# The Characteristics of Raindrop Size Distributions in Different Climatological Regions in South Korea

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## Abstract

**:**

_{H}and Z

_{DR}were shown highest (lowest) value at the coastal region of BOS (mountain area of CPO) site for both rain types. The Dm-rose, which shows the Dm distributions with the wind direction, was used in this study. In the coastal area (mountain and middle land area), the dominant wind was east–southeast (east) direction. The ratio of the smaller diameter to the middle size at BOS was much smaller than that at CPO. In the analysis of the hourly distribution of the Dm and logNw, there were two and four peaks of Dm at BUS and BOS, respectively. There was one peak of the Dm at the CPO and JIN sites. The time variation of the Dm was much higher than that of the logNw.

## 1. Introduction

_{DP}, Z

_{DR}) is the least sensitive to variations in DSDs, and R(Z

_{H}) is the most sensitive to them. Zhang et al. [13] improved the parameterization of rain microphysics obtained from the disdrometer and polarimetric radar for a numerical model using Kessler-type parameterization. They found that simplified constrained-gamma DSD model parameterization outperformed Marshall–Parmel model parameterization.

^{2}in Switzerland. They found that the significant variability of the DSDs at a small scale was in the order of 20% for the total number concentration (N

_{t}), 10% for the mass-weighted diameter (D

_{m}), and 30% for the rain rate. Bringi et al. [26] estimated the spatial correlation between the DSD variables and the rain rate for the two precipitation types using S-band polarimetric radar and a 2-D video disdrometer. They found that the convective rain showed a shorter decorrelation distance than stratiform rain in the rain rate, and the correlation between the DSD variables and the rain rate from the radar and 2-D video disdrometer were in good agreement over distances ranging from 1.5 to 7 km.

## 2. Materials and Methods

#### 2.1. Datasets

^{−1}or higher than 200 mm h

^{−1}, the corresponding spectra were removed as unreliable data. The sample numbers used for the analysis after the quality control algorithm for each site were 30,605 for BOS, 34,890 for BUS, 49,818 for CPO, and 28,041 for JIN. To propose a way of showing the Dm distribution with wind direction, the wind direction measured by Automatic Weather System (AWS) as the same period of Parsivel disdrometer.

#### 2.2. Methodology

^{−1}m

^{−3}) is the number concentration per unit volume for each drop diameter, N

_{0}(mm

^{−1−μ}m

^{−3}) is an intercept parameter, Λ (mm

^{−1}) is the slope, and μ (dimensionless) indicates the shape parameter of the Gamma model. The n

_{th}moment for the DSDs, M

_{n}, was calculated using Equation (4). Moments of the 2nd, 4th, and 6th orders were used to describe the DSD parameters in this study.

^{−1}(0.5 mm h

^{−1}) and the standard deviation for five minutes rainfall rate is larger (smaller) than 1.5 mm h

^{−1}, then it is classified as convective (stratiform) rain. They used a 2 min averaged rain rate for the analysis; however, 1 min data were used in this study to retain more sampling numbers.

^{−1}and divided into 16 directions. Then, average Dm values and their frequency with 16 wind directions were calculated. The workflow of this study is shown in Figure 3.

## 3. Results

#### 3.1. Average Drop Size Distributions

^{−1}(weak rain rate), 5.0 < R < 10.0 mm h

^{−1}(moderate rain rate), and 10.0 mm h

^{−1}< R (severe rain rate). Figure 5 shows the number concentration of the diameters with the three different rain rate categories. At the number concentration of a raindrop diameter of less than 1 mm, the CPO (BUS) site had the largest (smallest) number density in all rain rate categories. There were no samples observed at a diameter larger than 5 mm, and the three sites of BUS, CPO, and JIN had similar number concentrations in the weak rain rate category (Figure 5a). At the moderate rain rate (Figure 5b), the number density of the smaller diameter (less than 1 mm) at CPO was much higher than at the other sites, and the BOS site had a larger number concentration of middle and large size of diameters (larger than 1 mm). At the severe rain rate, the number density of all sites had similar patterns except for the BUS site, with a drop diameter of larger than 4 mm (Figure 5c).

#### 3.2. Average Drop Size Distributions with Rain Types

^{−1}(17.97 mm h

^{−1}), 1.98 mm h

^{−1}(17.31 mm h

^{−1}), 2.30 mm h

^{−1}(13.93 mm h

^{−1}), and 2.03 mm h

^{−1}(18.56 mm h

^{−1}), respectively (Table 1).

#### 3.3. The Characteristics of Z-R Relationship and Polarimetric Variables

^{−1}of RMSE was obtained at the BUS site.

_{H}), differential reflectivity (Z

_{DR}), and specific differential phase (K

_{DP}) were calculated at the four studied sites. Figure 12 shows the occurrence frequency of reflectivity with rain types at each site. The frequency of stratiform rain was larger than that of convective rain weaker than 31 dBZ at BOS, 30 dBZ at BUS, 27 dBZ at CPO, and 29 dBZ at JIN. The average reflectivity of stratiform and convective rain were 22.6 dBZ and 38.0 dBZ at BOS, 22.4 dBZ and 36.6 dBZ at BUS, 21.9 dBZ and 35.1 dBZ at CPO, and 22.4 dBZ and 37.0 dBZ at JIN.

^{−1}. The average specific differential phase of convective rain was 0.25 deg km

^{−1}at BOS, 0.19 deg km

^{−1}at BUS, 0.16 deg km

^{−1}at CPO, and 0.22 deg km

^{−1}at JIN. This would be one of research topic on separation of rain types using polarimetric radar observation.

#### 3.4. Raindrop Size Distribution with Wind Direction and Its Hourly Variation

## 4. Conclusions

_{H}and Z

_{DR}were shown highest (lowest) value at the coastal region of BOS (mountain area of CPO) site for both rain types. These results are consistent with larger Dm at the coastal area than that at the mountain area. The average K

_{DP}had same value at the four studied sites for stratiform rain and had the highest (lowest) value at the coastal area of BOS (mountain area of CPO) for convective rain.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The locations of the four PARSIVEL disdrometers (full circle), with topography. CPO site is located at the mountain area (849.15 m in altitude), JIN is a middle land area (111 m in altitude), BUS (1.41 m in altitude) and BOS (10 m in altitude) in a coastal area.

**Figure 2.**The time series of annual rainfall (blue) and the trend (red) for 30 years at (

**a**) CPO, (

**b**) JIN, (

**c**) BOS, and (

**d**) BUS site. Cheonan is the nearest official station to JIN, Goheung is the nearest site to BOS, and Pusan is the nearest site to BUS.

**Figure 4.**Average raindrop number concentration with diameter at four different sites. The rectangles in blue represent BOS, the triangles in red represent BUS, the circles in purple represent CPO, and the arrows in green represent the JIN site. The numbers in the legend are sampling numbers at each site.

**Figure 5.**Average raindrop number concentration with diameter at four different sites with respect to rain rate (

**a**) 0.1 < R < 5.0 mm h

^{−1}, (

**b**) 5.0 < R < 10.0 mm h

^{−1}, and (

**c**) 10.0 mm h

^{−1}< R. The rectangles in blue represent BOS, the triangles in red represent BUS, the circles in purple represent CPO, and the arrows in green represent the JIN site. The numbers in the legend represent the percentage of each rain rate.

**Figure 6.**The contribution ratios of the raindrop diameter to (

**a**) the rain rate and (

**b**) the total number concentration. The blue represents BOS site, the red represents BUS site, the purple represents CPO site, and the green represents JIN site.

**Figure 7.**Average number concentrations of diameter with rain types (

**a**) stratiform and (

**b**) convective rain at the four studied sites. The number in the legend represent the sample number. The rectangles in blue represent BOS, the triangles in red represent BUS, the circles in purple represent CPO, and the arrows in green represent the JIN site.

**Figure 8.**The occurrence frequency of shape parameters with rain type at (

**a**) BOS, (

**b**) BUS, (

**c**) CPO, and (

**d**) JIN site. The blue represents stratiform rain and the red represents convective rain. The legend shows the average (Avg.), standard deviation (Std.), and skewness (Skew) of shape parameter.

**Figure 9.**The occurrence frequency of slope parameters with rain type at (

**a**) BOS, (

**b**) BUS, (

**c**) CPO, and (

**d**) JIN site. The blue represents stratiform rain and the red represents convective rain. The legend shows the average (Avg.), standard deviation (Std.), and skewness (Skew) of slope parameter.

**Figure 10.**Boxplot of Dm and logNw values of convective and stratiform rain for each site. The line curve represents the separation line of rain types proposed by BR09. The section above (below) this line represents convective (stratiform) rain.

**Figure 11.**The scatter plots of rain rate measured by DSD and R(Z) relations were obtained from DSDs at (

**a**) BOS, (

**b**) BUS, (

**c**) CPO, and (

**d**) JIN sites. The legend shows the Z-R relation, root mean square error (RMSE), and cross-correlation coefficient (CC).

**Figure 12.**The occurrence frequency of reflectivity with rain types at (

**a**) BOS, (

**b**) BUS, (

**c**) CPO, and (

**d**) JIN site. The blue represents stratiform rain and the red represents convective rain. The legend shows the average (Avg.), standard deviation (Std.), and skewness (Skew) of reflectivity for both rain types.

**Figure 13.**The occurrence frequency of differential reflectivity with rain types at (

**a**) BOS, (

**b**) BUS, (

**c**) CPO, and (

**d**) JIN site. The blue represents stratiform rain and the red represents convective rain. The legend shows the average (Avg.), standard deviation (Std.), and skewness (Skew) of differential reflectivity for both rain types.

**Figure 14.**The occurrence frequency of specific differential phase with rain types at (

**a**) BOS, (

**b**) BUS, (

**c**) CPO, and (

**d**) JIN site. The blue represents stratiform rain and the red represents convective rain. The legend shows the average (Avg.), standard deviation (Std.), and skewness (Skew) of specific differential phase for both rain types.

**Figure 15.**The Dm distribution with wind direction of the (

**a**) BOS, (

**b**) BUS, (

**c**) CPO, and (

**d**) JIN sites.

**Figure 16.**Time series of average (

**a**) Dm and (

**b**) logNw at the four studied sites. The rectangles in blue represent BOS, the triangles in red represent BUS, the circles in purple represent CPO, and the arrows in green represent the JIN site.

**Table 1.**The average DSDs variables, rain rates, and sample numbers of rain types at the four studied sites.

BOS | BUS | CPO | JIN | |||||
---|---|---|---|---|---|---|---|---|

Types | Str. | Con | Str. | Con. | Str. | Con. | Str. | Con. |

Dm (mm) | 1.24 | 1.84 | 1.11 | 1.55 | 0.97 | 1.46 | 1.05 | 1.59 |

LogNw (mm^{−1} m^{−3}) | 3.62 | 3.70 | 3.83 | 4.04 | 4.23 | 4.14 | 3.97 | 4.02 |

Rain rate (mm h^{−1}) | 1.96 | 17.97 | 1.98 | 17.31 | 2.30 | 13.93 | 2.03 | 18.56 |

No. (%) | 11350 (66) | 5884 (34) | 14376 (68) | 6670 (32) | 20209 (71) | 8329 (29) | 12136 (75) | 4062 (25) |

Site | Z-R Relations | ||
---|---|---|---|

ALL | Convective | Stratiform | |

BOS | R = 0.058Z^{0.621} | R = 0.075Z^{0.596} | R = 0.067Z^{0.591} |

BUS | R = 0.058Z^{0.641} | R = 0.070Z^{0.623} | R = 0.067Z^{0.608} |

CPO | R = 0.106Z^{0.575} | R = 0.132Z^{0.548} | R = 0.040Z^{0.773} |

JIN | R = 0.064Z^{0.626} | R = 0.080Z^{0.603} | R = 0.067Z^{0.612} |

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**MDPI and ACS Style**

You, C.-H.; Kim, H.-J.; Suh, S.-H.; Jung, W.; Kang, M.-Y.
The Characteristics of Raindrop Size Distributions in Different Climatological Regions in South Korea. *Remote Sens.* **2022**, *14*, 5137.
https://doi.org/10.3390/rs14205137

**AMA Style**

You C-H, Kim H-J, Suh S-H, Jung W, Kang M-Y.
The Characteristics of Raindrop Size Distributions in Different Climatological Regions in South Korea. *Remote Sensing*. 2022; 14(20):5137.
https://doi.org/10.3390/rs14205137

**Chicago/Turabian Style**

You, Cheol-Hwan, Hyeon-Joon Kim, Sung-Ho Suh, Woonseon Jung, and Mi-Young Kang.
2022. "The Characteristics of Raindrop Size Distributions in Different Climatological Regions in South Korea" *Remote Sensing* 14, no. 20: 5137.
https://doi.org/10.3390/rs14205137