1. Introduction
Particle identification using radars with dual-polarization capability has been investigated for several decades. Seliga and Bringi (1976) first interpreted measurements of the radar reflectivity factor at horizontal polarization ZHH (see appendix A for a complete list of variables) and differential reflectivity ZDR using theoretical calculations of the electromagnetic scattering by spheroids (Gans 1912) to relate the sizes and shapes of raindrops to rainfall rate. Hall et al. (1980), Aydin et al. (1986), and Bringi et al. (1986) subsequently attempted to interpret hydrometeor type by using dual-polarization techniques to distinguish between ice (primarily in the form of hail) and water in cloud.
Much research has been done using polarization variables to characterize ice and water hydrometeor species. Hall et al. (1984) systematically identified classes of hydrometeors (wet and dry hail, wet and dry snow, high and low density ice, drizzle, and rain) as well as nonmeteorological targets such as ground clutter and insects, whereas Bringi et al. (1986) used scattering simulations and measurements of ZHH, ZDR, dual-frequency ratio, and linear depolarization ratio (LDR) in convective storms to detect hail.
Following these earlier efforts, numerous studies have applied a statistical approach to determine the dominant particle type within a radar sample volume. The Boolean decision-tree method was originally used to classify hydrometeor types on the basis of predefined boundaries of radar measurements such as ZHH and ZDR (Höller et al. 1994; El-Magd et al. 2000; Schuur et al. 2012). The use of static boundaries for ZHH and ZDR, however, may lead to misclassification given that expected values of ZHH and ZDR are not mutually exclusive for different hydrometeor types, and measurement errors in the data may wrongly associate a variable’s value with a particular hydrometeor type (Lim et al. 2005; Al-Sakka et al. 2013). As a result, the fuzzy-logic technique has been more widely implemented in classification algorithms (e.g., Straka and Zrnić 1993; Vivekanandan et al. 1999; Straka et al. 2000; Zrnić et al. 2000, 2001; Dolan and Rutledge 2009; Park et al. 2009; Lim et al. 2013; Melnikov and Straka 2013; Thompson et al. 2014; Picca et al. 2014; Kouketsu et al. 2015; Ortega et al. 2016). With fuzzy logic, the use of probability distribution functions for polarimetric variables such as ZHH, ZDR, LDR, specific differential phase KDP, and copolar cross-correlation coefficient ρHV, in addition to brightband location and temperature for each hydrometeor type, permits decisions on dominant hydrometeor type despite data that overlap hydrometeor types or are contaminated by noise (Liu and Chandrasekar 2000). Most recently, a K-means clustering technique used by Bechini and Chandrasekar (2015) and Wen et al. (2015) and a K-medoids clustering technique applied by Besic et al. (2016) improved the use of fuzzy-logic algorithms by imposing additional spatial contiguity constraints for particular hydrometeor classes.
The hydrometeor classification algorithm implemented across the WSR-88D network today uses ZHH, ZDR, ρHV, KDP, and parameters characterizing fluctuations of the fields of ZHH and differential phase ϕDP along a radial to distinguish among 10 different hydrometeor classes (big drops, rain, heavy rain, rain/hail, dry snow, wet snow, crystals, graupel, biological scatterers, and ground clutter) for each radar sample volume (Park et al. 2009). In its current state, the membership functions associated with this hydrometeor classification algorithm are largely based on theoretical scattering simulations of particles (Al-Sakka et al. 2013) and a limited understanding of how hydrometeors are manifested in the polarization variables. There has been insufficient verification of these algorithms using in situ data. Some studies have used coincident datasets of in situ observations of hydrometeor type along with radar polarization variables (Liu and Chandrasekar 2000; Barthazy et al. 2001; Lim et al. 2005; Plummer et al. 2010; Alcoba et al. 2016; Cazenave et al. 2016; Lasher-Trapp et al. 2016), but aircraft in situ verification of hydrometeor classification is relatively rare.
Given the frequent nature of overlapping polarimetric properties for different particle habits, the probability distribution functions may at times be close among several hydrometeor types (Tang et al. 2013). While these hydrometeor classification algorithms may identify several potential hydrometeor classes for a given volume, their assignment of a single hydrometeor species to a particular radar pixel may not be the most appropriate technique. Plummer et al. (2010) used a different approach by evaluating the probability that a particular phase (supercooled water vs ice) was occurring in the radar volume. This probabilistic approach may also be suitable for identification of ice particle habits given the frequent inhomogeneity of hydrometeors in a given volume but has yet to be tested.
The goal of this study is to relate in situ measurements of ice particle habits, bulk cloud properties, and measurements of particle morphology to ZHH and ZDR measured by an X-band ground-based dual-polarization radar during the Profiling of Winter Storms (PLOWS) field campaign. A probabilistic approach, similar to that of Plummer et al. (2010), is used to establish possible habits of ice particles and microphysical quantities within a radar sample volume. Further, we explore whether it is more appropriate to use a deterministic approach to assign one habit to each radar pixel or a probabilistic approach that assigns multiple habits simultaneously to the same pixel. A description of the processing techniques for radar and aircraft instrumentation is provided in section 2. A brief synoptic overview of the two winter cyclones that were sampled is provided in section 3. Results of individual particle microphysical properties are presented in section 4, and findings of habit contributions as they relate to the radar-measured variables are given in section 5. A summary and major conclusions are provided in section 6.
2. Data and methodology
The data in this study were collected within the 14–15 and 21–22 February 2010 winter cyclones that were sampled during the 2009/10 Profiling of Winter Storms field campaign. A description of PLOWS can be found in Rauber et al. (2014). The study that is presented here uses data from the University of Alabama in Huntsville Mobile Alabama X-band (MAX) dual-polarization radar and from in situ probes aboard the “NSF/NCAR Hercules C-130” aircraft [doi:10.5065/D6WM1BTG0; the plane is maintained and managed by the National Center for Atmospheric Research (NCAR), which is in turn managed by the University Corporation for Atmospheric Research and sponsored by the National Science Foundation (NSF)].
a. Identification of coincident aircraft/radar data
During PLOWS, an attempt was made to place the C-130 aircraft in the same plane as range–height indicator (RHI) scans from the ground-based MAX radar. This was done continuously for 7 h on 14–15 February and for 2 h on 21–22 February as the storms evolved. The azimuth angle of the MAX radar was flipped 180° to match the aircraft’s heading as it passed back and forth directly over the radar site. The aircraft made vertically stacked passes to obtain microphysical data at different altitudes below cloud top.
The aircraft was defined to be within the domain of the MAX radar when the aircraft was within 100 km of the radar and within 2° of the RHI plane. Each coincident observation is exclusive to an RHI scan and encompasses several seconds of aircraft microphysical data and radar gates in the vicinity of the aircraft’s location, as outlined below.
Specific criteria were developed to determine the temporal and spatial limits for when the microphysical and radar measurements were collocated. Example RHI scans of ZHH (dBZ) with the plane’s collocated position are shown in Fig. 1, with the inset showing gates (including gates contaminated by aircraft echo) that are considered to be coincident. Particle data within 5 s of flight from the collocated point (corresponding to ~0.5 km on either side given an aircraft speed of 100 m s−1), and radar gates between 250 and 500 m on either side of the point with a maximum altitude difference of no more than 25 m from the aircraft altitude were used for the comparison. To avoid contamination of the radar signal by the aircraft, radar gates within 250 m of the aircraft location were ignored irrespective of whether the aircraft directly intersected the radar beam. Data associated with a coincident point were verified to have no contamination from the aircraft by analyzing the variance in reflectivity values from all applicable gates. The ZHH and ZDR measurements were then averaged for all radar data collocated within 50 m vertically and 250–500 m horizontally on either side of the coincident point. A sensitivity study showed that averaging over greater horizontal (between 250 m and 1 km) and vertical (100 m) distances yielded an average difference of 12% in the mean ZHH for gates associated with the coincident point relative to the averaging criteria used in this study while averaging over smaller horizontal (between 250 and 400 m) and vertical (50 m) distances only yielded an average difference of 5%. Direct comparison of particle information (habit, size distribution, and axis ratio) with coincident radar data was thus possible using this approach.
RHI scan of equivalent radar reflectivity (dBZe) at (a) 0657 UTC 15 Feb and (b) 0104 UTC 22 Feb 2010 with an aircraft echo indicating the C-130 aircraft’s position at the time that the scan was conducted. The inset shows a 1 km × 100 m region surrounding the aircraft’s position, with radar gates within the outlined boxes being considered coincident. Gray bars on the left axis denote altitudes of all aircraft flight legs during each event.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
RHI scan of equivalent radar reflectivity (dBZe) at (a) 0657 UTC 15 Feb and (b) 0104 UTC 22 Feb 2010 with an aircraft echo indicating the C-130 aircraft’s position at the time that the scan was conducted. The inset shows a 1 km × 100 m region surrounding the aircraft’s position, with radar gates within the outlined boxes being considered coincident. Gray bars on the left axis denote altitudes of all aircraft flight legs during each event.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
RHI scan of equivalent radar reflectivity (dBZe) at (a) 0657 UTC 15 Feb and (b) 0104 UTC 22 Feb 2010 with an aircraft echo indicating the C-130 aircraft’s position at the time that the scan was conducted. The inset shows a 1 km × 100 m region surrounding the aircraft’s position, with radar gates within the outlined boxes being considered coincident. Gray bars on the left axis denote altitudes of all aircraft flight legs during each event.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
A total of 576 coincident observations (343 in cloud) were collected during the 14–15 February cyclone, and 202 (142 in cloud) were collected during the 21–22 February cyclone. Table 1 lists the number of coincident observations in cloud for each of the constant-altitude flight legs flown and the average temperature of each.
Summary of constant-altitude flight legs that are coincident with MAX radar data acquired during the 14–15 and 21–22 Feb 2010 events. For each constant-altitude leg through the system, the number of coincident observations in the cloud, mean altitude (km), and mean temperature (°C) are listed.
b. In situ measurements
Data from the two-dimensional cloud (2D-C) and precipitation (2D-P) optical array probes (OAPs) were used to derive microphysical quantities. The probes were installed such that the probe arms were oriented horizontally so that the photodiode arrays were oriented vertically. Data from the OAPs were processed using algorithms originally developed at NCAR and thereafter modified at the University of Illinois. Jackson et al. (2014) describe the processing techniques, including criteria to accept and reject particles. Processing details specific to the PLOWS dataset can be found in Plummer et al. (2014, 2015). The 2D-C was used to characterize the number distribution function N(D) for 500 < D < 2100 μm, and the 2D-P was used for 2100 < D < 9600 μm. Following the methods of Heymsfield and Baumgardner (1985) and Field (1999), only particles with a center of mass within the OAP’s field of view were considered so as to avoid classification when there was too much uncertainty in particle shape. Particles smaller than 500 μm were not used in the analysis because of uncertainties that result from particle shattering (Korolev et al. 2011, 2014; Jackson and McFarquhar 2014) and, in any event, do not make substantial contributions to ZHH, which is dominated by larger particles.
A 2D-C particle image, where LH is the particle length in the horizontal dimension, LV is the particle length in the vertical dimension, A is the cross-sectional area, and P is the perimeter.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
A 2D-C particle image, where LH is the particle length in the horizontal dimension, LV is the particle length in the vertical dimension, A is the cross-sectional area, and P is the perimeter.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
A 2D-C particle image, where LH is the particle length in the horizontal dimension, LV is the particle length in the vertical dimension, A is the cross-sectional area, and P is the perimeter.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Particle habits were identified using the classification scheme of Holroyd (1987), modified to classify particles into nine categories: aggregate, bullet rosette, hexagonal, graupel, spherical, linear, oriented, irregular, and tiny. A series of decisions about the particle’s size, perimeter, axis ratio, orientation, and number of unshadowed diodes within the particle boundaries was used to determine habit. Given the coarser resolution of the 2D-P probe and its inability to resolve more-intricate particle features, information on particle shape was only derived using the 2D-C data. The reflectivity distributions computed below show that these particles measured by the 2D-C with 500 < D < 2100 μm contributed 94% on average to the total reflectivity over the entire flight sampling period, justifying this approach.
Figure 3 shows examples of particles classified into each category. Extensive visual analysis of crystals classified by the original Holroyd scheme as dendrites showed that they are typically a collection of columnar crystals rather than being branched in nature. This visual analysis, together with the fact that temperatures were generally colder than that typical for dendritic growth (Table 1), justified classifying those particles as bullet rosettes. Because particles smaller than 500 μm were eliminated to avoid shattered artifacts, very few particles classified as “tiny” remained, and this habit category was ignored in subsequent analyses. Oriented columns were classified as being positioned 30°–60° from the vertical axis. Although turbulence around the probe inlets and disturbed flow around the aircraft fuselage (King 1985, 1986; Hogan et al. 2012) cannot be ruled out as an explanation for the presence of oriented crystals, electric field mill data collected at the radar site during these cases did not indicate that strong electrostatic fields were present. Although these crystals are treated separately from other columns in the analysis, differences in the analysis would likely be minimal if all columns were treated the same.
Representative particle images for (a) irregular, (b) bullet rosette, (c) aggregate, (d) hexagonal, (e) graupel, (f) linear, (g) oriented, and (h) spherical habits from the 2D-C probe.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Representative particle images for (a) irregular, (b) bullet rosette, (c) aggregate, (d) hexagonal, (e) graupel, (f) linear, (g) oriented, and (h) spherical habits from the 2D-C probe.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Representative particle images for (a) irregular, (b) bullet rosette, (c) aggregate, (d) hexagonal, (e) graupel, (f) linear, (g) oriented, and (h) spherical habits from the 2D-C probe.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Particle mass m is needed for calculating the radar reflectivity factor for each particle. Two approaches were used to estimate m. The first estimates m from the projected area A of each particle as originally applied to the PLOWS data by Plummer et al. (2014, 2015) following the method of Baker and Lawson (2006, hereinafter BL06). The second uses mass–diameter (m–D) relationships that are specific to each habit as outlined in McFarquhar et al. (2002, hereinafter M02) and subsequently applied by Jackson et al. (2014). Figure 4 shows how the mass of an individual particle of length D varies for different habits. To compare with mass estimated from BL06, the area of particles with a given D is estimated for area ratios Ar of 0.2, 0.5, and 0.8, where area ratio is the ratio of a particle’s projected area to the area of a circumscribed circle (McFarquhar and Heymsfield 1996). Particles with the same diameter can have substantially different masses, with particles of D at 500 μm (2000 μm), for example, having masses that vary between 0.002 (0.055) and 0.012 (0.541) mg, depending on the assumed habit or area ratio.
Mass of an individual particle as a function of D using two approaches in estimating m. Black curves represent m at varying Ar as in BL06, and colored curves denote m–D relationships specific to each habit as in M02.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Mass of an individual particle as a function of D using two approaches in estimating m. Black curves represent m at varying Ar as in BL06, and colored curves denote m–D relationships specific to each habit as in M02.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Mass of an individual particle as a function of D using two approaches in estimating m. Black curves represent m at varying Ar as in BL06, and colored curves denote m–D relationships specific to each habit as in M02.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
c. Mobile Alabama X-band radar
The MAX radar, transmitting at a wavelength of 3.17 cm (9450 MHz) with a range gate spacing of 125 m and beamwidth of 1°, retrieved polarization measurements of ZHH, ZDR, KDP, and ρHV, as well as radial velocity and spectrum width. To verify that the horizontally and vertically polarized signals used to calculate ZDR are not biased by the radar elevation angle, the dependence of the radar elevation angle at the aircraft’s location on ZDR was examined. The lack of correlation between the radar elevation angle and ZDR measured at the aircraft’s position (not shown) indicates that ZDR is not influenced by the elevation angle over the range of elevations used in this study and gives confidence that ZDR can be properly compared with a particle’s axis ratio. The high spatial variation of KDP at X band and low ZHH in snow (Goddard et al. 1994; Bringi and Chandrasekar 2001; Ryzhkov et al. 2005), in addition to high KDP variance from neighboring radar gates during PLOWS, prompted the exclusion of KDP in this study. Further details regarding the MAX radar can be found in Mullins and Knupp (2009) and Knupp et al. (2014). Processing techniques specific to the PLOWS data are described below, and an explanation of corrections made to the elevation angle is discussed in appendix B.
The variables ZHH and ZDR are biased at X band as a result of attenuation and differential attenuation, respectively, especially in regions of liquid precipitation. Increasingly sophisticated algorithms (e.g., Bringi et al. 1990; Delrieu et al. 2000; Testud et al. 2000; Bringi et al. 2001; Gorgucci and Chandrasekar 2005; Park et al. 2005; Chandrasekar et al. 2006; Chang et al. 2014) are available for attenuation correction, with applications for rainfall estimation (Ryzhkov et al. 2014; Diederich et al. 2015a,b) and hydrometeor classification (Snyder et al. 2010).
The reliance of most of the above algorithms on KDP combined with the omission of KDP data for this study prompted the use of the Park et al. (2005) algorithm to correct for attenuation for points up to the top of the radar bright band where precipitation fell as liquid or as a mixture of rain and snow. The vertical extent of the bright band (~1 km above ground) for the 21–22 February cyclone was determined for each RHI by first exploring the mean height of maximum ZHH and ZDR values and of minimum ρHV values for a series of radar beams along the RHI. Analysis among the three polarization variables (not shown) indicates that the most consistent brightband height was observed among the radar beams of each RHI and between the RHI scans when ZHH was used. No corrections to ZHH and ZDR were needed for the 14–15 February event given that temperatures at all levels remained below 0°C and precipitation fell as snow.
d. Analysis of coincident datasets
The per-particle reflectivity Zp was calculated following the method of Hogan et al. (2006) for the entire flight sampling period and for times when the C-130 aircraft and MAX radar were coincident. Figure 5 shows the reflectivity distribution function Z(D) of particles from a 10-s sample at 0701 UTC 15 February when the ZHH near the aircraft’s location was 11.1 dBZ. It is shown that the contribution to the reflectivity for particles with D > 2250 μm, namely particle sizes measured by the 2D-P, is <20% despite sampling a region of higher reflectivity (a few minutes after the RHI shown in Fig. 1). The Z(D) for particles at larger sizes are an order of magnitude less than Z(D) for size bins toward the high end of the 2D-C size range. Over the entire flight sampling period, particles with D > 2100 μm sampled by the 2D-P probe contributed 6% on average to the total reflectivity. For cases in which ZHH > 9 dBZ, particles with D > 2100 μm contributed between 10% and 20% to the total reflectivity. If it is assumed that there is a 50% uncertainty in estimating particle mass from the 2D particle images (e.g., Jackson et al. 2012), then there is a 100% uncertainty in estimating the particle reflectivity, which is much larger than the 10%–20% contributions from these larger particles. Herein, only particles sampled by the 2D-C with 500 < D < 2100 μm were used to calculate Zp to remain consistent with the habit analysis.
Reflectivity distribution function (black line) and cumulative contribution (blue line) during a 10-s interval at 0701 UTC 15 Feb 2010 when the C-130 flew through a region of high ZHH from a joint distribution spanning cloud and precipitation particle sizes using the mass relationship from BL06.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Reflectivity distribution function (black line) and cumulative contribution (blue line) during a 10-s interval at 0701 UTC 15 Feb 2010 when the C-130 flew through a region of high ZHH from a joint distribution spanning cloud and precipitation particle sizes using the mass relationship from BL06.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Reflectivity distribution function (black line) and cumulative contribution (blue line) during a 10-s interval at 0701 UTC 15 Feb 2010 when the C-130 flew through a region of high ZHH from a joint distribution spanning cloud and precipitation particle sizes using the mass relationship from BL06.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
To relate the aircraft derived microphysical properties (distribution of Zp, 
Distribution of (a) ZHH and (b) ZDR measurements for the 14–15 and 21–22 Feb 2010 events when the C-130 aircraft was coincident with the MAX radar. The range of ZHH and ZDR values chosen for the ZHH–ZDR domain is indicated.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Distribution of (a) ZHH and (b) ZDR measurements for the 14–15 and 21–22 Feb 2010 events when the C-130 aircraft was coincident with the MAX radar. The range of ZHH and ZDR values chosen for the ZHH–ZDR domain is indicated.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Distribution of (a) ZHH and (b) ZDR measurements for the 14–15 and 21–22 Feb 2010 events when the C-130 aircraft was coincident with the MAX radar. The range of ZHH and ZDR values chosen for the ZHH–ZDR domain is indicated.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Number of accepted particles sampled by the 2D-C OAP (top numbers and colored scale) and aircraft sampling duration (s; bottom numbers) during times when the aircraft was coincident with the MAX radar and within a particular ZHH–ZDR binned interval (squares) for (a) 14–15 and (b) 21–22 Feb 2010.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Number of accepted particles sampled by the 2D-C OAP (top numbers and colored scale) and aircraft sampling duration (s; bottom numbers) during times when the aircraft was coincident with the MAX radar and within a particular ZHH–ZDR binned interval (squares) for (a) 14–15 and (b) 21–22 Feb 2010.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Number of accepted particles sampled by the 2D-C OAP (top numbers and colored scale) and aircraft sampling duration (s; bottom numbers) during times when the aircraft was coincident with the MAX radar and within a particular ZHH–ZDR binned interval (squares) for (a) 14–15 and (b) 21–22 Feb 2010.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Number of particles sampled for coincident points by the 2D-C probe for each habit during the 14–15 and 21–22 Feb 2010 cyclones.
3. Cyclone events
The 14–15 and 21–22 February 2010 cyclones were chosen for analysis because of the extended duration that the aircraft sampled within the domain of the MAX radar. The first cyclone examined, an Alberta Clipper–type cyclone, moved over the western Ohio River valley on 15 February 2010 as a short wave originating from the Canadian Rockies. A 350-hPa jet streak was present at the time of the PLOWS operations (0200–1600 UTC), with the surface cyclone underneath its left exit region. The low pressure center traveled from northern Alberta to northern Kentucky over a three-day period, with its center located in western Kentucky at the time of the aircraft flight (Fig. 8a). At that time the minimum pressure was 1009 hPa, with the comma-head region extending from southwestern Missouri to eastern Illinois. The C-130 made repeated passes directly north of the cyclone between southern Illinois and southern Indiana (Table 1; Fig. 8a). Rosenow et al. (2014), Plummer et al. (2014, 2015), and Keeler et al. (2016) provide a more complete overview of the synoptic conditions, vertical velocity, and microphysical structure associated with the cyclone.
WSR-88D composites from (a) 0400 UTC 15 Feb 2010 and (b) 0030 UTC 22 Feb 2010. Overlaid on the images is the location of the MAX radar (white star), C-130 flight track and azimuthal angle of RHI scans (black line), and the sea level pressure field (black contours; hPa − 1000) from the Rapid Update Cycle model initialization at 0400 UTC in (a) and 0000 UTC in (b).
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
WSR-88D composites from (a) 0400 UTC 15 Feb 2010 and (b) 0030 UTC 22 Feb 2010. Overlaid on the images is the location of the MAX radar (white star), C-130 flight track and azimuthal angle of RHI scans (black line), and the sea level pressure field (black contours; hPa − 1000) from the Rapid Update Cycle model initialization at 0400 UTC in (a) and 0000 UTC in (b).
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
WSR-88D composites from (a) 0400 UTC 15 Feb 2010 and (b) 0030 UTC 22 Feb 2010. Overlaid on the images is the location of the MAX radar (white star), C-130 flight track and azimuthal angle of RHI scans (black line), and the sea level pressure field (black contours; hPa − 1000) from the Rapid Update Cycle model initialization at 0400 UTC in (a) and 0000 UTC in (b).
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The second cyclone examined here, which originated over eastern New Mexico, developed as a weak 500-hPa short wave that exited the Rocky Mountains and then moved over the midwestern Great Plains states. An area of surface low pressure developed from an inverted surface trough by 0000 UTC 21 February, with the comma-head precipitation forming as the cyclone moved from eastern New Mexico to northwestern Ohio over a 2-day period. At the time of the C-130 flight, the surface cyclone had a minimum pressure of 1006 hPa in southeastern Missouri, with the comma-head region extending from eastern Kansas to central Illinois. The C-130 repeatedly flew along a track (Table 1; Fig. 8b) between northern and southern Illinois.
The two cyclones exhibited considerable differences in their precipitation extent and thermodynamic structure. Temperatures at the surface (0°–2°C) and aloft were warmer for the 21–22 February cyclone as evidenced by temperatures from flight legs of comparable altitude (Table 1) and the presence of a melting layer and a radar bright band (Fig. 1b). Maximum reflectivity values from the RHIs were comparable between both cyclones (Fig. 1), but the range of measured ZHH at the aircraft’s location (Fig. 6a) was notably greater for the 14–15 February case (−15 < ZHH < 15 dBZ) than for the 21–22 February case (−15 < ZHH < 2.5 dBZ) because of a greater penetration depth below cloud top as the aircraft made vertically stacked passes (Fig. 1a). The range of ZDR values at the aircraft’s location (Fig. 6b) was found to be similar (−2 < ZDR < 4 dB) between the two cases.
4. Habit microphysical properties
This section discusses the distributions of Zp, α, and β at points with coincident in situ and radar data (hereinafter called coincident points) for each of the eight different habit categories, their representativeness for the entire sampling period, similarity between the 14–15 and 21–22 February cyclones, and sensitivity between the two approaches used to estimate the masses of the particles.
a. Particle representativeness of coincident points to the entire sampling period
Figure 9 shows distributions of Zp for particles of each habit sampled at coincident points (red) and for the entire flight sampling period (blue) using mass estimations from BL06. Statistics on the distribution mean μc and median 
The Zp distribution (dBZ) for the same eight habits as in Fig. 3 for coincident measurements (red) and the entire flight sampling period (blue) for both cyclones using the mass relationship from BL06. Solid (dashed) curves denote the cumulative frequency of particles having a Zp up to a particular value for coincident time frames (the entire sampling period). The distribution mean and median for both datasets are given in Table 3.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The Zp distribution (dBZ) for the same eight habits as in Fig. 3 for coincident measurements (red) and the entire flight sampling period (blue) for both cyclones using the mass relationship from BL06. Solid (dashed) curves denote the cumulative frequency of particles having a Zp up to a particular value for coincident time frames (the entire sampling period). The distribution mean and median for both datasets are given in Table 3.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The Zp distribution (dBZ) for the same eight habits as in Fig. 3 for coincident measurements (red) and the entire flight sampling period (blue) for both cyclones using the mass relationship from BL06. Solid (dashed) curves denote the cumulative frequency of particles having a Zp up to a particular value for coincident time frames (the entire sampling period). The distribution mean and median for both datasets are given in Table 3.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Statistics of the Zp distribution mean μc and median 
Cohen’s effect size d for distributions from particles sampled during coincident timeframes vs the entire flight for the 14–15 and 21–22 Feb 2010 events. Values of 0.2 or less indicate a statistically small difference between two distributions (Cohen 1988); values above this suggested threshold are highlighted with boldface type.
b. Habit distributions of Zp, α, and β
The estimates of Zp are dependent on how the particle masses are estimated. To examine the importance of the assumptions that go into the particle mass calculations, Fig. 10 compares the distributions of Zp for the coincident data points computed according to the BL06 and M02 computation techniques as a function of particle habit. The lines for each distribution denote the cumulative percentage of particles, sampled during all coincident periods, that have a Zp of less than or equal to the values along the abscissa. The histograms and cumulative frequency curves show that, while many of the habits have a similar mean and median in the Zp distributions between BL06 and M02 (Table 5), notable differences do exist for bullet rosettes and graupel. The median Zp when using M02 is around 4 dBZ lower for bullet rosettes (Figs. 10c,d; Table 5) and around 4.5 dBZ higher for graupel (Figs. 10i,j; Table 5) relative to that estimated from BL06. These differences are the result of the way particle mass is derived using BL06 versus using M02. For the same particle, BL06 derives mass from the area of the particle while M02 uses D in different equations to derive mass for different habits. For example, as seen in Fig. 4, a particle’s mass with a D of 1 (2) mm would be 0.017 (0.081) mg for bullet rosettes and 0.078 (0.541) mg for graupel using the M02 approach as compared with 0.037 (0.199) mg for an Ar of 0.5 using the BL06 approach. The Cohen’s d statistic is greater than 0.2 for bullet rosettes and graupel (not shown), suggesting that differences in Zp derived from the different approaches are not trivial for all habits. Differences in the mean Zp derived from BL06 and M02 for aggregates on 21–22 February are minimal (Table 5), but more notable differences were present in the mean Zp on 14–15 February. These are likely explained by a higher concentration (~7% greater) of aggregates with 1800 < D < 2100 μm. Within this diameter range, Zp from each mass-estimation approach varies more substantially for aggregates.
The Zp distribution (dBZ) for the same eight habits as in Fig. 3 for coincident measurements for both cyclones using the mass-estimation methods from BL06 (blue) and M02 (red). Dashed (solid) curves denote the cumulative frequency of particles having a Zp up to a particular value for BL06 (M02). Distribution statistics for both datasets are given in Table 5.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The Zp distribution (dBZ) for the same eight habits as in Fig. 3 for coincident measurements for both cyclones using the mass-estimation methods from BL06 (blue) and M02 (red). Dashed (solid) curves denote the cumulative frequency of particles having a Zp up to a particular value for BL06 (M02). Distribution statistics for both datasets are given in Table 5.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The Zp distribution (dBZ) for the same eight habits as in Fig. 3 for coincident measurements for both cyclones using the mass-estimation methods from BL06 (blue) and M02 (red). Dashed (solid) curves denote the cumulative frequency of particles having a Zp up to a particular value for BL06 (M02). Distribution statistics for both datasets are given in Table 5.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Statistics of the Zp distribution mean μM02 and median 
The distributions of Zp can be used to assess which habits contribute most to the reflectivity. Aggregates have the greatest Zp values among the eight habits, with a median Zp between −11.9 and −8.3 dBZ, depending on the mass relationship used and cyclone sampled (Figs. 10e,f; Table 5). Irregular crystals, bullet rosettes, and graupel have the next highest median values of Zp. Median Zp for irregular crystals and bullet rosettes ranges between −25 and −20 dBZ (Figs. 10a–d; Table 5), and graupel typically has higher median Zp values of between −19 and −13 dBZ (Figs. 10i,j; Table 5), given its greater density and resultant mass (Fig. 4). Median Zp was around −30 dBZ or lower for hexagonal plates (Figs. 10g,h), linear (Figs. 10k,l) and oriented (Figs. 10m,n) columns, and spherical crystals (Figs. 10o,p), and so these habits yielded much smaller contributions to the reflectivity. To determine the contributions that the different habits make to the observed reflectivity in a particular range gate ZHH, both Zp and the concentrations of particles with specific habits must be considered.
To gain insight into particle shape as it relates to ZDR, it is necessary to first understand how the distributions of α (Fig. 11) and β (Fig. 12) vary according to particle shape. The mean and median of α and β, and statistics on the distribution standard deviation σ and skewness Sk are shown for each habit in Tables 6 and 7, respectively.
The α distribution for the same eight habits as in Fig. 3 for 14–15 Feb (red) and 21–22 Feb 2010 (blue). Solid (dashed) curves denote the cumulative frequency of particles having an α up to a particular value for 14–15 Feb (21–22 Feb). The distribution mean, median, standard deviation, and skewness for both datasets are given in Table 6.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The α distribution for the same eight habits as in Fig. 3 for 14–15 Feb (red) and 21–22 Feb 2010 (blue). Solid (dashed) curves denote the cumulative frequency of particles having an α up to a particular value for 14–15 Feb (21–22 Feb). The distribution mean, median, standard deviation, and skewness for both datasets are given in Table 6.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The α distribution for the same eight habits as in Fig. 3 for 14–15 Feb (red) and 21–22 Feb 2010 (blue). Solid (dashed) curves denote the cumulative frequency of particles having an α up to a particular value for 14–15 Feb (21–22 Feb). The distribution mean, median, standard deviation, and skewness for both datasets are given in Table 6.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 11, but for β. Distribution statistics for both datasets are given in Table 7.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 11, but for β. Distribution statistics for both datasets are given in Table 7.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 11, but for β. Distribution statistics for both datasets are given in Table 7.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Statistics of the α distribution mean, median, standard deviation, and skewness of each habit for the 14–15 and 21–22 Feb 2010 cyclones.
The α distributions indicate that bullet rosettes (Fig. 11b), aggregates (Fig. 11c), and linear columns (Fig. 11f) are most oblate, with median α between 1.19 and 1.31 (Table 6). Large skewness values between 1.03 and 2.11 for these habits also suggest that their horizontal dimensions can vary and can be up to 3–5 times as great as the vertical dimensions and thus lead to higher ZDR in clouds. As explained in section 2b, linear columns that fall with their major axis a few degrees from the horizontal direction will yield α values that are underestimated relative to a horizontal orientation. This trend was particularly evident for particles under 1 mm, given limitations of the Holroyd classification scheme at the probe’s resolution, and as a result yielded α values that were lower than that of aggregates. Lower α values for hexagonal plates (Fig. 11d), graupel (Fig. 11e), and spherical particles (Fig. 11h) are the result of the ratio of the particle’s horizontal and vertical dimensions being closer to unity. At a median value of 0.6, α values for spherical and hexagonal crystals differ from typical geometric representations. These particles were examined carefully. Nearly all particles were small, and those classified as spheres were not precisely spherical (McFarquhar et al. 2013). The images were typically oriented such that the long axis was vertical, which may have been due to reorientation of the particles as they passed through the sample volume. The 2D-C electronics also does not record the first slice of pixels when a particle is first detected by the laser. This clipping of the first slice can lead to a vertical orientation for small spheres and hexagonal plates.
The median β values for aggregates are less than those of linear columns (Table 7) because an aggregate’s complex structure along the particle’s boundary yields a smaller area-to-perimeter ratio. Given that the maximum possible β value for a spherical particle at the 2D-C pixel resolution is 0.34, β > 0.2 for hexagonal plates (Fig. 12d), graupel (Fig. 12e), and spherical particles (Fig. 12h) affirms their circular nature when projected onto a 2D plane. Although the distributions of α for oriented and linear columns differ substantially (Table 6) because of differences in orientation, β values for these habits are very similar because they have similar shapes.
c. Particle comparison between cyclones
Variations in the distributions of Zp, α, and β were determined for each of the habits in the two cyclones separately. The Cohen’s effect size d was computed, and the results are shown in Table 8. Although differences between the distributions of Zp, α, and β for some habits were smaller than 0.2, representing trivial differences, values greater than 0.2 in the distributions of Zp calculated from M02 and from BL06 were observed for five and three habit categories, respectively. Aggregates, graupel, and spherical particles were statistically distinct between the cyclones using either mass estimate. This suggests that the characteristics of these habits vary between cyclones. This is not surprising given that the density of graupel may vary depending on the temperature, fall velocity, and amount of riming while the characteristics of aggregates may vary depending on the compositional makeup of individual crystals. The temperatures at similar altitudes were over 10°C higher for the 21–22 February 2010 cyclone than for the 14–15 February cyclone (Table 1), and there were different penetration depths by the aircraft below cloud top within the comma-head region on both days. All habits except for spherical particles had a Cohen’s effect size d of less than 0.2 for α, indicating that the ratios of horizontal to vertical length of the particles composing each habit were similar. In contrast, five of the eight habits have Cohen’s effect size d of greater than 0.2 for β. This suggests that both the size and, in the case of aggregates, the shapes of the particles differ between the cyclones. As a result, analysis of each habit’s contribution as it relates to observed ZHH and ZDR is performed separately for each cyclone in section 5.
d. Comparing in situ derived reflectivity with reflectivity from the MAX radar
Figure 13 shows the total reflectivity Zensemble computed by summing the contributions of all particles within 5 s (500 m) of the coincident radar gate using the particle mass derived from BL06 and from M02 as a function of the ZHH measured by the MAX radar. The colored lines represent the mean Zensemble value for all points within 2.5-dBZ-wide ZHH bins, with values above (below) the black 1:1 line indicating that derived reflectivities were greater than (less than) those measured by the MAX radar.
Reflectivity calculated from particles surrounding a coincident point Zensemble on (a) 14–15 and (b) 21–22 Feb 2010 using mass estimates that are based on habit-dependent m–D relations (M02) and the particle’s projected area (BL06) is compared with ZHH measured from the MAX radar at the same location. Colored lines represent the mean Zensemble value at coincident points corresponding to a ZHH value within a 2.5-dB interval. The black line is the 1:1 line.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Reflectivity calculated from particles surrounding a coincident point Zensemble on (a) 14–15 and (b) 21–22 Feb 2010 using mass estimates that are based on habit-dependent m–D relations (M02) and the particle’s projected area (BL06) is compared with ZHH measured from the MAX radar at the same location. Colored lines represent the mean Zensemble value at coincident points corresponding to a ZHH value within a 2.5-dB interval. The black line is the 1:1 line.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Reflectivity calculated from particles surrounding a coincident point Zensemble on (a) 14–15 and (b) 21–22 Feb 2010 using mass estimates that are based on habit-dependent m–D relations (M02) and the particle’s projected area (BL06) is compared with ZHH measured from the MAX radar at the same location. Colored lines represent the mean Zensemble value at coincident points corresponding to a ZHH value within a 2.5-dB interval. The black line is the 1:1 line.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The mean difference in Zensemble between the two approaches was 1.6 dBZ, with some coincident points yielding a maximum difference of 8.3 dBZ. Some of the points at which ZHH = −5 dBZ on 14–15 February corresponded to cases in which graupel contributed 77% of the total reflectivity using the M02 approach and 41% using the BL06 approach. The root-mean-square difference (RMSD) between Zensemble from each approach and ZHH from the MAX radar varied between the two cyclones, with the RMSD being 6% lower (1% higher) using the BL06 approach on 14–15 (21–22) February. These data suggest that mass estimated using the BL06 (M02) approach more consistently agrees with the radar measurements on 14–15 (21–22) February for the conditions at which the measurements were made.
5. Habit relationships to ZHH and ZDR
In this section, the contributions of the different habits to the total reflectivity are examined for a range of temperatures and heights within the cloud. The purpose of this section is to demonstrate a probabilistic approach for assigning particle habits to specific ZHH and ZDR measurements in ice clouds.
a. Habit reflectivity contribution
Contribution of a habit’s calculated reflectivity using the mass–area relationship from BL06 to the total reflectivity for all particles coincident with radar measurements at specific ZHH and ZDR binned intervals.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Contribution of a habit’s calculated reflectivity using the mass–area relationship from BL06 to the total reflectivity for all particles coincident with radar measurements at specific ZHH and ZDR binned intervals.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Contribution of a habit’s calculated reflectivity using the mass–area relationship from BL06 to the total reflectivity for all particles coincident with radar measurements at specific ZHH and ZDR binned intervals.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 14, but using habit-specific m–D relationships that are outlined in M02.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 14, but using habit-specific m–D relationships that are outlined in M02.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 14, but using habit-specific m–D relationships that are outlined in M02.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The general distribution of Z* for each habit in the ZHH–ZDR domain looks similar for the different mass-estimation approaches aside from a few exceptions. Contribution of bullet rosettes to the reflectivity approaches 35% using the BL06 approach for ZDR > 2 dB (Figs. 14c,d) but is no greater than 20% using the M02 approach (Figs. 15c,d). Graupel, on the other hand, has Z* values that are over 50% for 53% of the ZHH–ZDR bins with ZDR < 2.5 dB on 14–15 February with M02, whereas only 13% of the bins have Z* of greater than 50% using the BL06 approach in the same ZDR range.
Overall, there are mostly continuous transitions in Z* for any habit for small variations in either ZHH or ZDR. The bins encompassing 9 < ZHH < 15 dBZ and 2 < ZDR < 3 dB, for instance, have Z* values that vary by no more than 20% for bullet rosettes and aggregates. Bins that do have a noticeable jump in Z*, like the bin for 3 < ZHH < 5 dBZ and 1 < ZDR < 1.5 dB for hexagonal plates, have a Z* value that is 45% greater than surrounding ZHH–ZDR bins (Fig. 14g). Jumps of this magnitude are explained by fewer than 100 particles sampled within the ZHH–ZDR bin (Fig. 7).
Some trends are evident in Figs. 14 and 15 about which habits make the largest contributions to the reflectivity. Irregularly shaped crystals contribute at most 70% to the total reflectivity for bins where −11 < ZHH < 3 dBZ and 2 < ZDR < 4 dB (Figs. 14a,b and 15a,b). This is consistent with the results from Korolev et al. (1999, 2000), who indicated that roughly 80%–95% of particles sampled were of “irregular” shape. Stoelinga et al. (2007) note that, when viewed under a microscope, irregular particles are less dominant than in previous studies in which a broader definition of irregular crystals was used in the classification of particle type. For example, nearly all of the bins where ZHH is greater than 3 dBZ have irregular crystals contributing at most 40% to the reflectivity. Of the particles sampled during the coincident periods, 40% were of irregular shape; 55% of the ZHH–ZDR bins had irregular particles that contributed over 40% to the reflectivity. Therefore, in 45% of the coincident samples, irregular crystals did not dominate the reflectivity because contributions come from other habits.
The reflectivity contributions of bullet rosettes (Figs. 14c,d and 15c,d) and aggregates (Figs. 14e,f and 15e,f) are generally larger at higher reflectivity (ZHH 
The N(D) spanning cloud particle sizes 500 < D < 2100 μm, with colors representing the fraction of a habit’s concentration in each bin (a) during a 10-s interval at 0701 UTC 15 Feb when ZHH was 11.1 dBZ and (b) during a 10-s interval at 0458 UTC 15 Feb 2010 when the ZHH was −14.7 dBZ.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The N(D) spanning cloud particle sizes 500 < D < 2100 μm, with colors representing the fraction of a habit’s concentration in each bin (a) during a 10-s interval at 0701 UTC 15 Feb when ZHH was 11.1 dBZ and (b) during a 10-s interval at 0458 UTC 15 Feb 2010 when the ZHH was −14.7 dBZ.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The N(D) spanning cloud particle sizes 500 < D < 2100 μm, with colors representing the fraction of a habit’s concentration in each bin (a) during a 10-s interval at 0701 UTC 15 Feb when ZHH was 11.1 dBZ and (b) during a 10-s interval at 0458 UTC 15 Feb 2010 when the ZHH was −14.7 dBZ.
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Hexagonal plates are shown to contribute slightly more to the reflectivity when ZHH at the aircraft’s location is less than −5 dBZ (Figs. 14g,h and 15g,h). Since very few particles are generally observed during these cases for D > 1300 μm (Fig. 16b), concentrations of hexagonal plates for D < 800 μm yield greater contributions to the particle population as opposed to cases in which the reflectivity is higher (Fig. 16a).
The contribution to the reflectivity from graupel (Figs. 14i,j and 15i,j) fluctuates over small changes in ZHH and ZDR—in particular, when ZDR < 2.5 dB on 14–15 February. The sensitivity of Z* is greater when using the M02 relationship (Fig. 15i), where Z* varies by as much as 25% for the ZHH–ZDR bins encompassing −7 < ZHH < −3 dBZ and 1 < ZDR < 1.5 dB. A median Zp of −13.3 dBZ for graupel (Table 5) is larger than most habits and thus greatly affects Z*, depending on the number of graupel particles observed in a ZHH–ZDR bin.
Linear, oriented, and spherical crystals make smaller contributions toward the total reflectivity because of their small sizes (Figs. 14k–p and 15k–p). Their contributions to the total concentrations are also minimal across most particle sizes (Fig. 16). The Z* are less than 20% for these habits for nearly all ZHH and ZDR in the domain, with Z* < 5% for spherical crystals over all measured ZHH and ZDR. Linear and oriented columns are observed for D as large as 1900 μm (Fig. 16), but their concentrations are smaller than those of other habits. The median Zp was between −28.8 and −20.6 dBZ for linear and oriented columns and was lower than other habits (Table 5). Their oblate shape, as evidenced by median β between 0.17 and 0.19 (Table 7), yields a smaller radar backscatter cross section when compared with habits of the same size that are more spherical (e.g., graupel). Furthermore, the observed concentrations of oriented columns are too small to contribute much to the reflectivity within the ZHH–ZDR domain in Figs. 14 and 15 since their typical α values of less than 1 (Fig. 11g) correspond to negative ZDR values.
b. Microphysics–polarization relationships
Trends in the variation of 
The 
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
The
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 17, but for 
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 17, but for
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
As in Fig. 17, but for
Citation: Journal of Applied Meteorology and Climatology 55, 12; 10.1175/JAMC-D-16-0059.1
Values between 1.17 and 1.3 for 
For ZHH < 1 dBZ, values of 
While 40% of the bins within the ZHH–ZDR domain can be attributed to a dominant habit or small set of habits, the remaining bins do not have a particular habit contribute over 50% to the total reflectivity (Fig. 14). The Z* for each habit reflects the inhomogeneity of crystal habits present for a given ZHH and ZDR. This suggests that specifying the percentage contribution for specific habits would be a more accurate approach to interpret polarization signatures in ice clouds.
6. Summary and conclusions
This paper presented analyses of the microphysical properties of ice particles derived from data collected by cloud probes installed on the NSF/NCAR C-130 aircraft within the comma heads of two winter cyclones. The microphysical measurements were coincident with measurements made by a ground-based polarization radar, the University of Alabama in Huntsville MAX 3.17-cm radar, during RHI scans through the same plane as the aircraft’s flight path. This sampling strategy allowed for the direct comparison of particle sizes, habits, and calculated reflectivity with coincident and simultaneous measurements of polarization variables ZHH and ZDR from the radar. Distributions of estimated single-particle reflectivity Zp were used to understand how particles with specific habits contributed to the total reflectivity, and calculations of particle axis ratio α and sphericity β were used to understand how various habits relate to ZDR. The impact of using different methods to estimate ice particle mass to determine the Zp was also assessed. The ratio of the reflectivity contributed by a specific habit (derived from optical array probe images) to the total reflectivity (also derived from optical array probe images), expressed as a percentage, was displayed in a matrix of 13 ZHH and 8 ZDR bins (as measured by the MAX radar) encompassing −11 < ZHH < 15 dBZ and 0 < ZDR < 4 dB. The reflectivity-weighted mean axis ratio 
The key findings of the paper are as follows:
No dominant crystal habits were observed for the majority of radar ZHH and ZDR measurements, with only 40% of the ZHH–ZDR bins having a habit that contributed over 50% to the reflectivity in that bin. Of these bins, only 12% had a habit that contributed over 75% to the reflectivity.
Differences in particle mass according to whether it was estimated from the particle’s projected area or from habit-dependent mass–diameter relations yielded, on average, a 1.6-dBZ difference in Zp for all coincident observations and up to an 8.3-dBZ difference for habits such as bullet rosettes and graupel. This highlights the need to know particle density for accurate estimates of reflectivity from a particle size distribution. Mass estimates using the particle’s projected area yielded derived reflectivities that were closer to ZHH values measured by the radar than did the habit-dependent mass–diameter relations for the 14–15 February cyclone (6% lower RMSD), with the opposite result for the 21–22 February cyclone (1% lower RMSD using the mass estimated from habit-dependent mass–diameter relations).
Irregular particles made the largest contributions to the reflectivity in both cyclones, with contributions ranging from 3% to 72% with a mean of 36%. Only 55% of the ZHH–ZDR bins had irregular crystals that contributed to over 40% of the reflectivity in that bin, however.
Bins with greater contributions from bullet rosettes and aggregates (ZHH > 7 dBZ and ZDR > 2 dB) were associated with larger particle axis ratios (as measured by
Contributions of hexagonal plates and graupel to the reflectivity exceeded 50% for 47% of the bins where ZHH < 1 dBZ and were associated with
The coexistence of bullet rosettes and aggregates for ZHH > 7 dBZ and ZDR > 2 dB is consistent with previous studies (e.g., Hobbs et al. 1974). Their coexistence suggests that bullet rosettes are favored for aggregate formation.
Mixing and turbulence processes and the various growth histories of particles are potential causes for the variety in habit types observed for a coincident observation. Given that no particular crystal habit contributes over 80% to the reflectivity for a given ZHH and ZDR value, assigning a single hydrometeor species to a particular radar pixel may not be the most appropriate technique for habit classification in ice clouds. Expressing the probability of specific habits present in radar volumes may be more suitable than deterministic methods that assign one habit.
The implication of this study is that lookup tables should be used to quantify a habit’s contribution to the reflectivity at given ZHH and ZDR values. The sampling strategy used in this study provided a large number of coincident observations in two storms but clearly did not provide enough to map out the full matrix of potential ZHH and ZDR values needed to operationally implement probabilistic habit classification in ice clouds across a wide range of storms. Further studies utilizing sampling strategies that collect coincident radar and microphysical data in other cloud and meteorological environments may help to further understand the dependence of microphysical properties on polarization variables so as to implement lookup tables that can be used operationally, as well as to assess the validity of simulations of radar variables from microphysical data (e.g., Wolde et al. 2003; Kollias et al. 2011; Tyynelä et al. 2011; Zong et al. 2013).
Acknowledgments
The operational, technical, and scientific support provided by NCAR’s Earth Observing Laboratory—in particular, Alan Schanot and the Research Aviation Facility staff for their efforts with the C-130—and the support of the MAX radar deployment provided by the staff of the University of Alabama in Huntsville Severe Weather Institute and Radar and Lightning Laboratories facility are acknowledged. We thank Major Donald K. Carpenter and the U.S. Air Force Peoria National Guard for housing the C-130 during the project. The composite radar analyses in Fig. 8 were provided by the Iowa Environmental Mesonet maintained by the Iowa State University Department of Agronomy. This work was funded under National Science Foundation Grants ATM-0833828 and AGS-1247404 to the University of Illinois, AGS-1247412 to the University of Alabama in Huntsville, and AGS-1247473 to the University of Wyoming.
APPENDIX A
List of Variables and Descriptions
| α | Particle axis ratio |
 | Reflectivity-weighted axis ratio |
| Ar | Particle area ratio |
| β | Particle sphericity |
 | Reflectivity-weighted sphericity |
| d | Cohen’s effect size |
| D | Maximum particle dimension |
| KDP | Specific differential phase |
| LDR | Linear depolarization ratio |
| m | Particle mass |
| N(D) | Number distribution function |
| ϕDP | Differential phase |
| ρHV | Cross-correlation coefficient |
| Z* | Habit contribution to the ensemble reflectivity |
| Z(D) | Reflectivity distribution function |
| ZDR | Differential reflectivity |
| Zensemble | Estimated reflectivity at a coincident radar gate |
| ZHH | Radar reflectivity at horizontal polarization |
| Zp | Estimated individual particle reflectivity |
APPENDIX B
MAX Radar Elevation Corrections
REFERENCES
Alcoba, M., M. Gosset, M. Kacou, F. Cazenave, and E. Fontaine, 2016: Characterization of hydrometeors in Sahelian convective systems with an X-band radar and comparison with in situ measurements. Part II: A simple brightband method to infer the density of icy hydrometeors. J. Appl. Meteor. Climatol., 55, 251–263, doi:10.1175/JAMC-D-15-0014.1.
Al-Sakka, H., A.-A. Boumahmoud, B. Fradon, S. J. Frasier, and P. Tabary, 2013: A new fuzzy logic hydrometeor classification scheme applied to the French X-, C-, and S-band polarimetric radars. J. Appl. Meteor. Climatol., 52, 2328–2344, doi:10.1175/JAMC-D-12-0236.1.
Aydin, K., T. A. Seliga, and V. Balaji, 1986: Remote sensing of hail with a dual linear polarization radar. J. Climate Appl. Meteor., 25, 1475–1484, doi:10.1175/1520-0450(1986)025<1475:RSOHWA>2.0.CO;2.
Baker, B., and R. P. Lawson, 2006: Improvement in determination of ice water content from two-dimensional particle imagery. Part I: Image-to-mass relationships. J. Appl. Meteor. Climatol., 45, 1282–1290, doi:10.1175/JAM2398.1.
Barthazy, E., S. Göke, J. Vivekanandan, and S. M. Ellis, 2001: Detection of snow and ice crystals using polarization radar measurements: Comparison between ground-based in situ and S-Pol observations. Atmos. Res., 59–60, 137–162, doi:10.1016/S0169-8095(01)00114-4.
Bechini, R., and V. Chandrasekar, 2015: A semisupervised robust hydrometeor classification method for dual-polarization radar applications. J. Atmos. Oceanic Technol., 32, 22–47, doi:10.1175/JTECH-D-14-00097.1.
Besic, N., J. Figueras i Ventura, J. Grazioli, M. Gabella, U. Germann, and A. Berne, 2016: Hydrometeor classification through statistical clustering of polarimetric radar measurements: A semi-supervised approach. Atmos. Meas. Tech., 9, 4425–4445, doi:10.5194/amt-2016-105.
Bringi, V. N., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.
Bringi, V. N., J. Vivekanandan, and J. D. Tuttle, 1986: Multiparameter radar measurements in Colorado convective storms. Part II: Hail detection studies. J. Atmos. Sci., 43, 2564–2577, doi:10.1175/1520-0469(1986)043<2564:MRMICC>2.0.CO;2.
Bringi, V. N., V. Chandrasekar, N. Balakrishnan, and D. S. Zrnić, 1990: An examination of propagation effects in rainfall on radar measurements at microwave frequencies. J. Atmos. Oceanic Technol., 7, 829–840, doi:10.1175/1520-0426(1990)007<0829:AEOPEI>2.0.CO;2.
Bringi, V. N., T. D. Keenan, and V. Chandrasekar, 2001: Correcting C-band radar reflectivity and differential reflectivity data for rain attenuation: A self-consistent method with constraints. IEEE Trans. Geosci. Remote Sens., 39, 1906–1915, doi:10.1109/36.951081.
Cazenave, F., M. Gosset, M. Kacou, M. Alcoba, E. Fontaine, C. Duroure, and B. Dolan, 2016: Characterization of hydrometeors in Sahelian convective systems with an X-band radar and comparison with in situ measurements. Part I: Sensitivity of polarimetric radar particle identification retrieval and case study evaluation. J. Appl. Meteor. Climatol., 55, 231–249, doi:10.1175/JAMC-D-15-0013.1.
Chandrasekar, V., S. Lim, and E. Gorgucci, 2006: Simulation of X-band rainfall observations from S-band radar data. J. Atmos. Oceanic Technol., 23, 1195–1205, doi:10.1175/JTECH1909.1.
Chang, W.-Y., J. Vivekanandan, and T.-C. C. Wang, 2014: Estimation of X-band polarimetric radar attenuation and measurement uncertainty using a variational method. J. Appl. Meteor. Climatol., 53, 1099–1119, doi:10.1175/JAMC-D-13-0191.1.
Cohen, J., 1988: Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Routledge, 400 pp.
Delrieu, G., H. Andrieu, and J. D. Creutin, 2000: Quantification of path-integrated attenuation for X- and C-band weather radar systems operating in Mediterranean heavy rainfall. J. Appl. Meteor., 39, 840–850, doi:10.1175/1520-0450(2000)039<0840:QOPIAF>2.0.CO;2.
Diederich, M., A. Ryzhkov, C. Simmer, P. Zhang, and S. Trömel, 2015a: Use of specific attenuation for rainfall measurement at X-band radar wavelengths. Part I: Radar calibration and partial beam blockage estimation. J. Hydrometeor., 16, 487–502, doi:10.1175/JHM-D-14-0066.1.
Diederich, M., A. Ryzhkov, C. Simmer, P. Zhang, and S. Trömel, 2015b: Use of specific attenuation for rainfall measurement at X-band radar wavelengths. Part II: Rainfall estimates and comparison with rain gauges. J. Hydrometeor., 16, 503–516, doi:10.1175/JHM-D-14-0067.1.
Dolan, B., and S. A. Rutledge, 2009: A theory-based hydrometeor identification algorithm for X-band polarimetric radars. J. Atmos. Oceanic Technol., 26, 2071–2088, doi:10.1175/2009JTECHA1208.1.
El-Magd, A., V. Chandrasekar, V. N. Bringi, and W. Strapp, 2000: Multiparameter radar and in situ aircraft observation of graupel and hail. IEEE Trans. Geosci. Remote Sens., 38, 570–578, doi:10.1109/36.823951.
Field, P. R., 1999: Aircraft observations of ice crystal evolution in an altostratus cloud. J. Atmos. Sci., 56, 1925–1941, doi:10.1175/1520-0469(1999)056<1925:AOOICE>2.0.CO;2.
Fujiyoshi, Y., and G. Wakahama, 1985: On snow particles comprising an aggregate. J. Atmos. Sci., 42, 1667–1674, doi:10.1175/1520-0469(1985)042<1667:OSPCAA>2.0.CO;2.
Gans, R., 1912: Über die Form ultramikroskopischer Goldteilchen (On the shape of ultramicroscopic gold particles). Ann. Phys., 342, 881–900, doi:10.1002/andp.19123420503.
Goddard, J. W. F., J. Tan, and M. Thurai, 1994: Technique for calibration of meteorological radars using differential phase. Electron. Lett., 30, 166–167, doi:10.1049/el:19940119.
Gorgucci, E., and V. Chandrasekar, 2005: Evaluation of attenuation correction methodology for dual-polarization radars: Application to X-band systems. J. Atmos. Oceanic Technol., 22, 1195–1206, doi:10.1175/JTECH1763.1.
Hall, M. P., S. M. Cherry, and J. W. F. Goddard, 1980: Use of dual-polarisation radar to measure rainfall rates and distinguish rain from ice particles. Proc. IEEE 1980 Int. Radar Conf., Arlington, VA, Institute of Electrical and Electronics Engineers, 83–87.
Hall, M. P., J. W. F. Goddard, and S. M. Cherry, 1984: Identification of hydrometeors and other targets by dual-polarization radar. Radio Sci., 19, 132–140, doi:10.1029/RS019i001p00132.
Heymsfield, A. J., and D. Baumgardner, 1985: Summary of a workshop on processing 2D probe data. Bull. Amer. Meteor. Soc., 66, 437–440.
Hobbs, P. V., S. Chang, and J. D. Locatelli, 1974: The dimensions and aggregation of ice crystals in natural clouds. J. Geophys. Res., 79, 2199–2206, doi:10.1029/JC079i015p02199.
Hogan, R. J., M. P. Mittermaier, and A. J. Illingworth, 2006: The retrieval of ice water content from radar reflectivity factor and temperature and its use in evaluating a mesoscale model. J. Appl. Meteor. Climatol., 45, 301–317, doi:10.1175/JAM2340.1.
Hogan, R. J., L. Tian, P. R. A. Brown, C. D. Westbrook, A. J. Heymsfield, and J. D. Eastment, 2012: Radar scattering from ice aggregates using the horizontally aligned oblate spheroid approximation. J. Appl. Meteor. Climatol., 51, 655–671, doi:10.1175/JAMC-D-11-074.1.
Höller, H., M. Hagen, P. F. Meischner, V. N. Bringi, and J. Hubbert, 1994: Life cycle and precipitation formation in a hybrid-type hailstorm revealed by polarimetric and Doppler radar measurements. J. Atmos. Sci., 51, 2500–2522, doi:10.1175/1520-0469(1994)051<2500:LCAPFI>2.0.CO;2.
Holroyd, E. W., III, 1987: Some techniques and uses of 2D-C habit classification software for snow particles. J. Atmos. Oceanic Technol., 4, 498–511, doi:10.1175/1520-0426(1987)004<0498:STAUOC>2.0.CO;2.
Jackson, R. C., and G. M. McFarquhar, 2014: An assessment of the impact of antishattering tips and artifact removal techniques on bulk cloud ice microphysical and optical properties measured by the 2D cloud probe. J. Atmos. Oceanic Technol., 31, 2131–2144, doi:10.1175/JTECH-D-14-00018.1.
Jackson, R. C., and Coauthors, 2012: The dependence of ice microphysics on aerosol concentration in arctic mixed-phase stratus clouds during ISDAC and M-PACE. J. Geophys. Res., 117, D15207, doi:10.1029/2012JD017668.
Jackson, R. C., G. M. McFarquhar, J. Stith, M. Beals, R. A. Shaw, J. Jensen, J. Fugal, and A. Korolev, 2014: An assessment of the impact of antishattering tips and artifact removal techniques on cloud ice size distributions measured by the 2D cloud probe. J. Atmos. Oceanic Technol., 31, 2567–2590, doi:10.1175/JTECH-D-13-00239.1.
Keeler, J. M., B. F. Jewett, R. M. Rauber, G. M. McFarquhar, R. M. Rasmussen, L. Xue, C. Liu, and G. Thompson, 2016: Dynamics of cloud-top generating cells in winter cyclones. Part I: Idealized simulations in the context of field observations. J. Atmos. Sci., 73, 1507–1527, doi:10.1175/JAS-D-15-0126.1.
King, W. D., 1985: Air flow and particle trajectories around aircraft fuselages. Part III: Extensions to particles of arbitrary shape. J. Atmos. Oceanic Technol., 2, 539–547, doi:10.1175/1520-0426(1985)002<0539:AFAPTA>2.0.CO;2.
King, W. D., 1986: Air flow and particle trajectories around aircraft fuselages. IV: Orientation of ice crystals. J. Atmos. Oceanic Technol., 3, 433–439, doi:10.1175/1520-0426(1986)003<0433:AFAPTA>2.0.CO;2.
Knupp, K. R., and Coauthors, 2014: Meteorological overview of the devastating 27 April 2011 tornado outbreak. Bull. Amer. Meteor. Soc., 95, 1041–1062, doi:10.1175/BAMS-D-11-00229.1.
Kollias, P., J. Rémillard, E. Luke, and W. Szyrmer, 2011: Cloud radar Doppler spectra in drizzling stratiform clouds: 1. Forward modeling and remote sensing applications. J. Geophys. Res., 116, D13201, doi:10.1029/2010JD015237.
Korolev, A. V., G. A. Isaac, and J. Hallett, 1999: Ice particle habits in arctic clouds. Geophys. Res. Lett., 26, 1299–1302, doi:10.1029/1999GL900232.
Korolev, A. V., G. A. Isaac, and J. Hallett, 2000: Ice particle habits in stratiform clouds. Quart. J. Roy. Meteor. Soc., 126, 2873–2902, doi:10.1002/qj.49712656913.
Korolev, A. V., E. F. Emery, J. W. Strapp, S. G. Cober, G. A. Isaac, M. Wasey, and D. Marcotte, 2011: Small ice particles in tropospheric clouds: Fact or artifact? Airborne icing instrumentation evaluation experiment. Bull. Amer. Meteor. Soc., 92, 967–973, doi:10.1175/2010BAMS3141.1.
Korolev, A. V., A. Shashkov, and H. Barker, 2014: Calibrations and performance of the airborne cloud extinction probe. J. Atmos. Oceanic Technol., 31, 326–345, doi:10.1175/JTECH-D-13-00020.1.
Kouketsu, T., and Coauthors, 2015: A hydrometeor classification method for X-band polarimetric radar: Construction and validation focusing on solid hydrometeors under moist environments. J. Atmos. Oceanic Technol., 32, 2052–2074, doi:10.1175/JTECH-D-14-00124.1.
Lasher-Trapp, S., D. C. Leon, P. J. DeMott, C. M. Villanueva-Birriel, A. V. Johnson, D. H. Moser, C. S. Tully, and W. Wu, 2016: A multisensor investigation of rime splintering in tropical maritime cumuli. J. Atmos. Sci., 73, 2547–2564, doi:10.1175/JAS-D-15-0285.1.
Lim, S., V. Chandrasekar, and V. N. Bringi, 2005: Hydrometeor classification system using dual-polarization radar measurements: Model improvements and in situ verification. IEEE Trans. Geosci. Remote Sens., 43, 792–801, doi:10.1109/TGRS.2004.843077.
Lim, S., R. Cifelli, V. Chandrasekar, and S. Y. Matrosov, 2013: Precipitation classification and quantification using X-band dual-polarization weather radar: Application in the Hydrometeorology Testbed. J. Atmos. Oceanic Technol., 30, 2108–2120, doi:10.1175/JTECH-D-12-00123.1.
Liu, H., and V. Chandrasekar, 2000: Classification of hydrometeors based on polarimetric radar measurements: Development of fuzzy logic and neuro-fuzzy systems, and in situ verification. J. Atmos. Oceanic Technol., 17, 140–164, doi:10.1175/1520-0426(2000)017<0140:COHBOP>2.0.CO;2.
Magono, C., 1954: On the falling velocity of solid precipitation elements. Science Reports of the Yokohama National University, Section I, No. 3, 33–40. [Available online at http://ci.nii.ac.jp/naid/110006151417.]
McFarquhar, G. M., and A. J. Heymsfield, 1996: Microphysical characteristics of three anvils sampled during the Central Equatorial Pacific Experiment. J. Atmos. Sci., 53, 2401–2423, doi:10.1175/1520-0469(1996)053<2401:MCOTAS>2.0.CO;2.
McFarquhar, G. M., P. Yang, A. Macke, and A. J. Baran, 2002: A new parameterization of single scattering solar radiative properties for tropical anvils using observed ice crystal size and shape distributions. J. Atmos. Sci., 59, 2458–2478, doi:10.1175/1520-0469(2002)059<2458:ANPOSS>2.0.CO;2.
McFarquhar, G. M., M. S. Timlin, T. Nousiainen, and P. Yang, 2005: A new representation of the single-scattering properties for mid-latitude clouds and its impacts. Proc. 15th ARM Science Team Meeting, Daytona Beach, FL, ARM Program, 10 pp. [Available online at https://www.arm.gov/publications/proceedings/conf15/extended_abs/mcfarquhar_gm2.pdf.]
McFarquhar, G. M., M. S. Timlin, R. M. Rauber, B. F. Jewett, J. A. Grim, and D. P. Jorgensen, 2007: Vertical variability of cloud hydrometeors in the stratiform region of mesoscale convective systems and bow echoes. Mon. Wea. Rev., 135, 3405–3428, doi:10.1175/MWR3444.1.
McFarquhar, G. M., J. Um, and R. Jackson, 2013: Small cloud particle shapes in mixed-phase clouds. J. Appl. Meteor. Climatol., 52, 1277–1293, doi:10.1175/JAMC-D-12-0114.1.