a dual-polarization radar hydrometeor classiﬁcation

A Dual-Polarization Radar Hydrometeor Classification Algorithm for WinterPrecipitation

ELIZABETH J. THOMPSON, STEVEN A. RUTLEDGE, AND BRENDA DOLAN

Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

V. CHANDRASEKAR

Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, Colorado

BOON LENG CHEONG

Advanced Radar Research Center, University of Oklahoma, Norman, Oklahoma

(Manuscript received 20 May 2013, in final form 16 February 2014)

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 mem-

bership 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 al-

gorithm 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.

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; Zrni�c

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; Andri�c 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

Corresponding author address: Elizabeth J. Thompson, De-

partment of Atmospheric Science, Colorado State University, 1371

Campus Delivery, Fort Collins, CO 80523-1371.

E-mail: [email protected]

1 Sleet and ice pellets refer to the same thing and are used

interchangeably in this study.

VOLUME 31 JOURNAL OF ATMOSPHER I C AND OCEAN IC TECHNOLOGY JULY 2014

DOI: 10.1175/JTECH-D-13-00119.1

� 2014 American Meteorological Society 1457

mailto:[email protected]

production and subsequent aggregation of large dendritic

crystals aloft can lead to high precipitation rates, degra-

dation 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 dis-

crimination 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 dis-

tribution of sizes, orientations, shapes, and diversity of

hydrometeors within a particular radar sample volume

can be garnered from the differential reflectivity (Zdr),

correlation coefficient (rhy), 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 andKdp

are both positive (negative) for horizontally (vertically)

aligned hydrometeors and zero for spherical particles,

including those that effectively appear spherical to a ra-

dar 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 dis-

cerning crystal characteristics or their growth environ-

ment using radar. A cloud’s humidity and temperature

may change under the influence of vapor-rich updrafts

(Rauber and Tokay 1991) or during precipitation de-

scent. 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 super-

imposed on previous growth, so the radar only provides

a snapshot of current ice crystal characteristics. Addi-

tionally, 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 nu-

merical models (Cotton et al. 2011). Rauber et al. (2001)

suggest the key to developing a mixed-phase precipi-

tation 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 pro-

cess. 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 (Th�eriault

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 indepen-

dently 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 at-

mospheric soundings with polarimetric radar observa-

tions have been successful for warm-season, convective

precipitation (Liu and Chandrasekar 2000; Zrni�c 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 pre-

cipitation though, which motivates use of a polarimetric

radar-based melting-layer detection algorithm to iden-

tify wet or melting snow and then inform additional

classification steps below and above this radar bright-

band layer (Giangrande et al. 2008; Boodoo et al. 2010).

To date, wintertime polarimetric classification algo-

rithms using melting-layer detection techniques and ex-

ternal temperature information (from either a sounding or

model forecast) have attempted to identify winter hydro-

meteor 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 themelting-layer

detection algorithm led to poor overall performance in

diagnosing surfaceweather 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 methodol-

ogy presented by Schuur et al. (2012) is particularly valu-

able 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.

1458 JOURNAL OF ATMOSPHER IC AND OCEAN IC TECHNOLOGY VOLUME 31

Polarimetric signatures for plate and dendritic crys-

tals, as well as the recently discovered refreezing sig-

nature (Kumjian et al. 2013), have been documented

and can be long lived but have not yet been im-

plemented in any hydrometeor classification scheme. It

is important to note that these signatures have been

validated with external temperature data in aforemen-

tioned studies, but they do not require temperature in-

formation 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 tem-

perature information (Zrni�c et al. 2001), possibly re-

ducing computational expenses.

To develop such a cold-season HCA that is as au-

tonomous as possible and to assess its performance at

various wavelengths, scattering simulations of polari-

metric 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 algo-

rithm use and improvement.

2. Electromagnetic scattering simulationmethodology

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), Zrni�c 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 dif-

ferent particles. Then the Mueller matrix calculates po-

larimetric radar observations for each homogeneous,

parameterized size distribution. These simulations were

aggregated together to produce a range of expected

values for each precipitation type.

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 el-

evation angles, 308 and 18, were simulated to determine

how the radar would perceive higher-altitude ice parti-

cles. Sleet and rain should only exist below the melting

level, so they were simply modeled at 18.Hydrometeor bulk density (rbulk) is defined as the

particle’s mass per unit volume. The axis ratio is as-

sumed 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 (DD), number

concentration (N0 or NW), slope (l), and functional

shape (m) are parameterized, from which we calculate

D0 (median diameter of the PSD). To represent the

natural variability of precipitation in turbulent back-

ground flow, all hydrometeors are assumed to have

a Gaussian distribution of canting angles about a mean

(um) 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 (s) 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 s values that best characterized how

each particle type might fall differently from another.

b. Model parameterizations for varioushydrometeors

Wet ormelting snowwas notmodeled 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 approxima-

tion 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 rbulk between 0.3 and 0.5 g cm23

JULY 2014 THOMPSON ET AL . 1459

(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

s 5 158 (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 ag-

gregation. Many studies have confirmed that an expo-

nential 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 in-

formation 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 un-

saturated 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 ap-

proximately 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 parameteriza-

tions were still deemed sufficient becauseD0 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 quali-

tatively 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),

TABLE 1. Microphysical parameters for T matrix and Mueller matrix used to calculate polarimetric radar variables for various hy-

drometeor types. The CANTMAT module was used to simulate normalized gamma drop size distributions of rain, freezing rain (lower

temperature), and sleet, and theseNW and m values are denoted with an asterisk (*). Term DDwas 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.

Type

Axis ratio (y/x)

or shape model

Temp

(8C)rbulk

(g cm23)

DMIN

(cm)

DMAX

(cm)

Std dev

canting

angle s (8)PSD

type

N0 or NW(*)

(cm21m23)

D0

(cm)

Slope l or size

parmeter m(*)

(cm21 unitless)

(Freezing) Shapes 1,3,4, (21) 1.0 0.01 0.5 1 Norm 2000* 0.05 0.5*

Rain 5,8 10 4 Gamma 8000* 0.10 1.0*

10 20 000* 0.15 1.5*

60 000* 0.20 2.0*

Sleet Shapes 1,3,4, 24 0.9169 0.01 0.5 60 Norm 2000* 0.05 0.5*

5,8 70 Gamma 8000* 0.10 1.0*

20 000* 0.15 1.5*

60 000* 0.20 2.0*

Dry 0.7 215 Hogan et al. (2000) 0.08 1.0 30 Exp 20 000 0.282 11

Aggregated 0.8 21 40 000 0.306 12

Snowflakes 0.9 60 000 0.334 13

Dendrites 0.135 215 0.3 0.02 1.0 15 Exp 100 000 0.122 30

0.15 0.4 200 000 0.105 35

0.2 0.5 300 000 0.092 40

Plates 0.2 213 0.9 0.0015 0.5 15 Exp 100 000 0.061 60

0.3 300 000 0.052 70

0.4 600 000 0.046 80

900 000


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 thanwe are able to

simulate.

2) DRY AGGREGATES

Snowflake aggregation is most prolific when temper-

atures approach 08 and 2158C 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 maxi-

mum diameter. However, simulated snowflakeDMIN 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 aggre-

gate 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 rbulk as a function of size.

Clumps of dendrites with very large combined diameters

have extremely low rbulk from air pockets between

branches and since mass is distributed across a larger

volume. The majority of naturally occurring, larger ag-

gregates should have rbulk ; 0.05 g cm23, while rbulkcould range from 0.01 to 0.2 g cm23. Only the smallest,

most compact snowflakeswill approach rbulk. 0.15g cm23

(Pruppacher and Klett 1997), but they are usually re-

sponsible for the majority of positive, albeit small, Kdp

and Zdr contributions (Kennedy and Rutledge 2011;

Lautaportti et al. 2012; Andri�c et al. 2013).

Large, irregular aggregates cant or tumble more dra-

matically than pristine crystals (Kajikawa 1982). The ag-

gregate s value was accordingly doubled from that of

dendrites and plates to 308 (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 s (manual approxima-

tion of nature). Since small ice crystals and large con-

glomerations of dendrites should have identically lowZdr

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 vari-

ability 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

bymelted snow typically have diameters, 3mm (Stewart

et al. 1984). Both raindrops and wet snowflakes freeze

into ice pellets (IP) either individually at subzero tem-

peratures (IP-a type) or by colliding with snowflakes, ice

pellets, or other suitable freezing nuclei (IP-b type;

Th�eriault et al. 2006; Th�eriault et al. 2010). Sleet is

modeled at 248C because raindrops introduced to this

temperature should become some formof sleet (Spengler

and Gokhale 1972). Freezing rain usually begins to occur

at temperatures at or just below freezing and was mod-

eled at 218C. 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 ac-

count for increasing raindrop axis ratios for D . 1mm.

Because raindrops deform into quasi-equilibrium shapes

during descent, their s values are relatively low,;18–108(Ryzhkov 2001). Ice pellets were modeled with com-

pletely frozen raindrop shapes. Gibson and Stewart

(2007) and Spengler and Gokhale (1972) indicate that

sleet’s rigid body should tumble. Correspondingly high s

values between 608 and 708 typically used for graupel

(Knight and Knight 1970; Kennedy et al. 2001) were

adopted. More complex, realistic electromagnetic scat-

tering 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 parameteri-

zations in Table 1 between five winter hydrometeor

types of interest: dendrites, plates, aggregates, sleet, and

cold-season rain. These polarimetric radar (PR) vari-

able ranges were comparable to available literature ex-

amples without major fault or disagreement (Table 3).

There is a slight, almost negligible increase in Zh and a

decrease in Zdr with increasing l 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 rhy values for all our homogenous

hydrometer populations were above 0.99. This is a re-

flection of our idealistic model, which cannot simulate

more realistic mixtures of particles or explicitly describe

their natural variability (Balakrishnan and Zrni�c 1990).

Resonance effects (especially at C band; Zrni�c et al.

2000) are avoided in these simulations by limiting the

raindrop diameter, 5mmbased on observations (Stewart

et al. 1984).

The remainder of this section explains and justifies

these theoretical scattering simulations before discus-

sing 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 pre-

cipitation as viewed by radar instead of tuning the al-

gorithm 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 platesmight exhibit lower reflectivity than

dendrites. Our simulations of these crystals are not ex-

haustive (Table 3), but Kdp for dendrites is consistently

about 2 times greater than for plates at all ls. This was

initially counterintuitive because plates havemuch higher

bulk density and higher N0. Sensitivity studies showed

that dendrites have higherKdp primarily because they are

more oblate and haveD0 andDMAX values about twice

as large as plates. While higher-density crystals do ex-

hibit higher Kdp in our simulations, when all other

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.


factors remain the same, diameter is also very impor-

tant, since mass ;D3 and larger plates/dendrites are

more oblate.

While dendrites appear to have higherKdp than plates

in our simulations (Table 2; Fig. 1), as well as observa-

tions 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

ls. 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 var-

iables 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 ori-

ented 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 18 and308 are shown in Table 4. Reductions in Kdp are in-

versely proportional to l, 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 iso-

tropic ice crystals. Since plan position indicator (PPI)

elevation angles rarely reach 308, 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. EnhancedZdr from decreasing signal-

to-noise ratio (SNR) with range, especially at pre-

cipitation echo edges, is actually more likely to degrade

algorithmperformance (Ryzhkov et al. 2005b). LowSNR

artifacts should be distinguishable frompositiveZdr areas

associated with oriented ice crystals because only the

latter will follow meteorological storm evolution.

In summary, the microphysical differences between

plates and dendrites are manifested in radar data by an

TABLE 2. TermsKdp, 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 atX-, C-, and S-band frequencies according tomicrophysical

parameterizations in Table 1.

Variable Wavelength Plates Dendrites Aggregates Sleet Rain

Zh X [21.01, 18.6] [9.94, 28.5] [22.6, 31.3] [217.5, 40.2] [210.3, 49.5]

C [21.00, 18.7] [10.1, 28.8] [23.2, 31.9] [217.5, 40.2] [210.3, 49.4]

S [20.99, 18.7] [10.2, 30.0] [23.3, 32.1] [217.5, 40.2] [210.3, 47.8]

Zdr X [1.83, 5.24] [1.35, 3.96] [0.01, 0.08] [0.00, 0.44] [0.04, 2.56]

C [1.83, 5.22] [1.35, 3.92] [0.01, 0.07] [0.00, 0.42] [0.04, 2.23]

S [1.83, 5.22] [1.35, 3.90] [0.01, 0.07] [0.00, 0.41] [0.04, 2.01]

Kdp X [0.01, 0.91] [0.04, 1.98] [0.00, 0.10] [0.00, 0.32] [0.00, 3.54]

C [0.01, 0.53] [0.03, 1.15] [0.00, 0.05] [0.00, 0.17] [0.00, 2.36]

S [0.01, 0.26] [0.02, 0.57] [0.00, 0.03] [0.00, 0.09] [0.00, 1.01]

TABLE 3. References for verifying and modifying scattering simulation results in Figs. 1 and 2 as well as Table 2, specified by hydro-

meteor 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.

Dendrites Plates Aggregates Sleet Rain

Straka et al. 2000 (S)

combo snow*

Straka et al. 2000 (S)

combo snow*

Straka et al. 2000 (S) Kumjian et al. 2013 (C/S) Straka et al. 2000 (S)

D , 3mm

Trapp et al. 2001 (S) Wolde and Vali 2001 (X) Ryzhkov et al. 2005a (S) Bringi and Chandrasekar

2001 (X/C/S)

Ryzhkov et al. 2005a (S) Williams et al. 2011,

2013 (C)

Dolan and Rutledge

2009 (X/S)

Dolan and Rutledge

2009 (X/S)

Kennedy and Rutledge

2011 (S)

Andri�c et al. 2013 (X/C/S)


inverse Kdp–Zdr relationship, which may help distin-

guish the two categories. This is promising because snow

crystals always have relatively lowZh and high rhy. Some

observations of slightly reduced rhy to 0.90 within DGZs

have been reported (Kennedy and Rutledge 2011;

Andri�c 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

rhy 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 lowmagnitudeKdp andZdr

because of low rbulk and increased canting. However,

they also have the highest Zh compared to plates, den-

drites, or any other ice crystals because of their larger

diameters (Ohtake and Henmi 1970; Ryzhkov and Zrni�c

1998; Boucher and Wieler 1985). Trapp et al. (2001) and

Ryzhkov et al. (2005b) propose thatZdr 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 20dBZ, 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) be-

cause of increased canting as well as decreased dielectric

factor of ice compared to liquid water. Figure 2 shows the

results of anX-, 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 5 218C,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 de-

crease, noZdr change, and only 0.038km21Kdp decrease

at C band from rain to sleet), which leads us to conclude

that temperature has only a minor effect on these sim-

ulations. 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-dBZdr decrease, as well as 1.5, 1.25,

and 1.08 km21 Kdp decrease for X, C, and S bands

compared to rain, respectively. When ice pellets were

more realistically allowed to tumble (SL_25 version of

sleet used in Fig. 1 and the rest of this study), the addi-

tional decrease in Zh is nearly zero, but there is a 25%

further decrease in themaximumKdp andZdr.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.

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 hydro-

meteor 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 as-

sociated with the production of sleet because those ex-

pected 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 rhy and Zh. If 2D

MBFs (Zrni�c et al. 2001) and/or texture fields (Ryzhkov

et al. 2005a) were incorporated into the HCA, then

the spatially correlated variability of rhy, 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 tem-

perature to classify rain and the combined possibility of

sleet and/or freezing rain below the melting layer, where

T , 08C, without assessing other possible thermody-

namic factors as in Schuur et al. (2012).

TABLE 4. Terms Kdp and Zdr electromagnetic scattering simu-

lation ranges, i.e., [min, max] rounded to three significant figures, at

18 and 308 radar elevation angles for plates and dendrites at X-, C-,

and S-band frequency according to microphysical parameteriza-

tions in Table 1. Elevation-induced Zdr changes were not signifi-

cantly different between X, C, and S bands. The [Dmin, Dmax]

represents the differences in simulated ranges with increasing el-

evation angle from 18 to 308.

Category Plates

18 (Elev angle) 308 (Elev angle) [Dmin, Dmax]

Zdr X/C/S [2.65, 5.22] [1.83, 3.50] [20.82, 21.72]

Kdp X [0.01, 0.91] [0.01, 0.68] [0.00, 20.23]

C [0.01, 0.53] [0.01, 0.38] [0.00, 20.15]

S [0.01, 0.26] [0.01, 0.19] [0.00, 20.07]

Category Dendrites

18 (Elev angle) 308 (Elev angle) [Dmin, Dmax]

Zdr X/C/S [2.2, 3.92] [1.35, 2.7] [20.85, 21.22]

Kdp X [0.05, 1.98] [0.04, 1.49] [0.01, 20.49]

C [0.03, 1.15] [0.03, 0.87] [0.01, 20.28]

S [0.02, 0.57] [0.02, 0.42] [0.01, 20.15]


4. Algorithm development and testing

A fuzzy-logic winter hydrometeor classification algo-

rithm 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) ne-

cessitated (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 ex-

amples of these features, decreased its reliance on ex-

ternal temperature data to make classifications, and

allowed it to work well on a variety of radar platforms.

This algorithm assumes ice or mixed-phase pre-

cipitation 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 ofZh. 5 dBZ and SNR. 7–10 dBwere used

in the HCA to avoidmisclassifications at echo edges due

to nonmeteorological Zdr increases.

a. Algorithm procedures

As is typical for many HCAs, classification is per-

formed 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 eachmajor 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,

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 be-

havior consistent with graupel was simulated in SL_2. SL_2 values appear in Fig. 1 and Tables 1

and 2 as sleet.


and cold-season precipitation. Thus, our HCA is designed

for stratiform winter precipitation. We explain our meth-

odology with a freezing rain case study using the C-band

University of Oklahoma Polarimetric Radar for In-

novations inMeteorology andEngineering (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 2.98PPI 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 rhy appears aloft toward the south-

west, but Zdr is generally#1.25dB. 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.

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 fourHCAsteps 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 (.10dB)

is handled with the same general methodology presented

byGiangrande et al. (2008) to account for variablemelting-

layer heights in each 108 azimuthal sector of a PPI or for

a single RHI. Following themethodology ofGiangrande

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 sam-

pling errors that degrade the quality of polarimetric

variables at extremely close and far ranges, and any

substantial beam ascent with range.

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 ra-

dar’s data quality and spatial resolution. Thresholds

were tested with surface observations during precipi-

tation 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 . 10 000; 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 in-

form 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, andZh are used to

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.


classify dendrites, plates, ice crystals, and aggregates

above the ML in Fig. 5c. A possible DGZ with aggre-

gation below was identified in the southwest domain

amid ice crystals. The DGZ is appropriately contained

within 258 to 2158C according to the 1500 UTC

sounding. TermKdp within this potential DGZ reached

1.78 km21, which was 0.68km21 higher than the maxi-

mum 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 oc-

curring.

Now theMLnum is used to inform the finalHCA,Fig. 5d.

If no melting is detected, then the above-ML HCA is

applied everywhere. If partial melting occurs, then the

above-MLHCA is used throughout the domain, but the

ML is painted into the classification for reference. If

completemelting 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,

FIG. 4. C-band OU-PRIMEZh, Zdr,Kdp, and rhy PPI scans at 2.98 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.


above-ML, and below-ML HCA MBFs in Figs. 6–8 and

Table 5 as follows:

1) Implement b parameters to gradually widen the

MBFs but preserve the boundaries between cate-

gories predicted by scattering simulations.

2) IncreasemaximumZdr for aggregates to 1 dB,which is

regarded as acceptable for classification purposes

considering noise, uncertainty, and the varying degree

of aggregation byBader 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 l.

These increments were subjectively derived and

tested with the case studies in section 5.

4) Decrease minimum Zdr for aggregates to 21 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 den-

drites and slightly increase the maximum Zh allowed

for plates and aggregates to match radar observation

examples herein and in Table 3.

The wet snow MBF (Fig. 6) is substantially wide to ac-

count for noise, non-Rayleigh scattering, and differential

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.


attenuation based on Knight (1979), Fujiyoshi (1986),

Barthazy et al. (1988), Zrni�c et al. (1993), Vivekanandan

et al. (1993), Ryzhkov and Zrni�c (1998), Straka et al.

(2000), Brandes and Ikeda (2004), and Dolan et al.

(2013). We implemented overlapping rhy MBFs be-

tween wet snow (0.6–0.95; Illingworth and Caylor 1989;

Ryzhkov and Zrni�c 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 bright-

band 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

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.

FIG. 7. X-, C-, and S-band MBFs for the HCA used below the ML. Categories include

freezing/frozen rain and rain.


consistently identify the radar bright band, dendritic

growth zone, aggregates, etc., where applicable and in-

dicated 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, rhy is

heavily weighted for wet snow identification, but not

100% because the rhy ML signature is quite narrow and

increased weighting. 56% resulted in misclassifications.

TermZdr was weighted second highest for ML detection.

Figure 4 shows how the Zh brightband signature is not

always consistent or well defined inwintertime. TermKdp

is not trustworthy in and around the ML, so it was ex-

cluded from the ML detection algorithm.

TermsKdp andZdr are themost important and heavily

weighted variables for distinguishing dendrites, plates,

and aggregates, since rhy and Zh are usually innocuous

(Trapp et al. 2001). However, Zh was weighted highest

FIG. 8. X-, C-, and S-band MBFs for the above ML HCA. Categories include dry aggregated snowflakes, ice crystals, dendrites,

and plates.

TABLE 5. MBF weights (w), slope (b), and center (m)6 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 finalHCAuses the below- and above-ML

HCAs according to how much melting is estimated to occur from the ML detection HCA.

HCA Step ML detection HCA Below-ML HCA Above-ML HCA

Variable MBF OT WS FZ RN PL DN IC AG

Zh w, b 16%, 5 10, 16% 33%, 15 33%, 15 20%, 10 20%, 5 48%, 5 24%, 10

m 6 a 16 6 17 25 6 20 116 196 12 6 13 17 6 14 6 6 11 28 6 12

[min, max] [21,33] [5,45] [217,39] [211,49] [21,25] [3,31] [25,17] [16,40]

Zdr w, b 28%, 15 28%, 10 — — 36%, 10 36%, 10 24%, 20 36%, 20

m 6 a 0.5 6 1.5 25 6 20 5.5 6 3.7 2.6 6 1.3 0 6 1 0 6 1

[min, max] [40,6] [40,6] [1.8,9.2] [1.3,3.9] [21,1] [21,1]

Kdp w, b — — — — 44%, 5 44%, 5 28%, 5 40%, 5

X: m 6 a 0.46 6 0.45 1.32 6 1.28 0 6 0.55 0 6 0.55

[min, max] [0,0.9] [0.04.2.6] [20.55,0.55] [20.55,0.55]

C: m 6 a — — — — 0.27 6 0.26 1.0 6 0.7 0 6 0.325 0 6 0.325

[min, max] [0,0.53] [0.03,1.7] [20.325,0.325] [20.325,0.325]

S: m 6 a — — — — 0.13 6 0.13 0.31 6 0.3 0 6 0.2 0 6 0.2

[min, max] [0,0.26] [0.01,0.61] [20.2,0.2] [20.2,0.2]

rhy w, b 56%, 10 56%, 30 — — — — — —

m 6 a 0.96 6 0.06 0.75 6 0.2

[min, max] [0.90,1.00] [0.55,0.95]

T (8C) w, b — — 66%, 20 66%, 40 — — — —

m 6 a — — 24 6 3 25 6 25

[min, max] [27,21] [0,50]


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

thanZdr for classifying dendrites, plates, aggregates, and

isotropic ice crystals. We presume that Kdp is less af-

fected by aggregation and radar calibration than Zdr

(Vivekanandan et al. 1994), so it is perhaps a better in-

dicator 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; Andri�c et al.

2013). Aggregates seem most prevalent below dendritic

growth zones. Otherwise, small, individual, nonoriented

ice crystals are ubiquitous. Aircraft observations of en-

vironmental conditions and precipitation type would

provide further in situ algorithm validation of these

phenomena.

5. Hydrometeor classification algorithm casestudies

This winter HCA was tested on four different po-

larimetric 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 Sur-

veillance 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.

FIG. 9. C-bandOU-PRIMEZh,Zdr, rhy, andHCA3308RHI scans at 2220UTC 28 Jan 2010 through stratiformprecipitation once sleet had

been reported in the Oklahoma City, OK, area by METAR.


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 rhy 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 iden-

tified 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 de-

scending below the ML, perhaps contributing toward

or showing evidence of the transition from freezing rain

to sleet observed by other means. A refreezing signa-

ture 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 tem-

perature level. As previously discussed, the algorithm

presented herein is not capable of identifying the re-

freezing signature but it is nonetheless an important

phenomenon relevant to this study that should be in-

cluded in future winter HCAs (Stewart 1992; Heymsfield

et al. 2004; Schuur et al. 2012).

b. 24 December 2009 Oklahoma blizzard

A transition zone from convective rain to snow asso-

ciated with a vertical bright band (Stewart 1992) prop-

agated eastward through central Oklahoma prior to

FIG. 10. X-band CASA KSAO (Chickasha, OK) Zh, Zdr, rhy, and HCA 2708 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 be-

tween 1400 and 1600 UTC.


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 re-

gion 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

highZh andZdr but have very different rhy. 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 sig-

nature indicative of sleet as described in Kumjian et al.

(2013) was briefly observed ahead of the vertical

brightband passage near the 08C level in a different radar

scan (not shown), but the algorithm did not correctly

classify this near-surface process as previously explained.

Once the surface precipitation type changed to snow

within the CASA radar network over the next hour,

particularly high Kdp up to 2.68 km21 was observed

within a classic DGZ in Fig. 11. This exceeded the

maximum X-band Kdp simulated for dendrites by

0.68km21, 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 the2158C 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 gra-

dient 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

FIG. 11. X-band CASAKCYR (Cyril, OK) Zh, Zdr,Kdp, and HCA 508RHI 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.


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.

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 So-

lutions, 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. Ex-

tremely high Zdr values (6.7 dB) were observed within

the plate classification whereKdp, 0.258km21 andZh,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 in-

crease 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.

d. 3 February 2012 Colorado snowstorm

To demonstrate algorithm performance at various

wavelengths, simultaneous, dual-wavelength observa-

tions 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 ;0.68km21, while the X-band RHI (Fig. 14) ex-

hibited values correspondingly 3.7 times greater near

2.28 km21. Note the proximity of this DGZ to the

mountains, blocked out in white, and the potential el-

evation angle induced Kdp reductions close to the ra-

dar, 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

FIG. 12. S-band KICT (Wichita, KS)Zh,Zdr,Kdp, and HCA 278RHI 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.


below the DGZ, where both Kdp and Zdr decrease to-

ward 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.

Nearly equivalent X- and S-band classifications of

dendrites centered directly on the 2158C level were

made possible by the l-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 l, 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 dis-

criminatory, so the X-band HCA seems more trust-

worthy.While theX-bandCHILL systemhas a beamwidth

3 times narrower than at S band (0.38 vs 18), 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

Fdp statistical noise (Matrosov et al. 2005). As an ex-

ample, Fig. 11 from an X-band CASA radar, which has

a wide 1.88 beamwidth, also seemed to offer more in-

formation about the location of hydrometer transition

zones due to strong Kdp signatures.

6. Conclusions

The simple fuzzy-logic polarimetric radar hydrome-

teor 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 aggre-

gation, 4) finescalemelting-layer fluctuations, and 5)ML

descent into a vertical bright band. These phenomenawere

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

FIG. 13. S-band CSU–CHILL Zh, Zdr, Kdp, and HCA 2458 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

UTCDNR(Denver) sounding isotherms.Mountain beamblockage has been taken out but partial beamblockage still affects lower elevations.


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 theo-

retical understanding of dendrites, plates, aggregates,

other ice crystals, stratiform rain, freezing rain, and

sleet. We found plates to have higher Zdr but lower Kdp

andZh 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 1Dmembership 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 rea-

sonable 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 polari-

metric data are well calibrated, no additional modifica-

tions 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 gar-

nered from multiple dual-polarization radar variables into

a single product to diagnose melting and additional mi-

crophysical processes during winter storms. HCA output

could be used in concert with vertical velocity measure-

ments and in situ thermodynamic data to determine re-

lationships between DGZs, supercooled liquid water,

aircraft icing reports, and updraft speeds. Graupel and

heavy-rain categories could also be incorporated in the

FIG. 14. X-band CSU–CHILL Zh, Zdr, Kdp, and HCA 2458 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.


future. The descent of semimelted particles classified aswet

snow could be studied for their importance in forecast-

ing near-surface phase changes. Methodologies described

herein could also be applied to a multiple-wavelength hy-

drometeor classification algorithm for dual-frequency ra-

dars 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 com-

pletion of a master’s thesis at Colorado State University

and was supported by NSF Engineering Research Cen-

ter for Collaborative Adaptive Sensing of the Atmo-

sphere 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 ac-

knowledge 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 withEarleWilliams

(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 fromM. Kumjian and two anonymous

reviewers improved the manuscript.

APPENDIX

Radar Data Processing

Radar data must be thoroughly quality controlled be-

fore 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 ofZh 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 backscat-

tering differential phase d effects and smooth/filter

fluctuations of the propagation differential phase Fdp

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 polari-

metric signatures. Term rhy is sensitive to noise and

should also be quality controlled.

Term rhy 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 zdr/SNR in the denominator of the second

term instead of just zdr (V. Chandrasekar 2011, personal

communication). Individual Zdr biases were also cor-

rected for each CASA radar for particular cases. Ground

clutter was removed fromOU-PRIMEandCSU–CHILL

data. Term Kdp was calculated for each radar system us-

ing the Wang and Chandrasekar (2009) method. This

technique removes backscattering differential phase d

effects and filtersFdp. Many X- and C-band observations

of nonzero d in the melting layer confirmed departure

from the Rayleigh scattering regime (Zrni�c et al. 2000).

Therefore, Kdp is never used in melting-layer classifica-

tion. We also built a Kdp error window into the aggregate

and ice crystal categories to accommodate this uncer-

tainty.

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. Attenu-

ation correction for wet snowflakes is an ongoing topic

of research and therefore no attenuation correction was

performed on these data. Differential attenuation ren-

ders the Zdr information above the melting layer unus-

able 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 re-

flectivity. Regular horizontal attenuation was not a no-

ticeable problem in these datasets.

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