# Estimating Optimal Design Frequency and Future Hydrological Risk in Local River Basins According to RCP Scenarios

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Bayesian Inference

#### 2.2. Poisson Cluster Rainfall Generation Model

#### 2.3. Performance Measures of Poisson Cluster Rainfall Generation Model

## 3. Estimation of Optimal Design Frequency for Local Rivers

#### 3.1. Study Area

^{2}, accounting for approximately 8.6% of the total area of South Korea, 99,617 km

^{2}.

#### 3.2. Weight Calculation Based on Bayesian Theory

^{2}, which is more than double the “201,494 m

^{2}or larger” standard corresponding to the perfect score (18 points, see Table 2). Among the river basins that showed a lower design frequency, the Namchangcheon is a very small river with a watershed area of 1.86 km

^{2}, but the design frequency was 80 years of a return period. The urban flooding area of the Namchangcheon was 2043 m

^{2}, and the stream order was 3. It was estimated to have a return period of 50.84 years because it was highly underestimated compared to the existing one.

## 4. Hydrological Risks According to Climate Change Scenarios

#### 4.1. Generation of Daily Rainfall Time Series

#### 4.2. Estimation of Optimal Design Frequency According to Climate Change Scenarios

#### 4.3. Evaluation of Hydrological Risks According to Climate Change Scenarios

## 5. Conclusions

- (1)
- Data for each evaluation factor were collected for 413 local river basins in Chungcheongnam-do, for which the basic plans were established. The evaluation sections were divided into equal parts, and weights were calculated using Bayesian theory. When the calculated optimal design frequencies were compared to the existing design frequencies, 253 river basins showed increased design frequencies and 160 river basins showed decreased design frequencies. The design frequency increased compared to that found by Chungcheongnam-do [3] because the urban areas of Chungcheongnam-do are relatively small. As a result, the weights for urban flooding area were calculated to be small.
- (2)
- This study secured statistical objectivity using Bayesian inference to complement the problem of weight calculation using the AHP used by Chungcheongnam-do [3]. However, in the case of urban flooding areas that were emphasized by many researchers, the weight was 18 points (in this study), which was highly underestimated compared to the 40-point weighting values in previous studies. This weight problem may be limited to Chungcheongnam-do, because the urban flooding area of Chungcheongnam-do is smaller than those of other municipalities. Therefore, if the urban flooding area increases beyond Chungcheongnam-do to metropolitan cities (which can be explored in future studies), it is expected that different weights will be derived.
- (3)
- The calculated hydrological flood risk showed that polarization will worsen with future climate change, and the risk increased by approximately 2.96% on average. This result indicates that the design frequency is likely to decrease in the future than in the present, and that the stability of flooding will decrease while the risk increases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Category | Indicator | Distribution Parameter | |
---|---|---|---|

Mean (μ) | Standard Deviation (σ) | ||

Watershed characteristic | Watershed area (km^{2}) | 22.52 | 41.51 |

Shape factor | 0.31 | 0.12 | |

River characteristics | River channel slope (%) | 0.87 | 0.73 |

Stream order | 1.76 | 1.01 | |

Backwater effect reach | 0.29 | 0.45 | |

Extreme flood characteristics | Extreme rainfall frequency | 875.94 | 82.72 |

Urban flooding area (m^{2}) | 107,801.31 | 335,821.81 |

Category | Indicator | Ratio of Occurrence Probability | Score |
---|---|---|---|

Watershed characteristic | Watershed area (km^{2}) | 0.81 | 15 |

Shape parameter | 0.59 | 11 | |

River characteristics | River channel slope (%) | 0.82 | 15 |

Stream order | 0.66 | 12 | |

Backwater effect reach | 0.64 | 11 | |

Extreme flood characteristics | Extreme rainfall frequency | 1.00 | 18 |

Urban flooding area (m^{2}) | 1.00 | 18 |

GCM | RCP | RMSE | NRMSE | RMSLE |
---|---|---|---|---|

HadGEM2-AO | RCP 4.5 | 0.17 | 4.91 | 1.44 |

RCP 8.5 | 0.19 | 4.32 | 1.46 | |

HadGEM2-ES | RCP 4.5 | 0.17 | 4.30 | 1.37 |

RCP 8.5 | 0.17 | 4.21 | 1.37 |

**Table 4.**The number of river basins with changes in the estimated design frequency considering climate change scenarios (HadGEM2-ES).

HadGEM2-ES, RCP 4.5 | HadGEM2-ES, RCP 8.5 | |||||||
---|---|---|---|---|---|---|---|---|

P1 | P2 | P3 | TP | P1 | P2 | P3 | TP | |

Increase | 218 | 269 | 252 | 253 | 262 | 239 | 226 | 245 |

Decrease | 195 | 144 | 161 | 160 | 151 | 174 | 187 | 168 |

Mean of return period(year) | 1.35 | 9.50 | 7.48 | 7.64 | 9.05 | 4.92 | 3.30 | 5.80 |

Climate Scenario | Period | |||
---|---|---|---|---|

P1 | P2 | P3 | TP | |

RCP 4.5 | 0.62 | 4.58 | 3.62 | 3.70 |

RCP 8.5 | 4.39 | 2.38 | 1.59 | 2.83 |

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**MDPI and ACS Style**

Ryu, J.-H.; Kim, J.-E.; Lee, J.-Y.; Kwon, H.-H.; Kim, T.-W.
Estimating Optimal Design Frequency and Future Hydrological Risk in Local River Basins According to RCP Scenarios. *Water* **2022**, *14*, 945.
https://doi.org/10.3390/w14060945

**AMA Style**

Ryu J-H, Kim J-E, Lee J-Y, Kwon H-H, Kim T-W.
Estimating Optimal Design Frequency and Future Hydrological Risk in Local River Basins According to RCP Scenarios. *Water*. 2022; 14(6):945.
https://doi.org/10.3390/w14060945

**Chicago/Turabian Style**

Ryu, Jae-Hee, Ji-Eun Kim, Jin-Young Lee, Hyun-Han Kwon, and Tae-Woong Kim.
2022. "Estimating Optimal Design Frequency and Future Hydrological Risk in Local River Basins According to RCP Scenarios" *Water* 14, no. 6: 945.
https://doi.org/10.3390/w14060945