Microphysical Insights into Ice Pellet Formation Revealed by Fully Polarimetric Ka-Band Doppler Radar

Matthew R. Kumjian Department of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, Pennsylvania

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Dana M. Tobin Department of Meteorology and Atmospheric Science, The Pennsylvania State University, University Park, Pennsylvania

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Mariko Oue School of Marine and Atmospheric Sciences, Stony Brook University, State University of New York, Stony Brook, New York

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Pavlos Kollias School of Marine and Atmospheric Sciences, Stony Brook University, State University of New York, Stony Brook, and Brookhaven National Laboratory, Upton, New York

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Abstract

Fully polarimetric scanning and vertically pointing Doppler spectral data from the state-of-the-art Stony Brook University Ka-band Scanning Polarimetric Radar (KASPR) are analyzed for a long-duration case of ice pellets over central Long Island in New York from 12 February 2019. Throughout the period of ice pellets, a classic refreezing signature was present, consisting of a secondary enhancement of differential reflectivity ZDR beneath the melting layer within a region of decreasing reflectivity factor at horizontal polarization ZH and reduced copolar correlation coefficient ρhv. The KASPR radar data allow for evaluation of previously proposed hypotheses to explain the refreezing signature. It is found that, upon entering a layer of locally generated columnar ice crystals and undergoing contact nucleation, smaller raindrops preferentially refreeze into ice pellets prior to the complete freezing of larger drops. Refreezing particles exhibit deformations in shape during freezing, leading to reduced ρhv, reduced co-to-cross-polar correlation coefficient ρxh, and enhanced linear depolarization ratio, but these shape changes do not explain the ZDR signature. The presence of columnar ice crystals, though apparently crucial for instigating the refreezing process, does not contribute enough backscattered power to affect the ZDR signature, either.

Corresponding author: Matthew R. Kumjian, kumjian@psu.edu

Abstract

Fully polarimetric scanning and vertically pointing Doppler spectral data from the state-of-the-art Stony Brook University Ka-band Scanning Polarimetric Radar (KASPR) are analyzed for a long-duration case of ice pellets over central Long Island in New York from 12 February 2019. Throughout the period of ice pellets, a classic refreezing signature was present, consisting of a secondary enhancement of differential reflectivity ZDR beneath the melting layer within a region of decreasing reflectivity factor at horizontal polarization ZH and reduced copolar correlation coefficient ρhv. The KASPR radar data allow for evaluation of previously proposed hypotheses to explain the refreezing signature. It is found that, upon entering a layer of locally generated columnar ice crystals and undergoing contact nucleation, smaller raindrops preferentially refreeze into ice pellets prior to the complete freezing of larger drops. Refreezing particles exhibit deformations in shape during freezing, leading to reduced ρhv, reduced co-to-cross-polar correlation coefficient ρxh, and enhanced linear depolarization ratio, but these shape changes do not explain the ZDR signature. The presence of columnar ice crystals, though apparently crucial for instigating the refreezing process, does not contribute enough backscattered power to affect the ZDR signature, either.

Corresponding author: Matthew R. Kumjian, kumjian@psu.edu

1. Introduction

Freezing and frozen precipitation during winter storms can pose significant societal hazards. These storms can be disruptive to airline travel via aircraft icing (e.g., Bernstein et al. 1998), increase the risk of motor vehicle crashes on roadways (e.g., Black and Mote 2015; Tobin et al. 2020, manuscript submitted to Accid. Anal. Prev.), and have the potential to cause power outages and property damage or loss (e.g., Rauber et al. 2001; Call 2010). The hazard of freezing precipitation lies primarily in the ice glaze produced on exposed surfaces that can weigh down and damage tree limbs and overhead wires, or slick sidewalks and roadways for pedestrian and vehicle traffic, whereas frozen precipitation (i.e., snow, ice pellets) can be less destructive with the absence of such ice glaze (e.g., Zerr 1997).

Two of these hazardous winter precipitation types—ice pellets and freezing rain—can form in similar environments in which warm (>0°C) air aloft overlies a near-surface cold (<0°C) layer. Snow may melt fully in the warm layer, and subsequently may (i) remain as supercooled liquid and freeze on contact with the surface (which we call freezing rain), or (ii) refreeze partially or fully into ice pellets prior to reaching the surface. Snow that partially melts may also refreeze (typically as irregular ice pellets) or reach the surface as slush. Details of the lower-tropospheric thermodynamic profiles—perhaps subtle—may govern the fates of precipitation particles as they approach the ground. Such nuances create a forecasting and detection challenge (e.g., Ralph et al. 2005; Stewart et al. 2015). As such, additional means to detect or distinguish precipitation types are crucial.

Previous work has established that there is a dual-polarization radar signature associated with ice pellet formation in at least some cases (Kumjian et al. 2013; Kumjian and Schenkman 2014; Ryzhkov et al. 2016; Van Den Broeke et al. 2016; Tobin and Kumjian 2017; Nagumo et al. 2019). This hydrometeor “refreezing signature” is an enhancement of differential reflectivity ZDR beneath the melting layer, typically collocated with the coldest point in the lower-tropospheric temperature profile, and usually is found within a layer of decreasing (toward the ground) radar reflectivity factor at horizontal polarization ZH. Subtle reductions in the copolar correlation coefficient ρhv are found in this layer, as well. The aforementioned studies collectively have found the refreezing signature, when present, is a robust indicator of ice pellets. Further, Tobin and Kumjian (2017) found that a descending refreezing signature can be used to forecast or anticipate a changeover in precipitation type from ice pellets to freezing rain.

The refreezing signature has been partly explained by Kumjian et al. (2013, hereinafter K13). The reduction in ZH toward the ground is well understood as the reversion of hydrometeor relative permittivity to that of ice from liquid at microwave frequencies (i.e., opposite of the contribution to enhanced ZH in the melting layer “bright band”). However, although the large increase in fall speeds upon melting is a major contributor to the appearance of the ZH brightband bottom (e.g., Szyrmer and Zawadzki 1999; Zawadzki et al. 2005; Fabry 2015), such significant changes in hydrometeor fall speeds typically are not present in the refreezing layer. The reduction in ρhv arises because of the diversity of particle shapes and likely increased wobbling of particles as they begin to freeze. Because the diversity in particle shapes is much less in the refreezing layer (where raindrops freeze into spherical or spheroidal ice pellets) compared to in the melting layer (where irregularly shaped snow aggregates acquire liquid water as they melt), the ρhv reduction is smaller in magnitude than in the melting layer. The ZDR enhancement, however, has not been adequately explained, though several hypotheses have been put forward in the literature. These are described below, along with their limitations.

The first hypothesis to explain the ZDR enhancement is preferential refreezing of smaller raindrops (K13). If the smaller raindrops freeze first, their contribution to the overall ZH decreases, thereby increasing the relative contribution to ZH from large raindrops. This results in an increase in ZDR, analogous to evaporation (Kumjian and Ryzhkov 2010; Xie et al. 2016) or size sorting (Kumjian and Ryzhkov 2012). Once all liquid drops freeze into ice pellets, the reduced relative permittivity and increased wobbling lead to a ZDR reduction. Idealized calculations in K13 support this; however, microphysically it is inconsistent with expectations based on theory: via the immersion mode, larger drops should have a greater probability of nucleating and thus freezing, ceteris paribus (e.g., Bigg 1953; Vali 1994; Pruppacher and Klett 1997; Kumjian et al. 2012).

The second hypothesis is that pristine ice crystals, generated locally within the cold near-surface layer, contribute to increased ZDR (K13). The presence of such pristine ice crystals could help kick-start freezing via contact nucleation. Small crystals falling into a subsaturated layer and sublimating and/or being captured during contact nucleation could explain their disappearance and thus reduction of ZDR beneath the enhancement. However, the previous radar-based studies did not have evidence for such crystals, although 75% of the cases analyzed in Stewart and Crawford (1995) featured coincident observations of ice pellets and ice needles. Cortinas et al. (2004) found snow reported concurrently with ice pellets 37% of the time when ice pellets were reported in hourly surface observations across the United States and Canada.

Nagumo et al. (2019) recently argued that hydrometeor deformation or bulging during freezing leads to more extreme aspect ratios, and, prior to the onset of wobbling, this leads to increased ZDR values. Once hydrometeors begin to wobble, ZDR decreases. It is unclear from their study why wobbling would be delayed after the initial deformation of shape because the change in a hydrometeor’s cross-sectional area should directly affect its fall behavior. Further, the 2D-video disdrometer-observed aspect ratios reported in their paper are not very extreme, and no scattering calculations were performed to test whether such aspect ratio changes could explain the enhanced ZDR signature.

The main goal of this study is to evaluate the previously published hypotheses on the emergence of the polarimetric refreezing ZDR signature: (i) preferential refreezing of smaller drops (K13), (ii) the local generation of ice crystals in the near-surface cold layer (K13), and (iii) particle deformation and wobbling behavior (e.g., Nagumo et al. 2019). We evaluate these hypotheses using novel observations from a prolonged ice pellet case over central Long Island, collected with Stony Brook University’s fully polarimetric, Ka-band Scanning Polarimetric Radar (KASPR). These radar observations provide new microphysical insights into ice pellet formation and allow us to evaluate the hypotheses described above. The next section provides an overview of the ice pellet case and the radar dataset. Section 3 presents the data analysis, and section 4 is the discussion and conclusions.

2. Data and case overview

a. 12 February 2019 event

At 1200 UTC 12 February 2019, a strong (1039 hPa) surface high over southeastern Canada helped to set up cold-air damming along the eastern slopes of the Appalachian Mountains. At the same time, a strong, negatively tilted upper-level trough was approaching from the Midwest. At 1800 UTC, an associated strengthening surface low was present over Lake Michigan. This setup allowed for warm-air advection between roughly 700 and 900 hPa on the east side of the trough to override the near-surface cold, dry air present over the region, leading to a well-anticipated ice pellet event over Long Island in New York.

Figure 1 shows the evolution of the vertical profiles of temperature and dewpoint temperature over Stony Brook, on Long Island. Unfortunately, no intermediate (1800 UTC) sounding is available, so the 1800 UTC profiles come from the RAP model analysis (Benjamin et al. 2016). The profiles’ evolution reveals the formation and intensification of a warm-air layer aloft owing to the low-level warm-air advection. At 1800 UTC, the warm-air layer aloft was shallow, and the underlying cold-air features a minimum of about −7°C near 800 m AGL. Surface observations at nearby stations (not shown) suggest the 1800 UTC RAP analysis has a negative temperature bias of 1°–2°. If this negative bias is also present aloft, the minimum temperature at 1800 UTC may be closer to −5°C, which is still supportive of ice pellets (e.g., K13) and does not affect the microphysical interpretation of our analysis.

Fig. 1.
Fig. 1.

Vertical temperature (T; solid) and dewpoint temperature (Td; dashed) profiles over SBU on central Long Island at 1200 UTC 12 (green), 1800 UTC 12 (cyan), and 0000 UTC 13 (dark blue) Feb 2019. The 1200 and 0000 UTC profiles are from observed soundings in Upton, New York (KOKX), whereas the 1800 UTC profiles are from the RAP model analysis at the grid box closest to SBU. The shaded cyan region represents the radar-indicated refreezing layer at about 1800 UTC.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

The near-surface cold layer has moistened significantly in this time, in part owing to precipitation falling into the layer. By 0000 UTC, the warm nose has increased in magnitude and depth, with the surface temperature exceeding 0°C. The evolution of these profiles would suggest a transition from snow to ice pellets/freezing rain and ultimately to rain over the 12-h period.

Indeed, precipitation type observations from around the region confirm the transition from snow to ice pellets and/or freezing rain, and finally rain at most sites (Fig. 2). All human-augmented observing stations [LaGuardia Airport (LGA), Islip Airport (ISP), John F. Kennedy International Airport (JFK), and White Plains (HPN), New York] reported ice pellets (PL) for a several-hour period beginning around 1600 UTC. Nonaugmented observing stations are only capable of reporting rain (RA) and snow (SN), so “unknown precipitation” may be PL (e.g., Jones et al. 2004; Tobin and Kumjian 2017). Observations at ISP (the closest reporting station to Stony Brook University) reported PL from 1622 to 2308 UTC, with concurrent observations of freezing rain (FZRA) from 1651 to 1729 UTC, and SN from 1405 to 1654, 1800 to 1912, and 1952 to 2023 UTC. The RA began there at 2153 UTC.

Fig. 2.
Fig. 2.

Overview of precipitation type observed throughout the event. (left) The map of the observation stations of interest, with ASOS/AWOS stations in red and the locations of SBU and KOKX in black. The black frame around some of the red symbols indicates that those observing stations are human augmented. The purple wedge shows the ranges and azimuths included in the range–azimuth-defined QVP in Fig. 3, below. (right) The observed precipitation types at each station, with top-to-bottom order indicating geographic location from west to east. The bars show precipitation occurrences, with gray for snow (SN), salmon for unknown precipitation type (UP), purple for ice pellets (PL), blue for freezing rain (FZRA), and green for rain (RA).

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Data from the nearby KOKX WSR-88D may be summarized in time–height form using quasi-vertical profiles1 (QVPs; K13; Ryzhkov et al. 2016; Kumjian and Lombardo 2017). In particular, we apply a variant referred to as range- and azimuth-defined QVPs (raQVPs; Tobin and Kumjian 2017) that are shown in Fig. 3. The data come from the ranges and azimuths over Stony Brook University (SBU), as indicated by the purple wedge in Fig. 2, where range has been converted to height above the KASPR. Thus, all radar data and analyses are shown with the same vertical coordinates of height above the KASPR [or above radar level (ARL)], which is located ~2 m AGL and 48 m above sea level. The emergence of the melting layer just after 1600 UTC is consistent with surface reports of ice pellets and freezing rain around this time (cf. Fig. 2). A refreezing signature in ZDR (Fig. 3b) becomes prominent at about 1730 UTC, around the cessation time of freezing rain at ISP. The ZDR enhancement associated with refreezing starts at about 1 km ARL, but quickly descends to ~700 m ARL by 1800 UTC. Throughout the next few hours, the melting-layer height increases, implying a deepening of the warm nose associated with warm-air advection. The refreezing signature persists until at least 2200 UTC, after which precipitation becomes sparser as indicated by reduced ZH, and ISP begins reporting rain.

Fig. 3.
Fig. 3.

The raQVP from KOKX, constructed with data from the purple wedge in Fig. 2: (a) ZH, (b) ZDR, and (c) ρhv. (d) The time series of precipitation types from the nearby Islip airport human-augmented observing station (ISP). Gray, purple, blue, and green bars represent SN, PL, FZRA, and RA, respectively.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

b. Stony Brook University KASPR

The SBU KASPR is a state-of-the-art system operated from the SBU campus. Technical specifications of KASPR are provided in Table 1. Its 0.32° beamwidth and 2.2-kW peak power offer fine resolution and good sensitivity well suited for winter precipitation studies. Of particular interest for this study is its fully polarimetric capabilities; that is, by switching transmit polarizations from pulse to pulse while receiving simultaneous horizontal (H) and vertical (V) polarizations, it measures all components of the covariance matrix described in, for example, Ryzhkov (2001).

Table 1.

KASPR technical specifications.

Table 1.

In addition to the typical suite of polarimetric radar measurements, including reflectivity factor at horizontal polarization ZH, differential reflectivity ZDR, differential phase shift ΦDP, and the copolar correlation coefficient ρhv, KASPR’s fully polarimetric capabilities allows for measurements of the linear depolarization ratio (LDR), the co-to-cross-polar correlation coefficients ρxh and ρxv, and the cross-polar differential phase shifts Φxh and Φxv. Only a few studies have explored these quantities theoretically (e.g., Ryzhkov 2001; Moisseev et al. 2002) or observationally (e.g., Ryzhkov et al. 2002; Melnikov et al. 2019). Whereas ρhv decreases for larger pulse-to-pulse variations in ZDR (i.e., greater diversity of ZDR for scatterers within the radar sampling volume), ρxh decreases for larger pulse-to-pulse variations in LDR (i.e., greater diversity of LDR within the sampling volume). Thus, increases in canting angle dispersion or emergence of irregular shapes can reduce ρxh. However, cross coupling of the co- and cross-polar channels positively bias ρxh in regions of low intrinsic ρxh, such as may be expected in pure rain (e.g., Moisseev et al. 2002; Melnikov 2006). A conceptual description of these quantities is included in the appendix.

During the ice pellet event, KASPR executed a scanning strategy that consisted of a surveillance (PPI) scan at 15° elevation angle, hemispheric range–height indicator (HRHI) scans at four azimuth angles (0°, 45°, 99°, which is toward KOKX, and 135°), and a 5-min vertically pointing mode (VPT) during which Doppler spectrum data were collected. This pattern was repeated and took approximately 15 min to complete. The PPI and HRHI scans were performed with a full polarimetry mode and scan speeds of 6° and 2° s−1, respectively, to collect data with a 30-m range-gate spacing, 0.6° PPI azimuthal spacing, and 0.3° HRHI elevation spacing. The VPT mode was executed with only horizontally polarized waves transmitted and both horizontally and vertically polarized waves received. Thus, ZDR and ΦDP are unavailable for VPT scans, but LDR and ρxh are. During the VPT mode, the Doppler spectra were collected every second with a 15-m range-gate spacing and 0.04 m s−1 velocity bin spacing.

3. Observational analysis

QVPs obtained from the KASPR 15° elevation angle PPI scans are plotted in Fig. 4 for the event in height versus time. The color bars and scaling are identical to Fig. 3 for direct comparison of the KASPR QVPs to the KOKX range- and azimuth-defined QVPs. The physical sampling space of each plot varies as a result of the methodological differences between the two averaging techniques; however, both are sufficient to identify locations of the melting and refreezing layers contained with approximately 2–3 and 0.5–1 km, respectively. Note there is no “brightband” signature at Ka band owing to the impact of resonance scattering effects of large, wet snow aggregates (e.g., Kollias and Albrecht 2005). The refreezing signature is clearly evident in the KASPR QVPs as enhanced ZDR, reduced ρhv, and enhanced LDR. It is evident that the KASPR has improved resolution of these features over KOKX.

Fig. 4.
Fig. 4.

QVP from KASPR: (a) ZH, (b) ZDR, (c) ρhv, and (d) LDR. (e) The time series of precipitation types from the nearby ISP. Gray, purple, blue, and green bars represent SN, PL, FZRA, and RA, respectively.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Figure 5 shows PPIs of polarimetric fields at 1817 UTC when PL were ongoing at the radar location. ZH (Fig. 5a) shows a clear transition from ice to liquid, with larger ZH values caused by the greater relative permittivity of liquid, and again without a bright band for the reason mentioned above. Within about 3-km range of the radar, a noticeable decrease in ZH occurs as the hydrometeors freeze and the relative permittivity reverts back to that of ice. ZDR (Fig. 5b) shows a remarkable double-ring enhancement structure, with the outer ring indicating the melting layer and the inner ring indicating the refreezing layer; this is the classic refreezing signature (K13). LDR (Fig. 5c) shows an enhancement in the melting layer as nonspherical ice particles acquire liquid water via melting (increased relative permittivity) and wobble. The sudden reduction of LDR occurs when these particles collapse into spheroidal raindrops with more stable orientation and symmetric shapes. Near the surface (within 5-km radius), a subtle LDR enhancement of ~3 dB is evident, indicating some degree of scattering asymmetry, either through enhanced wobbling or the emergence of irregular shapes. Figure 5d shows the ΦDP field, which exhibits a double-ring enhancement structure similar to that of ZDR. In both cases, the local enhancements are associated with copolar backscatter differential phase δco, originating from nonspherical, wet hydrometeors large enough relative to the wavelength to cause resonance scattering. The difference is that the melting layer features large, melting aggregates, whereas the refreezing layer contains partially frozen/refreezing raindrops. The copolar correlation coefficient (Fig. 5e) shows a clear reduction in the melting layer, followed by increased values near 1.0 in the pure liquid layer. In the layer of refreezing near the surface, there is a subtle decrease in ρhv to about 0.98, indicative of more diversity of hydrometeor shapes as they either begin wobbling or acquire irregularities. Gibson and Stewart (2007) found that 9% of ice pellets observed at the ground during winter storm were aggregates of 2–5 individual ice pellets. Although such aggregates would contribute to reduced ρhv and increased LDR, the monotonically decreasing ZH, increase of ρhv, and decrease of LDR below this layer argue against such aggregates contributing significantly to the observed signatures. Last, the ρxh field (Fig. 5f) shows two reductions: one in the melting layer, and one in the refreezing layer (mirroring LDR), where the reductions indicate a diversity of LDR values owing to irregular, wet particles with some distribution of wobbling. The minimum value of ~0.3 in the pure rain region is a bias owing to some combination of cross coupling by the antenna (e.g., Ryzhkov et al. 2002; Moisseev et al. 2002) and low SNR (Melnikov 2006).

Fig. 5.
Fig. 5.

Fields of (a) ZH, (b) ZDR, (c) LDR, (d) ΦDP, (e) ρhv, and (f) ρxh taken at 15° elevation angle at 1817 UTC by KASPR.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

The PPI data are summarized as QVPs in Fig. 6. These reveal a steady increase toward the ground in ZH and ZDR in the pure rain layer2; this may be a manifestation of raindrop coalescence (Kumjian and Prat 2014) or attenuation and differential attenuation through the layer. For ~30 dBZ in rain, Matrosov (2005) suggests one-way specific attenuation is <1 dB km−1. This, and the fact that ΦDP changes through this layer are minimal, suggest that attenuation and differential attenuation are not the major contributors. The increase in ZDR within the refreezing layer begins around 900 m ARL (i.e., 3.6-km range at 15° elevation angle), whereas the decrease in ZH occurs slightly below this point. The peak in ZDR occurs between 500 and 600 m ARL, squarely in the middle of the reduction of ZH. The LDR peak is just below 400 m ARL (though LDR starts increasing at about 700 to 800 m), which is below the ZDR peak. The ΦDP trace is similar to that of ZDR, suggesting the same underlying physical processes. At Ka band, small-to-medium-sized (1–4-mm equivalent volume spherical diameter) raindrops that produce enhanced ZDR can also produce significant backscatter differential phase δco (e.g., Matrosov et al. 1999, their Fig. 3). Given that the observed δco is an integration of signals from particles in the sampling volume, it would respond similarly to ZDR, which may explain the strong similarities of the observed profiles. The ρhv minimum is found just above 400 m ARL, between the ZDR and LDR peaks, whereas the ρxh reduction occurs coincident with the increase in LDR.

Fig. 6.
Fig. 6.

QVPs from the PPIs shown in Fig. 5.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Hemispheric RHIs with KASPR provide additional microphysical insights (e.g., Kollias et al. 2014). Figure 7 shows a portion of the HRHI scan from 1813 UTC, when a well-developed refreezing signature was present. A decrease in Ze around 0.5 km ARL is evident, as before, associated with the change in relative permittivity as particles refreeze. The dual ZDR enhancements associated with melting (at just below 2.5 km ARL) and refreezing (just above 0.5 km ARL) are evident at lower antenna elevation angles, but diminish as the antenna elevation moves toward zenith pointing. This indicates that hydrometeors are either (i) isometric when viewed from below, as is true for spherical or oblate particles with their maximum dimension in the horizontal plane, on average, or (ii) irregularly shaped particles have no preferred orientation in the horizontal plane, such that on average ZDR is 0 dB (analogous to random orientations leading to 0 dB for side incidence). The HRHIs of ρhv (Fig. 7c) and LDR (Fig. 7d) provide the answer. For both HRHIs, the melting and refreezing layers are clearly visible as reduced ρhv or enhanced LDR, even when the antenna is pointing at zenith. This implies a diversity of shapes for particles when viewed from below, including some whose major axes do not align with the principal polarization directions. In other words, the particles in both the melting and refreezing layers do not have rotational symmetry about a vertical axis, but rather are irregular with their maximum dimensions in the horizontal plane having no preferred azimuthal orientation. However, the refreezing-layer signals are far weaker than those in the melting layer, indicating far less particle anisotropy.

Fig. 7.
Fig. 7.

HRHI scans from 1813 UTC. Fields shown are (a) Ze, (b) ZDR, (c) ρhv, (d) LDR, and (e) mean Doppler velocity. Data are taken along the azimuth 135°.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

As an assessment of the refreezing signature’s robustness, we extracted vertical profiles from ranges from −3 to −4 km in the HRHI and binned the data into 100-m increments. Data in each 100-m bin were averaged, and the standard deviation of data within the bin was computed. Despite more subtle magnitudes to these refreezing-layer signatures, averaged vertical profiles (and the variability about the mean) extracted from the RHI (Fig. 8) demonstrate that these features are statistically significant insomuch as the changes in the mean are greater than the variability about that mean, indicated by ±one standard deviation error bars.

Fig. 8.
Fig. 8.

Average vertical profiles extracted from HRHI scans from 1813 UTC (solid blue lines) with error bars showing ±1 standard deviation included. Vertical profiles are extracted from the range interval from −4 to −3 km in the hemispheric RHI scan from Fig. 7.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

As part of the scanning sequence, the KASPR antenna was pointed vertically and rotated for a 5-min period, during which spectral data were collected. An example of a time–height plot of the average moments during such a zenith-pointing scan are shown in Fig. 9. Figure 9a reveals fall streaks in snow and rain, and the reduction in Ze near the surface associated with refreezing. The mean Doppler velocity (Fig. 9b) also shows the clear transition from snow to rain at the melting layer as the rapid increase in fall speeds. Note our convention is negative radial velocities indicate scatterers moving toward the radar (i.e., falling). Within the refreezing layer, however, we do not see large reduction of fall speeds as is reported in some studies (e.g., Nagumo and Fujiyoshi 2015; Bukovčić et al. 2017), but rather increased variability in mean Doppler velocity presumably owing to boundary layer turbulence beneath the inversion. This is also evident from the HRHI in Fig. 7e, and in the Doppler spectrum width field (not shown). LDR shows a clear increase in the refreezing layer, coincident with a decrease in ρxh. The decrease in ρxh and increase in LDR from this vertically pointing mode indicate asymmetries in the horizontal plane (when viewed from below) during refreezing. The time-averaged profiles (Fig. 10) show these features clearly. The ±1-standard-deviation error bars indicate the robustness of the signals.

Fig. 9.
Fig. 9.

Time–height depictions from KASPR vertically pointing mode showing (a) Ze, (b) mean Doppler velocity, (c) LDR, and (d), ρxh. Data were collected over a 5-min period beginning at 1820 UTC.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Fig. 10.
Fig. 10.

Average vertical profiles from the vertically pointing KASPR scans shown in Fig. 9. Solid lines are the average, with error bars showing ±1 standard deviation overlaid. Data are averaged starting at 1820 UTC.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

The Doppler spectra collected during the vertically pointing scan offer additional microphysical insights. We tested several methods of censoring the noise from the spectra presented here. For example, we estimated the mean noise level at each height from the copolar spectral power and the standard deviation about that mean and censored any data within five standard deviations of the noise estimate (e.g., Li and Moisseev 2020). We also examined more stringent thresholds, including multiple values of copolar spectral power well above the estimated noise floor. Doing so revealed that the less stringent thresholds resulted in positively biased LDR at the edges of the spectra, despite having signals well above the noise floor. As such, we went with a stringent −70-dB threshold in copolar power (this is approximately 20 dB above the estimated noise floor). This threshold is applied to all spectral data presented herein. Instantaneous spectra at 1822:57 UTC are shown in Fig. 11. We also take a 30-s average3 of the spectra to bring out the robust features and reduce the statistical fluctuations owing to noise. Figure 12a shows the spectral reflectivity (equivalent reflectivity factor Ze as a function of radial velocity υr and height), whereas Fig. 12b is the standard deviation of this average to highlight regions where the data are more variable. Similar depictions of spectral LDR and spectral ρxh are shown in Figs. 13 and 14, respectively. Animations of these spectra are available as part of the online supplemental material.

Fig. 11.
Fig. 11.

The 1-s spectral data from a vertically pointing KASPR scan at 1822:57 UTC: (a) spectral Ze, (b) spectral LDR, and (c) spectral ρxh. The horizontal dashed lines show the domain featured in Fig. 15, below.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Fig. 12.
Fig. 12.

The 30-s average spectrograph of (a) spectral Ze and (b) its standard deviation, both in decibels, shaded according to the color bars. The horizontal dashed lines represent the domain shown in Fig. 15 below, where refreezing occurs. Data are averaged from 1821:57 to 1822:27 UTC.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Fig. 13.
Fig. 13.

As in Fig. 12, but for spectral LDR.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Fig. 14.
Fig. 14.

As in Fig. 12, but for spectral ρxh (unitless).

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Beneath the melting layer (but above the refreezing layer), several features of note appear in the instantaneous spectral Ze (Fig. 11a) as well as the averaged spectral Ze (Fig. 12). A few new-particle modes appear, including one at about 1300 m ARL associated with υr = from −1 to −2 m s−1, and one at about 750 m ARL and −0.5 m s−1. The upper new-particle mode emerges just beneath a shear layer evident in the HRHI of mean Doppler velocity (Fig. 7e) at the base of the warm air aloft, and could be new particle formation associated with turbulence4 in this layer. Figures 11b and 13a reveal low LDR values for this mode, strongly suggesting liquid drops and thus drizzle formation. In contrast, the lower secondary spectral peak originates in the near-surface cold layer and exhibits enhanced LDR values (Figs. 11 and 13a) and reduced ρxh values (Figs. 11c and 14a) suggestive of ice crystals and will be discussed in detail below.

In addition to the new spectral peaks, there is a noticeable reduction in the spectral Ze starting around 600–700 m ARL (a result of refreezing and reversion of the relative permittivity back to that of ice), with a slope such that the drop-off in Ze appears to occur at lower altitudes for faster-falling hydrometeors (particularly evident in the averaged Fig. 12a). There is also a general LDR enhancement for the entire spectrum in this layer, with larger values for the larger (faster falling) hydrometeors (Fig. 13a). Similarly, the faster-falling hydrometeors exhibit somewhat lower ρxh values in this layer than their slower-falling counterparts (Fig. 14a), which suggests more nonsphericity, wobbling, and/or shape irregularities upon freezing.

To further elucidate the microphysical processes ongoing in this refreezing signature, we averaged the spectral Ze and LDR within velocity bins in 0.5 m s−1 increments for velocity bins characteristic of raindrops (fall speeds >3 m s−1; Figs. 15a,b). This range of velocity bins is also consistent with the reduction in Ze seen in Fig. 12a. Because of the size dependence of Ze, we normalized the spectral Ze values to display the patterns more clearly on the same scale. These normalized spectral Ze profiles reveal that all fall speed bins exhibit substantial decreases in Ze toward the ground associated with refreezing, with the smaller size bins experiencing their Ze decrease at higher altitudes (Fig. 15a). Similarly, all fall speed bins exhibit LDR increases toward the ground, with larger fall speed bins revealing greater LDR magnitudes (Fig. 15b).

Fig. 15.
Fig. 15.

(a) Vertical profiles of normalized Ze by velocity bin (colored according to legend); (b) as in (a), but for LDR; (c) vertical gradient of Ze by spectral velocity bin, where negative values indicate Ze decreases toward the ground; (d) as in (c), but for LDR gradients. The data are from the 30-s averages (1821:57–1822:27 UTC) shown in Figs. 1214.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

We also compute the vertical gradients (defined toward the ground, so that positive values indicate increases toward the ground, and negative values indicate decreases toward the ground) of Ze and LDR, which are plotted as a function of size bin in Figs. 15c and 15d. These data clearly show maximum negative Ze gradient magnitudes at higher altitudes for the slower-falling hydrometeors. In other words, the smaller drops are undergoing their relative permittivity change as a result of refreezing further aloft than the larger drops. (In fact, given the negative Ze gradients and positive LDR gradients present for the largest 3 velocity bins, these largest drops likely have not yet fully frozen at the bottom of the layer shown in Fig. 15.) The increase in LDR toward the ground (positive gradient values) follow a similar trend with particle size, though less clearly than the Ze gradients. Note that these changes are within a 200–300-m layer, so they occur rapidly. The negative ∂Ze/∂z occur exactly where the enhanced ZDR peak is found within the refreezing layer (cf. Figs. 6 and 8). This and the fact that small drops are refreezing at higher altitudes provides strong observational evidence for the “preferential refreezing” hypothesis of K13 outlined above. However, it does not explain why the small drops are preferentially refreezing first. To do that, we focus our attention on the cold-layer secondary spectral peak.

Spectra for three range bins (heights above the radar) from the vertical scan starting at 1820 UTC containing this new hydrometeor mode identified at ~700 m ARL and υr > −0.5 m s−1 (hereinafter “secondary peak”) are shown in Fig. 16. The secondary peak is clearly >10 dB above the surroundings (and ~20 dB above the noise floor, not shown), indicating it is not a spurious artifact or noise. Further, the animations of these spectra (see the online supplemental material) show the peak wobbling about and responding to turbulence similarly to the rest of the spectra. This provides strong support that the secondary peak is a physical signal of a secondary mode of precipitation forming at altitudes below 1 km. When consulting the spectral LDR (Fig. 16b), we see enhanced values for this spectral feature (up to about −15 dB), well above those of the main peak, consistent with the averaged spectra shown earlier. Such values are suggestive of highly nonspherical particles like columnar ice crystals. According to the RAP-analyzed temperature profile, the temperature at the level at which this secondary spectral peak emerges is approximately −7°C (cf. Fig. 1). Ice crystals growing by vapor deposition between −3° and −8°C have columnar habits (e.g., Bailey and Hallett 2009). Columnar ice crystals with fall speeds of a few tenths of a m s−1 have maximum dimensions <1 mm (e.g., Kajikawa 1972). The observed LDR values are consistent with such columnar crystals, according to scattering calculations and observations reported in Oue et al. (2015), as well as the range of LDR values (from −14 to −18 dB) reported for columnar crystals at vertical incidence in several other studies (e.g., Matrosov 1991; Aydin and Walsh 1999; Matrosov et al. 2001; Reinking et al. 2002). Thus, the available data strongly suggest the local generation of columnar ice crystals in the near-surface cold layer.

Fig. 16.
Fig. 16.

Example 1-s Doppler spectral (a) Z and (b) LDR from the 1821:57 UTC vertically pointing scan, at ranges 715, 730, and 745 m (colored according to legend). The copolar power threshold used here is −80 dB.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Do these columnar ice crystals contribute to the observed polarimetric refreezing signature, as alternatively hypothesized in K13? Following Oue et al. (2015, 2018), we can estimate the contributions of the main precipitation spectral peak (associated with the rain/ice pellets) and from this secondary peak to the overall Ze and LDR by integrating over the power contained in subsets of the velocity bins. To do this, we define the secondary peak as the power contained between 0 and −0.61 m s−1, and the main peak from −0.85 to −9 m s−1 (these thresholds were varied by several bins in either direction and the results are not significantly different). Over the 5-min vertically pointing scan at 1820 UTC, the integrated main peak Ze is consistently between about 30 and 35 dBZ, whereas the integrated secondary peak Ze is below −10 dBZ (Fig. 17). In contrast, the main peak LDR is at the system lower limit (approximately −30 dB), whereas the secondary peak has LDR between about −15 and −21 dB. The secondary peak’s contribution to the overall Ze is thus more than 40 dB lower than the Ze contribution from the main precipitation peak. Thus, even if the columnar crystals had extremely large intrinsic ZDR, their overall contribution to Ze is so small that the total observed ZDR would be unaffected. So, although crystals are generated locally (as hypothesized by K13), they do not contribute to the observed refreezing signature in this case.

Fig. 17.
Fig. 17.

Time series of the main (blue) and secondary (orange) peak contributions to the (a) total Ze and (b) LDR, for the 5-min period beginning at 1820 UTC. The spectra were integrated at a height of 655 m ARL.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

But do these columnar crystals have any relationship to the refreezing process? Do the crystals originate from splintering during drop freezing (e.g., Koenig 1965; Pitter and Pruppacher 1973; Chisnell and Latham 1976; Lawson et al. 2015), or are the crystals generated by other means but then facilitate raindrop freezing through contact nucleation? Or are they not involved at all? For example, some studies (e.g., Hobbs 1965; Alkezweeny 1969; Czys 1989) have proposed that collisions between supercooled liquid drops may initiate freezing, which may be related to a deformation or distortion of the drop’s liquid–air interface upon colliding with another (Fukuta 1975; Yang et al. 2018, 2019).

To help provide insight into this “chicken or the egg” type question, we construct time–height depictions of the main and secondary (ice crystal) peak Ze and LDR (Fig. 18). The secondary peak’s −19-dBZ Ze contour (a conservative estimate of its emergence level from Fig. 18b) is overlaid on all panels for reference. In Fig. 18a, the main peak Ze features a significant decrease toward the ground centered at about 500 m AGL. The secondary peak’s −19-dBZ contour is located well above the sharpest gradient in main peak’s Ze. This implies that the columnar ice crystals appear several hundred meters above the greatest change in relative permittivity of the larger hydrometeors undergoing refreezing. When consulting the main peak’s LDR (Fig. 18c), we see clearly that appreciable increases in LDR occur well below this −19-dBZ contour, as well.5 This means that deformations or irregularities in the refreezing hydrometeors occur well below where the columnar crystals appear. On the other hand, the main peak’s enhanced LDR field follows very closely the −19-dBZ contour, suggesting that the same physical mechanisms are involved.

Fig. 18.
Fig. 18.

Time–height depictions of the (a) main peak Ze (dBZ), (b) secondary peak Ze (dB), (c) main peak LDR (dB), and (d) secondary peak LDR (dB). In each panel, the −19-dB contour of the secondary peak Ze is overlaid for reference. Data are shown as seconds from 1820:14 UTC.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

So, to address the chicken-or-the-egg question: if the columnar crystals were a result of the refreezing raindrops splintering, such splintering would have to occur prior to significant amounts of liquid freezing (responsible for the relative permittivity decrease) and prior to the appearance of any significant deformities or irregularities in the freezing drop shapes. On the other hand, the hypothesis of locally generated ice crystals jump-starting the freezing process through contact nucleation is supported by these observations. Contact nucleation would initiate the freezing process, which would progress for some time (~10 s of seconds for the larger drops; e.g., Kumjian et al. 2012) before the raindrops completely freeze, creating some vertical separation between the level of nucleation and the subsequent observable response in the radar variables. The presence of columnar ice crystals prior to raindrop refreezing also would help explain the preferential refreezing of smaller drops first—as these are unlikely to nucleate first owing to immersion freezing (e.g., Pruppacher and Klett 1997). Rather, contact nucleation could instigate the process at more or less the same time for all raindrops falling into the layer, but the longer time scale for freezing larger drops (e.g., Pruppacher and Klett 1997; Kumjian et al. 2012) means they would completely freeze at lower altitudes than smaller drops. Thus, the smaller drops finish freezing prior to the larger drops, leading to the observed ZDR enhancement associated with the classic refreezing signature.

What is the origin of these small columnar ice crystals? The Stony Brook University radar observatory also has a Vaisala ceilometer and a Doppler lidar. Observations from these during the event (Fig. 19) reveal signals of several liquid layers, including the primary cloud base (~400–500 m AGL), as well as another in the ~900–1000 m AGL layer. This latter signal indicates supercooled liquid droplets just above the layer where KASPR observes the secondary spectral peak associated with the columnar ice crystals. We speculate that the presence of these liquid cloud droplets may have facilitated ice nucleation, though the exact mechanism is unknown (particularly given the relatively high temperature; see, e.g., Kanji et al. 2017, and references therein).

Fig. 19.
Fig. 19.

SBU ceilometer and lidar data from the event. (a) Time–height depiction of ceilometer backscatter, (b) vertical profile of the mode values of ceilometer backscatter for the 5-min period indicated by the black arrows in (a) and (c); (c) time–height depiction of the Doppler lidar backscatter; (d) vertical profile of mode values of the lidar backscatter for the 5-min period indicated by the black arrows in (a) and (c). The arrows indicate the time period shown in Figs. 17 and 18.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

4. Summary and discussion

A long-duration ice pellet event occurred over Long Island on 12 February 2019 and was well-sampled by the Stony Brook University Ka-band Scanning Polarimetric Radar. The KASPR observations revealed a classic hydrometeor refreezing signature first described by K13, but the versatile scanning, Doppler spectral, and fully polarimetric capabilities of KASPR provided novel insights into the origins and microphysical processes leading to the hydrometeor refreezing signature. This new information allows us to evaluate published hypotheses on the refreezing signature’s origin, namely preferential refreezing of smaller drops (K13), local generation of ice crystals in the near-surface cold layer (K13), and particle shape deformations/bulging and changes to the orientation distributions during freezing (Nagumo et al. 2019).

PPI scans of the refreezing signature at Ka band show similarities to previous signatures documented at S and C bands; namely, an enhanced ZDR coincident with a reduction in ZH within the near-surface cold layer, as well as reduced ρhv. For the first time, with KASPR we also find the refreezing layer (at least in this case) characterized by low ρxh, enhanced LDR, and enhanced δco. The close correspondence of ZDR and δco features strongly suggests the same underlying physics is responsible for both. Preferential refreezing of smaller raindrops first would reduce their contribution to the total ZH and thus increase the relative contribution of larger drops with larger intrinsic ZDR and δco at Ka band. Owing to their small size and low relative permittivity, ice crystals would not produce appreciable δco at Ka band. Similarly, deformed ice pellets could be resonance scatterers at Ka band, but owing to the low imaginary part of the relative permittivity of ice at this wavelength, δco is negligibly small.

Hemispheric RHIs reveal the enhanced LDR and reduced ρhv and ρxh signals at vertical incidence in the refreezing layer, suggesting the hydrometeor asymmetries introduced during freezing are not favored in any particular plane. Randomly oriented deformities in the particle shape owing to freezing/bulging could explain the signatures. However, LDR “recovers” to some extent in the QVPs beneath the refreezing layer, after total freezing. This strongly suggests that the presence of liquid in partially frozen particles is the leading contributor to amplifying the asymmetries, whether viewed at side incidence (PPIs) or vertical incidence (vertically pointing scans and/or hemispheric RHI scans). Freezing by contact nucleation would initiate ice at some point or points on the particle surface, which would subsequently spread around the outside and then inward (e.g., Pruppacher and Klett 1997). This would lead to asymmetric liquid regions in the otherwise spherical/spheroidal particle, which would more substantially enhance LDR than deformities (e.g., bulges, spikes, or other irregular shapes) in a completely frozen ice particle owing to the difference in relative permittivity between liquid and ice. Such deformities in a partially frozen particle could also lead to asymmetric shapes of the liquid portion, which could also enhance the LDR.

The Doppler spectra from KASPR’s vertically pointing scans confirm that the small drops undergo freezing first, providing strong evidence for the “preferential refreezing of smaller drops” hypothesis. As shown by idealized calculations in K13, such preferential refreezing of small drops will lead to a ZDR enhancement similar to that observed. The KASPR spectral data also show that the largest negative Ze gradients (implying decreases toward the ground) and positive LDR gradients (implying increases toward the ground) occur at progressively lower heights for faster-falling and presumably larger particles. The spectra also reveal the presence of small columnar ice crystals emerging just above the refreezing layer; however, their overall contribution to ZH (and thus ZDR) is negligible. The crystals appear above the level where significant changes to larger hydrometeors’ relative permittivities or shapes, strongly suggesting they do not result from splintering during freezing. Rather, if generated locally by some other means, they could facilitate rapid refreezing through contact nucleation. The origin of these columnar crystals, however, remains a mystery. Additional cases should be analyzed to understand the prevalence of these small ice crystals and to determine their importance for ice pellet formation in general.

In summary, KASPR observations provided substantial microphysical insights into ice pellet formation for the 12 February 2019 event. The data provide strong support for the hypothesis that preferential refreezing of smaller drops leads to the observed dual-polarization refreezing signature (particularly in ZDR). In this case, small ice crystals generated locally appear to have contributed to nucleation of all drops falling into the layer via contact nucleation. The smaller fall speeds and shorter times to complete freezing for the smallest drops allowed them to completely freeze at altitudes above the total freezing of larger drops, leading to the observed refreezing signature. The crystals did not provide sufficient ZH to affect the observed ZDR enhancement. Further, there is no need to implicate complicated orientation behaviors of bulged particles to explain the ZDR signature (Nagumo et al. 2019), though asymmetries arising during the freezing process (whether bulges or asymmetric liquid regions within a freezing particle) are likely given the signals in LDR, ρhv, and ρxh. The ZDR enhancement from preferential refreezing of small drops may be augmented if the liquid portion within refreezing particles deforms considerably (i.e., to axis ratios more extreme than the particle itself and/or those of equivalent-sized raindrops) as a result of bulging or asymmetric freezing, and the particle orientation does not change appreciably during this process. The analysis presented here is from a single case, so clearly more well-documented events are needed to determine the generality of the findings from this study. The advent of advanced, fully polarimetric Doppler observations such as those available from KASPR will improve our understanding of microphysical processes, especially the inherent complexities of transitional winter precipitation.

Acknowledgments

Authors Kollias and Oue acknowledge support by the National Science Foundation Grant AGS-1841215. We thank the three anonymous reviewers for their detailed and thoughtful comments and suggestions that considerably improved the paper.

APPENDIX

Physical Interpretation of the Fully Polarimetric Radar Variables

The conventional dual-polarization radar variables are described fully in texts (e.g., Doviak and Zrnić 1993; Bringi and Chandrasekar 2001; Zhang 2016; Ryzhkov and Zrnić 2019) and in the literature (e.g., Zrnić and Ryzhkov 1999; Ryzhkov et al. 2005; Kumjian 2013a,b,c, 2018). In contrast, the fully polarimetric radar variables have received less attention. These quantities include the co-to-cross-polar correlation coefficients ρxh and ρxv, the cross-polar differential phase shifts ΦXH and ΦXV, and the backscatter depolarization phase δcr. Only a few studies have explored these correlation coefficients or phase shifts theoretically (Ryzhkov 2001; Moisseev et al. 2002; Melnikov 2006) or observationally (Ryzhkov et al. 2002; Melnikov et al. 2019). Here, we provide a conceptual description of LDR and ρxh with an emphasis on their physical interpretation. We do so by comparison with the more familiar copolar quantities ZDR and ρhv.

a. ZDR and LDR

The ZDR is a measure of the difference in ZH and ZV (in logarithmic scale) and provides information on hydrometeor shapes (Seliga and Bringi 1976). For particles with more mass aligned in the horizontal than in the vertical, ZH > ZV, and thus ZDR > 0 dB. For particles with more mass aligned in the vertical than in the horizontal, ZH < ZV, and thus ZDR < 0 dB. (These rules no longer apply when particles are large relative to the radar wavelength.) This happens because near-field interactions (e.g., Kumjian 2018; Schrom and Kumjian 2018) between the tiny radiating volumes in a particle reinforce each other’s internal electric field along the incident polarization direction, enhancing the backscattering magnitude, whereas they weaken each other’s internal electric field in the direction orthogonal to the incident polarization (within the polarization plane), thereby reducing the backscattering magnitude. So, for a hydrometeor with its major axis in the horizontal, its backscatter is enhanced at horizontal polarization and reduced at vertical polarization (i.e., ZH > ZV). The strength of these near-field interactions increases with increasing relative permittivity εr and/or increases in the mass density within the particle’s bounding volume. Thus, for a given nonspherical particle shape, ZDR is larger for liquid than for solid ice (e.g., ice pellet), which is larger than for sparsely packed ice (e.g., graupel or snow aggregate).

LDR is the difference in radar reflectivity factors between the cross-polarized component (i.e., transmit radiation at one polarization and receive at the orthogonal polarization) and the copolarized component (i.e., transmit and receive radiation at the same polarization). For a hydrometeor to depolarize the incident radiation, it must be (i) nonspherical and (ii) have some asymmetry in its distribution of mass relative to the polarization axes. The second factor is required because particle symmetry about the polarization axes leads to cancellation of the near-field interactions that lead to the depolarization (e.g., Kumjian 2018). For example, spheroids can only depolarize the incident radiation their major axis does not align with the horizontal or vertical polarization directions. Irregular particles that have asymmetries, such as bulges or lobes, also lead to depolarization (e.g., Jiang et al. 2019). As with ZDR, near-field interactions are stronger for larger εr and/or closer packing of the particle’s mass. If there is no depolarization, the intrinsic LDR is −∞ dB. However, in real radar systems, some of the copolar signal is leaked into the cross-polar channel (i.e., there is cross coupling). Thus, there is always a measured finite LDR signal (the “LDR limit”), which for KASPR is about −30 dB. The impacts of cross coupling are further described below.

ZDR and LDR are compared in Fig. A1. In the top row, all particles are spheres, so ZDR = 0 dB and LDR = −∞ dB, regardless of the particles’ εr. In the second row, the particles are oblate spheroids perfectly oriented with their maximum dimension in the horizontal. Thus, ZDR is maximized for the liquid particles (owing to the larger εr and thus larger near-field interactions) and decreases from left to right in the figure. LDR is still equal to −∞ dB for each population in this row, because the particles are well oriented and have no asymmetries about the polarization axes. In the third row, the same oblate particles now have some slight dispersion of orientation angles. This leads to a reduction in ZDR for all three populations, although ZDR still decreases from left to right. Now, however, the canted hydrometeors depolarize the signal, so LDR > −∞ dB for all populations, and decreases from left to right owing to the decreasing εr. The bottom row shows the same particle populations, but with further increased dispersion of orientation angles. This drives ZDR down closer to 0 dB but increases LDR further. LDR is maximized for the liquid particles and decreases from left to right in the figure toward the lower εr.

Fig. A1.
Fig. A1.

Conceptual diagram comparing ZDR and LDR for different populations of particles. In the top row, the particles are all spheres. In the other rows, particles are oblate spheroids, but with increasing dispersion of orientation angles for each row. Shown are (left) liquid particles, (center) solid ice particles, and (right) “low density” ice particles (i.e., particles like graupel or snow aggregates that have some air pockets within the volume bounded by the particle).

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

b. Conceptual model for copolar and co-to-cross-polar correlation coefficients

In practice, the radar probes a volume of the atmosphere using several pulses, between which the hydrometeors “reshuffle” their respective positions (e.g., Doviak and Zrnić 1993). Because the radar pulse volume is much wider than a single wavelength, the phases of the waves scattered by each hydrometeor add together in complicated ways, leading to constructive and destructive interference of these scattered waves [for an excellent visualization, see Fabry (2015)]. As such, at certain instances, we may think of certain hydrometeors being “invisible” to the radar (because their signals have destructively interfered with others and thus cancelled out), whereas others are “visible.” From pulse to pulse, the reshuffling of hydrometeors means that the particles that are “visible” versus “invisible” will change. A sufficiently large number of pulses, then, will represent the ensemble average of particles in the sampling volume.

Consider a population of spherical particles of varying sizes within a radar sampling volume (Fig. A2). At the three times shown, different particles are “faded” out of view (i.e., do not contribute significantly to the overall received signal) because of reshuffling. Thus, ZH and ZV both fluctuate in time. However, because the particles are spheres, they scatter identically at horizontal and vertical polarizations, so ZH and ZV fluctuate identically. Thus, ZDR = 0 dB and is constant in time. Because there is no diversity of shapes or ZDR in the sample volume (i.e., the ZH and ZV signals are perfectly correlated), the ρhv is unity. The same reasoning applies even if the particles were nonspherical but the same shape (i.e., some nonzero ZDR but constant in time).

Fig. A2.
Fig. A2.

(top) Populations of spherical particles at three different times, with fading of the color showing how different particles contribute more or less significantly to the overall received signal. Also shown are the time series of (bottom left) ZH (green filled circles and solid line) and ZV (blue open squares and dashed line) and (bottom right) ZDR (orange circles and line).

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Figure A3 is the same concept, but with nonspherical particles of different shapes and sizes. Now, ZH and ZV fluctuate differently (i.e., they are not perfectly correlated) because the particles fading “into” and “out of” view are of different shapes. This causes the ZDR of each pulse to fluctuate, signaling a diversity of ZDR within the sampling volume and thus a decrease in ρhv.

Fig. A3.
Fig. A3.

Populations of nonspherical particles at three different times, with fading showing how different particles contribute more or less significantly to the overall received signal. Also shown are the time series of (bottom left) ZH (green filled circles and solid line) and ZV (blue open squares and dashed line) and (bottom right) ZDR (orange circles and line).

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Now, we consider again the same population of nonspherical particles (Fig. A4). This time, we consider the copolar ZH, and the cross-polar component ZVH (transmit H, receive V). Because all of our particles are spheroidal and perfectly aligned with their major axes along the polarization axes, there is no depolarization. Thus, LDR = −∞ dB, and, intrinsically, ρxh = 0. However, because of cross coupling, there is a cross-polar signal (faded green line in the ZH time series) that is perfectly correlated with the received copolar signal because it comes entirely from the copolar signal. Thus, the LDR is at the system limit and constant from pulse to pulse. Because there is no LDR diversity, ρxh = 1.0. (In practice, ρxh < 1.0 even for purely cross-coupled signals because the copolar and cross-polar antenna beam patterns are not identical. As such, they illuminate different volumes of particles and thus have decorrelated signals (e.g., Moisseev et al. 2002). This is analogous to why ρhv is never identically equal to 1.0, though typically the horizontal and vertical polarization beam patterns are more closely matched than the copolar and cross-polar beam patterns, so ρhv can be very close to 1.0 with high-quality antennas.)

Fig. A4.
Fig. A4.

Populations of nonspherical particles at three different times, with fading showing how different particles contribute more or less significantly to the overall received signal. Also shown are the time series of (bottom left) ZH (green line and filled circles) and ZVH (blue dashed line and open squares) and (bottom right) LDR (yellow circles and line), with the system lower limit indicated by the gray dashed line. The faded green line on the bottom left indicates cross coupling from the copolar channel into the cross-polar channel.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

Last, we consider the same population yet again, but now the particles have some dispersion of orientation angles (Fig. A5). Because their major axes are not aligned with the polarization axes, depolarization occurs. The amount of depolarization depends on which particles are “in view” and how they are wobbling. Thus, LDR fluctuates from pulse to pulse (but never goes below the system limit). This “diversity of LDR” in from pulse to pulse indicates the co- and cross-polar signals are not perfectly correlated, so ρxh is low. In practice, it is reduced from its “background” value in nondepolarizing media (itself a result of cross coupling and antenna imperfections described above).

Fig. A5.
Fig. A5.

As in Fig. A4, but for a dispersion of canting angles. Cross coupling is not shown for clarity.

Citation: Journal of Applied Meteorology and Climatology 59, 10; 10.1175/JAMC-D-20-0054.1

c. Applications to real data

Figures 9d and 10d in the main text show data taken at vertical incidence. We see that LDR is somewhat larger in dry snow aggregates (~−27 dB) just above the melting-layer top than in the rain region (−30 dB), despite the much larger εr of liquid. This is for three reasons. First, aggregates are not spheroids, better represented by prolate triaxial ellipsoids (e.g., Dunnavan et al. 2019). In contrast, rain is approximately spheroidal, and thus appears isotropic when viewed from below owing to their vertically oriented (on average) rotational symmetry axis. Second, snow aggregates have a larger dispersion of orientation angles than raindrops (e.g., Dunnavan 2020, manuscript submitted to J. Atmos. Sci.). The measured ρxh in rain is greater than in aggregates because the intrinsic LDR is lower in rain, and thus cross coupling dominates the signal and leads to a positive bias (e.g., Moisseev et al. 2002; Melnikov 2006). Third, large snow aggregates can lead to resonance scattering effects, which enhance LDR particularly at shorter radar wavelengths (e.g., Tyynelä et al. 2011).

In the melting layer, LDR is strongly enhanced and ρxh decreased. These are both explained by the highly nonspherical and chaotically oriented particles acquiring liquid (and thus a significant increase in their εr). Analogously to the melting-layer signature in ρhv, the increase in εr augments the near-field interactions and thus the signals in all polarimetric radar quantities. Ryzhkov et al. (2002) attribute locally lower values of ρxh at side incidence in the melting layer to increased snowflake wobbling. However, dry snow also wobbles, but exhibits larger ρxh. Thus, increased εr of particles beginning to melt exaggerates the diversity of LDR (much like ρhv minima deepen when particles are wet). Also, diversity of δcr for wet, nonspherical, non-Rayleigh particles lowers ρxh, much like diversity of δco decreases ρhv.

From the rain region to the refreezing layer (RFL), we observe an LDR increase and ρxh decrease in both the cases of vertical and side incidence, despite the decreasing particle εr as they undergo freezing. Here, increases in particle wobbling and/or increases in particle shape irregularities/asymmetries must be occurring. Also, note both LDR and ρxh in snow aggregates and in the RFL are similar. However, larger near-field interactions are expected for solid ice particles (ice pellets) compared to fluffier snow aggregates or graupel. This indicates particles in the RFL feature fewer asymmetries/irregular shapes and/or less wobbling than aggregates (but more than in rain). In other words, the ice pellets or refreezing particles are not spheroids, and have some asymmetries.

REFERENCES

  • Alkezweeny, A., 1969: Freezing of supercooled water droplets due to collision. J. Appl. Meteor., 8, 994995, https://doi.org/10.1175/1520-0450(1969)008<0994:FOSWDD>2.0.CO;2.

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