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) andequivalent radar reflectivity (Ze) at 94 GHz for clouds consisting of nonspherical iceparticles with geometrical shapes of hexagonal solid and hollow columns, plates, 6-branchbullet rosettes, aggregates, and droxtals. The IWC is calculated from a set of 1119 iceparticle size distributions (PSDs) measured during several field campaigns, which arediscretized to 46 size bins based on particle maximum dimensions ranging from 2 to10500 mm. The Ze at 94 GHz is calculated from the radar backscattering propertiesobtained by integrating over the PSD and chosen particle habit distributions. The influenceof ice habit on the Ze-IWC relationship is investigated for ice clouds composed ofindividual ice particle habits and a habit mixture. The Ze-IWC relationship is found to besensitive to cloud effective particle size and cloud temperature. For an ice cloud with agiven 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 IWCover 0.01 g/m3. These features are consistent with the observed relationship betweeneffective particle sizes and cloud temperatures. The present investigation of the effect oftemperature on the Ze-IWC relationship indicates that including temperature in the Ze-IWCrelationship may not improve the estimates of IWC. However, the dependence ofthe Ze-IWC relationship on the effective particle size within a given temperature range ismore pronounced, and may be potentially useful for inferring the cloud effective particlesize 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 radarreflectivity 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 heightscorresponding to pressures lower than 400 hPa [e.g., Wylieet al., 2005; Hong et al., 2007]. These high-altitude iceclouds are composed of nonspherical particles. Synopticcirrus, formed in environments of relatively low updraftvelocities, and tend to be composed of pristine habits asdroxtals, hexagonal columns and plates, bullet rosettes, andaggregates of these habits. However, in convective situationsthe 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 absorptionproperties 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; Baumet al., 2005a]. Recent improvements offer the capabilities to

infer the scattering properties consistently over the electro-magnetic spectrum from the ultraviolet (UV) through the farinfrared (Far IR). However, relatively little research hasfocused on the interpretation of millimeter wavelengthradar measurements of ice clouds based on the calculatedscattering/absorption properties of nonspherical particles.[4] This work is aimed at understanding the effect of ice

particle nonsphericity on the relationship between ice watercontent (IWC) and equivalent radar reflectivity (Ze). Inparticular, the focus is on measurements offered by Cloud-Sat, a spaceborne radar launched on 28 April 2006, whichprovides 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 estimatethe 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 andOkamoto, 2006; Boudala et al., 2006]. The scatteringcharacteristics of nonspherical ice particles at 94 GHz havebeen done for various ice particle habits [e.g., Aydin andTang, 1997; Lemke and Quante, 1999; Okamoto, 2002;Battaglia et al., 2001; Sato and Okamoto, 2006]. Recently,Hong [2007a] parameterized the radar backscattering prop-erties at 94 GHz for nonspherical ice particles includingsolid and hollow hexagonal columns, plates, 6-branched

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1Department of Atmospheric Sciences, Texas A&M University, CollegeStation, Texas, USA.

2Space Science and Engineering Center, University of Wisconsin-Madison, Madison, Wisconsin, USA.

3National Center for Atmospheric Research, Boulder, Colorado, USA.

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bullet rosettes, aggregates, and droxtals, which are the icecrystal models extensively used for ice cloud retrievalsbased on observations made by infrared and visible satellitesensors [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 forice clouds. These Ze-IWC relationships have been intercom-pared by Sassen et al. [2002], Boudala et al. [2006], andHong [2007a]. The pronounced differences among the inter-comparison results reveal that the sensitivity of Ze-IWCrelationship to assumed ice cloud microphysical propertiesand the methods used to derive the relationship. The Ze-IWCrelationship is sensitive to the variability in the particlesize distributions (PSD) of ice particles [Schneider andStephens, 1995; Brown et al., 1995; Aydin and Tang, 1997;Liu and Illingworth, 2000; Sassen et al., 2002].Heymsfield etal. [2005] note that Ze and IWC depend on the distribution ofparticle mass versus size. An issue to be reckoned with is toaccount adequately for small particles at lower radar Ze andlarge particles at higher Ze.[7] Additional, the relationship between cloud tempera-

ture 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 issensitive to cloud temperature [e.g., Sassen et al., 2002;Boudala et al., 2006]. Boudala et al. [2006] developed anIWC retrieval algorithms based on temperature and Ze usingice particle distributions measured in stratiform ice clouds inmidlatitude and Arctic regions and assumed irregular iceparticle shapes represented by aggregates of plates anddendrites.[8] In this paper we explore the sensitivity of a derived

Ze-IWC relationship to assumed ice particle habit. The basisfor this analysis is a set of 1119 ice PSDs measured duringseveral field campaigns in tropical and midlatitude regions,which are described in detail by Baum et al. [2005a]. Thesensitivity of Ze-IWC relationships to nonspherical iceparticle habits is investigated on the basis of a set ofsix habits (hexagonal solid and hollow columns, plates,6-branch bullet rosettes, aggregates of columns, and drox-tals). These are the same habits as those used for the bulkscattering models from visible through the Far-IR wave-lengths in some previous studies [e.g., Platnick et al.,2003; King et al., 2004, 2006; Yang et al., 2005; Baum etal., 2005a, 2005b, 2007]. The effect of cloud environmenttemperature and ice particle size on the Ze-IWC relation-ship is also investigated.

2. Data and Methodology

[9] Sassen et al. [2002] introduced three approaches toderive the Ze-IWC relationship. In this study, we employ analgorithm to derive Ze from ground-based or airbornemicrophysical measurements. A set of PSDs used in thisstudy were obtained from in situ measurements in severalfield campaigns covering tropical to midlatitude regions.The tropical measurements used in this study include twocampaigns conducted in Kwajalein, Marshall Islands in1999 under the auspices of the Tropical Rainfall MeasuringMission (TRMM) [Stith et al., 2002, 2004], and the CirrusRegional Study of Tropical Anvils and Cirrus Layers

(CRYSTAL) Florida Area Cirrus Experiment (FACE) in2002. The midlatitude measurements include the FirstInternational Satellite Cloud Climatology Project RegionalExperiments (henceforth FIRE-1) in Madison, Wisconsin in1986, Coffeyville, Kansas in 1991 (FIRE-II), and the Atmo-spheric Radiative Measurement Program (ARM) IntensiveOperational Period (IOP) near Lamont, Oklahoma in 2000.Detailed information about the microphysical measurementsare provided by Miloshevish and Heymsfield [1997],Heymsfield et al. [2002, 2003, 2004], and Heymsfield andMiloshevich [2003]. A resulting set of 1119 PSDs aresummarized by Baum et al. [2005a]. Each PSD is representedin the form of a gamma distribution [e.g.,Kosarev andMazin,1991; Mitchell, 1991; Heymsfield et al., 2002] as follows:

N D! " # N0Dme$lD; !1"

where D is the maximum dimension of an ice crystalparticle, N(D) is the number density of ice crystal particleswith a D, N0 is the intercept, l is the slope, and m is thedispersion.[10] The IWC is derived from

IWC # rZ Dmax

Dmin

X

N

i#1

fi D! "Vi D! "" #

N D! "dD; !2"

where r is the ice density with a value of 0.917 g cm$3,P

N

i#1fi(D) = 1, where i denotes the ice crystal habit in the icecloud, fi(D) is the ice particle habit fraction for habit i at aD, Vi(D) is the volume of the habit i for a given D, andDmin and Dmax are the minimum and maximum sizes ofD 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 fromequation (2) for each of the 1119 PSDs. Different ice cloudhabit distributions have been used for ice cloud retrievalsfrom 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] isused in this study. The habit distribution consists of 100%droxtals when D < 60 mm, 15% bullet rosettes, 50% solidcolumns, and 35% plates when 60 mm < D < 1000 mm, 45%hollow columns, 45% solid columns, and 10% aggregateswhen 1000 mm < D < 2500 mm, and 97% bullet rosettes and3% aggregates when D > 2500 mm.[12] We assume that the Ze-IWC relationship has a form

of IWC = aZeb, 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 radarequivalent 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]

Ze #l4

0:93p5

Z Dmax

Dmin

X

N

i#1

fi D! "si D! "" #

N D! "dD; !3"

where l is the wavelength at 94 GHz, si is the back-scattering cross section for the ith ice crystal habit at a D.The nonspherical ice particles in general have been assumed

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to be randomly orientated so that Shh = Sw and Shv = Svh. Thebackscattering cross section s for each of the habits iscomputed from the DDA model [Hong, 2007a] at 46discrete 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 etal., 2004; Yang et al., 2005; Baum et al., 2005b]:

De #3

2

RDmax

Dmin

P

N

i#1

fi D! "Vi D! "! "

N D! "dD

RDmax

Dmin

P

N

i#1

fi D! "Ai D! "! "

N D! "dD; !4"

where Ai(D) is the averaged projected area of the habit i fora given D.

3. Results

[14] Figure 1 shows the Ze-IWC relationship for cloudscomposed of six individual habits: hexagonal solid andhollow columns, plates, 3D bullet rosettes, aggregates,and droxtals. The differences in the Ze-IWC relationshipsfor different habits show some sensitivity to the choice ofhabit 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 calculatedfor each of the PSDs (i.e., equation (2)). These IWC valuescan be compared to those derived using the Ze-IWC relation-ships for the various habits shown in Figure 1, with results

shown in Figure 2. The correlation coefficients of theIWC values are lower for hollow and solid columns and3D bullet rosettes than for plates, droxtals, and aggre-gates. The correlation coefficient for aggregates is thehighest of the various individual habits. This is in agreementwith the representation of aggregates for irregular iceparticles by Boudala et al. [2002].[16] Under natural conditions, ice clouds consist of a

variety of habits, with the smallest particles having aspectratios of near unity (like droxtals) and larger particles withvarious shapes. It may be unrealistic to apply the Ze-IWCrelationships shown in Figure 1 to naturally occurring iceclouds. To gain some sense of the variability caused by theassumption of habit, however, we can develop a Ze-IWCrelationship from the entire set of PSDs based on this set ofsix individual habits (i.e., 6 % 1119 pairs of IWC and Ze) tobuild the Ze-IWC relationship. The resulting Ze-IWC rela-tionship is shown in Figure 3 along with those previouslyshown in Figure 1. It is clear that the Ze-IWC relationshipsfor ice clouds composed of individual habits have distinctdifferences. The relationship is very similar for ice cloudscomposed of solid columns, hollow columns, and 3D bulletrosettes. With a given value of Ze, the inferred IWC can varyby a factor of 1.5–2.0. In particular, the variability in IWCincreases when Ze has negative values of dBZ. When the Zevalues are above 0 dBZ, the Ze-IWC relationship moreclosely approximates the individual relationships for aggre-gates, droxtals, and plates. However, when the Ze values areless than 0 dBZ, the Ze-IWC relationship more closelyapproximates the individual relationships for 3D bulletrosettes, solid columns, and hollow columns.

Figure 1. The relationship between ice water content (IWC) and equivalent radar backscatteringreflectivity (Ze) at 94 GHz for clouds consisting of individual habits: (a) solid columns, (b) hollowcolumns, (c) plates, (d) 3D bullet rosettes, (e) aggregates, and (f) droxtals.

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[17] In addition to the assumption of habit, ambiguities inthe Ze-IWC relationship arise from the characterization ofthe particle size distribution. The PSD is often characterizedby 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 effec-

tive size (De) on the Ze-IWC relationship is investigated,with results shown in Figure 4. Instead of using individualhabits, a habit mixture based on the study by Baum et al.[2005a] is assumed, which was derived by comparing thecalculated median mass equivalent diameters and IWC fromin situ measured PSD with those in situ measurements.For each of the 1119 PSDs, the De is calculated fromequation (4). The 1119 values of De range in value fromless than 50 mm to greater than 200 mm. Six groups areformed with De ranging from 50 mm to 200 mm at aninterval of 25 mm. Two additional groups are formed withDe < 50 mm and De > 200 mm. The coefficient a andexponent b for the Ze-IWC relationships are given in Table 1for 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 IWCincreases with decreasing De. In contrast, for a given IWC,Ze increases with increasing De. The slopes of the Ze-IWCrelationships are close for Dm > 50 mm but the slope for thesmallest 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 forthese 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 particlesobserved in the CRYSTAL-FACE are hexagonal columns.However, the habit mixture derived by Baum et al. [2005a]

Figure 2. Comparisons between the ice water contents (IWC) inferred from the Ze-IWC relationshipsand 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) 3Dbullet rosettes, (e) aggregates, and (f) droxtals.

Figure 3. The relationship between ice water content(IWC) and equivalent radar backscattering reflectivity (Ze) at94 GHz derived on the basis of all 6 habits discussed previously(black dots are for calculations on the basis of the measuredice particle size distributions). The previously derived (seeFigure 1) Ze-IWC relationships for clouds consisting solely ofindividual habits are superimposed for reference.

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is used to derive the Ze-IWC relationship in the presentstudy.[20] Moreover, the Ze-IWC relationships for De in the

range of 50-100 mm and for De > 100 mm have similarslopes. These features are indicated by the values of thecoefficient a and exponent b shown in Table 1. The regulardependence of the Ze-IWC relationships on De, except forthe smallest De, may be potentially useful for deriving theDe from observed Ze for a given IWC or to derive the IWCfrom the observed Ze for a given De. This result indicatesthat the vertical distributions of De or IWC could be derivedfrom similar lookup table as Figure 4a.[21] Liu and Illingworth [2000] and Sassen et al. [2002]

documented that the inclusion of temperature for retrievingIWC from Ze can improve the accuracy of retrieved IWC.Recently, Boudala et al. [2006] developed a parameterizedradar retrieval algorithm of IWC in terms of temperature and

Ze which is based on in situ aircraft measurements. Sincecloud temperature is given for each of our PSDs, thedependence of the Ze-IWC relationship on temperature isinvestigated. Figure 4b shows the Ze-IWC relationships forsix groups of temperatures. The coefficient a and exponentb of the Ze-IWC relationships for the six groups are alsolisted in Table 1.[22] Unlike the systematic effect of De on the Ze-IWC

relationship, the effect of temperature on the Ze-IWC rela-tionship shows more variability. While Boudala et al.[2006] suggested that Ze generally increases with increasingtemperature for a given IWC; in this study, this feature isgenerally observed only when Ze are above $10 dBZ. Thusone cannot draw firm conclusions from the current analysisthat an explicit inclusion of temperature in the Ze-IWCrelationship can improve the accuracy of IWC derivedfrom Ze.[23] The effect of temperatures on De has been investi-

gated by numerous groups [e.g., Ou and Liou, 1995; Ou etal., 1995; Wyser, 1998; Garrett et al., 2003]. If De should bea function of temperature, it would make sense to includetemperature in the Ze-IWC relationship. The De as a functionof temperature for the 1119 measurements during theCRYSTAL-FACE, TRMM, ARM, FIRE-I, are FIRE-II areshown in Figure 5. In general, the De of ice clouds increasewith increasing temperatures. However, the relationshipbetween De and temperature shows much variability. Thisfeature is distinctly shown by the evident separation of themeasurements in the TRMM campaign. The TRMM meas-urements came from cirrus anvils, and thus from an envi-ronment denoted by high updraft velocities, whereas theother PSDs came from cirrus having much lower updraftvelocities. Our analysis suggests that the temperature cannotbe included into the Ze-IWC relationship through a commonrelationship between temperature and De.[24] Because of the pronounced variability in the rela-

tionship between De and temperatures, the effect of De onthe Ze-IWC relationship for ice clouds is investigated fortwo temperature ranges with different De ranges. Note thatthe deriving Ze-IWC relationships do not involving the

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 habitsfor specific ranges of (a) effective particle sizes (De) and(b) cloud temperatures (T).

Table 1. Fitting Coefficient a and Exponent b for the Relation-ships Between Ice Water Content (IWC) and Equivalent RadarBackscattering Reflectivity (Ze) at 94 GHz for Clouds Consistingof a Mixture of Ice Particle Habitsa

Ice Cloud Properties

IWC =a Zeb

a b

Effective particle size, De (mm) De < 50 0.3121 0.685250 < De < 75 0.3429 0.793075 < De < 100 0.2071 0.7880100 < De < 125 0.1073 0.8369125 <De < 150 0.0679 0.8797150 < De < 175 0.0483 0.8948175 < De < 200 0.0405 0.8938

200 < De 0.0314 0.8701Temperature, T (!C) $30 < T < $25 0.0670 0.5703

$35 < T < $30 0.0714 0.5967$40 < T < $35 0.0876 0.5374$45 < T < $40 0.1001 0.6327$50 < T < $45 0.1242 0.6415

T < $50 0.2115 0.6470aThe results are provided for a number of ranges of effective particle

sizes (De) and cloud temperatures (T).

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temperatures directly. Two temperature ranges of $50!C to$40!C and $40!C to $25!C are used to separate themeasured ice cloud PSDs first. The separated PSDs arethen used to derive the Ze-IWC relationships for the De inthe range of 50–150 mm and 50–200 mm at the twotemperature ranges, respectively. The two temperatureranges and De ranges are chosen in order to have sufficientsamples for the analyses. Similarly to the results shown inFigure 4a, the De values are grouped with an intervalof 25 mm. The Ze-IWC relationships in Figure 6 show asimilar feature as Figure 4a, but for a given temperaturerange, the dependence of Ze-IWC relationship on De is morepronounced.[25] For the derived Ze-IWC relationships in the two

given temperature ranges (Figure 6), the IWC values arecompared to those from the Ze-IWC relationships withoutconsidering the influence from the temperatures (Figure 4a)for different De. The correlations between the two derivedIWC are similar, and the average deviations of the twoderived IWC with respect to the IWC calculated from theparticle size distributions are similar. This indicates againthat including temperature for the Ze-IWC relationship doesnot provide a significant improvement of the accuracy of theIWC 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-IWCrelationships may be useful for inferring the De from theZe-IWC relationship. For different De, the exponent b ofthe Ze-IWC relationships are similar. This agrees well withthe results presented by Brown et al. [1995], who showedthat the exponents of the Ze-IWC relationships for inverse-exponential size distributions of varying scale diameter arethe same. Thus the mean values of the exponents for the Ze-

IWC relationships for different De ranges, with a sizeinterval of 25 mm are used for the exponent a of the Ze-IWC relationship developed for the entire size range of 50–200 mm. The coefficients a of the Ze-IWC as a function ofDe based on the mean values of each size bin are shown inFigure 7. A fitting is performed for the relationshipsbetween 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 andZe calculated from the individual PSDs are also shown inthe 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 afunction of temperature (T) for the set of 1119 individualPSDs obtained from the CRYSTAL-FACE, TRMM, ARM,FIRE-I, and FIRE-II campaigns.

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 particlehabits as a function of effective particle size (De) whencloud temperatures (T) are in the range of (a) $50!C to$40!C and (b) $40!C to $25!C.

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from the other two from the previously built lookup tables atdifferent temperature ranges. The two lookup tables for theZe-IWC relationships with different De at two temperatureranges $50!C < T < $40!C and $40!C < T < $25!C)shown in Figure 8 are used to estimate ice cloud De. Theestimated ice cloud De agree well with the De calculatedusing the ice particle size distributions (Figure 9). Therelative errors for the two temperatures ranges of $50!C <T < $40!C and $40!C < T < $25!C are less than 32% and24%, respectively. The RMS of estimated De are about 8 mmand the correlation coefficients between the estimated icecloud De and the De calculated using the ice particle sizedistributions are over 94%.

4. Summary and Conclusions

[28] The effect of ice particle habits on Ze-IWC relation-ships is investigated using six different ice habits includinghexagonal solid and hollow columns, plates, 3D bulletrosettes, aggregates, and droxtals. The Ze-IWC relationshipsfor ice clouds composed of these habits are derived by thecalculated Ze and IWC from 1119 measured particle sizedistributions obtained from a variety of field campaigns.The Ze-IWC relationships obtained for these individualhabits show distinct differences. For a given Ze, the IWCvary in a factor of 1.5–2.0 for ice cloud composed ofdifferent habits, and in particular, the variations in IWC arelarger when the Ze are negative than when the Ze arepositive.[29] Rather than using a single habit, a habit mixture

from Baum et al. [2005a] is used additionally to derive theZe-IWC relationships. These Ze-IWC relationships showpronounced scattering, indicating the difficulty in findinga single Ze-IWC relationship for all ice clouds [e.g., Atlaset al., 1995; Aydin and Tang, 1997; Liu and Illingworth,2000; Sassen et al., 2002; Boudala et al., 2006].

[30] The Ze-IWC relationship has been found to besensitive to the variability in the ice particle spectrum [Atlaset 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 the1119 measured measurement particle size distributions, theeffect of the particle effective size (De) on the Ze-IWCrelationships is investigated by deriving the Ze-IWC rela-tionships for different ranges of De. The IWC generallyincreases with decreasing De for a given Ze. The depen-dence of Ze-IWC relationships on De shows a regularfeature, which may be potentially useful for estimating De

from observed Ze.[31] The effect of temperature on the Ze-IWC relation-

ships reveals that the inclusion of temperature in Ze-IWCrelationship has no significant improvement for estimatingIWC. This is also revealed by the relationships between

Figure 7. Coefficient a of the Ze-IWC relationships as afunction of effective particle size (De) when cloudtemperatures (T) are in the range of $50!C to $40!C and$40!C to $25!C.

Figure 8. Same as Figure 6 but for the Ze-IWC relation-ships using the fitting coefficient a as a function of De

shown in Figure 7.

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temperatures and De derived from 1119 data sets measuredfor ice clouds. However, for a given temperature range, thedependence of the Ze-IWC relationship on De is pro-nounced. This provides an opportunity to obtain De fromthe Ze-IWC relationship. The Ze-IWC relationship is derivedfor different De for the two temperature ranges. Thedependence of the Ze-IWC relationship on the effectiveparticle size within a given temperature range is pro-nounced, and may be useful for inferring the cloud effectiveparticle size from a Ze-IWC relationship. It is difficult to

apply the Ze-IWC relationships derived for different De

within given temperature ranges to operational radar re-trieval because the information about De (for estimatingIWC) or IWC (for estimating De) is needed. However, theinformation can be provided by observations made by otheractive and passive sensors. Moreover, these relationshipscan be used to simulate radar Ze of ice clouds simulatedfrom the weather forecasting, mesoscale, climate modelsthat 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 alsothank the three anonymous reviewers for constructive comments andsuggestion. Ping Yang’s research is supported by a National ScienceFoundation (NSF) grant (ATM-0239605).

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Figure 9. Comparison between the estimated De from theZe-IWC relationships shown in Figure 8 and the De frommeasured ice particle size distributions for cloud tempera-tures (T) in the ranges of (a)$50!C to$40!C and (b)$40!Cto $25!C.

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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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