Possibility of Solid Hydrometeor Growth Zone Identification Using Radar Spectrum Width

Ice crystals falling from the sky appear as jewels with different shapes. The International Commission on Snow and Ice has defined seven principal snow crystal types: columns, plates, needles, stellar crystals, capped columns, spatial dendrites, and irregular forms (Mason, 1971). Different classes of solid hydrometeors have been introduced and further subdivided (e.g., Kikuchi et al., 2013) based on investigations with photomicrographs (e.g., Kuroiwa et al., 1967). The hydrometeor shapes are determined by the water vapor pressure at the time of formation, which depends on the ambient temperature (T in °C). Ice crystals are mainly formed from fine dust particles in the atmosphere at T above –40°C, as well as directly from water vapor at lower T. The dendrites growth zone (DGZ) can be found at an altitude (H) corresponding to approximately –15°C, whereas the needles growth zone (NGZ) is located near an altitude corresponding to –5°C (Nakaya and Terada, 1935).

Gaining more concrete knowledge about the accumulation amount and period of winter precipitation is critical for forecasting and ensuring safety (Ralph et al., 2005; Nygaard et al., 2011). The identification and classification of hydrometeor types helps in: i) aviation safety (e.g., Williams et al., 2011; 2013), ii) understanding the mechanisms of lightnings (e.g., Ribaud et al., 2016), and iii) quantitative precipitation estimation in radar meteorology (e.g., Giangrande and Ryzhkov, 2008; Kennedy and Rutledge, 2011; Bechini et al., 2013).

Aircraft icing caused by ice crystal accretion, which is a process in which supercooled water droplets impinge and freeze on the body of an aircraft, is a major phenomenon that negatively affects aviation safety (Gent et al., 2000). Almost 58% of national aviation system delays are caused by weather problems (March-August, 2017), while aircraft icing has been the cause of 18% of all recorded commercial accidents since 1990 (O'Connor and Kearney, 2018). The icing factors that severely affect flight performance include the icing conditions (i.e., temperature, density, and liquid water contents) and atmospheric conditions (i.e., relative wind speed and flight altitude). Aircraft icing generally occurs between –20°C and 0°C because supercooled water droplets are generally formed in this T range (Politovich, 2003). This indicates that dangerous aircraft icing can occur between two growth zones, and thus, advance identification of these conditions in crucial for flight safety.

The use of weather radars by research institutes worldwide has improved the understanding of many precipitation events. In particular, measurements made using dual-polarization (dual-pol) radar provide information on the sizes, shapes, and orientations of various particles detected within the clouds, indicating that dual polarization is essential for distinguishing among the various hydrometeor types. The development of DGZs (Kennedy and Rutledge, 2011; Andrić et al., 2013; Bechini et al., 2013) can be explained using dual-pol weather radar variables through modulations of the ice crystal density and shape owing to aggregation, riming, and melting processes (Vivekanandan et al., 1994; Ryzhkov et al., 1998); and via growth of plates (Wolde and Vali, 2001; Williams et al., 2011, 2013).

The radar velocity spectrum width (σ_v) represents the irregularity in target movement within the observed resolution volume (e.g., Zhang et al., 2009). Typically, σ_v contains contributions from five spectral factors, i.e., mean wind shear (σ_s), turbulence (σ_t), antenna rate (σ_α), terminal velocities (σ_d), and orientations of hydrometeors (σ_o), among which the latter three factors (σ_α, σ_d, and σ_o) exhibit minor effects on the spectrum width (Brewster and Zrnić, 1986; Doviak and Zrnić, 2006). Previously, several researchers have studied the eddy dissipation rate (EDR) using σ_v (Knupp and Cotton, 1982; Istok and Doviak, 1986) to promote flight safety (Lee, 1977); for instance, Zhang et al. (2009) investigated the EDR from 14 cases with different weather conditions observed by the Hong Kong Terminal Doppler Weather Radar.

The particle motion is influenced by the combination of drag force and gravity in a fluid and depends on the physical conditions, i.e., size, density and cross-sectional area. Further, the cross-sectional area is determined by the particle shape (e.g., oblate, prolate, and spherical spheroid) and behavior (i.e., vibration, orientation, and tumbling). One of the particle characteristics—fall-attitudes of particles—has been studied based on field observations (e.g., Nakaya and Terada, 1935) as well as using artificial ice crystals in viscous liquids (e.g., Willmarth et al., 1964; List and Schemenauer, 1971) and theoretical simulations (e.g., Ji and Wang, 1991; Wang and Ji, 1997, 2000; Wang, 2002; Hashino et al., 2014). In recent studies, researchers have investigated the fall attitude of ice crystals based on weather radar observations (e.g., Matrosov et al., 2005). These studies explain that the particle behavior depends on its shape, implying that a particle can exhibit various motions even under the same external force. This further implies that even under the same wind conditions, σ_v may depend on the hydrometeor shape, indicating that these properties become clear when the hydrometeors are homogenized, such as solid hydrometeor growth zones in a radar bin.

In this study, the altitudes of growth zones of dendrites (DN, oblate) and needles (NE, prolate), in which particle shapes can be clearly classified, were estimated based on σ_v, which explains the irregularities in particle movements. The temperature and altitudes of the two growth zones were verified with reanalysis data. To investigate the particle motion in a fluid field according to the solid hydrometeor shapes, simulation experiments were performed to characterize the behavior of the DN, NE, and plates (PL). The PL experiment was designed with the same axis ratio as that of a DN to compare their behaviors (the microphysical processes such as aggregation and riming that occur in solid hydrometeors were not considered in the simulation experiments).

The rest of the paper is presented as follows: section 2 provides details on the instruments and methods, including the design of the simulation experiments, used for analyzing the aerodynamic properties of ice crystals as well as the hydrometeor classification scheme for winter precipitation. The results obtained from the experiments are discussed in section 3, and the conclusions of this study are presented in section 4.

The Yongin Testbed S-band dual-pol weather radar (YIT) was used for the data acquisition and analysis (Fig. 1) in this study. The YIT was manufactured by the Enterprise Electronics Corporation (EEC) and has been operated by the Weather Radar Center of the Korea Meteorological Administration (KMA) in Yongin city since July 2014. The detailed specifications are presented in Table 1.

Figure 1.  Origin of the YIT dual-pol weather radar data (red dot) obtained in South Korea.

Two winter precipitation cases (27 and 28 February 2016) in the central region of the Republic of Korea observed by the YIT were selected for this study (Fig. 2). These cases have the following common characteristics: i) the precipitation phenomena occurred for more than 3 h, ii) the vertical depth of the precipitation system exceeded 2 km, and iii) the scales of vertical wind shear at the two hydrometeor growth zones are similar, which minimizes the differences in σ_v contribution.

Figure 2.  Cumulated maximum PPI at θ = 1.1º for: (a) C1 (27 February 2016) and (b) C2 (28 February 2016). The red arrow indicates the moving direction of the precipitation system, and the grey blank area is caused by beam blockage. The range rings are centered on the YIT radar in 50-km increments.

Meteorological parameters [i.e., T and average wind speed ($ \bar{v} $)] for 16 pressure altitudes obtained from the mesoscale model (MSM) reanalysis data provided by the Japan Meteorological Agency were used to determine the growth zones of the two solid hydrometeors. The MSM reanalysis data supports 39-h forecasts for every 3-h interval from the initial time.

The following schemes were applied in this study:

i) the quasi-vertical profile (QVP) method, proposed by Ryzhkov et al. (2016), was applied to find the growth zones of the solid hydrometeors (in particular, DN and NE). The QVP method is a computationally efficient scheme in which azimuthal averaged radar measurements are expressed in the altitude-versus-time format. Using this method, it is possible to calculate the vertical profiles of the radar variables with only one sweep. Moreover, this method is particularly valuable for analyzing the hydrometeor classifications (Ryzhkov et al., 2016). To confirm the σ_v features of the DN and NE, a QVP analysis was performed at a θ of 19° for the two winter precipitation cases on 27 and 28 February 2016. In the YIT, a slant range of approximately 2.5 km from the radar is a dead zone, which corresponds to H of approximately 0.8 km from the ground in the QVP of θ = 19°. However, it is not included in the analysis area because the research target is the sub-zero level at H of more than 1 km.

ii) Because liquid- and solid-phase hydrometeors can be identified using dual-pol radar variables, many researchers have proposed hydrometeor classification algorithms (HCAs) (e.g., Ryzhkov et al., 2005b; Giangrande et al., 2008; Dolan and Rutledge, 2009; Park et al., 2009; Boodoo et al., 2010; Chandrasekar et al., 2013), which can be roughly divided into three groups: Boolean tree methods, Bayesian methods, and fuzzy logic (Ribaud et al., 2019). These supervised methods are used to identify hydrometeor types manually using theoretical or empirical relationships about dual-pol radar measurements. In this study, the HCA for winter precipitation proposed by Thompson et al. (2014) was applied to compare the DGZs, which were estimated based on σ_v. This algorithm was applied by deriving the bulk electromagnetic scattering properties of the winter precipitation at various wavelengths from X- to S-band, based on the microphysical theory and results from previously published observational studies. Further, based on the results of the scattering simulations, eight classes of hydrometeors were assumed: ice crystals (IC), DN, PL, dry aggregated snowflakes (AG), wet snow (WS), freezing/frozen raindrops (FZ), rain (RN), and not available (N/A). Notably, the temperature information is necessary to classify the liquid-phase hydrometeors.

Although radar operation and quality control (QC) are performed well by the KMA, further fundamental QC procedures were performed in this study. First, non-meteorological targets were identified and removed by a fuzzy logic algorithm suggested by Gourley et al. (2007). Then, QC for σ_v, which is the major variable in this study, was performed. Here, the σ_v that satisfies a signal-to-noise ratio (SNR) condition of SNR < 20 dB was removed because for low SNRs, σ_v exhibits a large variance (Zhang et al., 2009).

After the fundamental QC procedures were applied, the following three QC procedures for QVP were performed. The radar PPI data was ignored under two conditions: i) if the number of data points with horizontal radar reflectivities (Z_H) higher than 5 dBZ for the ith radar bin is less than 20% of the total number of azimuths, and ii) if Z_H ≤ 5 dBZ in the QVP were removed. The radar measurements depend on the radar elevation angle (θ) , and in particular, the differential reflectivity (Z_DR, in dB) is affected because the cross-sectional area of the target is determined by the radar's line of sight. Because the θ for the QVP used in this study is high, Z_DR calibration was performed as follows (Ryzhkov et al., 2005a):

The axis ratio (γ) and particle density (ρ_s) depend on the shape of the solid hydrometeor (e.g., Auer and Veal, 1970; Ishizaka, 1993; Matrosov et al., 1996; Pruppacher and Klett, 1997; Nettesheim and Wang, 2018). Moreover, ice crystals generate different fluid-flow fields according to the type of hydrometeor, which influences the microphysics of the particles, e.g., the fall velocity, collision efficiency, ventilation effect, and diffusional growth rate (Wang and Denzer, 1983). The parameters γ and ρ_s of three solid hydrometeors (DN, PL, and NE) have been studied by numerous researchers, and the corresponding reported relationships between these parameters, shown in Table 2, were applied in the present study.

The aerodynamic variables of solid hydrometeors, which determine the shape and density (such as those of PL and NE crystals), can be described with the equations proposed in the previous studies. The terminal velocity (V_T) of a particle is a key variable related to the external conditions (e.g., the acceleration due to gravity (g), atmospheric density (ρ_g), and T) and physical properties (e.g., the Reynolds number (Re), drag coefficient (C_D), sphericity (Φ), ρ_s, and D). These properties can be estimated from the following theoretical terminal velocity equation (Kunii and Levenspiel, 1969):

The equation of C_D optimized for non-spherical particles suggested by Hölzer and Sommerfeld (2008) can be expressed as:

Furthermore, the sphericity (Φ) is defined as:

where SA is the surface area of the object (mm²), and Φ is the general shape of the particle. The lengthwise sphericity (Φ_||) is defined as follows:

where A_V is the vertical cross-sectional area of the particle. The crosswise sphericity (Φ_﬩) can be expressed as follows:

where A_H is the horizontal cross-sectional area of the particle. Here, V_T is used as V_t, which is the input parameter of Re, until it converges, as:

where μ represents the dynamic viscosity. In contrast, DN (which exhibit a larger difference between the effective area (A_e) and circumscribed area (A) than PL and NE) have different effective areas depending on the particle shapes and orientations (e.g., Böhm, 1989). The fall trajectory of the ice crystals involves complex translational and rotational motions (i.e., oscillations and tumbling), which are suggested based on observation or theoretical simulation. Based on this information, the fluid-flow fields and fall patterns of four planar-type ice crystals (i.e., crystals with sector-like branches, broad branches, stellar crystals, and ordinary DN) were simulated. In this study, the relationships among the basic physical variables of these four types of DN, reported by Nettesheim and Wang (2018), were applied. First, the V_T relationships for the DN are as follows:

where d is the particle diameter (in µm). The C_D–Re relationships of the four types of DN can be expressed based on the two-term power-law relationships as:

The parameter σ_v represents the standard deviation of the radial velocities (V_R in m s^–1) of the particles in a bin, observed with a Doppler radar. Thus, σ_v can be used to determine the instabilities in the fluid field, such as those created by wind shear or turbulence in the target volume. In other words, σ_v can be described as a measure of the particle motion irregularity. Therefore, in this study, simulation experiments were performed to analyze the aerodynamic properties of solid hydrometeors according to their shapes and compare the results with those obtained through observations.

The V_R for calculating σ_v can be obtained by the following equations (Fig. 3):

Figure 3.  A schematic image for the calculation process of V_R for the target, considering the line of sight. The symbols m and a represent the particle mass and acceleration (m s^–2), respectively.

where V_M and V_F are the horizontal velocity and the falling velocity of the particle (m s⁻¹), respectively. V_N is the vector sum of V_M and V_F. V_F is the vector sum of the vertical directional external force (F_g) and the drag force of F_g (F_Dg). It could be expressed by Eq. (1), as it was assumed to be the equilibrium state condition.

When Eq. (16) is applied to Eq. (15), V_R is derived as follows:

If θ is set to be 0° and 90° in Eq. (18), V_R is calculated to be –V_M and V_F by Eq. (17), respectively. The sign determines the moving direction of the target as “+” when approaching and “−” when moving away from the observer. And if θ is in the normal direction (=90−k) of the movement direction, V_R will be 0 m s^–1 by Eq. (18).

F_Da means the drag force of the horizontal directional external force (F_a), and it is expressed as follows:

where C_DH is the drag coefficient of the particle in the horizontal movement direction.

In the simulation experiments, four known factors that contribute in σ_v (σ_s, σ_o, σ_d, σ_o, and σ_α) were considered under the following conditions: i) wind fluctuations ($v' $), acceleration in seconds, are proportional to $ \bar{v} $, and $v' $ is sufficient to exceed 20 m s^–1 for $ \stackrel{-}{v} $ ~ 20 m s^–1 (e.g., Hannesdóttir et al., 2019; Xia et al., 2021). Based on previous studies, the wind shear contribution (σ_s) was expressed as $v' $ from 4 m s^–1 to 16 m s^–1, because $ \stackrel{-}{v} $ in the DGZs was between ~20 m s^–1 and 25 m s^–1 for the research cases; ii) the standard deviation of the canting angle was set to 30° to incorporate the orientation (σ_o) of the particles into simulations; iii) all the types of solid hydrometeors were assumed to have reached V_T (σ_d); and iv) the antenna scan rate (σ_α) was matched with that of the YIT (0.04 second per degree). The particle size distribution (PSD) of ice crystals at a certain altitude cannot be estimated through ground observations, and thus, a model equation was used. The number concentration [N(D) in mm^–1 m^–3] for a volume equivalent particle diameter (D in mm), ranging from 0.5 mm to 10.0 mm, was determined. To simulate conditions that are as realistic as possible, the D in each diameter channel was randomly selected for each simulation experiment. The model equation of the PSD for ice crystals proposed by Sekhon and Srivastava (1970) is as follows:

where N₀ (in mm^–1 m^–3) and $\varLambda $ (in cm^–1) are:

The snowfall intensity (R) was assumed to be 1 mm hr^–1, and the total number concentration (N_T) under these conditions was 10³. To consider the reliability of the results, a simulation experiment on the irregularity of particle motions was performed based on a PSD that corresponds to a cumulative N_T of 10⁵, and the experiment was repeated 10 times to assess the repeatability and reproducibility of the results. Notably, V_T depends on the atmospheric density and is related to the atmospheric pressure (P in hPa) and temperature (T in ºC), which depends on the altitude. Therefore, the simulation experiments of the DN (NE) were performed at 700 hPa and –15ºC (850 hPa and –5ºC) according to the weather conditions of the DGZ (NGZ). Weather conditions in the simulation of DN were implemented in the simulation of PL.

The first case study (27 February 2016, C1) covers a time period of 5 h from 0000 local standard time (LST, LST=UTC+ 9 hours) to 0500 LST. The resulting DGZ is in the range of 2.2 < H (km) < 4.2, which corresponds to –20 < T (ºC) < –10. In addition, $ \stackrel{-}{v} $ is in the range between ~10 m s^–1 and ~25 m s^–1. The NGZ is located in the region 1.1 < H (km) < 1.4 ,with T ~ –5ºC and $ \stackrel{-}{v} $ < 10 m s^–1. The top of the Z_H columns, which are a zone with radar reflectivity (Z_H in dBZ) > 20 dBZ, is located at the center of the DGZ, which is at an altitude of approximately 3 km (at T ~ –15ºC). This corresponds to a range of 15 < Z_H (dBZ) < 20 (Fig. 4a). In contrast, the center of the Z_H column is located around the NGZ, which corresponds to an altitude of ~ –5ºC, and the maximum Z_H exceeds 25 dBZ.

Figure 4.  QVP of (a, e) Z_H, (b, f) Z_DR, (c, g) ρ_hv, and (d, h) σ_v in C1 and C2. The radar elevation angle is set to be 19°. Solid black and dashed blue curves in the background are T and $ \stackrel{-}{v} $, respectively, obtained from the MSM reanalysis data. The temperature profile is expressed down to –15ºC.

The Z_DR has apparently positive correlations with H (Fig. 4b). At lower altitudes (below 2 km), Z_DR is negative, whereas it is positive in the middle layer (above 2.5 km). In particular, the strongest Z_DR can be found in the DGZ, while a Z_DR of –0.7 dB occurs at the bottom of the NGZ. Thus, it could be explained that oblate and prolate particles are dominant in the DGZ and NGZ, respectively. In the Z_H column, ρ_hv of the DGZ is relatively low (0.98), whereas that of the NGZ is relatively high (exceeds 0.995; Fig. 4c). This is because the DN crystals exhibit a significantly diverse particle morphology compared to the NE crystals (e.g., Nettesheim and Wang, 2018). In other words, it can be confirmed that the microphysical properties of the particles, estimated using the Z_DR and ρ_hv values, correspond to the expected results for the regions of occurrence of the two types of solid hydrometeors. This implies that Z_DR and ρ_hv can be used as major indicators for identifying the hydrometeor growth zones.

The value of σ_v exceeds 1.2 m s^–1 in the DGZ, whereas it remains below 0.6 m s^–1 in the NGZ (Fig. 4d). Evidently, the large σ_v matches that observed near the –15ºC altitude. In particular a maximum σ_v of approximately 1.5 m s^–1 is observed in the DGZ at 0050 LST (i.e., where Z_DR > 1.4 dB). In addition, the NGZ (–5ºC altitude) and the low-σ_v zone (where σ_v < 0.5 m s^–1) are strongly correlated because of the positive correlation between Z_DR (particle shape) and σ_v (aerodynamic property) according to the characteristics of the two hydrometeors in their respective growth zones. The shear contribution (σ_s) is estimated in the lower elevation angle (4.2°) because it is hard to deal with the finite beam width and errors in velocity estimates to measure the shear correctly at the higher elevation angles (Doviak and Zrnić, 2006). Furthermore, there are adjacent elevations (2.8°, 6.2°) required for the wind shear estimations. The radial velocity shear in elevation (k_θ) at θ = 4.2° for the two solid hydrometeor growth zones (DGZ, NGZ) is 2.43 (2.5 < H (km) < 3.5) and 4.69 (1 < H (km) < 2) m s^–1 km^–1 within the analysis period, and the contribution ratios of σ_s were 11.7% (0.48 m s^–1) and 12.5% (0.46 m s^–1), respectively.

The second case study (C2) covers winter precipitation that occurred on 28 February 2016, i.e., one day after C1, and the meteorological conditions are similar to those of C1. The precipitation passed the YIT observation area between 1200 LST and 1830 LST, indicating that the precipitation event in C2 occurred for a longer duration compared that in C1. The upper part of the Z_H column, which is close to 15 dBZ, is located at an altitude of –15ºC (H = 3.3–3.5 km), which corresponds to the center of the DGZ (Fig. 4e). Contrarily, the center of the Z_H column is located in the NGZ at an altitude of –5ºC (H = 1.0–1.7 km), and the maximum Z_H (25 dBZ) is similar to that in C1. A maximum Z_DR of 1.5 dB is observed in the temperature range of –15 < T (ºC) < –10 in the DGZ, while the Z_DR is in the range of –0.5 < Z_DR (dB) < –0.1 at a temperature of –5ºC, which corresponds to the NGZ (Fig. 4f). The ρ_hv in the Z_H column in the DGZ is relatively small (i.e., in the range of 0.975 < ρ_hv < 0.985), whereas that in the NGZ exceeds 0.99 (Fig. 4g).

Furthermore, the DGZ and NGZ in C2 are characterized by σ_v > 1.2 m s^–1 and σ_v < 0.7 m s^–1, respectively (Fig. 4h). k_θ at θ = 4.2° for the DGZ and NGZ is 2.94 m s^–1 km^–1 and 3.65 m s^–1 km^–1, and the contribution ratio of σ_s in DGZ and NGZ were 15.2% (0.66 m s^–1) and 10.9% (0.37 m s^–1), respectively. Evidently, σ_v decreases at altitudes above 3 km (–10ºC) from 1500 LST to 1600 LST, indicating that σ_v does not exhibit a simple gradual increase with the increasing altitude. From 1500 LST to 1600 LST, the σ_v exceeds 1.2 m s^–1 in the range of 2 < H (km) < 3 (i.e., the lower limit of the DGZ), although the Z_DR is relatively low (approximately 0.2 dB). It is assumed that a Z_DR close to 0 dB (spherical shapes) is caused by microphysical processes such as aggregation or riming when the ice crystals are falling.

The existence of the DGZ and NGZ was confirmed using the radar QVP analysis and MSM reanalysis data. For further analysis, the HCA for winter precipitation, developed by Thompson et al. (2014), was applied to classify the atmospheric hydrometeors of the two hydrometeor growth zones identified by QVP. This scheme focuses on the analysis of the DGZ because the identification of NE is limited. For consistency, the hydrometeor types are expressed by the QVPs. The difference from the QVPs of the radar variables is that the hydrometeor type that occupies the largest fraction is represented by the QVP scheme. For example, there are three types of hydrometeors (DN, IC, and AG) identified in the total radar ray (Σj = 360) of the ith range gate; if their numbers are 180 (50%), 90 (25%), and 60 (17 %), respectively, then the most frequently occurring hydrometeor, i.e., DN (50%), is finally expressed on the QVP.

First, to determine the representativeness of the QVP for hydrometeors (HQVP), the number of selected bin data for all the radar rays was reviewed (Fig. 5a). The number of radar bins included in the QVP of C1 is proportional to Z_H; data bins of more than 330 (>90%) for the total radar ray are found in the area with Z_H > 20 dBZ. The structure of the HQVP can be classified into AG and IC, and a positive correlation between the AG and the number of selected radar bins is observed (Fig. 5b). Overall, the area with more than 90% of the selected bin data corresponds to AG, and the remaining area belongs to the IC (Fig. 5c). The DN line connecting the altitude at which the maximum number of DN are detected in the PPI scan for the θ of QVP is centered at an altitude corresponding to a temperature of –10ºC, which is the lower limit of the DGZ. Here, the DN line is extracted from the PPI scan obtained at an altitude of more than 1 km from the ground. Accordingly, the DN identified at an altitude of approximately 0.8 km is not included in the DN line. The mixed IC–AG area (5:5) is predominant in the upper layer with respect to the DN line, whereas the AG phase is predominant (1:9) in the lower layer.

Figure 5.  QVP of (a, d) data fraction, (b, e) primary hydrometeor types, and (c, f) percentage of primary hydrometeor type in C1 and C2. The radar elevation angle is set to be 19°. The background curves are the same as those shown in Fig. 4, and the thick blue curve represents the DN line. The light blue and light green contours in (b, e) mean IC and AG, respectively.

In C2, similarly to C1, the area in which the radar bins of more than 330 (>90%) for the total radar ray are selected corresponds to the area in which Z_H in the QVP exceeds 20 dBZ (Fig. 5d). The structure of the HQVP is classified into AG and IC, and the AG area matches well with the area containing a large number of radar bins (more than 320) (Fig. 5e). The DN line is found at a temperature of –10ºC from 1200 LST to 1400 LST and at –15 < T (ºC) < –10 between 1500 LST and 1700 LST. Furthermore, the DN line is found in the mixed IC–AG layer, as in C1. Moreover, the compositions of IC and AG in C2 are similar to those in C1 (Fig. 5f).

Before performing the simulation experiment, the aerodynamic properties were analyzed by calculating the theoretical V_T of the solid hydrometeors based on the ground-based analysis conditions (P = 1004 hPa, T = –15ºC) for comparison with V_T suggested in previous studies. Among the hydrometeors investigated in this study, the DN crystals show the slowest V_T, whereas the NE crystals show the fastest V_T (Fig. 6a). Although the PL have the same γ as the DN, their V_T is slightly larger than that of the DN, possibly because of: i) the effective-to-circumscribed area ratio and ii) the effect of particle density. In addition, the wide interquartile range of the DN is approximately 0.5 m s^–1, irrespective of D. This observed range for DN is significantly different from that of the PL. A similar feature is observed for the NE crystals; however, the deviation in their interquartile range is proportional to D.

Figure 6.  Interquartile and median values of (a) V_T–D and (b) log(C_D)–log(Re) for the three solid hydrometers [DN (red), PL (blue), and NE (green)]. Solid and dashed curves in Fig. 5a are the regression curves and V_T–D relationships of the three solid hydrometers suggested by Lee et al. (2015), respectively. Grey shaded areas are (a) V_T–D and (b) log(C_D)–log(Re) relationships of DN, suggested by Nettesheim and Wang (2018). Black solid curves in Fig. 6b are for ρ_s = 1 g cm^–3.

The terminal velocity of the DN is theoretically determined by applying the C_D–Re relationship (Nettesheim and Wang, 2018) for the DN to the theoretical V_T relationship (Kunii and Levenspiel, 1969). The resulting V_T is greater than the simulated value reported by Nettesheim and Wang (2018) for 900 hPa. The values reported by Lee et al. (2015), measured with a two-dimensional video disdrometer, are similar to the values​ calculated in the present study. However, the simulated values ​​for the PL and NE obtained in our study are larger than those observed in the previous studies. The large V_T values obtained in our study are possibly due to differences in the analysis conditions and the influence of microphysical interactions such as aggregation or riming.

The C_D–Re relationships for the solid hydrometeors are obtained using Eqs. (2–6) for PL and NE, and using Eqs. (11–14) for DN (Fig. 6b). Each of the three solid water bodies exhibit a different C_D–Re relationship. Evidently, PL and NE exhibit the highest and lowest C_D, respectively, and the log(C_D) values for PL converge at around 1, irrespective of the Re values. The C_D values of the PL are within the range of those of the DN in 1 < log(Re) < 2, whereas, the values are higher than those of the DN for log(Re) > 2. These results indicate that the three types of particles analyzed in this study have different aerodynamic properties, and these differences are thought to be caused by the drag force of a particle, which strongly depends on the V_T (i.e., physical condition of the particle and its aerodynamic features) and fluid conditions (i.e., eddy or turbulent flow).

The DGZ corresponds to the range of 2.76 < H (km) < 3.34 and 2.85 < H (km) < 3.58 for C1 and C2, respectively, and the range of the NGZ is 1.05 < H (km) < 1.7 for the two cases. In these two layers, σ_v was observed in the range of 1.1 < σ_v (m s^–1) < 1.5 and 0.4 < σ_v (m s^–1) < 0.7 at θ = 19º, respectively. First, the σ_v for observations at the five elevation angles (6.2º, 9.1º, 13.1º, 19º, and 80º) and for simulations at the elevation angles from 0º to 90º are compared to validate the simulation results (Fig. 7). The simulated σ_v shown in Fig. 7 is the average value obtained over the entire simulation duration. It can be representative because v' shows only negligible deviation in σ_v according to the simulation time, and it depends on the type of hydrometeor (Fig. 8). All three hydrometeor types, except PL, have a small deviation of 0.2–0.3 m s^–1.

Figure 7.  Simulation results of σ_v with θ for $v' $ = 4–16 m s^–1 for an interval of 2 m s^–1. Red, blue, green, and gold solid curves represent DN, PL, NE, and ND07 respectively. The circle (C1) and square (C2) symbols represent the averaged mode σ_v for θ = 6.2º. 9.1º, 13.1º, 19º, and 80º. Vertical bars are ±1 standard deviation of measured σ_v. The grey and black colored symbols correspond to the DGZ and NGZ, respectively.

Figure 8.  Simulation results of σ_v with t for v’ = 4–16 m s^–1 for an interval of 4 m s^–1 at θ = 19º. Red, blue, green, and gold solid curves represent DN, PL, NE, and ND07, respectively.

The simulated DN for v' from 4–16 m s^–1 shows a negative σ_v–θ relationship and a positive v'–σ_v relationship (Fig. 7). The value of σ_v for the DN is the largest among all the hydrometeor types analyzed in this study, and it significantly depends on v'. These features correspond to the σ_v zone identified in the QVP. In both analysis cases, the observed σ_v has a negative relationship with θ and is included in the range suggested by the simulated σ_v. The variation of σ_v for PL with θ and with v' is quite small, with a maximum of ~0.2 m s^–1 and ~0.4 m s^–1, respectively. NE shows a positive σ_v–θ relationship and a smaller σ_v than DN shows. The positive relationship of σ_v with θ means that the influence of the terminal speed is large. The σ_v for the NGZ for both case studies exhibits a pattern similar to that shown by the simulated values ​​for NE, but the values are not included in the simulated range of NE. The reason is that an existence of only pure NE is not the case in the actual NGZ. In other words, in order to be similar to the actual observation environment, the mixing condition must be considered. Therefore, an additional simulation was performed using a mixing condition in which the ratio of NE to DN was 7:3 (ND07). It can be confirmed that the NGZ had mixed conditions in which the NE is dominant since the observed σ_v ​for the NGZ at the three elevation angles were within the range of the simulated values ​​for the ND07 (here, the mixing conditions were simulated to demonstrate that the NGZ does not contain only NE).

The σ_v for all the hydrometeor types at low θ has a positive correlation with v', which is also valid at θ = 19º—the main target (Fig. 9). The interquartile range identified in the NGZ is 0.6 < σ_v (m s^–1) < 0.9, which corresponds to v' = 4–7 m s^–1 for the DN and v' = 2–9 m s^–1 for the NE. However, the DGZ, where the interquartile range is 1.1 < σ_v (m s^–1) < 1.3, is acceptable under 8 < v' (m s^–1) < 12 for the DN; however, in any case, it is not included in the range of NE. In actual meteorological phenomena, more complex wind flow mechanisms and various aggregates due to interaction processes exist; therefore, there is a possibility that the estimates of v' for σ_v presented in the simulation results might be relatively overestimated. Nevertheless, the estimated range of v' for DN (8 < v' (m s^–1) < 12) can be considered reasonable based on the interquartile range of $ \stackrel{-}{v} $ in the DGZ with v' = 14–24 m s^–1. This result indicates that the σ_v zone showing a larger σ_v (more than 1.2 m s^–1) is the DGZ, in which only the DN is dominant. In addition, although the σ_v zone, which shows a smaller σ_v of less than 0.7 m s^–1, exhibits both DGZ and NGZ characteristics, the negative Z_DR values ​​are dominant in this zone, and thus, it can be inferred that NE, being prolate particles, is dominant in the σ_v zone. Based on these simulation results, the σ_v for DN appears to be strongly dependent on v', but a narrow range of σ_v (0.5 < σ_v (m s^–1) < 0.7) can be expected in the NGZ, owing to the weak correlation of σ_v with v' in the NGZ. In addition, the σ_v in NGZ, which is composed of pure NE particles, converges to ~0.55 m s^–1, irrespective of the wind conditions.

Figure 9.  Plot of the interquartile of observed σ_v with $\bar{v}$ and the simulated σ_v at different v’ from 4 m s^–1 to 16 m s^–1 at θ = 19º. Red, blue, green, and gold solid curves and shaded areas represent the mean and standard deviation of σ_v for DN, PL, NE, and ND07, respectively. The grey and black thick (narrow) lines are the interquartile of σ_v and $\bar{v}$ for the DGZ (NGZ) in C1 and C2.

It was possible to confirm qualitatively the dominant hydrometeors and aerodynamic properties in the two hydrometeor growth zones from the simulations of σ_v. However, the physical properties of the hydrometeors in growth zones can be interpreted by correlation analysis between σ_v and the dual-pol radar variables. Therefore, the correlations of the observed σ_v with Z_DR, ρ_hv, and Z_H in the growth zones were analyzed. The Z_DR histograms for both cases are similar. The DGZ showed a distribution concentrated over the positive Z_DR centered at around 0 dB, whereas the NGZ showed negative values with a mode of –0.4 < Z_DR (dB) < –0.2 (Fig. 10a). Overall, the DGZ showed a gentle distribution with ρ_hv = 0.98 as the mode, whereas in the NGZ, it was centered at ρ_hv = 0.99 (Figs. 10b–c). Accordingly, in the DGZ, the number of ρ_hv values of more than 0.94 is significant in the area of positive Z_DR, whereas in the NGZ, ρ_hv > 0.96 is dominant in all the ranges (Fig. 10a). The Z_DR in the DGZ shows a positive correlation with σ_v, but not in the NGZ. In addition, σ_v for both growth zones exhibits a negative correlation with ρ_hv. However, Z_DR shows a negative correlation with ρ_hv in the DGZ, but a positive correlation is observed in the NGZ. Moreover, a ρ_hv smaller than 0.96 in the DGZ is dominant in the area of positive Z_DR. It can be explained by the intrinsic property of the DN crystals, which are irregular oblates in shape. The σ_v in the NGZ appears to be more correlated with ρ_hv than with Z_DR. As it was confirmed in the simulation that the value of σ_v depends on the proportion of NE, it can be explained that the proportion of NE in the NGZ has a positive correlation with ρ_hv.

Figure 10.  (a) Scatter plot of the observed σ_v –Z_DR relationship for the DGZ and NGZ. The colors on the symbol and bar plot represent the value of ρ_hv. Histograms of ρ_hv for (b) C1 and (c) C2. The symbols and bar plots with solid black outlines correspond to the DGZ.

The Z_H in the DGZ was less than 20 dBZ, which corresponds to the expected result for DN (Fig. 11). It can be explained that the ratio of NE in NGZ would be decreased because of the influx of other hydrometeor types, which have relatively low ρ_s values from the upper layer to the NGZ. Therefore, the low Z_H of 14 < Z_H (dBZ) < 18 corresponds to a low ρ_hv less than 0.94.

Figure 11.  (a) Scatter plot of the observed σ_v–Z_DR relationship for the DGZ and NGZ. The colors on the symbol and bar plot represent the value of Z_H. Histograms of Z_H for (b) C1 and (c) C2. The symbols and bar plots with solid black outlines correspond to the DGZ.

In this study, DGZs and NGZs, which are the growth zones of DN and NE crystals, were studied via simulations. The correlations between σ_v and dual-pol radar variables corresponding to the aerodynamic properties of the solid hydrometeors were investigated through case studies. In the case studies, two hydrometeor growth zones, appearing as σ_v zones, could be clearly identified (σ_v > 1.1 m s^–1 and < 0.7 m s^–1 for DGZ and NGZ, respectively), and their altitudes correspond to temperatures around –15ºC and –5ºC, respectively.

According to the simulations, DN, which is strongly dependent on $v' $, exhibited a σ_v of up to ~1.6 m s^–1, whereas for NE, a simulated σ_v of up to ~ 0.55 m s^–1 was observed because of the weak dependence of NE on $v' $. In particular, the simulated σ_v of PL was approximately five times smaller than that of DN. In addition, the simulated σ_v values did not overlap with each other, except those for lower hv' (i.e., less than 6 m s^–1). Hence, it is unlikely that the NE exhibits σ_v values that are as high as those of DN. In contrast, the σ_v value of the DN for a low $v' $ decreased, and the DN could be included in the expected σ_v range for the NE. Under these conditions, the identification of DGZs may be restricted. These differences in the observations may be due to the interaction processes such as aggregation and riming and other hydrometeors included in the growth zones but not considered in the calculations.

The major indicators, Z_DR and ρ_hv, in the two growth zones were strongly correlated with σ_v in both cases (C1 and C2). DN crystals with irregular (lower ρ_hv) oblate (positive Z_DR) shapes were observed in the DGZ, which was specified as the strong σ_v zone. On the contrary, coherently shaped (higher ρ_hv) prolate (negative Z_DR) particles were observed in the NGZ, which was the weak σ_v zone.

The possibility of estimating particle aerodynamics and characteristics of solid hydrometeors at an altitude corresponding to the temperature range of –5ºC to –15ºC will be beneficial in the field of flight safety because aircraft flying at this particular level are vulnerable to icing, which significantly affects their flight performance. In addition, atmospheric instabilities such as turbulence and wind shear near the DGZ can be identified based on the properties of DN σ_v values, which are strongly dependent on v'. Moreover, the σ_v zones estimated to be the DGZ and NGZ are evidently centered around an altitude corresponding to –15ºC and –5°C, respectively; thus, it could be found that the possibility of the atmospheric temperature estimation based on the σ_v and dual-pol radar variables.

This study was performed with a focus on winter stratiform precipitation. Therefore, analysis of growth zones in warm rain, along with other types of precipitation such as convective precipitation, is still required. Moreover, the aerodynamic properties of ice crystals in DGZs under different weather conditions need to be quantitatively evaluated to interpret the σ_v for retrieving wind flows because the σ_v of DN strongly depends on v’. Therefore, a future goal is to estimate wind speed and other wind properties using σ_v over the growth zones through various case studies.