An Empirical Parameterization of Heterogeneous Ice ... - AMS Journals

VOLUME 65

JOURNAL OF THE ATMOSPHERIC SCIENCES

SEPTEMBER 2008

An Empirical Parameterization of Heterogeneous Ice Nucleation for Multiple Chemical Species of Aerosol VAUGHAN T. J. PHILLIPS Department of Meteorology, University of Hawaii at Manoa, Honolulu, Hawaii

PAUL J. DEMOTT Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

CONSTANTIN ANDRONACHE Boston College, Chestnut Hill, Massachusetts (Manuscript received 26 June 2007, in final form 5 December 2007) ABSTRACT A novel, flexible framework is proposed for parameterizing the heterogeneous nucleation of ice within clouds. It has empirically derived dependencies on the chemistry and surface area of multiple species of ice nucleus (IN) aerosols. Effects from variability in mean size, spectral width, and mass loading of aerosols are represented via their influences on surface area. The parameterization is intended for application in largescale atmospheric and cloud models that can predict 1) the supersaturation of water vapor, which requires a representation of vertical velocity on the cloud scale, and 2) concentrations of a variety of insoluble aerosol species. Observational data constraining the parameterization are principally from coincident field studies of IN activity and insoluble aerosol in the troposphere. The continuous flow diffusion chamber (CFDC) was deployed. Aerosol species are grouped by the parameterization into three basic types: dust and metallic compounds, inorganic black carbon, and insoluble organic aerosols. Further field observations inform the partitioning of measured IN concentrations among these basic groups of aerosol. The scarcity of heterogeneous nucleation, observed at humidities well below water saturation for warm subzero temperatures, is represented. Conventional and inside-out contact nucleation by IN is treated with a constant shift of their freezing temperatures. The empirical parameterization is described and compared with available field and laboratory observations and other schemes. Alternative schemes differ by up to five orders of magnitude in their freezing fractions (⫺30°C). New knowledge from future observational advances may be easily assimilated into the scheme’s framework. The essence of this versatile framework is the use of data concerning atmospheric IN sampled directly from the troposphere.

1. Introduction Clouds govern the transfers of radiation that drive the circulation of the earth’s atmosphere. How cloud radiative properties might change in response to changing concentrations and composition of aerosol in the future is a great source of uncertainty in the prediction

Corresponding author address: Vaughan T. J. Phillips, Department of Meteorology, HIG, University of Hawaii at Manoa, 2525 Correa Road, Honolulu, HI 96822. E-mail: [email protected]

of global climate change. Recently, there has been much interest in predicting both the number and mass of cloud particles (e.g., Lohmann and Feichter 1997; Lohmann et al. 1999; Ming et al. 2006) in general circulation models (GCMs). The goal of such a “doublemoment” approach is to predict the size of cloud particles, and hence the radiative and microphysical properties of clouds, as a function of the aerosol in the environment. Heterogeneous nucleation of ice, by which crystals are formed on the insoluble components of aerosol particles, is one of the processes to be represented when

DOI: 10.1175/2007JAS2546.1 © 2008 American Meteorological Society

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predicting the crystal number with models. Current empirical formulas for heterogeneous nucleation (e.g., Meyers et al. 1992) rely on data from instruments that measure ice activation by exposure of aerosol to controlled conditions of temperature and humidity representative of supercooled clouds. The continuous flow diffusion chamber (CFDC) is one such device. Some direct comparisons by Rogers and DeMott (1995, 2002) between number concentrations of ice nuclei (IN) measured by the CFDC and of ice crystals formed in orographic wave clouds at similar temperatures demonstrate agreement to within a factor of 2 (see also Prenni et al. 2007a). Those particular wave clouds were outside the region where the Hallett–Mossop (H–M) process (Hallett and Mossop 1974) of ice multiplication is active (⫺3° to ⫺8°C) and below levels where homogeneous freezing can occur. Although the residence time of aerosol exposure to specified conditions inside the CFDC is short (7–15 s, depending on the project), there is observational evidence that activation of most IN occurs very soon after their ambient conditions for freezing are reached. First, nucleation of ice by mineral dust (e.g., by deposition) was seen by Möhler et al. (2006, p. 1554) to stop in less than about 10 s just after the supersaturation with respect to ice, si, reached its peak value at the cessation of cooling. Similarly, Vali (1994) observed that the freezing rate of drops was reduced by 97% in less than 30 s just after a cessation of supercooling. Ice formation ensues sharply within a very short distance of cloud edge during smooth flow into it (Cooper and Vali 1981). Second, the probability of freezing per second for a given IN particle has been observed to increase from zero to an extremely high value over an interval of about 1 K during supercooling near its characteristic freezing temperature, which is invariant over many freezing cycles (Shaw et al. 2005). That is why the error in the freezing fraction from an assumption of perfectly instantaneous freezing is seen to be equivalent to a temperature error of about 1°C (Vali 1994, p. 1852; see also Vali 1969, 1971). Third, laboratory observations (e.g., DeMott 1990; Möhler et al. 2006) show that frozen fractions of IN populations are independent of the cooling rate. This is all consistent with the assumption of almost instantaneous freezing when IN reach their characteristic freezing temperatures (the “singular hypothesis”; see Rau 1944; Levine 1950; Langham and Mason 1958; Vali 1971), which may depend on si and have a probability distribution among a given population of IN. Vali and Stansbury (1966) and Vali (1994) observed a stochastic aspect superimposed on nucleation temperatures defined by the singular nature of nucleation sites on the surface of IN. However, the first-order de-

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scription of the nucleation that they observed is provided by the singular hypothesis according to their analysis (e.g., Vali 1994, p. 1852). Marcolli et al. (2007) have confirmed this picture with laboratory studies of immersion freezing. Marcolli et al. inferred a distribution of rare but efficient active sites over the IN surface where ice embryos can form, as invoked by the singular hypothesis (see section 2). Evidence supporting the singular hypothesis is now sufficient for it to no longer be viewed as a mere hypothesis, as far as immersion freezing is concerned. It may also be valid for other modes such as deposition nucleation (e.g., Möhler et al. 2006), if the characteristic freezing temperatures are a strong function of si. In fact, si has been seen to be a good single descriptor of deposition nucleation (Huffman 1973) in observations of natural IN between ⫺12° and ⫺20°C (at much colder temperatures there may be an additional, weaker temperature dependence). Consequently, measured IN concentrations may be expressed in terms of si (e.g., Meyers et al. 1992), an approach followed here. A disadvantage of formulas based on CFDC data hitherto has been that they include no explicit dependencies on the multiple chemical species of insoluble aerosol, because of the lack of simultaneous aerosol data from other probes. Chen et al. (1998) have shown that ice-nucleating aerosol species at least include categories that can be described as carbonaceous, metallic, and dust aerosols. Within a given category, IN activity has been seen to increase with the aerosol loading (Georgii and Kleinjung 1967; Berezinskiy et al. 1986). There is a need for parameterizations of heterogeneous ice nucleation to be developed that reflect the diversity of IN chemistry and that are empirical, based on observations of IN sampled from the earth’s atmosphere. Almost all other parameterizations proposed in the past are based either on laboratory observations (Lohmann and Diehl 2006; Diehl and Wurzler 2004; Diehl et al. 2006) or on a form of classical theory that does not assume the singular hypothesis (Karcher and Lohmann 2003; Khvorostyanov and Curry 2004; Liu and Penner 2005; Pruppacher and Klett 1997, 341–344). In the present paper, a versatile framework for parameterizing atmospheric ice nucleation is formulated that 1) accounts for contributions from different chemical species of aerosol, as constrained by in situ measurements of IN activity (e.g., by the CFDC) and composition, and 2) represents the relative scarcity of nucleation seen at humidities well below water saturation at temperatures warmer than ⫺40°C (“warm subzero temperatures”). An advantage of this approach is that it is empirical, being based mostly on observations of natural IN sampled from the background free troposphere.

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In the next section there is a discussion of the empirical basis of the parameterization, including the assumed dependency on aerosol surface area. This allows the scheme to be applied to a wide range of aerosol scenarios globally, despite being based on field measurements at a single location. In subsequent sections, there is a detailed description of the scheme’s framework for known modes of nucleation, followed by a comparison with independent observations and alternative existing schemes. Advice about how to implement the scheme is given in another section. Its merits and limitations, and our vision for its future development, are discussed in the concluding two sections.

2. Observational basis for key assumptions of the parameterization of heterogeneous ice nucleation a. Classification of IN by chemical composition Chen et al. (1998) observed that the set of icenucleating aerosol species includes carbonaceous, metallic, and dust aerosols. A common representation of insoluble aerosols in GCMs is in terms of dust, organic carbon, and inorganic black carbon. Consequently, we partition the components of IN identified by Chen et al. for compatibility with current GCM design, in terms of the following basic groups: 1) dust/metallic aerosols (DM); 2) inorganic black carbon (BC); and 3) insoluble organic particles (O). The last group includes IN from bacteria (Vali et al. 1976; Lindow et al. 1978), leaf litters (Schnell and Vali 1972, 1976), pollen (Diehl et al. 2001; Diehl and Wurzler 2004), and perhaps oxalic acid dihydrate (OAD; Zobrist et al. 2006). An area of uncertainty concerns the choice of a single aerosol species to represent the insoluble organic group of IN. Oxalic acid occurs in aerosols (e.g., Narukawa et al. 2003; Murphy et al. 1998) and has a solid hydrate, OAD, that can nucleate ice (Zobrist et al. 2006). But whether solid OAD occurs significantly in the atmosphere is a moot point. Biogenic aerosols may constitute about 10% of all submicron aerosols in the troposphere (Jaenicke 2005). A few species of bacteria can nucleate ice (e.g., Vali et al. 1976; Morris et al. 2004) and originate from plants (Lindemann et al. 1982; Lindemann and Upper 1985). Pollen (exceeding 10 ␮m) and leaf litter, for example, can nucleate ice, as noted above, but pollen is too large to stay in the atmosphere for long. If pollen or leaf litter break up, their fragments may be numerous at submicron sizes but have a nucleating ability that few studies have examined. That of ice-nucleation active (INA) strains of bacteria has been quantified in several studies (e.g., Vali et al. 1976; Lindow et al. 1978; Hirano et al.

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1985). For these reasons, the nucleating ability of the O group of IN is constrained by observations of INA bacteria, as well as by analysis of crystal residual material (e.g., Targino et al. 2006).

b. Relation of numbers of active IN to total surface area of a given aerosol species A fundamental assumption of the proposed scheme is that the number of active IN of a particular species of insoluble aerosol is approximately proportional to the total surface area of its aerosol particles (see section 3a). There is a strong theoretical basis for such a dependence on surface area (e.g., Pruppacher and Klett 1997). Heterogeneous nucleation is an interface phenomenon involving the formation, on the surface of the IN material, of critical ice embryos on the nanometer scale at specific sites. Such active sites have a certain probability of occurrence per unit area of the surface of a given IN material. The sites are determined by (e.g., crystallographic) features of the surface, and each one nucleates ice close to a unique, characteristic temperature (e.g., Vali 1994; Shaw et al. 2005). Such active sites have a high compatibility with the lattice structure of the ice embryo, but they are rare. Larger IN particles have more and better active sites than smaller ones, which is why they are more likely to have a highernucleating efficiency. The natural singular character of IN emerges from the probability distribution of nucleation efficiencies, and hence of characteristic freezing temperatures, among IN particles (e.g., Marcolli et al. 2007). This distribution of nucleation efficiencies arises from that of the “contact angle” (i.e., suitability of an individual site to trigger nucleation) among active sites on IN particles. At least two strands of observational evidence support this assumed dependence on surface area for soot and dust, respectively. First, the number of crystals nucleated by immersion freezing of acetylene soot has been observed to be proportional to its total surface area (DeMott 1990). Second, observations of atmospheric IN sampled from the free troposphere by the CFDC described by Rogers et al. (2001a) are analyzed here for two contrasting cases: 1) the First Ice Nuclei Spectroscopy Study (INSPECT-1) during 1–19 November 2001 at Mt. Werner [106.73°W, 40.45°N; 3.22-km altitude above mean sea level (MSL)] in Colorado (DeMott et al. 2003a), with aerosol surface area derived from measurements with various probes and aerosol loadings measured by the Interagency Monitoring Program for Visual Environment filter data (IMPROVE; http://vista.cira.colostate.edu/improve) at Mt. Zirkel nearby; and 2) the Second Ice Nuclei Spectroscopy Study (INSPECT-2) during April–May 2004 also at Mt.

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FIG. 1. Daily averages of the ratio ␨ of the measured IN number to surface area (number per meter squared) of dust particles smaller than 2.5 ␮m in diameter as a function of supersaturation with respect to ice within the CFDC for periods from two field campaigns near Mt. Werner (INSPECT-1 and INSPECT-2). CFDC observing periods were at least 40 min on any day. Averages from two brief samples (10 min each) for Saharan dust layers (28–29 Jul 2002) over Florida in CRYSTAL-FACE (DeMott et al. 2003b) are also shown. Also shown are corresponding values of ␨ that we have inferred for the dust (100–200 nm in diameter) sampled from the earth’s crust in Asia and studied by Archuleta et al. (2005).

Werner (Richardson et al. 2007), where similar aerosol measurements were made. Surface area of dust (larger than 500 nm) was inferred from aerosol size distribution data from the TSI Aerodynamic Particle Sizer (APS) instrument (INSPECT-1), Differential Mobility Analyzer (DMA), and an optical particle counter (INSPECT-2; Richardson et al. 2007), combined with measurements of dust loading either near Mt. Werner on a daily basis (INSPECT-2) or by IMPROVE nearby at Mt. Zirkel (INSPECT-1; DeMott et al. 2003a). Spherical equivalent sizes and ␳DM ⫽ 2.3 g cm⫺3 were assumed. Figure 1 shows daily averages of the ratio (␨) of the number of active IN to total surface area of dust particles inside the CFDC (smaller than about 1 ␮m in equivalent spherical diameter) as a function of the supersaturation with respect to ice, si, imposed inside the CFDC. Despite the average dust loadings of both campaigns (INSPECT-1 and -2) differing by an order of magnitude (about 0.2 and 1.3 ␮g m⫺3) and despite limited fluctuations in dust size, approximately the same relation between ␨ and si is seen throughout both cases. This normalized IN number increases logarithmically with si, resembling the trend seen by Meyers et al. (1992). Mineral dust was the most prevalent IN measured (by CFDC) during INSPECT (e.g., section 3a; Fig. 2). The constancy of the relation between ␨ and si seen throughout both cases is consistent with the above

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FIG. 2. Percent elemental composition of IN residual material from crystals collected from the troposphere under conditions of heterogeneous freezing in the following field campaigns: 1) National Aeronautics and Space Administration (NASA) subsonic aircraft: Contrail and cloud effects special study (SUCCESS; Chen et al. 1998); 2) NASA FIRE-ACE (Rogers et al. 2001b); 3) NASA CRYSTAL-FACE (DeMott et al. 2003b); 4) INSPECT-1 (DeMott et al. 2003a); 5) INSPECT-2 (Richardson et al. 2007); and 6) the Mixed-Phase Arctic Cloud Experiment (M-PACE) (Prenni et al. 2007b). The chemical composition was determined by transmission electron microscopy energy dispersive X-ray spectral analysis (TEM-EDS). The DM category represents dust and metallic material, while C denotes all carbonaceous aerosol (both organic and inorganic). The inference of a C categorization is based on the absence of any X-ray spectral signal (above grid blank values) from other elements, which could still be present at less than 10% of particle mass without being seen. The category denoted as “other” includes unusual mixed particles (not dustsulfate mixtures, which are categorized as DM) and particles for which sulfates and salts provided the major elemental signatures. The number of residual particles classified is denoted in brackets.

assumption of proportionality between IN activity and total surface area of the dust, at any given value of si. Also shown in Fig. 1 are two brief episodes (10 min each) of data from dusty days (28–29 July 2002) of the Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida-Area Cirrus Experiment (CRYSTALFACE) (DeMott et al. 2003b). The upper size limit for surface area relevant to the CFDC measurements was 1.5 ␮m in CRYSTAL-FACE, instead of 1.0 ␮m in the INSPECT studies, because of the choice of the inlet impactor used for all instruments. The surface area of dust (larger than 500 nm) in CRYSTAL-FACE is derived from aircraft measurements from the Cloud and Aerosol Spectrometer (CAS; Droplet Measurement

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Technologies, Boulder, Colorado). Although all samples displayed in Fig. 1 are significant with regard to total numbers of IN acquired, the sampling of the troposphere is much less extensive in CRYSTAL-FACE. The Saharan atmospheric dust (80 ␮g m⫺3) seen in CRYSTAL-FACE was advected to Florida within a dry layer (all particles larger than 500 nm were assumed to be dust). The value of ␨ is slightly higher (CRYSTAL-FACE) by almost an order of magnitude than for the background troposphere (INSPECT). We speculate that dust in the layer is likely to be freshly emitted and younger than dust in the background free troposphere. Moreover, our analysis of laboratory observations by Archuleta et al. (2005) of unprocessed Asian dust (0.1 and 0.2 ␮m in diameter) sampled from the earth’s crust reveals values of ␨ consistently higher by almost two orders of magnitude than for INSPECT over a wide range of si (Fig. 1). These observations are at least consistent with a hypothesis of microphysical and/or chemical atmospheric processing of dust acting to lower the nucleating ability during long-range transport after emission from the earth’s surface (section 7). In summary, concentrations of active IN of a given species are proportional to its aerosol surface area (in the large mode, for atmospheric IN). However, the constant of proportionality differs with aerosol age and other environmental factors (section 7).

c. Scarcity of heterogeneous ice nucleation caused by subsaturated conditions at warm subzero temperatures An area of uncertainty concerns the degree to which heterogeneous nucleation occurs in the troposphere at low humidities well below water saturation at warm subzero temperatures (i.e., warmer than about ⫺40°C). Heymsfield and Miloshevich (1995) observed that ice formed only at relative humidities exceeding 90% in the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment, phase II (FIRE-II), for temperatures between ⫺35° and ⫺40°C. Soot particles produced virtually no nucleation when held in constant conditions subsaturated with respect to water at temperatures warmer than ⫺30°C (Dymarska et al. 2006). DeMott et al. (1999) observed that nucleation of ice by soot at ⫺30°C occurred only at water saturation (see also Möhler et al. 2005a). When humidities well below water saturation were imposed in the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) chamber, dust was seen to act as IN (e.g., by deposition) at temperatures colder (but not warmer) than ⫺15°C with “active fractions” (fraction of the number lost by ice nucleation) that were higher than 0.1% (the threshold for their detection) and lower than

for the immersion mode (3%–8% at about ⫺20°C) at the same temperature (O. Möhler 2006, personal communication). Field et al. (2006) observed no heterogeneous nucleation of desert dust at detectable active fractions higher than 0.5% for temperatures warmer than about ⫺40°C at humidities well below water saturation at AIDA. Consequently, the active fraction for dust studied at AIDA is on the order of 0.1% at ⫺20°C at humidities well below water saturation.

3. Description of empirical parameterization of heterogeneous ice nucleation for dust, black carbon, and insoluble organic particles For compatibility with current GCM design, icenucleating aerosol species are partitioned into three groups: dust/metallic, black carbon, and insoluble organic aerosols (see section 2). The proposed parameterization of heterogeneous ice nucleation for these species is described here. Variables and constants are defined in appendix A.

a. Nucleation of ice by condensation and immersion freezing and by deposition 1) REFERENCE

ACTIVITY SPECTRUM OF TOTAL

ACTIVITY FROM

CFDC

IN

DATA IN

BACKGROUND-TROPOSPHERE SCENARIO

A reference activity spectrum of the average number concentration of IN, nIN,1,* (number of active IN per kilogram of air), is constructed from field observations with the CFDC (Rogers et al. 2001a) for a backgroundtroposphere scenario (denoted by the subscript *) at the Storm Peak Laboratory on Mt. Werner (see section 2) for 1–19 November 2001 (INSPECT-1; DeMott et al. 2003a). The reference spectrum describes the IN activity at water saturation for this scenario, as inferred from the CFDC observations. The CFDC was modified for the field experiment to operate at temperatures colder than ⫺60°C. The scenario is so called because the INSPECT-1 data are assumed to be representative of the background state of the free troposphere. It includes a diverse mixture of IN species. During the background-troposphere scenario, loadings of aerosol particles with equivalent spherical (dry) diameters smaller than 2.5 ␮m were measured by IMPROVE at Mt. Zirkel near the site at Mt. Werner (DeMott et al. 2003a). Measurements with the CFDC were made at temperatures between about ⫺40° and ⫺60°C, at humidities below those for the onset of any homogeneous aerosol freezing, and at aerosol (dry) diameters less than 1 ␮m (denoted by the subscript 1; the aerodynamic size of the CFDC inlet impactor). They

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are characterized by this expression, which is extrapolated to ⫺35°C and to temperatures (T ) colder than ⫺70°C (the deposition mode depends mainly on Si; see section 1): C nIN,1,* 共T, Si兲 ⫽ c1{ exp关12.96共Si ⫺ 1.1兲兴}0.3Ⲑ␳C for

T ⱕ ⫺ 35⬚C

and

1 ⬍ Si ⱕ S hom . i

共1兲

Si(T, Q␷) is the saturation ratio of water vapor with respect to ice, where Q␷ is the vapor mixing ratio and S hom i is the value of Si at the onset of homogeneous aerosol freezing. Also, c1 ⫽ 1000 m⫺3, and ␳C ⫽ 0.76 kg m⫺3 is the air density inside the CFDC (for an operating pressure of 500 mb). This empirical formula includes nucleation by deposition and by condensation and immersion freezing, resembling that presented by DeMott et al. (2004). These CFDC measurements were done below water saturation and only involved ice nucleation by interstitial IN. At high humidities approaching water saturation, the full contribution from condensation and immersion freezing is difficult to measure because of the onset of homogeneous freezing. Equation (1) is extrapolated to the value of Si at water saturation, Sw i (T ). A factor of ␥ ⯝ 2 then yields the reference activity spectrum, describing heterogeneous nucleation in the background-troposphere scenario at water saturation: C nIN,1,*共T, Si兲 ⫽ nIN,1,* 共T, Si兲␥ for

T ⱕ ⫺ 35⬚C

and 1 ⬍ Si ⱕ S w i .

共2兲

Justification for our choice of ␥ is that the IN concentration measured by the CFDC between ⫺30° and ⫺35°C in INSPECT-1 (DeMott et al. 2003a) doubles w ⫺1 from about 3 L⫺1 [⬇ nC as the IN,1,*(T, S i )␳C] to 6 L relative humidity with respect to water increases from 97% to 100%. Such jumps of IN activity are explicable in terms of an intensification of condensation and im-

mersion freezing when IN-containing aerosols swell with uptake of water as water saturation is approached, diluting the associated dissolved solute and raising the heterogeneous freezing temperature. This is consistent with our estimate (appendix B) that the dissolved solute’s depression of the heterogeneous freezing temperature must change from about 4 K (97% relative humidity) to less than about 0.1 K (water saturation) at ⫺30°C, boosting IN activity by about a factor of 2. Jumps of IN activity are excluded from Eq. (1) because they coincide with onset conditions for homogeneous aerosol freezing. Both forms of freezing, with and without IN, are suppressed by the humidity-sensitive solute concentration. The reference spectrum above is then extrapolated to temperatures warmer than ⫺25° by rescaling the formula from Meyers et al. (1992) with a normalization factor ⌿: nIN,1,*共T, Si兲 ⫽ ⌿c1 exp关12.96共Si ⫺ 1兲 ⫺ 0.639兴 for T ⱖ ⫺ 25⬚C

冋

n˜IN,1,*共T, Si兲 nÎN,1,*共T, Si兲

册

and

1 ⬍ Si ⱕ S w i .

共3兲

Here, ⌿ is selected to be 0.058707␥/␳C m3 kg⫺1, so as to match it with nIN,1,* in Eq. (2) at ⫺30°C (with extrapolation of both equations) and water saturation (in the case of condensation- and immersion-freezing modes). The factor ⌿ is much less than unity, probably because of a difference in aerosol mass loading due to height and other factors (e.g., time of year, geographic location) between the two datasets from Meyers et al. (1992) (continental boundary layer, rich with IN) and DeMott et al. (2003a) (free troposphere). For T between ⫺35° and ⫺25°C, nIN,1,* is interpolated between values ñIN,1,* and nÎN,1,* (appendix A) obtained from extrapolation to T of Eqs. (2) and (3), respectively:

nIN,1,*共T, Si兲 ⫽ min 关 nIN,1,*共T, Si兲, nmax共T 兲兴 for ⫺35 ⬍ T ⬍ ⫺25⬚C

nIN,1,*共T, Si兲 ⫽ nÎN,1,*共T, Si兲

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and

1 ⬍ Si ⱕ S w i ,

共4兲

0

␦1共T,⫺35,⫺25兲

for ⫺35 ⬍ T ⬍ ⫺ 25⬚C; 1 ⬍ Si ⱕ S w i ,

0.3 for ⫺35 ⬍ T ⱕ ⫺30⬚C, nmax共T 兲 ⫽ c1兵exp关12.96共S w i 共T 兲 ⫺ 1.1 兲兴其 ␥Ⲑ␳C

nmax共T 兲 ⫽ ⌿c1 exp关12.96共S w for ⫺30 ⬍ T ⬍ ⫺25⬚C . i 共T 兲 ⫺ 1 兲 ⫺ 0.639兴

Such an interpolation is necessary to acquire a smooth transition between temperature ranges of validity of Eqs.

and

共5兲共6兲共7兲

(2) and (3). For Eqs. (2)–(7), the input value of Si is artificially prevented from exceeding water saturation.

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2) GENERAL

EQUATIONS OF SOURCE OF CRYSTAL

NUMBER FOR ANY AEROSOL SIZE DISTRIBUTION AND LOADING

CFDC measurements in the background-troposphere scenario are assumed to have contributions from the basic groups [DM, BC, and O (roman upper case “O,” short for “organic”)] of insoluble aerosol (nIN,1,* ⫽ nIN,DM,* ⫹ nIN,BC,* ⫹ nIN,O,*). In general, for any scenario of aerosol loading, the number mixing ratio of active IN (all aerosol sizes) also has contributions from the same groups: nIN ⫽

兺n

共8兲

IN,X ,

X

where X ⫽ DM, BC, O for dust/metallic, black carbon, and organic aerosols, respectively. As justified in section 2, the number concentration of active IN from group X within the size interval d logDX increases with aerosol surface area: nIN,X ⫽

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冕

⬁

兵1 ⫺ exp关⫺␮X 共DX, Si, T 兲兴其

log关0.1 ␮m兴

⫻

dnX d logDX, d logDX

␮X ⫽ HX 共Si, T 兲␰共T 兲 T ⬍ 0⬚C

and

冉

共9兲

冊

d⍀X ␣X nIN,1,* ⫻ for ⍀X,1,* dnX

1 ⬍ Si ⱕ S w i .

共10兲

⌻he term ⍀X is the total surface area of all aerosols with dry diameters larger than 0.1 ␮m, per unit mass of air (the surface area mixing ratio) in group X (including interstitial IN and IN immersed in cloud liquid), and d⍀X /dnX ⬇ ␲D2X . Here, ␮X is the average of the number of activated ice embryos per insoluble aerosol particle of size DX . This integer number is assumed to be statistically (Poisson) distributed. The number mixing ratio of aerosols in group X is nX . This minimum value of IN diameter (0.1 ␮m) has been introduced because central (aerosol) residual particles of snow crystals have been observed to be usually larger than that size (e.g.,

Pruppacher and Klett 1997; Chen et al. 1998; Prenni et al. 2007a; see also Marcolli et al. 2007). Here, ⍀X,1,* is the component of ⍀X due to aerosols with diameters between 0.1 and 1 ␮m in the background-troposphere scenario. Such aerosols caused the observed ice nucleation inside the CFDC. Note that at low freezing fractions (e.g., at warm subzero temperatures) ␮X K 1 and nIN,X ⬇ HX (Si, T )␰(T )(␣X nIN,1,*/⍀X,1,*) ⫻ ⍀X. Hence, Eqs. (9)–(10) express the fundamental assumption justified in section 2 that the number concentration of active IN from aerosol particles (larger than 0.1 ␮m) in group X is approximately proportional to their surface area. Values of ⍀X or dnX /d logDX may be inferred from the predicted mass (and/or number) mixing ratio QX (and/or nX) of environmental aerosols in group X, for an assumed form of the aerosol size distribution. Until the cloud-free environment is reached, ⍀X and QX (and/or nX) are not depleted by ice nucleation. The term HX (Si , T ) in Eq. (10) is an empirically determined fraction (0 ⱕ HX ⱕ 1) representing the scarcity of heterogeneous nucleation of ice seen in substantially subsaturated conditions (see section 2). At water saturation, H X ⫽ 1. In the backgroundtroposphere scenario, ␣X is the fractional contribution from aerosol group X to the IN concentration (when HX ⫽ 1) inferred from CFDC data. The factor ␰ takes into account the observation that drops containing IN are typically seen not to freeze at temperatures warmer than about ⫺2°C (e.g., Fig. 9). At temperatures colder than ⫺5°C and warmer than ⫺2°C, ␰ is assigned values of unity and zero, respectively, with a cubic interpolation (␦; appendix A) in between. Measurements with the CFDC cannot be made at such warm temperatures, as the instrument relies on a gradient of temperature being established between its walls to create supersaturation. Laboratory observations suggest that when Si and T (°C) are less than critical thresholds (S X i,0 and TX 0 ), rates of nucleation of ice are negligible or very low. Consequently, HX for X ⫽ DM and BC is defined as

HX 共Si, T 兲 ⫽ min 兵 fC ⫹ 共1 ⫺ fC 兲␦10关 Sw共Si, T 兲, Sw,0, 1兴, 1其, X

and,

X 1 X X fC ⫽ ␦ h1 共T, T X 0 , T 0 ⫹ ⌬T 兲␦0共Si, S i,0 , S i,0 ⫹ ⌬Si 兲Ⲑ␥.

Here, fC represents the contribution to HX from modes of nucleation (e.g., deposition) in subsaturated conditions giving rise to the CFDC data fitted by Eq. (1). This data was measured at humidities below the onset

共11兲共12兲

of homogeneous aerosol freezing. At such humidities HX ⬃ 1/␥, because the contributions from group X to the IN concentration observed (␣X n C IN,1,*) and predicted [Eqs. (2) and (9)–(10)] for the background-

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FIG. 3. Visualization of HX plotted as a function of temperature (°C) and saturation ratio with respect to ice (Si) for (a) dust and (b) soot. The diagonal upper edge of the surface, where HX → 1, corresponds to exact water saturation.

troposphere scenario in the same aerosol size range (approximately nIN,X,* ⍀X,1,*/⍀X,*) must then be equal. The extra term in Eq. (11) involving Sw, which is the saturation ratio with respect to water, represents enhancement of immersion and condensation freezing at higher humidities approaching water saturation (the jump noted above). Uptake of liquid by soluble coatings on IN particles then reduces the concentration of dissolved solute, making freezing more likely. Here, ␦ba provides an interpolation (appendix A) over intervals ⌬⌻ and ⌬Si of temperature and saturation ratio with respect to ice, while hX is the small fraction to which ␦ is reduced by warming over ⌬⌻. Figure 3 displays HX for dust and black carbon. The number of crystals generated in a time step ⌬t is given by ⌬ni ⫽

兺 max共n

IN,X

X

⫺ nX,a, 0兲 ⬅

兺 ⌬n

X,a ,

共13兲

X

where nX,a is the number mixing ratio of IN from group X that has already been activated. When incrementing ni by ⌬ni, then nX,a is also incremented by ⌬nX,a ⫽ max(nIN,X ⫺ nX,a, 0) for each group X. In the cloud-free environment, nX,a is set to zero in the manner of Cohard and Pinty (2000), while QX (and/or nX) is reduced to account for previous losses from ice nucleation. This

implicitly assumes that insoluble matter from the three basic groups of IN is not mixed together (“internally”) in the same aerosol particle, which seems realistic for dust (e.g., Clarke et al. 2004). Nonetheless, fragments of biogenic material may stick to dust in the troposphere (e.g., Schnell and Vali 1976; Griffin et al. 2001). Insoluble organic and inorganic carbon often tends to be mixed internally; such internal mixing may optionally be treated by modifying Eq. (13) (e.g., increment nX,a for each insoluble component of an internal mixture whenever one component nucleates ice). In summary, Eqs. (1)–(13) predict the change in crystal number ⌬ni which is the output from the empirical parameterization. The inputs are Si and T, while ⍀X (e.g., inferred from QX, nX), as well as nX,a are all both inputs and outputs. The essence of the scheme’s versatile framework lies in Eqs. (8)–(10), which may easily be adapted for extra groups of IN and empirical refinements to parameters (e.g., HX). In principle, it would be possible to resolve explicitly the nucleation of ice by IN immersed in cloud liquid (condensation- and immersion-freezing modes) created by the cloud condensation nuclei (CCN) activation of their solute, if “in-cloud” scavenging of IN, involving the removal of their cloud liquid by precipitation, is included (see section 5). The number of immersed (or

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PHILLIPS ET AL.

interstitial), active IN, nIN,X,imm (or nIN,X,int), could be derived from Eqs. (9)–(10) by replacing ⍀X with ⍀X,imm (or ⍀X,int) and applying it to nIN,1,* a shift, ⌬TX,imm, of the freezing temperature of IN between interstitial and immersed states at water saturation (or applying none). However, ⌬TX,imm is so small (⬍0.1 K; appendix B) for soluble coatings typically seen in the free troposphere that there seems little point in doing this. At water saturation, nucleation by such IN seems insensitive to whether they are immersed or interstitial.

3) EMPIRICAL

DETERMINATION OF VALUES OF

PARAMETERS

Following Chen et al. (1998), DeMott et al. (2003a), and Heintzenberg et al. (1996), and in view of the observed composition of IN from heterogeneous crystals collected in six field campaigns shown in Fig. 2, we assign ␣DM ⫽ 2/3, requiring that ␣BC ⫹ ␣O ⫽ 1/3, the fraction for all carbonaceous aerosol. The relative assignments of values for ␣BC and ␣O are not evident from such studies, as few data were collected to distinguish the nature of the carbonaceous aerosols. Although the fractions ␣X in Eq. (10) might be expected to depend on temperature and humidity, in the absence of unequivocal observational data they are assumed to have constant values. Future advances in knowledge may change this (section 7). For group O, INA strains of bacteria have been selected as partially representative (see section 2). Cells belonging to INA strains may form only a small fraction, fINA ⬃ 1% (Lindemann et al. 1982), of all bacteria in the troposphere. In view of the wide range of available estimates (⬃10–1000 L⫺1; appendix C), the concentration of all bacterial cells in the backgroundtroposphere scenario is assigned as Nbac ⫽ 100 L⫺1. The freezing fraction of cells belonging to INA strains is assumed to be about 10⫺4 at ⫺5°C (Gross et al. 1983; Hirano et al. 1985) and about gfr,30 ⫽ 0.1 at ⫺30°C by extrapolation with observed temperature dependencies (Vali et al. 1976; Gross et al. 1983). Impurities in water used for diluting cultures contributed to a lack of observational data at colder temperatures. The estimated number of crystals nucleated by bacteria in the background-troposphere scenario at water saturation and ⫺30°C is gfr,30 fINANbac ⬃ 0.1 L⫺1. In view of CFDC observations in such conditions [Eq. (3)], INA bacteria may contribute about 0.03 to ␣O. Yet there is significant uncertainty in Nbac (appendix C), fINA, and ␣O. Also, there is uncertainty about how representative Pseudomonas syringae (Ps) is for the nucleation by bacteria in the troposphere. Other species with INA strains (e.g., Erwinia herbicola) have been seen to

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be sometimes more significant in ice nucleation than Ps (e.g., Lindow et al. 1978; Kaneda 1986). In nature, there may be many contributions to ␣O from nucleation of ice by various types of biogenic and/ or nonbiogenic insoluble organic aerosol. Of the residual aerosol particles from heterogeneous ice crystals sampled from wave clouds, 14% was found to be composed of organic carbon and not sulfate (Targino et al. 2006). Other analyses (e.g., DeMott et al. 2003a; Cziczo et al. 2004; Richardson et al. 2007) have revealed that about 13%–20% of residual particles are dominated by either sulfate or organic carbonaceous matter. This organic/sulfate residual material might not have been responsible for nucleation of the ice sampled. Also, sulfate can crystallize and then nucleate ice (e.g., Abbatt et al. 2006). In view of the paucity of observational data, a parsimonious assumption is that up to about half of residual particles classified as partially organic may have acted as insoluble organic IN. That would suggest ␣⌷ is between 0.03 and 0.1, approximately. An intermediate value of ␣O ⫽ 0.06 is assumed here, so that ␣BC ⫽ 1/3 ⫺ 0.06 from the constraint noted above. This value of ␣⌷ is much larger than the fraction (0.005) of oxalate-containing heterogeneous crystals observed in CRYSTAL-FACE (Cziczo et al. 2004). Origins of parameters for the factor HX and most other parameters in Eqs. (10)–(12) are summarized in Table 1 (see also appendix A). Soot in the free troposphere is assumed to be coated with so much soluble material that its onset of nucleation occurs by condensation and immersion freezing. Experimental data in subsaturated conditions are scarce (e.g., Levin et al. 1980; Diehl et al. 2001), so it is assumed that HO ⫽ HBC always. Values of ⍀X,1,* (Table 2) are partially constrained by IMPROVE measurements of the mass loading of aerosols smaller than 2.5 ␮m in (dry) diameter (QX,2.5,*; appendixes A and D) made during observing periods of the CFDC in the backgroundtroposphere scenario. For the carbanaceous aerosol, recent tropospheric observations of average sizes and spectral widths of aerosol size distributions and bulk densities (Table 3) are invoked to infer ⍀X,1,* from QX,2.5,*.

b. Conventional and inside-out contact freezing The fundamental assumption here is that each IN particle can nucleate ice either by contact freezing or by immersion or condensation freezing, depending on local conditions of temperature, humidity, and availability of supercooled liquid. Shaw et al. (2005) observed that a given IN particle of about 0.1 mm in size has a freezing temperature for the surface mode (contact nucleation) that is ⌬TCIN ⬇ 4.5°C higher than for the

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TABLE 1. Origins of values for most empirical parameters (e.g., HX) in Eqs. (10)–(12) together with their values. These include Heymsfield and Miloshevich (1995), DeMott et al. (1999), Zuberi et al. (2002), DeMott et al. (2003a), Field et al. (2006), and Möhler et al. (2006) (referred to as HM95, D99, Z02, D03, F06, and M06, respectively). Note that HO ⬅ HBC. Also, S DM i,0 was estimated with a cubic fit to data from HM95 (between ⫺45° and ⫺56°C), M06 for Saharan dust (colder than ⫺60°C), F06 (⫺40°C), and assuming S DM i,0 ⫽ 1.1 near ⫺20°C to reproduce some very recent observations from the AIDA chamber (see section 2c), which also determined hDM. Also, Sw,0 is constrained by the observed humidity threshold for the jump of IN activity near water saturation seen by D03 (⫺30° to ⫺35°C), assumed to be obscured by homogeneous aerosol freezing at colder temperatures. Finally, the value of S BC i,0 at temperatures colder than ⫺50°C is inferred by shifting the Si value, for the onset of immersion freezing of giant dust (Z02), to match corresponding observations for soot by D99. At temperatures outside the ranges of validity shown for polynomials, T may be thresholded to their upper or lower bounds. Symbol

Value

Origin

DM

0.15 0 1 ⫹ 10x for ⫺80 ⬍ T ⬍ 0°C a0 ⫹ a1(T ⫹ 273.15) ⫹ a2(T ⫹ 273.15)2 ⫺ ⌬Si for 198 ⬍ T ⫹ 273.15 ⬍ 239 K where a0 ⫽ 0.5652, a1 ⫽ 1.085 ⫻ 10⫺2 and a2 ⫽ ⫺3.118 ⫻ 10⫺5 0.97 0.1 ⫺40°C ⫺50°C 5°C b0 ⫹ b1T ⫹ b2T 2 ⫹ b3T 3 for ⫺80 ⬍ T ⬍ 0°C where b0 ⫽ ⫺1.0261, b1 ⫽ 3.1656 ⫻ 10⫺3, b2 ⫽ 5.3938 ⫻ 10⫺4 and b3 ⫽ 8.2584 ⫻ 10⫺6 2/3 1/3–0.06 0.06 2 ␦01(T, ⫺5, ⫺2)

Section 2 D99, section 2 M06, F06, HM95, section 2 Z02/D99

h hBC S DM i,0 S BC i,0 Sw,0 ⌬Si T DM 0 T BC 0 ⌬T x

␣DM ␣BC ␣O ␥ ␰ (T )

bulk-water mode (immersion and condensation freezing), irrespective of the following factors: 1) whether the contact-IN (CIN) approaches the air–water interface from inside or outside the liquid; 2) the chemical composition of IN particles examined, which were glassy and/or crystalline; and 3) their size (larger than 0.1 mm; R. Shaw 2006, personal communication). Thus, it is assumed that the same temperature difference applies to atmospheric IN. Yet there is significant experimental uncertainty associated with this assumption (e.g., DeMott 1995). The number mixing ratio of potentially active, interstitial CIN nX,cn is then simply related to that of immersion- and condensation-freezing IN [Eqs. (2) and (3)]: nX,cn ⯝ ␣X ␰共T 兲

再

冎

nIN,1*关T ⫺ ⌬TCIN, S w i 共T ⫺ ⌬TCIN 兲兴 ⍀X,int. ⍀X,1,* 共14兲

Here, ⍀X,int is the component of ⍀X for interstitial IN. The fundamental behavior of water molecules near the air–water interface is known strongly to favor freezing there (e.g., Vrbka and Jungwirth 2006). This is consis-

D03 M06 F06 D99 D99 See caption D03/section 3a(3) Section 3a(3) Section 3a(3) D03 Section 3a(2)

tent with the above observation that the exact nature of the IN is not the first-order dependence of ⌬TCIN. For an interstitial CIN to nucleate an ice crystal, it must collide with a supercooled cloud droplet. Sources for the rate of CIN-droplet collisions arise from the forces of Brownian diffusion (Br), thermophoresis (Th), and diffusiophoresis (Di) acting on the CIN aerosol. Electrophoretic forces may also be included, if deemed significant. The increment of crystal number

TABLE 2. Origins and observed values from the backgroundtroposphere scenario of baseline surface area mixing ratios, ⍀X,1,*, of insoluble aerosols (all dry diameters between 0.1 and 1 ␮m) in groups X ⫽ {DM, BC, O}. A water-soluble fraction for organic carbon of gW ⫽ 0.83 (Zappoli et al. 1999, Z99; see also Mayol-Bracero et al. 2002, MB02; Yang et al. 2004, Y04) has been assumed, which matches the volatile fraction assumed (appendix D). For X ⫽ DM, the geometric mean of daily values of surface area mixing ratio was estimated, based on measurements of aerosol size distributions (ASDs) seen during INSPECT-1 (section 2; Fig. 1). X

⍀X,1,*

DM BC O

⫺7

Origin ⫺1

5.0 ⫻ 10 m kg 2.7 ⫻ 10⫺7 m2 kg⫺1 9.1 ⫻ 10⫺7 m2 kg⫺1 2

INSPECT-1 (ASD data) IMPROVE, appendix D IMPROVE, appendix D, Z99, MB02, Y04

SEPTEMBER 2008

mixing ratio ni due to contact nucleation in time step ⌬t is given by ⌬ni ⫽

兺 min再⌬t 兺 max冋冉 ⭸t 冊 ⭸ni

j

⫹

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PHILLIPS ET AL.

冉冊 ⭸ni ⭸t

X

⫹ Di,X, j

冉冊 ⭸ni ⭸t

Th,X, j

册冎

, 0 , nw, j . Br,X, j

共15兲

All three source terms are described by Young (1974), Cotton et al. (1986), Pruppacher and Klett (1997, 724– 728), and Ovtchinnikov and Kogan (2000). The thermophoretic source, which usually prevails, is a function of the in-cloud supersaturation. These sources are a

⌬ni ⫽ min

再兺冋 max

X

function of max (nX,cn ⫺ nX,a, 0). Contact nucleation is performed separately for each jth size bin of cloud droplets. Thermal conductivities of CIN are Kaero,X ⫽ 0.25, 4.2, and 0.2 W m⫺1 K⫺1 for X ⫽ DM, BC, and O (Seinfeld and Pandis 1998; Ovtchinnikov and Kogan 2000). Their mean radii (Raero,X) may be prescribed (appendix A) or predicted. The exotic mechanism of inside-out contact nucleation (Durant and Shaw 2005; Shaw et al. 2005) may also be represented, if in-cloud scavenging of insoluble aerosol is treated (see section 5). An extra source then arises:

册冎

nX,cn共T 兲⍀X,imm Ⲑ⍀X,int ⫺ nX,a,imm |⌬nw|, 0 , |⌬nw| . nw

Here, nX,a,imm and ⍀X,imm are components of nX,a and ⍀X, respectively, for IN immersed in cloud liquid. Then nX,a,imm ⬇ nX,a⍀X,imm/⍀X, where ⍀X ⫽ ⍀X,int ⫹ ⍀X,imm. All CIN particles immersed inside evaporating cloud droplets are assumed to be brought into contact, eventually, with their vanishing liquid surfaces. Here, |⌬nw|

共16兲

is the number of supercooled cloud droplets depleted by total evaporation (e.g., Phillips et al. 2007) in ⌬t. Also, nw is their number at the start of the time step. Finally, there is the option of incrementing nX,a by the number of CIN lost by freezing during ⌬t.

4. Results from empirical parameterization TABLE 3. Origins of parameters governing the lognormal size distributions of insoluble aerosol (bimodal for dust, monomodal otherwise) in the background-troposphere scenario, together with their values and uncertainty. They are the geometric mean diameters (Dg,X), standard deviation ratios (␴X), and bulk density (␳X) for aerosols in group X. For dust, total particle numbers in both modes [Pruppacher and Klett 1997, Eq. (8-43) therein] are assumed to be in the ratio of 150:1 (n1:n2), in view of the ratio of 5 between masses of dust in corresponding (0.6–2 and 6–20 ␮m dry diameter) bins predicted by a global model (Liao et al. 2004; data provided by H. Liao 2007, personal communication) for the Mt. Werner station in November. Values for X ⫽ O are assumed to be the same as for X ⫽ BC (except for ␳O), in light of INTEX/ ICARTT observations of refractory organic aerosol from Clarke et al. (2007, C07). Studies referred to here include Maring et al. (2000, 2003, M00 and M03), Clarke et al. (1997, C97), Alfaro et al. (1998, A98), Clarke et al. (2004, C04), and Hoffer et al. (2004, H04). Symbol

Value

Relative error

Origin

Dg,DM Dg,BC Dg,O ␳DM ␳BC ␳O

0.8 (3.0) ␮m 0.2 ␮m 0.2 ␮m 2300 kg m⫺3 1860 kg m⫺3 1500 kg m⫺3

⫾20% ⫾60% ⫾60% ⫾10% ⫾10% ⫾20%

M03 (also C04) C04 C07 M00 C04 H04, C07 (value for HULIS) M03 (A98) (also C04) C97, C04 C04, C07

␴DM ␴BC ␴O

1.9 (1.6) 1.6 1.6

10% 10% 10%

a. Comparison with observational data for dust, black carbon, and insoluble organic IN Available laboratory data are compared here with the empirical parameterization for each of the three basic groups of insoluble aerosol. All laboratory data concern specific types of artificial aerosol, either manufactured or sampled from beneath the surface of the earth’s crust. By contrast, the scheme is mostly based on a very different set of observations (from CFDC and crystal residual analysis) of the diverse mixture of natural atmospheric IN. Even within the same group of IN, vast differences in nucleating ability are seen for different aerosol samples (section 7). Consequently, exact agreement in the comparison is not to be expected, and discrepancies do not necessarily imply inaccuracy of the scheme. Only a limited subset of this laboratory data has informed selection of the scheme’s parameter values during design (see section 3). In the following figures, the few data points already used to determine such parameters are plotted differently (open symbols) from laboratory data, which are independent (plotted with filled symbols or other line styles). Temperature and humidity were varied as prescribed inputs to the empirical parameterization. For predictions of condensation and immersion freezing, the prescribed humidity corre-

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sponded to exact water saturation at all temperatures [Si ⫽ S w i (T )]. For nucleation (e.g., by deposition) in subsaturated conditions, the vapor mixing ratio was prescribed as Q␷ ⫽ Qs,i ⫹ (Qs,w ⫺ Qs,i)(2/3) for Sw less than Sw,0. Formulas for vapor pressures at water and ice saturation are from Murphy and Koop (2005). The frozen (or freezing) fraction for group X is defined here as the ratio between the numbers of its crystals nucleated and of its insoluble aerosols (per kilogram of air). It is proportional to the average surface area per insoluble aerosol particle [⍀X/nX ; see Eq. (10)]. Constant values from tropospheric observations are assumed for the average size and spectral width of (lognormal) aerosol size distributions (Table 3). Thus, the average surface area per particle here is independent of the group’s aerosol concentration. Tropospheric values are used here because the scheme and many of the observations are intended to portray atmospheric nucleation. Because the predicted freezing fraction is independent of aerosol concentration, the comparison is robust for a wide range of aerosol loadings. Uncertainty in the predicted freezing fraction arises from that of the scheme’s parameters (e.g., ␣X) and from natural variability of average surface area per particle (estimated from Table 3). In view of nonlinear dependencies of the predicted freezing fraction on some of the uncertain parameters, a statistical model has been used to estimate its relative error. The model has seven uncertain input parameters for X ⫽ DM [lnDg,DM and ␴DM for both modes; ␥, ln(nC IN,1,* /⍀DM,1,*), and ln␣DM], and eight for X ⫽ BC, O (lnDg,X and ␴X twice; ␳X, ␥, lnQX,2.5,*, and ln␣X), all assumed to be independent. For each uncertain input parameter, 106 synthetic values were generated by drawing random perturbations from an independent normal distribution and adding them to the observed mean value. The variance of the predicted freezing fraction was estimated from the variance of the sample of 106 frozen fractions evaluated from the synthetic sets of values of input parameters. For dust, nC IN,1,* /⍀DM,1,* is one such parameter with a relative error (⫺55% to 120%) at any given value of si being assumed to arise from sampling uncertainty due to the natural variability of ␨ in the local troposphere during INSPECT-1. This relative error corresponds to a 95% confidence interval for the average value of ␨ there and is derived from the standard deviation of the sample of daily values of ln[␨(si)] ⫺ ln[具␨典(si)], where TY denotes the line of best fit plotted on Fig. 1. A t distribution of their sample mean is assumed. Finally, error lines for the prediction are plotted in the following figures.

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FIG. 4. Comparison of the frozen fraction of dust predicted by the parameterization with laboratory AIDA results for immersion and condensation freezing from Field et al. (2006, F06). The selected AIDA data are close to water saturation. Error lines around the predicted scheme are estimated with a statistical model, being based on uncertainties (relative errors) in its parameters, namely ␣DM (⫾20%), ␥ (⫾20%), and nC IN,1,* /⍀ DM,1,* (⫺55%–125%, for a given value of si inside the CFDC; see Fig. 1). Natural variability in average surface area per particle (⍀DM/nDM) from that of Dg,DM and ␴DM (Table 3) is also included. None of the displayed data was used in constructing the scheme.

1) DUST/METALLIC

GROUP

Field et al. (2006) have measured the frozen fractions of dust sampled from the earth’s crust in Asian and Saharan desert regions (Möhler et al. 2006) in the AIDA aerosol chamber between ⫺20° and ⫺60°C. Figure 4 shows that the frozen fraction predicted by the parameterization has the same order of magnitude as most of the observed fractions at AIDA for immersion and condensation freezing (Si ⬎ S w i ⫺ 0.15). The observed fractions are consistently higher (by about one standard deviation) than the scheme’s prediction, possibly because the artificial dust studied in the AIDA chamber was sampled from the earth’s crust and not the atmosphere (see section 7). The low-average diameter of their artificial dust (about 400 nm) has prevented this difference from being even larger. Figure 5 shows a comparison with corresponding AIDA observations for nucleation in subsaturated conditions (Si ⱕ Sw i ⫺ 0.15; Field et al. 2006). The scheme’s prediction has a similar order of magnitude compared to the AIDA data, which again is significantly higher (by about two standard deviations). The prediction is slightly higher than for Asian aeolian dust sampled from the earth’s crust (Archuleta et al. 2005), because of the latter’s very low size (200 nm). By design, in warm subsaturated conditions (Si ⬍ 1.3 here), the pre-

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PHILLIPS ET AL.

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FIG. 5. Comparison of the frozen fraction of dust predicted by the parameterization with laboratory AIDA results for nucleation (e.g., by deposition) in subsaturated conditions. The selected AIDA data are well below water saturation. Also shown are data from Archuleta et al. (2005, A05) for Asian dust particles with a diameter of 200 nm. Errors are estimated for the scheme’s prediction in the same way as for Fig. 4. None of the displayed AIDA data was used in constructing the scheme.

diction is mostly consistent with observations of the scarcity of ice nucleation noted above (e.g., from AIDA; section 2c). Figure 6 shows the frozen fraction of dust as a function of increasing humidity at a constant temperature (⫺50°, then again at ⫺60°C). The prediction is compared with laboratory observations of Asian dust sampled from the earth’s crust (Archuleta et al. 2005). Their observed saturation ratio, and that of giant dust (larger than 10 ␮m) immersed in sulfate solution (Zuberi et al. 2002), differ by about one and three standard deviations, respectively, from the prediction, which is intermediate between both, partly because of differences in size compared to atmospheric dust. Moreover, the predicted freezing onset occurs at a saturation ratio that is only about 0.15 lower than that observed in situ for cirrus formation in the interhemispheric differences in cirrus properties from anthropogenic emissions project (INCA, the United Kingdom; Haag et al. 2003). Dust is assumed to be the ice nucleant responsible for their in situ observations. Agreement with cirrus observations from FIRE-II (Heymsfield and Miloshevich 1995) is by design. Finally, the predicted active fraction agrees with AIDA observations at ⫺50°C of dust sampled from the earth’s crust (Möhler et al. 2006), also shown in Fig. 6, though it is slightly lower (by about one standard deviation mostly). At ⫺60°C, the prediction becomes similar to, though slightly lower than, the freezing frac-

FIG. 6. The frozen fraction of dust particles predicted by the parameterization (solid line) at a constant temperature of (a) ⫺50°C, and then again at (b) ⫺60°C, during a steady increase of the saturation ratio with respect to ice (Si) up to water saturation. This is compared with laboratory observations by Archuleta et al. (2005; A05, filled triangles) for 200-nm Asian dust particles and by Zuberi et al. (2002, Z02, open diamonds) for giant dust particles (larger than 10 ␮m) immersed in ammonium sulfate solutions. Also shown are observations of artificial dust from the AIDA aerosol chamber (Möhler et al. 2006, M06) sampled from Asia (dotted–dashed line) and the Sahara (dotted lines, open stars). Ranges of uncertainty are shown (⫾␴), with those for the scheme (parallel dashed lines) being evaluated as in Fig. 4. Critical saturation ratios for cirrus formation from field observations analyzed by Heymsfield and Miloshevich (1995, HM95, open circles) for FIRE-II and by Haag et al. (2003, H03, filled squares) for INCA are shown. The freezing fraction for detection of first ice in INCA and FIRE-II is about 0.1% for an assumed dust concentration of about 100 L⫺1. Except for observations (open symbols) of Saharan dust by M06, giant dust by Z02, and the FIRE-II data points, the displayed data have not been used in constructing the scheme.

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FIG. 7. Fraction of black carbon that is frozen, predicted by the parameterization and observed in laboratory studies of artificial samples of soot by DeMott (1990, D90), DeMott et al. (1999, D99), and Möhler et al. (2005a, AIDA). The D90, D99, and AIDA observations concern sulfate-coated artificial soot from combustion of acetylene, lamp-black, and the sparking of graphite electrodes, respectively. Errors are displayed for the scheme’s prediction, being estimated using a statistical model, with relative errors in its parameters, namely ⍀BC,1,* (⫺65% to 180% inferred from relative errors of ⫺60%–140% in QBC,2.5,* and of aerosol parameters in Table 3), ␥ (⫾20%), and ␣0 ⫽ 1/3 ⫺ ␣BC (⫺70% to 200%, assuming ␣0 ⬍ 1/6). Natural variability in average surface area per particle (⍀BC/nBC) from that of Dg,BC and ␴BC is also included. None of the displayed observational data was used quantitatively in constructing the scheme.

tion seen by Archuleta et al. (2005) when the latter is adjusted to correspond to a more realistic dust size (e.g., 400 nm, as studied by Möhler et al., would correspond to a freezing fraction of 0.04 at Si ⫽ 1.36), assuming proportionality to surface area per particle (see section 2). The freezing fraction seen by Möhler et al. is much higher—by about one to two orders of magnitude—than either the prediction or the data from Archuleta et al. at most observed humidities at that temperature. There would still be a discrepancy between both observational datasets even after the same type of adjustment of the data at ⫺60°C from Archuleta et al. (2005) to a more realistic size. More experiments are needed to clarify reasons for this discrepancy between the datasets of Archuleta et al. and Möhler et al. In summary, differences between the prediction and the various sources of observational data are less than or comparable to differences between these sources of data.

2) BLACK

CARBON GROUP

Figure 7 shows a comparison of the parameterization with various laboratory observations for condensation

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FIG. 8. Comparison of the relative humidity (RHw) for the onset of freezing of black carbon between the CFDC parameterization (without the parcel model) and laboratory observations. The experimental data are from studies of lamp-black soot coated with multiple layers of sulfate (DeMott et al. 1999, D99) and of soot produced by sparks between graphite rods (Möhler et al. 2005a, AIDA). The graphite soot was then coated with sulfate. Except for observations of lamp-black soot at substantially subsaturated humidities by DeMott et al. (open squares), the displayed data have not been used in construction of the scheme.

and immersion freezing of artificial soot, coated with sulfate. The prediction from the empirical parameterization agrees with recent observations by DeMott et al. (1999) and Möhler et al. (2005a), though it is slightly lower than the former, which has the more realistic size. Median diameters were about 240 and 90 nm, respectively. The freezing fraction for acetylene soot (DeMott 1990) is significantly higher (by about one standard deviation) than the other observations and the prediction. Figure 8 shows the relative humidity for the freezing onset of black carbon predicted by the parameterization at a freezing fraction of 0.1% and observed in two laboratory studies (DeMott et al. 1999; Möhler et al. 2005a). Of course, agreement with one of the two datasets is by design (HX). This is not the case for the other (Möhler et al. 2005a), which agrees with the prediction.

3) INSOLUBLE

ORGANIC GROUP

Figure 9 shows the predicted frozen fraction for all insoluble organic particles, compared with various laboratory studies for immersion and condensation freezing by bacteria. The predicted frozen fraction is within the range of values inferred from laboratory data not used to constrain the scheme. Their spread is great, reflecting a lognormal distribution of freezing fractions seen among individual INA strains in nature (Hirano et

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FIG. 9. Frozen fraction of insoluble organic particles predicted by the scheme (solid line) and inferred from laboratory studies of the immersion freezing of bacteria. Hundreds of INA strains of Pseudomonas syringae (Ps) from orchards in the United States and a bacterial library were analyzed by Gross et al. (1983, open six-pointed stars) and Hirano et al. (1985, open five-pointed stars). Results from other studies are shown for single INA strains of Ps (Maki et al. 1974, filled diamond; Vali et al. 1976, open squares; Lindow 1982, L82a, thin dashed line; Lindow et al. 1982, L82b, dotted–dashed line; Lindow et al. 1989, dotted line), the M1 strain (Levin and Yankofsky 1983, filled circle) and Erwinia herbicola (Eh; L82a, b; crosses along dashed and dotted–dashed lines, respectively). Observed fractions are multiplied by fINA ⫽ 0.01, to infer those of cells in all strains. Errors are displayed for the scheme (parallel dashed lines), being estimated using a statistical model, with uncertainties in ␣O (⫺70%–200%), ␥ (⫾20%), and ⍀O,1,* (⫺60% to 150%, due to errors of ⫺50%–100% in QO,2.5,* from gW and of aerosol parameters in Table 3). Natural variability in aerosol parameters is also included. Except for observations by Gross et al., Hirano et al., and Vali et al., the displayed data have not been used in construction of the scheme.

al. 1985). In summary, available experimental data on the freezing fraction of bacteria are consistent with the prediction at warm subzero temperatures.

b. Comparison with existing schemes The empirical parameterization was compared with four other schemes that predict heterogeneous freezing, by Lohmann and Diehl (2006, referred to as L–D), Liu and Penner (2005, L–P), Khvorostyanov and Curry (2004, K–C) and Meyers et al. (1992, MDC). The MDC scheme has no dependence on aerosol chemistry or amounts, and here it is applied only at temperatures warmer than ⫺30°C (e.g., Phillips et al. 2005). For all schemes, water saturation was artificially maintained at 500 mb during cooling to ⫺70°C. All contact and nonheterogeneous nucleation of ice were prohibited. Note that the test is idealized in the sense that vapor growth of crystals does not affect the humid-

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ity. Nevertheless, it mimics typical conditions in a natural mixed-phase cloud containing supercooled cloud liquid, which can only persist if the humidity is close to water saturation. Aerosol concentrations were prescribed with typical values observed by Clarke et al. (2007) in pollution and biomass-burning plumes during Intercontinental Chemical Transport Experiment/International Consortium for Atmospheric Research on Transport and Transformation (INTEX /ICARTT) in 2004 (QBC,2.5 ⫽ 3 ⫻ 10⫺10; QO,2.5 ⫽ 3 ⫻ 10⫺9 kg kg⫺1; QDM,2.5 ⫽ 2.9 ⫻ 10⫺10 kg kg⫺1 was arbitrarily prescribed). Size distribution parameters specified in Table 3 were assumed, to infer ⍀X/nX and freezing fractions. Figure 10 shows the predicted number concentration of crystals nucleated by various IN species. At temperatures colder than ⫺30°C, the empirical parameterization as well as the MDC and L–P schemes all predict similar orders of magnitude for the total crystal concentration (about 10–100 L⫺1). All five schemes differ by up to almost 5 orders of magnitude in their predicted concentrations (and freezing fractions) at temperatures of about ⫺30°C. The K–C and L–D schemes predict extremely high concentrations, with absolutely all insoluble aerosols in each represented group being predicted to freeze at all temperatures colder than about ⫺20°C. (For the L–D scheme, the freezing fraction for all IN is less than unity and the peak IN concentration is less than for the K–C scheme, because no freezing by insoluble organic IN is represented by it). The K–C scheme neglects the probability distribution of contact angles among active sites on the IN surface, which in reality determines that of the nucleation efficiencies among IN, so the singular character of IN is not represented naturally (see sections 1 and 2). The L–D scheme is based on data from artificial drops that may each have contained multiple IN (see section 6) and neglects a dependence of nucleating ability on IN size, in contrast to the empirical parameterization. The empirical parameterization predicts a concentration of heterogeneous crystals of 29 L⫺1 at ⫺30°C, with 40% from insoluble organic (X ⫽ O) IN, 15% from dust (X ⫽ DM), and 45% from soot (X ⫽ BC). This composition of IN differs from that seen in the background troposphere (Fig. 2) because an aerosol mixture for the above plumes has been assumed. The L–P scheme also predicts that most crystals originate from soot. Also shown in Fig. 10 is the freezing fraction from all schemes. Comparison with all observations (Figs. 4, 7) of condensation and immersion freezing by dust (Archuleta et al. 2005; Field et al. 2006) and soot (DeMott 1990; DeMott et al. 1999; Möhler et al. 2005a) generally

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FIG. 10. (a) Number concentration of heterogeneous crystals and (b) their freezing fraction for the three species of insoluble aerosol, as represented by the present empirical parameterization and by the schemes by Lohmann and Diehl (2006, L–D), Liu and Penner (2005, L–P), Khvorostyanov and Curry (2004, K–C), and Meyers et al. (1992). Aerosol conditions are specified with values typical for a plume observed during INTEX/ICARTT (Clarke et al. 2007; see text). Exact water saturation was artificially imposed at all temperatures. Freezing fractions are the ratios of the crystal number from (a) and the total initial number of dust, soot, and insoluble organic particles. Freezing is only allowed in any scheme’s group if the original number of insoluble aerosols in that group exceeds the number of crystals it has nucleated. For the L–D and L–P schemes, a droplet concentration of 100 ⫻ 106 kg⫺1 and a cloud liquid mixing ratio of 1 g kg⫺1 were arbitrarily prescribed as well as a vertical velocity of 1 m s⫺1. The unique type of freezing by insoluble organic IN is predicted only by the empirical parameterization (the K–C scheme treats the freezing of such IN only generically).

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shows better agreement for the empirical parameterization than for alternative schemes at most subzero temperatures. Its prediction is mostly intermediate, compared to other schemes. The empirical parameterization reproduces the qualitative trend of a smooth increase in freezing fraction during extensive supercooling, as seen in laboratory observations at water saturation. Moreover, it represents insoluble organic carbonaceous IN.

5. Implementation of empirical parameterization in a large-scale or cloud model In the troposphere, insoluble IN material is mixed with various soluble compounds inside the same aerosol particle (e.g., Chen et al. 1998; Clarke et al. 2004). Consequently, in-cloud scavenging of a typical IN particle in an updraft may occur when its soluble material activates a cloud droplet, which is then removed by precipitation. Optionally, such scavenging of IN can be represented by assuming that an IN particle’s soluble material constitutes a certain fraction of its total mass (e.g., appendix B). If the supersaturation reaches a critical value, then the soluble material activates as a cloud droplet and the IN material is assumed to become immersed in

冋

d共⌬nIN,rain兲 ⬇ ⌬tmin 共w ⫺ ␷t兲

册

it. The critical supersaturation emerges from ␬-Kohler theory (Petters and Kreidenweis 2007, Eqs. (7) and (10) therein; see also Snider et al. 2003). Each group X of IN is then partitioned into prognostic components that are interstitial and immersed in cloud liquid. Extra scalars constraining the IN size distributions are the number mixing ratio of interstitial IN lost by becoming immersed in cloud liquid without necessarily freezing (nX,a,liq), and the actual number mixing ratio of immersed IN (nX,imm). A temporary grid of size bins for IN is applied. The immersed and interstitial IN size distributions have a cutoff size determined by nX,a,liq and QX. Inside clouds, QX is hypothetical insofar as it is unaltered there, either by immersion of IN in cloud droplets or by ice nucleation. The fraction of clouddroplet number accreted onto precipitation equals the fraction removed of nX,imm and nX,a,imm, while nX,a is also reduced. Inclusion of in-cloud scavenging of IN means that heterogeneous freezing of rain may be represented as follows: accretion of cloud liquid by rain provides the source of mass of IN contained inside rain, QX,rain, which falls with the rain mass. A temporary grid of size bins discretizes the raindrop size distribution. For each bin with mass mixing ratio dQr of rain, the number of the rain’s IN particles that activate in ⌬t is given by

⭸T d ,0 关T, S w 兵n i 共T 兲兴其 ⭸z dT IN,1,*

For that size bin, d⍀X,rain ⫽ ⍀X,raindQr /Qr is the surface area mixing ratio of IN contained inside its raindrops and ␷t is their fall speed, while w is the vertical air velocity. Optionally, ⍀X,rain ⬇ ⍀X,immQr /Qw. The integer number of active IN in any drop in the bin is assumed to follow a Poisson distribution and the fraction frozen of the bin’s drops is then [1 ⫺ exp(⫺d␮)] (e.g., Phillips et al. 2001), where d␮ is the average number of IN activated per drop in ⌬t. A challenge when implementing the parameterization in a model is that the supersaturation with respect to ice is an input and must be predicted. A method for predicting the supersaturation was given by Phillips et al. (2007). Ascent is the source of supersaturation with respect to water in liquid or mixed phase clouds [e.g., Howell 1949; Mordy 1959; Rogers and Yau 1989, Eq. (7.29), p. 110, therein] and with respect to ice in ice clouds. Consequently, a representation of the vertical velocity on the cloud scale is required in general for prediction of the supersaturation. Several ways of representing the subgrid-scale variability of vertical veloc-

兺冉 X

冊

␣X d⍀X,rain . ⍀X,1,*

共17兲

ity have been proposed (e.g., Donner 1993; Chuang and Penner 1995; Lohmann et al. 1999) for models that cannot resolve convective elements. For global models, evaluation of the supersaturation with which to represent nucleation remains one of the most difficult problems because of the multiscale nature of mesoscale dynamics. Finally, if the model in which the scheme is applied cannot represent accurately the average sizes of insoluble aerosol, then it is best to prescribe values of parameters of the aerosol size distribution according to Table 3. Naturally, heterogeneous ice nucleation is one of many possible avenues (e.g., Hallett and Mossop 1974; Heymsfield et al. 2005) for crystal formation in the atmosphere (e.g., Phillips et al. 2007). They must all be included in the large-scale or cloud model.

6. Discussion of the scheme’s accuracy In construction of the empirical parameterization, coincident field measurements of aerosol particles

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(from IMPROVE), their size distributions, and IN (from INSPECT-1; CFDC data between ⫺40° and ⫺62°C, from ice saturation to the onset of homogeneous freezing) were combined. They have been extrapolated to the wider range of conditions found throughout the troposphere (temperatures of 0° to ⫺70°C or colder, humidities from ice to water saturation, and all conditions of aerosol loading, chemistry, and size) as follows: first, a reference activity spectrum has been fitted to the CFDC data and extrapolated to warmer temperatures using other CFDC datasets (Meyers et al. 1992). The extended set of all CFDC data used here ranges from ⫺7° to ⫺62°C. Second, extra observations of nucleation in subsaturated conditions (HX) have been combined with the spectrum. Third, the observed composition of residual IN from heterogeneous crystals from the troposphere has determined contributions (␣X) from aerosol groups. Finally, other field observations (section 2) justify extrapolation of the spectrum into any scenario of aerosol species. There is some uncertainty in these steps of extrapolation. For instance, when determining HX, observations of artificial aerosol have necessarily been used. Data about the role of soluble coatings on IN are scarce, which limits the accuracy of HX . Dependencies on temperature of empirical parameters (e.g., ␣X, ␥) are uncertain. Although such omissions may introduce limited biases, they are not overly serious for three reasons. First, for all three basic groups of IN, differences between the scheme’s prediction and independent observational data not used to construct it are either comparable with or less than differences among the sources of this data. The parameterization has better agreement with these observations than with alternative schemes. Second, each step is justified with observations of IN. Lastly, a flexible framework [Eqs. (8)–(10)] expresses species’ IN activity in terms of observable quantities. Any biases may be reduced as observations improve (see section 7). Limited inconsistencies between the scheme and laboratory observations may be partly due to 1) crystallographic, chemical, and size differences of the insoluble IN material between the artificial laboratory samples and the real atmosphere; 2) differences in composition and amount of soluble material mixed inside individual IN particles between laboratory samples and the atmosphere; 3) the limited sampling of the troposphere for data constraining the scheme; and 4) any limitations of the residual analysis and CFDC. The CFDC has at least three potential limitations, though they do not cause very great inaccuracy here. First, the CFDC can measure neither contact nucleation nor all of the immersion and condensation freez-

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ing at temperatures colder than ⫺40°C at humidities approaching water saturation. The latter is not such a problem because homogeneous aerosol freezing is prolific in such conditions, producing many more crystals than heterogeneous nucleation typically. Second, the IN activity of aerosols larger than 1–1.5 ␮m was not measured in datasets used here. Also, the optical detection technique presently used, requiring growth of crystals beyond about 1 ␮m, may limit the ability to detect nucleated ice at very cold temperatures. Both detection issues may soon be resolved. Last, the CFDC cannot resolve the separate contributions to the total activity from IN that are interstitial and immersed in cloud liquid at a given (positive) supersaturation (sw) with respect to water imposed within it. However, this is not a great limitation because whether an IN is interstitial or immersed does not affect its heterogeneous freezing temperature very greatly for estimated soluble coatings on IN at water saturation (appendix B). Essentially, uptake of liquid water by an interstitial IN dilutes the dissolved solute, minimizing its depression of the freezing temperature. This is why the sensitivity to positive sw above water saturation is often seen to be quite limited (e.g., Al-Naimi and Saunders 1985; Rosinski and Morgan 1988; Meyers et al. 1992; Rogers et al. 2001b). Measured IN concentrations only changed by a factor of 2 when sw increased from zero to 5% in Arctic flights (Rogers et al. 2001b); this must have immersed the IN inside the CFDC (see appendix B; Rogers and Yau 1989, p. 89). Hence, the ice-nucleating behavior of many interstitial and immersed IN seems similar at water saturation. Yet sometimes a higher sensitivity to sw inside the CFDC is seen (DeMott et al. 1998; Rogers et al. 1998), for example, due to poor soluble coatings. The CFDC does not measure the volume of cloud droplets that immerse IN but does not need to, so this is not a limitation. The volume dependence of freezing fractions of drops seen in early laboratory studies (e.g., Bigg 1953) arose because drops artificially sampled from bulk water contain multiple IN with a spectrum of freezing temperatures (Langham and Mason 1958; Vali 1971). The larger the artificial drop, the more numerous were its IN and the warmer was the maximum freezing temperature among its multiple IN, which is the drop’s freezing temperature. Consequently, such volume dependence is not expected for most cloud droplets in nature, which each form by condensation onto only one aerosol particle. At low subsaturated humidities, the parameterization represents modes of deposition and condensation freezing in terms of their empirical dependencies on humidity and temperature (via HX). Both depression of

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the freezing temperature by the solute concentration (condensation freezing) and whether liquid water is absent (deposition nucleation) are represented implicitly by the scheme. Finally, the omission from the scheme [Eq. (10)] of any dependence, of the number of crystals nucleated per unit area of aerosol surface, on the aerosol particle’s size means that any effects from areal density and average efficiency of active sites varying width particle size (e.g., Marcolli et al. 2007, section 4.2.4 therein) are not represented yet. Future experiments are needed to clarify this extra dependence, though those by Marcolli et al. revealed no clear effect from its inclusion. If it exists in nature, whenever the average aerosol size is very different from that of the background-troposphere scenario (e.g., Table 3) some inaccuracy of the scheme might conceivably arise, though the average size of dust has been seen not to vary very greatly geographically (e.g., Maring et al. 2003). Yet the scheme does implicitly represent, albeit in a simplified fashion, the proper rarity of active sites and the way in which the occurrence probability of rare active sites on an IN particle increases with its surface area (section 2). This makes larger particles better IN than smaller ones, as seen by Marcolli et al. and represented by the empirical parameterization.

7. Conclusions A versatile framework for an empirical parameterization has been proposed to predict crystal numbers as a function of the amounts of multiple species of IN aerosol. It is derived from coincident field observations of the composition and activity of natural IN and aerosol in the troposphere. This method is an improvement on the standard method of Meyers et al. (1992) because it has a wider valid range of temperatures (0° to ⫺70°C or colder) and humidities (ice to water saturation), allowing for dependencies on the chemistry and total surface area of IN aerosols. It represents all known modes of heterogeneous ice nucleation including two types of contact nucleation. A comparison of the parameterization with available field and laboratory observations has been presented for modes other than contact freezing, for which available laboratory data are scarce. Moreover, the scheme is computationally efficient and easy to implement. The scheme is applicable over the wide range of temperature, humidity, and aerosol conditions commonly seen throughout the global troposphere (see section 6). For all three basic groups of IN, differences between the prediction from the empirical parameterization and independent observational data not used to construct it are generally comparable to or less than differences

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among the various sources of this data. Because the predicted freezing fraction does not depend on aerosol concentration (see section 4), the comparison robustly represents the scheme’s behavior for many aerosol scenarios throughout the troposphere. The scheme displays better agreement with independent observations than do some alternative existing schemes. Disagreement between alternative schemes— by up to five orders of magnitude (⫺30°C) in crystal concentrations and freezing fractions—motivates the empirical approach taken here. The disagreement is not restricted to any particular aerosol loading. Moreover, the empirical parameterization includes nucleation of ice by insoluble organic carbonaceous IN, a potentially significant source of crystals in some situations (e.g., section 4b). It is not certain how much of the insoluble organic aerosol was actually biogenic in the plume simulated here, and the scheme’s prediction has significant uncertainty for this species (see section 3a). Nevertheless, Rogers et al. (2001b) have observed that insoluble carbonaceous aerosol can dominate the residual IN particles collected from heterogeneous crystals in a few (e.g., polluted) situations. The comparison with laboratory studies was complicated by their use of artificial aerosol either manufactured or sampled from the earth’s crust, the representativeness of which for atmospheric IN is unknown. As the scheme is based on measurements of atmospheric IN, limited inconsistencies in the comparison arose partly from crystallographic, chemical, and size differences between atmospheric and artificial IN (see section 6). Different soluble coatings also were a factor. Indeed, various laboratory studies have shown vast differences in nucleating ability among samples of artificial aerosol belonging to the same general group of IN but generated by different methods (e.g., Figs. 6, 7, 8; see also Gorbunov et al. 2001). Hence, caution is needed when making inferences about atmospheric nucleation of ice from such laboratory studies. An atmospheric IN particle typically consists of a mixture of various compounds (e.g., Clarke et al. 2004), which is another reason why artificial aerosols in the same general group of IN display highly variable nucleating abilities in attempts to represent atmospheric IN. Increasing the content of organic carbon in soot reduced its nucleating ability (Möhler et al. 2005b). Soluble coatings deposited on atmospheric IN during transport can alter their nucleating ability (e.g., Bertram et al. 2000; Zuberi et al. 2002; Archuleta et al. 2005; Möhler et al. 2005a). Soluble coatings on soot during a pollution episode (2 May 2004) were seen in the ambient population but not in residual IN from heterogeneous crystals in INSPECT-2 (Richardson et al. 2007), so they may have

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inhibited ice nucleation. Also, geographical locations of the highly localized sources of natural tropospheric dust (e.g., Ginoux et al. 2001) are still quite uncertain. This further complicates the task of sampling dust from the earth’s crust with the goal of studying nucleation by atmospheric dust. Complex chemical and microphysical processing of insoluble aerosol during long-range transport in the real atmosphere may alter its nucleating ability after emission from the surface. Such atmospheric processing is a challenge to mimic in the laboratory or to simulate numerically. Preferential removal of particles with a higher ability for ice nucleation may reduce the average nucleating ability of atmospheric IN during long-range transport. Chemical processing coats them with soluble material that inhibits their ability for deposition nucleation (e.g., Möhler et al. 2005a), as noted above, while altering their potential behavior in the condensation mode. Atmospheric processing of IN may explain the observations shown in this paper of dust sampled from the earth’s crust (e.g., Figs. 4–6) or from desert-dust plumes (Fig. 1, CRYSTAL-FACE, probably freshly emitted) having significantly higher freezing fractions than for atmospheric dust from the background free troposphere (INSPECT) that is probably older. This difference becomes especially evident when freezing fractions observed in laboratory studies (e.g., from AIDA) are adjusted to remove effects from size differences between artificial and atmospheric IN. Consequently, a direct empirical approach would seem advantageous when parameterizing heterogeneous ice nucleation. With the CFDC or any other in situ instrument for measuring IN, samples of natural aerosol are taken directly from the atmosphere. The representativeness of the nucleating ability of the aerosol sampled is then optimal. Geographic variability of soluble coatings on IN particles and of their chemical/crystallographic properties may modify ice-nucleating ability. The former modifies HX, while the latter must alter the constant of proportionality between IN activity and total surface area. The number of crystals nucleated per unit surface area of aerosols in any group at given conditions of temperature and humidity (e.g., ␣X nIN,1,*/⍀X,1,* here) may have a spatial and temporal variability across the globe, depending on various environmental factors (e.g., the maritime or continental character of the aerosol, latitude, altitude, time of day) and varying with the age of, soluble coatings on, and perhaps even size (section 6) of, insoluble aerosol particles. The present study has found limited samples of dust, sampled from the earth’s crust or probably freshly emitted into the atmosphere, to have a significantly higher nucleating ability than is

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typical for the background troposphere, as noted above. This may reflect the longer history of atmospheric processing of IN particles within the background-free troposphere. Influences on atmospheric IN from such environmental factors and aerosol age, however, have not been extensively quantified yet with field observations. There may be chemical species of IN within the real atmosphere not considered in the present study. In the future, the number of groups of IN in Eq. (8) could be increased beyond three within the general framework proposed here, if experiments reveal their icenucleating properties. A potential new species of IN could be solid ammonium sulfate at very cold temperatures (e.g., Tabazadeh and Toon 1998; Abbatt et al. 2006), which may explain the low-saturation ratios for freezing seen by Mangold et al. (2005). Currently, neither the fraction of all sulfates in aerosol in the troposphere that can act in this way nor the dependence on particle size of their hypothesized nucleation has been quantified extensively. Equally, biogenic aerosols other than bacteria, such as particles of leaf litter and pollen fragments, can nucleate ice (e.g., Schnell and Vali 1972, 1976; Diehl and Wurzler 2004). They may be ubiquitous in the free troposphere, and few studies have as yet quantified aspects of their nucleating ability. Future advances in knowledge and observational technology may better constrain the relations between IN concentrations, aerosol, and other environmental factors. New species of atmospheric IN may be identified. Insoluble organic IN from the free troposphere, warm nucleation by atmospheric soot, and the scarce activity at low subsaturated humidities all merit further experimental investigation. More accurate, extensive, and correlated data on atmospheric IN may be provided by more advanced in situ instruments that will become available in the future. Associated changes to the way in which heterogeneous ice nucleation is represented may be assimilated into the conceptual framework of the empirical parameterization proposed here. Central to this framework is the use of observations of atmospheric IN sampled directly from the troposphere. Acknowledgments. The first and second authors were partially funded by two awards (NNG05HL30i and NNG06GB60G, respectively) from the National Aeronautics and Space Administration (NASA). Statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the views of NASA. The work is directly applicable to these awards, which concern impacts of dust on storms in the Tropical Cloud Systems and Processes (TCSP) project and modeling studies of aerosol–cold cloud in-

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teractions, respectively. Aircraft observations for the Aerosol Characterization Experiment (ACE-1) were provided by Y. Shinozuka in the Marine Sciences Department of Hawaii University at Manoa. Data for estimates of soluble fractions and size distributions of dust were given by Hong Liao from the Chinese Academy of Sciences and by Yunha Lee and Peter Adams at

Carnegie Mellon University. The first author is grateful to Cindy Morris, Sonia Kreidenweiss, Susan Hirano, Trude Eidhammer, Dimitri Georgakopoulos, Ottmar Möhler, Paul Field, Zev Levin, Raymond Shaw, SongMiao Fan, Larry Horowitz, Anthony Clarke, Barry Huebert, and Ruprecht Jaenicke, for the valuable advice and/or data they provided.

APPENDIX A List of Symbols Notation BC c1 Dg,X DM fINA fC gfr,30 gW hX HX j Kaero,X ni nIN nIN,1,* nC IN,1,* n˜ IN,1,* nˆ IN,1,* nIN,1,* nIN,X nIN,X,* nmax nw |⌬nw| nw,j nX nX,a nX,a,imm nX,a,liq nX,cn nX,int nX,imm n1:n2 Nbac O Qr QX QX,2.5 QX,2.5,* Qs,w Qs,i Q␷ Qw Raero,X

Description Inorganic black carbon Constant for IN number Geometric mean diameter of aerosol in group X for X ⫽ {DM, BC, O} Dust and metallic aerosols Fraction of all bacterial cells in INA strains Contribution, from CFDC data fitted by Eq. (1), to HX Freezing fraction of cells in INA strains at ⫺30°C Water-soluble fraction of organic carbon aerosol Fraction K 1 in expression for HX for X ⫽ {DM, BC} Fraction-reducing IN activity at low Si, warm T Integer index for size bin of cloud liquid Thermal conductivity of aerosol group for X ⫽ {DM, BC, O} Number mixing ratio (m.r.) of cloud ice particles Total number m. r. of active IN predicted Number m.r. of reference activity spectrum for water saturation in background-troposphere scenario Number m.r. of fit to CFDC data in background-troposphere scenario ⫽ min (c1{exp [12.96(Si ⫺ 1.1)]}0.3 ␥/␳C, nmax(T )) ⫽ min {⌿ c1exp [12.96(Si ⫺ 1) ⫺0.639], nmax(T )} For interpolation between ⫺25° and ⫺35°C Contribution to nIN from aerosol group X Contribution to nIN,1,* from aerosol group X Maximum number m.r. of reference activity spectrum (Si ⫽ Sw i ) Number m.r. of cloud droplets Number (⬎0) of cloud droplets evaporated away in ⌬t Droplet number m.r. in jth droplet size bin Number m.r. of particles in aerosol group X (not depleted by ice nucleation while inside cloud) Number of aerosols in group X lost by ice nucleation Component of nX,a from IN immersed in cloud liquid Number of interstitial IN in group X lost by becoming immersed Number m.r. of CIN for group X Component of nX that is interstitial Number of IN of group X immersed in cloud liquid Ratio of total numbers of particles in (1st, 2nd) dust modes Concentration of all bacteria cells in troposphere Insoluble organic carbon (QO includes noncarbon elements) Mixing ratio of rain Mixing ratio of aerosols in group X (not depleted by ice nucleation while inside cloud) Component of QX for aerosols smaller than 2.5 ␮m in diameter Value of QX,2.5 in the background-troposphere scenario for X ⫽ {DM, BC, O} Saturation m.r. with respect to water Saturation m.r. with respect to ice Vapor m.r. Cloud liquid m.r. Predicted (prescribed) radius of particles in group X of aerosols for X ⫽ {DM, BC, O}

Value and units 1000 m⫺3 {0.8(3), 0.2, 0.2} ␮m 0.01 0.1 0.83 {0.15, 0} ⱖ1 {0.25, 4.2, 0.2} W m⫺1 K⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 kg⫺1 100 L⫺1 kg kg⫺1 kg kg⫺1 kg kg⫺1 {2.9, 0.3, 0.8} ⫻ 10⫺10 kg kg⫺1 kg kg⫺1 kg kg⫺1 kg kg⫺1 kg kg⫺1 ({0.4, 0.1, 0.1} ⫻ 10⫺6) m

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Notation

Description

si sw Si SX i,0 ⌬Si S hom i Sw i Sw Sw,0 t ⌬t T ⌬T ⌬TCIN ⌬TX,imm

Supersaturation of vapor with respect to ice Supersaturation of vapor with respect to water Saturation ratio of vapor with respect to ice Threshold of Si in HX for X ⫽ {DM, BC} Range in Si for transition of HX Value of Si at onset of homogeneous aerosol freezing Value of Si at water saturation Saturation ratio of vapor with respect to (plane) water Threshold of Sw in HX Time Model time step Physical temperature of ambient air Range in T for transition of HX near T X 0 Difference in freezing temperature between surface and bulk-water modes Depression of freezing temperature for X ⫽ {DM, BC, O} between interstitial and immersed states of IN Coldest temperature in test for INA strains Threshold of T in HX for X ⫽ {DM, BC} Warmest temperature in first heating of IMPROVE test Fall speed of raindrops in a given size bin Vertical air velocity Interpolation variable Label for group of insoluble aerosol Fraction of nIN,1,* (HX ⫽ 1) from IN activity of group X ⫽ {DM, BC, O} Altitude Factor boosting IN concentration due to bulk-liquid modes Cubic interpolation function equal to a at y ⱕ y1 and to b for y ⱖ y2, while ␦ba ⫽ a0 ⫹ a1y ⫹ a2y2 ⫹ a3y3 for y1 ⬍ y ⬍ y2, where a0 ⫽ B, a1 ⫽ Ay1y2, a2 ⫽ ⫺A( y1 ⫹ y2)/2, and a3 ⫽ A/3, with A ⫽ 6(a ⫺ b)/ (y2 ⫺ y1)3 and B ⫽ a ⫹ Ay31/6 ⫺ Ay21y2/2 Ratio of number of active IN to dust surface area Hygroscopicity parameter Average number of IN activated per raindrop Average number of ice embryos per aerosol particle in group X Density of ambient air Air density at which CFDC data were reported Bulk density of aerosols for X ⫽ {DM, BC, O} Function that is 0 for T ⬎ ⫺2°C and 1 for T ⬍ ⫺5°C, being ␦ 01(T, ⫺5, ⫺2) for ⫺5 ⬍ T ⬍ ⫺2°C Standard deviation ratio of aerosols for X ⫽ {DM, BC, O} Factor to match Eqs. (2) and (3) at ⫺30°C Total surface area of all aerosols larger than 0.1 ␮m in diameter from group X (not depleted by ice nucleation while inside cloud) Interstitial component of ⍀X Component of ⍀X immersed in cloud liquid Total surface area of all aerosols larger than 0.1 ␮m in group X inside liquid raindrops Component of ⍀X in background-troposphere scenario for aerosol diameters between 0.1 and 1 ␮m with X ⫽ {DM, BC, O}

TINA TX 0 T␹ ␷t w x X ␣X z ␥ ␦ba(y, y1, y2)

␨ ␬ d␮ ␮X ␳ ␳C ␳X ␰ (T ) ␴X ⌿ ⍀X ⍀X,int ⍀X,imm ⍀X,rain ⍀X,1,*

APPENDIX B Estimation of the Depression of the Heterogeneous Freezing Temperature by the Dissolved Solute on Interstitial IN at Water Saturation Following Diehl and Wurzler (2004), the depression of the heterogeneous freezing temperature by the dis-

VOLUME 65 Value and units % % See Table 1. 0.1

0.97 s s °C 5°C 4.5°C {0.07, 0.09, 0.1}°C °C {⫺40, ⫺50}°C °C m s⫺1 m s⫺1 See Table 3. DM, BC, or O {2/3, 1/3 ⫺ 0.06, 0.06} m 2 aⱕyⱕb

[dust] m⫺2

kg m⫺3 0.76 kg m⫺3 {2300, 1800, 1500} kg m⫺3 0ⱕ␰ⱕ1 {1.9(1.6), 1.6, 1.6} 0.058 707␥/␳C m3 kg⫺1 [aerosol] m2 [air] kg⫺1 [aerosol] m2 [air] kg⫺1 [aerosol] m2 [air] kg⫺1 [aerosol] m2 [air] kg⫺1 {5.0, 2.7, 9.1} ⫻ 10⫺7 [aerosol] m2 [air] kg⫺1

solved solute associated with a typical interstitial IN particle is approximated by the depression of the homogeneous freezing temperature (at a rate of 1 cm⫺3 s⫺1; Koop et al. 2000) by the same mass of solute in a sulfate CCN. The mass of solute is estimated from the average size of an IN insoluble core (see section 4) and the fraction of the IN-containing particle’s mass that is water soluble in the background-troposphere scenario. This soluble fraction for dust is about 0.1–0.2, in view of

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predictions over Colorado by Hong Liao (e.g., Liao et al. 2004) and over the North Pacific Ocean by Y. Lee and P. Adams (2007, personal communication), and for soot is about 0.8 (Clarke et al. 2004). The dissolved solute’s concentration in the hypothetical sulfate CCN is inferred from Kohler theory for exact water saturation and determines the water activity (Pruppacher and Klett 1997). This yields a shift of the freezing temperature of ⌬TX,imm ⫽ 0.07, 0.09 and 0.1°C for X ⫽ DM, BC, and O due to the solute concentration at water saturation in the background-troposphere scenario. By contrast, at a relative humidity of 97%, a similar calculation shows that the corresponding depression of the heterogeneous freezing temperature is 4°C.

APPENDIX C Estimation of the Occurrence of Bacteria in the Troposphere Recent advances in measurement techniques allow all cells in the atmosphere, whether culturable or not, to be counted. Even killed bacteria can nucleate ice (Maki and Willoughby 1978). In the atmosphere, ultraviolet light can render bacteria nonculturable (e.g., Griffin et al. 2001), as can desiccation. Bacterial cells in cloud-free air 120 m above the surface of the Southern Ocean have been observed by transmission electron microscopy at number concentrations that are about 0.2%–25% of those of sea-salt particles (larger than 0.2 ␮m) during ACE-1 (Posfai et al. 2003, p. 233). A concentration of about 200–3000 L⫺1 with a geometric mean of 400 L⫺1, for all bacterial cells, whether alive or not, is inferred from simultaneous observations of the sea-salt concentration (larger than 0.2 ␮m) for the same altitude during ACE-1 by Y. Shinozuka (2006, personal communication) at University of Hawaii at Manoa (see also Shinozuka et al. 2004). Similarly, total concentrations of bacterial cells in cloud-free air of about 10 L⫺1 were seen on an alpine mountain and inland (Pershore, United Kingdom) by epifluorescence microscopy (Bauer et al. 2002; Harrison et al. 2005). Additionally, concentrations of all bacteria of 10– 1000 L⫺1 in the free troposphere and boundary layer are obtained by applying the observed ratio of nonculturable to culturable bacteria of about 1000 (Lighthart 1997; Bussmann et al. 2001) to counts of culturable cells (Bovallius et al. 1978; Mandrioli et al. 1984; Shaffer and Lighthart 1997; Whitman et al. 1998; Andreeva et al. 2001). Observations by Andreeva et al. and Mandrioli et al. at levels up to about 7 km MSL revealed bacterial concentrations that were quite uniform over altitude in the free troposphere.

APPENDIX D Estimation of the Inorganic Black Carbon Content at Mt. Werner from In Situ Observations In the IMPROVE technique for measuring lightabsorbing carbon (LAC; Chow et al. 1993), some but not all organic carbon is burned off in a preliminary heating cycle up to about TX ⫽ 550°C. LAC (or “elemental carbon”) is assumed to be what remains at temperatures warmer than TX in the subsequent heating cycle. Contamination by refractory organic material remaining above 550°C in that extra heating cycle is not corrected for, as it does not pyrolyze (e.g., Subramanian et al. 2006; Andreae and Gelencser 2006). Observations of polluted and biomass-burning plumes over North America (INTEX/ICARTT) in 2004 have shown that 5%–25% and 15%–30%, respectively, of the organic carbon remains refractory at 400°C (Clarke et al. 2007). These fractions may remain refractory to 550°C because of their likely formation during combustion at even higher temperatures. The total carbon content near Mt. Werner during 1–19 November 2001 was observed by IMPROVE to be 0.45 ␮g m⫺3. By assuming that about 20% of the organic carbon content remains refractory at 550°C for reasons noted above, the LAC measurement (0.11 ␮g m⫺3) is iteratively estimated to include about 0.08 ␮g m⫺3 of refractory organic carbon, 0.42 ␮g m⫺3 of total organic carbon, and 0.03 ␮g m⫺3 of inorganic black carbon. This implies that QBC,2.5,* ⬇ 3 ⫻ 10⫺11 and QBC,2.5,* ⬇ 8 ⫻ 10⫺11 kg kg⫺3. Significant uncertainty is associated with this estimate for black carbon. It depends critically on the choice of fraction of organic carbon assumed to be refractory, which depends, in turn, on the nature of the source of soot emissions. REFERENCES Abbatt, J. P. D., S. Benz, D. J. Cziczo, Z. Kanji, U. Lohmann, and O. Möhler, 2006: Solid ammonium sulfate aerosols as ice nuclei: A pathway for cirrus cloud formation. Science, 313, 1770–1773. Alfaro, S. C., A. Gaudichet, L. Gomes, and M. Maille, 1998: Mineral aerosol production by wind erosion: Aerosol particle sizes and binding energies. Geophys. Res. Lett., 25, 991–994. Al-Naimi, R., and C. P. R. Saunders, 1985: Measurements of natural deposition and condensation-freezing ice nuclei with a continuous flow chamber. Atmos. Environ., 19, 1871–1882. Andreae, M. O., and A. Gelencser, 2006: Black carbon or brown carbon? The nature of light-absorbing carbonaceous aerosols. Atmos. Chem. Phys., 6, 3131–3148. Andreeva, I. S., and Coauthors, 2001: Variability of the content of live microorganisms in the atmospheric aerosol in southern regions of western Siberia. Dokl. Biol. Sci., 381, 530–534. Archuleta, C. M., P. J. DeMott, and S. M. Kreidenweis, 2005: Ice nucleation by surrogates for atmospheric mineral dust and

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