1. Introduction
a. Overview
The Multi-Angle Snowflake Camera and Radar project (MASCRAD) was designed to characterize the microphysics of winter precipitation and modeling of associated polarimetric radar observables, with a longer-term goal of significantly improving radar-based quantitative precipitation estimation (Notaros et al. 2015). To support this effort, two optical instruments that are capable of making detailed observations of individual hydrometeors, a two-dimensional video disdrometer (Schönhuber et al. 2008) and a multiangle snowflake camera (Garrett et al. 2012), were installed at a site located 13 km south-southeast of the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar in northeastern Colorado. To provide a reference for these hydrometeor observations, dedicated CSU–CHILL radar scans were conducted over the surface instrumentation site when precipitation was in progress. One event of particular interest during the MASCRAD observational campaign was the occurrence of several graupel showers that affected the surface instrumentation site during the afternoon hours of 16 February 2015 (Bringi et al. 2015; Kennedy et al. 2015). The surface hydrometeor observations showed that these showers were primarily composed of irregularly shaped graupel particles, while the radar detected fractionally negative values of differential reflectivity Zdr in the graupel-shower echo cores.
In this paper, we relate the time evolution of the hydrometeor physical characteristics as derived from the optical-instrument data to the dual-polarization radar data collected in the immediate vicinity of the optical sensors. The paper is organized as follows: Section 1 continues with background information on the formation processes and structural characteristics of graupel. Section 2 describes the instrumentation for the MASCRAD project and gives an overview of the 16 February 2015 event in terms of the synoptic meteorological setting and the evolution of the radar echoes. Section 3 describes observations at the Easton/Valley View Airport (Colorado) site and presents details of the graupel-shower hydrometeor characteristics and analysis of measured data. Section 4 provides estimations of the axis ratio and dielectric constant of recorded particles and scattering computations in comparison with radar measurements. Conclusions are offered in section 5.
b. Graupel formation and dual-polarization radar characteristics
It has been recognized for some time that graupel particles are the outcome of rime accumulations that are heavy enough to obscure the original embryo particle (Knight and Knight 1973). Laboratory measurements (Cober and List 1993) have shown that the density of the rime deposit varies with the rate at which supercooled droplets impact the collecting graupel particle, the size distribution of the impacting supercooled drops, and the graupel surface temperature. The measured rime-density values were generally between 0.2 and 0.4 g cm−3 in these experiments (Cober and List 1993). Naturally occurring graupel-particle shapes have been classified into hexagonal, conical, or irregular-lump categories (Magono and Lee 1966). Wind-tunnel studies have shown that the conical shape begins as the expanding rime deposit accumulates on the upwind (lower) surface of the growing particle (Pflaum et al. 1978). Pflaum et al. (1978) also noted that slight asymmetries in the graupel particle’s surface roughness, mass accumulation, and so on frequently induced pendulum-swing-type motions. Rime collected during this swinging-motion regime yields a conical shape for the particles. The final diameters of the graupel particles grown in this wind-tunnel study averaged 1.1 mm. At larger diameters and higher terminal velocities (Reynolds numbers above ~500), the orientations of ~2-cm-diameter conically shaped plastic graupel replicas falling through a liquid bath were observed to be more unstable, with quasi-random tumbling motions becoming preferred (List and Schemenauer 1971). Rime deposition during such tumbling particle motions leads to more spherical particle shapes.
These variations in graupel density, shape, and orientation greatly affect the particle’s microwave backscatter properties. Dry, low-density rime composition will reduce the bulk complex dielectric constant, making the particle’s shape properties less apparent in dual-polarization radar measurements (Aydin and Seliga 1984). The apex angle in conical graupel particles controls the maximum dimensions in the horizontal (H) and vertical (V) directions, and variations in the ratio of the vertical to horizontal dimensions (loosely termed as axis ratio) can alter the sign of Zdr. The scattering calculations of Evaristo et al. (2013) show that positive Zdr develops as the apex angle becomes larger than ~50°–70° depending upon the assumed particle geometry. At smaller apex angles, the axis ratio (ratio of maximum vertical dimension to maximum horizontal dimension) is greater than 1 (or prolate-like shaped), resulting in negative Zdr, whereas spherical particle shapes produce Zdr of 0 dB. Oue et al. (2015) report on negative Zdr, as well as negative specific differential phase Kdp, from X-band polarimetric radar that were ascribed to conical graupel formed in Arctic mixed-phase clouds, but they did not provide in situ verification.
Dual-polarization radar hydrometeor classification schemes generally associate graupel with reflectivity levels between 20 and 50 dBZ and differential reflectivity levels between −0.5 and +1–2 dB (Liu and Chandrasekar 2000; Straka et al. 2000). Most of these broad radar parameter ranges are due to variations in the shape and effective density of the graupel particles (for Zdr) as well as the particle size distribution (PSD) (for horizontal reflectivity Zh). Here, measurements of the PSD along with the axis ratio from two orthogonal views are utilized along with estimation of density (via fall speed measurements and Böhm’s method; Böhm 1989; Huang et al. 2015) to compute Zh and Zdr for comparison with direct radar measurements of the same. This approach is expected to provide a more realistic method of comparing radar-measured variations in the Zh–Zdr plane with scattering calculations. Some earlier scattering studies assumed fixed conical shapes and particle densities to explain the negative Zdr signature observed by radar (Evaristo et al. 2013; Oue et al. 2015).
2. 16 February 2015 graupel-shower observations
a. MASCRAD project instrumentation
The MASCRAD ground instrumentation site was established on the grounds of a small agricultural aviation airport (Easton/Valley View) located at a range of 13.03 km on the 171.3° azimuth of the CSU–CHILL radar (Fig. 1; Notaros et al. 2015; Kennedy et al. 2015). A site at relatively close range was desired to reduce the vertical separation between the center of the radar beam and the underlying ground surface. This effort was advanced by the ~30-m-greater terrain height at the Easton site versus at the CSU–CHILL location. The lowest antenna elevation angle that was free of ground-clutter contamination at Easton was 1.5°. At this elevation angle, the CSU–CHILL main beam was located between the heights of ~192 and 420 m AGL over Easton.
Locations of the primary observing sites used in the 2014/15 MASCRAD operations. Horizontal distances are in kilometers from the CSU–CHILL radar.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
To reduce the effects of surface winds on the collection efficiency of the surface instruments, a two-thirds-scale (8-m diameter) double-fence intercomparison reference (DFIR) wind screen was constructed at the Easton site. The DFIR enclosure housed an OTT Hydromet GmbH Pluvio model 200 precipitation gauge and a surface mesonet station (measuring wind speed and direction, free air temperature, dewpoint, and atmospheric pressure) that was supplied by the National Center for Atmospheric Research (NCAR). NCAR also installed mobile sounding equipment that allowed radiosondes to be launched from Easton during periods of intensive observations. The NCAR S-band dual-polarization (S-Pol) radar that was located ~33 km southwest of Easton documented larger-scale radar echo patterns during the MASCRAD project. A summary of the operating characteristics of the CSU–CHILL radar is given in Table 1.
CSU–CHILL radar characteristics in the MASCRAD 2014/15 winter campaign.
In addition to the sensors described above, two optical hydrometeor-sensing instruments, a two-dimensional video disdrometer (2DVD) and a multiangle snowflake camera (MASC), were also installed at the Easton site. The primary function of these optical instruments was to provide data to develop detailed three-dimensional representations of the individual hydrometeor’s ice–air structures to support microwave scattering calculations. Since the 3D particle reconstructions are not the primary thrusts of this paper, only a general overview of the observations provided by these optical instruments is given.
Of the two optical hydrometeor instruments installed at Easton, the 2DVD has a longer history of usage. The 2DVD used in the MASCRAD project was a low-profile, third-generation version of the instrument (Schönhuber et al. 2008). The 2DVD generates two horizontal planes of visible light that are focused on line-scan cameras composed of linear arrays of 625 active pixels and a horizontal resolution of 160 μm (Fig. 2). Hydrometeors falling through the light beams shadow the individual diodes; the shadowing status of the diode arrays is recorded at a 55.17-kHz sampling rate. The two camera planes are perpendicular to each other, allowing two orthogonal silhouette views of the particles to be constructed. The camera planes are separated in the vertical direction by a calibrated distance of ~6.2 mm. Particle fall speeds are calculated from the time difference between the shadowing of the upper and lower light beams. The vertical resolution depends on the fall speed and is 100 μm for a 5 m s−1 fall speed. The virtual sampling area of the 2DVD is approximately 10 cm × 10 cm.
Schematic diagram of the 2DVD (after Schönhuber et al. 2008).
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The MASC was more recently developed at the University of Utah (Garrett et al. 2012). The basic MASC design uses three identical digital cameras mounted in a common horizontal plane with viewing angles that are separated by 36° (Fig. 3a). Two infrared motion-detection beams with a vertical separation of 32 mm are located immediately above the common imaging volume of the cameras. Falling hydrometeors interrupt the IR beams, triggering a bank of light-emitting diode (LED) flash lamps as well as the cameras. Particle fall speeds are calculated on the basis of the time delay between the interruptions in the upper and lower IR beams. The combination of camera and lens equipment used in the CSU MASC produces 2448 × 2048 pixel grayscale images with a resolution of 35 μm per pixel.
(a) Schematic diagram of the basic MASC (Garrett et al. 2012). The irregular yellow-shaded area indicates the region in which falling hydrometeors will trigger the lights and cameras. (b) The CSU MASC installation, including two additional externally added cameras, at the Easton site.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
To improve the 3D particle reconstructions (Kleinkort et al. 2015), two additional lower-resolution (1288 × 964 pixel) cameras with a downward-looking view into the sample volume were added (Fig. 3b). The MASC horizontal sampling area is appreciably smaller than that of the 2DVD (~3 cm × 10 cm vs 10 cm × 10 cm).
b. Synoptic setting and summary of radar data
The 16 February 2015 graupel-shower activity in the MASCRAD project area took place during a general regime of northwesterly flow at the 500-hPa level. At 1200 UTC 15 February, a short-wavelength trough containing 500-hPa temperatures in the range from −25° to −27°C was analyzed over western Montana and central Idaho. The general project-forecast expectations were that periods of fairly widespread light-to-moderate snow would occur during the afternoon and overnight hours of Sunday 15 February through the early morning of Monday 16 February as the short-wave trough and associated surface cold front crossed the area. Coordinated S-Pol and CSU–CHILL data collection took place between ~1900 UTC 15 February through ~1600 UTC 16 February. Three soundings from the NCAR mobile GPS advanced upper-air system (MGAUS) were launched from Easton between 0500 and 1300 UTC 16 February. Formal MASCRAD operations ended around 1600 UTC 16 February as most of the synoptic-scale lift associated with the short wave had moved south of the region. Overnight snow accumulations of ~25–75 mm were recorded in the Rocky Mountain foothills 40–60 km west of the CSU–CHILL radar. The immediate Easton area only received ~12 mm of snow.
In the wake of the passage of the nocturnal short-wave trough, the tropopause level in the 1300 UTC Easton sounding had lowered to ~350 hPa (~6.5 km AGL; Fig. 4, top panel). The National Weather Service (NWS) 1200 UTC constant-pressure-level analyses at the 700- and 500-hPa levels (not shown) indicated that cold-air advection was occurring in the MASCRAD project area. This is consistent with the overall backing wind directions that were observed between the surface and ~400 hPa in the Easton sounding. Early-morning forecast discussions issued by the NWS Denver–Boulder (Colorado) office noted the possibility of midday shower development as surface heating in conjunction with the cold-air advection aloft acted to promote steep lapse rates. This synoptic setting is very similar to that described in an examination of two graupel-shower events in Evaristo et al. (2013). Figure 5 shows the NWS sounding from one of the Evaristo et al. (2013) cases in which conical graupel was observed at Lexington, Massachusetts. As in the Easton sounding, the close proximity of a midtropospheric low pressure system resulted in a low tropopause height that surmounted a surface-based moist layer containing relatively steep lapse rates. The Evaristo et al. study linked surface heating in this synoptic environment to the development of low-topped convective showers that were observed to produce small (~8-mm diameter) conical graupel at the ground.
(top) Skew T–logp plot of the data launched at 1301 UTC 16 Feb 2015 from the Easton site. Wind speeds are plotted in meters per second. (bottom) Magnified view of the lower, graupel-shower-bearing portion of the sounding shown in the top panel. For reference, the 700-hPa height (−12.5°C) is at 1550 m AGL and the 500-hPa height (−30.6°C) is at 4030 m AGL. The graupel-shower echo-top height was ~3.5 km AGL (see Fig. 11, below). The sounding temperature at this height was −26°C.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
Skew T–logp plot of the NWS sounding from Chatham, Massachusetts, at 1200 UTC 12 Apr 2012. Showers producing small, conical graupel at the surface were observed later on this day (Evaristo et al. 2013).
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
Visibly growing cumulus clouds, some with opaque precipitation shafts, were first observed from the CSU–CHILL radar site at approximately 1810 UTC 16 February 2015. At 1826 UTC, these initial shower echoes, with maximum low-elevation reflectivity levels of 30–35 dBZ, were located along an axis that curved to the south and west of the Easton site (Fig. 6).
Reflectivity from the CSU–CHILL radar at 1824 UTC 16 Feb 2015. The elevation angle is 3°; the axis labels are in kilometers from an origin at the CSU–CHILL radar.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The vertical structure of one of the more intense echo cores centered 28 km west of CSU–CHILL was sampled in an RHI scan at 1836 UTC (Fig. 7a). The convective echoes were shallow, with the 0-dBZ reflectivity level reaching a maximum height of only ~3.5 km AGL. This height was nearly 2 km less than the depth of the moist layer in the 1300 UTC Easton sounding (Fig. 4, top panel). The vertical echo development may have been restrained by the slightly more stable lapse rates near the ~600-hPa level in the Easton sounding (Fig. 4, bottom panel). The reflectivity cores in this RHI scan were consistently associated with negative Zdr values in the range from −0.5 to −0.2 dB (Fig. 7b). Within the >21-dBZ regions of these echo cores, a localized Zdr minimum sometimes occurred near the height layer from 3.5 to 4.0 km MSL (2.1–2.6 km AGL). These CSU–CHILL Zdr values incorporate an adjustment to correct the −0.2-dB bias that was quantified using vertically pointed data obtained during a heavy-snow event that occurred 5 days later. As an additional check on the CSU–CHILL Zdr calibration, comparisons of the CHILL and S-Pol Zdr values observed over the Easton site were done for the 0300–0800 UTC period on 16 February 2015 when the weakening precipitation echoes were still of usable strength. These comparisons indicated that the CSU–CHILL Zdr values had a maximum uncertainty of less than ~0.05 dB (see the appendix for details). The Zdr data recorded by the NWS KFTG radar located near Denver (roughly 60 km south of the echo band shown in Fig. 6) also contained fractionally negative Zdr values in the high-reflectivity areas of these showers. Negative Zdr regions have been noted in the upper portions of thunderstorms where strong electric fields act to rotate the major axes of ice crystals toward vertical (Hubbert et al. 2014). The Northern Colorado Lightning Mapping Array (LMA) is located in the immediate CSU–CHILL area; this technology has demonstrated good sensitivity in the detection and 3D mapping of the VHF signals generated by various lightning phenomena (stepped leaders, etc.; Thomas et al. 2004). The LMA network did not detect any discharges during the afternoon hours of 16 February 2016. From this fact, we suspect that cloud electrification played a minimal role in producing the observed negative Zdr patterns.
(a) Reflectivity (dBZ) and (b) differential reflectivity (dB) from a CSU–CHILL RHI scan on an azimuth of 261° at 1835 UTC 16 Feb 2015. For reference with (a), the solid blue contours in (b) are 21 and 27 dBZ.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The cellular nature of the precipitation echoes that developed during the afternoon hours of 16 February 2015 implied that graupel production was localized. To take advantage of an observing network with higher density than that provided by the NWS surface observation, the reports filed by the Community Collaborative Rain, Hail and Snow Network (CoCoRaHS; http://cocorahs.org/) were examined. These observers routinely file precipitation totals recorded over 24-h intervals. They also are encouraged to enter remarks describing notable precipitation characteristics, such as the occurrence of graupel. A total of 140 reports were filed from Larimer and Weld Counties in Colorado (i.e., the immediate MASCRAD project area). The remarks section in five of these reports mentioned observations of graupel. The data archive for the Meteorological Phenomena Identification Near the Ground (mPING; http://mping.nssl.noaa.gov/) was also examined for the local afternoon hours of 16 February 2015. This archive contained six reports mentioning either graupel or ice pellets. The locations of the four graupel reports (all from CoCoRaHs) within the geographical domain of Fig. 6 are marked with orange/red dots. Three of these reports were in the vicinity of the convective echo with the negative Zdr core characteristics as shown in Fig. 6.
3. Observations at the Easton site and detailed analysis of measured data
Three consecutive, but separate, showers were recorded at the Easton site: (i) from 1930 to 1934 UTC, (ii) from 1938 to 1942 UTC, and (iii) from 1958 to 2005 UTC. As these showers began to affect the Easton site, repeated RHI scans with a cycle time of ~2.25 min were started. Figures 8–10 show a sample of the echo evolution as period i began; similar evolution was also observed during periods ii and iii. The RHI data showed a repeated tendency for echo development to initially occur aloft in the height interval from 2 to 3 km AGL. These reflectivity cores typically contained an elevated echo maximum that remained near 2 km AGL. Narrow curtains of enhanced reflectivity developed downward from these elevated cores and reached the surface within ~3–5 min. The majority of these developing/descending higher-reflectivity cores were characterized by negative Zdr values approximately from −0.5 to −0.2 dB.
As in Fig. 7, but on the azimuth of the Easton site (171°) at 1926:43 UTC 16 Feb 2015. Easton is located essentially at the 13-km-range mark.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
As in Fig. 8, but for the volume start time at 1929:20 UTC 16 Feb 2015.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
As in Fig. 8, but for the volume start time at 1931:57 UTC 16 Feb 2015.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
a. Analysis of period i from 1930 to 1934 UTC
Figure 11 shows the vertical profile of radar data at 1932 UTC over the Easton site. At this time, the reflectivity near the surface was ~25 dBZ and was more or less uniform with height up to 2 km; it then decreased rapidly to 0 dBZ at echo top. On the other hand, Zdr was noted to be uniform at −0.2 dB below 2 km to the surface and rapidly increasing with height from 2 km upward to 0.8 dB at 3.5-km height, where the sounding temperature was −26°C (see Fig. 4, bottom panel). Such a vertical profile is suggestive of graupel particles below 2 km that originated via riming of the pristine crystals that were probably the predominant particle type in the higher-altitude positive Zdr region.
Height profiles of Zh (blue) and Zdr (red) averaged over a range interval of ±0.25 km of the Easton site at 1932 UTC 16 Feb 2015. Temperatures (°C) from the 1300 UTC Easton sounding are indicated on the abscissa at height intervals of 0.5 km. Temperatures from the 0000 UTC NWS Denver sounding are also given. Note that above a height of 3.8 km the Zdr data were classified as being due to nonmeteorological echoes and should be disregarded.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
Figure 12 shows a sample image recorded by one of the 2DVD cameras at 1930:08 UTC. The equivolume diameter was 3.5 mm, and the measured fall speed was 2.6 ms−1. These quantities are typical values for small-diameter graupel. A corresponding sample image from the MASC cameras is shown in Fig. 13 at 1930:18 UTC. The MASC-derived diameter (4.3 mm) and fall speed (2.6 ms−1) are in good agreement with the 2DVD observations.
Sample graupel image from one camera of the 2DVD collected at 1930:08 UTC 16 Feb 2015 at the Easton site. The equivolume spherical D is 3.5 mm using the images from both cameras. The measured fall speed was 2.6 m s−1.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
Sample graupel image from one camera of the MASC (in Fig. 3b) at 1930:18 UTC. Via 3D reconstruction using five images, the equivolume spherical D is 4.3 mm, and the fall speed was measured to be 2.6 m s−1.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The mean vertical velocity versus diameter from the 2DVD for period i from 1930 to 1934 UTC is shown in Fig. 14. The equivolume diameter D and fall speed are obtained by processing the raw line-scan data from the two orthogonal cameras as described in Huang et al. (2015). Here, the mean fall speed in discrete bins of D is shown (with the bars that indicate ±1 standard deviation) along with an exponential-type fit to the mean fall speed (dashed line). The fit to the mean fall speed versus D is representative of typical graupel reported in the literature (e.g., Locatelli and Hobbs 1974). A better fit to the observations was obtained by using an exponential relationship than by using a power law.
The bin-averaged vertical velocity vs equivolume diameter D from the 2DVD for period i (1930–1934 UTC 16 Feb 2015). The bars that indicate ±1 std dev are shown, along with an exponential fit (dashed blue line). The power-law fit is shown by the dashed red line. The hydrometeors were predominantly small graupel during this time period.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The hydrometeor size distributions for each of the three shower periods were developed using the methods of Huang et al. (2015) as applied to the 2DVD data (Fig. 15). It is clear that sampling issues are evident for the larger sizes with D > 5 mm (mainly for period ii, which is discussed below) but the shape is reasonably close to exponential for 0.5 < D < 3 mm with different slopes and intercept parameters.
Hydrometeor size distribution N vs D for the three precipitation-shower events. The presence of larger-diameter snow aggregates is apparent during period ii (plotted in black). The total numbers of particles sampled during periods i, ii, and iii were respectively 1917, 619, and 513.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
b. Analysis of period ii from 1938 to 1942 UTC
The second shower occurred between 1938 and 1942 UTC. The associated vertical profiles of Zh and Zdr over Easton are shown in Fig. 16. The general features of the vertical profiles shown in Figs. 11 and 16 are similar, but the 2DVD data showed a mix of smaller graupel and larger aggregate particles during the later (1938–1942 UTC) period. The largest particle recorded by the 2DVD at 1941:24 UTC is shown in Fig. 17 and is seen to be clearly an aggregate (with an apparent D of 8.2 mm and a measured fall speed of 1.3 m s−1).
As in Fig. 11, but for 1940 UTC (shower-event period ii).
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
Sample 2DVD image of a large aggregate (D = 8.2 mm; fall speed of 1.3 m s−1) at 1941:24 UTC.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
An example MASC image of one of these large aggregates observed at 1941:32 UTC is shown in Fig. 18. This particle’s diameter and measured fall speed were 5.6 mm and 1.5 m s−1, respectively. Evidence of this aggregate’s complex structure and moderate degree of riming is also apparent in Fig. 18.
Sample MASC image of a large aggregate (D = 5.6 mm; fall speed of 1.5 m s−1) at 1941:32 UTC.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The distribution of the hydrometeor vertical velocities obtained from the 2DVD measurements during the 1938–1942 UTC period is shown in Fig. 19. This distribution clearly shows a population of both faster-falling graupel (D < 2 mm) and slower, higher-drag-coefficient snow aggregates (D > 2 mm). The plotted points are the fall speeds for each individual particle, and no fit is attempted for the mixture. One can picture visually that a a power-law fit is possible for D < 1 mm with more or less constant fall speed of 1.5 m s−1 being characteristic of the aggregates with D > 2 mm. The latter fall speed is typical for aggregates of dendrites (Brandes et al. 2008). The particle size distribution averaged over this same 4-min period (1938–1942 UTC) is shown in Fig. 20. This distribution is consistent with a mixture of smaller graupel (D < 2 mm) and larger snow aggregates (D > 3 mm, with maximum of 8 mm).
Scatterplot of the vertical velocity vs D from the 2DVD for period ii (1938–1942 UTC).
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
Particle size distribution N(D) for period ii.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
4. Scattering simulations and comparisons with radar measurements
a. Estimation of the height/width ratio of particles from 2DVD images
To understand the origin of the observed weak negative Zdr signatures we have used the 2DVD images to estimate the height-to-width ratio h/w for all of the particles recorded for the three periods as a function of D. Figure 21 illustrates the dimensions (h and w) obtained from the vertical “stack” of line scans from one camera. The height is simply the vertical velocity multiplied by the total time needed to complete the stack of line scans, which is not dependent on the horizontal movement of the particle. The width is taken as the maximum line-scan dimension in the stack, which is also not dependent on horizontal movement (in the presence of horizontal movement, the line scans are shifted horizontally so that the stack appears to be skewed but the maximum line scan dimension is not altered). A similar height-to-width ratio is performed for the orthogonal camera image, and the final h/w is computed as the geometric mean of the two camera measurements.
Example of the estimation of height h and width w from a sample single-camera 2DVD image. The h/w ratio is here loosely referred to as “axis ratio.”
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
One can loosely refer to h/w ratio as the axis ratio of an equivalent spheroid (prolate if h/w > 1 and oblate if h/w < 1). Figure 22 shows the results in terms of bin-averaged mean and bars showing ±1 standard deviation of the axis ratio (i.e., averaged over bins of D). While there is substantial scatter in the axis ratios, the fit to the mean axis ratios shows oblate-like shapes for D < 1 mm and weak prolate-like shapes for D > 2 mm. One can consider this as a relation of bulk axis ratio versus D for this dataset (encompassing all three periods over Easton site). It is clear that the mean axis ratio is prolate-like when D > 1 mm, whereas it is oblate-like for D < 1 mm. For Rayleigh scattering, the corresponding single-particle Zdr will be respectively negative and positive (in decibel units). The graupel shape varies considerably, but the details of the shape are less important in determining the Zdr than is whether the gross shape is oblate-like (positive Zdr) or prolate-like (negative Zdr).
Plot of the bin-averaged mean (red dots and solid line) of the height/width vs D from the 2DVD for the entire graupel-shower period. The vertical bars that indicate the ±1 std dev extent of the axis ratio values in each diameter bin are shown in red. The solid blue line gives the fit to the mean values. The dashed line represents a height/width of 1.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
b. Dielectric constant estimation and 
To complete the scattering model (Mishchenko 2014) (given the size distribution and the axis ratio vs D), the particle density must be estimated, from which the dielectric constant can be calculated using the Maxwell Garnett mixing formula (ice–air two-component mixture). The method for computing the density follows Böhm (1989) and is adapted for 2DVD data by Huang et al. (2015), which adaptation is used herein. In brief, from the terminal fall speed, area ratio (ratio of shadowed pixel area to minimum circumscribed ellipse), apparent D, and environmental parameters, the mass is calculated for each particle [the error in derived particle mass has been estimated by Szyrmer and Zawadzki (2010) to be around 40%–50%]. Since the apparent volume is computed from the two orthogonal stacks, the density follows as the ratio of mass to volume. Last, a power-law fit to the mean density versus D is performed for the entire period (Fig. 23; the dielectric constant follows directly). The mean density for each period is also computed as the ratio of the mean mass to the mean volume. For the three periods they are 0.18, 0.06, and 0.19 g cm−3, respectively. The lower value obtained during period ii reflects the presence of large aggregates. The densities so computed appear to be on the low side relative to the literature (Pruppacher and Klett 2010). As demonstrated below, however, the computed reflectivity would be too large when compared with the radar measurements if ad hoc assumptions of fixed graupel density from the literature were assumed (≈0.5–0.7 g cm−3).
Hydrometeor bulk density vs diameter for the entire observation period. Vertical bars indicate the ±1 std dev range around the mean value in each diameter bin. The red line is a fifth-order polynomial fit to the observations: note that we assume ρ(D > 2.875 mm) = ρ(D = 2.875 mm) for the polynomial fit. The green dashed line is the fitted relationship of power-law density vs diameter.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The size distribution averaged over each of the three periods, axis ratio versus D, and dielectric constant are input to the 
The Zdr vs Zh from radar measurements for all three time periods compared with scattering simulations that are based on the N(D), mean axis ratio, and density from the 2DVD (various density models are as indicated in the legend). For each density model the lowest, intermediate, and largest Zh correspond respectively to periods iii, i, and ii.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
The trend from the scattering calculations shows weakly negative Zdr (lower bound of −0.4 dB) independent of Zh. For each density model described above, the lowest, intermediate, and largest Zh correspond respectively to periods iii, i, and ii, which is consistent with the occurrence of larger sizes in the respective N(D) (see Fig. 15). The |Zdr| is relatively constant for each density model independent of Zh, however.
The scatter from the different density assumptions falls within the scatter from the radar measurements although the radar Zdr values span both positive and negative Zdr. This is shown more clearly in Fig. 25, depicting the histogram of radar-measured Zdr, which is skewed to negative values. Overall, the scattering simulations that use 2DVD-derived parameters of the variation of Zdr versus Zh capture the weak trend toward negative Zdr that was observed by radar.
Histogram of radar-measured Zdr from all RHI scans over the Easton site from 1934 to 2011 UTC. Data are selected from range interval 10–22 km (the range to the Easton site is ~13 km) and height interval 0.5–1.0 km AGL.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
c. Analysis of LDR radar measurements from RHI scans over Easton
Figure 26 shows a scatterplot of the linear depolarization ratio (LDR: transmit H and receive V) versus reflectivity (at H polarization) to illustrate the range of LDR in the winter graupel example. The radar is capable of measuring LDR values as low as from −40 to −43 dB (Bringi et al. 2011). The LDR system bias was corrected using solar scans (Brunkow et al. 2000). To avoid noise biasing the LDR measurement, the data shown in Fig. 26 were selected with the crosspolar signal-to-noise ratio (SNR) > 5 dB. Note that the radar data were collected using alternate pulsing of the H and V transmitters with pulse repetition time (PRT) of 0.5 ms. The high-speed transfer switch (after the low-noise amplifiers) was exercised to route the copolar (i.e., HH and VV) signals to one receiver and the crosspolar (i.e., VH and HV) signals to the second receiver (Brunkow et al. 2000).
Scatterplot of LDR vs reflectivity radar measurements from RHI scans over Easton. Data are selected from the range interval between 10 and 22 km and the height interval between 0.5 and 3.0 km AGL. Bin-averaged LDR is also shown in red, along with bars that indicate ±1 std dev.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
Whereas Zdr is related to the reflectivity-weighted mean axis ratio of the backscattering particles within the radar pulse volume, the LDR is responsive to the presence of nonspherical, relatively high dielectric particles that are oriented at appreciable angles to the incident H-polarized radar waves. Since the graupel particles observed in this case had only modest departures from spherical shapes and were composed of low-bulk-density ice, LDR are expected to be small (i.e., below the ~−26-dB values associated with large raindrops; Bringi and Chandrasekar 2001). The LDR values from the graupel showers range from −36 to −29 dB, with an average of approximately −32 dB, independent of reflectivity. In general, the LDR will vary with the particle-density, canting-angle, and axis-ratio distributions, and less so with reflectivity (excluding the rain case in which the mean axis ratio decreases with increasing size; Bringi and Chandrasekar 2001). As such, scattering simulations of LDR using bulk assumptions about particle density, canting angle, and shape cannot give the range of values obtained from direct measurements. Rather, a “particle by particle” scattering simulation approach is needed (Thurai et al. 2009).
5. Conclusions
Graupel in this case was produced by low-topped convective cells whose development was promoted by cold midtropospheric temperatures (500-hPa environmental temperature of ~−27°C). Although no in situ data are available, we surmise that the updraft magnitudes of several meters per second that typically exist in the active regions of clouds of this type were strong enough to generate a supercooled liquid environment in which graupel particles grew by riming. Subfreezing temperatures and relatively humid conditions between the midtropospheric and near-surface levels aided the survival of the graupel particles as they descended to the ground. The most distinctive dual-polarization radar characteristic of these graupel showers was their slightly, but consistently, negative Zdr. These graupel-shower synoptic-environment and radar characteristics are consistent with those found by Evaristo et al. (2013).
This study has provided more-detailed observations in terms of high-time-resolution RHI scans of the parent convective echoes and physical characterizations of the individual graupel particles obtained from surface-based optical instruments. The RHI data showed that the negative Zdr values extended vertically through much of the reflectivity cores. Within these echo cores, there was a tendency for slightly more negative Zdr to occur in the height region from 2.1 to 2.6 km AGL. Wind-tunnel studies of “freely falling” graupel particles have shown that various swinging, pendulum-type motions occur as rime accumulates on the bottom (upstream) surface of the particle (Pflaum et al. 1978). The resultant conical shapes tend to fall with the major axis oriented toward the vertical direction with the apex up (Zikmunda and Vali 1972), promoting negative Zdr values. Graupel particles that reach larger diameters and higher Reynolds numbers have a greater tendency to develop tumbling motions that would result in Zdr ≈ 0 dB (List and Schemenauer 1971). We speculate that conical graupel shapes may have been more prevalent in the levels of the echo cores at ~2.1–2.6 km AGL where Zdr tended to be slightly more negative. The growth and reorientation processes that were active during the particle’s subsequent descent to the surface apparently caused the graupel shapes to tend more toward the irregular lumps seen in the optical-instrument images. The height-to-width-ratio statistics calculated from the 2DVD data show that the primarily lump-type graupel particles observed in this case still had a slightly prolate mean shape characteristic. The growth-related transition to quasi-spherical graupel shapes, with a characteristic Zdr of ~0 dB, was apparently not completed in this event.
Three consecutive periods (each lasting ~4 min) of graupel showers were recorded by the 2DVD and the MASC at the Easton measurement site in coordination with high-resolution radar RHI scans. The 2DVD measurements of fall speed and size were used to estimate the mean density for each period as well as the density versus size fit to data from all three periods using Böhm’s (1989) method. The height-to-width ratio was determined for each particle, and a mean fit of this ratio with size was obtained along with the average PSD for each period. The 
Acknowledgments
This work was supported by the National Science Foundation under Grant AGS-1344862. Author Kennedy was also supported under National Science Foundation Grant 1460585. We also acknowledge Bob Easton, owner of the Easton/Valley View Airport, for providing us the location for the MASCRAD Field Site; Walter Petersen of the NASA Wallops Flight Facility for lending the 2DVD SN36 and PLUVIO200 to us for the MASCRAD snow season of 2014/15; Robert Bowie for off-hour CSU–CHILL radar operations; Andrew Newman of the National Center for Atmospheric Research (NCAR) for forecasting support during the project; Timothy Lim and William Brown of NCAR for performing MGAUS soundings during the 2014/15 MASCRAD winter campaign; and John Hubbert of NCAR for collaboration in running the NCAR S-Pol radar observations.
APPENDIX
CSU–CHILL Radar Zdr Calibration Verification
During the MASCRAD campaign, NCAR’s S-Pol radar was also used to perform regular scans over Easton during significant events. Although the S-Pol radar did not operate during the time of the graupel event on 16 February 2015, it did, however, perform the (predefined) Easton schedule scans during a widespread snow event about 12 h earlier. As with the CHILL scan schedule, the S-Pol scans also included regular RHI scans over the Easton site. Figure A1a shows the locations of the CHILL radar and the S-Pol radar (marked with solid black dots) as well as the directions of the RHI scans over Easton (black lines). The Easton site was 13 km away from the CHILL radar, and the range from the S-Pol radar site was 33 km along 45° azimuth. The hypothesis is that by comparing the Zdr histograms from the two independently calibrated radars from a widespread snow event (albeit some 12 h earlier than the graupel event) will give strong credibility to the physical interpretation of the weak negative CHILL Zdr measurements in the graupel event reported in this article. One caveat is that the two radars have different viewing angles of the snow, but the Zdr difference (in our case of aggregated low-density snow) is expected to be negligible.
(a) Depiction of the locations of the CSU–CHILL and NCAR S-Pol radars relative to the Easton instrumentation site. (b) Histograms of Zdr data in the immediate Easton area during widespread snow in the 0300–0800 UTC period on 16 Feb 2015. S-Pol data are plotted in black, and CSU–CHILL data are shown in gray.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
For S-Pol, the Zdr offset was determined by the method described by J. Hubbert (2016, personal communication), which depends on (among other factors) the ambient temperature at the S-Pol radar site. The accuracy of the S-Pol Zdr calibration using this technique (which was fine tuned for the snow event) is expected to be within ±0.01 dB or better. In the case of CHILL Zdr, the calibration was obtained by analysis of vertical-pointing (VP) data from another snow event 5 days later that was applied to the graupel case reported in this article and to the snow event reported in this appendix.
To account for possible small receiver front-end drifts (affecting bias in Zdr) due to the warming trend from the snow event to the graupel event, we have made use of data from test pulses that were regularly injected at the receiver front-end inputs during operations and have determined that the relative change in the Zdr drift due to the receiver front ends only is a further −0.07 dB. The drift appears to be correlated with temperature change at the University of Northern Colorado (located ~7 km southwest of CSU–CHILL), as shown in Figs. A2a and A2b. Thus, assuming there is no differential change in the passive H and V microwave paths (due to temperature change) from antenna feed to the test-pulse injection plane, the best estimate for the Zdr offset adjustment (over and above the VP-scan-based calibration) during the graupel event is inferred to be −0.02 dB. To conclude, the Zdr calibration as applied to the graupel event is expected to be accurate to within ±0.05 dB.
(a) Difference (dB) of the test-pulse signal levels recorded in the H and V receiver channels of the CSU–CHILL radar as a function of time on 16 Feb 2015; the data gap during the 1700–1800 UTC period occurred when the radar was put into standby mode to await echo development. (b) Ambient air temperature measurements for the same time period as recorded at the University of Northern Colorado Earth Science Department. This measurement site is approximately 7 km southwest of the CSU–CHILL radar.
Citation: Journal of Applied Meteorology and Climatology 56, 2; 10.1175/JAMC-D-16-0197.1
REFERENCES
Aydin, K., and T. A. Seliga, 1984: Radar polarimetric backscattering properties of conical graupel. J. Atmos. Sci., 41, 1887–1892, doi:10.1175/1520-0469(1984)041<1887:RPBPOC>2.0.CO;2.
Böhm, H. P., 1989: A general equation for the terminal fall speed of solid hydrometeors. J. Atmos. Sci., 46, 2419–2427, doi:10.1175/1520-0469(1989)046<2419:AGEFTT>2.0.CO;2.
Brandes, E. A., K. Ikeda, G. Thompson, and M. Schönhuber, 2008: Aggregate terminal velocity/temperature relations. J. Appl. Meteor. Climatol., 47, 2729–2736, doi:10.1175/2008JAMC1869.1.
Bringi, V. N., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.
Bringi, V. N., R. Hoferer, D. A. Brunkow, R. Schwerdtfeger, V. Chandrasekar, S. A. Rutledge, J. George, and P. C. Kennedy, 2011: Design and performance characteristics of the new 8.5-m dual-offset Gregorian antenna for the CSU–CHILL radar. J. Atmos. Oceanic Technol., 28, 907–920, doi:10.1175/2011JTECHA1493.1.
Bringi, V. N., B. Notaroš, C. Kleinkort, G.-J. Huang, M. Thurai, and P. Kennedy, 2015: Comprehensive analysis of an unusual winter graupel shower event recorded by an S-band polarimetric radar and two optical imaging surface instruments. 37th Conf. on Radar Meteorology, Norman, OK, Amer. Meteor. Soc., 1A.4. [Available online at https://ams.confex.com/ams/37RADAR/webprogram/Paper276208.html.]
Brunkow, D., V. N. Bringi, P. C. Kennedy, S. A. Rutledge, V. Chandrasekar, E. A. Mueller, and R. K. Bowie, 2000: A description of the CSU–CHILL National Radar Facility. J. Atmos. Oceanic Technol., 17, 1596–1608, doi:10.1175/1520-0426(2000)017<1596:ADOTCC>2.0.CO;2.
Cober, S. G., and R. List, 1993: Measurements of the heat and mass transfer parameters characterizing conical graupel growth. J. Atmos. Sci., 50, 1591–1609, doi:10.1175/1520-0469(1993)050<1591:MOTHAM>2.0.CO;2.
Evaristo, R., T. Bals-Elsholz, E. Williams, A. J. Fenn, M. Donovan, and D. Smalley, 2013: Relationship of graupel shape to differential reflectivity: Theory and observations. 29th Conf. on Environmental Information Processing Technologies, Austin, TX, Amer. Meteor. Soc., 14. [Available online at https://ams.confex.com/ams/93Annual/webprogram/Paper214462.html.]
Garrett, T. J., C. Fallgatter, K. Shkurko, and D. Howlett, 2012: Fall speed measurement and high-resolution multi-angle photography of hydrometeors in free fall. Atmos. Meas. Tech., 5, 2625–2633, doi:10.5194/amt-5-2625-2012.
Huang, G.-J., V. N. Bringi, D. Moisseev, W. A. Petersen, L. Bliven, D. Hudak, 2015: Use of 2D-video disdrometer to derive mean density–size and Ze–SR relations: Four snow cases from the Light Precipitation Validation Experiment. Atmos. Res., 153, 34–48, doi:10.1016/j.atmosres.2014.07.013.
Hubbert, J. C., S. M. Ellis, W.-Y. Chang, S. Rutledge, and M. Dixon, 2014: Modeling and interpretation of S-band ice crystal depolarization signatures from data obtained by simultaneously transmitted horizontally and vertically polarized fields. J. Appl. Meteor. Climatol., 53, 1659–1677, doi:10.1175/JAMC-D-13-0158.1.
Kennedy, P. C., and Coauthors, 2015: Preliminary results from the Multi-Angle Snowflake Camera and Radar (MASCRAD) project. 37th Conf. on Radar Meteorology, Norman, OK, Amer. Meteor. Soc., 1A.1. [Available online at https://ams.confex.com/ams/37RADAR/webprogram/Paper275327.html.]
Kleinkort, C., G.-J. Huang, E. Chobanyan, A. Manic, M. Ilic, A. Pezeshki, V. N. Bringi, and B. Notaros, 2015: Visual hull method based shape reconstruction of snowflakes from MASC photographs. Proc. 2015 IEEE Int. Symp. on Antennas and Propagation and North American Radio Science Meeting, Vancouver, BC, Canada, Institute of Electrical and Electronics Engineers, 1122–1123, doi:10.1109/APS.2015.7304949.
Knight, C. A., and N. C. Knight, 1973: Conical graupel. J. Atmos. Sci., 30, 118–124, doi:10.1175/1520-0469(1973)030<0118:CG>2.0.CO;2.
List, R., and R. S. Schemenauer, 1971: Free-fall behavior of planar snow crystals, conical graupel and small hail. J. Atmos. Sci., 28, 110–115, doi:10.1175/1520-0469(1971)028<0110:FFBOPS>2.0.CO;2.
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.
Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79, 2185–2197, doi:10.1029/JC079i015p02185.
Magono, C., and C. W. Lee, 1966: Meteorological classification of natural snow crystals. J. Fac. Sci. Hokkaido Univ., 2, 321–335. [Available online at http://eprints.lib.hokudai.ac.jp/dspace/handle/2115/8672.]
Mishchenko, M. I., 2014: Electromagnetic Scattering by Particles and Particle Groups: An Introduction. Cambridge University Press, 450 pp.
Notaros, B., and Coauthors, 2015: Measurement and characterization of winter precipitation at MASCRAD snow field site. Proc. 2015 IEEE Int. Symp. on Antennas and Propagation and North American Radio Science Meeting, Vancouver, BC, Canada, Institute of Electrical and Electronics Engineers, 979–980, doi:10.1109/APS.2015.7304877.
Oue, M., M. R. Kumjian, Y. Lu, Z. Jiang, E. E. Clothiaux, J. Verlinde, and K. Aydin, 2015: X-band polarimetric and Ka-band Doppler spectral radar observations of a graupel-producing Arctic mixed-phase cloud. J. Appl. Meteor. Climatol., 54, 1335–1351, doi:10.1175/JAMC-D-14-0315.1.
Pflaum, J. C., J. J. Martin, and H. R. Pruppacher, 1978: A wind tunnel investigation of the hydrodynamic behaviour of growing, freely falling graupel. Quart. J. Roy. Meteor. Soc., 104, 179–187, doi:10.1002/qj.49710443913.
Pruppacher, H. R., and J. D. Klett, 2010: Microphysics of Clouds and Precipitation. Springer, 954 pp.
Schönhuber, M., G. Lammer, and W. L. Randeu, 2008: The 2D-video-distrometer. Precipitation: Advances in Measurement, Estimation and Prediction, S. C. Michaelides, Ed., Springer, 3–31, doi:10.1007/978-3-540-77655-0_1.
Straka, J. M., D. S. Zrnić, and A. V. Ryzhkov, 2000: Bulk hydrometeor classification and quantification using polarimetric radar data: Synthesis of relations. J. Appl. Meteor., 39, 1341–1372, doi:10.1175/1520-0450(2000)039<1341:BHCAQU>2.0.CO;2.
Szyrmer, W., and I. Zawadzki, 2010: Snow studies. Part II: Average relationship between mass of snowflakes and their terminal fall fall velocity. J. Atmos. Sci., 67, 3319–3335, doi:10.1175/2010JAS3390.1.
Thomas, R. J., P. R. Krehbiel, W. Rison, S. J. Hunyady, W. P. Winn, T. Hamlin, and J. Harlin, 2004: Accuracy of the lightning mapping array. J. Geophys. Res., 109, D14207, doi:10.1029/2004JD004549.
Thurai, M., V. N. Bringi, and W. A. Petersen, 2009: Rain microstructure retrievals using 2-D video disdrometer and C-band polarimetric radar. Adv. Geosci., 20, 13–18, doi:10.5194/adgeo-20-13-2009.
Zikmunda, J., and G. Vali, 1972: Fall patterns and fall velocities of rimed ice crystals. J. Atmos. Sci., 29, 1334–1347, doi:10.1175/1520-0469(1972)029<1334:FPAFVO>2.0.CO;2.
