# Probability Distribution and Characterization of Daily Precipitation Related to Tropical Cyclones over the Korean Peninsula

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

## 3. Methodologies

#### 3.1. TC and Non-TC Rainfall Estimation

#### 3.2. TC and Non-TC Rainfall Contributions

#### 3.3. Optimal Distributions for TC and Non-TC Rainfall

## 4. Results

#### 4.1. TC and Non-TC Rainfall Estimation

#### 4.2. TC and Non-TC Rainfall Contributions

#### 4.3. Optimal Distributions for TC and Non-TC Rainfall

## 5. Discussions and Conclusions

## Author Contributions

## Funding

## Acknowledgements

## Conflicts of Interest

## References

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**Figure 1.**Map of the study area and gauge networks. In this map, the average summer precipitation amount from 1973–2018 is presented. Also, the intra-annual variations of areal precipitation are demonstrated as boxplots. Jeju Island is represented by a hash (#), while Station KR184 is represented by an asterisk (*).

**Figure 2.**Example of a TC traversing South Korea. Shown is the track of Tropical Cyclone Rusa from 27 August to 1 September 2002.

**Figure 3.**(

**a**) Aerial precipitation in South Korea plotted as a function of the distance of each station from the TC center and (

**b**) the distances (top bars) and their corresponding precipitation depths (bottom bars) recorded at Station KR184.

**Figure 4.**First column displays the relative contribution of TCs to the seasonal (

**a**) amount and (

**d**) annual maximum rainfall (percentage). The second column shows the (

**b**) duration (days) and (

**e**) intensity (mm/day) of TC rainfall, while the third column displays the (

**c**) duration and (

**f**) intensity of non-TC rainfall.

**Figure 5.**The relative contribution of TCs to the amount of rainfall (percentage) and the duration of non-TC and TC rainfall (days) in the months of June, July, August and September.

**Figure 6.**The intensity of non-TC and TC rainfall (mm/day) and the relative contribution of TCs to the annual maximum rainfall (percentage) in the months of June, July, August and September.

**Figure 7.**L-Cv and L-skewness L-moment ratio diagram of the (

**a**) TC and (

**b**) non-TC wet-day series with the theoretical curves of several two-parameter distributions. L-kurtosis and L-skewness L-moment ratio diagram of (

**c**) TC and (

**d**) non-TC wet-day series and theoretical curves of three-parameter and points of two-parameter candidate distributions.

**Figure 8.**The PPCC values of the six distributions fitted to the (

**a**) TC and (

**b**) non-TC wet- day series and the AIC values of the candidate distributions for the (

**c**) TC and (

**d**) non-TC wet-day series.

Distribution | Abbreviation | Probability Density Function (PDF) |
---|---|---|

Exponential | EXP | $f\left(x\right)=\{\begin{array}{c}\lambda \mathrm{exp}\left(-\lambda x\right),x\ge 0\\ 0,x0\end{array}$ |

Gamma | GAM | $f\left(x\right)=\frac{{x}^{\gamma -1}\mathrm{exp}\left(-\frac{x}{\beta}\right)}{{\beta}^{\gamma}\mathsf{\Gamma}\left(\mathsf{\gamma}\right)}$ |

Gumbel | GUM | $f\left(x\right)=\frac{1}{\beta}\mathrm{exp}\left[\frac{x-\alpha}{\beta}-\mathrm{exp}\left(\frac{x-\alpha}{\beta}\right)\right]$ |

Lognormal | LN2 | $f\left(x\right)=\frac{1}{x\beta \sqrt{2\pi}}\mathrm{exp}\left(-\frac{{(\mathrm{ln}\left(x\right)-\alpha )}^{2}}{2{\beta}^{2}}\right)$ |

Uniform | UNI | $f\left(x\right)=\{\begin{array}{c}\frac{1}{b-a},axb\\ 0,xaorxb\end{array}$ |

Normal | NOR | $f\left(x\right)=\frac{1}{\sqrt{2\pi {\beta}^{2}}}\mathrm{exp}\left(-\frac{{\left(x-\alpha \right)}^{2}}{2{\beta}^{2}}\right)$ |

Weibull | WEI2 | $f\left(x\right)=\frac{\gamma}{\beta}{\left(\frac{x}{\beta}\right)}^{\gamma -1}\mathrm{exp}\left[-{\left(\frac{x}{\beta}\right)}^{\gamma}\right],x\ge 0$ |

Generalized extreme value type III | GEV | $f\left(x\right)=\frac{1}{\beta}{\left(1+\gamma \frac{x-\alpha}{\beta}\right)}^{-\frac{-1}{\gamma -1}}\mathrm{exp}\left[-1{\left(1+\gamma \frac{x-\alpha}{\beta}\right)}^{-\frac{1}{\gamma}}\right]$ |

Generalized Logistic | GLO | $f\left(x\right)=\frac{\gamma \mathrm{exp}\left(-\frac{x-\alpha}{\beta}\right)}{\beta {\left(1+\mathrm{exp}\left(-\frac{x-\alpha}{\beta}\right)\right)}^{\gamma +1}}$ |

Lognormal | LN3 | $f\left(x\right)=\frac{1}{\left(x-\gamma \right)\sqrt{2\pi}\beta}\mathrm{exp}[-\frac{1}{2}{\left(\frac{\mathrm{ln}\left(x-\gamma \right)-\alpha}{\beta}\right)}^{2}$ |

Pearson Type III | PT3 | $f\left(x\right)=\frac{1}{{\beta}^{\gamma}\mathsf{\Gamma}\left(\mathsf{\gamma}\right)}{\left(x-\alpha \right)}^{\gamma -1}\mathrm{exp}\left(-\frac{x-\alpha}{\beta}\right)$ |

Weibull | WEI3 | $f\left(x\right)=\frac{\gamma}{\beta}{\left(\frac{x-\alpha}{\beta}\right)}^{\gamma -1}{e}^{-{\left(\frac{x-\alpha}{\beta}\right)}^{\gamma}}$ |

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**MDPI and ACS Style**

Alcantara, A.L.; Ahn, K.-H.
Probability Distribution and Characterization of Daily Precipitation Related to Tropical Cyclones over the Korean Peninsula. *Water* **2020**, *12*, 1214.
https://doi.org/10.3390/w12041214

**AMA Style**

Alcantara AL, Ahn K-H.
Probability Distribution and Characterization of Daily Precipitation Related to Tropical Cyclones over the Korean Peninsula. *Water*. 2020; 12(4):1214.
https://doi.org/10.3390/w12041214

**Chicago/Turabian Style**

Alcantara, Angelika L., and Kuk-Hyun Ahn.
2020. "Probability Distribution and Characterization of Daily Precipitation Related to Tropical Cyclones over the Korean Peninsula" *Water* 12, no. 4: 1214.
https://doi.org/10.3390/w12041214