# 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

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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