9 (GFDL-ESM2M) | 7 (HadGEM2-AO) | 10 (CESM1-BGC) | |

Highest | 25 (MPI-ESM-MR) | 25 (MPI-ESM-MR) | 25 (MPI-ESM-MR) | 19 (CESM1-CAM5) | 29 (MPI-ESM-MR) | ||

Average | 13.2 | 11.9 | 14.1 | 12.0 | 13.8 | ||

Average Severity (mm) | Observed data | 2673.7 | 2127.6 | 2745.7 | 2238.8 | 2307.5 | |

GCMs | Lowest | 2169.9 (CESM1-BGC) | 1474.1 (CESM1-BGC) | 2526.3 (CMCC-CM) | 2020.7 (HadGEM2-AO) | 2073.1 (NorESM1-M) | |

Highest | 5081.9 (MPI-ESM-MR) | 3964.9 (MPI-ESM-MR) | 4793.6 (CanESM2) | 3823.5 (IPSL-CM5A-LR) | 4920.2 (MPI-ESM-MR) | ||

Average | 3132.62 | 2178.64 | 3278.40 | 2707.99 | 2757.99 |

Basin (River) | CanESM2 | CCSM4 | CESM1-BGC | CESM1-CAM5 | CMCC-CM | CMCC-CMS | CNRM-CM5 | GFDL-ESM2G | GFDL-ESM2M | HadGEM2-AO | HadGEM2-ES | INM-CM4 | IPSL-CM5A-LR | IPSL-CM5A-MR | MIROC5 | MPI-ESM-LR | MPI-ESM-MR | MRI-CGCM3 | NorESM1-M |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Han River | 0.64 | 0.53 | 0.56 | 0.65 | 0.83 | 0.84 | 0.68 | 0.55 | 0.55 | 0.62 | 0.72 | 0.61 | 0.59 | 0.51 | 0.73 | 0.78 | 0.67 | 0.78 | 0.48 |

Nakdong River | 0.79 | 0.73 | 0.83 | 0.51 | 0.54 | 0.89 | 0.85 | 0.71 | 0.70 | 0.69 | 0.73 | 0.66 | 0.78 | 0.56 | 0.73 | 0.63 | 0.60 | 0.69 | 0.58 |

Geum River | 0.65 | 0.58 | 0.75 | 0.45 | 0.57 | 0.94 | 0.55 | 0.67 | 0.71 | 0.58 | 0.78 | 0.46 | 0.77 | 0.59 | 0.68 | 0.64 | 0.68 | 0.91 | 0.38 |

Seomjin River | 0.68 | 0.82 | 0.62 | 0.78 | 0.81 | 0.82 | 0.84 | 0.60 | 0.67 | 0.52 | 0.62 | 0.83 | 0.81 | 0.57 | 0.84 | 0.84 | 0.75 | 0.71 | - |

Yeongsan River | 0.26 | 0.54 | 0.66 | 0.63 | 0.65 | 0.80 | 0.80 | 0.52 | 0.68 | 0.41 | - | 0.45 | 0.79 | 0.38 | 0.69 | 0.75 | 0.96 | 0.70 | 0.31 |

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## Share and Cite

**MDPI and ACS Style**

Kim, J.E.; Yoo, J.; Chung, G.H.; Kim, T.-W.
Hydrologic Risk Assessment of Future Extreme Drought in South Korea Using Bivariate Frequency Analysis. *Water* **2019**, *11*, 2052.
https://doi.org/10.3390/w11102052

**AMA Style**

Kim JE, Yoo J, Chung GH, Kim T-W.
Hydrologic Risk Assessment of Future Extreme Drought in South Korea Using Bivariate Frequency Analysis. *Water*. 2019; 11(10):2052.
https://doi.org/10.3390/w11102052

**Chicago/Turabian Style**

Kim, Ji Eun, Jiyoung Yoo, Gun Hui Chung, and Tae-Woong Kim.
2019. "Hydrologic Risk Assessment of Future Extreme Drought in South Korea Using Bivariate Frequency Analysis" *Water* 11, no. 10: 2052.
https://doi.org/10.3390/w11102052