Characteristics of the Bright Band Based on Quasi-Vertical Proﬁles of Polarimetric Observations from an S-Band Weather Radar Network

: Bright band (BB) characteristics obtained via dual-polarization weather radars elucidate thermodynamic and microphysical processes within precipitation systems. This study identiﬁed BB using morphological features from quasi-vertical proﬁles (QVPs) of polarimetric observations, and their geometric, thermodynamic, and polarimetric characteristics were statistically examined using nine operational S-band weather radars in South Korea. For comparable analysis among weather radars in the network, the calibration biases in reﬂectivity (Z H ) and di ﬀ erential reﬂectivity (Z DR ) were corrected based on self-consistency. The cross-correlation coe ﬃ cient ( ρ HV ) bias in the weak echo regions was corrected using the signal-to-noise ratio (SNR). First, we analyzed the heights of BB PEAK derived from the Z H as a function of season and compared the heights of BB PEAK derived from the Z H , Z DR , and ρ HV . The heights of BB PEAK were highest in the summer season when the surface temperature was high. However, they showed distinct di ﬀ erences depending on the location (e.g., latitude) within the radar network, even in the same season. The height where the size of melting particles was at a maximum (BB PEAK from the Z H ) was above that where the oblateness of these particles maximized (BB PEAK from Z DR ). The height at which the inhomogeneity of hydometeors was at maximum (BB PEAK from the ρ HV ) was also below that of BB PEAK from the Z H . Second, BB thickness and relative position of BB PEAK were investigated to characterize the geometric structure of the BBs. The BB thickness increased as the Z H at BB BOTTOM increased, which indicated that large snowﬂakes melt more slowly than small snowﬂakes. The geometrical structure of the BBs was asymmetric, since the melting particles spent more time forming the thin shell of meltwater around them, and they rapidly collapsed to form a raindrop at the ﬁnal stage of melting. Third, the heights of BB TOP , BB PEAK , and BB BOTTOM were compared with the zero-isotherm heights. The dry-temperature zero-isotherm heights were between BB TOP and BB BOTTOM , while the wet-bulb temperature zero-isotherm heights were close to the height of BB PEAK . Finally, we examined the polarimetric observations to understand the involved microphysical processes. The correlation among Z H at BB TOP , BB PEAK , and BB BOTTOM was high ( > 0.94), and the Z DR at BB BOTTOM was high when the BB’s intensity was strong. This proved that the size and concentration of snowﬂakes above the BB inﬂuence the size and concentration of raindrops below the BB. There was no depression in the ρ HV for a weak BB. Finally, the mean proﬁle of the Z H and Z DR depended on the Z H at BB BOTTOM . In conclusion, the growth process of snowﬂakes above the BB controls polarimetric observations of BB. structure of the BB and the rainfall intensity below the BB. The Z DR decreased above the BB as the snowﬂake particles smoothen when they start to melt. Large snowﬂakes (high Z H Bottom class) with a high axis ratio have a low Z DR above the BB. The Z DR within the BB with a high Z H Bottom class was greater than that with a low Z H Bottom class. The Z DR below the BB was larger at the high Z H Bottom class. The shape and orientation of snowﬂakes determined the Z DR structure of the BB.


Introduction
When falling snowflakes pass through the zero-isotherm layers into the warmer air, they melt and collapse to form raindrops, causing an increase in radar reflectivity (known as the bright band, hereafter BB). The reflectivity (Z H ) increases owing to the increase in the dielectric constant. Afterwards, the Z H decreases upon the formation of raindrops, owing to the decrease in the size and number concentration of snowflakes caused by the increase in fall velocity [1,2]. The overestimation in Z H causes a significant error in radar rainfall estimates under the BB region. The identification of BB and correction of related errors are necessary for accurate estimations of precipitation [3][4][5]. The study of the vertical structure of the precipitation system associated with the melting layer and its characteristic analysis using remote sensing instruments is essential to understand cloud physics and rain microphysics. Weather radar can provide crucial information on melting layers with high spatiotemporal resolution. Therefore, detection and characterization of the BB using weather radar is one of the primary keys for understanding the microphysical processes related to the vertical structure of precipitation.
Most single-polarimetric techniques have identified the BB (i.e., peak, top, and bottom) based on a geometric feature from the vertical profile of Z H (VPR) [1,[6][7][8][9][10]. The gradient of VPR has been commonly used to define the boundary of BB. Klaassen [11] and White et al. [12] used the change in radial velocity when snowflakes turn into raindrops as they pass through the melting layer to identify the BB. Dual-polarization radar can provide information on the size, shape, and phase of hydrometeors, resulting in improved BB detection [13][14][15][16][17]. Ryzhkov and Zrnić [13] showed that polarimetric signatures pronounce the presence of BB. Brandes and Ikeda [14] identified BB by matching observed and modelled profiles of polarimetric observations. Giangrande et al. [16] proposed thresholds for Z H , the differential reflectivity (Z DR ), and the cross-correlation coefficient (ρ HV ) to detect top and bottom boundaries of BB in an operational environment. Boodoo et al. [18] modified the technique developed by Giangrande et al. [16] for a C-band radar in southern Ontario, Canada. The top of the BB effectively matched the 0 • C wet-bulb temperature layer. Illingworth and Thompson [19] showed that the linear depolarization ratio (LDR) was valuable for identifying BB and correcting an increase in Z H due to BB. Hall et al. (2015) developed a fuzzy logic-based BB detection technique using Z H , Z DR , ρ HV , and LDR.
Fabry and Zawadzki [1] analyzed the vertical structure of BB revealed by X-band vertically pointing radar and wind profiler. The intensity of BB depends on variations in the refractive index, shape, and density of hydrometeors. Zawadzki [20] developed a BB model that showed that dense particles reduce the difference in Z H at the peak height of the BB and in the rain region. Wolfensberger et al. [21] analyzed the characteristics of BB using the range-height indicator (RHI) scan mode at various climatic regions (i.e., South of France; Swiss Alps and plateau; and Iowa, USA). The distribution of polarimetric observations within the BB was similar regardless of the season and climatic regions. They also showed that the thickness of BB is highly related to the presence of rimed particles, the fall velocity of the hydrometeors, and BB intensity.
Recently, quasi-vertical profiles (QVPs) of polarimetric observations (described in more detail in Section 3) were used to investigate the vertical structure and microphysical processes of the precipitation system [22][23][24][25]. Kumjian et al. [22] first used QVP to detect refreezing signals of precipitation during winter storms. According to Ryzhkov et al. [24], QVP is a useful tool for the examination of microphysical processes resulting in precipitation on the surface and aids in the determination of the growth process of snowflakes. Kumjian and Lombardo [23] analyzed the microphysical and dynamic characteristics of winter snowstorms. They found that an increase in differential reflectivity (Z DR ) represented the initial stage of planar crystal growth, and an increase in the specific differential phase (K DP ) indicated the high number concentrations of planar crystals. The supersaturation caused by the ascent boosts the depositional growth and raises the potential of an increase in K DP . Trömel et al. [26] showed the potential of ground precipitation nowcasting by identifying microphysical processes of stratiform snowfall storms. The K DP increase in the dendritic growth layer (DGL, between −10 and −20 • C) exhibited a very high correlation with rainfall on the ground after half an hour. Griffin et al. [27] detected Remote Sens. 2020, 12, 4061 3 of 18 BB and analyzed the microphysical processes associated with BB and DGL for stratiform precipitation in winter. Using the QVPs of polarimetric observations, they identified a weak BB (Z H of < 20 dBZ) whose detection failed when using the vertical profile of Z H only. They also compared polarimetric observations above, within, and below the BB using QVPs for the first time at the S band.
In this study, we identified BB using the QVPs of polarimetric observations obtained from nine S-band dual-polarization radars operated by the Korea Meteorological Administration (KMA). For the analysis of BB characteristics, geometric features (including heights of the BB peak, top, and bottom at QVPs) were analyzed statistically, and then compared to the height of the 0 • C isotherm. Finally, the characteristics of polarimetric observations at the top, peak, and bottom of the BB were examined to determine the microphysical processes related to the BB.

Materials and Data
The KMA has operated a nationwide weather radar network composed of 10 S-band weather radars since 2008 and sequentially replaced all radars of the network with S-band dual-polarization radars during the period from 2014 to 2019. Figure 1 shows the deployment of the KMA S-band dual-polarization weather radar. The replacement began with the BRI radar at the northwestern island in 2014 and ended with the GNG radar at the northeastern coast in November 2019. We used a total of nine weather radars, except for the GNG radar, to analyze the characteristics of the BB from March to November 2019. Table 1 shows the volumetric scan strategies of the weather radar in the KMA network. All strategies consisted of nine elevation angles, including a wind profiling mode of 15 • and were repeated every 5 min. Notably, several radars (i.e., KWK, MYN, and PSN) installed at a relatively high altitude (>600 m mean sea level (MSL)) employed a negative (−) elevation as the lowest elevation angle. The elevation angles for the lowest scan were determined based on a radar beam blockage simulation for standard beam propagation using the digital elevation model with a horizontal resolution of 1 arc second. The radar transmits a long pulse with a width of 2 µs at low elevation angles (less than 3 • ) to enhance the detectability of weak low-level echoes, such as winter snowstorms, whereas a short pulse of 1 µs pulse width is used at higher elevation angles (>3 • ) to increase the Nyquist velocity using high pulse repetition frequency (PRF). This configuration of the pulse length is based on the sensitivity test by Lee et al. [28]. They found that a longer pulse length (i.e., 2 µs) improved radar sensitivity and increased the spatial extent of the precipitation echo for radar reflectivity and all dual-polarimetric observations. The azimuthal and radial resolutions were 1.0 • and 250 m, regardless of the elevation angle. The BB was identified using QVPs of polarimetric observations at the highest elevation angle of 15.0 • .
To analyze the thermodynamic characteristics of BB, three-dimensional dry-bulb temperature (T), dew point temperature (T d ) and wet-bulb temperature (T w ) data from three-dimensional atmospheric fields (T, T d , and pressure) were generated by multi-quadric interpolation using observational data and very short-range data assimilation and prediction systems (VDAPS) [29] were used every 5 min. The horizontal resolution of three-dimensional atmospheric field data was 4 km, and the vertical resolution was 100 m at altitudes of 0-2 km and 200 m at altitudes of 2-10 km. The three-dimensional data consisted of 60 × 257 × 257 (10 km × 1024 km × 1024 km) grids. The temperature data was interpolated to the same vertical resolution of the QVPs (20 m).  To analyze the thermodynamic characteristics of BB, three-dimensional dry-bulb temperature (T), dew point temperature (Td) and wet-bulb temperature (Tw) data from three-dimensional atmospheric fields (T, Td, and pressure) were generated by multi-quadric interpolation using observational data and very short-range data assimilation and prediction systems (VDAPS) [29] were used every 5 min. The horizontal resolution of three-dimensional atmospheric field data was 4 km, and the vertical resolution was 100 m at altitudes of 0-2 km and 200 m at altitudes of 2-10 km. The three-dimensional data consisted of 60 × 257 × 257 (10 km × 1024 km × 1024 km) grids. The temperature data was interpolated to the same vertical resolution of the QVPs (20 m).

Construction of the QVPs
The QVPs were obtained by azimuthal averaging individual polarimetric observations at each range gate and for the highest elevation angle (15°). According to Ryzhkov et al. [24], the QVP at an elevation angle between 10 and 20° can reduce horizontal inhomogeneity. The QVP provides a stable vertical structure of the precipitation system for the BB identification, where ZH and ZDR increase and ρHV decreases.  The QVPs were obtained by azimuthal averaging individual polarimetric observations at each range gate and for the highest elevation angle (15 • ). According to Ryzhkov et al. [24], the QVP at an elevation angle between 10 and 20 • can reduce horizontal inhomogeneity. The QVP provides a stable vertical structure of the precipitation system for the BB identification, where Z H and Z DR increase and ρ HV decreases.
Two kinds of corrections were required for all KMA radars before constructing the QVPs of polarimetric observations as follows: (1) the calibration biases in the power-based polarimetric measurements (i.e., Z H and Z DR ) and (2) the correction of ρ HV in the low SNR area. First, the calibration biases in Z H and Z DR lead to an unsuitable identification of the BB, and the different calibration biases among radars within the network resulted in a misunderstanding of the spatial and temporal statistics of BB. In this study, the Z H bias was corrected based on the self-consistency principle between Z H and differential phase (Φ DP ) [30,31]. The Z DR bias was calibrated by comparing the empirical relationship between Z H and Z DR obtained from the drop size distribution of a two-dimensional video disdrometer Remote Sens. 2020, 12, 4061 5 of 18 (2DVD) to the Z H -Z DR distribution of polarimetric measurements. Kwon et al. [31] described these two procedures in detail.
The noise caused by a radar receiver, waveguide, and antenna affects the quality of the polarimetric observations, even if the radar is properly calibrated [32]. The ρ HV is biased in the low signal-to-noise ratio (SNR) areas. Meteorological echoes with a ρ HV less than 0.98 are observed due to the bias related to the noise. The ρ HV was corrected using the SNR as follows: where ρ HV (m) and ρ HV are the measured and corrected ρ HV , respectively. The snr (=10 0.1SNR(dB) ) is the SNR in linear units. Radar observations included non-meteorological echoes. The regions with ρ HV < 0.7, or with SNR < 10 dB, were removed to avoid contamination by non-meteorological echoes. The QVPs of polarimetric observations were constructed by obtaining the azimuthal average of Z H , Z DR , and ρ HV . As the radar beam broadens, the QVP resolution is reduced at high altitudes. In this study, QVPs were converted to high resolution by interpolating them to a vertical resolution of 20 m. The QVPs of Z H , Z DR , and ρ HV were used to analyze the characteristics of polarimetric observations at the top, peak, and bottom of the BB.

Detection of the Bright Band (BB)
Most BB detection algorithms apply the first and second derivatives of Z H (dZ/dh and d 2 Z/dh 2 ). However, local variations of Z H can make the detection of the boundary of the BB challenging. A sharp curvature of Z H is required for the detection of the top and bottom of the BB. The coordinate rotation method developed by Rico-Ramire and Cluckie [9] was used to detect the boundaries of the BB. This method is simple and has the advantage of reliably detecting the BB signature,.The Z H and Z DR increase due to the increase in the hydrometeor dielectric constants and densities, and the ρ HV decreases due to the diversity of the hydrometeor shapes, orientations, and densities. Before applying the coordinate rotation method, the ρ HV was normalized to a value ranging between 0 and 100, and then converted to a new variable (new ρ HV = 100 − 100*ρ HV ), which increased in the BB as a result of this conversion.
The procedures for BB detection using the QVPs of the Z H , Z DR , and new ρ HV were divided into the following two steps: (1) detection of the peak of the BB (BB PEAK ) and (2) detection of the top and bottom of the BB (BB TOP and BB BOTTOM ) using the coordinate rotation method. BB PEAK was identified by calculating the first derivative of polarimetric observations. The first derivative was calculated from the difference in the polarimetric observations at a height of 60 m above and below a given height. BB PEAK was obtained from the maximum polarimetric observations (Z H , Z DR , and new ρ HV ) within a height of 400 m above and below the height at which the first gradient was at maximum. The Z H , Z DR , and new ρ HV at BB PEAK should be greater than 0.0 dBZ, 0.0 dB, and 2 (=0.98), respectively. In this study, we briefly describe the coordinate rotation method. Figure 2 shows a diagram of the procedures for detecting BB TOP and BB BOTTOM from the QVP of the Z H . First, the QVP was separated by the upper and lower parts of BB PEAK relative to the line connecting BB PEAK and Z lower, upper . The original coordinate was rotated 90 • in the clockwise (counterclockwise) direction to obtain the new coordinate with h upper −Z upper (h lower −Z lower ). Then, the height of 1200 m (800 m) above (below) BB PEAK was selected to set the rotation angle ∅. The coordinate was again rotated ∅ degrees in the clockwise (counterclockwise) direction, and h" upper (h" lower ) and Z" upper (Z" lower ) are the x-axis and y-axis in the final coordinate. The maximum value in the final coordinate was defined as BB TOP (BB BOTTOM ). (ranging from −30 to 20 • C). BB PEAK is located at the Z H maxima, Z DR maxima, and ρ HV minima. BB TOP and BB BOTTOM are within a height of 500 m above and below BB PEAK . In Figure 3b,d,f, the solid and dashed lines indicate the heights where T is 0 • C and T w is 0 • C, respectively. The height of BB TOP is closer to the zero-isotherm layer (T = 0 • C) than that of BB PEAK and BB BOTTOM .    Figure 3a,c,e, the black solid line indicates BB height and the black dotted lines indicate T with a 5 °C interval (ranging from −30 to 20 °C). BBPEAK is located at the ZH maxima, ZDR maxima, and ρHV minima. BBTOP and BBBOTTOM are within a height of 500 m above and below BBPEAK. In Figure 3b,d,f, the solid and dashed lines indicate the heights where T is 0 °C and Tw is 0 °C, respectively. The height of BBTOP is closer to the zero-isotherm layer (T = 0 °C) than that of BBPEAK and BBBOTTOM.

Variables for Characterizing the BB
The definitions of the feature parameters used to characterize the BB are presented in Table 2. These parameters are related to the geometric, thermodynamic, and polarimetric properties of the BB. The heights of the BB (BBTOP, BBPEAK, and BBBOTTOM) obtained by each polarimetric observation are

Height of the BB
The monthly average H(Z H Peak) is shown in Figure 4 and Table 3. The cold (warm) color indicates that the radar is located at higher (lower) latitude. All H(Z H Peak) values in the warm season were higher than those in the cold season. The H(Z H Peak), which ranged from 4.14 to 4.71 km, on average, during the summer, showed an annual variation with a peak in July or August. The mean H (Z H Peak) in March, April, and November was less than 3.0 km, and that in September was greater than 4.0 km. The differences in H(Z H Peak) among radars during the cold seasons were greater than those during warm seasons. Overall, the H(Z H Peak) from radars at higher latitudes was lower than that from radar at lower latitudes. The H(Z H Peak) at the GSN and SSP radars, which are located at relatively low latitudes, reached 4 km in May, whereas those at the KWK, MYN, KSN, PSN, and JNI radars exceeded 4 km in June. The H(Z H Peak) at the BRI and GDK radars, which are located at relatively high altitudes, exceeded 4 km in July. than 4.0 km. The differences in H(ZH Peak) among radars during the cold seasons were greater than those during warm seasons. Overall, the H(ZH Peak) from radars at higher latitudes was lower than that from radar at lower latitudes. The H(ZH Peak) at the GSN and SSP radars, which are located at relatively low latitudes, reached 4 km in May, whereas those at the KWK, MYN, KSN, PSN, and JNI radars exceeded 4 km in June. The H(ZH Peak) at the BRI and GDK radars, which are located at relatively high altitudes, exceeded 4 km in July.    Figure 5 shows the two-dimensional frequency distribution between H(Z DR Peak) and H(Z H Peak) and between H(ρ HV Peak) and H(Z H Peak). H(Z H Peak) was 70 m and 100 m higher than H(Z DR Peak) and H(ρ HV Peak), respectively. The Z H depends on the size, refractive index, and number concentration of hydrometeors in the melting layer. When the snowflakes enter the 0 • C isotherm layer, they start to melt at the tips of the crystal branches (mainly at the bottom side). Small snowflakes melt faster than large snowflakes, which boosts the aggregation and coalescence due to the difference in fall velocity. The Z H increase below the 0 • C isotherm layer is due to the increase in the particle size (aggregation) or number density (no aggregation). The maximum of the Z H results from melting particles covered by meltwater with a large size and a high dielectric constant. The fall velocity increases as large particles turn into raindrops below Z H Peak. This process reduces the Z H due to a decrease in the number concentration. In the BB, the Z DR increases due to the oblate shape of the melting particles. The oblateness of the particles is maximized below Z H Peak (where their size is at maximum). The decrease in the Z DR below the BB is due to the break-up of large melted snowflakes, since the Z DR is not related to the number concentration. The ρ HV begins to decrease when the snowflakes and raindrops mix to a sufficient degree; therefore, it occurs at a relatively lower altitude than where the Z H starts to increase via melting [16,21]. In other words, the Z H depends on the change in size and number concentration of melting snowflakes, whereas the Z DR and ρ HV are subject to the non-spherical shape of melting snowflakes. The mean height difference between BB PEAK from the Z H and ρ HV was 100 m in this study, which is consistent with the heights of 90, 96, and 121 m obtained in previous studies [21,33,34]. BB detection based on the ρ HV can cause the underestimation of the height Remote Sens. 2020, 12, 4061 9 of 18 of the BB, as mentioned by Wolfensberger et al. [21]. According to Trömel et al. [26], the height of the maximum Z H was very close to that of the maximum backscatter differential phase (δ) and was higher than that of the minimum ρ HV . Trömel et al. [26] suggested that differences between heights should be analyzed in various climatic conditions to determine whether the aforementioned phenomenon is caused by differences in microphysical processes. since the ZDR is not related to the number concentration. The ρHV begins to decrease when the snowflakes and raindrops mix to a sufficient degree; therefore, it occurs at a relatively lower altitude than where the ZH starts to increase via melting [16,21]. In other words, the ZH depends on the change in size and number concentration of melting snowflakes, whereas the ZDR and ρHV are subject to the non-spherical shape of melting snowflakes. The mean height difference between BBPEAK from the ZH and ρHV was 100 m in this study, which is consistent with the heights of 90, 96, and 121 m obtained in previous studies [21,33,34]. BB detection based on the ρHV can cause the underestimation of the height of the BB, as mentioned by Wolfensberger et al. [21]. According to Trömel et al. [26], the height of the maximum ZH was very close to that of the maximum backscatter differential phase (δ) and was higher than that of the minimum ρHV. Trömel et al. [26] suggested that differences between heights should be analyzed in various climatic conditions to determine whether the aforementioned phenomenon is caused by differences in microphysical processes.

Geometric Structure of the BB
The heights of BBTOP, BBPEAK, and BBBOTTOM were analyzed to characterize the vertical structure of the BB. Figure 7 shows the frequency distributions among the heights of BBTOP, BBBOTTOM, and BBPEAK for ZH, ZDR, and ρHV, respectively. BBTOP was 430-460 m higher than BBPEAK, and BBBOTTOM was 340 m lower than BBPEAK on average, indicating that the structure of the BB was asymmetric. Physically, the melting particles spend more time covering the thin shell of meltwater around them, while they rapidly collapse to form a raindrop at the final stage of melting. The difference between the heights of BBTOP and BBBOTTOM is considered to be the BB thickness, and the relative position (r) is considered to be the difference between the heights of BBPEAK and BBBOTTOM to the BB thickness as expressed below: r = (H(BBPEAK) − H(BBBOTTOM))/BB thickness (2)

Geometric Structure of the BB
The heights of BB TOP , BB PEAK , and BB BOTTOM were analyzed to characterize the vertical structure of the BB. Figure 7 shows the frequency distributions among the heights of BB TOP , BB BOTTOM , and BB PEAK for Z H , Z DR , and ρ HV , respectively. BB TOP was 430-460 m higher than BB PEAK , and BB BOTTOM was 340 m lower than BB PEAK on average, indicating that the structure of the BB was asymmetric. Physically, the melting particles spend more time covering the thin shell of meltwater around them, while they rapidly collapse to form a raindrop at the final stage of melting. The difference between the heights of BB TOP and BB BOTTOM is considered to be the BB thickness, and the relative position (r) is considered to be the difference between the heights of BB PEAK and BB BOTTOM to the BB thickness as expressed below: r = (H(BB PEAK ) − H(BB BOTTOM ))/BB thickness (2) Remote Sens. 2020, 12, x 11 of 20

Figure 7. Two-dimensional frequency distributions. (a) Between H(ZH Top) and H(ZH Peak); (b) Between H(ZDR Top) and H(ZDR Peak); (c) Between H(ρHV Top) and H(ρHV Peak); (d) Between H(ZH Bottom) and H(ZH Peak); (e) Between H(ZDR Bottom) and H(ZDR Peak); and (f) between H(ρHV Bottom)
and H(ρHV Peak). Figure 8 shows box plots of the BB's thickness (left) and r (right) according to ZH Bottom at intervals of 5 dB. For the ZH and ZDR, the thicknesses of the BB increased with increasing ZH Bottom. The weak ZH in the BB represents non-aggregated snowflakes that are small in size. On the one hand, small snowflakes melt quickly and result in a thin BB. On the other hand, heavily aggregated snowflakes cause a thick and strong BB due to the fact that they need more time to completely melt than small particles. Interestingly, the BB thickness slowly increased until 20 dBZ, and rapidly increased above 20 dBZ, as shown in [34]. The BB thickness estimated using the ZH and ZDR exceeded 980 m and 870 m in the 35-40 dBZ range of ZH Bottom. The BB thickness estimated using ρHV was 800 m in the 10-15 dBZ range of ZH Bottom and 875 m in the 35-40 dBZ range of ZH Bottom. The ρHV related to the diversity of hydrometeors had a relatively constant thickness regardless of ZH at BBBOTTOM and a smaller variation as compared with the ZH and ZDR. The r was 0.45 for the ZH and ρHV regardless of ZH Bottom, and BBPEAK was closer to BBBOTTOM than BBTOP. The r of the ZDR decreased from 0.5 to 0.4 as ZH Bottom increased from the range of 10-15 dBZ to 35-40 dBZ. The non-symmetric structure of the ZDR resulted from a rapid decrease in the ZDR, due to the break-up of large melted particles at the final state of melting process [34].  The weak Z H in the BB represents non-aggregated snowflakes that are small in size. On the one hand, small snowflakes melt quickly and result in a thin BB. On the other hand, heavily aggregated snowflakes cause a thick and strong BB due to the fact that they need more time to completely melt than small particles. Interestingly, the BB thickness slowly increased until 20 dBZ, and rapidly increased above 20 dBZ, as shown in [34]. The BB thickness estimated using the Z H and Z DR exceeded 980 m and 870 m in the 35-40 dBZ range of Z H Bottom. The BB thickness estimated using ρ HV was 800 m in the 10-15 dBZ range of Z H Bottom and 875 m in the 35-40 dBZ range of Z H Bottom. The ρ HV related to the diversity of hydrometeors had a relatively constant thickness regardless of Z H at BB BOTTOM and a smaller variation as compared with the Z H and Z DR . The r was 0.45 for the Z H and ρ HV regardless of Z H Bottom, and BB PEAK was closer to BB BOTTOM than BB TOP . The r of the Z DR decreased from 0.5 to 0.4 as Z H Bottom increased from the range of 10-15 dBZ to 35-40 dBZ. The non-symmetric structure of the Z DR resulted from a rapid decrease in the Z DR , due to the break-up of large melted particles at the final state of melting process [34].  , and H(T w = 0 • C) was closer to H(Z H Peak) than H(T = 0 • C). As mentioned in Zhang et. al. [10], the BB height detected from radars can be used to improve T for the numerical weather prediction (NWP).
The distributions of T, T d , and T w at BB TOP , BB PEAK , and BB BOTTOM are shown in Figure 11, and Table 4   The distributions of T, Td, and Tw at BBTOP, BBPEAK, and BBBOTTOM are shown in Figure 11, and Table 4    The distributions of T, Td, and Tw at BBTOP, BBPEAK, and BBBOTTOM are shown in Figure 11, and Table 4 Table 4. Mean and standard deviation (STD) of temperature (T), dew point temperature (T d ), and wet-bulb temperature (T w ) at the top, peak, and bottom of the BB.

Polarimetric Observation of the BB
The distributions of polarimetric observations at BBTOP (blue), BBPEAK (black), and BBBOTTOM (red) are shown in Figure 12. ZH Peak mainly ranged between 10 and 45 dBZ, and the average ZH Peak was 27.2 dBZ. The average ZH Top (ZH Bottom) was 21.2 dBZ (17.5 dBZ). The ZH, when the ice particles completely melted, was lower than that when they began to melt. ZDR Peak was distributed between 0.0 and 3.0 dB with an average of 1.28 dB. The average values of ZDR Top and ZDR Bottom were almost similar (0.26 and 0.24 dB). The melting snowflakes were observed to be more oblate than snowflakes and raindrops. ρHV Peak was distributed between the range of 0.86 and 0.97 and was 0.92 on average.

Polarimetric Observation of the BB
The distributions of polarimetric observations at BB TOP (blue), BB PEAK (black), and BB BOTTOM (red) are shown in Figure 12. Z H Peak mainly ranged between 10 and 45 dBZ, and the average Z H Peak was 27.2 dBZ. The average Z H Top (Z H Bottom) was 21.2 dBZ (17.5 dBZ). The Z H , when the ice particles completely melted, was lower than that when they began to melt. Z DR Peak was distributed between 0.0 and 3.0 dB with an average of 1.28 dB. The average values of Z DR Top and Z DR Bottom were almost similar (0.26 and 0.24 dB). The melting snowflakes were observed to be more oblate than snowflakes and raindrops. ρ HV Peak was distributed between the range of 0.86 and 0.97 and was 0.92 on average. The average ρ HV Top and ρ HV Bottom, which are the threshold values commonly used for BB detection, were identical (0.97).
Remote Sens. 2020, 12, x 15 of 20 The average ρHV Top and ρHV Bottom, which are the threshold values commonly used for BB detection, were identical (0.97). The results were compared with those obtained under various climatic conditions. In [21] and [26], the authors used X-band radar and [27] used S-band radar to analyze the BB. [21] detected the BB using RHI data from Davos (Swiss Alps), Ardeche (South of France), Iowa (Midwestern USA), and Payerne (Swiss Plateau). [26] constructed the QVPs from a radar located in Born (Germany), while [27] constructed theirs from the WSR-88D radar in the USA. Their BB detection technique was very similar to that of [21] and [26], and [27] applied a technique based on the ρHV. According to [27], The results were compared with those obtained under various climatic conditions. In [21,26], the authors used X-band radar and [27] used S-band radar to analyze the BB. [21] detected the BB using RHI data from Davos (Swiss Alps), Ardeche (South of France), Iowa (Midwestern USA), and Payerne (Swiss Plateau). Ref. [26] constructed the QVPs from a radar located in Born (Germany), while [27] constructed theirs from the WSR-88D radar in the USA. Their BB detection technique was very similar to that of [21,26], and [27] applied a technique based on the ρ HV . According to [27], QVP allows for more accurate quantification of polarimetric observations than RHI data. Therefore, the results of this study were comparable to those of previous studies. The distribution of Z H Peak, Z DR Peak, and ρ HV Peak in Figure 12 were very similar to those in previous study. The average of Z H Peak (27.2 dBZ) was slightly lower than that in the Payerne region (29.0 dBZ), higher than that in the Iowa region (25.46 dBZ), and higher than that obtained by [27] (25.42 dBZ). The average Z DR Peak (1.28 dB) was slightly different from that in the Ardeche region (1.29 dB) and that obtained by [27] (1.13 dB). The ρ HV Peak (0.92) was higher than those obtained in Davos and Iowa (0.82), but very consistent with those obtained in the Born region (0.93) and [27] (0.94). Figure 13 shows scatterplots between Z H Peak and Z H Top/Z H Bottom, Z DR Peak and Z DR Top/Z DR Bottom, and ρ HV Peak and ρ HV Top/ρ HV Bottom. The color of the diamond symbol indicates the Z H Peak. According to [27], a high Z H in the BB represented large snowflakes enlarged via aggregation, and a low Z H mainly represented pristine ice crystals. In addition, a high number of snowflake concentrations increased the number of raindrops after passing the BB. It is apparent from Figure 13a that the mean difference between Z H Top and Z H Peak was 9.68, with a standard deviation of 2.88 dB, and the mean difference between Z H Peak and Z H Bottom was 6.00 dB with a standard deviation of 2.49 dB. Large snowflakes result in an intense BB, which leads to overestimation of rainfall at the surface. Z DR Top and Z DR Peak showed a correlation of 0.58 and a mean difference of −1.04 dB, while Z DR Peak and Z DR Bottom showed a correlation of 0.33. Large snowflakes with high Z H Bottom turn into large raindrops with high Z DR Bottom. Large snowflakes grown by aggregation (represented by high Z H Peak) turn into large raindrops (high Z DR Bottom). In other words, the size of raindrops is related to the growth process of snowflakes above the BB. The difference between ρ HV Peak and ρ HV Top (between ρ HV Peak and ρ HV Bottom) increased even more as Z H Peak increased. This results from the inhomogeneity of the hydrometeors' shape, orientation, and size within the BB since large snowflakes melt more slowly than small snowflakes. In addition, ρ HV Peak, ρ HV Top, and ρ HV Bottom with low Z H Bottom were similar (close to the 1:1 line). This mean that the ρ HV shows no distinctive signature for a weak BB. Figure 14 represents the mean profiles of the (a) Z H and (b) Z DR at the Z H Bottom classes with 5 dBZ intervals. H(Z H Peak) and H(Z DR Peak) are reference heights. The maximum Z H and Z DR were located at 0.0 km. The difference in the Z H above the BB and Z H Peak was greater than the difference in the Z H below the BB and Z H Peak. The intensity of the BB depended on Z H Bottom, and the Z H below the BB was almost constant at every class. The size and concentration of snowflakes determined the Z H structure of the BB and the rainfall intensity below the BB. The Z DR decreased above the BB as the snowflake particles smoothen when they start to melt. Large snowflakes (high Z H Bottom class) with a high axis ratio have a low Z DR above the BB. The Z DR within the BB with a high Z H Bottom class was greater than that with a low Z H Bottom class. The Z DR below the BB was larger at the high Z H Bottom class. The shape and orientation of snowflakes determined the Z DR structure of the BB.
above the BB as the snowflake particles smoothen when they start to melt. Large snowflakes (high ZH Bottom class) with a high axis ratio have a low ZDR above the BB. The ZDR within the BB with a high ZH Bottom class was greater than that with a low ZH Bottom class. The ZDR below the BB was larger at the high ZH Bottom class. The shape and orientation of snowflakes determined the ZDR structure of the BB.

Conclusions
In this study, we investigated the characteristics of BB in South Korea using QVPs from an operational S-band dual-polarization weather radar network. The BB was automatically identified based on the morphological features from the QVPs of polarimetric observations (ZH, ZDR, and ρHV)

Conclusions
In this study, we investigated the characteristics of BB in South Korea using QVPs from an operational S-band dual-polarization weather radar network. The BB was automatically identified based on the morphological features from the QVPs of polarimetric observations (Z H , Z DR , and ρ HV ) using the coordinate rotation technique proposed by [9], and their geometric, thermodynamic, and polarimetric characteristics were statistically examined. The polarimetric observations were corrected before constructing the QVPs for comparable analysis among weather radars in the network. First, the system calibration bias in power-related polarimetric observations (Z H and Z DR ) was corrected based on the self-consistency principle between power-and phase-based measurements. Second, the ρ HV was biased at low SNR due to noise effects. The precipitation echoes yielded a value that was equal to or greater than 0.98. Unfortunately, an abnormal ρ HV was observed in meteorological echoes at a low SNR. The ρ HV in low SNR areas was corrected using the SNR. Quality control was performed using the ρ HV and SNR to minimize non-meteorological echoes, and then the Z H , Z DR , and ρ HV were averaged in the azimuth direction to generate QVPs of polarimetric observations. The ρ HV was converted to a new variable to apply the same procedure for the detection of the BB. In this study, the peak of the BB (BB PEAK ) was defined as the maximum value by calculating the first gradient. The top and bottom of the BB (BB TOP and BB BOTTOM ) were identified via application of the coordinate rotation method developed by [9].
We analyzed the monthly mean height of BB PEAK for all radars in the KMA network. The heights of BB PEAK showed a seasonal variation in all radars (e.g., the highest occurred in the summer). The maximum height of BB PEAK derived from the Z H was 5 km, and the average heights varied within the range from 4.14 to 4.71 km in summer. However, they showed distinct differences depending on the location (e.g., latitude) and the altitude of the radar within the radar network, even in the same season. The heights of BB PEAK differed among the polarimetric observations. The height where melting particles had the most oblate shapes (BB PEAK derived from Z DR ) were below that where their size was at maximum (BB PEAK derived from Z H ). The inhomogeneity of the hydrometeors was also at maximum (BB PEAK derived from ρ HV ) below BB PEAK derived from Z H . The height difference of BB PEAK between the Z H and Z DR, and that between Z H and ρ HV increased with increasing Z H Bottom. The difference in heights of Z H Peak and ρ HV Peak was similar to that in previous studies under various climatic conditions.
The relative position (r) of BB PEAK (defined as the height difference between BB PEAK and BB BOTTOM to the BB thickness) and the BB thickness were calculated to analyze the geometric characteristics of the BB. The difference in heights between BB PEAK and BB TOP (BB BOTTOM ) was 430-460 m (350 m). The BB thickness represented by the Z H and Z DR tended to increase with increasing Z H Bottom. The r was less than 0.5 for all variables, and BB PEAK was close to BB BOTTOM . The r for the QVP of Z DR was close to 0.5 if Z H Bottom was low, and the r decreased to 0.4 if Z H Bottom was high. We confirmed from these results that the structure of the BB was asymmetrical and depended on Z H Bottom.
The thermodynamic characteristics were analyzed by comparing the BB heights and zero isothermal layers of dry-bulb, dew point, and wet-bulb temperatures. The zero-isotherm layer of the dry-bulb temperature was located between BB TOP and BB BOTTOM and was closer to the zero-isotherm layer of the welt-bulb temperature. BB TOP was located above the zero temperature (−1.96 to −1.03 • C), and BB PEAK was located below the zero temperature (0.73 to 1.16 • C).
The microphysical process associated with the BB was investigated by analyzing the polarimetric observations in the BB. The polarimetric observations at BB PEAK were compared with those in previous studies. The distribution of polarimetric observations was very similar, although previous studies utilized different frequencies, radar scan strategies, and BB detection techniques. The Z H at BB PEAK averaged 27.2 dB, with a difference of 9.68 (6.00) dB from that at BB TOP (BB BOTTOM ). The Z DR at BB PEAK was 1.28 dB, which was higher than the Z DR at BB TOP (0.26 dB) and BB BOTTOM (0.24 dB). The ρ HV at BB PEAK was 0.92, whereas that at BB TOP and BB BOTTOM was 0.97, which is the threshold traditionally used for the detection of the BB. The relation between polarimetric observations at BB PEAK , BB TOP , and BB BOTTOM represented the microphysical properties of the BB. The Z H at BB PEAK , BB TOP , and BB BOTTOM was highly correlated. This means that large snowflakes turn into large raindrops. It was also confirmed that the Z DR at BB BOTTOM and BB PEAK showed a positive relation with a high Z H at BB PEAK . The mean profiles of Z H and Z DR also depended on the size and concentration of the snowflakes above the BB.
In conclusion, the characteristics of BB from the QVPs of polarimetric observations were investigated in this study. The three-dimensional detection of BB and its intensity correction remain a challenge. Especially, this is more difficult in the cold season because the vertical structure of BB cannot be fully identified when they occur near the surface. The polarimetric observations above, within, and below the BB revealed in this study provide the characteristics of the BB related to microphysical processes. The results contribute by promoting an understanding of polarimetric signatures within BB and ultimately improve the performance of BB correction techniques. Furthermore, the NWP can represent the microphysical processes within BB, and the zero isothermal layer identified from radar observations can be used for NWP data assimilation.