Discrimination of Mixed- versus Ice

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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
VOLUME 49
Discrimination of Mixed- versus Ice-Phase Clouds Using Dual-Polarization Radar
with Application to Detection of Aircraft Icing Regions*
DAVID M. PLUMMER
Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
SABINE GÖKE
Department of Physics, University of Helsinki, Helsinki, Finland
ROBERT M. RAUBER AND LARRY DI GIROLAMO
Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois
(Manuscript received 29 April 2009, in final form 30 October 2009)
ABSTRACT
Dual-polarization radar measurements and in situ measurements of supercooled liquid water and ice
particles within orographic cloud systems are used to develop probabilistic criteria for identifying mixedphase versus ice-phase regions of sub-08C clouds. The motivation for this study is the development of
quantitative criteria for identification of potential aircraft icing conditions in clouds using polarization radar.
The measurements were obtained during the Mesoscale Alpine Programme (MAP) with the National Center
for Atmospheric Research S-band dual-polarization Doppler radar (S-Pol) and Electra aircraft. The comparison of the radar and aircraft measurements required the development of an automated algorithm to match
radar and aircraft observations in time and space. This algorithm is described, and evaluations are presented to
verify its accuracy. Three polarization radar parameters, the radar reflectivity factor at horizontal polarization
(ZH), the differential reflectivity (ZDR), and the specific differential phase (KDP), are first separately shown to
be statistically distinguishable between conditions in mixed- and ice-phase clouds, even when an estimate of
measurement uncertainty is included. Probability distributions for discrimination of mixed-phase versus icephase clouds are then developed using the matched radar and aircraft measurements. The probability distributions correspond well to a basic physical understanding of ice particle growth by riming and vapor deposition, both of which may occur in mixed-phase conditions. To the extent that the probability distributions
derived for the MAP orographic clouds can be applied to other cloud systems, they provide a simple tool for
warning aircraft of the likelihood that supercooled water may be encountered in regions of clouds.
1. Introduction
Supercooled liquid water (SLW) is an important
component of cloud systems and precipitation development. Ice crystals, in the presence of SLW, can
accrete supercooled droplets and grow more rapidly into
precipitation-size particles. When ice particles are not
present, supercooled drops may grow by collision and
* Supplemental material related to this paper is available at the
Journals Online Web site: http://dx.doi.org/10.1175/2009JAMC2267.s1.
Corresponding author address: David M. Plummer, Department of Atmospheric Sciences, University of Illinois at Urbana–
Champaign, 105 S. Gregory St., Urbana, IL 61801.
E-mail: [email protected]
DOI: 10.1175/2009JAMC2267.1
Ó 2010 American Meteorological Society
coalescence through the supercooled ‘‘warm rain’’ process (Huffman and Norman 1988; Pobanz et al. 1994;
Cober et al. 1996; Rauber et al. 2000). Supercooled
water’s potential to enhance ice growth through the
Bergeron–Findeisen process and accretion has made it
an important topic of research for weather modification,
which has led to a large number of publications characterizing the SLW distribution in orographic and
stratiform cloud systems (e.g., Hill 1980; Heggli et al.
1983; Rauber et al. 1986; Rauber and Grant 1986, 1987;
Heggli and Rauber 1988; Rauber 1992; Sassen and Zhao
1993). Most modern research related to SLW is concerned with particle growth processes in mixed-phase
clouds (e.g., Young et al. 2000; Korolev and Mazin 2003;
McFarquhar and Cober 2004; Korolev and Isaac 2006).
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Supercooled liquid water has a practical importance
to the aviation community. Supercooled droplets can
freeze on contact with exposed airframe surfaces, reducing an aircraft’s aerodynamic properties and degrading its mechanical controls. Detection of icing conditions
is of significant importance to aviation because of this
danger. Numerous studies have been devoted to the
characterization and identification of cloud systems for
which icing is a hazard (e.g., Sand et al. 1984; Rasmussen
et al. 1992; Pobanz et al. 1994; Politovitch and Bernstein
1995; Cober et al. 2001b).
Remote detection of SLW is important both for microphysical studies and for aviation safety. Numerous
research efforts have been made to detect SLW remotely.
Rauber et al. (1986) and Heggli and Rauber (1988), for
example, used a microwave radiometer to detect variations in SLW content in orographic storms over northern
Colorado and the Sierra Nevada. Vivekanandan et al.
(1999a) used differences in reflectivity and attenuation
between dual-wavelength radar observations to identify
water content for both liquid and mixed-phase clouds.
Zawadzki et al. (2001) used a vertically pointing X-band
Doppler radar to infer the presence of supercooled droplets from observed bimodal Doppler spectra. Hogan et al.
(2003) combined lidar and radar observations to identify
concentrations of supercooled droplets even when radar
observations were dominated by larger frozen particles.
Several field campaigns [Winter Icing and Storms Project (WISP), Mount Washington Icing Sensors Project
(MWISP), and the Alliance Icing Research Studies I and
II (AIRS I and II); see Rasmussen et al. 1992; Ryerson
et al. 2000; Isaac et al. 2001; Isaac et al. 2005] have also
used short-wavelength (W, Ka, and X band) radars
to detect icing conditions (e.g., Reinking et al. 1997;
Vivekanandan et al. 2001; Reinking et al. 2002; Wolde
et al. 2006; Williams and Vivekanandan 2007).
All of these studies employ instrumentation that is not
generally available for operational use. Polarizationcapable radar systems, however, will provide a potentially useful source of data for remote SLW identification
as they become more widely available when the Weather
Surveillance Radar-1988 Doppler (WSR-88D) is upgraded
(Ryzhkov et al. 2005). Various automated hydrometeor classification algorithms have been developed to
use the variables measured by polarization radar systems (e.g., Vivekanandan et al. 1999b; Straka et al. 2000;
Liu and Chandrasekar 2000). Although some classification schemes include a category for SLW, the polarization signatures currently used to classify this particle
type feature significant ambiguities, and in situ verification of SLW with S-band radar has been very limited.
The only studies we are aware of are those of Hudak
et al. (2002), Wolde et al. (2003), and Field et al. (2004).
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Hudak et al. (2002) showed scatterplots of ZDR and KDP
measurements in low- and high-reflectivity regions of
winter stratiform clouds over southeastern Canada. They
concluded that these parameters had potential for distinguishing mixed-phase from glaciated conditions. Wolde
et al. (2003) computed radar polarimetric parameters
from in situ measurements in mixed-phase and ice
clouds and compared those with radar measurements of
ZH, ZDR, and KDP. They found that ZH computed from
in situ data agreed with the radar data, but ZDR showed
agreement only in selected regions of the clouds. Field
et al. (2004) examined the ZH and ZDR signatures of
mixed-phase and ice clouds for three aircraft flights,
finding that large ZDR values (.2 dB) above the melting
layer were coincident with SLW, provided the particles
were growing by vapor deposition. However, ZDR decreased when ice particles grew by aggregation, although SLW sometimes was still present.
As suggested by this previous work, improved understanding of SLW detection with polarization radars
may be achieved by employing combined aircraft and
radar measurements. Orographic cloud systems, in particular, provide an excellent opportunity to make these
observations. Topographic features provide a constant
obstacle to lower-tropospheric flow, with the potential
for long-term, consistent lifting of air. This vertical forcing can result in persistent SLW production as lifted air
cools and saturates (e.g., Hill 1980; Rauber et al. 1986;
Heggli and Rauber 1988). Orographic storms provide
the opportunity to make SLW observations over lengthy
time periods. However, even with large-scale consistency between cases, orographic cloud systems do vary
in structure and precipitation intensity. Observations
from the Mediterranean Alps, the American Cascades,
the Sierra Nevada, and the Rocky Mountains, among
others, have shown variations in precipitation development and SLW production associated with local topography and airflow (e.g., Heggli and Rauber 1988;
Rasmussen et al. 1995; Medina and Houze 2003; Houze
and Medina 2005; Woods et al. 2005; Ikeda et al. 2007).
In this paper, dual-polarization radar measurements
and in situ measurements of SLW and ice particles within
orographic cloud systems are used to develop probabilistic criteria for identifying mixed-phase versus ice-phase
regions of sub-08C clouds. We first present an algorithm
to obtain ‘‘matched’’ observations for direct comparison
of aircraft and radar measurements. We then show that
polarization radar data can be used to statistically distinguish between mixed-phase clouds (which, by definition, contain SLW) and ice-phase clouds. Finally, we
develop probabilistic criteria for SLW detection that are
consistent with a basic physical understanding of cloud
microphysical processes.
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2. Data sources
The radar and aircraft data used in this study were
collected during the Mesoscale Alpine Programme (MAP),
a multinational field campaign involving intensive observations of cloud systems influenced by the topography of the Mediterranean Alps (Bougeault et al. 2001).
Cloud systems moving through this region have the potential to be modified by the Alpine topography. Lowertropospheric flow often transports warm, moist air from
the Mediterranean into this area, and enhanced precipitation development can result if a significant upslope
flow component is present. A variety of weather systems
occurred during MAP. Widespread stratiform precipitation was observed during the cases used here, with
embedded convection also apparent in some cases depending on the atmospheric stability and the orientation
of the lower-tropospheric flow relative to local topography. ‘‘Unblocked’’ flow occurred in some cases when
the low-level flow was forced most directly over the topography, enhancing vertical forcing, which resulted in
the potential for significant and long-lasting SLW production (Peterson et al. 1991; Medina and Houze 2003).
Several cases during MAP resulted in significant precipitation developing over short time periods. This is
likely the result of substantial riming in areas of enhanced
SLW production, as described by Medina and Houze
(2003), Houze and Medina (2005), Lascaux et al. (2006),
and others.
The data for this study were from MAP intensive observation periods (IOPs) that concentrated on orographic
cloud systems that produced precipitation. The National
Center for Atmospheric Research (NCAR) Electra obtained measurements within the S-band dual-polarization
Doppler radar (S-Pol) observation area for IOPs 2b, 3, 4,
6, 7, 9, and 15. IOPs 7 and 9 did not have Rosemount
probe data, which were required for the detection of SLW,
and were therefore rejected for this study. Data from all
of the flights during the five remaining IOPs were used.
The synoptic characteristics of each IOP have been
documented by the science directors involved in MAP,
with more detailed discussion of most IOPs in the published literature. IOP 2b has been extensively examined,
for example, by Medina and Houze (2003), Rotunno and
Ferretti (2003), and Chiao et al. (2004). IOP 3 has been
described by Pujol et al. (2005) and Rotunno and Houze
(2007), and IOP 4 by Pradier et al. (2004) and Rotunno
and Houze (2007). IOP 6 has less documentation in the
formal literature, but details of the synoptic forcing can
be found from Internet sources (see http://www.atmos.
washington.edu/gcg/MG/MAP/iop_summ.html). IOP 15
has been described by Buzzi et al. (2003) and Rotunno
and Houze (2007).
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The NCAR S-Pol radar (Keeler et al. 2000) was used
during MAP. The radar primarily performed plan position indicator (PPI) scans, but also performed RHI
scans occasionally. Data for both scan types were used
for this study. This 10-cm wavelength, dual polarization
radar system was situated in the Lago Maggiore region
just south of the Italian Alps (see Fig. 1 of Medina and
Houze 2003). The radar transmits radiation alternately
between horizontal and vertical polarizations, allowing
measurement of several radar parameters including the
radar reflectivity factor at horizontal polarization (ZH),
the Doppler velocity, the differential reflectivity (ZDR),
the specific differential phase (KDP), and the correlation
coefficient between copolar horizontally and vertically
polarized echoes (rHV) [see Zrnić and Ryzhkov (1999),
Straka et al. (2000), or Bringi and Chandrasekar (2001)
for definitions of these variables]. Because of a misaligned feedhorn during the first part of the project, the
majority of the linear depolarization ratio (LDR) data
were of low quality and were not used in this study
(http://www.eol.ucar.edu/rsf/MAP/SPOL/).
The hydrometeor classification scheme developed by
Vivekanandan et al. (1999b) was operational with the
NCAR S-Pol during MAP. This scheme features a category for SLW, although the category is particularly
ambiguous, as the polarization signatures used to identify this particle type significantly overlap with those
for several other particle categories. As described by
Vivekanandan et al. (1999b), the polarization signatures
used to classify the ‘‘irregular ice crystal’’ type are particularly similar to those used to classify SLW. The data
used in this study provide an opportunity to further
understand SLW’s polarization signatures and decrease
these ambiguities in its identification.
The NCAR Electra research aircraft transected many
of the cloud systems observed by S-Pol. This study used
measurements from several aircraft-based instruments.
The output from the Rosemount Model 871 icing detector was used as a binary measure of the presence of
SLW. The LWC detection threshold of this instrument
was calculated by Cober et al. (2001a) to be 0.007 6
0.01 g m23 for an aircraft traveling at 97 6 10 m s21.
Baumgardner and Rodi (1989) show that an LWC of
0.01 g m23 is detectable over a 500-m distance, and an
LWC of 0.05 g m23 over a 100-m distance. For all radar
observations described below, the beamwidth exceeded
500 m, so the detection thresholds were acceptable for
this study. Particle Measuring Systems two-dimensional
(2D-C, 2D-P) optical array probes (OAP; Knollenberg
1970) were used as a binary measure of the presence of
ice. The OAP images in all regions of the flights where
the Rosemount probe was active were visually examined
to identify predominant particle habits and to determine
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if droplets or distinctly rimed quasi-spherical ice particles
were present. The binary measures (rather than concentrations or size distribution parameters) were used to be
consistent with the binary nature of SLW detection expected to be used operationally with polarization radar.
3. Automated aircraft–radar matching algorithm
The purpose of this section is to describe the method
developed to locate matched observations from the Electra aircraft and the S-Pol radar. This problem is nontrivial.
Radars observe large spatial volumes, while in situ observations are essentially point measurements. The relative locations of both measurements must be taken into
account before comparisons can be made between the
two. The simplest solution would be to use exactly collocated observations, where the aircraft is located within
a radar pulse volume. Unfortunately, the radar observations will be contaminated by the aircraft’s radar echo.
This contamination has been avoided (e.g., Plank et al.
1980) by using radar measurements from one radar
range gate away from the contaminated echo. A second
issue, however, is the number of data points available for
comparisons. Unless radar scan strategies and aircraft
flight paths are specifically designed to sample the same
volumes, collocated data points are rare. The absence of
sufficient data is a problem when in situ measurements
are used to verify radar measurements (e.g., Ryzhkov
et al. 1998; Vivekanandan et al. 1999b).
The method for locating matched data points presented here is an automated method applicable to large
datasets. The procedure transforms the aircraft’s position (initially in elevation, latitude, and longitude) into
the radar’s coordinate system (range, elevation, and azimuth). Mean particle trajectories are calculated forward
and backward in time from the in situ measurements,
increasing the number of possible matches available between the datasets.
The S-Pol data are in spherical coordinates with locations represented by range from the radar, as well as
azimuth and elevation angles with respect to 08 north
and 08 elevation, respectively. The Electra data also use
a spherical coordinate system, although locations are
calculated with respect to the earth’s center. The aircraft’s location along its flight path was calculated from
Global Positioning System (GPS) satellites in terms of
altitude above ground level and longitude and latitude
with respect to the earth’s center, with 1-s temporal resolution. For field projects that took place prior to May
2000 (as was the case for MAP), the GPS system featured some accuracy issues, with location accuracy potentially reduced to 100 m at times. The GPS data can
also feature missing or erroneous data if the GPS satellite
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signal retrieval was disrupted. Positional data were also
calculated using the Electra’s Inertial Reference System
(IRS) to improve accuracy. The IRS data were more
continuous than the GPS measurements but could accumulate large errors over time. The two sets of positions were filtered and combined, retaining the accuracy
from the GPS but using the continuity of the IRS when
the GPS featured data spikes or dropouts (Miller and
Friesen 1987). All of these navigation corrections were
done by NCAR prior to release of the MAP datasets.
The aircraft position in radar coordinates was obtained
using the coordinate transformation described in the appendix. The uncertainty in the aircraft position in radar
coordinates was determined by considering ‘‘skinpaints,’’
which occur when an aircraft is within a radar pulse
volume. Skinpaints appear on a radar display as a few
pixels with large radar reflectivity factor values (Fig. 1).
In this paper, a 40-dBZ minimum threshold was used.
Typically, the radar pixel containing the aircraft is the
most prominent and features a larger reflectivity value
than those surrounding it. Sometimes neighboring pixels
also exhibit high reflectivity, a likely result of sidelobe
contamination. The positioning error was determined
by considering 64 points in the MAP radar data where
skinpaints were clearly identifiable.
For each of these skinpaints, the difference in position
between the center of the radar range gate and the aircraft was calculated in terms of range, elevation, azimuth,
and absolute distance, as a fraction of the radar volume
radius (Fig. 2). The mean and standard deviation of the
range differences were 278.9 6 81.2 m. The maximum
radar range resolution possible is 75 m for the S-Pol, half
of its range gate length during MAP. The mean range
error is only slightly larger than this value, and the range
error is still approximately within one range gate when
the standard deviation is included, suggesting good accuracy with respect to range. The elevation and azimuth
angle differences (Figs. 2b,c) were 20.20 6 0.368 and
0.07 6 0.458, both within the S-Pol’s 0.918 angular resolution. The total distance between the aircraft and the
radar pulse volume (Fig. 2d), as a fraction of the radar
beam’s radius, was 1.06 6 0.50. The mean difference was
only slightly larger than half the radar volume’s radius,
again similar to the positional uncertainty inherent to
the radar data itself. The positional differences calculated
using skinpaints suggest that the coordinate transformation does not introduce significant error in its calculations beyond uncertainties inherent in the data.
The next step in the matching algorithm was to calculate approximate forward and backward trajectories
for the ensemble of particles observed at the position of
the aircraft. The trajectories were calculated forward and
backward over a 300-s period using the aircraft-observed
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FIG. 1. Example of ‘‘skinpaint’’ in PPI scan of radar reflectivity factor (dBZ) from MAP IOP 2b,
0612:42 UTC 20 Sep 1999.
wind speed and direction and a fall velocity of 0.4 m s21
for every second that the aircraft was above the freezing
level. The fall velocity was an average of the negligible
fall speed for SLW droplets and an estimate of 0.8 m s21
for ice crystals (e.g., Cronce et al. 2007), with an assumed
negligibly weak updraft. At 300 s for these velocities,
the maximum separation of the liquid and ice particles
would be 240 m.
The matching algorithm calculated the distance between the particle ensemble and the nearest radar pulse
volume at each point along these trajectories. For this
distance calculation, simple geometry shows that the unit
FIG. 2. Positional differences (aircraft 2 radar) in terms of (a) range in meters, (b) azimuth in
degrees, (c) elevation in degrees, and (d) perpendicular distance as a fraction of corresponding
radar volume radius.
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FIG. 3. (a) Geometry of radar beam, showing components of unit
vector c, in direction of beam: cx 5 sinuR cosuR, cy 5 cosuR cosuR,
and cz 5 sinuR, given beam elevation uR, and azimuth fR. (b) Diagram showing shortest distance d from air parcel and particle
ensemble at location t to radar beam p.
vector c 5 (cx, cy, cz) in the direction of the radar beam is
given by
cx 5 sinfR cosuR ,
cy 5 cosfR cosuR ,
cz 5 sinuR ,
(1)
and
(2)
(3)
where uR and fR are the beam’s elevation and azimuth
(Fig. 3a). As shown in Fig. 3b, the projection p of the
particles’ location (t) onto the radar beam (unit vector c)
is given by
p5t c
(4)
and the distance (d) between the particles and the radar
beam at each point is found using
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d 5 jtj2 jpj2 .
(5)
The matching algorithm compared these calculated
distances and located the smallest value, dm, for each
trajectory. At this point, the assumed trajectory was at
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its closest to a radar pulse volume. If dm was within set
thresholds (250 m vertically and 1000 m horizontally for
this study), the observations were considered matched,
allowing the in situ measurements to be compared
directly to the radar measurements. These thresholds
are well below the thresholds recommended for dm of
500 m vertically and 3000 m horizontally by Hudak
et al. (2004). Inherent in these calculations is the assumption that there is no structure on scales smaller than
these thresholds, and that while some very thin SLW
layers can occur (e.g., altocumulus clouds) these are
unlikely to be important for icing.
The mean particle trajectory calculations assume that
measurements made by the aircraft instrumentation are
valid for some distance temporally and spatially about
the aircraft’s location. The distance over which in situ
measurements are representative of local conditions
depends on the inherent variability of the cloud system.
The standard deviations of the aircraft-observed horizontal and vertical wind velocities were used as a measure of this local variability. From these, estimates of the
maximum positional uncertainty of particles along their
trajectories were calculated using the wind variability
and a maximum time window of 300 s. These positional
uncertainties were related to the width of the S-Pol radar
beam, which increases with range from the radar. The
width of the radar beam is given by h 5 2r tan(DuR/2),
where r is the range from the radar and DuR is the angular beamwidth, 0.918. Figure 4 shows the maximum
positional uncertainty along the particle trajectories,
both as the total distance (Fig. 4a) and normalized by the
width of the radar beam at the corresponding range of
each matched data point (Fig. 4b). The positional uncertainty of nearly all matched points was less than the
width of the radar beam.
The automated algorithm was applied to five Electra
flights, resulting in a set of matched S-Pol and aircraftbased observations. If the Rosemount probe indicated
SLW across the width or greater in the matched radar
pixel, the matched point was classified as containing
SLW. SLW was only assumed to be present if the voltage
increased nearly continuously across the distance of the
radar pixel. Single voltage spikes were rejected if the
voltage returned to its original level after the spike.
Otherwise, it was classified as ice only (IO).
Figure 5a shows the frequency distribution of the radar range for each matched data point. The median
range was 62 km. Since the rotation rate of the radar
antenna during MAP was ;108 s21, the sweep velocity
of the beam in the azimuthal direction at the median
range was 10.9 km s21. The aircraft’s true airspeed at
the matched points was 140 6 9 m s21, with an absolute uncertainty of approximately 4 m s21. Since in our
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FIG. 5. (a) Range from radar (km) for all matched data points.
(b) Observed air temperature (8C) for all matched data points for
SLW conditions. (c) Observed air temperature (8C) for all matched
data points for IO conditions.
FIG. 4. Maximum positional uncertainty along particle ensemble
trajectory, represented as (a) total distance in kilometers and (b)
a fraction of radar beamwidth at corresponding range.
analysis, no more than one matched data point was retrieved per second of aircraft data, and the aircraft velocity
and sweep velocity of the radar were vastly different, the
probability that more than one matched data point could
occur at the same altitude per radar volume was vanishingly small. Thus, we are confident that the matched
data points are independent.
The distribution of the temperatures at the matched
data points for SLW and IO is shown in Figs. 5b and 5c.
Matched data points from individual flights tended to be
concentrated in narrow temperature ranges. However,
taken together, the observations from all flights featuring SLW span the temperature range from 08 to 2228C,
while the IO range was from 08 to 2268C.
4. Choice of polarization signatures
The polarization radar parameters ZH, ZDR, KDP, and
rHV were determined for each of the matched data
points. Figure 6a shows the distribution of rHV versus
signal-to-noise ratio (SNR) for all the matched data
points. SNR was not recorded during MAP, but was
calculated as the ratio of the raw power received over
the average noise power (2115.9 dBm during MAP).
Based on recommendations in Melnikov and Zrnić
(2007), a threshold was applied to remove data with
SNR , 15 dB. Also, based on recommendations from the
NCAR Earth Observing Laboratory (R. Rilling 2009,
personal communication), a second threshold was applied, removing data with rHV , 0.92, since intrinsic rHV
values should be close to one for observations of mixedphase clouds (Bringi and Chandrasekar 2001). Thirtyone percent of the matched data points were removed
using these filters. Figures 6b–e show the impact of each
threshold on the number of observations as a function of
SNR. Frequency distributions of each variable were constructed separately for SLW and IO conditions (Fig. 7).
Figures 7a and 7b show the distribution of observed ZH
for the matched data points. The range of values was
similar between the SLW and IO observations, with
nearly all values less than 25 dBZ. The median ZH value
was 10.3 dBZ for SLW and 11.0 dBZ for IO. The IO
histogram features a more distinct peak at larger ZH.
Distributions for ZDR and KDP are shown in Figs. 7c,d
and 7e,f, respectively. While the total range of observed
ZDR values was similar between the two distributions,
the median value for the SLW observations was 0.01 dB
as compared with 0.20 dB for the IO observations. The
median KDP value for the SLW observations was 0.018
km21, slightly smaller than the median of 0.068 km21 for
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FIG. 6. (a) Correlation coefficient vs SNR (dB) for all matched data points. Horizontal line
shows 0.92 threshold for correlation coefficient, and vertical line shows 15-dB threshold for
SNR. Frequency histograms of observed SNR values shown for (b) all matched data points, (c)
matched data points after 0.92 correlation coefficient threshold applied, (d) matched data
points after 15 dB SNR threshold applied, and (e) matched data points after both thresholds
applied.
IO observations. Additionally, the distributions show
that larger KDP values appeared more frequently when
IO conditions were present. Finally, the frequency histograms for rHV feature a distinct maximum near one
for both the SLW and IO cases (Figs. 6g,h).
The Mann–Whitney U test (Wilcoxon 1945; Mann
and Whitney 1947) uses the cumulative ranking of two
observed distributions to identify the likelihood that
the distributions’ medians are statistically distinct, by
comparing the sum of observed rankings to the distribution of all possible rankings. A finite number of possible
cumulative rankings exists, following a Gaussian distribution that is based solely on the total number of data
points used. The observed ranking is transformed into
a standard Z score using the mean and standard deviation of the Gaussian ranking distribution, allowing
a p value to be obtained using common statistical procedures (e.g., Wilks 2006). The standardized Z score
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FIG. 7. Frequency histograms of observed values of radar reflectivity factor (dBZ) for (a) SLW and
(b) IO; differential reflectivity (dB) for (c) SLW and (d) IO; specific differential phase (8 km21) for
(e) SLW and (f) IO; correlation coefficient for (g) SLW and (h) IO.
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indicates the point at which the observed result appears
on a normalized Gaussian distribution, which has a mean
of zero and a standard deviation of one. The p value
indicates the likelihood of the observed (or any more
extreme) result appearing because of chance, and is used
here to evaluate the null hypothesis that the medians
of the two observed distributions arise from statistically
indistinguishable populations, given the known cumulative ranking. The null hypothesis was rejected here for
p values of 0.05 or less, indicating that the observed distributions were statistically distinct with 95% or greater
certainty.
The calculations used here follow Hollander and
Wolfe (1999). The scores calculated for the SLW and IO
observations of ZH were jZj 5 2 and p 5 0.02, and for
ZDR and KDP were jZj . 19 and p , 1025, indicating that
the medians of the SLW and IO distributions of the
three variables are very likely to be statistically distinct.
Significantly more matched data points were located for
IO conditions than for SLW conditions. To ensure that
the U test was not biased because one of the distributions contained many more data points than the other,
the IO observations were randomly sampled and reduced in size to match the number of SLW observations.
The Mann–Whitney U test was applied to these paired
distributions and the results were found to be consistent
with those using the full sample datasets for the ZDR and
KDP measurements. The calculated p values for the ZH
measurements varied between 0.02 and 0.10 depending
on the random sample of IO observations chosen.
As a second statistical test of the distinctness of the
distributions, the bootstrap method (e.g., Efron and Gong
1983; Hesterberg et al. 2005) was used to determine the
likelihood that the means of the distributions of ZH,
ZDR, and KDP were statistically distinct. Bootstrapping
involves the creation of new sample distributions by
randomly resampling data from the original observations. Each bootstrap sample features the same number
of data points as the original dataset but is sampled with
replacement, meaning that any particular observation
may appear more than once within the bootstrap sample. The original observations are considered to represent a sample from the polarization parameter’s true
population. A large number of bootstrap samples are
created to supplement these original observations by
functioning as additional sample estimates of the true
population. A statistical parameter (e.g., the mean) can
be calculated for each bootstrap sample. Because the
bootstrap samples function as estimates of the true population, the most likely value of the mean and a 95%
confidence interval for the mean are easily estimated
(Hesterberg et al. 2005). These bootstrap calculations
were applied to the ZH, ZDR, and KDP observations,
with the statistical mean estimated for 1000 bootstrap
samples of each variable, creating a distribution of estimated population means for the SLW and IO observations. Figures 8a–c show these distributions. The
distributions of the likely means of ZDR and KDP are
completely distinct with no overlapping values, with the
distributions’ means separated by 0.22 dB for ZDR and
0.06 8 km21 for KDP. The distributions of the ZH mean
estimates have some overlap, with the distributions’
means separated by 0.23 dBZ. The ZH distributions are
distinct at the 98% confidence level, lending confidence
that the variables may be used to develop probabilistic
estimates of the presence of SLW and IO conditions.
The probabilistic application of these results requires an
in-depth assessment using an independent dataset. This
is necessary to determine the degree to which uncertainties in any given set of polarimetric radar measurements affect the usefulness of the algorithm developed.
5. Supercooled water identification
The purpose of this section is to develop a threedimensional lookup table that provides estimates of the
probability that SLW is present in a cloud, given a
measurement of ZH, ZDR, and KDP. For this purpose,
the matched radar observations were sorted into bins
based on their ZH, ZDR, and KDP values. The conditional probability of SLW’s occurrence given a known
radar signature was calculated using
P(BjA) 5
SLWA
,
ALLA
(6)
where P(BjA) is the probability that SLW is present (B)
given a radar measurement (A), SLWA is the number of
measurements of SLW in the binned radar interval A,
and ALLA is the number of measurements of SLW and
IO in A. A variety of bin sizes was tested for these calculations. Larger bins allowed more observations to
be used in each probability calculation, increasing the
confidence in the results. However, larger bins also decrease the resolution of the calculated probabilities. The
final bin sizes used to sort the data represent a balance
between these two concerns. Additionally, the results
shown below are for bins containing 10 or more observations. Probability values (P) were calculated for all
bins, but a minimum of 10 observations was used as an
arbitrary threshold for reporting the probability calculations. The data are represented in Figs. 9–11. Tabular
values of SLWA and ALLA for the data used to construct
Figs. 10 and 11 are given in the electronic supplement
(http://dx.doi.org/10.1175/2009JAMC2267.s1).
Between 10 and 30 bin divisions were tested for the
ZH and ZDR observations (Figs. 9a–d). The use of fewer
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FIG. 8. Bootstrap estimates of statistical mean of (a) radar reflectivity factor (dBZ),
(b) differential reflectivity (dB), and (c) specific differential phase (8 km21). SLW shown in dark
gray and IO in light gray.
than 15 bins for ZH or ZDR resulted in a very coarse
resolution for the calculated probabilities, although they
covered a wider range of values (Fig. 9a). Increasing the
number of ZH and ZDR bins (Figs. 9b–d) provided better
resolution but reduced the range of bins with at least 10
observations. Based on this analysis, we chose 25 bins for
ZH (1.6-dBZ binwidth) and 20 bins for ZDR (0.15-dB
binwidth). Additionally, between one and five bins were
tested for KDP. Using three or fewer bins tended to
cluster nearly all of the observations into one KDP bin,
effectively ignoring its contribution to the identification
criteria. Four bins of 0.1258 km21 width were used.
Figure 10 shows the probability distribution for SLW
presence for all KDP. The P values between 0.25 and 0.90
occur over the entire range of observed ZH values, but
most commonly for ZDR values below 0.3 dB. The majority of P values greater than 0.50 over this ZH range
are associated with slightly negative ZDR values. These
P values occur for ZDR between 0.0 and 20.3 dB when
ZH is below 20 dBZ, but some larger P values are also
associated with ZDR between 0.0 and 0.3 dB for larger
ZH values of 20–25 dBZ. With the exception of some
values associated with negative ZH, P generally decreases
from 0.25 toward zero as ZDR increases above 0.2–0.3 dB.
Figures 11a–c show P for the same ZH and ZDR bins
but with observed KDP values divided into four separate
bins. The first KDP bin, including KDP values less than
20.0758 km21, does not feature usable data after the 10
observation per bin threshold was applied, although the
number of observations is reported in tabular form in
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PLUMMER ET AL.
931
FIG. 9. Probability of correct identification of SLW, using (a) 10, (b) 15, (c) 20, and (d) 25 bins each for radar reflectivity factor (dBZ) and
differential reflectivity (dB), for all specific differential phase (8 km21) values. Probability values between 0 and 1 are indicated by color
scale for bins featuring at least 10 total observations.
the electronic supplement cited on the title page. A
majority of the observations is contained in the second
and third KDP bin divisions, which are from 20.0758 to
0.0508 km21 and from 0.0508 to 0.1758 km21, respectively
(Figs. 11a,b). In Fig. 11a, the largest P values (between
0.50 and 0.80) are most common for ZH between 5 and
20 dBZ, with ZDR between 20.3 and 0.3 dB. The P values
decrease below 0.30 as ZDR increases, particularly for
ZDR . 0.2 dB and ZH , 15 dBZ. In Fig. 11b, P values are
significantly lower than those shown in Fig. 11a, with only
one value above 0.50 and most values below 0.25. The
P values above 0.25 are mainly associated with ZH between 5 and 15 dBZ and near-zero ZDR. Again, P values
decrease as ZDR increases. For ZH between 5 and 20 dBZ,
P decreases from 0.25 to 0 as ZDR increases to approximately 0.7 dB. Similarly low P values are apparent
in Fig. 11c. Although the data coverage is less extensive in
Fig. 11c, P values of zero (and one value of 0.07) occur for
ZH between 10 and 25 dBZ with ZDR up to 0.7 dB. Additionally, comparison of Figs. 11a–c reveals a trend associated with KDP. Nearly all P values greater than 0.50
occur with near-zero KDP, and P typically decreases for
the larger KDP categories.
6. Discussion
The P values and polarization signatures discussed in
the previous section conform to a microphysical understanding of particle growth mechanisms in mixedphase conditions. Particle development is dependent on
the relative concentrations of SLW and ice particles.
Supercooled liquid water droplets alone are typically
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FIG. 10. Probability of SLW identifications as in Fig. 9, but using
25 bins for radar reflectivity factor (dBZ) and 20 bins for differential
reflectivity (dB). Corresponds to Tables 1 and 2 in the supplemental
material cited on the title page.
small and result in weak ZH signatures. Because ZDR
and KDP are sensitive to particles’ size and mass characteristics in the horizontal and vertical dimensions, these
droplets’ roundness results in near-zero ZDR and KDP
values (e.g., Doviak and Zrnić 1993). However, mixtures
of SLW and ice particles result in more distinctive polarization signatures. Ice particles are able to grow by
riming when SLW is present in sufficient quantity. Rimed
particles dominate the polarization signal compared to
the smaller SLW droplets, with larger ZH values possible
than for SLW alone. However, riming produces relatively rounded ice particles with similar size and mass
in their horizontal and vertical dimensions, and so ZDR
and KDP values near zero result from these statistically
isotropic particles. When mixed-phase conditions exist,
crystals grow at the expense of SLW droplets through
the Bergeron–Findeisen process. Again, the larger crystals
dominate the radar reflectivity, with larger ZH values
possible depending on their size, concentration, and density. Additionally, these crystals tend to develop a horizontal orientation relative to the wind, resulting in a
larger ZDR and KDP than is evident for rimed particles
(e.g., Straka et al. 2000).
These microphysical characteristics are apparent in the
observed polarization signatures and calculated P values
described in the previous section. The signatures associated with rimed particle growth are evident in Figs. 10
and 11 for the P values above 0.50. These occur over the
range of observed ZH values but for near-zero ZDR, as
expected in mixed-phase conditions where SLW contributes to ice particle riming. These P values are also
more evident for near-zero KDP in Fig. 11a than for the
larger KDP values in Figs. 11b and 11c, again as expected
FIG. 11. Probability of SLW identification as in Fig. 10 but for (a)
20.0758 km21 # KDP , 0.0508 km21, (b) 0.0508 km21 # KDP ,
0.1758 km21, and (c) KDP $ 0.1758 km21. Data for KDP ,
20.0758 km21 are not shown as all bins featured fewer than 10
observations. Corresponds to Tables 5–10 in the supplemental material cited on the title page.
when SLW is present in sufficient quantities to produce
significant riming. Conditions associated primarily with
ice-phase clouds are also evident in these figures. As
ZDR increases in each figure, P values show a distinct
decrease. Also, P values significantly decrease as KDP
MAY 2010
933
PLUMMER ET AL.
becomes larger, as shown in Figs. 11a–c. The calculated
P values and observed signatures are consistent with the
characteristics expected for ice particle growth in the
absence of significant riming. Overall, the observed P
values and polarization signatures correspond well to
known particle growth mechanisms.
7. Conclusions
With the future upgrade of the WSR-88D network to
dual-polarization capability on the horizon, it is important that the potential of these radars to detect hazardous conditions in clouds be explored. The motivation for
this study was the development of quantitative criteria
for identification of potential aircraft icing conditions in
clouds using polarization radar. The data presented here
provide a first step toward this effort.
This study’s primary goal was to examine polarization radar signatures associated with SLW in orographic
cloud systems and quantify their use as probabilistic remote SLW identification criteria. Verification of SLW’s
presence was accomplished with the use of in situ microphysical measurements. This verification necessitated
the development of an automated routine used to locate
‘‘matched’’ data between sets of radar and aircraft-based
observations. This algorithm’s method was described,
along with the evaluations used to verify that it did not
introduce significant positional errors into the data. This
automated routine was developed specifically to compare radar- and aircraft-based observations for this study,
but it is also applicable for comparison of radar measurements with other airborne instrumentation.
Probability distributions for SLW detection were developed using these matched dual-polarization radar
and in situ observations. Three polarization radar parameters, ZH, ZDR, and KDP, were separately shown to
be statistically distinguishable between SLW and IO
conditions, even when considering measurement uncertainty. The matched dataset was used as the training
set to develop probabilistic criteria for remote SLW
identification, with the end result being a probability
distribution of the likelihood of SLW’s presence as a
function of binned polarization variables. The probability distributions correspond well to a basic physical
understanding of ice particle growth by riming and vapor deposition, both of which may occur in mixed-phase
conditions.
Acknowledgments. This material is based upon work
supported by the National Science Foundation under
Award NSF-ATM-0438071. We thank Scott M. Ellis
and William A. Cooper of the National Center for Atmospheric Research for their contributions to this effort.
FIG. A1. Aircraft position vector (xi, yi, zi) relative to Earth’s
center (Ec), where xi 5 RA cosQA cosFA, yi 5 RA cosQA sinFA, and
zi 5 RA sinQA, given range from the radar RA, aircraft latitude QA,
and aircraft longitude FA.
APPENDIX
Transformation of Aircraft Position into Radar
Coordinates
The aircraft’s location in space is initially specified
using its latitude, longitude, and altitude. We can redefine its position at time i in a Cartesian coordinate system (CA) with respect to the earth (xi, yi, zi), where
p
xi 5 RA sin QA cosFA 5 RA cosQA cosFA , (A1)
2
p
yi 5 RA sin QA sinFA 5 RA cosQA sinFA , and
2
(A2)
p
zi 5 RA cos QA 5 RA sinQA ,
(A3)
2
with RA is the earth’s effective radius [corrected for
nonsphericity and beam propagation using the 4/ 3R approximation (Doviak and Zrnić 1993, p. 21), where R is
the earth’s actual radius] plus the aircraft’s altitude
above sea level, QA is the aircraft’s latitude, and FA is its
longitude (Fig. A1). The unit vectors of this system are
such that x points from the earth’s center toward the
equator at 08 longitude, z points from the earth’s center
north along its rotation axis, and y is orthogonal to x and
z, pointing toward the equator at 908E longitude.
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FIG. A2. (a) Translation of aircraft coordinates from CA to CR, where RA 2 RR 5 (Dx, Dy,
Dz). (b) Rotation counterclockwise about z by FR. (c) Rotation clockwise about y9 by G 5
(p/2) 2 QR (illustration assumes x9 parallel to xearth for simplicity). (d) Rotation counterclockwise about z0 by (p/2). Aircraft and radar location RA and RR, radar longitude FR, and
radar latitude QR, all with respect to the earth’s center.
The aircraft’s position (xi, yi, zi) in CA is translated to
its position in a Cartesian coordinate system (CR) centered at the radar location with axes parallel to CA using
orienting y9 tangential to the earth’s surface at the radar’s
location (Fig. A2b). The coordinate system is then rotated
clockwise about y9 by an angle of G 5 (p/2) 2 QR using
Dxi 5 RA cosQA cosFA RR cosQR cosFR ,
(A4)
xi0 5 xi9 cosG zi9 sinG 5 xi9 sinQR zi9 cosQR ,
(A10)
(A5)
yi0 5 yi9,
(A11)
(A6)
zi0 5 xi9 sinG 1 zi9cosG 5 xi9 cosQR 1 zi9 sinQR
Dyi 5 RA cosQA sinFA RR cosQR sinFR ,
and
Dzi 5 RA sinQA RR sinQR ,
where RR is the earth’s effective radius plus the radar’s
altitude above sea level, and QR and FR are the radar’s
latitude and longitude (Fig. A2a). This coordinate system is still oriented with z parallel to the earth’s rotation
axis. In the next step, the coordinate system is rotated
counterclockwise around z by an angle of FR, using
xi9 5 Dxi cosFR 1 Dyi sinFR ,
yi9 5 Dxi sinFR 1 Dyi cosFR ,
zi9 5 Dzi ,
(A7)
and
(A8)
(A9)
and
(A12)
to orient z0 perpendicular to the earth’s surface at the
location of the radar (Fig. A2c). Finally, the coordinate
system is rotated counterclockwise about z0 by an angle
of (p/2):
xi09 5 yi0 5 yi9,
yi09 5 xi0 5 xi9 sinQR 1 zi9 cosQR ,
zi09 5 zi0 5 xi9 cosQR 1 zi9 sinQR
(A13)
and
(A14)
(A15)
to align the coordinate system so that x999 points east, y999
points north, and z999 points upward at the radar location
(Fig. A2d).
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PLUMMER ET AL.
Finally, the aircraft’s location is expressed in standard
radar coordinates, using
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(A16)
rA 5 (xi09)2 1 ( yi09)2 1 (zi09)2 ,
sinuA 5 zi09/rA , and
tanfA 5 xi09/yi09,
(A17)
(A18)
where rA is the aircraft’s range with respect to the radar,
uA is its elevation, and fA is its azimuth from the radar.
The aircraft’s position at any point along its flight path in
radar coordinates may be calculated with this method.
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