sensitivity of the global distribution of cirrus ice...

Sensitivity of the global distribution of cirrus ice crystalconcentration to heterogeneous freezing

D. Barahona,1 J. Rodriguez,2 and A. Nenes1,3

Received 3 April 2010; revised 14 August 2010; accepted 25 August 2010; published 14 December 2010.

[1] This study presents the sensitivity of global ice crystal number concentration, Nc, tothe parameterization of heterogeneous ice nuclei (IN). Simulations are carried out withthe NASA Global Modeling Initiative chemical and transport model coupled to ananalytical ice microphysics parameterization. Heterogeneous freezing is described usingnucleation spectra derived from theoretical considerations and empirical data for dust,black carbon, ammonium sulfate, and glassy aerosol as IN precursors. When competitionbetween homogeneous and heterogeneous freezing is considered, global mean Nc varyby up to a factor of twenty depending on the heterogeneous freezing spectrum used.IN effects on Nc strongly depend on dust and black carbon concentrations and arestrongest under conditions of weak updraft and high temperature. Regardless of theheterogeneous spectrum used, dust is an important contributor of IN over large regions ofthe Northern Hemisphere. Black carbon however exhibits appreciable effects on Nc whenthe freezing fraction is greater than 1%. Compared to in situ observations, Nc isoverpredicted at temperatures below 205 K, even if a fraction of liquid aerosol is allowedto act as glassy IN. Assuming that cirrus formation is forced by weak updraft addressedthis overprediction but promoted heterogeneous freezing effects to the point wherehomogeneous freezing is inhibited for IN concentrations as low as 1 L−1. Chemistry anddynamics must be considered to explain cirrus characteristics at low temperature. Onlycloud formation scenarios where competition between homogeneous and heterogeneousfreezing is the dominant feature would result in maximum supersaturation levels consistentwith observations.

Citation: Barahona, D., J. Rodriguez, and A. Nenes (2010), Sensitivity of the global distribution of cirrus ice crystalconcentration to heterogeneous freezing, J. Geophys. Res., 115, D23213, doi:10.1029/2010JD014273.

1. Introduction

[2] The role of cirrus clouds in a changing climate systemconstitutes a major source of uncertainty in anthropogenicclimate change assessment and prediction [Baker and Peter,2008; Cantrell and Heymsfield, 2005; Seinfeld, 1998]. Cirrusclouds form by homogeneous freezing of deliquesced aerosoland heterogeneous freezing of ice nuclei (IN) [Pruppacherand Klett, 1997]. Analysis of ice crystal residues from fieldcampaigns shows that both freezing mechanisms interactduring cirrus formation [e.g.,DeMott et al., 2003;Haag et al.,2003; Prenni et al., 2007], suggesting that IN can stronglyaffect cloud ice crystal concentration and size distribution[Barahona and Nenes, 2009a; DeMott et al., 1994; Gierens,2003; Kärcher and Lohmann, 2003; Spichtinger and Gierens,2009a, 2009b].

[3] Global modeling studies have shown that heterogeneousIN emissions can impact the global distribution of ice crystalconcentration,Nc, resulting in a potentially large climatic effect.Lohmann et al. [2004] performed simulations consideringeither pure homogeneous or pure heterogeneous freezing(both from sulfate aerosol) as limits of variability induced fromheterogeneous IN effects. Compared to homogeneous freezing,heterogeneous freezing resulted in lower Nc, higher precipita-tion rates, and smaller ice water paths. Hendricks et al. [2005]studied the effect of aircraft emissions of black carbon on Nc,assuming that the freezing mechanism shifted from homo-geneous to heterogeneous when the grid cell black carbonconcentration, Nbc, exceeded a threshold value (around0.5 cm−3); considering IN effects reducedNc between 10% and40% at the midlatitudes of the Northern Hemisphere. A similarapproach was used by Lohmann et al. [2008] to study the effectof IN from dust on Nc; it was found that considering INeffects decreased the shortwave cloud forcing associatedwith cirrus clouds by 2.7 W m−2. Competition betweenhomogeneous and heterogeneous freezing of dust and blackcarbon IN during cloud formation was considered by Penneret al. [2009] using the parameterizations of Liu and Penner[2005] and Kärcher et al. [2006] to describe ice crystal

1School of Chemical and Biomolecular Engineering, Georgia Instituteof Technology, Atlanta, Georgia, USA.

2NASA Goddard Space Flight Center, Greenbelt, Maryland, USA.3School of Earth and Atmospheric Sciences, Georgia Institute of

Technology, Atlanta, Georgia, USA.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2010JD014273

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, D23213, doi:10.1029/2010JD014273, 2010

D23213 1 of 19

http://dx.doi.org/10.1029/2010JD014273

production. The aerosol indirect forcing from black carbonIN emissions ranged between −0.72 and 0.04 W m−2.[4] At atmospherically‐relevant conditions, dust, soot,

and biogenic particles can act as IN [DeMott et al., 2003;Fridlind et al., 2004; Pratt et al., 2009; Prenni et al., 2009;Uno et al., 2009]. The large seasonal and geographicalvariability of aerosol and the limited understanding ofheterogeneous nucleation challenge the prediction of INconcentrations [Baker and Peter, 2008; Cantrell andHeymsfield, 2005; Lin et al., 2002; Waliser et al.,2009]. Most of the uncertainty in predicting the impact ofaerosol emissions on cirrus clouds is associated with estimatingthe fraction of the aerosol that freezes heterogeneously,i.e., the IN concentration,NIN [Baker and Peter, 2008;Cantrelland Heymsfield, 2005; Lin et al., 2002]. Typically, hetero-geneous freezing is treated as an extension of homogeneousnucleation [Kärcher and Lohmann, 2003] or using classicalnucleation theory (CNT) [Khvorostyanov and Curry, 2004].Empirical correlations [e.g., DeMott et al., 1998; Meyerset al., 1992; Phillips et al., 2008] are also heavily used.[5] Cloud studies have shown that Nc can be very sensitive

to the assumptions made in the calculation of NIN [e.g.,Barahona and Nenes, 2009b; Eidhammer et al., 2009;Hendricks et al., 2005]. Lin et al. [2002] compared Nc fromseveral parcel models using different parameterizations forNIN, leading to 2 orders of magnitude difference amongstmodels. Monier et al. [2006] used several empirical expres-sions [DeMott et al., 1997, 1998; Meyers et al., 1992] andCNT methods to describe heterogeneous nucleation withinthe same cloud parcel model. It was found that a factor of10 variation in NIN translated into a factor of three differencein calculated Nc from the combined effects of homogeneousand heterogeneous freezing. A similar approachwas followedby Eidhammer et al. [2009] who found several orders ofmagnitude variation in Nc when empirical parameterizationsand CNT‐derived approaches where used to calculate NIN.[6] The large sensitivity of Nc to NIN reported in parcel

model studies has not been reflected in global circulationmodel (GCM) studies to date. This is largely because cirrusformation parameterizations used in GCM studies [e.g.,Kärcher et al., 2006; Liu and Penner, 2005] are highlyconstrained, considering specific NIN parameterizations witha prescribed dependency on T, p, si, and aerosol concen-

tration. This limitation can be relaxed using the Barahonaand Nenes [2008, 2009a, 2009b] framework, which pre-dicts Nc using any form of NIN parameterization (theoreticalor experimental) and unravels the dependency of Nc onthermodynamic, chemical and dynamic factors that drivecloud formation. In this study, this parameterization isincorporated within the NASA Global Modeling Initiative(GMI) framework [Liu et al., 2005; Rotman et al., 2001] tostudy the sensitivity of Nc that would form in cirrus cloudsusing several common parameterizations of NIN. Thesensitivity of our findings to the meteorological features isalso considered, by carrying out simulations using mete-orological fields from the NASA Goddard Institute forSpace Studies GCM (GISS) and the NASA former GlobalData Assimilation Office (DAO) GCMs.

2. Model Description

[7] The Global Modeling Initiative (GMI) is a state‐of‐the‐art modular 3‐D chemical and transport model developedfor assessment calculations of anthropogenic effects onclimate [Liu et al., 2007b; Rotman et al., 2001]. GMIutilizes off‐line meteorological fields to calculate advectiveand convective transport of chemical species, transformation,and removal by wet and dry deposition [Rotman et al., 2001].Here we use fields derived from the NASA Goddard Institutefor Space Studies (GISS) and from the NASA former DataAssimilation Office (DAO) GCMs. Each of the archived datasets spans over 1 year and represents the period from March1997 to February 1998 archived as 6 h averages. The GISSfield has a resolution of 23 vertical levels, from the surface to0.02 mb [Rind and Lerner, 1996]. DAO has a verticalresolution of 46 vertical levels, which extend from the surfaceto 0.15 mb. The horizontal resolution in both meteorologicalfields is 4° × 5°.[8] The GMI aerosol module is coupled to the GMI‐CTM

advection core and includes primary emissions, chemicalproduction of sulfate, gravitational sedimentation, drydeposition, wet scavenging, and hygroscopic growth[Liu et al., 2005, 2007b]. Anthropogenic and natural aerosoland precursor emissions include SO2, organic matter, blackcarbon, oceanic DMS, dust and sea salt. Model prognosticvariables include dimethylsulfide, sulfur dioxide, sulfateaerosol, hydrogen peroxide, black carbon (biomass burningand fossil fuel), and organic matter. Mineral dust and sea‐saltmass are predicted in four size bins: 0.01–0.63 mm, 0.63–1.26 mm, 1.26–2.5 mm, and 2.5–10 mm [Liu et al., 2007b].Explicit aerosol microphysics is not considered and aerosolsize distributions are assumed to follow those derived fromobservations (shown in Table 1).

2.1. Ice Crystal Number ConcentrationParameterization

[9] The number concentration of ice crystals that wouldnucleate in cirrus is calculated using the analytical frameworkof Barahona and Nenes [2008, 2009a, 2009b] referredhereinafter as BN09. Competition between homogeneous andheterogeneous freezing is explicitly considered, while thedependency of Nc on the conditions of cloud formation(i.e., T, p), updraft velocity, deposition coefficient, and

Table 1. Dry Number Size Distributions for Sulfate, Dust, andBlack Carbon Aerosola

AerosolNumberFraction

Dg

(mm) sgDensity(g cm−3)

Sulfate 1 0.04 2.3 1.7Dust 0.152 0.02 2.3 2.6

0.727 0.09 1.60.121 0.55 2.5

Black carbon(Fuel and biomass burning)

1 0.14 1.5 1.5

aDg and sg are the geometric mean diameter and standard deviation,respectively [Lin et al., 2002; Liu et al., 2007b; Penner et al., 2009].

BARAHONA ET AL.: CIRRUS ICE CRYSTAL CONCENTRATION D23213D23213

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soluble and insoluble aerosol concentrations is resolved.Nc isgiven by

Nc ¼ Nhom þ NhetðshomÞ ; NhetðshomÞ < Nlim

NhetðsmaxÞ ; NhetðshomÞ � Nlim

�; ð1Þ

where smax is the maximum supersaturation that develops inthe cirrus, shom is the homogeneous freezing threshold[Koop et al., 2000], and Nhom and Nhet are the number of icecrystals forming from homogeneous and heterogeneousfreezing, respectively. Nlim is the IN concentration thatcompletely inhibits homogenous nucleation (calculatedbelow) and sets the limit between combined heterogeneous‐homogeneous freezing and pure heterogeneous freezing only.Nlim is given by

Nlim ¼ N*ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDs*char

��shom

r 1þ shomð Þshom

e2

�shom ; ð2Þ

where N* and l are functions of cloud formation conditions(i.e., T, p, V, and deposition coefficient) defined in thenotation section, and

Ds*char

��si¼

Dschar4

3Dschar þ 2ðsi �DscharÞ

� �ð1þ si �DscharÞ ; ð3Þ

where Dschar ¼ min d lnNhetðsiÞdsi

� ��1; si

� �is a characteristic

of the IN population related to the slope of the IN spec-

trum at supersaturation si.[10] For the special case of a monodisperse IN population

with freezing threshold sh,mono, equation (2) simplifies to[Barahona and Nenes, 2009a],

Nlim ¼ �V

�

�a�i

2

�

shom þ 1

shom

G1Dlim þ G2

D2lim

; ð4Þ

where Dlim ¼ �� þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�2 þ 2

G1�VDs*char

��shom

r, � ¼ G2

G1, and

Dschar = si − sh,mono.[11] ForNhet(shom) <Nlim, smax is equal to the homogeneous

freezing threshold shom [Koop et al., 2000]. For Nhet(shom) ≥Nlim, smax is below shom and homogeneous freezing does notoccur (smax for this case is calculated below). For smax = shom,it is assumed that only heterogeneous freezing takes place,which however does not introduce substantial error inNc [Barahona and Nenes, 2009a]. The heterogeneous con-tribution toNc is equal toNhet(smax) when only heterogeneousfreezing is active and equal to Nhet(shom) when homogeneousand heterogeneous freezing are both active. The functionalform of Nhet(si) is discussed in section 2.2. The homogeneouscontribution to Nc is given by

Nhom ¼Noe�fcð1� e�fcÞ fc < 0:6

No 1þ exp9� 2fc

7

� ��1

fc � 0:6

8>><>>: ; ð5Þ

where No is the number concentration of the supercooledliquid droplet population and fc is the droplet freezing fractionfor cirrus clouds formed in situ [Barahona and Nenes, 2008,

2009a] (calculated below). The original expression in BN09[Barahona and Nenes, 2008] for Nhom was developed formaximum homogeneous freezing fractions below 25%(which accounts for most conditions of cirrus cloud for-mation). To account for high homogeneous freezingfractions where Nhom is limited by the available sulfateaerosol concentration (as for example in convective cloudsand sensitivity studies), the second term in equation (5)(for fc ≥ 0.6) is added to the result of Barahona andNenes [2008, cf. equation (30)]. This term is derived byfitting a sigmoidal function for NhomðfcÞ

No> 0:25 to parcel

model simulations [Barahona and Nenes, 2008], in agree-ment with published observations for convective clouds andcloud studies [Barahona and Nenes, 2008; Phillips et al.,2007]; fc = 0.6 is chosen as the value where both Nhom

( fc) anddNhomdfc

in the high and low freezing fraction expres-sions are equal. fc depends on the active freezing mechanismand is calculated below.[12] When homogeneous and heterogeneous freezing are

active, heterogeneously frozen crystals deplete water vapor[Barahona and Nenes, 2009a; DeMott et al., 1994; Kärcheret al., 2006] and weaken the homogeneous freezing pulse.In this case, smax ≈ shom, NIN = Nhet (shom), and fc depends onNIN and the freezing characteristics of the IN population as,

fc ¼ fc;hom 1� NhetðshomÞNlim

3=2( )3=2

; ð6Þ

where fc;hom ¼ �a�i

k1=2hom�No

2�V ðshomþ1Þ�Gshom

h i3=2is the droplet freezing

fraction in absence of IN, i.e., for pure homogeneousfreezing [Barahona and Nenes, 2008]. Other symbols aredefined in the notation section.[13] If NIN is high enough, heterogeneously frozen crystals

may deplete enough water vapor so that smax < shom,inhibiting homogeneous freezing [Barahona and Nenes,2009a; Gierens, 2003]. In this regime, Nc = Nhet (smax)(equation (1)), and smax is given by the solution of

NhetðsmaxÞN*

¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDs*char

��smax

r 1þ smaxð Þsmax

e2

�smax ; ð7Þ

where � ¼ G1G2

ffiffiffiffiffiffiffiffiffi1

�VG1

q. Other symbols are defined in the

notation section.

2.2. Heterogeneous IN Spectra

[14] The freezing spectrum function Nhet(si) gives thenumber concentration of IN at conditions of T, p, and si,accounting for the contribution of individual insolubleaerosol species and different freezing modes [Barahona andNenes, 2009b]. Nhet(si) can be obtained from theoreticalconsiderations, field campaign, and laboratory data [e.g.,Barahona and Nenes, 2009b; Field et al., 2006;Khvorostyanov and Curry, 2009; Meyers et al., 1992;Möhler et al., 2006; Phillips et al., 2008; Welti et al., 2009].BN09 is developed so that any expression for Nhet(si)(experimental or theoretical) can be used without loss ofaccuracy.[15] Table 2 describes the heterogeneous freezing spectra

used in this study. Three empirically derived expressions areused: the spectra of Meyers et al. [1992, MY], Phillips et al.


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[2007, BKG], and Phillips et al. [2008, PDA] (Figure 1).MY and BKG depend only on si and have a similar functionalform. BKG yields about tenfold lower NIN than MY for thesame si; this is because MY is derived from surface mea-surements and therefore represents an upper limit in NIN.PDA is derived from several field campaign data sets; apartfrom si and T, the contribution of individual aerosol species(dust, black carbon and organics) and freezing modes (i.e.,immersion and deposition) to Nhet(si) is provided. PDA usesBKG as a “background” IN spectrum from which the indi-vidual contribution of dust, black carbon, and organic aerosolspecies are scaled according to their surface area distribution.In this study, PDA is applied assuming the Phillips et al.[2008] background size distribution for dust and blackcarbon.[16] Theoretically derived Nhet(si) are also used in this

study. The simplest Nhet(si) scheme is the so‐called“monodisperse IN” (MONO) approximation, in which IN

are assumed to be monodisperse and chemically homoge-neous [Barahona and Nenes, 2009a]. Nhet(si) is then a stepfunction at a prespecified freezing threshold, sh,mono < shom,

NhetðsiÞ ¼ Ndust þ Nbcð Þ ; si � sh;mono

0 ; si < sh;mono

�: ð8Þ

Where Ndust, Nbc are the number concentrations of blackcarbon and dust, respectively. The steep increase in Nhet(si)about sh,mono is a behavior predicted by classical nucleationtheory (CNT) [Khvorostyanov and Curry, 2004, 2009]; it isalso obtained by generalizing expressions derived forhomogeneous nucleation [Kärcher and Lohmann, 2003]. The“monodisperse approximation” is the main type of INparameterization currently implemented in GCMs [e.g.,Liu et al., 2007a; Lohmann et al., 2004; Penner et al.,2009] with sh,mono typically treated as a free parameterconstrained by observations. Lohmann et al. [2004] assumedsh,mono = 0.3, based on reported measurements of blackcarbon freezing [DeMott et al., 1999]. Liu and Penner [2005]did not directly assume a value for sh,mono, but rather usedprescribed parameters as input to a CNT expression[Khvorostyanov and Curry, 2004], which effectively resultsin sh,mono ∼0.2 for black carbon [Barahona and Nenes,2009b]. Laboratory studies [e.g., Eastwood et al., 2008;Field et al., 2006; Möhler et al., 2006; Welti et al., 2009]suggest that ice nucleates on dust in the deposition modearound si ∼0.1–0.3. Theoretical studies show that for sh,mono

between 0.1 and 0.3 the effect of IN onNc is not very sensitiveto sh,mono [Barahona and Nenes, 2009a; Gierens, 2003]. Onthe basis of these considerations, sh,mono = 0.3 is assumed inthis study (Table 2).[17] Experimental observations [e.g., Eidhammer et al.,

2009; Field et al., 2006; Phillips et al., 2008; Welti et al.,2009] suggest that Nhet(si) is an smooth function of si,and, the freezing fraction varies between aerosol species(generally less than unity for black carbon) [e.g.,Eidhammer et al., 2009; Meyers et al., 1992; Phillips et al.,2008]. These features are at odds with the assumption of amonodisperse, single type IN [Eidhammer et al., 2009]. In apolydisperse, chemically heterogeneous aerosol, each aerosolsize and composition type would freeze at a characteristic sithreshold. On the basis of this and other theoretical con-siderations, Barahona and Nenes [2009b] proposed that for

Figure 1. Examples of heterogeneous freezing spectra usedin this study (presented in Table 2). Conditions consideredwere Ndust = 0.01 cm−3, Nbc = 0.5 cm−3, T = 210 K, andp = 22000 hPa. For the GLASS spectrum, T = 200 K andNglassy = 50 cm−3. The vertical line represents the onset ofhomogeneous freezing at T = 210 K [Koop et al., 2000].

Table 2. Heterogeneous Nucleation Spectra Used in This Study

Nhet(si) Description Type

HOM No heterogeneous freezing allowed [Barahona and Nenes, 2008;Koop et al., 2000]

Semiempirical

MONO Monodisperse IN with sh,mono = 0.3 (equation (8))[Barahona and Nenes, 2009a]

Theoretical

CNT‐BN Equation (9) with sh,dust = 0.2, sh,bc = si,sat, fh,dust = 0.011 (�dust = 16°),fh,bc = 0.039 (�bc = 40°) [Chen et al., 2008], and khom fromBarahona and Nenes [2008]

Semiempirical

MY Meyers et al. [1992] EmpiricalBKG Phillips et al. [2007] EmpiricalPDA Phillips et al. [2008] EmpiricalGLASS Murray et al. [2010]. The fraction of deliquesced aerosol in glassy

state was assumed asNglassy

No¼ 0:8min

212� T

32; 1

for T < 212 K

andNglassy

No¼ 0 for T > 212 K [Murray, 2008; Murray et al., 2010].

Empirical


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polydisperse IN, the relative concentration of monodisperseIN classes is approximately equal to the ratio of their het-erogeneous nucleation rates at si (calculated using CNT[Khvorostyanov and Curry, 2004]). This result in a semi-empirical freezing spectrum derived from CNT (referred to asCNT‐BN) but constrained with observations. When appliedto dust and black carbon, it takes the form

NhetðsiÞ � minsi

sh;dustexp �khom fh;dustðsh;dust � siÞ

� �; 1

� Ndust

þminsi

sh;bcexp �khom fh;bcðsh;bc � siÞ

� �; 1

� Nbc; ð9Þ

where sh,dust and sh,bc are the values of si at which the dustand black carbon freezing fraction is unity, respectively(other symbols are defined in the notation section), and can beconstrained using measurements of nucleation rate [e.g.,Chen et al., 2008]. On the basis of published laboratorystudies, we assume sh,dust = 0.2 [e.g., Eastwood et al., 2008;Field et al., 2006;Möhler et al., 2006;Welti et al., 2009]. Asblack carbon tends to freeze in both the immersion anddeposition modes, sh,bc is highly variable and depends onthe IN concentration, the water activity in the deli-quesced aerosol, and the particle history [Dymarska et al.,2006; Kärcher et al., 2007; Möhler et al., 2005;Popovicheva et al., 2008; Zobrist et al., 2008b]. Laboratoryresults however indicate that when water saturation isreached, black carbon is an active IN in the condensationmode [DeMott et al., 1999; Dymarska et al., 2006]. Thus,it is assumed that sh,bc = si,sat, where si,sat is the super-saturation with respect to ice at liquid water saturation(e.g., sh,bc = 0.51 at T = 230 K, and sh,bc = 0.85 at T = 200 K)[Murphy and Koop, 2005].[18] Besides dust and black carbon, glassy organic aerosol

[Murray et al., 2010] have been proposed as a source of INin the upper troposphere. Laboratory measurements indicatethat the vitreous transition temperature of organic aerosolsolutions can be as high as 210 K [Murray, 2008; Murrayet al., 2010; Zobrist et al., 2008a]. Liquid droplets con-taining organic solutes can thus become “glassy” at cirrusconditions. The fraction of deliquesced aerosol in glassystate depends on composition (e.g., organic fraction) andtemperature but is still uncertain. To test the potential sen-sitivity of Nc to this type of IN, the fraction of deliquescedaerosol in glassy state is assumed to depend linearly on T,from zero at T ≥ 210 K to 80% for T ≤ 185 K. The freezingfraction of glassy aerosol is then calculated using the hetero-geneous freezing spectrum reported by Murray et al. [2010].[19] Solid ammonium sulfate can also act as IN [Abbatt

et al., 2006; Shilling et al., 2006]. For this, the liquidaerosol must pass by a state of very low relative humidity,effloresce, and then freeze before deliquescence can takeplace [Shilling et al., 2006]. Recent studies [Jensen et al.,2010] suggest that this is preferred at very low temperature(T < 200 K) where the saturation ratio with respect toliquid water remains low even if the environment issupersaturated with respect to ice [Jensen et al., 2010]. Atwarmer conditions, most air parcels pass through states ofhigh relative humidity before reaching the upper troposphere

[Wiacek et al., 2010] and solid ammonium sulfate IN may beless common. It is however very difficult to estimate thefraction of ammonium sulfate particles that act as IN in theupper troposphere, as it depends on the history of individualparcels. Thus, the effect of ammonium sulfate IN is left forfuture work.

2.3. Implementation of Ice Crystal ConcentrationParameterization Within GMI

[20] In this study we assume that Nc that can form in cirrusis equal to the nucleated ice crystal concentration. Cloudfraction and relative humidity are not available in GMI; thisis not a limitation however, as BN09 uses the cloud‐scaleupdraft velocity to calculate the maximum in‐cloud smax

and Nc. The spatial distribution of cirrus is analyzed insection 3.2 using climatology data. To obtain the maximumsensitivity of ice crystal concentration to heterogeneousfreezing, ice crystal sedimentation and sublimation are notconsidered (the consequences of this assumption arediscussed in section 4).[21] Calculation of Nc using the BN09 parameterization

requires the knowledge of T, p, V, and the concentration ofindividual aerosol species (i.e., deliquesced droplets, dust,and black carbon). T and p were assumed to be those of thegrid cell (subgrid cell fluctuation in cooling rate is also con-sidered as described below). Following Chen and Penner[2005, and references therein], the total number of deli-quesced aerosol available for homogeneous freezing No isassumed equal to the sulfate aerosol number (calculatedfrom the sulfate mass by using a lognormal size distributionfunction derived from observations; Table 1). Since Nhom israrely limited by the available aerosol (i.e., Nhom � No)[Kärcher and Lohmann, 2002; Seifert et al., 2004] thisassumption is not expected to introduce a significant bias inNc. A similar approach is used to calculate Ndust and Nbc;prescribed dust and black carbon size distribution functionsare shown in Table 1 (the consequences of assuming a fixedsize distribution for dust and black carbon is assessed insection 4). In agreement with theoretical studies and fieldcampaign data, the vapor‐to‐ice deposition coefficient, ad,was set to 0.1 [e.g., Barahona and Nenes, 2008; Gayet et al.,2004; Hoyle et al., 2005; Jensen et al., 2008; Khvorostyanovet al., 2006; Liu and Penner, 2005; Monier et al., 2006].[22] The cloud scale updraft velocity V sets the rate

of expansion cooling during cloud formation and is consid-erably different from the grid scale value resolved in a large‐scale model. Subgrid scale variations in V are associated withturbulence and gravity waves [Comstock et al., 2008; Haagand Kärcher, 2004; Hoyle et al., 2005; Joos et al., 2008;Kärcher and Ström, 2003; Kim et al., 2003; Lohmann andKärcher, 2002], the effect of which on Nc can be accountedfor by averaging over the probability distribution function(PDF) of updraft velocities PV(V),

Nc ¼

RVmax

Vmin

Nc V ; smaxðV Þ½ �PVðV ÞdV

RVmax

Vmin

PVðV ÞdV: ð10Þ


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PDF averaging is also applied to calculate grid cell averageNIN, smax, and Nlim. According to equation (10), the grid cellin‐cloud Nc results from a weighted average of cirrus for-mation events where homogeneous and heterogeneousfreezing take place (Figure 2). Thus, for a givenNIN, there arealways a fraction of cirrus formation events (associated withthe lowest updrafts) for which homogeneous freezing iscompletely inhibited.[23] In this study, PV(V) is assumed to be a normal

distribution with zero mean and standard deviation sV of25 cm s−1 [Gayet et al., 2004], reflective of the gravity waveactivity and small scale turbulence in the upper troposphere[Bacmeister et al., 1999; Haag and Kärcher, 2004; Jensenand Pfister, 2004; Kärcher and Ström, 2003]. The sensitiv-ity of Nc to sV is addressed by assuming a linear variation ofsV with temperature from 25 cm s−1 at 238 K to 1 cm s−1 at198 K [Wang and Penner, 2009] and constant outside thisrange, suggesting that the influence of gravity wave motionon cirrus formation decreases with altitude and is driven bylarge‐scale dynamics (and therefore weak updrafts) at thetropopause level [e.g., Jensen et al., 2008; Khvorostyanovet al., 2006; Spichtinger and Gierens, 2009a, 2009b]. Vmin

andVmax are set to 1 and 50 cm s−1, respectively, in agreementwith field measurements [Comstock et al., 2008; Herzog andVial, 2001; Khvorostyanov et al., 2006; Lawson et al., 2008].

3. Results and Discussion

[24] The global distributions of Nc, smax, and NIN arecalculated by solving equations (1)–(7) and (10) using pand T, Ndust, Nbc, and No (provided by GMI) and PV (V)as described in section 2.2. NIN is calculated as Nhet (smax)

(equation (10)) when only heterogeneous freezing is activeand as Nhet (shom) when both homogeneous and hetero-geneous freezing are active. Sections 3.1–3.6 focus on theinfluence of dust and black carbon on Nc. The effect ofglassy aerosol on Nc at low temperature is analyzed insection 3.7.

3.1. Global Distribution of IN Concentration

[25] Figure 3 shows the annual zonal average of NIN, forthe different IN spectra of Table 2. The spatial distributionof NIN depends strongly on the freezing spectra employed todescribe heterogeneous freezing. The lowest global meanNIN (for all grid cells with Nc > 0 and T < 235 K) was foundfor BKG and PDA (∼3 L−1) and the highest for MONO(∼2.4 cm−3). As MY and BKG do not account for the spatialvariation of dust and black carbon concentration, NIN isquite uniform across the globe and only increases near thetropical tropopause level in response to an increase in smax

associated with decreasing T. The dependency of NIN on thedust and black carbon concentration is considered using theMONO, PDA, and CNT‐BN spectra (section 2.2). Forlevels below 300 hPa, NIN is larger in the NorthernHemisphere than in the Southern Hemisphere, decreasingwith altitude. The PDA spectrum yields NIN below 10−3 cm−3

for most of the upper troposphere, being even lower than withthe BKG spectrum. This is likely because Ndust and Nbc

predicted by the GMI model [Liu et al., 2007b] are belowthe background levels assumed by Phillips et al. [2008].When using the MONO spectrum, black carbon is thepredominant IN precursor (as Nbc is typically much higherthan Ndust [Liu et al., 2007b]). CNT‐BN and PDA how-ever predict a much higher freezing fraction for dust thanfor black carbon, and in some regions (around 30°N) Ndust

dominates NIN; these features are further analyzed insection 3.3. NIN from glassy aerosol (GLASS) is typicallybelow 10−3 cm−3 and reaches about 10−2 cm−3 at thetropical tropopause level (TTL), where their effect is mostprominent (section 3.7).

3.2. Global Distribution of Ice Crystal NumberConcentration

[26] The variation in NIN from application of the freezingspectra of Table 2 (glassy aerosol IN is only significant atlow T and its effect is analyzed in section 3.7) results in afactor of 20 variation in global mean Nc (Figure 4). Con-sidering only homogeneous freezing (HOM) produces highNc (greater than 10 cm−3) near the tropical tropopause level(TTL) which decreases with increasing T. When heteroge-neous freezing is considered, usage of the MY spectrumresults in the lowest Nc (0.12 cm−3) whereas the MONOspectrum gives the highest Nc (2.5 cm−3). All the spectrapresented in Table 2 (except for MONO) resulted in averageNc below the level for pure homogeneous freezing (HOM);this means that competition between homogeneous andheterogeneous freezing could occur globally. The MONOspectrum resulted in global mean Nc higher than in HOM,suggesting that NIN is high enough to completely preventhomogeneous freezing over large regions of the globe.Using BKG and PDA resulted in global mean Nc close to theHOM case (0.58 cm−3), whereas using CNT‐BN resulted ina global mean Nc about 35% below HOM.

Figure 2. Example of Nc calculated over a distribution ofupdraft velocities using the BN09 parameterization[Barahona and Nenes, 2009a, 2009b] and the PDAheterogeneous freezing spectrum [Phillips et al., 2008].The minimum in each curve defines the transitionbetween “pure heterogeneous” and “combined homogeneous‐heterogeneous” freezing regimes. Conditions considered wereNbc = 1 cm−3, T = 230 K, and p = 34000 hPa.


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[27] It is important to identify regions of the globe wherecirrus could be susceptible to competition effects from IN.Figure 5 presents the frequency and visible cloud opticaldepth (COD) of cirrus, obtained from ISCCP climatology[Rossow and Schiffer, 1999]. Cirrus are more frequentlyobserved in the tropics than in the midlatitudes and morecommon over the continents than over the oceans (except inthe tropics). COD is about 0.8–1.4 in the northern midlati-

tudes and in the southernmost latitudes of the SouthernHemisphere, and slightly lower in the tropics and the mid-latitudes of the Southern Hemisphere (∼0.4–1). Cirrus formtypically at around 8 km in the midlatitudes and above12 km (hence very low T) in the tropics [Dowling andRadke, 1990; Liou, 2002]. Thus, the effect of IN on thespatial distribution of Nc is analyzed at two different ver-tical levels, p = 281 hPa and p = 171 hPa. At the p = 281

Figure 4. Annual zonal average Nc that would form in cirrus clouds obtained for the heterogeneousnucleation spectra of Table 2. Only in‐cloud Nc is considered so that events with T > 235 K andNc = 0 are excluded from the average. Vertical axes represent pressure in hPa.

Figure 3. Annual zonal mean average NIN (equal to Nhet(smax)) using the heterogeneous freezing spectraof Table 2. Only in‐cloud NIN is considered so that events with T > 235 K and Nc = 0 (i.e., white area) areexcluded from the average. Vertical axes represent pressure in hPa.


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hPa level, competition effects from IN on Nc are strongest,as this is the minimum height where cirrus could form(i.e., T is less than 235 K over the entire year) and aerosolconcentrations (i.e., NIN) are highest (for the CNT‐BN, PDAandMONO spectra). Cirrus formation at p = 171 hPa exhibitsless pronounced IN competition, a consequence of decreasingaerosol concentration with height and lower T.[28] Figure 6 shows global maps of Nc normalized with Nc

from pure homogeneous freezing, Nc,HOM.Nc

Nc;HOMis used to

express relative changes in total crystal concentration fromthe effect of IN (and is preferred over using NIN

NINþNhom, since

Nc can be greatly affected by IN even if the contributionof heterogeneous freezing to Nc is very small [Barahonaand Nenes, 2009a]). At p = 281 hPa, usage of empirical INspectra that only depend on si (BKG and MY) predict auniform global distribution of Nc

Nc;HOMwith slight variations

occurring from variations in T (e.g., Figure 4). At this level,Nc for the CNT‐BN, PDA, and MONO spectra is controlledby the spatial distribution of dust and black carbon concen-tration (e.g., Figures 3 and 8). For the PDA spectrum, het-erogeneous effects are confined to the midlatitudes of the

Northern Hemisphere and are the strongest NcNc;HOM

� 0:5� �

in

regions of high dust concentration in north of Africa, SouthEast Asia, and the west coast of North America (Ndust between0.1 and 0.5 cm−3 [Liu et al., 2007b]). The high frequency ofcirrus (and the relatively large COD, Figure 5) in these regions(except in North Africa) indicates that IN effects may have asignificant impact on regional climate. This is also evidentwhen using the CNT‐BN spectrum, yielding Nc

Nc;HOMaround 0.6

in the same regions. Usage of CNT‐BN however results in lowNc

Nc;HOMover the Caribbean, Central America, and the remote

Pacific Ocean, caused by the high Nbc [Liu et al., 2007b] inthese regions. The relatively low frequency of cirrus in theseregions (except near the tropics, Figure 5) and their relativelylow COD however suggest that IN effects (at the p = 281 hPalevel) on regional climate may not be as significant as in theNorthern Hemisphere. The strongest effect of IN on Nc

is found with the MONO spectrum, where NcNc;HOM

> 1

over most of the Northern Hemisphere. NcNc;HOM

for MONO ishowever close to unity over large areas of the southernhemisphere and the tropics. This however does not indicatea weak IN effect but complete inhibition of homogeneousfreezing, and NIN close to Nc,HOM, as analyzed below(Figure 7).[29] Comparison between the Nc

Nc;HOMcontours at the 281

and 171 hPa vertical levels (Figure 6) show that NcNc;HOM

increases with height for the PDA, CNT‐BN, and BKGspectra and decreases for the MONO and MY spectra. ForPDA and CNT‐BN this results from a decrease in Ndustand Nbc with height that limits competition effects. Withthe MONO spectrum, the predominance of heterogeneousfreezing results in a direct correlation of Nc (hence Nc

Nc;HOM)

with NIN. The decrease in NcNc;HOM

with height seen with theMY spectrum results from a slightly higher NIN caused bythe lower T (and higher smax) at the 171 hPa level thanat p = 281 hPa (Figure 3). NIN predicted by BKG alsoincreases with decreasing T; Nc

Nc;HOMhowever still increases

as competition effects are weak and homogeneousfreezing is more vigorous at lower T [Barahona andNenes, 2008]. At the p = 171 hPa level, the MONOand MY spectra result in an appreciable effect of INemissions on Nc in the Southern Hemisphere and the

tropics. Using CNT‐BN results in NcNc;HOM

� 0:6� 0:8 over

most of the Southern Hemisphere, but it is close to 1 in thetropics (except over the Atlantic Ocean). For the other spectraof Table 2 (BKG and PDA), NIN is too low to impact Nc,which is agreement with in situ observations [Haag et al.,2003]. This would indicate that IN spectra that predict highblack carbon freezing fraction would tend to overestimate INeffects at the high levels of the upper troposphere, affectingmainly tropical regions, where cirrus are more frequent(Figure 5).[30] The active freezing mechanisms can be deduced from

NINNlim

. When NINNlim

< 1, homogeneous and heterogeneousfreezing actively contribute to Nc; when NIN

Nlim> 1, only

heterogeneous freezing takes place (equation (6)). Figure 7presents the annual average NIN

Nlimfor the spectra of Table 2

Figure 5. Cirrus cloud frequency and optical depth obtained from the ISCCP climatology [Rossow andSchiffer, 1999].


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Figure 6. Annual average ice crystal concentration obtained in the GMI model at (top) p = 281 hPa and(bottom) p = 171 hPa, normalized with Nc from pure homogeneous freezing (HOM).


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at the p = 281 hPa level. For the MONO spectrum,NINNlim

> 1, which indicates that NIN is high enough to inhibithomogeneous freezing over most of the globe. Figure 3indicates that this is the case up to very high levels inthe atmosphere. If MONO reflected atmospheric IN, cirruswould show a marked difference in Nc between thenorthern and the southern hemisphere, resulting from theinterhemispheric differences in Ndust and Nbc (e.g., Figure 6,bottom). This behavior was seen in the global modeling studyof Penner et al. [2009], whom used an IN framework derivedfrom classical nucleation theory. For the CNT‐BN spectrum,NINNlim

> 1 in the Northern Hemisphere (although lower thanfor MONO). In the midlatitudes of the southern hemi-sphere (30°S to 60°S), NIN

Nlim� 1 and Nc

Nc;HOM� 0:1 (Figure 6,

top), indicating strong competition between homogeneousand heterogeneous freezing; heterogeneous IN impactswould however not manifest given the low frequency ofcirrus in these regions (Figure 5). At the southernmostlatitudes, NIN decreases (NIN

Nlim� 0:2 and Nc

Nc;HOM> 0:7) due to

the scarcity of dust and black carbon in these regions. Athigher levels (p < 281 hPa), NIN predicted by the CNT‐BN spectrum decreases (Figure 3) and competition effectsvanish in the southern hemisphere and the tropics(NINNlim

< 0:2, not shown). As NIN predicted by the PDA andBKG spectra is generally low (Figure 3), competitioneffects are weak over most of the globe (i.e., NIN

Nlim� 1)

except near dust sources in the Northern Hemisphere;PDA results in NIN

Nlimup to 0.4, depleting Nc to about half of

the homogeneous freezing value NcNc;HOM

� 0:5� �

. Compe-tition effects are very strong for the MY spectrum beingNINNlim

� 1 around the globe, which results in very low NcNc;HOM

(about 0.1–0.2, Figure 6).

3.3. The Role of Dust and Black Carbon as INPrecursors

[31] As dust and black carbon emissions originate fromdifferent sources [Liu et al., 2007b], it is important to dis-tinguish their relative contribution to the IN population.Figure 8 shows Nc

Nc;HOMfor the CNT‐BN and PDA spectra

considering either only black carbon (Ndust = 0) or dust(Nbc = 0) as IN precursor. Generally, ice nucleates on dustat low si (∼0.1–0.3) [Eastwood et al., 2008]; dust also hasa higher freezing fraction than black carbon (i.e., it is amore “efficient” IN). Therefore lower Ndust than Nbc isneeded to impact homogeneous freezing. The numberconcentration of black carbon is however higher in theupper troposphere (Nbc�Ndust) [Liu et al., 2007b] so, even ifit is not a very efficient IN, heterogeneous freezing of blackcarbon still contribute appreciably to NIN.[32] Using CNT‐BN and assuming dust as the only IN

precursor produces a global annual mean NIN (at the p = 281hPa vertical level) around 0.05 cm−3, about 0.1 cm−3 in mostof the Northern Hemisphere and as high as 0.3 cm−3 neardust sources (not shown). The spatial variability of dustconcentration results in near pure homogeneous freezing inTropical cirrus ( Nc

Nc;HOM� 1 and NIN

Nlim� 1) and strong competition

between freezing mechanisms in the Northern midlatitudes

Figure 7. Annual average NIN/Nlim maps corresponding to the p = 281 hPa level.


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( NcNc;HOM

� 0:1 and NINNlim

� 1). Regions of NcNc;HOM

� 0:5 result fromdominant heterogeneous freezing (NIN >Nlim) near dust sourcesin the northen hemisphere, and, partially inhibited homoge-neous freezing (NIN < Nlim) in the midlatitudes of the SouthernHemisphere. Using the PDA spectrum results in mean NIN

around 0.001 cm−3 (and up to 0.01 cm−3 near dust sources).Given the simulated Ndust ∼ 0.1 cm−3 at p = 281 hPa (notshown), PDA on average predicts that ice nucleates on about1% of the dust aerosol (as opposed to ∼100% predicted byCNT‐BN). Thus, only in regions of high Ndust (around0.5 cm−3) are IN numerous enough to impact Nc.[33] If black carbon is assumed to be the only species

freezing heterogeneously (Ndust = 0, Figure 8, “bc‐only”) theCNT‐BN spectrum predicts NIN around 0.04 cm−3 and up to0.07 cm−3 in the midlatitudes of the Northern Hemisphere(at p = 281 hPa). As NIN ∼ Nlim, there is strong competitionbetween freezing mechanisms, resulting in very low Nc overmost of the Northern Hemisphere. Using the PDA spectrumfor this case gives a mean NIN around 0.001 cm−3 (up to0.01 cm−3) and black carbon freezing fraction around0.01%, which is too low to impact freezing (i.e., Nc

Nc;HOM� 1

and NINNlim

< 0:1).[34] Comparison of Figures 6 and 8 shows that the com-

bined effect of dust and black carbon on Nc is not additiveand depends on their relative freezing characteristics. ForCNT‐BN, there are enough IN from black carbon alone tostrongly reduce Nc from pure homogeneous freezing con-centrations (Figure 8, “bc‐only”). Most of the black carbon

however does not freeze in the presence of dust (Figure 6)because smax does not exceed its freezing threshold.Therefore sufficient amounts of dust prevent the freezing ofsupercooled droplets and black carbon. In the southernhemisphere and the tropics Ndust is very low and blackcarbon is the dominant factor controlling Nc, leading tocompetition between homogeneous and heterogeneousfreezing (which however is not significant at high altitudes,section 3.2). This is not the case for PDA, as the black carbonfreezing fraction is too small to have an appreciable impacton Nc and dust is the only significant source of IN. How-ever, the presence of low dust concentration may reduce theNbc required to have an appreciable effect on Nc; the verysmall black carbon freezing fractions predicted by the PDAspectrum may thus exert a noticeable effect of IN on Nc.This is illustrated by the values of Nc

Nc;HOMat the northern

latitudes of the Atlantic Ocean (around 50°); for both thedust‐only and bc‐only cases, Nc

Nc;HOM� 1 (Figure 8, PDA),

but NcNc;HOM

� 0:8 when both dust and black carbon act as INprecursors (Figure 6, top, PDA).

3.4. Sensitivity to Dynamical Forcing

[35] When sV is assumed to decrease with temperature(Figure 9) Nc near the tropical tropopause level (TTL,p ∼ 100 hPa) is much lower (Nc ∼ 1 cm−3) than whenusing a fixed sV (Nc ∼ 10 cm−3). In terms of the globalannual mean Nc for the whole atmosphere, this variation in

Figure 8. Annual average ice Nc at p = 281 hPa normalized with Nc from pure homogeneous freezing(HOM). Results shown assuming only dust (Nbc = 0, “dust‐only”) or black carbon (Ndust = 0, “bc‐only”)contribute IN.


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sV leads to about a threefold decrease for all the spectra ofTable 2, primarily because reductions in updraft velocitydecrease Nhom [Barahona and Nenes, 2008; Kärcher andLohmann, 2002], which inevitably limits Nc. However,small values of sV also exacerbate the effect of IN on Nc

because Nlim decreases with decreasing V (i.e., fewer INare required to perturb homogeneous freezing, Figure 2)[Barahona and Nenes, 2009a]. For the CNT‐BN, MONO,and PDA spectra, NIN decreases with height (as Ndust andNbc decrease); if sV decreases with T, Nlim also drops,allowing for significant heterogeneous effects even at verylow NIN (∼1 L−1; Figure 3). Because of this, using the

BKG and MY spectra, where NIN does not depend onaerosol concentration (therefore does not decrease withheight), leads to the predominance of heterogeneousfreezing at low T. This behavior is further analyzed insections 3.6 and 3.7.

3.5. Effect of Temperature on Nc

[36] As NIN is limited by the available aerosol concen-tration, Nc in cirrus formed by heterogeneous freezing is lesssensitive to changes in T than clouds where homogeneousfreezing dominates [Barahona and Nenes, 2009a; Lohmannet al., 2008]. Figure 10 compares the results of the GMImodel for the runs of Figure 3 against in situ data reported

Figure 9. Similar to Figure 3 with sV decreasing from 25 cm s−1 (at 238 K) to 1 cm s−1 (for T ≤ 198 K).

Figure 10. Ice crystal concentration against grid cell temperature using the spectra of Table 2. Resultsshown assuming (left) sV = 25 cm s−1 and (right) sV decreasing from 25 cm s−1 (at 238 K) to 1 cm s−1

(for T ≤ 198 K). Error bars represent one standard deviation about the mean Nc (error bars are omitted iflower than a factor of two about the mean). The shaded area corresponds to a factor of two from the meanNc observed in situ [Krämer et al., 2009].


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by Krämer et al. [2009]. The extensive data of Krämer et al.[2009] is based on aircraft measurements of relativehumidity and ice crystal concentration in cirrus taken during28 flights in several field campaigns in the Arctic, atmidlatitudes, and in the tropics, covering regions from 20°Sto 75°N, and temperatures between 183 and 240 K [Krämeret al., 2009]. Nc measurements from Krämer et al. [2009] arein good agreement with independent studies [Gayet et al.,2004; Hoyle et al., 2005; Lawson et al., 2008] and thereforeare considered representative of global cirrus.[37] Agreement of simulations to within a factor of two

with observations is obtained for T > 205 K for all INspectra except MY (which underpredicts Nc). The positiveslope of Nc versus T given by observations (as opposed tothe slightly negative slope predicted by the model), may be aresult of observational uncertainties or artifacts (e.g., icecrystal shattering in FSSP probes [Krämer et al., 2009]) thattend to introduce positive bias (mostly within a factor of 2[Field et al., 2003]) in observed Nc at high T. For T < 205 Kand assuming a fixed sV (Figure 10, left), the model largelyoverestimates Nc by at least tenfold, even in cases whereheterogeneous effects are the strongest (e.g., MONO andMY). Assuming that sV decreases with T (hence height)yields low Nc at low T (section 3.4), giving a much betteragreement with observations for the CNT‐BN, HOM, andPDA spectra than when a fixed sV is used. Nc is howeverunderestimated for the BKG and MY spectra from anoverestimation in NIN at high altitudes. For T > 205 K, theCNT‐BN, BKG, HOM, and MONO spectra display roughlysimilar Nc (mostly within a factor of 3). However, similar Nc

may result from very different interactions between homo-geneous and heterogeneous freezing (Figures 6 and 7;section 3.2). The distribution of smax that results fromapplication of each IN spectrum considered in this study canhelp elucidate whether lowering sV with altitude is consis-tent with other available cirrus microphysical characteristics.

3.6. Maximum Supersaturation Statistics

[38] The frequency distribution of maximum supersatu-ration achieved during cloud formation, P(smax) is shown in

Figure 11, for fixed sV (right) and for sV decreasing withT (left). As homogeneous freezing occurs over a verynarrow si interval [Barahona and Nenes, 2008; Kärcherand Lohmann, 2002], P(smax) for HOM is insensitive tosV and depends only on T; smax ranges mostly between0.4 and 0.65 with a mean around 0.5. Predominance ofpure heterogeneous freezing forMONO andMY is expressedby a shift in P(smax) toward low smax (mean around 0.2–0.3).Competition between homogeneous and heterogeneousfreezing (e.g., BKG and CNT‐BN) results in a broad P(smax)with a maximum about the homogeneous freezing threshold(smax ∼ 0.5) extending to low smax. Assuming a T‐dependentsV exacerbates IN effects on smax; P(smax) therefore residesmostly below the homogeneous freezing threshold for all theIN spectra (except in PDA where NIN is too low to signifi-cantly impact smax).[39] Observations can be used to diagnose smax as it is

related to the upper limit of the relative humidity distributionin recently formed clouds [Haag et al., 2003; Heymsfieldet al., 1998]. As freezing and subsequent crystal growthlimit the maximum supersaturation within the cloud, smax

is also associated with the predominant freezing thresholdin the cirrus cloud. Unfortunately no systematic study ofthe global distribution of freezing thresholds (hence ofP(smax)) has been carried out to date. We can howeverstudy which of the distributions presented in Figure 11agrees with common features observed in different fieldcampaigns. Field campaign data consistently show smax nearthe homogeneous freezing threshold (i.e., between 0.45and 0.7) [e.g., Comstock et al., 2008; DeMott et al., 2003;Gayet et al., 2004; Haag et al., 2003; Heymsfield andSabin, 1989; Heymsfield et al., 1998; Krämer et al.,2009] at temperatures below 235 K. Haag et al. [2003]and Ström et al. [2003] have shown however that insome regions of the Northern Hemisphere, smax can belower (∼0.3) due to heterogeneous freezing, which is alsoconsistent with theoretical considerations [Barahona andNenes, 2009b; Kärcher and Lohmann, 2003]. The uncer-tainty associated with relative humidity measurements inthe upper troposphere is typically about 0.1 (in absolute

Figure 11. Global annual average probability distribution of smax for T > 195 K calculated by the BN09parameterization, for the different heterogeneous freezing spectra of Table 2. sV was assumed (left)constant equal to 25 cm s−1 or (right) decreasing from 25 cm s−1 at 238 K to 1 cm s−1 for T ≤ 198 K.


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units) [Hegg and Noone, 2005; Krämer et al., 2009; Strömet al., 2003]. Thus, to be consistent with these observations,P(smax) should exhibit a mean around smax ∼ 0.4–0.6, with abroad tail toward lower smax values. Figure 11 shows thatthese features cannot be reconciled assuming weak dynami-cal forcing (a T‐dependent sV; Figure 10, right), or whenheterogeneous IN completely inhibits homogeneous freezingduring cloud formation (i.e., MY and MONO spectra).Indeed, only cloud formation scenarios where competitionbetween homogeneous and heterogeneous freezing is thedominant feature (e.g., CNT‐BN, BKG) would result inP(smax) consistent with observations. Thus, simulationsthat prescribe a weakening of dynamical forcing (sV)with height provide Nc predictions that are closer toobservations, but for the wrong reason.

3.7. Glassy Aerosol as IN at Low Temperature

[40] At T < 210 K, NIN from glassy aerosol is high enoughto impact Nc and P(smax). Figure 10 shows that using theGLASS spectrum leads to Nc

Nc;HOM� 0:2 for T < 190 K and

fixed sV. For this case, P(smax) (for T between 180 and200 K, Figure 12) is centered around 0.5, indicating thathomogeneous freezing is the predominant freezing mecha-nism, leading to high Nc compared to observations. Thus,NIN is not enough to complete inhibit homogeneous freezingand only at low V (typically below 5 cm s−1) heterogeneousfreezing dominates. When sV decreases with decreasing T(leading to V mostly around 1 cm s−1, for T < 200 K)heterogeneous freezing dominates, which is evidenced byP(smax) centered around smax ∼ 0.3 (Figure 12). Thishowever results in Nc much below observations at low T(Figure 11), i.e., NIN is high enough to completely preventhomogeneous freezing but still much lower than observedNc.[41] Few measurements of in‐cloud relative humidity are

available at low T; Krämer et al. [2009] reported values ofrelative humidity up to the homogeneous freezing threshold(and some few episodes above, also consistent with otherstudies [Jensen et al., 2005; Lawson et al., 2008]), which isconsistent with the predominance of homogeneous freezingat the TTL. Froyd et al. [2009] reported cloud episodes withcutoff supersaturations up to 0.3, providing support to thehypothesis of predominant heterogeneous freezing at theTTL. The dynamics of the TTL may be not be passiveenough to lead to a heterogeneous‐only scenario (i.e., Tfluctuations around leading to V ∼ 10–30 cm s−1 are quitecommon at the TTL [Bacmeister et al., 1999; Herzog andVial, 2001; Jensen et al., 2010; Sato, 1990]), and competi-tion between homogeneous and heterogeneous freezing ismore likely to occur.

3.8. Sensitivity of Nc Distributions to MeteorologicalField

[42] The global distribution of temperature, as well asof aerosol concentration, can be greatly affected by themeteorological field employed to drive the aerosolsimulation [Liu et al., 2007b]. To study how this sensitivity

Figure 12. Global annual average probability distributionof smax for T between 180 and 200 K, calculated by theBN09 parameterization using the GLASS heterogeneousfreezing spectrum [Murray et al., 2010]; sV was assumedconstant either equal to 25 cm s−1 (solid line) or equalto 1 cm s−1 (dashed line).

Figure 13. Annual zonal average Nc that would form in cirrus clouds for the spectra of Table 2.Simulations are carried out using the DAO meteorological field. Only in‐cloud Nc is considered so thatevents with T > 235 K and Nc = 0 are excluded from the average. Vertical axes represent pressure in hPa.


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would affect the global distribution of Nc, GMI runs werecarried out using the DAO meteorological field (instead ofGISS) for the HOM, CNT‐BN, and PDA spectra (Figures 13and 14). When no heterogeneous effects are considered(HOM) the global annual mean Nc obtained with the DAOfield (0.60 cm−3) is very close to that obtained using GISS(0.62 cm−3), although the spatial distribution of Nc differs.Upper tropospheric (p < 200 hPa) Nc is generally larger inDAO than in GISS and vice versa at lower levels. This resultsfrom a weaker vertical transport in DAO (compared to GISS)and slightly lower temperature (for the same vertical level) inDAO than in GISS [Liu et al., 2007b]. For the CNT‐BNspectra, Nc in the Northern Hemisphere (for p > 300 hPa) ismuch lower using the DAO field than obtained with the GISSfield. For simulations with the PDA spectrum, the DAO fieldresults in even weaker IN effects on Nc than obtained with theGISS field (Figure 4). These features originate fromdifferences in predicted Ndust and Nbc (therefore differentinteraction between homogeneous and heterogeneousfreezing) and can be understood in terms of Nc

Nc;HOMand NIN

Nlim.

[43] The spatial distribution of NcNc;HOM

at the p = 258 hPa levelobtained with the DAO field is shown in Figure 14 for thePDA (right) and CNT‐BN (left) spectra. Compared to si-mulations with the GISS meteorological field (Figure 6), theCNT‐BN spectrum generally results in lower Nc around theglobe. The opposite occurs for the PDA spectrum whereNc

Nc;HOM� 1 (and NIN

Nlim� 1) is considerably different from si-

mulations with the GISS field ( NcNc;HOM

� 0:5 near dustsources, section 3.2). These differences result from weakerdust transport to the upper troposphere in the DAO(compared to the GISS field). Indeed, the mean upper level(p below 300 hPa) Ndust and Nbc predicted with DAO(0.05 and 0.8 cm−3, respectively) are about a factor of twolower than for GISS (0.1 and 1.17 cm−3, respectively).Thus, NIN is insufficient to prevent freezing of black carbonwhen using the CNT‐BN spectrum with the DAO field. Thisimplies that instead of pure heterogeneous freezingNINNlim

> 1� �

caused by dust for the GISS field, there is com-

petition between freezingmechanisms NINNlim

� 1� �

when using

the DAO field. Lower Ndust with DAO winds also resulted inlowerNIN when using PDA, therefore a weaker impact of dust

on NcNc

Nc;HOM� 1

� �than simulated with GISS. However, this

can partly result from the slightly lower pressure level usedfor comparison in the DAO field (DAO does not have thep = 281 hPa vertical level and p = 258 hPa is the lowest levelfor which T < 235 K over the entire year). At p = 301 hPa,DAO field simulations result in slightly lower Nc

Nc;HOM(global

mean 0.95) for PDA and slightly higher (global mean 0.27)for CNT‐BN, than at p = 258 hPa. Such difference is stilllower than the difference in Nc

Nc;HOMbetween GISS and

DAO; both meteorological fields however consistentlyoverpredict Nc at the TTL (Figures 4 and 13) and a sig-nificant contribution of dust to NIN in the NorthernHemisphere.

4. Summary and Conclusions

[44] A parameterization of cirrus cloud formation thataccounts for competition between homogeneous andheterogeneous freezing was implemented in the GlobalModeling Initiative (GMI) chemical and transport model.Simulations were then carried out to study the sensitivityof ice crystal number concentration to dust and blackcarbon aerosol concentrations. Ammonium sulfate wasassumed to deliquesce and contribute supercooled dropletsthat freeze homogeneously or heterogeneously if a fraction isin a glassy state (GLASS). Dust and black carbon wereassumed to heterogeneously freeze, using spectra derivedfrom empirical data (PDA, BKG, and MY) and theory(CNT‐BN and MONO). The global annual mean NIN

predicted by these formulations varied between 0.003and 2.4 cm−3. When included into the cirrus formationframework, this variation resulted in up to a factor of 20difference (0.13–2.5 cm−3) in the predicted global meanNc. Although this value may likely represent an upper limitof variability (as ice crystal sedimentation and transport arenot considered), it shows the large sensitivity of Nc (andtherefore of cloud properties) to the parameterization ofNIN. For low NIN (PDA spectrum), homogeneous freezing

Figure 14. Annual average ice crystal concentration at p = 258 hPa, normalized with Nc from purehomogeneous freezing (HOM). Simulations obtained using the DAO meteorological field.


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was predominant and vice versa for high NIN (MONOspectrum), giving Nc even higher than for pure homo-geneous freezing. The lowest Nc resulted when strongcompetition between homogeneous and heterogeneousfreezing NIN

Nlim� 1

� �was predominant (MY spectrum).

[45] The sensitivity of Nc to IN is a strong function of theheterogeneous IN spectrum. Empirical parameterizationsthat only depend on supersaturation (BKG and MY) pre-dicted a uniform NIN around the globe and little variation ofNIN with height. Explicitly accounting for the dependency ofdust and black carbon concentration (MONO, CNT‐BN,and PDA) resulted in a highly variable spatial distribution ofNIN. In the latter, heterogeneous effects on Nc were thestrongest at the lowest levels of cirrus formation (T ∼ 230 K)in the midlatitudes of the Northern Hemisphere, mostly nearregions impacted by transport of dust and black carbon. Inthe tropics and midlatitudes of the Southern Hemisphere, itwas found that IN would affect cirrus formation only if thefreezing fraction of black carbon is close to unity. In gen-eral, heterogeneous effects were less significant at lowtemperatures as dust and black carbon concentration werelow and the NIN needed to impact homogeneous freezing(i.e., Nlim) was higher than at warmer levels. Dust wasfound to be an important contributor of IN over large re-gions of the Northern Hemisphere. The effect of blackcarbon as heterogeneous IN is still controversial, as itdepends on the functional form of the freezing spectrum.The simulations carried out in this study suggest that atleast 1% of black carbon aerosol should freeze at cirruslevels in the Northern Hemisphere to have an appreciableeffect on Nc. The larger NIN from dust and black carbonfor the CNT‐BN, PDA, and MONO spectra also results ina larger fraction of events dominated by heterogeneousfreezing, and stronger competition between homogeneousand heterogeneous freezing in the Northern Hemisphere(Figures 6 and 7). This will lead to lower smax (i.e., lowerfreezing thresholds) in the Northern Hemisphere than inthe Southern Hemisphere (particularly for p > 200 hPa),consistent with field campaign studies [Gayet et al., 2004;Haag et al., 2003].[46] The sensitivity of the global distribution of Nc to

large scale meteorological features was tested by running theGMI model using two different meteorological data sets(GISS and DAO). Differences in the vertical transport ofdust and black carbon to the upper troposphere lead tosignificant variation in Ndust and Nbc (therefore on NIN andNc). The largest sensitivity to the meteorological fieldresulted in regions where NIN ∼ Nlim (midlatitudes of theNorthern Hemisphere and near the tropics). For suchconditions, a factor of two decrease in Ndust and Nbc atcirrus levels may change the predominant freezing regime

from pure heterogeneous NINNlim

> 1� �

to competition between

homogeneous and heterogeneous freezing NINNlim

< 1� �

, and

therefore the predicted response of cirrus to increased IN

emissions. Despite this, runs with DAO and GISS meteoro-logical fields consistently show high Nc at the TTL (Figure 4)and a significant contribution of dust to NIN in the NorthernHemisphere.[47] Comparison of Nc predicted with the GMI model

against reported observations [Krämer et al., 2009] showed

agreement for T > 205 K for most of the freezing spectratested. However, at least a tenfold overprediction in Nc forT < 200 K where Nc was as high as 10 cm−3, resultingfrom a high fraction of sulfate freezing homogeneously alow temperature. It was shown that if cirrus formation atlow temperature forms in weak updrafts, Nc is in muchbetter agreement with observations. This however magnifiesthe sensitivity to heterogeneous nuclei, so thatNIN as low as 1L−1 was enough to affect homogeneous freezing. This resultsin smax distributions centered around values well below shom,in strong disagreement with available observations offreezing thresholds in cirrus clouds [e.g., DeMott et al.,2003; Haag et al., 2003; Krämer et al., 2009]. Sincesmax largely controls the steady state size of the ice crystalsand the ice water content [Korolev and Mazin, 2003],incorrect predictions of P(smax) will likely lead to biases inpredicted cirrus ice crystal size distribution. Thus, even if thebias of Nc can be addressed by reducing sV, this would likelyintroduce other biases in the effective radius of ice crystalsand ice water path with potentially important implicationsfor radiative forcing. Altogether this reveals a fundamentalweakness in the “classical” theory of cirrus formation atlow T.[48] The effect of glassy aerosol on the formation of cirrus

clouds at low temperature was also studied. It was foundthat for sV ∼ 25 cm s−1, insufficient IN are produced fromglassy aerosol to completely prevent homogeneous freezing,thus leading to Nc much higher than observed [Krämeret al., 2009]. Using sV ∼ 1 cm s−1 at T < 198 K led topredominant heterogeneous freezing; the low freezing frac-tion of glassy aerosol however results in Nc ∼ 0.01 cm−3,below observed values. Murray et al. [2010] found Nc

∼ 0.05 cm−3 for V ∼ 3 cm s−1 at T ∼ 190 K for pureheterogeneous freezing. The slightly lower Nc in Figure 12(right) results from the lower V ∼ 1–2 cm s−1 used in thiswork. The large sensitivity of Nc to sV, even in thepresence of glassy aerosol, suggests that “chemical effects”(such as glassy IN) may not be the sole underlying causefor the characteristics of cirrus at low T. Dynamics, icesedimentation and transport effects [Spichtinger and Gierens,2009a, 2009b], and the existence of other sources of IN(e.g., solid ammonium sulfate) at the TTL [Abbatt et al.,2006; Jensen et al., 2010] may also play a role in ex-plaining the characteristic of low temperature cirrus.[49] The results presented in this work must be interpreted

as the potential of IN to alter Nc whenever a cirrus cloud isformed. Cirrus cloud fraction was not calculated explicitly(i.e., grid cell cloud fraction was unity for T < 235 K);regions where IN effects are expected to be climaticallyimportant where however identified by focusing on areaswith high cloud frequency and high cirrus optical depth(using climatological data from ISCCP). Anotherassumption made in this work was to consider Nc at itsmaximum, i.e., no sedimentation or sublimation effectswere accounted for. Sedimentation may structure the cirruscloud layer and reduce the ice crystal concentration,particularly at low updraft velocity [Spichtinger andGierens, 2009a, 2009b]. Sublimation may impact the icecrystal concentration in dry regions at high temperatures(T > 235 K) [Kärcher and Burkhardt, 2008]. Althoughimportant, these effects are not expected to introduce Nc

variability comparable to the variability introduced by NIN


16 of 19

and will not modify the conclusions of this study. However,the ice crystal concentrations presented in Figure 10 mayhave a positive bias, particularly at warmer temperatureswhere sedimentation and evaporation are more significant.Nevertheless, the comparison of Nc with available measure-ments (T > 205 K) suggests that they are usually within afactor of two of predictions.[50] The ice water content of cirrus clouds is also sensitive

to heterogeneous IN. High smax (associated with homoge-neous freezing) favors the diffusional growth of crystals;high Nc however implies the distribution of ice mass amongmore particles [Korolev and Mazin, 2003]. Thus, high Nc

leads to small ice crystal sizes and reduced sedimentationrates. Small Nc (resulting from strong competition betweenhomogeneous and heterogeneous freezing) leads to largeice crystals but may also lead to increased sedimentationrates, which in turn reduces the ice water content of thecloud. Further research is needed to assess what process(sedimentation/nucleation) determines the cirrus cloud icewater content under atmospheric conditions.[51] The size distribution of different aerosol species was

assumed to follow prescribed functions as presented inTable 1. This is not expected to introduce a bias forhomogeneous freezing however may introduce errors inNdust and Nbc, and therefore in NIN. The freezing fraction ofthe dust and black carbon is also expected to be higher forlarger aerosol size [e.g., Khvorostyanov and Curry, 2004;Welti et al., 2009]. Explicit aerosol dynamics is currently notconsidered but will be the subject of future work. Someuncertainty may also originate from the coarse GMI reso-lution (4° × 5°) used in this work. Using a finer resolutionmay lead to a slightly different Nc from differences in T andaerosol concentrations, particularly when competitionbetween homogeneous and heterogeneous freezing isimportant (although not enough to explain the features ofFigures 10 and 11). This, however, is not likely to signifi-cantly influence the relative difference in Nc from applica-tion of different heterogeneous freezing spectra. Thus, wehave favored the ability to run a large number of cases overusing a high resolution GCM. Nevertheless, the plethora ofIN treatments is placed for the first time within the sameglobal modeling dynamical framework. Despite the verylarge variability in IN concentration and relative contribu-tion of freezing seen, ice crystal number concentrations areless variable than we had initially anticipated. However, thelarge sensitivity of smax to the prevailing mechanism clearlypoints out that it too needs to be sufficiently constrained forcirrus optical properties and climate forcing to be correctlyrepresented in climate models.

Notation

agDHsMw

cpRT2� gMa

RT:

ad deposition coefficient of water vapor to ice.g acceleration of gravity.

bMap

Mwpoi�DH2

s Mw

cpRT2:

g G2G1:

cp specific heat capacity of air.DHs enthalpy of sublimation of water.

Ds*charjsi growth integral calculated at si (equation (3)).

Dv water vapor mass transfer coefficient.fc,hom, fc fraction of frozen particles at shomwith and with-

out IN present, respectively.fdust, fbc shape factor of the dust and black carbon,

respectively.

G1�iRT

4poiDvMwþDHs�i

4kaT

DHsMw

RT� 1

:

G2�iRT

2poiMw

ffiffiffiffiffiffiffiffiffiffiffiffi2�Mw

RT

r1

�d:

G effective growth parameter [cf. Barahona andNenes, 2008, equation (25)].

Jhom(shom) homogenous nucleation rate coefficient at shom.ka thermal conductivity of air corrected for non-

continuum effects.khom h om o g e n e o u s f r e e z i n g p a r a m e t e r ,

ln JhomðshomÞJhomðsiÞ ðshom � siÞ�1 [Barahona and Nenes,

2008].

lffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

�VG1�2

r:

Mw, Ma molar mass of water and air, respectively.

N*ffiffiffi2

p�V G1ð Þ3=2 � �

2�i�a

� ��1:

Ndust, Nbc number concentration of dust and black carbon,respectively.

Nc ice crystal number concentration.Nhet(si) cumulative heterogeneous freezing spectrum; IN

number concentration at si.Nhom ice crystal concentration from homogeneous

freezing.NIN IN number concentration.Nlim limiting NIN (minimum) that prevents homoge-

neous freezing.No number concentration of the supercooled liquid

droplet population.p ambient pressure.pio ice saturation vapor pressure.R universal gas constant.

ri, ra ice and air density, respectively.sh,dust, sh,bc value of si at which the dust and black freez-

ing fraction reaches unity, respectively.sh,mono characteristic freezing threshold of a monodis-

perse IN population.shom homogeneous freezing threshold.

si water vapor supersaturation ratio with respect toice.

si,sat value of si at 100% relative humidity.smax maximum ice supersaturation ratio.

T temperature.t time.V updraft velocity.

[52] Acknowledgments. This study was supported by NASAACMAP.

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D. Barahona and A. Nenes, School of Chemical and BiomolecularEngineering, Georgia Institute of Technology, Atlanta, GA 30332‐0340,USA. ([email protected])J. Rodriguez, NASA Goddard Space Flight Center, Greenbelt, MD

20770‐2548, USA.


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