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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D20205, doi:10.1029/2008JD009890, 2008
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Relationship between ice water content and equivalent radar
reflectivity for clouds consisting of nonspherical ice particles
Gang Hong,1 Ping Yang,1 Bryan A. Baum,2 and Andrew J. Heymsfield3
Received 30 January 2008; revised 23 July 2008; accepted 7 August 2008; published 21 October 2008.
[1] This study investigates the relationship between ice water content (IWC) and
equivalent radar reflectivity (Ze) at 94 GHz for clouds consisting of nonspherical ice
particles with geometrical shapes of hexagonal solid and hollow columns, plates, 6-branch
bullet rosettes, aggregates, and droxtals. The IWC is calculated from a set of 1119 ice
particle size distributions (PSDs) measured during several field campaigns, which are
discretized to 46 size bins based on particle maximum dimensions ranging from 2 to
10500 mm. The Ze at 94 GHz is calculated from the radar backscattering properties
obtained by integrating over the PSD and chosen particle habit distributions. The influence
of ice habit on the Ze-IWC relationship is investigated for ice clouds composed of
individual ice particle habits and a habit mixture. The Ze-IWC relationship is found to be
sensitive to cloud effective particle size and cloud temperature. For an ice cloud with a
given IWC, the Ze tends to increase with increasing effective particle size. Similarly,
the Ze generally increases with increasing cloud temperature, at least for clouds with IWC
over 0.01 g/m3. These features are consistent with the observed relationship between
effective particle sizes and cloud temperatures. The present investigation of the effect of
temperature on the Ze-IWC relationship indicates that including temperature in the Ze-IWC
relationship may not improve the estimates of IWC. However, the dependence of
the Ze-IWC relationship on the effective particle size within a given temperature range is
more pronounced, and may be potentially useful for inferring the cloud effective particle
size from the Ze-IWC relationship.
Citation: Hong, G., P. Yang, B. A. Baum, and A. J. Heymsfield (2008), Relationship between ice water content and equivalent radar
reflectivity for clouds consisting of nonspherical ice particles, J. Geophys. Res., 113, D20205, doi:10.1029/2008JD009890.
1. Introduction
[2] Clouds generally cover between 65-70% of the Earth.
Approximately, 30% of these clouds reside at heights
corresponding to pressures lower than 400 hPa [e.g., Wylie
et al., 2005; Hong et al., 2007]. These high-altitude ice
clouds are composed of nonspherical particles. Synoptic
cirrus, formed in environments of relatively low updraft
velocities, and tend to be composed of pristine habits as
droxtals, hexagonal columns and plates, bullet rosettes, and
aggregates of these habits. However, in convective situations
the habits of ice particles tend to be much more complex.
[3] In the past decade, significant efforts have been
focused on the calculation of the scattering and absorption
properties of these ice particles [e.g., Macke et al., 1998;
Mishchenko et al., 2000; Bailey and Hallet, 2004;
Heymsfield and Miloshevich, 2003; Yang et al., 2005; Baum
et al., 2005a]. Recent improvements offer the capabilities to
1
Department of Atmospheric Sciences, Texas A&M University, College
Station, Texas, USA.
2
Space Science and Engineering Center, University of WisconsinMadison, Madison, Wisconsin, USA.
3
National Center for Atmospheric Research, Boulder, Colorado, USA.
Copyright 2008 by the American Geophysical Union.
0148-0227/08/2008JD009890$09.00
infer the scattering properties consistently over the electromagnetic spectrum from the ultraviolet (UV) through the far
infrared (Far IR). However, relatively little research has
focused on the interpretation of millimeter wavelength
radar measurements of ice clouds based on the calculated
scattering/absorption properties of nonspherical particles.
[4] This work is aimed at understanding the effect of ice
particle nonsphericity on the relationship between ice water
content (IWC) and equivalent radar reflectivity (Ze). In
particular, the focus is on measurements offered by CloudSat, a spaceborne radar launched on 28 April 2006, which
provides millimeter wavelength measurements at 94 GHz
[Stephens et al., 2002].
[5] A number of articles have explored the use of
millimeter-wavelength radar reflectivity (Ze) to estimate
the IWC of ice clouds [e.g., Liu and Illingworth, 2000;
Sassen et al., 2002; Matrosov et al., 2002; Mace et al.,
2002; Heymsfield et al., 2005; Shupe et al., 2005; Sato and
Okamoto, 2006; Boudala et al., 2006]. The scattering
characteristics of nonspherical ice particles at 94 GHz have
been done for various ice particle habits [e.g., Aydin and
Tang, 1997; Lemke and Quante, 1999; Okamoto, 2002;
Battaglia et al., 2001; Sato and Okamoto, 2006]. Recently,
Hong [2007a] parameterized the radar backscattering properties at 94 GHz for nonspherical ice particles including
solid and hollow hexagonal columns, plates, 6-branched
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bullet rosettes, aggregates, and droxtals, which are the ice
crystal models extensively used for ice cloud retrievals
based on observations made by infrared and visible satellite
sensors [Yang et al., 2005; Baum et al., 2005a, 2005b, 2007;
Platnick et al., 2003; King et al., 2003, 2004, 2006].
[6] Sassen et al. [2002] described three approaches for
deriving the empirical relationship between Ze the IWC for
ice clouds. These Ze-IWC relationships have been intercompared by Sassen et al. [2002], Boudala et al. [2006], and
Hong [2007a]. The pronounced differences among the intercomparison results reveal that the sensitivity of Ze-IWC
relationship to assumed ice cloud microphysical properties
and the methods used to derive the relationship. The Ze-IWC
relationship is sensitive to the variability in the particle
size distributions (PSD) of ice particles [Schneider and
Stephens, 1995; Brown et al., 1995; Aydin and Tang, 1997;
Liu and Illingworth, 2000; Sassen et al., 2002]. Heymsfield et
al. [2005] note that Ze and IWC depend on the distribution of
particle mass versus size. An issue to be reckoned with is to
account adequately for small particles at lower radar Ze and
large particles at higher Ze.
[7] Additional, the relationship between cloud temperature and particle size for ice clouds has been investigated
[e.g., Heymsfield and Platt, 1984; Garrett et al., 2003].
There is some evidence that the Ze-IWC relationship is
sensitive to cloud temperature [e.g., Sassen et al., 2002;
Boudala et al., 2006]. Boudala et al. [2006] developed an
IWC retrieval algorithms based on temperature and Ze using
ice particle distributions measured in stratiform ice clouds in
midlatitude and Arctic regions and assumed irregular ice
particle shapes represented by aggregates of plates and
dendrites.
[8] In this paper we explore the sensitivity of a derived
Ze-IWC relationship to assumed ice particle habit. The basis
for this analysis is a set of 1119 ice PSDs measured during
several field campaigns in tropical and midlatitude regions,
which are described in detail by Baum et al. [2005a]. The
sensitivity of Ze-IWC relationships to nonspherical ice
particle habits is investigated on the basis of a set of
six habits (hexagonal solid and hollow columns, plates,
6-branch bullet rosettes, aggregates of columns, and droxtals). These are the same habits as those used for the bulk
scattering models from visible through the Far-IR wavelengths in some previous studies [e.g., Platnick et al.,
2003; King et al., 2004, 2006; Yang et al., 2005; Baum et
al., 2005a, 2005b, 2007]. The effect of cloud environment
temperature and ice particle size on the Ze-IWC relationship is also investigated.
2. Data and Methodology
[9] Sassen et al. [2002] introduced three approaches to
derive the Ze-IWC relationship. In this study, we employ an
algorithm to derive Ze from ground-based or airborne
microphysical measurements. A set of PSDs used in this
study were obtained from in situ measurements in several
field campaigns covering tropical to midlatitude regions.
The tropical measurements used in this study include two
campaigns conducted in Kwajalein, Marshall Islands in
1999 under the auspices of the Tropical Rainfall Measuring
Mission (TRMM) [Stith et al., 2002, 2004], and the Cirrus
Regional Study of Tropical Anvils and Cirrus Layers
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(CRYSTAL) Florida Area Cirrus Experiment (FACE) in
2002. The midlatitude measurements include the First
International Satellite Cloud Climatology Project Regional
Experiments (henceforth FIRE-1) in Madison, Wisconsin in
1986, Coffeyville, Kansas in 1991 (FIRE-II), and the Atmospheric Radiative Measurement Program (ARM) Intensive
Operational Period (IOP) near Lamont, Oklahoma in 2000.
Detailed information about the microphysical measurements
are provided by Miloshevish and Heymsfield [1997],
Heymsfield et al. [2002, 2003, 2004], and Heymsfield and
Miloshevich [2003]. A resulting set of 1119 PSDs are
summarized by Baum et al. [2005a]. Each PSD is represented
in the form of a gamma distribution [e.g., Kosarev and Mazin,
1991; Mitchell, 1991; Heymsfield et al., 2002] as follows:
N ð DÞ ¼ N0 Dm e$lD ;
ð1Þ
where D is the maximum dimension of an ice crystal
particle, N(D) is the number density of ice crystal particles
with a D, N0 is the intercept, l is the slope, and m is the
dispersion.
[10] The IWC is derived from
IWC ¼ r
Z
Dmax
Dmin
"
N
X
i¼1
#
fi ð DÞVi ð DÞ N ð DÞdD;
ð2Þ
N
P
where r is the ice density with a value of 0.917 g cm$3,
i¼1
fi(D) = 1, where i denotes the ice crystal habit in the ice
cloud, fi(D) is the ice particle habit fraction for habit i at a
D, Vi(D) is the volume of the habit i for a given D, and
Dmin and Dmax are the minimum and maximum sizes of
D in the given particle size distribution N(D), respectively.
[11] The IWC for a cloud composed of either a single habit
(i = 1) or a given habit mixture (i > 1) is calculated from
equation (2) for each of the 1119 PSDs. Different ice cloud
habit distributions have been used for ice cloud retrievals
from solar and infrared measurements [e.g., Yang et al., 2005;
Baum et al., 2005b; King et al., 2004, 2006; Hong, 2007a,
2007b]. The habit distribution derived by Baum et al. [2005a]
for MODIS Collection 5 cloud retrieval [King et al., 2006] is
used in this study. The habit distribution consists of 100%
droxtals when D < 60 mm, 15% bullet rosettes, 50% solid
columns, and 35% plates when 60 mm < D < 1000 mm, 45%
hollow columns, 45% solid columns, and 10% aggregates
when 1000 mm < D < 2500 mm, and 97% bullet rosettes and
3% aggregates when D > 2500 mm.
[12] We assume that the Ze-IWC relationship has a form
of IWC = aZbe , where IWC is in units of g m$3 and Ze is in
units of mm6 m$3 (dBZ in terms of 10log Ze). The radar
equivalent reflectivity factor Ze at horizontal (vertical)
copolarization in units of mm6 m$3 is defined as [e.g.,
Atlas et al., 1995; Donovan et al., 2004; Sato and Okamoto,
2006; Hong, 2007a]
l4
Ze ¼
0:93p5
Z
Dmax
Dmin
"
N
X
i¼1
#
fi ð DÞsi ð DÞ N ð DÞdD;
ð3Þ
where l is the wavelength at 94 GHz, si is the backscattering cross section for the ith ice crystal habit at a D.
The nonspherical ice particles in general have been assumed
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Figure 1. The relationship between ice water content (IWC) and equivalent radar backscattering
reflectivity (Ze) at 94 GHz for clouds consisting of individual habits: (a) solid columns, (b) hollow
columns, (c) plates, (d) 3D bullet rosettes, (e) aggregates, and (f) droxtals.
to be randomly orientated so that Shh = Sw and Shv = Svh. The
backscattering cross section s for each of the habits is
computed from the DDA model [Hong, 2007a] at 46
discrete values of D in a range of 2 – 10500 mm.
[13] The particle effective size De is calculated for each of
the 1119 PSDs, and is given by [e.g., Foot, 1988; King et
al., 2004; Yang et al., 2005; Baum et al., 2005b]:
!N
R Dmax P
"
fi ð DÞVi ð DÞ N ð DÞdD
3 Dmin i¼1
!N
"
;
De ¼
2 R Dmax P
f
ð
D
ÞA
ð
D
Þ
N
ð
D
ÞdD
i
i
Dmin
ð4Þ
i¼1
where Ai(D) is the averaged projected area of the habit i for
a given D.
3. Results
[14] Figure 1 shows the Ze-IWC relationship for clouds
composed of six individual habits: hexagonal solid and
hollow columns, plates, 3D bullet rosettes, aggregates,
and droxtals. The differences in the Ze-IWC relationships
for different habits show some sensitivity to the choice of
habit for deriving the relationship.
[15] On the basis of the mass-volume-size relationship
assumed for each of the 6 individual habits [Yang et al.,
2005; Hong, 2007a, 2007b], a value of IWC can be calculated
for each of the PSDs (i.e., equation (2)). These IWC values
can be compared to those derived using the Ze-IWC relationships for the various habits shown in Figure 1, with results
shown in Figure 2. The correlation coefficients of the
IWC values are lower for hollow and solid columns and
3D bullet rosettes than for plates, droxtals, and aggregates. The correlation coefficient for aggregates is the
highest of the various individual habits. This is in agreement
with the representation of aggregates for irregular ice
particles by Boudala et al. [2002].
[16] Under natural conditions, ice clouds consist of a
variety of habits, with the smallest particles having aspect
ratios of near unity (like droxtals) and larger particles with
various shapes. It may be unrealistic to apply the Ze-IWC
relationships shown in Figure 1 to naturally occurring ice
clouds. To gain some sense of the variability caused by the
assumption of habit, however, we can develop a Ze-IWC
relationship from the entire set of PSDs based on this set of
six individual habits (i.e., 6 % 1119 pairs of IWC and Ze) to
build the Ze-IWC relationship. The resulting Ze-IWC relationship is shown in Figure 3 along with those previously
shown in Figure 1. It is clear that the Ze-IWC relationships
for ice clouds composed of individual habits have distinct
differences. The relationship is very similar for ice clouds
composed of solid columns, hollow columns, and 3D bullet
rosettes. With a given value of Ze, the inferred IWC can vary
by a factor of 1.5 – 2.0. In particular, the variability in IWC
increases when Ze has negative values of dBZ. When the Ze
values are above 0 dBZ, the Ze-IWC relationship more
closely approximates the individual relationships for aggregates, droxtals, and plates. However, when the Ze values are
less than 0 dBZ, the Ze-IWC relationship more closely
approximates the individual relationships for 3D bullet
rosettes, solid columns, and hollow columns.
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Figure 2. Comparisons between the ice water contents (IWC) inferred from the Ze-IWC relationships
and the IWC derived from the microphysical measurements for a set of 1119 ice particle size distributions
(PSDs) for clouds consisting of individual habits: (a) solid columns, (b) hollow columns, (c) plates, (d) 3D
bullet rosettes, (e) aggregates, and (f) droxtals.
[17] In addition to the assumption of habit, ambiguities in
the Ze-IWC relationship arise from the characterization of
the particle size distribution. The PSD is often characterized
by the effective diameter and also the median mass diameter
(Dm). The dependence of the Ze-IWC relationship on Dm
was investigated by Atlas et al. [1995], Brown et al. [1995],
Liu and Illingworth [2000], and Sassen et al. [2002].
[18] In the present study, the effect of the particle effective size (De) on the Ze-IWC relationship is investigated,
with results shown in Figure 4. Instead of using individual
habits, a habit mixture based on the study by Baum et al.
[2005a] is assumed, which was derived by comparing the
calculated median mass equivalent diameters and IWC from
in situ measured PSD with those in situ measurements.
For each of the 1119 PSDs, the De is calculated from
equation (4). The 1119 values of De range in value from
less than 50 mm to greater than 200 mm. Six groups are
formed with De ranging from 50 mm to 200 mm at an
interval of 25 mm. Two additional groups are formed with
De < 50 mm and De > 200 mm. The coefficient a and
exponent b for the Ze-IWC relationships are given in Table 1
for the 8 groups of De.
[19] The sensitivity of the Ze-IWC relationship to De is
shown in Figure 4a. In general, for a given Ze, the IWC
increases with decreasing De. In contrast, for a given IWC,
Ze increases with increasing De. The slopes of the Ze-IWC
relationships are close for Dm > 50 mm but the slope for the
smallest value of De is different. The smallest values of De
are mostly observed in the CRYSTAL-FACE (Figure 5).
The distinct different slope of the Ze-IWC relationship for
these ice clouds reveals again the influence of nonsphericity
of ice particles on the Ze-IWC relationship. Chepfer et al.
[2005] found that the main habits of the ice particles
observed in the CRYSTAL-FACE are hexagonal columns.
However, the habit mixture derived by Baum et al. [2005a]
Figure 3. The relationship between ice water content
(IWC) and equivalent radar backscattering reflectivity (Ze) at
94 GHz derived on the basis of all 6 habits discussed previously
(black dots are for calculations on the basis of the measured
ice particle size distributions). The previously derived (see
Figure 1) Ze-IWC relationships for clouds consisting solely of
individual habits are superimposed for reference.
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Figure 4. The relationships between ice water content
(IWC) and equivalent radar backscattering reflectivity (Ze)
at 94 GHz for clouds consisting of a mixture of habits
for specific ranges of (a) effective particle sizes (De) and
(b) cloud temperatures (T).
is used to derive the Ze-IWC relationship in the present
study.
[20] Moreover, the Ze-IWC relationships for De in the
range of 50-100 mm and for De > 100 mm have similar
slopes. These features are indicated by the values of the
coefficient a and exponent b shown in Table 1. The regular
dependence of the Ze-IWC relationships on De, except for
the smallest De, may be potentially useful for deriving the
De from observed Ze for a given IWC or to derive the IWC
from the observed Ze for a given De. This result indicates
that the vertical distributions of De or IWC could be derived
from similar lookup table as Figure 4a.
[21] Liu and Illingworth [2000] and Sassen et al. [2002]
documented that the inclusion of temperature for retrieving
IWC from Ze can improve the accuracy of retrieved IWC.
Recently, Boudala et al. [2006] developed a parameterized
radar retrieval algorithm of IWC in terms of temperature and
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Ze which is based on in situ aircraft measurements. Since
cloud temperature is given for each of our PSDs, the
dependence of the Ze-IWC relationship on temperature is
investigated. Figure 4b shows the Ze-IWC relationships for
six groups of temperatures. The coefficient a and exponent
b of the Ze-IWC relationships for the six groups are also
listed in Table 1.
[22] Unlike the systematic effect of De on the Ze-IWC
relationship, the effect of temperature on the Ze-IWC relationship shows more variability. While Boudala et al.
[2006] suggested that Ze generally increases with increasing
temperature for a given IWC; in this study, this feature is
generally observed only when Ze are above $10 dBZ. Thus
one cannot draw firm conclusions from the current analysis
that an explicit inclusion of temperature in the Ze-IWC
relationship can improve the accuracy of IWC derived
from Ze.
[23] The effect of temperatures on De has been investigated by numerous groups [e.g., Ou and Liou, 1995; Ou et
al., 1995; Wyser, 1998; Garrett et al., 2003]. If De should be
a function of temperature, it would make sense to include
temperature in the Ze-IWC relationship. The De as a function
of temperature for the 1119 measurements during the
CRYSTAL-FACE, TRMM, ARM, FIRE-I, are FIRE-II are
shown in Figure 5. In general, the De of ice clouds increase
with increasing temperatures. However, the relationship
between De and temperature shows much variability. This
feature is distinctly shown by the evident separation of the
measurements in the TRMM campaign. The TRMM measurements came from cirrus anvils, and thus from an environment denoted by high updraft velocities, whereas the
other PSDs came from cirrus having much lower updraft
velocities. Our analysis suggests that the temperature cannot
be included into the Ze-IWC relationship through a common
relationship between temperature and De.
[24] Because of the pronounced variability in the relationship between De and temperatures, the effect of De on
the Ze-IWC relationship for ice clouds is investigated for
two temperature ranges with different De ranges. Note that
the deriving Ze-IWC relationships do not involving the
Table 1. Fitting Coefficient a and Exponent b for the Relationships Between Ice Water Content (IWC) and Equivalent Radar
Backscattering Reflectivity (Ze) at 94 GHz for Clouds Consisting
of a Mixture of Ice Particle Habitsa
IWC =a Zeb
Effective particle size, De (mm)
Temperature, T (!C)
Ice Cloud Properties
a
b
De < 50
50 < De < 75
75 < De < 100
100 < De < 125
125 <De < 150
150 < De < 175
175 < De < 200
200 < De
$30 < T < $25
$35 < T < $30
$40 < T < $35
$45 < T < $40
$50 < T < $45
T < $50
0.3121
0.3429
0.2071
0.1073
0.0679
0.0483
0.0405
0.0314
0.0670
0.0714
0.0876
0.1001
0.1242
0.2115
0.6852
0.7930
0.7880
0.8369
0.8797
0.8948
0.8938
0.8701
0.5703
0.5967
0.5374
0.6327
0.6415
0.6470
a
The results are provided for a number of ranges of effective particle
sizes (De) and cloud temperatures (T).
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IWC relationships for different De ranges, with a size
interval of 25 mm are used for the exponent a of the ZeIWC relationship developed for the entire size range of 50–
200 mm. The coefficients a of the Ze-IWC as a function of
De based on the mean values of each size bin are shown in
Figure 7. A fitting is performed for the relationships
between De and the coefficient a in the range of 50 < De <
200 mm.
[27] The Ze-IWC relationships for different De, developed
for two temperature ranges of $50!C < T < $40!C and
$40!C < T < $25!C, are shown in Figure 8. The IWC and
Ze calculated from the individual PSDs are also shown in
the figure. The relationships among the Ze, IWC, and De
reveal again that one of the three parameters can be derived
Figure 5. Effective particle sizes (De) of ice clouds as a
function of temperature (T) for the set of 1119 individual
PSDs obtained from the CRYSTAL-FACE, TRMM, ARM,
FIRE-I, and FIRE-II campaigns.
temperatures directly. Two temperature ranges of $50!C to
$40!C and $40!C to $25!C are used to separate the
measured ice cloud PSDs first. The separated PSDs are
then used to derive the Ze-IWC relationships for the De in
the range of 50 – 150 mm and 50 – 200 mm at the two
temperature ranges, respectively. The two temperature
ranges and De ranges are chosen in order to have sufficient
samples for the analyses. Similarly to the results shown in
Figure 4a, the De values are grouped with an interval
of 25 mm. The Ze-IWC relationships in Figure 6 show a
similar feature as Figure 4a, but for a given temperature
range, the dependence of Ze-IWC relationship on De is more
pronounced.
[25] For the derived Ze-IWC relationships in the two
given temperature ranges (Figure 6), the IWC values are
compared to those from the Ze-IWC relationships without
considering the influence from the temperatures (Figure 4a)
for different De. The correlations between the two derived
IWC are similar, and the average deviations of the two
derived IWC with respect to the IWC calculated from the
particle size distributions are similar. This indicates again
that including temperature for the Ze-IWC relationship does
not provide a significant improvement of the accuracy of the
IWC from the Ze-IWC that includes cloud temperature.
[26] However, Figure 6 also indicates that separating the
effects of De and temperatures of ice clouds on the Ze-IWC
relationships may be useful for inferring the De from the
Ze-IWC relationship. For different De, the exponent b of
the Ze-IWC relationships are similar. This agrees well with
the results presented by Brown et al. [1995], who showed
that the exponents of the Ze-IWC relationships for inverseexponential size distributions of varying scale diameter are
the same. Thus the mean values of the exponents for the Ze-
Figure 6. The relationships between ice water content
(IWC) and equivalent radar backscattering reflectivity (Ze)
at 94 GHz for clouds consisting of a mixture of ice particle
habits as a function of effective particle size (De) when
cloud temperatures (T) are in the range of (a) $50!C to
$40!C and (b) $40!C to $25!C.
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[30] The Ze-IWC relationship has been found to be
sensitive to the variability in the ice particle spectrum [Atlas
et al., 1995; Schneider and Stephens, 1995; Brown et al.,
1995; Aydin and Tang, 1997; Liu and Illingworth, 2000;
Sassen et al., 2002]. In the present study, on the basis of the
1119 measured measurement particle size distributions, the
effect of the particle effective size (De) on the Ze-IWC
relationships is investigated by deriving the Ze-IWC relationships for different ranges of De. The IWC generally
increases with decreasing De for a given Ze. The dependence of Ze-IWC relationships on De shows a regular
feature, which may be potentially useful for estimating De
from observed Ze.
[31] The effect of temperature on the Ze-IWC relationships reveals that the inclusion of temperature in Ze-IWC
relationship has no significant improvement for estimating
IWC. This is also revealed by the relationships between
Figure 7. Coefficient a of the Ze-IWC relationships as a
function of effective particle size (De) when cloud
temperatures (T) are in the range of $50!C to $40!C and
$40!C to $25!C.
from the other two from the previously built lookup tables at
different temperature ranges. The two lookup tables for the
Ze-IWC relationships with different De at two temperature
ranges $50!C < T < $40!C and $40!C < T < $25!C)
shown in Figure 8 are used to estimate ice cloud De. The
estimated ice cloud De agree well with the De calculated
using the ice particle size distributions (Figure 9). The
relative errors for the two temperatures ranges of $50!C <
T < $40!C and $40!C < T < $25!C are less than 32% and
24%, respectively. The RMS of estimated De are about 8 mm
and the correlation coefficients between the estimated ice
cloud De and the De calculated using the ice particle size
distributions are over 94%.
4. Summary and Conclusions
[28] The effect of ice particle habits on Ze-IWC relationships is investigated using six different ice habits including
hexagonal solid and hollow columns, plates, 3D bullet
rosettes, aggregates, and droxtals. The Ze-IWC relationships
for ice clouds composed of these habits are derived by the
calculated Ze and IWC from 1119 measured particle size
distributions obtained from a variety of field campaigns.
The Ze-IWC relationships obtained for these individual
habits show distinct differences. For a given Ze, the IWC
vary in a factor of 1.5– 2.0 for ice cloud composed of
different habits, and in particular, the variations in IWC are
larger when the Ze are negative than when the Ze are
positive.
[29] Rather than using a single habit, a habit mixture
from Baum et al. [2005a] is used additionally to derive the
Ze-IWC relationships. These Ze-IWC relationships show
pronounced scattering, indicating the difficulty in finding
a single Ze-IWC relationship for all ice clouds [e.g., Atlas
et al., 1995; Aydin and Tang, 1997; Liu and Illingworth,
2000; Sassen et al., 2002; Boudala et al., 2006].
Figure 8. Same as Figure 6 but for the Ze-IWC relationships using the fitting coefficient a as a function of De
shown in Figure 7.
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apply the Ze-IWC relationships derived for different De
within given temperature ranges to operational radar retrieval because the information about De (for estimating
IWC) or IWC (for estimating De) is needed. However, the
information can be provided by observations made by other
active and passive sensors. Moreover, these relationships
can be used to simulate radar Ze of ice clouds simulated
from the weather forecasting, mesoscale, climate models
that output IWC, De, and temperatures.
[32] Acknowledgments. The authors thank B. T. Draine and P. J.
Flatau for providing their well-documented DDA model. The authors also
thank the three anonymous reviewers for constructive comments and
suggestion. Ping Yang’s research is supported by a National Science
Foundation (NSF) grant (ATM-0239605).
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Figure 9. Comparison between the estimated De from the
Ze-IWC relationships shown in Figure 8 and the De from
measured ice particle size distributions for cloud temperatures (T) in the ranges of (a) $50!C to $40!C and (b) $40!C
to $25!C.
temperatures and De derived from 1119 data sets measured
for ice clouds. However, for a given temperature range, the
dependence of the Ze-IWC relationship on De is pronounced. This provides an opportunity to obtain De from
the Ze-IWC relationship. The Ze-IWC relationship is derived
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$$$$$$$$$$$$$$$$$$$$$$
B. A. Baum, Space Science and Engineering Center, University of
Wisconsin-Madison, 1225 West Dayton St., Madison, WI 53706, USA.
A. J. Heymsfield, National Center for Atmospheric Research, 3450
Mitchell Lane, Boulder, CO 80307-3000, USA.
G. Hong and P. Yang, Department of Atmospheric Sciences, Texas A&M
University, 3150 TAMU College Station, TX 77843, USA. (hong@ariel.
met.tamu.edu)
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