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  • View in gallery

    Terms Kdp, Zdr, and Zh electromagnetic scattering simulations of plate crystals (purple), dendritic crystals (blue), dry aggregated snowflakes (green), sleet (orange), and rain (red) at X-, C-, and S-band frequency according to microphysical parameterizations in Table 1. Note: same color conventions used throughout this study.

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    Terms Kdp, Zdr, and Zh electromagnetic scattering simulations of rain (red) at X, C, and S bands; freezing rain (dark orange crosshatched) at C band only; and sleet (orange) at X, C, and S bands. Raindrop fall behavior was modeled for SL_1, while increased tumbling behavior consistent with graupel was simulated in SL_2. SL_2 values appear in Fig. 1 and Tables 1 and 2 as sleet.

  • View in gallery

    Skew T diagrams from KOUN, nearly collocated with OU-PRIME. OUN surface precipitation type was freezing rain at 1500 and 1800 UTC but sleet at 2100 UTC.

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    C-band OU-PRIME Zh, Zdr, Kdp, and ρ PPI scans at 2.9° elevation angle through stratiform precipitation with a possible dendritic growth zone aloft toward the southwest at 1545 UTC 28 Jan 2010 when OUN METAR reported freezing rain at the surface. The triangle represents the radar location.

  • View in gallery

    Winter hydrometeor classification algorithm steps: (a) ML detection, (b) below-ML, (c) above-ML, and (d) final HCA output for same C-band OU-PRIME PPI scans in Fig. 4. Final classification includes plates (PL: purple), dendrites (DN: blue), ice crystals (IC: pink), dry aggregated snowflakes (AG: green), wet snow (WS: yellow), freezing/frozen raindrops (FZ: orange), rain (RN: red), and not available (N/A: white) indicating clear air or ground clutter. The triangle represents the radar location.

  • View in gallery

    X-, C-, and S-band MBFs for the ML detection HCA. Categories include wet snow and other, which accounts for aggregates, ice crystals, and/or light rain.

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    X-, C-, and S-band MBFs for the HCA used below the ML. Categories include freezing/frozen rain and rain.

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    X-, C-, and S-band MBFs for the above ML HCA. Categories include dry aggregated snowflakes, ice crystals, dendrites, and plates.

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    C-band OU-PRIME Zh, Zdr, ρ, and HCA 330° RHI scans at 2220 UTC 28 Jan 2010 through stratiform precipitation once sleet had been reported in the Oklahoma City, OK, area by METAR.

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    X-band CASA KSAO (Chickasha, OK) Zh, Zdr, ρ, and HCA 270° RHI scans at 1422 UTC 24 Dec 2009 perpendicular to a vertical bright band. Freezing rain and sleet were classified between 0- and 10-km range with intermittent wet snow. A concentrated region of wet snowflakes reached the ground around 10–12-km range. Dry aggregated snowflakes and then ice crystals are indicated at farther ranges. Central and southwestern Oklahoma METAR reports confirmed passage of a similar precipitation transition event between 1400 and 1600 UTC.

  • View in gallery

    X-band CASA KCYR (Cyril, OK) Zh, Zdr, Kdp, and HCA 50° RHI scans at 1518 UTC 24 Dec 2009 through a dendritic growth zone aloft when Lawton and Chickasha, OK, METAR snow reports occurred at the surface within this vicinity. A temperature inversion existed around 1 km but did not cause complete melting. 1200 UTC OUN (Norman, OK) sounding isotherms.

  • View in gallery

    S-band KICT (Wichita, KS) Zh, Zdr, Kdp, and HCA 27° RHI scans at 0132 UTC 8 Feb 2012 through a supposed plate growth zone when platelike snow crystals were sighted at the ground in Wichita. 0000 UTC ICT (Wichita) sounding isotherms.

  • View in gallery

    S-band CSU–CHILL Zh, Zdr, Kdp, and HCA 245° RHI scans through a dendritic growth zone at 0625 UTC 3 Feb 2012 when METAR snow reports occurred across the Front Range between Denver and Fort Collins, CO. Coincident scan with Fig. 14 at X band. 0000 UTC DNR (Denver) sounding isotherms. Mountain beam blockage has been taken out but partial beam blockage still affects lower elevations.

  • View in gallery

    X-band CSU–CHILL Zh, Zdr, Kdp, and HCA 245° RHI scans through a dendritic growth zone at 0625 UTC 3 Feb 2012 when METAR snow reports occurred across the Front Range between Denver and Fort Collins. Coincident scan with Fig. 13 at S band. 0000 UTC DNR (Denver, CO) sounding isotherms. Mountain beam blockage has been taken out but partial beam blockage still affects lower elevations.

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A Dual-Polarization Radar Hydrometeor Classification Algorithm for Winter Precipitation

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  • 1 Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
  • | 2 Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, Colorado
  • | 3 Advanced Radar Research Center, University of Oklahoma, Norman, Oklahoma
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Abstract

The purpose of this study is to demonstrate the use of polarimetric observations in a radar-based winter hydrometeor classification algorithm. This is accomplished by deriving bulk electromagnetic scattering properties of stratiform, cold-season rain, freezing rain, sleet, dry aggregated snowflakes, dendritic snow crystals, and platelike snow crystals at X-, C-, and S-band wavelengths based on microphysical theory and previous observational studies. These results are then used to define the expected value ranges, or membership beta functions, of a simple fuzzy-logic hydrometeor classification algorithm. To test the algorithm’s validity and robustness, polarimetric radar data and algorithm output from four unique winter storms are investigated alongside surface observations and thermodynamic soundings. This analysis supports that the algorithm is able to realistically discern regions dominated by wet snow, aggregates, plates, dendrites, and other small ice crystals based solely on polarimetric data, with guidance from a melting-level detection algorithm but without external temperature information. Temperature is still used to distinguish rain from freezing rain or sleet below the radar-detected melting level. After appropriate data quality control, little modification of the algorithm was required to produce physically reasonable results on four different radar platforms at X, C, and S bands. However, classification seemed more robust at shorter wavelengths because the specific differential phase is heavily weighted in ice crystal classification decisions. It is suggested that parts, or all, of this algorithm could be applicable in both operational and research settings.

Corresponding author address: Elizabeth J. Thompson, Department of Atmospheric Science, Colorado State University, 1371 Campus Delivery, Fort Collins, CO 80523-1371. E-mail: liz@atmos.colostate.edu

Abstract

The purpose of this study is to demonstrate the use of polarimetric observations in a radar-based winter hydrometeor classification algorithm. This is accomplished by deriving bulk electromagnetic scattering properties of stratiform, cold-season rain, freezing rain, sleet, dry aggregated snowflakes, dendritic snow crystals, and platelike snow crystals at X-, C-, and S-band wavelengths based on microphysical theory and previous observational studies. These results are then used to define the expected value ranges, or membership beta functions, of a simple fuzzy-logic hydrometeor classification algorithm. To test the algorithm’s validity and robustness, polarimetric radar data and algorithm output from four unique winter storms are investigated alongside surface observations and thermodynamic soundings. This analysis supports that the algorithm is able to realistically discern regions dominated by wet snow, aggregates, plates, dendrites, and other small ice crystals based solely on polarimetric data, with guidance from a melting-level detection algorithm but without external temperature information. Temperature is still used to distinguish rain from freezing rain or sleet below the radar-detected melting level. After appropriate data quality control, little modification of the algorithm was required to produce physically reasonable results on four different radar platforms at X, C, and S bands. However, classification seemed more robust at shorter wavelengths because the specific differential phase is heavily weighted in ice crystal classification decisions. It is suggested that parts, or all, of this algorithm could be applicable in both operational and research settings.

Corresponding author address: Elizabeth J. Thompson, Department of Atmospheric Science, Colorado State University, 1371 Campus Delivery, Fort Collins, CO 80523-1371. E-mail: liz@atmos.colostate.edu

1. Introduction and background

Reducing uncertainty associated with winter storm precipitation type, accumulation, and timing is a major forecasting, safety, and socioeconomic challenge (Ralph et al. 2005; Kringlebotn Nygaard et al. 2011; Smith et al. 2012). These rapidly evolving mesoscale systems will be better understood with the national dual-polarization radar upgrade through use of hydrometeor classification algorithms (HCAs; Liu and Chandrasekar 2000; Zrnić et al. 2001; Park et al. 2009; Chandrasekar et al. 2013). Cold-season microphysical processes observable by polarimetric radars and whose origins are generally agreed upon include dendritic ice crystal growth zones (DGZs; Kennedy and Rutledge 2011; Andrić et al. 2013; Bechini et al. 2013), plate crystal growth (Pruppacher and Klett 1997; Wolde and Vali 2001; Williams et al. 2011, 2013), ice particle density and shape modulations caused by riming and crystal aggregation (Vivekanandan et al. 1994), hydrometeor melting (Ryzhkov et al. 1998), and near-surface refreezing of either rain or freezing rain into sleet1 (Kumjian et al. 2013).

Detection of these winter phenomena by dual-polarization HCAs is important. For instance, enhanced production and subsequent aggregation of large dendritic crystals aloft can lead to high precipitation rates, degradation of visibility, and disruptive snowfall accumulations (Fujiyoshi and Wakahama 1985; Kennedy and Rutledge 2011; Bechini et al. 2013). Relationships between Zh and snowfall for quantitative precipitation estimation and ice water content calculations could be improved by first determining the crystal type (Vivekanandan et al. 1994; Mitchell 1996; Ryzhkov et al. 1998; Wolfe and Snider 2012). The variable density of ice crystals is a major source of uncertainty in these techniques. Radar discrimination of plates and dendrites may also provide insight into the relative saturation of the environment and its ability to sustain aircraft icing conditions (Williams et al. 2011, 2013). Finally, radar detection of sleet (Kumjian et al. 2013) would provide valuable nowcasting information (Cortinas et al. 2004).

The goal of this paper is to develop and demonstrate a method for classifying these dominant, bulk winter hydrometeor types/processes based on the discriminatory power of polarimetric radar variables at X, C, and S bands. To this end, relevant information about the distribution of sizes, orientations, shapes, and diversity of hydrometeors within a particular radar sample volume can be garnered from the differential reflectivity (Zdr), correlation coefficient (ρ), and specific differential phase (Kdp). Review of variables and their application to HCAs can be found in Bringi and Chandrasekar (2001) and Straka et al. (2000). Simply stated, Zdr and Kdp are both positive (negative) for horizontally (vertically) aligned hydrometeors and zero for spherical particles, including those that effectively appear spherical to a radar because of excessive canting or tumbling. For a given oblate particle, Kdp and Zdr increase with ice or liquid water content, though only Kdp is inversely proportional to radar wavelength. The radar reflectivity (Zh) also gives an indication of hydrometeor size and concentration.

Competing processes such as riming (Fujiyoshi and Wakahama 1985; Mosimann 1995; Zawadzki et al. 2001) and aggregation contribute toward uncertainty in discerning crystal characteristics or their growth environment using radar. A cloud’s humidity and temperature may change under the influence of vapor-rich updrafts (Rauber and Tokay 1991) or during precipitation descent. The crystal growth regime might gradually or abruptly transition between thick plates, thin plates, sector plates, and finally to dendrites (Pruppacher and Klett 1997). Any new crystal habit growth is superimposed on previous growth, so the radar only provides a snapshot of current ice crystal characteristics. Additionally, several types of crystals may be present within a single radar gate, some of which may dominate the returned radar signal.

Nonetheless, routine, nationwide dual-polarization radar observations of precipitation type should provide a foundation for improving wintertime forecasts and mixed-phase microphysical parameterizations in numerical models (Cotton et al. 2011). Rauber et al. (2001) suggest the key to developing a mixed-phase precipitation forecast is accounting for complex phase change physics, including the effect of different ice particle habits falling through the melting layer. For instance, large aggregates may delay or prolong the melting process. If they survive descent through the melting layer, then these wet, semimelted snowflakes may promote the production of sleet instead of freezing rain in the presence of a sufficiently cold and deep surface layer (Thériault et al. 2006). Surface observation or mesonet systems such as the Automated Surface Observing System (ASOS) or routine weather reports (METAR), rapidly disseminated model output, and upper-air soundings cannot independently discern different snow crystal types, rain, freezing rain, or sleet with much confidence for several reasons (Elmore 2011; Schuur et al. 2012). These observational methods do not offer the temporal or spatial resolution available from radar, either.

Hydrometeor classification algorithms combining atmospheric soundings with polarimetric radar observations have been successful for warm-season, convective precipitation (Liu and Chandrasekar 2000; Zrnić et al. 2001; Ryzhkov et al. 2005b; Dolan and Rutledge 2009; Park et al. 2009; Chandrasekar et al. 2013; Dolan et al. 2013) because the freezing level does not vary much in space or time. This is not the case for winter precipitation though, which motivates use of a polarimetric radar-based melting-layer detection algorithm to identify wet or melting snow and then inform additional classification steps below and above this radar brightband layer (Giangrande et al. 2008; Boodoo et al. 2010).

To date, wintertime polarimetric classification algorithms using melting-layer detection techniques and external temperature information (from either a sounding or model forecast) have attempted to identify winter hydrometeor types with varying levels of success (Kouketsu and Uyeda 2010; Elmore 2011; Schuur et al. 2012). Elmore (2011) showed that the radar’s inability to identify the refreezing of raindrops and that errors in the melting-layer detection algorithm led to poor overall performance in diagnosing surface weather conditions. Schuur et al. (2012) produced satisfactory results using an algorithm based on rapidly updated model output temperature and moisture fields along with polarimetric radar data. The methodology presented by Schuur et al. (2012) is particularly valuable at far ranges where the radar resolution is degraded, and below the lowest elevation angle scan where surface weather conditions cannot be diagnosed by the radar at all.

Polarimetric signatures for plate and dendritic crystals, as well as the recently discovered refreezing signature (Kumjian et al. 2013), have been documented and can be long lived but have not yet been implemented in any hydrometeor classification scheme. It is important to note that these signatures have been validated with external temperature data in aforementioned studies, but they do not require temperature information for real-time detection. Furthermore, no previous winter HCA has fully exploited the potential uses of Kdp (especially at shorter radar wavelengths), which should be extremely useful in discerning ice crystal habit. Since a melting-layer detection algorithm can be used, the strong radar signatures demonstrated by certain winter hydrometeor types might be sufficient for classification with little to no use of external temperature information (Zrnić et al. 2001), possibly reducing computational expenses.

To develop such a cold-season HCA that is as autonomous as possible and to assess its performance at various wavelengths, scattering simulations of polarimetric radar variables at X, C, and S bands based on the physical properties of dendrites, plates, dry aggregated snowflakes, rain, freezing rain, and sleet are outlined in section 2 and discussed in section 3. Then the algorithm is developed based on these theoretical results in section 4 and validated with radar, thermodynamic, and surface data during four winter storms in section 5. Section 6 provides a summary and suggestions for future algorithm use and improvement.

2. Electromagnetic scattering simulation methodology

a. T-matrix and Mueller-matrix models

T-matrix and Mueller-matrix scattering models (Waterman 1965; Barber and Yeh 1975) were used to create HCA membership beta functions (MBFs) for various winter hydrometeor types. See Vivekanandan et al. (1991), Liu and Chandrasekar (2000), Zrnić et al. (2001), Dolan and Rutledge (2009), and Chandrasekar et al. (2013) for algorithm definitions and equations. Permutations of each hydrometeor’s input parameters shown in Table 1 were used in the T-matrix model to compute the radar backscattering cross section of different particles. Then the Mueller matrix calculates polarimetric radar observations for each homogeneous, parameterized size distribution. These simulations were aggregated together to produce a range of expected values for each precipitation type.

Table 1.

Microphysical parameters for T matrix and Mueller matrix used to calculate polarimetric radar variables for various hydrometeor types. The CANTMAT module was used to simulate normalized gamma drop size distributions of rain, freezing rain (lower temperature), and sleet, and these NW and μ values are denoted with an asterisk (*). Term ΔD was 0.001 for exponential distributions but was not specified for normalized gamma distributions because integrations were handled differently. The Hogan et al. (2000) snowflake relation for bulk density as a function of size was used for aggregates. Shape model numbers: 1 denotes Pruppacher and Pitter (1971); 3 denotes Beard and Chuang (1987); 4 denotes Andsager et al. (1999); 5 denotes Thurai and Bringi (2005), “Ogimi experiment”; 8 denotes Thurai and Bringi (2005) and Huang et al. (2008), “Bridge experiment.” Exp denotes exponential. Norm denotes normalized.

Table 1.

All hydrometeors are modeled as oblate spheroids without branched or otherwise irregular shapes, which is sufficient for X-, C-, and S-band weather radar applications (Bringi and Chandrasekar 2001; Botta et al. 2010; Hogan et al. 2012). While scattering simulations are sensitive to phase (ice vs liquid), the results were negligibly sensitive to changes in temperature. Two elevation angles, 30° and 1°, were simulated to determine how the radar would perceive higher-altitude ice particles. Sleet and rain should only exist below the melting level, so they were simply modeled at 1°.

Hydrometeor bulk density (ρbulk) is defined as the particle’s mass per unit volume. The axis ratio is assumed to compare the vertical (minor, “y”, basal, a-axis growth face) and horizontal (major, “x”, prism, c-axis face) dimensions of a particle (“y/x”), where the axis ratio is unity for spheres. The particle size distribution (PSD), DMIN, DMAX, diameter interval (ΔD), number concentration (N0 or NW), slope (λ), and functional shape (μ) are parameterized, from which we calculate D0 (median diameter of the PSD). To represent the natural variability of precipitation in turbulent background flow, all hydrometeors are assumed to have a Gaussian distribution of canting angles about a mean (θm) of zero (Hendry et al. 1976; Beard and Jameson 1983; Ryzhkov 2001; Spek et al. 2008). Then a certain standard deviation of the canting angle (σ) from zero is implemented to represent fluttering or tumbling. The fall behavior of individual particles may vary greatly, but in the interest of distinguishing bulk hydrometeor types, we implemented σ values that best characterized how each particle type might fall differently from another.

b. Model parameterizations for various hydrometeors

Wet or melting snow was not modeled in this study but its inclusion in the classification algorithm is discussed in section 4. A “blanket” ice crystal category [based on Dolan and Rutledge’s (2009) “ice crystals”] was also added to accommodate prevalent but innocuous small isometric ice crystals found above the melting layer with low Zh, Zdr, and Kdp. It should be noted that bullet-, rosette-, and stellar-crystal-shape extensions are too complex to be modeled with quasi-spherical approximation models (Botta et al. 2010), and the bulk differences between these hydrometeors cannot be appreciated by K- through S-band frequency radars (Vivekanandan et al. 1994). Although graupel can form in winter storms (Reinking 1975; Takahashi and Fukuta 1988; Takahashi et al. 1999), a graupel category was not included herein because we examine primarily stratiform winter case studies.

1) Dendrites and plates

Because of their skeletal framework, dendrites are modeled with low ρbulk between 0.3 and 0.5 g cm−3 (Heymsfield 1972; Fukuta and Takahashi 1999). These branched crystals tend to flutter as they slowly fall, with their maximum dimension oriented horizontally (Pruppacher and Klett 1997). This is represented with σ = 15° (Matrosov et al. 2006; Kennedy and Rutledge 2011). We modeled PSDs observed by Lo and Passarelli (1982) for pristine dendrites prior to the onset of aggregation. Many studies have confirmed that an exponential PSD is sufficient to describe crystal populations (Pruppacher and Klett 1997), but the exact PSD of particular ice crystals is still uncertain. The simulations presented here serve as a proof of concept for the information available in the literature. In section 5, we assess these results with radar observations.

The median and maximum diameter of dendrites can be longer (up to 1.3 cm; Mitchell 1996; Pruppacher and Klett 1997; Kennedy and Rutledge 2011) than plates, which have less favorable geometry for growth and are associated with lower ice supersaturations (usually unsaturated with respect to water; Pruppacher and Klett 1997; Foster and Hallett 2008). Plates are assumed to be solid ice (Pruppacher and Klett 1997) and exhibit approximately the same canting behavior as dendrites. However, plates have more sloped PSDs because of their muted growth, which results in more numerous small crystals (Bader et al. 1987; Ryan 2000). Small D ranges and D0 observations of unrimed plates (Pruppacher and Klett 1997) match those modeled herein. It should be noted that our scattering model could only simulate DMAX ≤ 1 cm. PSD parameterizations were still deemed sufficient because D0 was always well contained within DMAX (see Table 1) and agreed with crystal D0 observations.

The vertical thickness of plates and dendrites is the same but their horizontal dimensions differ based on growth conditions, and therefore dendrites are slightly more oblate (Auer and Veal 1970). We qualitatively followed the data from Auer and Veal (1970), but our model became computationally unstable for the very small axis ratios they suggest (y/x < 0.135; Matrosov et al. 2012). Therefore, plates were modeled with axis ratios of 0.2–0.5 (Williams et al. 2011, 2013), just above the 0.135–0.2 values accepted for dendrites (Kennedy and Rutledge 2011). Both these crystal types might have lower axis ratios in nature than we are able to simulate.

2) Dry aggregates

Snowflake aggregation is most prolific when temperatures approach 0° and −15°C because of sticking and because dendrites are the most common components of aggregates (Pruppacher and Klett 1997; Jiusto and Weickmann 1973). Aggregates of these crystals can easily exceed 2 cm, which is beyond our model’s maximum diameter. However, simulated snowflake DMIN and D0 values agree well with observations (Locatelli and Hobbs 1974; Lo and Passarelli 1982; Barthazy et al. 1988; Herzegh and Jameson 1992; Vivekanandan et al. 1994; Spek et al. 2008). Our simulations attempted to account for aggregation or consumption of many smaller-sized crystals into larger ones, which produces flatter aggregate PSDs compared to that of their pristine component crystals (Spek et al. 2008; Lo and Passarelli 1982; Kennedy and Rutledge 2011).

Hogan et al. (2000) derived a power-law relationship for aggregates that describes ρbulk as a function of size. Clumps of dendrites with very large combined diameters have extremely low ρbulk from air pockets between branches and since mass is distributed across a larger volume. The majority of naturally occurring, larger aggregates should have ρbulk ~ 0.05 g cm−3, while ρbulk could range from 0.01 to 0.2 g cm−3. Only the smallest, most compact snowflakes will approach ρbulk > 0.15 g cm−3 (Pruppacher and Klett 1997), but they are usually responsible for the majority of positive, albeit small, Kdp and Zdr contributions (Kennedy and Rutledge 2011; Lautaportti et al. 2012; Andrić et al. 2013).

Large, irregular aggregates cant or tumble more dramatically than pristine crystals (Kajikawa 1982). The aggregate σ value was accordingly doubled from that of dendrites and plates to 30° (Matrosov et al. 2006; Kennedy and Rutledge 2011). Instead of modeling aggregates with very oblate axis ratios, high diameters, and an extremely high standard deviation of canting angle (perhaps more true to nature), their axis ratios were raised (0.7–0.9; Barthazy et al. 1988; Vivekanandan et al. 1994; Herzegh and Jameson 1992; Dolan and Rutledge 2009; Kennedy and Rutledge 2011) to effectively represent a nearly spherical particle with moderate σ (manual approximation of nature). Since small ice crystals and large conglomerations of dendrites should have identically low Zdr and Kdp (for different reasons), we can only distinguish them with Zh, which alludes to their characteristically different sizes.

3) Stratiform rain, freezing rain, and sleet

A normalized gamma drop size distribution (DSD) was utilized to more accurately represent the natural variability of stratiform rain and sleet below the melting level (Waldvogel 1974; Ulbrich 1983; Willis 1984; Bringi et al. 2003; Gibson et al. 2009). Wintertime raindrops produced by melted snow typically have diameters < 3 mm (Stewart et al. 1984). Both raindrops and wet snowflakes freeze into ice pellets (IP) either individually at subzero temperatures (IP-a type) or by colliding with snowflakes, ice pellets, or other suitable freezing nuclei (IP-b type; Thériault et al. 2006; Thériault et al. 2010). Sleet is modeled at −4°C because raindrops introduced to this temperature should become some form of sleet (Spengler and Gokhale 1972). Freezing rain usually begins to occur at temperatures at or just below freezing and was modeled at −1°C. The stratiform rainfall DSD was used for sleet because the parameters in Table 1 are quite broad and previous studies have not conclusively documented sleet’s increased maximum size or alternative PSD from rain (Gibson et al. 2009; Stewart et al. 1990).

Raindrop-shape simulations described in Table 1 account for increasing raindrop axis ratios for D > 1 mm. Because raindrops deform into quasi-equilibrium shapes during descent, their σ values are relatively low, ~1°–10° (Ryzhkov 2001). Ice pellets were modeled with completely frozen raindrop shapes. Gibson and Stewart (2007) and Spengler and Gokhale (1972) indicate that sleet’s rigid body should tumble. Correspondingly high σ values between 60° and 70° typically used for graupel (Knight and Knight 1970; Kennedy et al. 2001) were adopted. More complex, realistic electromagnetic scattering simulations for mixtures of frozen, partially frozen, and unfrozen drops (Fujiyoshi and Wakahama 1985) are warranted to fully study sleet formation (Kumjian et al. 2012). However, these steps are beyond the scope of this study, where we focus on the polarimetric signatures of bulk hydrometeor populations and the ability of a fuzzy-logic algorithm to distinguish them.

3. Electromagnetic scattering simulation results

Figure 1 and Table 2 show simulated Kdp, Zdr, and Zh ranges for X, C, and S bands according to parameterizations in Table 1 between five winter hydrometeor types of interest: dendrites, plates, aggregates, sleet, and cold-season rain. These polarimetric radar (PR) variable ranges were comparable to available literature examples without major fault or disagreement (Table 3). There is a slight, almost negligible increase in Zh and a decrease in Zdr with increasing λ for all hydrometeors due to non-Rayleigh scattering effects by oblate spheroids (Matrosov et al. 2005). This argument also justifies why simulated X-band Kdp is actually 3.7 times greater than at S band, but the wavelength ratio (11.0/3.2) is only 3.4 (Matrosov et al. 2005; Dolan and Rutledge 2009). As expected, modeled ρ values for all our homogenous hydrometer populations were above 0.99. This is a reflection of our idealistic model, which cannot simulate more realistic mixtures of particles or explicitly describe their natural variability (Balakrishnan and Zrnić 1990). Resonance effects (especially at C band; Zrnić et al. 2000) are avoided in these simulations by limiting the raindrop diameter < 5 mm based on observations (Stewart et al. 1984).

Fig. 1.
Fig. 1.

Terms Kdp, Zdr, and Zh electromagnetic scattering simulations of plate crystals (purple), dendritic crystals (blue), dry aggregated snowflakes (green), sleet (orange), and rain (red) at X-, C-, and S-band frequency according to microphysical parameterizations in Table 1. Note: same color conventions used throughout this study.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Table 2.

Terms Kdp, Zdr, and Zh electromagnetic scattering simulation ranges, i.e., [min, max] rounded to three significant figures, for plate ice crystals, dendritic crystals, dry aggregated snowflakes, sleet, and rain at X-, C-, and S-band frequencies according to microphysical parameterizations in Table 1.

Table 2.
Table 3.

References for verifying and modifying scattering simulation results in Figs. 1 and 2 as well as Table 2, specified by hydrometeor category and radar wavelength, as shown by parentheses ( ). The asterisk denotes that Straka et al. (2000) described a combination (combo) snow–crystal category that exhibited Zdr consistent with plates but Kdr more consistent with dendrites. However, this study distinguishes between the two crystal types.

Table 3.

The remainder of this section explains and justifies these theoretical scattering simulations before discussing the modifications necessary for optimal algorithm performance on real, sometimes noisy data in section 4. Our goal was to construct a winter HCA based on the most current physical understanding of winter precipitation as viewed by radar instead of tuning the algorithm for particular hardware or locations.

a. Dendrites and plates

Dendrites and plates both have relatively low (<30 dBZ) Zh according to simulations, and there is some indication that plates might exhibit lower reflectivity than dendrites. Our simulations of these crystals are not exhaustive (Table 3), but Kdp for dendrites is consistently about 2 times greater than for plates at all λs. This was initially counterintuitive because plates have much higher bulk density and higher N0. Sensitivity studies showed that dendrites have higher Kdp primarily because they are more oblate and have D0 and DMAX values about twice as large as plates. While higher-density crystals do exhibit higher Kdp in our simulations, when all other factors remain the same, diameter is also very important, since mass ~D3 and larger plates/dendrites are more oblate.

While dendrites appear to have higher Kdp than plates in our simulations (Table 2; Fig. 1), as well as observations shown in section 5 and other studies (Table 3), plates have higher simulated maximum (and minimum) Zdr than dendrites by approximately 1.3 (0.5) dB for all λs. This upward shift in the Zdr range was surprising, since dendrites are more oblate, but it is reasonable considering that plates have much higher bulk density. This result speaks to the tendency for polarimetric variables to be dependent on many, sometimes competing physical factors. While Zh and Zdr are often derived from Rayleigh scattering assumptions for spheres, Rayleigh–Gans theory demonstrates that both these variables still depend on the density and phase of oblate hydrometeors, such as ice crystals, through the dielectric factor (Atlas 1953).

Postive Kdp and Zdr signatures of horizontally oriented crystals can systematically decrease as the radar elevation angle increases because the radar beam is no longer oriented along the major axis of oblate particles (Evans and Vivekanandan 1990; Ryzhkov et al. 2005a). Sensitivity tests for plates and dendrites between 1° and 30° are shown in Table 4. Reductions in Kdp are inversely proportional to λ, as expected according to Kdp definitions (Bringi and Chandrasekar 2001). The overall elevation angle effect on plates and dendrites is to decrease maximum Kdp, as well as decrease the entire Zdr range for each pristine crystal, making them less distinguishable from each other, aggregates, and isotropic ice crystals. Since plan position indicator (PPI) elevation angles rarely reach 30°, this effect should not hamper most snow classification efforts except on close-range RHI scans, as shown in section 5. The HCA membership beta function slopes (section 4) also help alleviate this issue. Enhanced Zdr from decreasing signal-to-noise ratio (SNR) with range, especially at precipitation echo edges, is actually more likely to degrade algorithm performance (Ryzhkov et al. 2005b). Low SNR artifacts should be distinguishable from positive Zdr areas associated with oriented ice crystals because only the latter will follow meteorological storm evolution.

Table 4.

Terms Kdp and Zdr electromagnetic scattering simulation ranges, i.e., [min, max] rounded to three significant figures, at 1° and 30° radar elevation angles for plates and dendrites at X-, C-, and S-band frequency according to microphysical parameterizations in Table 1. Elevation-induced Zdr changes were not significantly different between X, C, and S bands. The [Δmin, Δmax] represents the differences in simulated ranges with increasing elevation angle from 1° to 30°.

Table 4.

In summary, the microphysical differences between plates and dendrites are manifested in radar data by an inverse KdpZdr relationship, which may help distinguish the two categories. This is promising because snow crystals always have relatively low Zh and high ρ. Some observations of slightly reduced ρ to 0.90 within DGZs have been reported (Kennedy and Rutledge 2011; Andrić et al. 2013), perhaps due to PSD broadening, varying densities, as well as varying crystal shapes and therefore a wider spectrum of fall behavior under vigorous vapor deposition. Since this small magnitude ρ decrease is not seemingly present in every DGZ because it is hardly measurable and may depend on the intensity of crystal growth, it is not accounted for in this algorithm.

b. Dry aggregates

Aggregates have extremely low magnitude Kdp and Zdr because of low ρbulk and increased canting. However, they also have the highest Zh compared to plates, dendrites, or any other ice crystals because of their larger diameters (Ohtake and Henmi 1970; Ryzhkov and Zrnić 1998; Boucher and Wieler 1985). Trapp et al. (2001) and Ryzhkov et al. (2005b) propose that Zdr tends to decrease as Zh increases, or as aggregation progresses, density decreases, and fall behavior becomes more erratic. Our simulations also suggest a minimum reflectivity value associated with aggregates near 20 dBZ, which is used to differentiate aggregates from individual, nonoriented, small ice crystals in section 4. Texture fields (Ryzhkov et al. 2005a) could potentially be implemented in the future to detect the Zh gradient often associated with aggregating dendrites (Kennedy and Rutledge 2011).

c. Stratiform rain, freezing rain, and sleet

Sleet has lower Kdp, Zdr, and Zh than rain (Fig. 1) because of increased canting as well as decreased dielectric factor of ice compared to liquid water. Figure 2 shows the results of an X-, C-, and S-band sensitivity study conducted to isolate the relative impacts of these factors on radar variables for rain (RN), freezing rain (FR; T = −1°C, only at C band as a proof of concept), and sleet [version 1 (SL_1) or version 2 (SL_2)]. Not surprisingly, freezing rain is barely distinguishable from rain (2-dBZ Zh decrease, no Zdr change, and only 0.03° km−1 Kdp decrease at C band from rain to sleet), which leads us to conclude that temperature has only a minor effect on these simulations. Simulating frozen raindrops with decreased dielectric factor, density, and temperature without tumbling fall behavior (SL_1) resulted in a substantial 7-dBZ decrease, 1.4-dB Zdr decrease, as well as 1.5, 1.25, and 1.0° km−1 Kdp decrease for X, C, and S bands compared to rain, respectively. When ice pellets were more realistically allowed to tumble (SL_2 = version of sleet used in Fig. 1 and the rest of this study), the additional decrease in Zh is nearly zero, but there is a 25% further decrease in the maximum Kdp and Zdr. While it is obvious that these three radar variables should decrease once rain has completely frozen, these findings show that the dielectric factor and density decrease from liquid to ice dominates these trends; that canting has a secondary, nonnegligible effect; and that temperature makes little individual contribution.

Fig. 2.
Fig. 2.

Terms Kdp, Zdr, and Zh electromagnetic scattering simulations of rain (red) at X, C, and S bands; freezing rain (dark orange crosshatched) at C band only; and sleet (orange) at X, C, and S bands. Raindrop fall behavior was modeled for SL_1, while increased tumbling behavior consistent with graupel was simulated in SL_2. SL_2 values appear in Fig. 1 and Tables 1 and 2 as sleet.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

More importantly, since Figs. 1 and 2 show how radar variables associated with stratiform rain encompass that of both supercooled (freezing) and frozen rain (sleet), these latter two phenomena could simply be attributed to light rain. If the expected value ranges of a hydrometeor type are not unique from another type, then fuzzy-logic HCA MBFs cannot distinguish them. This simple algorithm also cannot accommodate detection of the localized, small magnitude refreezing signature associated with the production of sleet because those expected value ranges also lie within that of stratiform rain (Kumjian et al. 2013). These include a localized increase in Zdr and Kdp along with decreased ρ and Zh. If 2D MBFs (Zrnić et al. 2001) and/or texture fields (Ryzhkov et al. 2005a) were incorporated into the HCA, then the spatially correlated variability of ρ, Zdr, Kdp, and Zh within the refreezing signature might prompt more accurate rain/freezing rain/sleet classification. In the meantime, our methodology relies primarily on temperature to classify rain and the combined possibility of sleet and/or freezing rain below the melting layer, where T < 0°C, without assessing other possible thermodynamic factors as in Schuur et al. (2012).

4. Algorithm development and testing

A fuzzy-logic winter hydrometeor classification algorithm based on the methodology in Dolan and Rutledge (2009) was developed to include stratiform rain, freezing/frozen raindrops (i.e., freezing rain and/or sleet), wet snow (indicative of the melting layer), aggregates, small isotropic ice crystals, dendrites, and plates. Modifications to this algorithm from Dolan and Rutledge (2009) necessitated (i) new procedures, (ii) new membership beta functions, and (iii) a variable weighting system for each precipitation category. These three steps substantially increased the algorithm’s ability to distinguish between different precipitation types according to literature examples of these features, decreased its reliance on external temperature data to make classifications, and allowed it to work well on a variety of radar platforms.

This algorithm assumes ice or mixed-phase precipitation is occurring somewhere in the domain, so an appropriate convective warm-season algorithm should be consulted under other conditions. Classification should only be attempted on quality controlled radar data. The appendix details suggested quality control measures and postprocessing techniques used herein. For example, thresholds of Zh > 5 dBZ and SNR > 7–10 dB were used in the HCA to avoid misclassifications at echo edges due to nonmeteorological Zdr increases.

a. Algorithm procedures

As is typical for many HCAs, classification is performed on each pixel without knowledge of decisions made for nearby pixels or how the radar variables trend in time. Park et al. (2009) suggests that HCA performance can be optimized if individual algorithms are developed for each major precipitation regime. It may be unrealistic to design a single one-size-fits-all algorithm (or a single set of MBFs) to handle convective, stratiform, warm-season, and cold-season precipitation. Thus, our HCA is designed for stratiform winter precipitation. We explain our methodology with a freezing rain case study using the C-band University of Oklahoma Polarimetric Radar for Innovations in Meteorology and Engineering (OU-PRIME) radar in Norman, Oklahoma (Palmer et al. 2011). The nearby soundings for this event are shown in Fig. 3, which exhibit a strong temperature inversion and a cold surface layer from 1500 until 2100 UTC. Figure 4 shows the 2.9° PPI of OU-PRIME C-band polarimetric radar variables through the melting layer when METARs indicated freezing rain at the surface. A region of enhanced Kdp and slightly reduced ρ appears aloft toward the southwest, but Zdr is generally ≤1.25 dB. This could potentially be a weak dendritic growth zone. This particular radar scan was used to verify that the algorithm could handle certain peculiarities and classification difficulties such as a slanted melting-layer height from west-northwest to south-southeast throughout the domain, nonuniform precipitation, and less prominent DGZ signatures.

Fig. 3.
Fig. 3.

Skew T diagrams from KOUN, nearly collocated with OU-PRIME. OUN surface precipitation type was freezing rain at 1500 and 1800 UTC but sleet at 2100 UTC.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Fig. 4.
Fig. 4.

C-band OU-PRIME Zh, Zdr, Kdp, and ρ PPI scans at 2.9° elevation angle through stratiform precipitation with a possible dendritic growth zone aloft toward the southwest at 1545 UTC 28 Jan 2010 when OUN METAR reported freezing rain at the surface. The triangle represents the radar location.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

The complete classification algorithm includes three individual HCAs with different categories that are used to inform a final fourth classification based on melting-layer detection. The four HCA steps completed for data in Fig. 4 are illustrated in Fig. 5. First, the melting-layer detection HCA in Fig. 5a distinguishes wet snow (WS) from the other category (OT), which could be aggregates, isotropic ice crystals, or light rain. Melting-layer classification on these wet snow pixels with relatively high SNR (>10 dB) is handled with the same general methodology presented by Giangrande et al. (2008) to account for variable melting-layer heights in each 10° azimuthal sector of a PPI or for a single RHI. Following the methodology of Giangrande et al. (2008) and Boodoo et al. (2010), the melting-layer top, median, and base are defined by the heights (AGL) below which 80%, 50%, and 20%, respectively, of all wet snow gates reside in each sector. Only wet snow pixels between the 5–35-km range are used to determine these melting-layer (ML) height statistics to avoid nonuniform beam filling (Ryzhkov 2007), other sampling errors that degrade the quality of polarimetric variables at extremely close and far ranges, and any substantial beam ascent with range.

Fig. 5.
Fig. 5.

Winter hydrometeor classification algorithm steps: (a) ML detection, (b) below-ML, (c) above-ML, and (d) final HCA output for same C-band OU-PRIME PPI scans in Fig. 4. Final classification includes plates (PL: purple), dendrites (DN: blue), ice crystals (IC: pink), dry aggregated snowflakes (AG: green), wet snow (WS: yellow), freezing/frozen raindrops (FZ: orange), rain (RN: red), and not available (N/A: white) indicating clear air or ground clutter. The triangle represents the radar location.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

To detect precipitation transition events where the ML reaches the ground, ML height was also allowed to vary with range along a single PPI azimuth or RHI. For both the azimuth- and range-dependent methodologies, wet snow pixels are interrogated at all vertical levels of the radar volume because ground clutter is presumably removed a priori. To this end, a number of wet snow pixels (MLnum) from the near-radar high-quality data range are used to estimate the degree of melting (Giangrande et al. 2008) within a particular azimuth sector and/or range segment of the bright band. This MLnum threshold is subjective and depends on the radar’s data quality and spatial resolution. Thresholds were tested with surface observations during precipitation transition events. For example, OU-PRIME and the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) RHIs have very high spatial resolution, so complete melting along the azimuth/range segment was assumed to occur if MLnum > 10000; no melting was deemed to occur if MLnum < 100; and partial melting was assumed to happen when 100 < MLnum < 10 000, such that snow made it to the ground but there was still a temperature inversion aloft. These melting scenarios are used to inform the next HCA steps.

In the case of complete melting, a below-ML HCA defines rain (RN) and freezing/frozen rain (FZ) based on temperature and Zh below the melting-layer median height, as shown in Fig. 5b, which uses the 1500 UTC sounding from Fig. 3a. Next, Kdp, Zdr, and Zh are used to classify dendrites, plates, ice crystals, and aggregates above the ML in Fig. 5c. A possible DGZ with aggregation below was identified in the southwest domain amid ice crystals. The DGZ is appropriately contained within −5° to −15°C according to the 1500 UTC sounding. Term Kdp within this potential DGZ reached 1.7° km−1, which was 0.6° km−1 higher than the maximum value estimated by C-band scattering simulations. This is likely because our model could not simulate axis ratio < 0.135, D > 1 cm, and some riming could be occurring.

Now the MLnum is used to inform the final HCA, Fig. 5d. If no melting is detected, then the above-ML HCA is applied everywhere. If partial melting occurs, then the above-ML HCA is used throughout the domain, but the ML is painted into the classification for reference. If complete melting occurs, then the above- and below-ML HCAs are stitched together above and below the ML median height along with the wet snow pixels from the ML detection HCA, as shown in Fig. 5d.

b. Membership beta functions

The categories in each HCA step are assigned a score depending on the radar variables’ fit into that category’s MBF, which is defined by its center value (m), half-width (a), and slope (b). Each radar variable in an MBF is assigned a weight (w: 0%–100%) in calculating the score. The hydrometeor category with the highest score is determined to be the dominant bulk hydrometeor type of a particular radar gate. The expected value ranges of plates, dendrites, aggregates, sleet, and rain in Fig. 1 and Table 2 were modified to produce the ML detection, above-ML, and below-ML HCA MBFs in Figs. 68 and Table 5 as follows:

  1. Implement b parameters to gradually widen the MBFs but preserve the boundaries between categories predicted by scattering simulations.
  2. Increase maximum Zdr for aggregates to 1 dB, which is regarded as acceptable for classification purposes considering noise, uncertainty, and the varying degree of aggregation by Bader et al. (1987), Illingworth et al. (1987), and Straka et al. (2000).
  3. For the same reasoning as item 2, increase maximum aggregate Kdp values incrementally for decreasing λ. These increments were subjectively derived and tested with the case studies in section 5.
  4. Decrease minimum Zdr for aggregates to −1 dB to accommodate cases of differential attenuation above the melting layer and noise.
  5. Increase maximum Zdr for plates and maximum Kdp for dendrites based on our case studies and literature radar observations (Table 3) to account for larger diameter crystals than could be parameterized in our model, or other possible model uncertainties.
  6. Slightly decrease the minimum Zh allowed for dendrites and slightly increase the maximum Zh allowed for plates and aggregates to match radar observation examples herein and in Table 3.
Fig. 6.
Fig. 6.

X-, C-, and S-band MBFs for the ML detection HCA. Categories include wet snow and other, which accounts for aggregates, ice crystals, and/or light rain.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Fig. 7.
Fig. 7.

X-, C-, and S-band MBFs for the HCA used below the ML. Categories include freezing/frozen rain and rain.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Fig. 8.
Fig. 8.

X-, C-, and S-band MBFs for the above ML HCA. Categories include dry aggregated snowflakes, ice crystals, dendrites, and plates.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Table 5.

MBF weights (w), slope (b), and center (m) ± half-width (a) parameters as well as resultant expected value ranges for X-, C, and S-band plates (PL), dendrites (DN), ice crystals (IC), dry aggregated snowflakes (AG), wet snow (WS), other (OT), rain (RN), and freezing/frozen raindrops (FZ). MBFs are wavelength independent unless otherwise noted. The final HCA uses the below- and above-ML HCAs according to how much melting is estimated to occur from the ML detection HCA.

Table 5.

The wet snow MBF (Fig. 6) is substantially wide to account for noise, non-Rayleigh scattering, and differential attenuation based on Knight (1979), Fujiyoshi (1986), Barthazy et al. (1988), Zrnić et al. (1993), Vivekanandan et al. (1993), Ryzhkov and Zrnić (1998), Straka et al. (2000), Brandes and Ikeda (2004), and Dolan et al. (2013). We implemented overlapping ρ MBFs between wet snow (0.6–0.95; Illingworth and Caylor 1989; Ryzhkov and Zrnić 1998; Straka et al. 2000) and other hydrometeors (0.90–1.0) based on trial and error efforts to reduce misclassification of noise or dendrites as wet snow, especially within/around the ML where brightband signatures are not exactly collocated (Brandes and Ikeda 2004).

Simulated aggregates appear to have a lower limit of reflectivity near 23 dBZ and previous studies have shown that other small, individual, nonoriented ice crystals may have reflectivities up to 15 dBZ (Dolan and Rutledge 2009). Therefore, we applied a switchover point between the aggregated snowflake and ice crystal membership beta functions between 15 and 20 dBZ. The same Zdr and Kdp MBFs for aggregates (low magnitude but widened to account for noise) are used for isotropic ice crystals. This is illustrated in Fig. 8.

c. Variable weighting system

The variable weighting system was motivated by the scattering simulations and observations, which show that certain radar variables are inherently more useful in distinguishing certain hydrometeor types. Dolan and Rutledge (2009) use variable weights for each radar variable (depending mostly on data quality), which were applied to all their hydrometer categories. Using their same equations, we implement various weights depending on the radar variable, situation, and hydrometeor. This is a subjective version of confidence vectors from Park et al. (2009). Algorithm performance was very sensitive to small (5%) changes in the weighting system and those listed in Table 5 gave the most physically realistic results. When testing the weights, we ensured that the algorithm could consistently identify the radar bright band, dendritic growth zone, aggregates, etc., where applicable and indicated by other observations throughout the entirety of our four case studies (section 5). It is significant that the weighting system in Table 5 works well on four different radar platforms at X, C, and S bands during four unique winter storms, as demonstrated in section 5.

The weights allow the algorithm to capitalize on strengths of specific radar variables in differentiating between certain hydrometeors. For example, ρ is heavily weighted for wet snow identification, but not 100% because the ρ ML signature is quite narrow and increased weighting > 56% resulted in misclassifications. Term Zdr was weighted second highest for ML detection. Figure 4 shows how the Zh brightband signature is not always consistent or well defined in wintertime. Term Kdp is not trustworthy in and around the ML, so it was excluded from the ML detection algorithm.

Terms Kdp and Zdr are the most important and heavily weighted variables for distinguishing dendrites, plates, and aggregates, since ρ and Zh are usually innocuous (Trapp et al. 2001). However, Zh was weighted highest for the ice crystal category in order to differentiate from aggregates. The algorithm produced the most physically consistent results when Kdp was weighted slightly more than Zdr for classifying dendrites, plates, aggregates, and isotropic ice crystals. We presume that Kdp is less affected by aggregation and radar calibration than Zdr (Vivekanandan et al. 1994), so it is perhaps a better indicator of pristine, oriented crystals.

Temperature dominates the classification between freezing/frozen and liquid rain, but contrary to most previous HCAs, temperature is not included in any other decision process. We abandoned this temperature-dependent methodology early on because it tended to produce horizontally stratified, nonmeteorological crystal classifications above the melting layer. Dendritic and plate growth zone classification examples using polarimetric radar (supported by surface observations and sounding information aloft) within this study and others suggest that plates occur in a “cocoon” (Williams et al. 2011, 2013) near the top of the radar echo, while dendrites tend to be found in a “pocket” contained within the echo surrounded by decreasing values of Kdp and Zdr (Kennedy and Rutledge 2011; Andrić et al. 2013). Aggregates seem most prevalent below dendritic growth zones. Otherwise, small, individual, nonoriented ice crystals are ubiquitous. Aircraft observations of environmental conditions and precipitation type would provide further in situ algorithm validation of these phenomena.

5. Hydrometeor classification algorithm case studies

This winter HCA was tested on four different polarimetric radars spanning three different frequencies: C-band OU-PRIME (Palmer et al. 2011) and X-band Collaborative Adaptive Sensing of Atmosphere (CASA) radars in central Oklahoma (McLaughlin et al. 2009; Junyent et al. 2010); an S-band Polarimetric Weather Surveillance Radar-1988 Doppler (WSR-88DP) in Wichita, Kansas; and the dual-wavelength X- and S-band CSU–CHILL radar in northern Colorado (Brunkow et al. 2000). See the appendix for radar data postprocessing details. Observations from four different winter storms are now considered to demonstrate the algorithm’s utility.

a. 28 January 2010 Oklahoma ice storm

Freezing rain occurred throughout most of Oklahoma for nearly 6 h during an ice storm on 28 January 2010. Snow was falling through a strong inversion aloft, which descended and cooled slightly over the course of the soundings in Figs. 3a–c. Wet snow pixels from the ML HCA exhibited decreasing mean ρ from 1800 to 2300 UTC as the surface precipitation type switched from freezing rain to sleet around 2100 UTC according to METARs. The HCA indicated melting-layer depth also increased over time (determined by wet snow pixels within the 5–25-km range to avoid nonuniform beam filling; see section 4). One HCA RHI during these interesting ML trends is shown in Fig. 9. Much of the original melting-layer structure is preserved in the wet snow classification through diligent weighting of the polarimetric variables. Some aggregates are identified just above the ML but ice crystals are found where Zh < 15 dBZ. The most recent sounding helps classify either rain or freezing/frozen raindrops below the ML. The HCA shows some wet snow pixels descending below the ML, perhaps contributing toward or showing evidence of the transition from freezing rain to sleet observed by other means. A refreezing signature consistent with Kumjian et al. (2013) appeared in an alternate region of the OU-PRIME domain from 2100 to 2300 UTC around the coldest sounding temperature level. As previously discussed, the algorithm presented herein is not capable of identifying the refreezing signature but it is nonetheless an important phenomenon relevant to this study that should be included in future winter HCAs (Stewart 1992; Heymsfield et al. 2004; Schuur et al. 2012).

Fig. 9.
Fig. 9.

C-band OU-PRIME Zh, Zdr, ρ, and HCA 330° RHI scans at 2220 UTC 28 Jan 2010 through stratiform precipitation once sleet had been reported in the Oklahoma City, OK, area by METAR.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

b. 24 December 2009 Oklahoma blizzard

A transition zone from convective rain to snow associated with a vertical bright band (Stewart 1992) propagated eastward through central Oklahoma prior to blizzard conditions on 24 December 2009. The vertical bright band was easily detected in a CASA radar RHI (reconstructed from PPIs) as a vertically coherent region of wet snow extending toward the ground in Fig. 10 between the 10–12-km range. The HCA analysis matched METAR observations at the radar site as the vertical bright band surged southeastward. Rain was reported at first, then a transition to freezing rain, sleet, and some instances of snow were observed in advance of the main vertical bright band (10–12-km range), with snow consistently falling in the colder air beyond. This illustrates the ability of the algorithm to differentiate heavy rain from wet snow, both of which can produce high Zh and Zdr but have very different ρ. Figure 10 also shows the melting-layer detection algorithm’s versatility in identifying a descending bright band by accounting for varying ML heights with range (based on the degree of melting found in each 2-km segment of this RHI; see section 4). Rain and sleet were classified as a function of temperature and therefore height using the 1200 UTC upstream KOUN (Norman) sounding. A refreezing signature indicative of sleet as described in Kumjian et al. (2013) was briefly observed ahead of the vertical brightband passage near the 0°C level in a different radar scan (not shown), but the algorithm did not correctly classify this near-surface process as previously explained.

Fig. 10.
Fig. 10.

X-band CASA KSAO (Chickasha, OK) Zh, Zdr, ρ, and HCA 270° RHI scans at 1422 UTC 24 Dec 2009 perpendicular to a vertical bright band. Freezing rain and sleet were classified between 0- and 10-km range with intermittent wet snow. A concentrated region of wet snowflakes reached the ground around 10–12-km range. Dry aggregated snowflakes and then ice crystals are indicated at farther ranges. Central and southwestern Oklahoma METAR reports confirmed passage of a similar precipitation transition event between 1400 and 1600 UTC.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Once the surface precipitation type changed to snow within the CASA radar network over the next hour, particularly high Kdp up to 2.6° km−1 was observed within a classic DGZ in Fig. 11. This exceeded the maximum X-band Kdp simulated for dendrites by 0.6° km−1, perhaps because these dendrites exceeded the maximum diameter allowed in our scattering model (1 cm), were more oblate, had different PSDs, or were of greater density than modeled. The high Kdp, high Zdr pocket, and HCA dendrite identification in Fig. 11 were collocated with the −15°C isotherm from a nearby sounding taken 3 h prior. Wet snow is included in this HCA because a temperature inversion was still present but obviously not strong enough to prevent snow from reaching the ground according to surface observations. Aggregation is most likely occurring near the Zh gradient below the DGZ, but Kdp and Zdr are still high enough to warrant dendrite classification instead of aggregates until ~1 km above the radar bright band. Aggregates appear to reach the ground, which matches surface observations of heavy snowfall and suggests the role of dendrites aloft in promoting aggregation zones (Kennedy and Rutledge 2011). Ice crystals are only classified on the low Zh peripheries of this storm.

Fig. 11.
Fig. 11.

X-band CASA KCYR (Cyril, OK) Zh, Zdr, Kdp, and HCA 50° RHI scans at 1518 UTC 24 Dec 2009 through a dendritic growth zone aloft when Lawton and Chickasha, OK, METAR snow reports occurred at the surface within this vicinity. A temperature inversion existed around 1 km but did not cause complete melting. 1200 UTC OUN (Norman, OK) sounding isotherms.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

c. 7–8 February 2012 Great Plains snowstorm

The sole case study of platelike crystals available to us was provided by personal identification of hexagonal plates at the surface within range of the Wichita WSR-88DP radar (T. Dewvall, Accuweather Enterprise Solutions, Inc., 2012, personal communication). Figure 12 shows a reconstructed vertical cross section into the region classified as plates, which appear to fall toward the surface. Wichita sounding temperature ranges were suitable for plate growth throughout this region. Extremely high Zdr values (6.7 dB) were observed within the plate classification where Kdp < 0.25° km−1 and Zh < 20 dBZ, which matches plate scattering simulations of Kdp and Zh, respectively, but exceeds the simulated plate Zdr value by 1.5 dB. This indicates that our model parameterizations for plates might not have been oblate enough, or with the correct PSD. Term Zdr should increase as crystals attain higher densities or take on a more oblate, solid habit. Ice crystals were reasonably classified elsewhere, with some higher reflectivity values near the ground prompting identification of aggregates. Some dendrite classifications are made between isotropic crystal and plate regions, perhaps indicating a natural transition between the snow types according to varying environmental moisture content and temperature.

Fig. 12.
Fig. 12.

S-band KICT (Wichita, KS) Zh, Zdr, Kdp, and HCA 27° RHI scans at 0132 UTC 8 Feb 2012 through a supposed plate growth zone when platelike snow crystals were sighted at the ground in Wichita. 0000 UTC ICT (Wichita) sounding isotherms.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

d. 3 February 2012 Colorado snowstorm

To demonstrate algorithm performance at various wavelengths, simultaneous, dual-wavelength observations of a Colorado snowstorm were analyzed with the CSU–CHILL radar. When the dendritic growth zone signature was most established within range of both wavelength systems, the S-band RHI (Fig. 13) showed Kdp ~0.6° km−1, while the X-band RHI (Fig. 14) exhibited values correspondingly 3.7 times greater near 2.2° km−1. Note the proximity of this DGZ to the mountains, blocked out in white, and the potential elevation angle induced Kdp reductions close to the radar, where the DGZ might still exist. Maximum Zdr is between 2.5 and 3.0 dB and actually intersects the beam blockage in the S-band scan. Aggregates are identified below the DGZ, where both Kdp and Zdr decrease toward zero but Zh remains high. A reasonable mixture of isotropic ice crystals and dendrites is suggested near echo top in regions of low Zh, potentially where ice germs are growing to appreciable size in conditions favorable for rapid vapor deposition.

Fig. 13.
Fig. 13.

S-band CSU–CHILL Zh, Zdr, Kdp, and HCA 245° RHI scans through a dendritic growth zone at 0625 UTC 3 Feb 2012 when METAR snow reports occurred across the Front Range between Denver and Fort Collins, CO. Coincident scan with Fig. 14 at X band. 0000 UTC DNR (Denver) sounding isotherms. Mountain beam blockage has been taken out but partial beam blockage still affects lower elevations.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Fig. 14.
Fig. 14.

X-band CSU–CHILL Zh, Zdr, Kdp, and HCA 245° RHI scans through a dendritic growth zone at 0625 UTC 3 Feb 2012 when METAR snow reports occurred across the Front Range between Denver and Fort Collins. Coincident scan with Fig. 13 at S band. 0000 UTC DNR (Denver, CO) sounding isotherms. Mountain beam blockage has been taken out but partial beam blockage still affects lower elevations.

Citation: Journal of Atmospheric and Oceanic Technology 31, 7; 10.1175/JTECH-D-13-00119.1

Nearly equivalent X- and S-band classifications of dendrites centered directly on the −15°C level were made possible by the λ-dependent HCA MBFs but with the same weighting system used at all wavelengths. The HCA is able to distinguish between snow types at S band despite the low Kdp magnitudes at this λ, which is encouraging since this is the operating frequency of the WSR-88DPs. However, the higher-resolution and shorter-wavelength information offered by X band in this series of simultaneous CHILL RHIs is more discriminatory, so the X-band HCA seems more trustworthy. While the X-band CHILL system has a beamwidth 3 times narrower than at S band (0.3° vs 1°), we believe the wavelength dependence of Kdp has a greater impact on the differing crystal classifications between Figs. 13 and 14. Higher-magnitude phase shifts may be detected at X band because they stand out more from inherent Φdp statistical noise (Matrosov et al. 2005). As an example, Fig. 11 from an X-band CASA radar, which has a wide 1.8° beamwidth, also seemed to offer more information about the location of hydrometer transition zones due to strong Kdp signatures.

6. Conclusions

The simple fuzzy-logic polarimetric radar hydrometeor classification algorithm developed herein reveals five important microphysical features in winter storms without external temperature information: 1) dendritic and 2) plate crystal growth zones, 3) snowflake aggregation, 4) finescale melting-layer fluctuations, and 5) ML descent into a vertical bright band. These phenomena were consistent with sounding data and surface observations where available, but experiments with more in situ measurements should be performed. Furthermore, the national upgrade of S-band NEXRAD radars should offer more case studies with which to better understand winter storm polarimetric signatures and provide a much-needed quantitative evaluation of winter HCAs and their skill level at different wavelengths.

The expected polarimetric radar value ranges, or membership beta functions, used in the algorithm were derived from the most current observations and theoretical understanding of dendrites, plates, aggregates, other ice crystals, stratiform rain, freezing rain, and sleet. We found plates to have higher Zdr but lower Kdp and Zh than dendrites. This inverse relationship could be used to distinguish between the two crystal types. The radar variables are used to detect the melting layer and then separate above- and below-ML HCA scenarios. However, sleet and freezing rain do not have unique expected value ranges from each other or rain, and therefore these three hydrometeor types could not be discerned by our 1D membership beta functions. A more advanced algorithm with texture fields and/or 2D membership beta functions might be able to detect the refreezing signature itself. We simply use sounding temperature to classify the possibility of freezing/frozen raindrops below the melting layer.

The algorithm produced consistent, physically reasonable results on four different radar platforms at X, C, and S bands in various regions of the United States once a variable weighting system and wavelength-dependent snow membership beta functions were implemented to make the algorithm more efficient. So long as polarimetric data are well calibrated, no additional modifications from this text should be necessary to operate this algorithm on any winter precipitation event (without graupel). The algorithm tended to be more robust and trustworthy at shorter wavelengths because Kdp is the most heavily weighted variable for snow classifications.

This HCA is useful because it distills information garnered from multiple dual-polarization radar variables into a single product to diagnose melting and additional microphysical processes during winter storms. HCA output could be used in concert with vertical velocity measurements and in situ thermodynamic data to determine relationships between DGZs, supercooled liquid water, aircraft icing reports, and updraft speeds. Graupel and heavy-rain categories could also be incorporated in the future. The descent of semimelted particles classified as wet snow could be studied for their importance in forecasting near-surface phase changes. Methodologies described herein could also be applied to a multiple-wavelength hydrometeor classification algorithm for dual-frequency radars or different, collocated radars. Finally, hydrometeor classification efforts could be used to inform quantitative precipitation estimation, ice water content calculations, and perhaps numerical model schemes.

Acknowledgments

This work encompassed the completion of a master’s thesis at Colorado State University and was supported by NSF Engineering Research Center for Collaborative Adaptive Sensing of the Atmosphere Subcontract UM 04-002341 B10 PO0001203233, a Graduate Research Fellowship from the AMS, and NSF Grant AGS-1138116. OU-PRIME is maintained and operated by the Advanced Radar Research Center (ARRC) of the University of Oklahoma. We also acknowledge Patrick C. Kennedy for providing research insight and data (CSU–CHILL National Weather Radar Facility). Paul Hein (CSU) supplied much technical help. Thanks to Haonan Chen and Gwo-Jong Huang (CSU) for data processing. Useful discussions with Earle Williams (MIT) and Raquel Evaristo (Valparaiso University) helped clarify several aspects of analysis. The authors also thank Susan C. van den Heever (CSU) and Matthew R. Kumjian (PSU) for their constructive suggestions. Review comments from M. Kumjian and two anonymous reviewers improved the manuscript.

APPENDIX

Radar Data Processing

Radar data must be thoroughly quality controlled before attempting to operate this hydrometeor classification algorithm. Nonmeteorological echo must be removed. Term Zdr should be corrected for biases to within 0.2 dB. Absolute calibration of Zh should be performed. A 5-dBZ reflectivity threshold and a 7–10-dB SNR thresholds were used in the HCA to avoid misclassifications at echo edges due to nonmeteorological Zdr increases. These thresholds may vary for radar resolution and data quality. Term Kdp calculation should remove backscattering differential phase δ effects and smooth/filter fluctuations of the propagation differential phase Φdp over a sufficient range interval based on the radar’s gate length, but not so much as to smooth out the maximum differential phase shifts that reasonably contribute to Kdp. This will vary for each radar and for PPI versus RHI scans based on resolution and data accuracy. Keep in mind that Kdp is a range derivative, filtered field whose peaks may not always readily align with other polarimetric signatures. Term ρ is sensitive to noise and should also be quality controlled.

Term ρ correction for noise was required for CASA data. Equation 6.122 from Bringi and Chandrasekar (2001) was used, but it contained an error as printed and should have ζdr/SNR in the denominator of the second term instead of just ζdr (V. Chandrasekar 2011, personal communication). Individual Zdr biases were also corrected for each CASA radar for particular cases. Ground clutter was removed from OU-PRIME and CSU–CHILL data. Term Kdp was calculated for each radar system using the Wang and Chandrasekar (2009) method. This technique removes backscattering differential phase δ effects and filters Φdp. Many X- and C-band observations of nonzero δ in the melting layer confirmed departure from the Rayleigh scattering regime (Zrnić et al. 2000). Therefore, Kdp is never used in melting-layer classification. We also built a Kdp error window into the aggregate and ice crystal categories to accommodate this uncertainty.

Differential attenuation occurs in our datasets within and beyond the melting layer for low radar elevation angles during periods of heavy stratiform precipitation. When the radar beam intersects the bright band at these shallow angles, it becomes nearly oriented along the longest axis of large, water-coated aggregates. Attenuation correction for wet snowflakes is an ongoing topic of research and therefore no attenuation correction was performed on these data. Differential attenuation renders the Zdr information above the melting layer unusable for classification of dendrites or plates. However, crystals and aggregates have a wider (negative) Zdr error window to accommodate differential attenuation. These categories can still be distinguished based on their reflectivity. Regular horizontal attenuation was not a noticeable problem in these datasets.

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