1 A dual-polarization radar hydrometeor classification algorithm for ...

1234A dual-polarization radar hydrometeor classification algorithm for winter precipitationElizabeth J. Thompson *1 , Steven A. Rutledge 1 , Brenda Dolan 1 , V. Chandrasekar 2 , and BoonLeng Cheong 35678910111213141516171. Department of Atmospheric Science, Colorado State University, Fort Collins, CO2. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins,CO3. Atmospheric Radar Research Center, University of Oklahoma, Norman, Oklahomasubmitted to theJournal of Atmospheric and Oceanic TechnologyMay 201318* Corresponding author: Elizabeth J. Thompson, Department of Atmospheric Science, ColoradoState University, Fort Collins, CO, 80523-1371. E-mail: liz@atmos.colostate.edu1

1819202122232425262728293031323334Abstract.The purpose of this study is to demonstrate the extent to which polarimetric radarobservations can be used to operate a winter hydrometeor classification algorithm. This isaccomplished by deriving bulk electromagnetic scattering properties of stratiform, cold-seasonrain, freezing rain, sleet, dry aggregated snowflakes, dendritic snow crystals, and plate-like snowcrystals at X-, C-, and S-band wavelengths based on microphysical theory and previousobservational studies. These results are then used to define the expected value ranges, ormembership beta functions, of a simple fuzzy logic hydrometeor classification algorithm. To testthe algorithm’s validity and robustness, polarimetric radar data and algorithm output from fourunique winter storms are investigated alongside surface observations and thermodynamicsoundings. This analysis verifies that the algorithm is able to successfully discern dominantwinter hydrometeor types (except sleet and freezing rain) based solely on polarimetric data, withguidance from a melting level detection algorithm but without external temperature information.Little modification of the algorithm was required to produce positive results across four differentradar platforms at X, C, and S band, although classification seemed more robust at shorterwavelengths due to its dependence on the specific differential phase. It is suggested that parts, orall, of this algorithm could be applicable in both operational and research settings.352

353637383940414243444546474849505152535455561. Introduction and backgroundReducing uncertainty associated with winter storm precipitation type, accumulation andtiming is a paramount forecasting, safety, and socioeconomic challenge (Ralph et al. 2005,Nygaard et al. 2011, Smith et al. 2012). These rapidly evolving mesoscale systems will be betterunderstood with the national dual-polarization radar upgrade through use of hydrometeorclassification algorithms (HCAs; Liu and Chandrasekar 2000, Zrnic et al. 2001, Chandrasekar etal. 2011). Cold season microphysical processes observable by polarimetric radars and whoseorigins are generally agreed upon include dendritic ice crystal growth zones (DGZs; Kenndeyand Rutledge 2011-henceforth KR11, Andric et al. 2012, Bechini et al. 2012), plate crystalgrowth (Pruppacher and Klett 1997-henceforth PK97, Wolde and Vali 2001, Williams et al.2011), ice particle density and shape modulations caused by riming and aggregation(Vivekanandan et al. 1994), hydrometeor melting (Ryzhkov et al. 1998), and near-surfacerefreezing of either rain or freezing rain into sleet † (Kumjian et al. 2013).The goal of this paper is to develop and demonstrate a method for classifying thesedominant, bulk winter hydrometeor types/processes based on the discriminatory power ofpolarimetric radar variables at X, C, and S band. To this end, relevant information about thedistribution of sizes, orientations, shapes, and diversity of hydrometeors within a particular radarsample volume can be garnered from the differential reflectivity (Z DR ), correlation coefficient(! HV ), and specific differential phase (K DP ; Vivekanandan et al. 1994, Ryzhkov and Zrnic 1998b,Hubbert and Bringi 1995, Straka et al. 2000, Ryzhkov 2001, Bringi and Chandrasekar 2001).Simply stated, Z dr and K dp are both positive (negative) for oblate (prolate) hydrometeors, and nearzero for spherical particles or those that cant or tumble over large angles, effectively appearing† Sleet and ice pellets refer to the same thing are used interchangeably in this study.3

5758596061626364656667686970717273747576777879spherical to the radar. For a given oblate particle, K dp also increases with ice/liquid water contentand is inversely proportional to radar wavelength. The radar reflectivity (Z H ) also gives anindication of hydrometeor size and concentration.Winter hazards addressed by HCAs include enhanced production and subsequentaggregation of large, dendritic crystals aloft, which can lead to high precipitation rates,degradation of visibility, and disruptive snowfall accumulations (Fujiyoshi and Wakahama 1985,KR11). Z H -snowfall relationships for quantitative precipitation estimation and ice water contentcalculations could be improved by first determining the crystal type (Vivekanandan et al. 1994,Mitchell 1996, Wolfe and Snider 2012). The variable density of ice crystals is a major source ofuncertainty in these techniques. Radar discrimination of plates and dendrites may also provideinsight into the relative saturation of the environment and its ability to sustain aircraft icingconditions (Willims et al. 2011).Routine, nation-wide dual-polarimetric radar observations of precipitation type willprovide a foundation for improving mixed-phase microphysical parameterizations in numericalmodels (Cotton et al. 2011). Rauber et al. (2001) suggest the key to developing a mixed-phaseprecipitation forecast is accounting for complex phase change physics, including the effect ofdifferent ice particle habits falling through the melting layer. For instance, dendrites can easilycoagulate into large aggregates that may delay or prolong the melting process. Large, semimeltedaggregates that survive descent through the melting layer may then promote theproduction of sleet instead of freezing rain in the presence of a sufficiently cold and deep surfacelayer (Thériault et al. 2006). This process and that by which dendrites often aggregate duringdescent illustrate two winter storm processes where knowledge of the vertical distribution ofhydrometeors may help determine surface weather conditions. Surface observation or mesonet4

8081828384858687888990919293949596979899100101102systems such as ASOS or METAR, rapidly disseminated model output, and upper-air soundingscannot independently discern different snow crystal types, rain, freezing rain, or sleet with muchconfidence for several reasons (Elmore et al. 2011, Schuur et al. 2012). These observationalmethods do not provide the temporal or spatial resolution available from radar either.Hydrometeor classification algorithms combining atmospheric soundings withpolarimetric radar observations have been successful for warm-season, convective precipitation(Liu and Chandrasekar 2000, Zrnic et al. 2001, Ryzhkov et al. 2005a, Dolan and RutledgehenceforthDR09, Park et. al 2009, Chandrasekar et al. 2011) because the freezing level does notvary much in space or time. This is not the case for winter precipitation though, which motivatesuse of a polarimetric radar-based melting layer detection algorithm to identify wet or meltingsnow and then inform additional classification steps below and above this radar bright band layer(Giangrande et al. 2008 and Boodoo et al. 2010 - henceforth G8B1).To date, wintertime polarimetric algorithms using this melting layer detection techniqueand external temperature information from either a sounding or model forecast have attempted toidentify winter hydrometeor types with varying levels of success (Kouketsu and Uyeda 2010,Elmore et al. 2011, Schuur et al. 2012). Elmore et al. (2011) showed that the radar’s inability toidentify the refreezing of raindrops and errors in the melting layer detection algorithm led toHCA failures and poor overall performance in diagnosing surface weather conditions. Schuur etal. (2012) produced satisfactory results using an algorithm based on rapidly updated modeloutput temperature and moisture fields along with polarimetric radar data. The methodologypresented in Schuur et al. (2012) is particularly valuable at far ranges where the radar resolutionis degraded, and below the lowest elevation angle scan where surface weather conditions cannotbe diagnosed by the radar at all.5

103104105106107108109110111112113114115116117118119120121122123124125Polarimetric signatures for plate and dendritic crystals, as well as the recently discoveredrefreezing signature (Kumjian et al. 2013), are quite robust but have not yet been implemented inany hydrometeor classification scheme. It is important to note that these signatures have beenvalidated with external temperature data in aforementioned previous studies, but they do notrequire temperature information for real-time detection. Furthermore, no previous winter HCAhas fully exploited the potential uses of K dp (especially at shorter radar wavelengths), whichshould be extremely useful in discerning ice crystal habit. Since a melting layer detectionalgorithm can be used, the strong radar signatures demonstrated by certain winter hydrometeortypes might be sufficient for classification with little to no use of external temperatureinformation (Zrnic et al. 2001), possibly reducing computational expenses.In order to develop such a cold-season HCA that is as autonomous as possible and assessits performance at various wavelengths, scattering simulations of polarimetric radar variables atX, C, and S band based on the physical properties of dendrites, plates, dry aggregatedsnowflakes, 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 validatedwith radar, thermodynamic, and surface data during four winter storms in Section 5. Section 6provides a summary and suggestions for future algorithm use and improvement.2. Electromagnetic scattering simulation methodologya) T-matrix and Mueller-matrix modelsT-matrix and Mueller-matrix scattering models (Waterman 1965, Barber and Yeh 1975)were used to calculate the expected polarimetric radar variable ranges used to create the HCAmembership beta functions (MBFs) for various winter hydrometeor types (see Vivekanandan etal. 1991, Liu and Chandrasekar 2000, Zrnic et al. 2001, DR09, and Chandrasekar et al. 2011 for6

126127128129130131132133134135136137138139140141142143144145146147algorithm definitions and equations). The T-matrix model computes the radar backscatteringcross section of particular hydrometeors and the Mueller-matrix calculates polarimetric radarobservations for a homogeneous, parameterized population of a given hydrometeor type. Theseresults are sensitive to the input parameters in Table 1, which we elaborate on in the remainder ofthis section.All hydrometeors are modeled as oblate spheroids without branched or otherwiseirregular shapes, which is sufficient for X-, C-, and S-band weather radar applications (Bringiand Chandrasekar 2001). While scattering simulations are sensitive to phase (ice vs. liquid), theresults were negligibly sensitive to changes in temperature. 30° and 1° elevation angles weresimulated to determine how the radar would perceive high- and low-altitude ice particles. Sleetand rain are only expected to exist below the melting level so are simply modeled at 1°.Hydrometeor bulk density (! bulk ) is defined as the particle’s mass per unit volume. Theaxis ratio is assumed to compare the minor (“a”, basal, a-axis growth face) and major (“b”,prism, c-axis face) dimensions of a particle (“a/b”), where values approach one for spheres. Theparticle size distribution (PSD) D MIN , D MAX , diameter interval ("D), and functional shape areparameterized, from which we calculate D 0 . To represent the natural variability of precipitationin turbulent background flow, all hydrometeors are assumed to have a Gaussian distribution ofcanting angles about a mean (# m ) of zero (Beard and Jameson 1983, Hendry et al. 1976, Spek etal. 2008). The fall behavior of individual particles may vary greatly, but in the interest ofdistinguishing bulk hydrometeor types we used standard deviation of the canting angle ($) valueswhich best characterized how each particle type might fall differently from another.b) Model parameterizations for various hydrometeors7

148149150151152153154155156157158159160161162163164165166167Wet or melting snow was not modeled in this study but its inclusion in the classificationalgorithm is discussed in Section 4. A graupel category was not included because it was notobserved during any of our case studies, but can form in other winter storms around the world(Takahashi and Fukuta1988, Takahashi et al. 1999, Reinking 1975). Bullet, rosette, and stellarcrystal shape extensions are too complex to be resolved by K- through S- band frequency radars(Vivekanandan et al. 1994).i. Dendrites and platesBecause of their skeletal framework, dendrites are modeled with low ! bulk between 0.3-0.5 g cm -3 (Heymsfield 1972, Fukuta and Takahashi 1999). These branched crystals tend toflutter as they slowly fall with their maximum dimension oriented horizontally (PK97). This isrepresented with $ = 15° (Matrosov et al. 1996, KR11). We modeled PSDs observed by Lo andPassarelli (1982) for pristine dendrites prior to the onset of aggregation. Many studies haveconfirmed that an exponential PSD is sufficient to describe crystal populations (PK97).Dendrites can be longer (1.3 cm ‡ ; Mitchell et al. 1996, PK97, KR11) than plates, whichhave less favorable geometry for growth and are associated with lower ice supersaturations(usually unsaturated with respect to water; PK97, Foster and Hallett 2008). Plates are assumed tobe solid ice (PK97) and exhibit approximately the same canting behavior as dendrites. However,plates have more sloped PSDs because of their muted growth (Bader et al. 1987, Ryan 2000).Observed D and D 0 ranges from samples of unrimed plate populations (PK97) match thosemodeled for plates.‡ This scattering model could only simulate D MAX % 1 cm. PSD parameterizations were stilldeemed sufficient because D 0 was always well contained within D MAX (see Table 1) andsimulated D 0 ranges agree with D 0 observations for both snow types (see references in text).8

168169170171172173174175176177178179180181182183184185186187188189190The vertical thickness of plates and dendrites is the same but their horizontal dimensionsdiffer based on growth conditions and therefore dendrites are slightly more oblate (Auer andVeal 1970). We qualitatively followed the data from Auer and Veal (1970), but our modelbecomes computationally unstable for the very small a/b they suggest (

191192193194195196197198199200201202203204205206207208209210211212213Hogan et al. (2000) derived a power law relationship for aggregates that describes ! bilk asa function of size. Clumps of dendrites with very large combined diameters have extremely low! bilk from air pockets between branches and since mass is distributed across a larger volume. Themajority of naturally occurring, larger aggregates should have ! bulk ~ 0.05 g cm -3 , while ! bilkcould range from 0.01-0.2 g cm -3 . Only the smallest, most compact snowflakes will approach! bulk > 0.15 g cm -3 (PK97), but are usually responsible for the majority of positive, albeit small,K dp and Z dr contributions (KR11, Andric et al. 2102).Large, irregular aggregates cant over larger angles or tumble more dramatically thanpristine crystals (Kajikawa 1982). The aggregate $ value was accordingly doubled from that ofdendrites and plates to 30° (Matrosov et al. 1996, KR11). Instead of modeling aggregates withvery oblate axis ratios and extremely high standard deviation of canting angle (perhaps more trueto nature), their axis ratios are raised (0.7-0.9; Barthazy et al. 1988, Vivekanandan et al. 1994,Herzegh and Jameson 1992, DR09, KR11) to effectively represent a nearly spherical particlewith moderate $ (manual approximation of nature). Since small, compact aggregates and large,conglomerations of dendrites will look identical to a polarimetric radar because of their cantingeffect and low density, we cannot distinguish them in this study.iii. Stratiform rain, freezing rain, and sleetA normalized gamma drop size distribution (DSD) was utilized to more accuratelyrepresent the natural variability of stratiform rain and sleet below the melting level (Waldvogel1974, Ulbrich 1983, Willis 1984, Bringi et al. 2003a, Gibson et al. 2009). Raindrops produced bymelted snow typically have diameters < 3 mm (Stewart et al. 1984). Both raindrops and wetsnowflakes freeze into ice pellets either individually at subzero temperatures (IP-a type) or bycolliding with snowflakes, ice pellets, or other suitable freezing nuclei (IP-b type, Thériault et al.10

2142152162172182192202212222232242252262272282292302312322332342352362006 and 2010). Sleet is modeled at -4°C because temperature usually distinguishes clear fromopaque ice pellets (Spengler and Gokhale 1972), but sleet has been observed between -1°C to -9°C. Freezing rain is modeled at -1°C. The stratiform rainfall DSD was used for sleet becausethe parameters in Table 1 are quite broad and previous studies have not conclusively documentedsleet’s increased maximum size or alternative PSD from rain (Gibson et al. 2009, Stewart et al.1990b).Raindrop shape simulations described in Table 1 account for increasing raindrop axisratios for D > 1 mm. Because raindrops deform into quasi-equilibrium shapes during descent,their $ values are relatively low ~1-10° (Ryzhkov et al. 2001). Ice pellets were modeled ascompletely frozen raindrop shapes (according to observations in Gibson and Stewart 2007,Spengler and Gokhale 1972) that tumble due to their rigid body. Correspondingly high $ valuesbetween 60-80° typically used for graupel (Knight and Knight 1970, Kennedy et al. 2001) wereadopted.More complex, realistic electromagnetic scattering simulations for a mixture of frozen,partially frozen, and unfrozen drops (Fujiyoshi and Wakahama 1985) could be performed to testthe theories presented in Kumjian et al. (2013) on the origin of the refreezing signature observedwhen and where sleet forms during descent. However, these steps are beyond the scope of thisstudy where we focus on the polarimetric signatures of bulk hydrometeor populations and theability of a fuzzy logic algorithm to distinguish them.3. Electromagnetic scattering simulation resultsFig. 1 and Table 2 show simulated K dp, Z dr, and Z h ranges for X, C, and S band accordingto parameterizations in Table 1 between the five hydrometeor types of interest: dendrites, plates,aggregates, sleet, and rain. These polarimetric radar (PR) variable ranges were comparable to11

237238239240241242243244245246247248249250251252253254255256257258259available literature examples without major fault or disagreement (Table 3). There is a slight,negligible increase in Z h and decrease in Z dr with increasing & for all hydrometeors due to non-Rayleigh scattering effects by oblate spheroids (Matrosov et al. 2005). This argument alsojustifies why simulated X-band K dp is actually 3.7 times greater than at S-band, but thewavelength ratio (11.0/3.2) is only 3.4 (Matrosov et al. 2005, DR09). Modeled ! hv values ofthese homogenous hydrometer populations were all above 0.99 (Balakrishnan and Zrnic 1990b).The remainder of this section explains and justifies these theoretical scatteringsimulations before discussing the modifications necessary for optimal algorithm performance onreal, sometimes noisy data in Section 4. Our goal was to construct a winter storm HCA based onuniversal, physical properties of winter precipitation as viewed by radar instead of tuning thealgorithm for particular hardware or locations.a) Dendrites and platesK dp for dendrites is about two times greater than for plates, which was initiallycounterintuitive because plates have much higher density and lower N 0 . Sensitivity studiesshowed that dendrites have higher K dp primarily because they are more oblate and have D 0 valuesabout twice as large as plates. While higher density crystals do exhibit higher K dp in oursimulations, diameter is also important because it appears in both the ice water content and massweightedmean axis ratio terms used to express K dp (Bringi and Chandrasekar 2001), since massis proportional to D 3 .While dendrites have higher K dp than plates, plates have higher maximum (and minimum)Z dr than dendrites by approximately 1.3 (0.5) dB for all &s. This upward shift in the Z dr range wassurprising since dendrites are more oblate with larger diameters (which affects their Z hweighting), but it is reasonable considering that plates have much higher density. This result12

260261262263264265266267268269270271272273274275276277278279280281282speaks to the tendency for polarimetric variables to be dependent on many, sometimescompeting, physical factors. While Z h and Z dr are often derived from Rayleigh scatteringassumptions for spheres, Rayleigh-Gans theory demonstrates that both these variables stilldepend on the density and phase of oblate hydrometeors, such as ice crystals, through thedielectric factor (Atlas et al. 1953). For instance, sensitivity tests revealed that Z h is equally mostsensitive to N 0 and D 0 but secondarily to ! bulk for all hydrometeors.High elevation angle radar scans often exhibit decreasing K dp and Z dr for both plates anddendrites because the radar beam is no longer oriented along the major, horizontal axis of oblateparticles (Evans and Vivekanandan 1990, Ryzhkov et al. 2005b). Sensitivity tests for thesehydrometeors between 1° to 30° are shown in Table 4. K dp reductions are approximatelyinversely proportional to &, as expected. The overall elevation angle effect on plates anddendrites is to decrease maximum K dp as well as to decrease the entire Z dr range for each pristinecrystal, making them less exclusive from aggregates and perhaps each other. Since PPI elevationangles rarely reach 30°, this effect should not hamper most snow classification efforts except onclose-range RHI scans, as shown in Section 5. The MBF slopes (Section 4) also help alleviatethis issue. Enhanced Z dr from decreasing signal-to-noise ratio (SNR) with range, especially atprecipitation echo edges, is actually more likely to degrade algorithm performance (Ryzhkov etal. 2005a). Low SNR artifacts should be distinguishable from positive Z dr areas associated withoriented ice crystals because only the latter will follow meteorological storm evolution.In summary, the microphysical differences between plates and dendrites are manifestedin radar data by an inverse K dp- Z dr relationship, which may help distinguish the two categories.This is especially true since snow always has relatively low Z h and high ! HV . Some observationsof slightly reduced ! hv to 0.90 within DGZs have been reported (KR11, Andric et al. 2012),13

283284285286287288289290291292293294295296297298299300301302303304305perhaps due to PSD broadening under vigorous vapor deposition. Since this small magnitude ! hvdecrease is not seemingly present in every DGZ because it is hardly measurable and may dependon the intensity of crystal growth, it is not accounted for in this algorithm.b) Dry aggregatesAggregates have extremely low magnitude K dp and Z dr because of increased canting andlow ! bulk . However, they also have the highest Z h compared to plates and dendrites because oftheir larger diameters (Ohtake and Hemni 1970, Ryzkhov and Zrnic 1998a, Boucher and Wieler1985). Trapp et al. (2001) and Ryzhkov et al. (2005a) suggest that Z dr tends to decrease as Z hincreases, or as aggregation progresses, density decreases, fall behavior becomes more erratic,and the diameters of snowflakes increase. Texture fields (Ryzkov et al. 2005b) could potentiallybe used to detect the Z h gradient often associated with aggregating dendrites (KR11). Modeledradar variables for aggregates were most sensitive to density and axis ratio parameterizations.c) Stratiform rain, freezing rain, and sleetSleet has lower K dp, Z dr, and Z h than rain (Fig. 1) because of increased canting as well asdecreased dielectric factor, density, and temperature. Fig. 2 shows the results of an X-, C-, and S-band sensitivity study conducted to isolate the relative impacts of these factors on radar variablesfor rain (RN), freezing rain (FR; T = -1ºC, only at C-band), and sleet (SL_1 or SL_2). Notsurprisingly, freezing rain is barely distinguishable from rain (2 dBZ Z h decrease, no Z dr change,and only 0.03° km -1 K dp decrease at C-band), which leads us to conclude that temperature hasonly a minor effect on our simulations. Simulating frozen raindrops (SL_1) with decreaseddielectric factor, density, and temperature without tumbling fall behavior resulted in a substantial7 dBZ decrease, 1.4 dB Z dr decrease, as well as 1.5, 1.25, and 1.0° km -1 K dp decrease for X-, C-,and S- band respectively. When ice pellets were allowed to tumble (SL_2 = version of sleet used14

306307308309310311312313314315316317318319320321322323324325326327328in Fig. 1 and the rest of this study) as opposed to the small oscillations consistent with liquidraindrops deforming as they fall, the additional decrease in Z h is nearly zero but there is a 25%further decrease in both K dp and Z dr . While it is obvious that these three radar variables shoulddecrease once rain has completely frozen, these findings show that the dielectric factor anddensity decrease from liquid to ice dominates these trends, canting has a secondary, nonnegligibleeffect, and temperature has little importance.More importantly, since Figs.1 and 2 show how radar variables associated with stratiformrain encompass that of both supercooled and frozen rain, these latter two phenomena couldsimply be attributed to light rain. If the expected value ranges of a hydrometeor type are notunique from another type, fuzzy logic HCA MBFs cannot distinguish them. This simplealgorithm also cannot accommodate detection of the localized, small magnitude refreezingsignature associated with the production of sleet because those expected value ranges also liewithin that of stratiform rain (Kumjian et al. 2013). These include an increase in Z dr and K dpalong with decreased ! hv and Z H . If 2-D MBFs (Zrnic et al. 2001) and/or texture fields (Ryzkovet al. 2005b) were incorporated into the decision process, the spatial, correlated variability in ! hv,Z dr, K dp, and Z h within the refreezing signature might prompt more accurate rain/freezingrain/sleet classification. In the meantime, our methodology relies primarily on temperature toclassify rain and the combined possibility of sleet and/or freezing rain below the melting layerwhere T < 0 C without assessing other possible thermodynamic factors as in Schuur et al. (2012).4. Algorithm development and testingThe fuzzy-logic hydrometeor classification algorithm described in DR09 was adapted forwinter precipitation types to include stratiform rain, freezing/frozen raindrops (i.e., sleet and/orfreezing rain), wet snow (indicative of the melting layer), aggregates, dendrites, and plates.15

329330331332333334335336337338339340341342343344345346347348349350351Modifications to this algorithm necessitated (a) new procedures, (b) new membership betafunctions, and (c) a variable weighting system for each precipitation category. These three stepssubstantially increased the algorithm’s ability to distinguish different precipitation categoriesaccording to literature examples of these features, decreased its reliance on external temperaturedata 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 thedomain so an appropriate convective warm-season algorithm should be consulted under otherconditions. Non-meteorological echo must be removed a priori. A 5 dBZ reflectivity and 7-10 dBSNR threshold was also used to avoid misclassifications at echo edges due to nonmeteorologicalZ dr increases.a) Algorithm proceduresAs is typical for many HCAs, classification is performed on each pixel without knowledge ofdecisions made for nearby pixels or how the radar variables trend with height and time. Park etal. (2009) suggests that HCA performance can be optimized if individual algorithms aredeveloped for each major precipitation regime. It may be unrealistic to design a single algorithm(or single set of MBFs) to handle convective, stratiform, warm, and cold-season precipitation.Our HCA methodology is demonstrated during a stratiform freezing rain event in centralOklahoma with the C-band OU-PRIME radar in Norman, OK (Palmer et al. 2011). The nearbysoundings for this event are shown in Fig. 3, which exhibit a strong temperature inversion and acold surface layer from 15 UTC until 21 UTC. Fig. 4 shows the 2.4° PPI of OU-PRIME C-bandpolarimetric radar variables through the melting layer of stratiform precipitation when METARreports indicated freezing rain at the surface. A DGZ of enhanced K dp and Z dr with reduced ! hvappears aloft toward the southwest. This particular radar scan was used to verify that the16

352353354355356357358359360361362363364365366367368369370371372373374algorithm could handle certain peculiarities and difficulties such as a slanted melting layer heightfrom WNW-SSE throughout the domain and non-uniform precipitation.The complete classification algorithm includes three individual HCAs with differentcategories that are used to inform a final “fourth” classification based on melting layer detection.The four HCA steps completed for these polarimetric data are illustrated in Figure 5. First, the“melting layer detection HCA” in Fig. 5a distinguishes wet snow (WS) from the “other”category (OT), which represents aggregates and/or light rain. Melting layer classification onthese wet snow pixels with relatively high SNR (> 10 dB) is handled with the same generalmethodology presented by G8B1 to account for variable melting layer heights in each 10°azimuth sector of a PPI or for a single RHI. Following these previous studies, the melting layertop, median, and base are defined by the heights (AGL) below which 80%, 50%, and 20% of allwet snow gates reside in each sector. Only wet snow pixels between 5-35 km ranges are used todetermine the ML top, base, and median height to avoid non-uniform beam filling errors(Ryzhkov et al. 2007), other sampling errors that degrade the quality of polarimetric variables atextremely close and far ranges, and regions where the beam substantially ascends with range.The ML base, median, and top altitude classifications from this particular range segment areapplied to the whole sector of the radar’s polar coordinate system. Then the wet snow pixels withsufficiently high SNR identified throughout the whole domain are officially used to denote themelting layer in future HCA steps.In order to detect precipitation transition events where the ML reaches the ground, MLheight was also allowed to vary with range along a single PPI azimuth or RHI. For both theazimuth- and range-dependent methodologies, wet snow pixels are interrogated at all verticallevels of the radar volume because ground clutter is presumably removed a priori. To this end,17

375376377378379380381382383384385386387388389390391392393394395396397the number of wet snow pixels (ML # ) from the high-quality data range (5-35 km) are used toestimate the degree of melting (G8B1) within a particular azimuth sector or range segment of thebright band. This ML # threshold is subjective and depends on the radar’s data quality and spatialresolution. Thresholds were tested with surface observations during precipitation transitionevents. For example, OU-PRIME and CSU-CHILL RHIs have very high spatial resolution socomplete melting along the azimuth/range segment was assumed to occur if ML # > 10,000, nomelting was deemed to occur if ML # < 100, and partial melting is assumed to happen when 100> ML # > 10,000, such that snow makes it to the ground but there is still a temperature inversionaloft. These melting scenarios are used to inform the next HCA steps.For complete melting, a “below ML HCA” defines rain (RN) and freezing/frozen rain(FZ) based on temperature and reflectivity below the melting layer median height, as shown inFig. 5b which uses the 15 UTC sounding from Fig. 3a. Next, a reclassification of only dendrites,plates, and aggregates with more emphasis on Z dr and K dp is performed in the “above ML HCA”illustrated in Fig. 5c. An organized DGZ was classified in the southwest domain amidstaggregates according to their established polarimetric signatures. The DGZ heights correspond toappropriate temperatures between -5 to -15°C according to the 15 UTC sounding. K dp within thisDGZ reached 1.7° km -1 (in an adjacent radar scan), which was 0.6° km -1 higher than themaximum value estimated by C-band scattering simulations. This is likely because our modelcould not simulate D > 1 cm. Melting layer pixels are included in the above and below MLHCAs for reference but wet snow is not a category included in either HCA. Now the ML # is usedto inform the “final HCA,” Fig. 5d.If no melting was detected, the above ML HCA is applied everywhere since the ML isessentially below ground. If partial melting occurs, the above ML HCA is used throughout the18

398399400401402403404405406407408409410411412413414415416417418419domain but the ML is “painted” into the classification for reference, as in Fig. 5b and 5c. Ifcomplete melting occurs, the above and below ML HCAs are stitched together above and belowthe ML median height and the melting layer is also included. The latter iteration is chosen forFig. 5d. When K dp is noisy above and within the melting layer, it is useful to restrict plates anddendrites above 0.5-0.7 km of the ML top and keep wet snow pixels below this level. Thistechnique was used in Fig. 5.b) Membership beta functionsThe categories in each HCA step are assigned a score depending on the radar variables’ fitinto 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 (0-100%) in calculating the score. Thehydrometeor category with the highest score is determined to be the dominant bulk hydrometeortype in a particular radar gate. The expected value ranges in Fig. 1 and Table 2 were modified,usually by trial and error, to produce the MBFs in Figures 6-8 and Table 5 as follows:1. Implement slope (b) parameters to gradually widen the MBFs but preserve the preciseboundaries between categories predicted by scattering simulations.2. Increase maximum aggregate K dp values incrementally for decreasing & and slightly extendthe minimum K dp allowed for dendrites to reduce dendrite over-classification.3. Increase maximum Z dr for aggregates to 1 dB (regarded as acceptable for classificationpurposes considering noise, uncertainty, and the varying degree of aggregation by Bader etal. 1987, Illingsworth et al. 1987, and Straka et al. 2000).4. Decrease minimum Z h for dendrites and aggregates to -1 dBZ to account for not modelingspherical or extremely small particles for either category.19

4204215. Increase maximum Z dr for plates and maximum K dp for dendrites based on radar observationsto account for larger diameter crystals than could be parameterized in our model.422423424425426427428429430431432433434435436437438439440441442The wet snow MBF is substantially wide based on Knight (1979), Fujiyoshi (1986), Barthazyet al. (1988), Zrnic et al. (1993), Vivekanandan et al. (1993), Ryzhkov and Zrnic (1998a), Strakaet al. (2000), and Brandes and Ikeda (2004) as well as to account for noise, non-Rayleighscattering, and differential attenuation beyond the ML. We implemented overlapping ! hv MBFsbetween wet snow (0.6-0.95, Illingsworth and Caylor 1989, Ryzhkov and Zrnic 1998a, Straka etal. 2000) and “other” hydrometeors (0.90-1.0) based on trial and error efforts to reducemisclassification of noise or dendrites as wet snow, especially within/around the ML wherebright band signatures are not exactly collocated (Brandes and Ikeda 2004).c) Variable weighting systemAlgorithm performance was very sensitive to small (5%) changes in the weighting systemand those listed here gave the most physically-realistic results. We ensured that the algorithmcould identify the radar bright band, dendritic growth zone, aggregates, etc. on a case-by-casebasis according to examples in previous studies. It is significant that the weighting system inTable 5 works well on four different radar platforms at X-, C-, and S-band, as demonstrated inSection 5.The weights allow the algorithm to capitalize on strengths of specific radar variables indifferentiating between certain hydrometeors. For example, ! hv is heavily weighted for wet snowidentification, but not 100% because the ! hv ML signature is quite narrow and increasedweighting > 56% resulted in misclassifications. Z dr was weighted second highest for MLdetection because it was more helpful than Z H . Figure 4 shows an example of how the Z h bright20

443444445446447448449450451452453454455456457458459460461462463464465band signature is often not very consistent or well-defined in wintertime K dp is not trustworthy inand around the ML so it was excluded from the ML detection algorithm.K dp and Z dr are the most important and heavily weighted variables for distinguishingdendrites, plates, and aggregates since ! hv and Z h are usually innocuous (Trapp et al. 2001). Thealgorithm worked best when K dp was weighted slightly more than Z dr for classifying dendritesand plates, but with equal weights between K dp and Z dr for aggregates. This is presumablybecause K dp is less affected by aggregation and radar calibration than Z dr (Vivekanandan et al.2004), so it is perhaps a better indicator of pristine crystals.Temperature dominates the classification between freezing/frozen and liquid rain, butcontrary to most previous HCAs, temperature is not included in any other decision process. Weabandoned this methodology early on because it tended to produce horizontally stratified, nonmeteorologicalcrystal classifications above the melting layer. Dendritic and plate growth zoneclassification examples using polarimetric radar confirmed by surface observations and soundinginformation aloft within this study and others suggest that plates occur in a “cocoon” (Williamset al. 2011) near the top of the radar echo and dendrites tend to be found in “pockets” containedwithin the echo surrounded by decreasing values of K dp and Z dr (KR11, Andric et al. 2012).Aircraft observations of environmental conditions and precipitation type would provide furtheralgorithm validation of these phenomena.5. Hydrometeor classification algorithm case studiesThe winter HCA was tested on four different polarimetric radars spanning three differentfrequencies: C-band OU-PRIME and X-band CASA radars in central OK (McLaughlin et al.2005, Junyent et al. 2010, Palmer et al. 2011), an S-band WSR-88DP in Wichita, KS, and thedual-wavelength X- and S-band CSU-CHILL radar in northern CO (Brunkow et al. 2000). Please21

466467468469470471472473474475476477478479480481482483484485486487488see Appendix 1 for radar data post processing details. Observations from four different winterstorms are now considered to demonstrate the algorithm’s utility and validity.a) 28 Jan 2010 Oklahoma ice stormFreezing rain occurred throughout most of Oklahoma for nearly six hours during an icestorm on 28 January 2010. Snow was falling through a strong inversion aloft (Fig. 3a-c), whichdeepened vertically, descended, and cooled. Wet snow pixels in the ML exhibited decreasingmean ! hv from 18-23 UTC as the surface precipitation type switched from freezing rain to sleetaround 21 UTC according to METAR reports. One such HCA RHI during this time period ofprecipitation transition is shown in Fig. 9. Much of the original melting layer structure ispreserved in the wet snow classification through diligent weighting of the polarimetric variables.Aggregates are identified aloft and the most recent sounding helps classify either rain orfreezing/frozen raindrops below the melting layer. The HCA shows some wet snow pixelssurviving the melting layer toward the ground, perhaps contributing toward or showing evidenceof the transition from freezing rain to sleet. Future studies concerning these intriguing meltinglayer metrics as demonstrated by this algorithm could show utility in diagnosing surfaceprecipitation transitions (Stewart 1992, Heymsfield et al. 2004).A refreezing signature consistent with Kumjian et al. (2013) appeared in an alternateregion of the OU-PRIME domain from 21-23 UTC around the 0°C sounding temperature level.This provides further indication that a transition from freezing rain to sleet had occurred or wasoccurring. As previously discussed, the algorithm presented herein is not capable of identifyingthe refreezing signature but it is nonetheless an important phenomena relevant to this study thatshould be included in future winter HCAs.b) 24 Dec 2009 Oklahoma blizzard22

489490491492493494495496497498499500501502503504505506507508509510511A 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 24December 2009. The vertical bright band was easily detected in a reconstructed CASA radarRHI as an organized region of wet snow extending toward the ground in Fig. 10. The HCAanalysis matches METAR observations across this domain. Rain was reported at the radar sitewhile a transition to freezing rain, sleet, and then brief instances of snow were observed inadvance of the main vertical bright band (10-12 km range), with dry aggregated snowflakesconsistently falling in the cold air at increasing range. This illustrates the ability of the algorithmto differentiate heavy rain from wet snow, both of which produce high Z h and Z dr , based ondifferent expected ranges of ! HV . It also shows the melting layer detection algorithm’s versatilityin identifying a descending bright band by accounting for varying ML heights with range. Rainand sleet were classified as a function of temperature and therefore height using the 12 UTCupstream KOUN sounding. A refreezing signature indicative of sleet as described in Kumjian etal. (2013) was briefly observed ahead of the vertical bright band passage near the 0°C level in adifferent radar scan not shown, but the algorithm did not correctly classify this near-surfaceprocess as previously explained.Once the surface precipitation type changed to snow within the radar domain during thennext hour, particularly high K dp up to 2.6° km -1 was observed within a classic DGZ in Fig. 11.This exceeds the maximum X-band K dp expected for dendrites by 0.6° km -1 , perhaps becausethese dendrites exceeded the maximum diameter allowed in our scattering model (1 cm). Thehigh K dp -Z dr “pocket” and HCA dendrite identification in Fig. 11 was collocated with the -15°Cisotherm from a nearby sounding three hours prior. Wet snow is included in this HCA because atemperature inversion was still present but not strong enough to prevent snow from reaching the23

512513514515516517518519520521522523524525526527528529530531532533534ground according to surface observations. Aggregation is most likely occurring near the Z hgradient below the DGZ, but K dp and Z dr are still high enough to warrant dendrite classificationinstead of aggregates until just above the radar bright band according to the MBFs.c) 07-08 Feb 2012 Great Plains snowstormThe sole case study of plate-like crystals available to us was provided by personalidentification of “hexagonal plates” at the surface within range of the Wichita, KS WSR-88DPradar (c/o , Tyler Dewvall, Accuweather Enterprise Solutions, Inc.). Fig. 12 shows a verticalcross section into the region classified as plates, which appear to fall toward the surface.Extremely high Z dr values ~6.7 dB were observed while K dp < 0.25° km -1 , which matches platescattering simulations of K dp but exceeds the simulated Z dr value by 1.5 dB. The algorithmclassified dendrites until Z dr increased beyond the range expected for dendrites (Table 5). Z drshould increase as crystals attain higher densities or grow more solid than branched. It isimpossible to say whether the dendrite classifications in Fig. 12 were small plates or smalldendrites since we lack in-situ reports and the two are indistinguishable according to ourscattering simulations when diameters are small. Wichita sounding temperature ranges aresuitable for plate growth at these heights.d) 03 Feb 2012 Colorado snowstormTo demonstrate algorithm performance at various wavelengths, simultaneous, dualwavelengthobservations of a Colorado snowstorm were analyzed with the CSU-CHILL radar.When the dendritic growth zone signature was most established within range of both wavelengthsystems, the S-band RHI (Fig. 13) showed K dp ~ 0.6° km -1 while the X-band RHI (Fig. 14)exhibited values correspondingly 3.7 times greater near 2.2° km -1 . Maximum Z dr is between 2.5-3.0 dB. Aggregates are identified surrounding the DGZ where both K dp and Z dr decrease toward24

535536537538539540541542543544545546547548549550551552553554555556557zero. Nearly equivalent X- and S-band classifications of dendrites centered directly on the -15ºClevel were made possible by the &-dependent HCA MBFs. The HCA is able to distinguish snowtypes at S-band despite low K dp magnitudes, which is encouraging since this is the operatingfrequency of the National Weather Service radar network. However, the more detailedinformation offered by X-band in this series of simultaneous RHIs is more discriminatory so theX-band HCA seems more robust and precise. The X-band CASA radars also offer enhancedinformation about the location of transition zones between precipitation types, despite its muchcoarser resolution.Areas where Z dr > 1 dB and K dp ~ 0° km -1 toward the tops of these echoes closer to theradar may contain pristine crystals that are not being classified clearly because use of highelevation angles may be artificially reducing the measurable K dp and Z dr (see Section 3a, Table4). This is more evident in the X-band RHI because of its 0.3° beam width, which resolves someunorganized plate and dendrite classifications near 2.6 km AGL within 40 km range. Thealgorithm also cannot distinguish between small, compact crystals that likely exist above theDGZ in Figures 13 and 14, from the large aggregates of dendrites that surely form below. Thesetwo types of “aggregates,” from a broad meaning of the word, are not distinguishable withpolarimetric radar because both have low ! bulk and dielectric factor, despite differences inappearance and shape.6. ConclusionsThe simple fuzzy logic hydrometeor classification algorithm developed herein revealsfive important microphysical processes in winter storms. Efforts were made to reduce thenumber of categories within each HCA step, which make it easier to modify and use. Withoutusing external temperature information, the algorithm is able to identify active dendritic and25

558559560561562563564565566567568569570571572573574575576577578579580plate crystal growth, snowflake aggregation, as well as small-scale melting layer fluctuations andits descent into a vertical bright band. These phenomena were confirmed with externaltemperature sources and surface observations where available, but further testing with more insitumeasurements should be completed in the future.The expected polarimetric radar value ranges, or membership beta functions, used in thealgorithm are trustworthy because they were derived from the universal, physical properties ofdendrites, plates, stratiform rain, freezing rain, and sleet. It was interesting to find that plateshave higher Z dr but lower K dp than dendrites, and this relationship can be used to distinguish thetwo crystal types. Sleet and freezing rain do not have unique expected value ranges from rain andtherefore could not be discerned by the 1-D membership beta functions used here. However, amore advanced algorithm with texture fields and/or 2-D membership beta functions might beable to detect the refreezing signature itself. More thermodynamic information could also beincorporated to differentiate rain, freezing rain, and sleet properly. We simply use soundingtemperature to classify the possibility of freezing/frozen raindrops below the melting layer.The algorithm worked well on four different radar platforms at X-, C-, and S-band invarious regions across the US once a variable weighting system and wavelength-dependent snowmembership beta functions were implemented to make the algorithm more efficient. As long aspolarimetric data are well calibrated, no additional modifications from this text should benecessary to run the algorithm on any radar at these frequencies. The algorithm tended to bemore robust and precise at shorter wavelengths because of its dependence on K dp .HCA output could be used in concert with vertical velocity measurements and in-situthermodynamic data to determine relationships between DGZs, supercooled liquid water, andupdraft speeds. Graupel and heavy-rain categories should also be added to this algorithm in the26

581582583584585586future. The descent of semi-melted particles classified as wet snow could be studied for theirimportance in forecasting near-surface phase changes. Methodologies described herein couldalso be applied to a multiple-wavelength hydrometeor classification algorithm for dual-frequencyradars or different, collocated radars. Finally, hydrometeor classification efforts could be used toinform quantitative precipitation estimation, ice water content calculations, and numerical modelparameterizations.58727

587588589590591592593594595596597598Acknowledgements.This work encompassed the completion of an M.S. thesis at Colorado State University and wasprimarily supported by NSF Engineering Research Center for Collaborative Adaptive Sensing ofthe Atmosphere subcontract UM#04-002341 B10 PO0001203233 and NSF grant AGS-1138116.A Graduate Research Fellowship from the American Meteorological Society provided additionalfunding. OU-PRIME is maintained and operated by the Advanced Radar Research Center(ARRC) of the University of Oklahoma. We also acknowledge Mr. Patrick C. Kennedy forproviding research insight and data (CSU-CHILL National Weather Radar Facility). Mr. PaulHein (CSU) supplied much technical help. Thanks to Mr. Haonan Chen (CSU) for dataprocessing. Useful discussions with Dr. Earle Williams (MIT) and Dr. Raquel Evaristo(Valparaiso Univ.) helped clarify several aspects of analysis. The authors also thank Dr. Susan C.van den Heever (CSU) and Dr. Matthew R. Kumjian (NCAR) for constructive suggestions.28

599600601602603604605606607608609610Appendix 1: Radar data post processing.Co-polar correlation coefficient (! HV ) correction for noise (Bringi and Chandrasekar2001) and removal of Z dr bias was required for CASA data. Ground clutter was also removedfrom OU-PRIME and CSU-CHILL data. The specific differential phase (K DP ) was calculated foreach radar system using the Wang and Chandrasekar (2009) method. Many X- and C-bandobservations of non-zero backscatter differential phase (') in the melting layer confirmeddeparture from the Rayleigh scattering regime. Differential attenuation also occurs in ourdatasets within and beyond the melting layer for low radar elevation angles during periods ofheavy stratiform precipitation. When the radar beam intersects the bright band at a shallow angle,it becomes nearly oriented along the longest axis of large, water-coated aggregates. Attenuationcorrection for wet snowflakes is an ongoing topic of research (León et al. 2011) and therefore noattenuation correction was performed on these data.61129

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858859860861862863864865866867868869870871872873874875876877Table Captions.Table 1: Microphysical parameters for T-matrix and Mueller-matrix used to calculatepolarimetric radar variables for various hydrometeor types.Table 2: K dp, Z dr, and Z h electromagnetic scattering simulation ranges, i.e. [max, min] rounded tothree significant figures, for plate ice crystals, dendritic crystals, dry aggregated snowflakes,sleet, and rain at X-, C-, and S-band frequency according to microphysical parameterizations inTable 1.Table 3: References for verifying and modifying scattering simulation results in Table 2specified by hydrometeor category and radar wavelength ().Table 4: K dp and Z dr electromagnetic scattering simulation ranges, i.e. [max, min] rounded tothree significant figures, at 1° and 30° radar elevation angle for plates and dendrites at X-, C-,and S-band frequency according to microphysical parameterizations in Table 1. Elevationinduced Z dr changes were not significantly different between X-, C-, and S-band. ["max, "min]represents the differences in simulated ranges with increasing elevation angle from 1° to 30°.Table 5: Slope (b), center (m), and half-width (a) parameters as well as resultant expected valueranges and weighting used for X-, C, and S-band HCA membership beta functions (MBFs)between plates (PL), dendrites (DN), dry aggregated snowflakes (AG), wet snow (WS), other(OT), rain (RN), and freezing/frozen raindrops (FZ). MBFs are wavelength independent unlessotherwise noted. The final HCA uses the below and above ML HCAs according to how muchmelting is estimated to occur from the ML detection HCA.38

878879880881Tables.Table 1: Microphysical parameters for T-matrix and Mueller-matrix used to calculate polarimetric radar variables for varioushydrometeor types.HydrometeorTypeMeanCantingSD ofCantingSlope (%)or SizeAxisAngle AngleParameterRatio Temp ! bulk D min D max "D (# m ) ($) PSD Type N o or N W D o (µ)a/b °C g cm -3 cm cm cm ° ° cm -1 m -3 cm cm -1 °RadarElev.AngleRainSleet1,3,4,5,8 * 10 1.0 0.01 0.5 - 01,3,4,5,8 * -4 0.9169 0.01 0.5 - 01410607080normalizedgammanormalizedgamma2,0008,00020,00060,0002,0008,00020,00060,0000.050.10.150.20.050.10.150.20.51.01.52.0 10.51.01.52.0 1DryAggregatedSnowflakes0.70.80.9-15,-1Hoganet al.(2000) 0.08 1.0 0.001 0 30 exponential20,00040,00060,0000.3340.3060.282111213130882883884DendritesPlates0.1350.150.2 -150.30.40.5 0.02 1.0 0.001 0 15 exponential0.20.30.5 -13 0.9 0.0015 0.5 0.0005 0 15 exponential100,000200,000300,000100,000300,000600,000900,000* rain drop shape models: 1 = Pruppacher and Pitter (1971), 3 = Beard and Chuang (1987), 4 = Andsager et al. (1999), 5 = Thuraiand Bringi (2005) “ogimi”, 8 = Huang et al. (2008) “bridge”0.1220.1050.0920.0610.0520.04630354060708013013039

885886887888Table 2: K dp , Z dr , and Z h electromagnetic scattering simulation ranges, i.e. [max, min] rounded tothree significant figures, for plate ice crystals, dendritic crystals, dry aggregated snowflakes,sleet, and rain at X-, C-, and S-band frequency according to microphysical parameterizations inTable 1.Category plates dendrites aggregates sleet rainZh(dBZ)XCS[-1.01, 18.6][-1.00, 18.7][-0.99, 18.7][9.94, 28.5][10.1, 28.8][10.2, 30.0][22.6, 31.3][23.2, 31.9][23.3, 32.1][-17.5, 40.2][-17.5, 40.2][-17.5, 40.2][-10.3, 49.5][-10.3, 49.4][-10.3, 47.8]Zdr(dB)XCS[1.83, 5.24][1.83, 5.22][1.82, 5.22][1.35, 3.96][1.35, 3.92][1.35, 3.90][0.01, 0.08][0.01, 0.07][0.01, 0.07][0.00, 0.44][0.00, 0.42][0.00, 0.41][0.04, 2.56][0.04, 2.23][0.04, 2.01]Kdp(° km -1 )XCS[0.01, 0.91][0.01, 0.53][0.00, 0.26][0.04, 1.98][0.03, 1.15][0.02, 0.57][0.00, 0.10][0.00, 0.05][0.00, 0.03][0.00, 0.32][0.00, 0.17][0.00, 0.09][0.00, 3.54][0.00, 2.36][0.00, 1.01]88940

890891892893894Table 3: References for verifying and modifying scattering simulation results in Table 2specified by hydrometeor category and radar wavelength ().Dendrites Plates Aggregates Sleet RainStraka et al. 2000 Straka et al. 2000 Straka et al. Kumjian et al. Straka et al. 2000(S) - combo snow (S) - combo snow 2000 (S) 2013 (C/S) (S) - D < 3 mm)category category*Trapp et al. Wolde and Vali Ryzhkov et al.Bringi and2001 (S)Ryzhkov et al.2005a (S)2001 (X)Williams et al.2011 (C)2005a (S)Dolan andRutledge 2009(X/S)Chandrasekar 2001Dolan and Rutledge2009 (X/S)Kennedy andAndric et al.Rutledge 2011 (S)2012 (X/C/S)* Straka et al. (2000) described a combination snow crystal category that exhibited Zdrconsistent with plates but K dp more consistent with dendrites. However, this study distinguishesthe two crystal types.41

895896897898899900Table 4: K dp and Z dr electromagnetic scattering simulation ranges, i.e. [max, min] rounded tothree significant figures, at 1° and 30° radar elevation angle for plates and dendrites at X-, C-,and S-band frequency according to microphysical parameterizations in Table 1. Elevationinduced Zdr changes were not significantly different between X-, C-, and S-band. [!max, !min]represents the differences in simulated ranges with increasing elevation angle from 1° to 30°.CategoryplatesElevation angle 1° 30° [!max, !min]Z dr (dB) X/C/S [2.65, 5.22] [1.83, 3.50] [-0.82, -1.72]X [0.01, 0.91] [0.01, 0.68] [0.00, -0.23]K dp (° km -1 ) C [0.01, 0.53] [0.01, 0.38] [0.00, -0.15]S [0.01, 0.26] [0.00, 0.19] [0.00, -0.07]CategorydendritesElevation angle 1° 30° [!max, !min]Z dr (dB) X/C/S [2.2, 3.92] [1.35, 2.7] [-0.85, -1.22]K dp (° km -1 )XCS[0.05, 1.98][0.03, 1.15][0.02, 0.57][0.04, 1.49][0.03, 0.87][0.02, 0.42][0.01, -0.49][0.00, -0.28][0.00, -0.15]42

901902903904905906907Table 5: Slope (b), center (m), and half-width (a) parameters as well as resultant expected valueranges and weighting used for X-, C, and S-band HCA membership beta functions (MBFs)between plates (PL), dendrites (DN), dry aggregated snowflakes (AG), wet snow (WS), other(OT), rain (RN), and freezing/frozen raindrops (FZ). MBFs are wavelength independent unlessotherwise noted. The final HCA uses the below and above ML HCAs according to how muchmelting is estimated to occur from the ML detection HCA.HCA ML Detection Below MLAbove MLstep HCAHCAHCAMBF OT WS FZ RN PL DN AGb, w 5, 16% 10, 16% 15, 33% 15, 33% 5, 20% 5, 20% 5, 20%m±a 16±17 25±20 11±28 19±30 9±10 15±16 16±17min -1 5 -17 -11 -1 -1 -1max 33 45 39 49 19 31 33Zh (dBz)Zdr (dB)Kdp (º km -1 )"HVTemp (ºC)b, wm±aminmaxb, wm±a: Xmin: Xmax: Xm±a: Cmin: Cmax: Cm±a: Smin: Smax: Sb, wm±aminmaxb, wm±aminmax15, 28%0.5±1.540610, 28%3±5406- - 10, 36%4.9±3.11.88.0- - - - 5, 44%0.46±0.450.0010.91- - - - 0.27±0.26-0.0010.53- - - - 0.13±0.1300.2610, 56%0.96±0.060.901.56*30, 56%0.75±0.20.550.95- -- -20, 66%-4±3-7-140, 66%25±2505010, 36%2.6±1.31.33.95, 44%1.32±1.280.042.61.0±0.70.031.70.31±0.30.010.6115, 40%-1±2-315, 40%0±0.55-0.550.550±0.325-0.3250.3250±0.2-0.20.2- - -- - -* 1.56 is not a realistic " hv value but this ensured the MBF did not slope to zero at " hv = 1.0.43

908909910911912913914915916917918919920921922923924925926927928929930931932933934935936937938939940941942943944Figure Captions.Fig. 1: K dp , Z dr , and Z h electromagnetic scattering simulations of plate crystals (purple), dendriticcrystals (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 colorconventions used throughout this studFig. 2: K dp , Z dr , and Z h electromagnetic scattering simulations of rain (RN-red) at X-, C-, and S-band, freezing rain (FR-dark orange cross-hatched) at C-band only, and sleet (SL-orange) at X-,C-, and S-band. Rain fall behavior was modeled for sleet version SL_1, while increased tumblingbehavior consistent with graupel was simulated in sleet version SL_2 (whose values appear inFig 1. and Table 2).Fig. 3. Skew-T diagrams from KOUN (Norman, OK), nearly collocated with OU-PRIME.Surface precipitation type was freezing rain at 15 and 18 UTC but sleet at 21 UTC.Fig. 4: C-band OU-PRIME Z h , Z dr , K dp , and ! hv PPI scans at 2.4° elevation angle throughstratiform precipitation with a dendritic growth zone aloft in the southwest quadrant at 1545UTC on 28 Jan 2010 when METAR reported freezing rain at the surface.Fig. 5: Winter hydrometeor classification algorithm steps: a) melting layer (ML) detection, b)below ML, c) above ML, and d) final HCA output for same C-band OU-PRIME PPI scans inFig. 7. Final classification includes plates (PL-purple), dendrites (DN-blue), dry aggregatedsnowflakes (AG-green), wet snow (WS-yellow), freezing/frozen raindrops (FZ-orange), rain(RN-red), and no echo (NE-white) indicating clear air or ground clutter.Fig. 6: X-, C-, and S-band membership beta functions (MBFs) for the melting layer (ML)detection HCA. Categories include wet snow and “other,” which accounts for aggregates andlight rain.Fig. 7: X-, C-, and S-band membership beta functions (MBFs) for the HCA used below themelting layer (ML). Categories include freezing/frozen rain and rain.Fig. 8: X-, C-, and S-band membership beta functions (MBFs) for the HCA used above themelting layer (ML). Categories include dry aggregated snowflakes, dendrites, and plates.Fig 9: C-band OU-PRIME Z h , Z dr , K dp , and !hv 330° RHI scans at 2220 UTC on 28 Jan 2010through stratiform precipitation once sleet had been reported in the Oklahoma City area byMETAR.Fig. 10: X-band CASA KSAO Z h , Z dr , ! hv , and HCA 270° RHI scans at 1422 UTC on 24 Dec2009 perpendicular to a vertical bright band. Freezing rain and sleet are classified between 0-10km range, melting, a concentrated region of wet snowflakes reach the ground around 12 km, anddry aggregated snowflakes are indicated at farther ranges. Central and southwestern OK METARreports confirmed passage of a similar precipitation transition event between 14-16 UTC.Fig. 11: X-band CASA KCYR Z h , Z dr , K dp , and HCA 50° RHI scans at 1518 UTC on 24 Dec2009 through a dendritic growth zone aloft when METAR snow reports occurred at the surface44

945946947948949950951952953954955956957within this vicinity. A temperature inversion existed around 1 km but did not cause completemelting. 12 UTC OUN (Norman, OK) sounding isotherms.Fig. 12: S-band KICT Z h , Z dr , K dp , and HCA 27° RHI scans at 0132 UTC on 08 Feb 2012through a supposed plate growth zone when plate-like snow crystals were sighted at the groundin Wichita. 00 UTC ICT (Wichita, KS) sounding isotherms.Fig. 13: S-band CSU-CHILL Z h , Z dr , K dp , and HCA 245° RHI scans through a dendritic growthzone when METAR snow reports occurred across the Front Range between Denver and FortCollins. Coincident scan with Fig. 14 at X-band. 00 UTC DNR (Denver, CO) soundingisotherms.Fig. 14: X-band CSU-CHILL Z h , Z dr , K dp , and HCA 245° RHI scans through a dendritic growthzone when METAR snow reports occurred across the Front Range between Denver and FortCollins. Coincident scan with Fig. 13 at S-band. 00 UTC DNR (Denver, CO) soundingisotherms.45

958959960961962Fig. 1: K dp, Z dr, and Z h electromagnetic scattering simulations of plate crystals (purple), dendriticcrystals (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 colorconventions used throughout this study.46

963964965966967968Fig. 2: K dp, Z dr, and Z h electromagnetic scattering simulations of rain (RN-red) at X-, C-, and S-band, freezing rain (FR-dark orange cross-hatched) at C-band only, and sleet (SL-orange) at X-,C-, and S-band. Rain fall behavior was modeled for sleet version SL_1, while increased tumblingbehavior consistent with graupel was simulated in sleet version SL_2 (whose values appear inFig 1. and Table 2).47

a)969b)970c)971972973Fig. 3. Skew-T diagrams from KOUN (Norman, OK), nearly collocated with OU-PRIME.Surface precipitation type was freezing rain at 15 and 18 UTC but sleet at 21 UTC.48

974975976977Fig. 4: C-band OU-PRIME Z h, Z dr, K dp, and ! hv PPI scans at 2.4° elevation angle throughstratiform precipitation with a dendritic growth zone aloft in the southwest quadrant at 1545UTC on 28 Jan 2010 when METAR reported freezing rain at the surface.49

a) b)c) d)978979980981982983Fig. 5: Winter hydrometeor classification algorithm steps: a) melting layer (ML) detection, b)below ML, c) above ML, and d) final HCA output for same C-band OU-PRIME PPI scans inFig. 7. Final classification includes plates (PL-purple), dendrites (DN-blue), dry aggregatedsnowflakes (AG-green), wet snow (WS-yellow), freezing/frozen raindrops (FZ-orange), rain(RN-red), and no echo (NE-white) indicating clear air or ground clutter.50

984985986987Fig. 6: X-, C-, and S-band membership beta functions (MBFs) for the melting layer (ML)detection HCA. Categories include wet snow and “other,” which accounts for aggregates andlight rain.51

988989990Fig. 7: X-, C-, and S-band membership beta functions (MBFs) for the HCA used below themelting layer (ML). Categories include freezing/frozen rain and rain.52

991992993Fig. 8: X-, C-, and S-band membership beta functions (MBFs) for the HCA used above themelting layer (ML). Categories include dry aggregated snowflakes, dendrites, and plates53

994995996Fig. 9: C-band OU-PRIME Z h, Z dr, K dp, and ! hv 330° RHI scans at 2220 UTC on 28 Jan 2010 through stratiform precipitation once sleethad been reported in the Oklahoma City area by METAR.54

99799899910001001Fig. 10: X-band CASA KSAO Z h, Z dr, ! hv, and HCA 270° RHI scans at 1422 UTC on 24 Dec 2009 perpendicular to a vertical brightband. Freezing rain and sleet are classified between 0-10 km range, melting, a concentrated region of wet snowflakes reach the groundaround 12 km, and dry aggregated snowflakes are indicated at farther ranges. Central and southwestern OK METAR reportsconfirmed passage of a similar precipitation transition event between 14-16 UTC.55

1002100310041005Fig. 11: X-band CASA KCYR Z h, Z dr, K dp, and HCA 50° RHI scans at 1518 UTC on 24 Dec 2009 through a dendritic growth zonealoft when METAR snow reports occurred at the surface within this vicinity. A temperature inversion existed around 1 km but did notcause complete melting. 12 UTC OUN (Norman, OK) sounding isotherms.56

100610071008Fig. 12: S-band KICT Z h, Z dr, K dp, and HCA 27° RHI scans at 0132 UTC on 08 Feb 2012 through a supposed plate growth zone whenplate-like snow crystals were sighted at the ground in Wichita. 00 UTC ICT (Wichita, KS) sounding isotherms.57

1009101010111012Fig. 13: S-band CSU-CHILL Z h, Z dr, K dp, and HCA 245° RHI scans through a dendritic growth zone when METAR snow reportsoccurred across the Front Range between Denver and Fort Collins. Coincident scan with Fig. 14 at X-band. 00 UTC DNR (Denver,CO) sounding isotherms.58

1013101410151016Fig. 14: X-band CSU-CHILL Z h, Z dr, K dp, and HCA 245° RHI scans through a dendritic growth zone when METAR snow reportsoccurred across the Front Range between Denver and Fort Collins. Coincident scan with Fig. 13 at S-band. 00 UTC DNR (Denver,CO) sounding isotherms.59