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

Abstract

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 differential reflectivity (Z_DR) were corrected based on self-consistency. The cross-correlation coefficient (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 differences 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.

1. 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 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.

2. Materials and Methods

2.1. 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. Scan strategy of KMA operational S-band dual-polarization radars.

Radar	Elevation Angle (°)
GDK	−0.40	0.01	0.31	0.80	1.41	2.50	4.20	7.11	15.01
BRI	0.10	0.42	0.81	1.41	2.20	3.41	5.10	7.61	15.01
KWK	−0.19	0.00	0.30	0.81	1.50	2.60	4.40	7.30	15.01
MYN	−0.80	−0.39	0.01	0.41	0.91	1.91	3.60	7.00	15.01
KSN	0.00	0.30	0.70	1.30	2.10	3.21	5.00	7.61	15.01
PSN	−0.09	0.20	0.60	1.10	1.81	3.00	4.71	7.40	15.01
JNI	−0.09	0.20	0.60	1.10	1.81	3.00	4.71	7.42	15.02
SSP	0.20	0.50	1.01	1.60	2.41	3.50	5.20	7.60	15.00
GSN	0.20	0.50	1.01	1.60	2.41	3.50	5.20	7.60	15.01

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).

2.2. Methodology

2.2.1. 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 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 (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:

ρ_HV = ρ_HV^(m) (1 + 1/snr)

(1)

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.

2.2.2. Detection of the Bright Band (BB)

Most BB detection algorithms apply the first and second derivatives of Z_H (dZ/dh and d²Z/dh²). 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 $\varnothing$. The coordinate was again rotated $\varnothing$ 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).

Figure 3 shows the time series of the QVPs of the Z_H (top), Z_DR (middle), and ρ_HV (bottom), and the heights of BB_TOP (blue), BB_PEAK (black), and BB_BOTTOM (red) at an elevation angle of 15° for the BRI radar from 000 KST of 6 September 2019 to 1800 KST of 7 September 2019. In 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). 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.

2.2.3. Variables for Characterizing the BB

The definitions of the feature parameters used to characterize the BB are presented in

Table 2. Definitions of feature parameters for characterizing the BB.

Feature Parameters	Definition
H(ZH Top)	Height of ${\mathrm{BB}}_{\mathrm{TOP}}$ identified by QVP of ZH
H(ZH Peak)	Height of ${\mathrm{BB}}_{\mathrm{PEAK}}$ identified by QVP of ZH
H(ZH Bottom)	Height of ${\mathrm{BB}}_{\mathrm{BOTOM}}$ identified by QVP of ZH
H(ZDR Top)	Height of ${\mathrm{BB}}_{\mathrm{TOP}}$ identified by QVP of ZDR
H(ZDR Peak)	Height of ${\mathrm{BB}}_{\mathrm{PEAK}}$ identified by QVP of ZDR
H(ZDR Bottom)	Height of ${\mathrm{BB}}_{\mathrm{BOTTOM}}$ identified by QVP of ZDR
H(ρHV Top)	Height of ${\mathrm{BB}}_{\mathrm{TOP}}$ identified by QVP of ρHV
H(ρHV Peak)	Height of ${\mathrm{BB}}_{\mathrm{PEAK}}$ identified by QVP of ρHV
H(ρHV Bottom)	Height of ${\mathrm{BB}}_{\mathrm{BOTTOM}}$ identified by QVP of ρHV
H($\mathrm{T}$ = 0 °C)	Height where $\mathrm{T}$ is 0°
H(${\mathrm{T}}_{\mathrm{d}}$ = 0 °C)	Height where ${\mathrm{T}}_{\mathrm{d}}$ is 0°
H(${\mathrm{T}}_{\mathrm{w}}$ = 0 °C)	Height where ${\mathrm{T}}_{\mathrm{w}}$ is 0°
ZH Top	ZH value at H(ZH Top)
ZH Peak	ZH value at H(ZH Peak) (i.e., Maximum ZH in BB)
ZH Bottom	ZH value at H(ZH Bottom)
ZDR Top	ZDR value at H(ZDR Top)
ZDR Peak	ZDR value at H(ZDR Peak) (i.e., Maximum ZDR in BB)
ZDR Bottom	ZDR value at H(ZDR Bottom)
ρHV Top	ρHV value at H(ρHV Top)
ρHV Peak	ρHV value at H(ρHV Peak) (i.e., Minimum ρHV in BB)
ρHV Bottom	ρHV value at H(ρHV Bottom)

. These parameters are related to the geometric, thermodynamic, and polarimetric properties of the BB. The heights of the BB (BB_TOP, BB_PEAK, and BB_BOTTOM) obtained by each polarimetric observation are H(Z_H Top), H(Z_H Peak), H(Z_H Bottom), H(Z_DR Top), H(Z_DR Peak), H(Z_DR Bottom), H(ρ_HV Top), H(ρ_HV Peak), and H(ρ_HV Bottom). H(T = 0 °C), H(T_d = 0 °C), and H(T_w = 0 °C) are the heights where T, T_d, and T_w are 0 °C. Z_H Top, Z_H Peak, Z_H Bottom, Z_DR Top, Z_DR Peak, Z_DR Bottom, ρ_HV Top, ρ_HV Peak, and ρ_HV Bottom, which are the polarimetric observations at the heights of BB_TOP, BB_PEAK, and BB_BOTTOM were defined to analyze polarimetric characteristics in the BB.

3. Results and Discussion

3.1. Characterization of the BB

3.1.1. Height of the BB

The monthly average H(Z_H Peak) is shown in Figure 4 and

Table 3. Monthly mean height of BB_PEAK at each radar sorted in ascending order according to latitude.

Radar	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV
GDK	2.58	1.79	-	3.54	4.56	4.83	4.35	3.45	2.44
BRI	1.96	1.85	4.20	3.57	4.37	4.15	4.36	2.59	1.80
KWK	2.53	2.24	-	4.12	4.46	4.74	4.29	3.71	2.25
MYN	3.10	2.99	3.21	4.54	4.75	4.77	4.29	3.35	3.14
KSN	2.17	3.33	3.35	4.55	4.86	5.00	4.44	4.09	2.87
PSN	2.28	2.81	3.58	4.36	4.81	4.85	4.55	3.70	-
JNI	2.73	2.94	3.94	4.39	4.58	4.68	4.51	4.25	3.15
SSP	1.83	3.59	4.04	4.11	4.81	4.70	4.52	3.92	2.68
GSN	1.93	3.20	4.09	4.06	4.84	4.66	4.61	4.14	2.68
Mean	2.35	2.75	3.77	4.14	4.67	4.71	4.43	3.69	2.62

. 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.

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 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.

Figure 6 shows the difference between H(Z_H Peak) and H(Z_DR Peak) (black line), and that between H(Z_H Peak) and H(ρ_HV Peak) (red line) as a function of Z_H Bottom. The black (red) dotted line indicates no difference (the mean difference in heights shown in Figure 5). H(Z_DR Peak) was almost identical to H(Z_H Peak) in the range of 10 to 15 dBZ, whereas it was lower than 290 m than H(Z_H Peak) in the range of 35 to 40 dBZ. However, H(ρ_HV Peak) differed from H(Z_H Peak) by more than 60 m (200 m) in the range of 10 to 15 dBZ (35 to 40 dBZ). In summary, according to Figure 5 and Figure 6, H(Z_H Peak), H(Z_DR Peak), and H(ρ_HV Peak) did not match. The difference in heights of BB_PEAK increased with increasing Z_H Bottom. The larger size and higher number concentration of melting snowflakes result in more significant differences in the height of BB_PEAK based on polarimetric observations.

3.1.2. 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)

Figure 8 shows box plots of the BB’s thickness (left) and r (right) according to Z_H Bottom at intervals of 5 dB. For the Z_H and Z_DR, the thicknesses of the BB increased with increasing Z_H Bottom. 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].

3.1.3. Thermodynamic Characteristic of the BB

The seasonal variability of the height of the BB depends on the ground temperature. To further analyze the thermodynamic characteristics of the BB, we compared H (T = 0 °C), H (T_w = 0 °C), H(Z_H Top), and H(Z_H Peak) (Figure 9 and Figure 10). H(T = 0 °C) appears between H(Z_H Top) and H(Z_H Bottom), and H(T_w = 0°C) is close to H(Z_H Peak). H(Z_H Top) (H(Z_H Peak)) presented at 300 m (130 m) above (below) H(T = 0°C) on average with a standard deviation of 320 m (300 m). As compared with the NWP in [10], H(Z_H Peak) appeared at 100 m below H(T = 0 °C), on average, with a standard deviation of 386 m. As observed by Zhang et al. [10], the top height of the BB exceeded the 0 °C altitude owing to the beam spreading effect. H(T_w = 0 °C) was located 470 m below H(Z_H Top) and 30 m below H(Z_H Peak), 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. 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.

	$T$at H(ZH Bottom/Peak/Top)			$T_d$at H(ZH Bottom/Peak/Top)			$T_w$at H(ZH Bottom/Peak/Top)
MEAN	2.41	0.73	−1.33	0.64	−0.89	−2.90	1.53	−0.04	−2.03
STD	1.55	1.32	1.39	3.34	3.24	3.36	1.71	1.52	1.58
	$\mathbf{T}$at H(ZDR Bottom/Peak/Top)			$T_d$at H(ZDR Bottom/Peak/Top)			$T_w$at H(ZDR Bottom/Peak/Top)
MEAN	2.71	1.04	−1.96	0.92	−0.61	−2.63	1.82	0.25	−1.76
STD	1.63	1.47	1.42	3.39	3.31	3.38	1.79	1.65	1.60
	$\mathbf{T}$at H(ρHV Bottom/Peak/Top)			$T_d$at H(ρHV Bottom/Peak/Top)			$T_w$at H(ρHV Bottom/Peak/Top)
MEAN	2.84	1.16	−1.03	1.03	−0.49	−2.60	1.93	0.37	−1.73
STD	1.65	1.44	1.51	3.39	3.28	3.40	1.79	1.60	1.69

summarizes their mean and standard deviations. BB_TOP and BB_PEAK corresponded to temperatures ranging from −1.96 to −1.03 °C and 0.73 to 1.16 °C, respectively. The average T at BB_BOTTOM ranged from 2.41 to 2.84 °C. The average T_d at BB_TOP, BB_PEAK, and BB_BOTTOM ranged from −2.90 to −2.60 °C, from −0.89 to −0.49 °C, and from 0.64 to 1.03 °C. T_d refers to a longer tail on the left side of the distribution, with a standard deviation exceeding 3.00 °C. The average T_w at BB_TOP (BB_PEAK and BB_BOTTOM) was −2.03 to −1.73 °C (−0.04 to 0.37 °C and 1.53 to 1.93 °C).

3.2. 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).

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 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.

4. 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.