1. Introduction and background
Despite many advances in research involving dual-polarized radars, identification of regions of riming in stratiform precipitation continues to be a challenge. Early polarimetric radar research focused on hail detection, rain-rate estimation, and identification of hydrometeors and other targets (e.g., Hall et al. 1980, 1984; Bringi et al. 1984). As polarimetric radars have become more accessible for precipitation process research, the focus has initially been on hydrometeor identification, or fuzzy-logic systems, and, in particular, severe storm applications—hail and debris identification, detection of and increased lead time on tornadoes, etc. (Vivekanandan et al. 1999; Bringi and Chandrasekar 2001; Ryzhkov et al. 2005). Now that the upgrade of all National Weather Service WSR-88D radars to dual polarization is complete, a larger variety of weather phenomena are observed on a daily basis. Some recent studies have focused on polarimetric signatures of microphysical growth processes above the bright band in stratiform precipitation (e.g., Kennedy and Rutledge 2011; Andrić et al. 2013; Schrom et al. 2015), differential reflectivity ZDR columns in convective storms (e.g., Illingworth et al. 1987; Kumjian et al. 2014), and hydrometeor refreezing (Kumjian et al. 2013).
Above the melting layer, ice crystals grow by complex processes that depend on temperature, moisture content, updraft, and fall speeds. The main growth processes that shape crystal populations are vapor deposition, aggregation, and riming. Bailey and Hallett (2009) constructed a comprehensive habit diagram showing that, depending on temperature and supersaturation with respect to ice, depositional growth of crystals may form habits varying from dendritic and platelike to columnar, bullets, and rosettes. Previous studies have frequently observed the presence of a local maximum in ZDR around the −15°C region often concurrent with a local minimum in correlation coefficient ρHV (Kennedy and Rutledge 2011; Andrić et al. 2013; Bechini et al. 2013; Schneebeli et al. 2013; Moisseev et al. 2015; Ryzhkov et al. 2016). Figure 5.6 of Byers (1965) and Fig. 9.4 of Rogers and Yau (1989) have shown that the −15°C region also corresponds to a maximum in depositional growth rates, so it has been suggested that these signatures are due to the production and growth of dendritic crystals since this is a favored crystal shape at this temperature. As crystals fall and grow larger, the dominant growth mechanism transitions to aggregational growth. With aggregational growth, snowflakes grow in size, both in length and thickness, and decrease in density, the combination of which results in an increase in reflectivity Z, a decrease in ZDR, and an increase in ρHV (Ryzhkov and Zrnic 1998; Kumjian et al. 2012).
While depositional and aggregational growth mechanisms have been inferred from polarimetric signatures, observation and detection of riming on a large scale continues to be a challenge. Riming implies the presence of supercooled liquid water (SCLW), which can be dangerous for aviation. For riming to occur, local changes to thermodynamics and microphysics must be present; particularly, local updrafts that produce an excess supersaturation beyond what existing snow can use by deposition leading to the formation of SCLW (Zawadzki et al. 2000). Identification of these regions could also have implications for data assimilation or model microphysics above the melting layer (Barnes and Houze 2015).
A common remote sensing method to infer the presence of riming involves the detection of changes in fall speed. Unrimed individual crystals rarely fall faster than 1.5 m s−1, while unrimed aggregates rarely reach 2.0 m s−1 (Barthazy and Schefold 2006; Brandes et al. 2008). Several studies have shown that rimed particles fall at speeds ranging from 1.5 to 2.5 m s−1 or faster (e.g., Mosimann et al. 1993; Mosimann 1995; Barthazy and Schefold 2006). Additionally, a riming environment may lead to the formation of supercooled drizzle and/or secondary ice formed by rime splintering, both of which could produce a bimodal velocity spectrum (Hallett and Mossop 1974; Zawadzki et al. 2001). In this study, we attempted to link regions of riming identified by a vertically pointing radar to the corresponding polarimetric signatures from scanning radar. Since scanning radars are more prevalent than vertically pointing radars, being able to link signatures from both would reduce and/or eliminate the necessity of a vertically pointing radar to infer riming.
2. Methodology
At the J.S. Marshall Radar Observatory in Sainte-Anne de Bellevue, Quebec, Canada, we have an array of radars at our disposal. Located at the observatory, the McGill S-band radar is a scanning dual-polarization radar that completes a full scan of 24 elevations from 0.5° to 34.4° every 5 min. There are also two vertically pointing X-band Doppler radars (VertiX), one located at the observatory and another located at the McGill University campus in downtown Montreal, Quebec. Technical details of the VertiX and S-band radars can be found in Table 1. For this study, we utilized the downtown VertiX radar (marked with an × in Fig. 1) and McGill S-band radar data collected east of VertiX.
Radar characteristics (RPM is revolutions per minute).
Observation region east of the McGill S-band radar. The blue × designates the location of the VertiX radar, and the red line marks the 72° azimuth. After determining the speed and direction of motion from VET, the polarimetric variables are averaged over a region 10 km deep and 3° wide centered on the 40-km range ring. This map is used under the Open Database License from http://www.openstreetmap.org.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
a. Radar data averaging rationale
VertiX measurements as well as observations of ZDR and ρHV for dual-polarization radars like ours are prone to variability because of dynamical and microphysical processes—such as generating cells, atmospheric waves, updrafts, and downdrafts—on shorter spatial and temporal scales, on the order of 1–15 km or minutes. Averaging over the entire period of a given case removes these smaller, short-lived features and focuses on signatures of the dominant growth mechanism. It is also important to realize that any interpretation of profiles from VertiX and S band relies on the assumption that the rate of evolution of storm dynamics and microphysics is much slower than the time it takes snowflakes to fall through the region of interest. This is because the vertical profiles of snow are from particles formed at different times and viewed at one instant. To interpret such profiles as a history of growth following individual crystals, we have to assume that snowflake 1, observed at high levels now, and snowflake 2, at low levels now but at high levels before, share a common growth history; this is only possible in the context of a slow-evolving system. Therefore, averaging over both time and space is necessary for analysis to take care of both noise and representativeness errors associated with S-band data as well as their comparison with VertiX. Finally, combining S-band measurements made at different ranges also ensures that we can build vertical profiles continuous in height from our PPI data at 23 elevation angles, while some azimuthal averaging damps the discontinuities in the vertical profiles obtained by such an approach. All in all, a variety of technical, meteorological, and data quality reasons forced us to make comparisons between case-averaged VertiX data at one location and a small area of S-band data at another, but nearby, location, as well as ignore any smaller-scale variability.
b. Case selection using VertiX
As previously mentioned, the two most common signatures of riming from a vertically pointing radar are high fall speeds (we assume a Vf ≥ 2.0 m s−1) and bimodal velocity spectra. Cases with Vf ≤ 1.5 m s−1 and no bimodal spectra are assumed to be either unrimed or lightly rimed and classified as group NoR. Cases with expected riming are separated into two groups: (Rim) those with Vf ≥ 2.0 m s−1 and no detectable bimodal spectrum and (Bim) those with a manually observed bimodal spectrum. It should be noted that cases that fall into group Bim may have Vf lower than 2.0 m s−1, but the faster primary spectrum mode reaches fall speeds close to or faster than 2.0 m s−1.
For comparison with S-band polarimetric data, the VertiX Zx and Vf are averaged over the entire time period for each case to determine the mean vertical profiles. Because X-band reflectivity is prone to attenuation, particularly on the radome, the difference between the S and X bands is determined between the −5° and −15°C levels, and this offset is added to the entire Zx profile. Other altitudes were not used in computing the difference due to several factors, including S-band data contaminated by clutter near the surface, the impact of the bright band around 0°C on both radars, and possible noise contamination on S band at altitudes higher than −15°C.
c. Polarimetric data
After cases are selected using the VertiX radar, the S-band polarimetric data for a given time are averaged over a region with an area of 20 km2. The location of VertiX is at about 72° in azimuth and 29.7 km in range (marked with a blue × in Fig. 1); however, because of its proximity to Mount Royal and poorer data coverage at higher altitudes, S-band data were instead used from a region centered at 40 km in range with a width of 3° in azimuth and a depth of 10 km between 35 and 45 km in range. Since Mount Royal tops out at 150 m above radar level, blockage by topography should not affect our analysis.
Because the region of S-band data collection is not collocated with VertiX, the timing of the events does not directly match. Using the variational echo tracking (VET) developed by Laroche and Zawadzki (1995), the speed and direction of motion of the echoes are calculated. Using the direction and velocity, the time and azimuth at which the precipitation crosses the 40-km-range ring is determined, and the region with an area of 20 km2 described above is used to analyze S-band polarimetric signatures. The use of VET allows for flexibility in time and region matching as each event is unique and may have different ground speeds and directions. While some change in microphysics is possible during advection between the two locations, it will be shown in section 3d that polarimetric quantities are, on average, statistically similar between the VertiX location and the region of study.
Since our radar does not employ a signal-processing-based clutter filter, any pixels with Z < 0 dBZ, ρHV < 0.90, or a target identification (ID) of “ground echo” or “biological” are removed to eliminate ground clutter and noise contamination. The target ID is based on the fuzzy-logic system of Vivekanandan et al. (1999) with minor modifications based on our local climatology. For averaging, the height above ground level is calculated for each pixel and then the data are averaged by height in 200-m increments. So, for example, any pixel within the region between 1.0- and 1.2-km height would be included in the same averaged data point. These averages are calculated for each volume scan, that is, every 5 min.
The ZDR calibration may drift with time because of both environmental and hardware factors; therefore, it must be checked regularly for consistency. Because our S-band radar cannot point vertically, another method must be used. By observing the ZDR of the sun, we can correct for fluctuations of ZDR on a given day (Holleman et al. 2010). While this is not performed routinely, sun observations captured during volume scans used in this study were utilized to monitor ZDR calibration consistency. In parallel to the sun observations, the transmit chain is monitored separately, ZDR is also calibrated with drizzle observations as needed, and reflectivity calibration is ensured using a polarization-based self-consistency technique (Bellon and Fabry 2014). For ρHV, low signal is corrected by using the default algorithm used by our Sigmet RVP-8 processor, for signal-to-noise ratio less than 20 dB (Vaisala 2014). However, this correction does not perform well at signal-to-noise ratio (SNR) less than 5 dB, which affects our ability to properly estimate ρHV in snow. Unfortunately, this includes most data in the −15°C region. Because of this bias, all ρHV data where SNR < 5 dB have been removed.
3. Radar data analysis
Using the VertiX radar, stratiform weather events were identified as surface rain with an observable bright band or surface snow with little to no upward vertical motion. Cases were then divided into one of the three groups presented above based on the presence of riming or lack thereof. A total of 43.5 h of precipitation were used, with nine events totaling 23.6 h categorized as group NoR, six events totaling 7.1 h categorized as group Rim, and eight events totaling 12.8 h categorized as group Bim. While profiles of Z, ZDR, and ρHV are shown for each individual case, specific differential phase KDP is not shown because of the large amount of noise. Data are plotted as a function of temperature given from the RUC sounding for Montreal. Because of the proximity to the airport and assimilation of aircraft soundings, the RUC sounding is expected to be similar to the actual profiles. Additionally, the fidelity of temperature profiles was indirectly confirmed by the fact that the brightband top always occurred within ±1°C of the expected 0°C temperature, confirming previous studies that showed errors in temperature to be small (e.g., Laflin 2013).
a. Group NoR: Unrimed to lightly rimed cases
Mean profiles of S-band Z, ZDR, and ρHV as well as VertiX Zx and Vf observations are given in Fig. 2 for unrimed to lightly rimed events. While some case-to-case variability exists, on average, the profiles for group NoR events are consistent with the observations presented in numerous previous studies (e.g., Kennedy and Rutledge 2011; Andrić et al. 2013; Bechini et al. 2013; Schneebeli et al. 2013). At cloud top, ice nuclei are activated at some altitude forming likely small, quasi-spherical crystals where reflectivity initially increases. Somewhere between −19° and −11°C, though not always at the same temperature for each case, on average, the vertical gradient of Z increases, while ZDR reaches a local maximum. This has been previously suggested to be due to increased depositional growth rates leading to enhanced planar/dendritic growth of crystals (e.g., Kennedy and Rutledge 2011; Andrić et al. 2013; Bechini et al. 2013; Schneebeli et al. 2013). Individual crystals fall with their largest axis generally parallel to the ground, so depositional growth could increase Z because of the increase in size while enhancing ZDR because of their shape. Below this region, ZDR decreases while ρHV, Z, and Vf all increase; the transition of the dominant growth mechanism from deposition to aggregation could explain these signatures since, by aggregational growth, snowflakes will grow in size, both in length and thickness, and experience a decrease in density. For most cases, after correction, the Z and Zx profiles plotted in Fig. 2 are quite similar in both shape and value.
Case-average profiles of Z, Zx, Vf, ZDR, and ρHV vs temperature for each of the nine case in group NoR, with each case represented by a different color. The left column is data collected by S-band radar, and the right column is VertiX data. Here, Zx has been adjusted for attenuation by calculating the offset between Z and Zx between −5° and −15°C and applying it to the whole Zx profile. Because ρHV suffers from a low bias at low SNR, the ρHV data where SNR is <5 dB have been removed. Most of the noisiness in the S-band profiles is due to the fact that data at different temperatures, and hence heights, come from different PPIs at somewhat different ranges for each case.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
b. Group Rim: Riming without detectable bimodal spectra
Figure 3 shows S-band Z, ZDR, and ρHV as well as VertiX Zx and Vf mean profiles for riming events where no bimodal spectra were observed. The vertical profiles of radar observations exhibit some general similarities to the group NoR cases, as presented above, but with significant differences detected at altitudes where riming is occurring. In Fig. 3, between −19° and −11°C, though not always at the same temperature for each case, on average, the vertical gradient of Z increases while the ZDR peak is less pronounced than in the nonriming cases. Below, Z and ρHV increase while ZDR decreases implying the growth transitions to aggregation. At and below the −5°C altitude, fall speeds increase above 2.0 m s−1 while ZDR continues to decrease to values lower than those observed in group NoR cases. Finally, as the crystals melt near 0°C, bright band signatures similar to those previously documented by Fabry and Zawadzki (1995, 2000), including a broader melting layer and a weaker Z peak, are observed (not shown). Similar to group NoR, for most cases, after correction the Z and Zx profiles plotted in Fig. 3 are quite similar in both shape and value.
As in Fig. 2, but for the six cases in group Rim.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
While a reduction in ZDR was observed at altitudes where fall speeds indicate riming, it should also be noted that throughout the profile ZDR values are on average lower, while fall speeds are on average higher than observations at similar temperatures for group NoR events. For example, at −10°C in Fig. 2, all but one of the Vf and ZDR profiles are less than 1.0 m s−1 and greater than 0.6 dB, respectively, for group NoR, while, at −10°C in Fig. 3, all but two Vf and ZDR profiles are greater than 1.0 m s−1 and less than 0.6 dB, respectively. Since lower in the column, in group Rim events, riming is inferred by fall speeds reaching or exceeding 2.0 m s−1, riming should have been occurring before the snow reached this level; therefore, this suggests that riming may have been occurring higher the column. Physically, reduction in ZDR by riming makes sense as riming of any oblate crystals like dendrites or plates should make them less anisotropic and rimed aggregates become more spherelike as the thickness of all particles increases (Ono 1969; Lew et al. 1986a,b).
c. Group Bim: Bimodal spectra
Mean profiles of S-band Z, ZDR, and ρHV as well as VertiX Zx and Vf for cases with bimodal spectra are given in Fig. 4. Altitudes with no observable bimodal spectra are plotted with a dotted line, while altitudes with an observable bimodal spectrum are plotted with a solid line. The overall vertical profiles of radar observations are generally similar to group NoR events in regions where riming is not occurring with noticeable differences observed at the same altitudes as the occurrence of a bimodal spectrum. Examples of bimodal VertiX Doppler velocity spectra are presented in Fig. 5 with the altitudes of the −8° and 0°C isotherms annotated in the upper-right and lower-left corners, respectively.
As in Fig. 2, but for the eight cases in group Bim. For all profiles, dotted lines indicate altitudes with no bimodal spectra and solid lines indicate altitudes with detected bimodal spectra.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
Examples of 2-min Doppler velocity spectra measured by VertiX for cases from group Bim. Warmer colors correspond to stronger relative echo power for the specified height and velocity. The velocity spectra displayed are the uncorrected values observed by VertiX; density-corrected fall speeds are shown by the gray dashed lines between 0.0 and 3.0 m s−1 in 0.5 m s−1 intervals. The height of the −8°C isotherm is annotated in the upper-right corner and the height of the melting layer is annotated in the lower-left corner of each panel.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
In Fig. 4, between −19° and −11°C, individual events have variability in Z and ZDR signatures, which may be worthy of study but seem irrelevant to the signatures of riming occurring at lower levels. Below this level, the dominant growth likely transitions to aggregation that can be inferred from the increase in Z and ρHV while decreasing ZDR. Similar to group Rim, for most cases, after correction the Z and Zx profiles plotted in Fig. 4 show similarities in both shape and value. While some differences between Z and Zx are apparent at higher altitudes and colder temperatures, they are not occurring within the altitudes where bimodal spectra are observed. Figure 5 shows examples of a secondary spectrum mode forming at slower velocities followed by the growth of these new particles to higher fall speeds. In some cases, the secondary spectrum mode remains generally parallel to faster-falling original spectrum mode; in other cases, the velocity of the secondary spectrum mode rapidly increases to join the original spectrum mode. In all group Bim cases, an increase in ZDR and a decrease in ρHV are observed at heights corresponding to the bimodal spectra. This differs from riming observed in group Rim cases because, in group Rim, the ZDR signature is dominated entirely by the rimed particles; however, in this group, new crystal formation is occurring in conjunction with possible riming and therefore both contribute to the ZDR signature. When the bimodal spectrum does not persist in height, the characteristic ZDR and ρHV signatures also do not persist.
In all cases within this group, the bimodality generally forms in the temperature range from −3° to −8°C. Crystals produced in this temperature range would likely be needles, or perhaps plates (Bailey and Hallett 2009). The polarimetric signatures observed make physical sense for the type of crystals formed, as small, anisotropic particles would increase ZDR while the variety shapes of crystals present would reduce ρHV. In some group Bim cases, the newly formed crystals activate and grow at fall speeds generally parallel to the original spectrum mode. In these cases, the ZDR and ρHV signatures persist until the crystals reach the bright band. In other group Bim cases, the newly formed crystals may grow large enough or become aggregates of needles such that their fall speeds become comparable to that of the primary spectrum mode, and the two spectra merge. Preexisting aggregates may also collect the newly formed needles. In these latter examples, the local ZDR maxima and ρHV minima are observed near where the slower secondary spectrum mode first appears and then disappear near where the secondary spectrum mode disappears. While trends in ZDR and ρHV differ between group Bim and NoR cases, ultimately the observed values of ZDR and ρHV are not statistically different between the two groups.
d. Statistical comparison of S-band data
Because the VertiX and S-band data are not collocated, a statistical comparison was undertaken using the S-band data presented in the previous sections (labeled SR) and S-band data collected directly overhead of the VertiX (labeled VX). The VX location is annotated with an × in Fig. 1, while the SR location varies depending on the VET as described in section 2c. The mean S-band profiles of Z and ZDR for group NoR and group Rim over SR and VX were calculated (Fig. 6). Group Bim was not included because of a lack of uncontaminated S-band data at higher altitudes over VX.
Average vertical profiles of Z and ZDR vs temperature for all group NoR cases (in orange) and all group Rim cases (in blue). Dashed lines indicate mean S-band profiles taken over VX, and solid lines indicate mean S-band profiles taken from SR (see Fig. 1). Group Bim is not included here because of a lack of uncontaminated data at higher altitudes over VX.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
In Table 2, the bias, correlation, mean absolute difference (MAD), and root-mean-square difference (RMSD) were calculated between −10° and −2°C for ZDR. This calculation was done for each of the cases in the same group between the VX and SR regions (region-to-region comparison), between each of the cases within the same group over the same region (case-to-case comparison), and for each of the cases over the SR region between groups NoR and Rim (group-to-group comparison). Because ZDR data can be noisy, the correlation of ZDR profiles that were smoothed over a 2°C interval was also included. Despite the difference in the size of the two locations and the possibility for some change in microphysics, for all statistics, the relationship between the two locations within the same group (region to region) is always better than the relationship between the two groups over the same location (group to group).
Differences in case-averaged ZDR across regions, cases, and groups illustrating that region-to-region differences are much smaller than group-to-group differences.
e. Group averages
Figures 7 and 8 show the averaged vertical profiles for all the cases in each of the three groups. A total of 43.5 h of precipitation were used with nine events totaling 23.6 h categorized as group NoR, six events totaling 7.1 h categorized as group Rim, and eight events totaling 12.8 h categorized as group Bim. The shading in Fig. 7 displays the standard deviation of scan-by-scan-average profiles, while the shading in Fig. 8 shows the standard deviation of the case-average profiles. On average, the vertical profile for the groups generally agrees with previous studies of polarimetric signatures above the bright band (e.g., Kennedy and Rutledge 2011; Andrić et al. 2013; Bechini et al. 2013; Schneebeli et al. 2013; Schrom et al. 2015). In particular, the orange lines in Fig. 8 for group NoR events follow previously documented polarimetric profiles. All three groups, on average, show a local maximum in ZDR around the −15°C region corresponding with an increase in Z. Below, a shift in the dominant growth to aggregation would explain the Z increases, ZDR decreases, and ρHV increases. The most identifiable signature likely produced by riming was in ZDR above the bright band. Below about −7°C, bimodal spectra cases (group Bim, dark red lines) show the rate at which ZDR decreases slows, while riming without bimodal spectra cases (group Rim, dark blue lines) have lower ZDR and higher ρHV.
Average vertical profiles of Z, Vf, ZDR, and ρHV vs temperature for all cases: orange for group NoR, dark blue for group Rim, and dark red for group Bim. The shading indicates ±1 std dev from the mean of 5-min scans: yellow for group NoR, light blue for group Rim, red for group Bim, and green where any of the groups overlap. Significant overlap between each of the three groups illustrates the difficulty in identifying riming from nonriming events on a scan-by-scan basis. Because ρHV suffers from a low bias at low SNR, the ρHV data where SNR is <5 dB have been removed. The profiles have been smoothed using a boxcar smoothing over a 2°C temperature range.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
Similar to Fig. 7, but for average vertical profiles of Z, ZDR, ρHV, and KDP from S band and Zx and Vf from VertiX. The shading indicates ±1 std dev from the mean of case-average profiles. Separation between each of the three groups shows that the different underlying processes can be distinguished from these average profiles even though they are not clearly separated on a scan-by-scan basis. While KDP is also included here, the large overlap between groups makes it difficult to infer a reliable signature, even when averaging over whole cases.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
In Fig. 7, at most temperatures, there is much overlap between each of the three groups (shown in green) implying that different groups cannot be skillfully separated using scanning radar data alone. Below −10°C, 70% of the group NoR and group Rim 5-min ZDR profiles do not overlap; however, this is not enough to unambiguously detect riming on a scan-by-scan basis over areas similar to that of our analysis (10 km by 20°; Fig. 1). For case-average profiles at temperatures typical for riming, Fig. 8 shows that, except for Z, there is no significant overlap between the group NoR and group Rim. This indicates that the signatures of the underlying processes could be distinguished on time scales greater than 45 min and spatial scales similar the ones used in this study (10 km by 20°; Fig. 1), even though they are not significantly separated on a scan-by-scan basis. While the slope of ZDR below −7°C for group Bim is different than that of group NoR, the underlying signature is statistically similar for groups NoR and Bim. Finally, it is difficult to distinguish a reliable difference in KDP between each group because of the high amount of noise present in our KDP data (Fig. 8).
The frequency of occurrence of ZDR for a given fall speed between −10°C and the top of the bright band is shown in Fig. 9. For comparison purposes, the gray line in Fig. 9 shows the maximum frequency of ZDR for the group NoR cases. For group Rim cases, in regions where riming was occurring, the ZDR was observed to be lower than in group NoR cases. This is also seen in Fig. 9 where the majority of ZDR observations is about 0.1–0.2 dB lower. For group Bim cases, in regions where bimodal spectra occur, the ZDR is higher because of the formation of new crystals. Figure 9 supports this since, at velocities greater than 1.5 m s−1, the majority of ZDR observations for group Bim is up to 0.4 dB higher than for group NoR.
Contours of ZDR vs fall speed for all cases totaling 43.5 h. Data are from above the bright band up to −10°C for the 5-min average profiles. The frequency is normalized by the total number of occurrences within each particular group. The gray line shows the maximum frequencies for the group NoR data. The color shadings show that riming cases without bimodality are approximately 0.2 dB lower than nonriming cases and that riming cases with bimodality are about 0.2–0.4 dB higher than nonriming cases.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
4. T-matrix scattering model
To help interpret the polarimetric observations, a scattering model based on Mishchenko et al. (2000) and designed by Lee (2006) is used to produce simulated S-band polarimetric values. Using a variety of populations of aggregates, dendrites, and needles, idealistic simulations were performed in an attempt to find compatible conceptual models that support observed signatures of riming. While the following simulations are idealistic and other populations could also support the observed signatures, the populations used in these simulations are based on reasonable assumptions.
a. Model setup
For this model, a simplistic assumption was made whereby oblate spheroids are used to represent a variety of ice crystals and the canting and radar elevation angles were both set to 0°. By this assumption, we can obtain the strongest signal one might observe for any of the polarimetric variables, except ρHV. If the signatures of the microphysical processes are not different enough under these assumptions, then it can be assumed that these processes will be difficult to distinguish with operational S-band radars.
An exponential size distribution for aggregates Na(D) and dendrites Nd(D) from Lo and Passarelli (1982) was used as input for the model (Fig. 10). Following Kennedy and Rutledge (2011), particles with a diameter of 3 mm or smaller were assumed to be dendrites, while larger particles were assumed to be aggregates. Since our observations of riming generally occur in regions where aggregation is occurring or has taken place, a slope of 12 cm−1 and intercept of 4 × 104 cm−1 m−3, both representative of a population where aggregation has occurred, were used (Table 2 of Kennedy and Rutledge 2011).
Size distribution for the aggregates, dendrites, and needles used in the T-matrix simulation. For aggregates and dendrites, a slope of 12 cm−1 and intercept of 4 × 104 cm−1 m−3 were used (Lo and Passarelli 1982). Per Kennedy and Rutledge (2011), all crystals with D ≤ 3 mm are assumed to be dendrites (black line) and those with D > 3 mm are assumed to be aggregates (blue line). For needles (red lines), per Schrom et al. (2015), an estimated slope of 17.5 cm−1 and intercept of 5.6 × 104 cm−1 m−3 were used.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
Constants for calculating ice crystal properties in Eq. (2) used for the T-matrix scattering model. Values given are reproduced from Andrić et al. (2013) except for the thicknesses of dendrites and aggregates.
The axis ratio (black lines) and corresponding thickness (blue lines) for dendrites used in the scattering model. Dashed lines represent the values calculated using Table 2 from Andrić et al. (2013), and solid lines give the adjusted values calculated from Eq. (2) needed for model convergence.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
The axis ratio (black lines) and corresponding thickness (blue lines) for aggregates used in the scattering model. Solid lines correspond to aggregates with AR between 0.85 and 0.90, and dashed lines correspond to aggregates with AR between 0.60 and 0.65.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
To simulate riming, the thickness and density of the ice crystals are changed. The thickness is increased by an amount ranging from 0.0 to 0.3 mm in 0.05-mm increments to simulate the addition of layers of frozen droplets. The 0.05-mm increment is on the order of previous observations of the diameter of large cloud droplets or collected frozen rime droplets (Ono 1969; Wilkins and Auer 1970; Rogers and Yau 1989). The volume added due to the thickness increase is then filled with frozen rime droplets varying from 0% to 100% of the added volume in 25% increments, while the rest of the added volume is assumed to be air. This is done to simulate the extent of riming from a light coating up to graupel-like. The increase in volume Vr and the increase in mass mr due to riming is added to the respective values of the original ice crystal. The resulting values for the total mass mtot and volume Vtot are used to calculate the new density of the ice crystal and its K2 value. The thickness increase is used to calculate the new AR of the ice crystal. The model is then rerun, assuming all crystals have rimed by the same amount, to calculate the new polarimetric values. Since our cases take place during stratiform precipitation, events with heavy riming, such as graupel, are unlikely. We have chosen to only show riming simulations with 50% of the rimed volume filled with frozen droplets. A schematic of this can be seen in Fig. 13.
A schematic illustrating how a rimed and unrimed oblate particle may be represented in the T-matrix model. The blue ellipses represent the original ice crystal, the red circles are frozen rime droplets, and the dashed black ellipse represents how the model views a rimed particle.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
To simulate new crystal formation during periods of bimodal spectra, needlelike prolate spheroids were included. Temperatures at which these bimodal spectra occurred are favorable for the formation of needles or plates according to the Bailey and Hallett (2009) habit diagram. For the sizes shown in Fig. 10 and using Eq. (2), needles are the most likely to achieve the fall speeds and Z observed in the slower secondary spectrum mode. For a given Z and KDP, Fig. 15 of Schrom et al. (2015) showed the slope and intercept of the size distribution can be estimated. By using the Z of the slower secondary velocity spectrum mode and the observed KDP, we obtained a slope of 17.5 cm−1 and intercept of 5.6 × 104 cm−1 m−3 (red line, Fig. 10).
In an attempt to understand which crystal types could produce signatures similar to observations when rimed, several different simulations were run including only dendrites, only aggregates, aggregates and dendrites, aggregates with needles, and aggregates and dendrites with needles. Simulations of only aggregates or dendrites will allow us to understand the impact of each crystal type and size on polarimetric signatures. To recreate the observed profiles, different combinations of dendrites, aggregates, and needles were used and then rimed. First, to replicate the −15° region, simulations were conducted with a population consisting of primarily dendrites with a few aggregates. Second, for simulating the characteristic profiles of groups NoR and Rim in regions around −5°, a population of primarily aggregates with some dendrites was used. Third, for group Bim, a population consisting of a mixture of aggregates, dendrites, and needles was provided. These populations were chosen to show compatibility with observed profiles; however, numerous other combinations may also result in similar signatures. The following section discusses the results of individual crystals as well as collections of a variety of crystals.
b. Model output
1) Dendrites
To simulate radar signatures from dendrites, the model was run with only a distribution of dendrites: first with only dendrites of a physical diameter indicated on the x axis of Figs. 14a,b, then, with a collection of dendrites less than or equal to the physical diameter indicated on the x axis of Figs. 14c,d. In the −15°C region, we expect the observations to be dominated by dendritic growth. Figure 8 shows Z in the region ranges between 10 and 15 dBZ, while ZDR ranges from 0.6 to 1.0 dB. For modeled unrimed dendrites, the black lines in Figs. 14c,d show Z up to 10 dBZ and ZDR of 4.0 dB. While canting should reduce the ZDR, a simulation canting all dendrites in the population by the same amount resulted in ZDR values still much higher than observed (not shown). However, adding smaller aggregates to the population (up to a physical diameter of 4.4 mm, not shown) did result in producing similar modeled Z and ZDR values to that around −15°C in Fig. 8.
T-matrix simulations of (top) Z and (bottom) ZDR for (a),(b) dendrites of the physical diameter indicated and (c),(d) a collection of dendrites up to the physical diameter indicated. The effect of increasing amounts of riming in 0.05-mm increments is shown using colored lines from black (0 mm) to red (0.15 mm) to magenta (0.3 mm). Riming simulated in this figure is for 50% of the rimed volume filled with frozen droplets.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
Since observed ZDR values between −10° and 0°C (Fig. 8) are higher than simulated ZDR for aggregates (discussed below), in regions where riming is occurring it is unlikely that aggregates make up the entire population. Therefore, it is useful to simulate the signatures expected from rimed dendrites. The colored lines in Fig. 14 show Z and ZDR versus diameter for riming in 0.05-mm thickness intervals. In the context of uniform riming over the whole crystal, while Z increases with riming, the ZDR decreases because the thickness changes due to riming dominate over the addition of mass.
2) Aggregates
To simulate radar signatures of aggregates, the model was run with only a distribution of aggregates with an AR between 0.85 and 0.90: first, with only aggregates of the physical diameter indicated on the x axis of Figs. 15a,b; second, with a population of aggregates less than or equal to the physical diameter indicated on the x axis of Figs. 15c,d. This was repeated for a population of more oblate aggregates with an AR between 0.60 and 0.65 (Fig. 16). For the less oblate aggregates, the model shows riming has a marginal impact on ZDR with increases and decreases less than 0.05 dB in magnitude. For more oblate aggregates, the model shows that ZDR increases as riming increases. Increases in ZDR are dominated by adding mass by riming, while decreases in ZDR are dominated by thickness increases due to riming. For both types of aggregates, however, the changes to ZDR are less than 0.1 dB, which is generally too low to be routinely identified with operational S-band radars.
As in Fig. 14, but for aggregates with AR between 0.85 and 0.90.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
As in Fig. 14, but for aggregates with AR between 0.60 and 0.65.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
In the region between −10°C and the bright band, as the dominant growth shifts to aggregation, we expect aggregates to contribute more to the polarimetric signatures. For nonriming, Z values range from 18 to 20 dBZ and ZDR values are about 0.5–0.7 dB (orange profiles in Fig. 8). With the addition of riming, Z increases to 20–25 dBZ and ZDR decreases to about 0.3 dB (dark blue profiles in Fig. 8). Based on modeled results, both types of aggregates produce a ZDR much lower than observed; therefore, it is likely that a combination of aggregates and dendrites are present, which will be discussed later.
3) Needles in the presence of aggregates
Since bimodal spectra are typically observed at temperatures where aggregation is the dominant growth process, simulations were conducted with the same population of unrimed aggregates as in the previous section but with the addition of needles. Needles were added in increments of 0.2-mm-size bins with the longest physical dimension ranging from 0.1 to 1.9 mm. Small amounts of needles produced a negligible impact on Z and ZDR, so only two examples of needles are shown in Fig. 17: a dashed red line for a population of needles up to 1.5 mm and a solid red line for a population of needles up to 1.9 mm. For both populations of needles, generally less than a 1–2-dB increase in Z was seen in the presence of aggregates and an increase in ZDR similar to group Bim in Fig. 9 was produced. Together, aggregates and needles do not fully reproduce the signature expected for group Bim (Fig. 8); therefore, it is likely that some dendrites may not have aggregated and are still present in the population, which is discussed in the next section.
T-matrix simulations of (top) Z and (bottom) ZDR for a collection of unrimed aggregates up to the physical diameter indicated to which different amounts of needles are added. The black line is for a distribution of only aggregates, as shown in Figs. 15 and 16. The red lines correspond to the same amount of aggregates with the addition of a collection of needles corresponding to the number distribution shown in Fig. 10. The dashed red line is for needles with a D ≤ 1.5 mm, and the solid red line corresponds to needles with a D ≤ 2.0 mm. Panels (a) and (b) are for aggregates with AR between 0.60 and 0.65, and (c) and (d) are for aggregates with AR between 0.85 and 0.90.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
4) Combination of crystals
Based on the individual T-matrix simulations for different types of crystals presented above, we can infer which crystals are the most probable source of the observed signatures in Fig. 8. To verify this, additional simulations have been performed: one with a combination of aggregates and dendrites; another with a combination of aggregates, dendrites, and needles (Fig. 18). In these simulations, the aggregates and dendrites were rimed as described above but the needles were not. Since aggregates with an AR between 0.60 and 0.65 produced results more similar to the observations, the results for the larger AR are not shown.
T-matrix simulations of (top) Z and (bottom) ZDR for (a),(b) a combination of aggregates and dendrites and (c),(d) a combination of aggregates, dendrites, and needles. The effect of increasing amounts of riming in 0.05-mm increments for only aggregates and dendrites is shown using colored lines from black (0 mm) to red (0.15 mm) to magenta (0.3 mm). Riming simulated in this figure is for 50% of the rimed volume filed with frozen droplets. For all lines, the concentration of nonaggregated crystals from 0 to 2 mm follows Fig. 10, and the maximum physical diameter of aggregates varies according to the x axis.
Citation: Journal of Applied Meteorology and Climatology 57, 2; 10.1175/JAMC-D-16-0370.1
First, a T-matrix simulation for a population consisting of a collection of aggregates less than or equal to a given physical diameter and a collection of dendrites between 0.2 and 2.0 mm was run. For unrimed conditions (black line in Figs. 18a,b), this combination produced results similar to the average group NoR profile at temperatures warmer than −10°C (orange lines in Fig. 8) with Z of about 14 dBZ and ZDR of about 0.4 dB. Including riming for this population of dendrites and aggregates, Z increases to about 22 dBZ and ZDR decreases by about 0.1–0.3 dB. This is similar to the average group Rim profile (blue lines in Fig. 8).
Second, a T-matrix simulation was conducted for a population consisting of a collection of aggregates less than or equal to a given physical diameter, a collection of dendrites between 0.2 and 2.0 mm, and a collection of needles between 0.1 and 1.9 mm. While the unrimed Z is similar, the ZDR is much higher (black line in Figs. 18c,d) than observations. As the aggregates and dendrites rime, the reflectivity increases up to 22 dBZ, while the ZDR decreases to about 0.5 dB. For this population, the riming of aggregates and dendrites leads to the same trend in ZDR as group Rim, a reduction; however, the inclusion of needles produces higher ZDR values than for the same population without needles, as is expected from the average group Bim profile (dark red lines in Fig. 8).
c. Summary of T-matrix simulations
Simulations of 1) riming of dendrites, 2) riming of aggregates, 3) needles in the presence of aggregates, and 4) combinations of the three were conducted with a T-matrix scattering model. Riming was mimicked by increasing the thickness of the crystals in 0.05-mm increments up to 0.30 mm. The volume added due to the thickness increase was filled with frozen rime droplets varying from 0% to 100% in 25% increments. Since we are not dealing with convective events nor do we expect graupel-like riming, we have only shown the 50% riming cases. Additionally, for 50% riming, we found that riming of between 0.2 and 0.25 mm increases mass by an amount that would also increase fall speed to values similar to observations in riming.
Riming of aggregates was shown to increase Z by less than 10 dB. For rimed aggregates, changes in ZDR are less than 0.1 dB, indicating that aggregates alone do not produce the signatures observed by the radar. For dendrites, riming results in an increase in Z and a decrease in ZDR. The simulated values of ZDR for dendrites is much larger than our average observations around −15°C, suggesting a population of hydrometeors composed entirely of dendrites is unlikely. Adding needles to a population of aggregates does little to change the Z but does increase the ZDR by several tenths of a dB. Even though these simulations give indications of which crystal habits are more likely responsible for the signatures observed, they do not perfectly reproduce the observations. Therefore, simulations with ensembles of mixed crystal populations have also been performed.
Using aggregates and dendrites together produced similar values to those observed in group NoR (orange lines in Fig. 8). By including riming, the model produced changes in Z and ZDR similar to the changes observed for group Rim (blue lines in Fig. 8). Adding needles to the population of aggregates and dendrites results in increases in ZDR. While this ZDR decreases because of riming, it is still similar to that observed for group Bim (dark red lines in Fig. 8). Simulations with higher percentages of riming (>50%, not shown) produce similar trends to the signatures described above but lead to dendrites making up a larger portion of the total simulated Z, which produces a faster increase in Z than observed because of the increase in density of the crystals.
All these simulations were conducted to show idealistic results for these populations, which are ones without the effects of canting, viewing angles, or changes to size distributions. In a real-world case, adding these factors could reduce or alter the simulated signatures. Although these simulations, based on reasonable assumptions, portray highly idealized situations, they do reproduce most of the observations and lend support to the expected signature of riming in widespread precipitation being at most a few tenths of a decibel in ZDR. However, it should be noted that other crystal populations could lead to similar radar signatures.
5. Summary and conclusions
Observations with a vertically pointing X-band radar (VertiX) and a scanning polarimetric S-band radar have been categorized into three different groups: unrimed or lightly rimed, riming without a detectable bimodal spectrum, and riming with bimodal spectra. The fall speed and Doppler spectra observations with the VertiX have been used to distinguish between these groups. Characteristic polarimetric signatures have been identified for each group. Finally, the signatures have been reproduced using an idealistic T-matrix model setup. Nonriming cases exhibited profiles of polarimetric variables that have been previously identified in numerous other studies. Riming without bimodal spectra showed the existence of ZDR values lower than that observed in a nonriming event above the bright band. Based on T-matrix simulations, riming of aggregates would produce signatures too low to be confidently identified by our S-band radar. The simulations suggest that the ZDR signatures observed in this group are most likely due to the riming of smaller dendrites that were not collected by aggregates within the population. For cases where a bimodal spectrum was present, an increase in ZDR and a decrease in ρHV was observed at the same altitudes as the beginning of the slower secondary spectrum mode. In the range of temperatures and fall speeds observed, needles are most likely crystal produced in the secondary spectrum mode. T-matrix simulations of hydrometeor populations that include needles agree with the observed increases in ZDR. While these populations of crystals reproduced the observed signatures, other crystal populations could lead to similar radar signatures.
In regions above the bright band where riming is occurring, the ZDR values vary consistently between all three groups. Cases with bimodal spectra can have mean ZDR values of about 0.2–0.4 dB higher than nonriming cases, while riming cases without bimodal spectra can have mean ZDR values up to 0.2 dB lower than nonriming events. According to Lee (2006), the measurement noise of ZDR for individual radar cells is around 0.33 dB and the total standard deviation is around 0.35 dB. Cunningham et al. (2013) and Ice et al. (2014) have shown a systematic ZDR bias for the NEXRAD network of several tenths of a decibel. The observations given here were averaged over the region in Fig. 1 to reduce noise. On a scan-by-scan basis, 70% of group NoR and group Rim ZDR profiles do not overlap in Fig. 7, which is too low to unambiguously detect riming. Additionally, the presence of riming with bimodal spectra in group Bim leads to the ZDR values that are too similar to group NoR. At best, separation between each of the three groups in Fig. 8 suggests that different underlying processes can be distinguished from one case time sequence to another over spatial and temporal domains comparable to what was used (100 km2 and 1 h), assuming uniform microphysics. While we can infer riming with the VertiX, it appears that, for our S-band radar, these signatures are not significant enough to be indicative of riming without the presence of another aid, such as a vertically pointing radar within a few tens of kilometers of the region of interest for large-scale stratiform events.
Acknowledgments
This project was undertaken with the financial support of the Government of Canada provided through the Department of Environment and Climate Change as well as the Natural Sciences and Engineering Research Council of Canada. We thank Isztar Zawadzki for his comments, Alamelu Kilambi for her help accessing the McGill radar data, and Bernat Puigdomènech Treserras for use of the Profilers application for VertiX and S-band data as well as supplying the VET data. Finally, the thorough and insightful comments, corrections, and suggestions from anonymous reviewers and the editor led to marked improvements in the paper.
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