Introduction

In this chapter, we examine the physicochemical properties of atmospheric particles that determine which subsets of the ambient aerosol can serve as cloud particle precursors for both warm (liquid) and cold (mixed-phase and ice) clouds. We recognize that not only do the particle properties play a role in determining which particles participate in cloud formation, so do environmental variables such as the air mass thermodynamic history and vertical motions. For a discussion of this larger context, which determines the activation behavior of populations of particles and the resulting influences on the microphysical and radiative properties of clouds, the reader is referred to Feingold and Siebert as well as Kärcher and Spichtinger (this volume). Our focus here is on the atmospheric aerosol itself, linking various particle sources to their contributions to cloud particle precursor populations. To make these connections, we begin with a brief review of the current status of understanding of the relationships between aerosol properties and cloud condensation nuclei (CCN), and between aerosol properties and ice-forming nuclei, including identification of the sensitivities to the key variables needed for predictive closure. Thereafter we discuss how changes in aerosol sources induced by anthropogenic activities in the past as well as in the future might influence the cloud particle precursor properties, and highlight the major uncertainties that remain to be addressed.

Relevant Properties: Warm Cloud Particle Precursors

The well-known equation that expresses equilibrium between the environmental relative humidity with respect to liquid water, RHw, and the vapor pressure of water over a spherical, aqueous solution droplet of diameter D is:

( 4oslaMw ^ DPwRT

where RH has been expressed as a fraction, a is the water activity of the sow r ' w J

lution, as/a is the surface tension of the particle/air interface, R is the ideal gas constant, T is temperature, and the partial molar volume of water in solution has been approximated as the ratio of the molecular weight of water, Mw, to its density, pw. For a choice of dry diameter, ödry, known or assumed relationships between composition, drop density, and water activity can be used in Equation 13.1 to compute RHw(D). This curve has a maximum which is identified as the critical supersaturation needed for droplet activation, sc (s = RHw - 1).

Taking Equation 13.1 as the governing equation, it is possible to list the relevant particle-related variables for cloud drop formation. For individual particles, these are surface tension, appearing in the exponential term; temperature, which also appears in the exponential term explicitly and implicitly in water activity and density; particle composition, which affects both D, in the exponential term, and water activity; and particle size (expressed here as Ddry). Equation 13.1 assumes that the wet particle is spherical, and sphericity is generally assumed for both the wet and dry particles to compute volumes and masses from diameters. This assumption, however, may not be valid for atmospheric particles, and particle shape should also be included as a variable. An aqueous solution and corresponding water activity may not exist over the full range of assumed particle water contents. Thus, particle phase state and constituent solubilities must also be considered. Finally, for a population of particles, these variables and their distribution across the population must be important, and thus the mixing state (i.e., particle-to-particle variations in composition) is also a key property.

The classic Köhler equation is obtained from Equation 13.1 by first making an assumption about the form of the water activity—composition relationship—the most common of which is:

nw PwMs Vw where n is the moles of solute, n the moles of water, vO accounts for solute sw dissociation and solution nonidealities, ps is the density of dry solute, pw is the density of water, Vs is the volume of dry solute, and Vw the volume of water. This definition can be carried through an analysis to derive an expression for the critical supersaturation for a single solute, fully dissolved particle of size Ddry:

Because of the assumptions used to derive them, Equation 13.3 must be modified to treat multiple dry aerosol components, including insoluble species.

A number of recent studies have examined the sensitivity of predicted critical supersaturations to the various particle-related parameters. McFiggans et al. (2006) provide a comprehensive review of the literature regarding the effects of physical and chemical aerosol properties on cloud drop formation, including observational attempts at aerosol-CCN closure. With respect to properties controlling a particle's ability to serve as a CCN, their discussion highlights the poorly characterized CCN activity of the organic aerosol fraction and the role of surface tension and film-forming compounds in modifying activation behavior. They note that although surfactants are present in cloud water samples, partitioning of surfactants between the bulk and the surface of a droplet will modify calculated surface tension depressions. McFiggans et al. (2006) cite a need for better understanding of whether such partitioning effects are signifi cant in atmospheric droplets. Although they list numerous factors that can affect the critical supersaturation at which a particle activates, McFiggans et al. did not rank the various factors in relative importance. In this chapter, we present an analysis aimed at developing such a ranking.

To simplify the examination of the relative role of dry particle composition, we propose an alternate form of Equation 13.2 (Petters and Kreidenweis 2007; see also Rissler et al. 2006):

When used in Equation 13.1 to predict critical supersaturation as a function of dry diameter, lines of constant k describe the sc - Ddry relationship expected for a particle of fixed composition (Figure 13.1). Summarizing both theoretical calculations and available observations, Petters and Kreidenweis (2007) provided a table of values of k for many compounds, including inorganic species commonly found in atmospheric aerosols such as sodium chloride and ammonium sulfate, as well as values representative of the behavior of complex aerosols, such as secondary organic aerosol (SOA) generated in the ozo-nolysis of several different precursors. Figure 13.1 shows typical ranges of k for inorganic species, organic aerosols, and several other measured aerosol types. Petters and Kreidenweis (2007) demonstrated that the CCN activities of

Hygroscopicity (k)

Hygroscopicity (k)

Fulvic Acid Fractions

Figure 13.1 Relationship between critical supersaturation and dry diameter, adapted from Petters and Kreidenweis (2007). Fulvic acid and ammonium sulfate points are from Svenningsson et al. (2006) and demonstrate that experimental data organize approximately along lines of constant hygroscopicity. Shading indicates the hygroscopicity ranges for continental (light gray, 0.3±0.1) and marine (dark gray, 0.7±0.2) aerosols suggested by Andreae and Rosenfeld (2008). Also shown are ranges in hygroscopicity for biomass burning aerosols dominated by organic compounds (dotted line) and having substantial mass fractions of inorganic compounds (white line) (unpublished), and biogenic secondary organic aerosols (BSOA; Prenni et al. 2007b).

Figure 13.1 Relationship between critical supersaturation and dry diameter, adapted from Petters and Kreidenweis (2007). Fulvic acid and ammonium sulfate points are from Svenningsson et al. (2006) and demonstrate that experimental data organize approximately along lines of constant hygroscopicity. Shading indicates the hygroscopicity ranges for continental (light gray, 0.3±0.1) and marine (dark gray, 0.7±0.2) aerosols suggested by Andreae and Rosenfeld (2008). Also shown are ranges in hygroscopicity for biomass burning aerosols dominated by organic compounds (dotted line) and having substantial mass fractions of inorganic compounds (white line) (unpublished), and biogenic secondary organic aerosols (BSOA; Prenni et al. 2007b).

complex particle types, such as SOA, follow, to a good approximation, lines of constant k, greatly simplifying the calculation of the critical supersaturation; in particular, the intractable problem of establishing the complete speciation of the organic aerosol is avoided.

In Equation 13.4, k can represent a mixture of components by summing the volume of fraction-weighted component k values, including components with k = 0, that contribute to the initial dry volume but not to any subsequent water uptake. However, as written, Equation 13.4 does not take particle phase state into account. In other words, water uptake is assumed to be continuous over the full range 0 < aw < 1, unless some additional constraint is imposed. For compounds that are not infinitely soluble in water, a stable solution is formed only for water contents (and thus solution activities) larger than the solubility limit; this constraint is manifested as deliquescence of a particle at a size-dependent RH . For some sparingly soluble compounds and submicrometer particle sizes, deliquescence may occur only at water supersaturations (Hori et al. 2003; Bilde and Svenningsson 2004), leading to sc - Ddry relationships which do not follow the k isolines (Kreidenweis et al. 2006). In the general case, for multiple components each having individual solubilities, the k framework can be extended to account for gradual dissolution (Petters and Kreidenweis 2008).

In fitting experimental data to Equations 13.1 and 13.4 to obtain a value of k, an assumption is required for the particle/air surface tension, as/ . It is possible to attempt to fit both k and as/ using a single dataset, but these cannot be fitted uniquely. An assumption fixing the value of as/ is needed to fit humidified tandem differential mobility analyzer (H-TDMA) data or sc~Ddry data, but derived values of k are more sensitive to the assumption in the latter case. The literature contains a number of recent observational and laboratory studies which suggest that some constituents of the atmospheric aerosol depress surface tension and thus enhance CCN activity (e.g., Facchini et al. 1999), although it has also been argued that the overall effect in mixtures and at the typical dilutions experienced at activation are not large enough to play a significant role (e.g., Sorjamaa et al. 2004; Topping et al. 2007). Petters and Kreidenweis (2007) suggest that the surface tension of pure water at 298.15 K be used for purposes of fitting and applying k values. For surface-active compounds, this results in a derived value of k that is higher than would be determined from bulk thermodynamic data, reflecting the enhancement of CCN activity attributable to surface tension depression. When applied in mixture calculations, the fitted k value captures in part the effective contribution of the surface-active component to the lowering of the mixture surface tension.

Sensitivity of Liquid Cloud Particle Formation to Particle Properties

We now estimate the sensitivity of individual particle critical supersaturation to relevant particle properties. Although k isolines are not linear and parallel over the entire domain, for an infinitely soluble dry particle with k > 0.2, the analog of Equation 13.3c can be derived, where B = KD3dry, leading to:

KDdryT

We note that Equations 13.3a and 13.5 are inaccurate for small k, breaking down completely for k = 0, and also do not apply at subsaturated conditions (Petters and Kreidenweis 2007). From Equation 13.5, we can deduce the influence on critical supersaturation of variations in surface tension, composition, dry diameter, and temperature. For example, at fixed supersaturation, d^ «-3^. (13.6)

K Ddry

In other words, a 10% decrease in diameter must be compensated by a 30% increase in hygroscopicity to maintain constant critical supersaturation. This demonstrates that critical supersaturation is three times more sensitive to particle size variations than to composition variations. Similar considerations lead to the other entries in Table 13.1a.

Table 13.1a Matrix of the intrinsic sensitivities of the properties governing CCN activity. Each entry denotes the value of the partial derivative of the numerator (columns) with respect to the denominator (rows), where the numerator and denominators are the natural logarithm of the indicated parameter. The table can be used to assess the relative importance on critical supersaturation of particle size (expressed as dry particle diameter Ddry), composition (expressed as hygroscopicity parameter k), temperature (T) and surface tension (os/a). For example, for liquid drop nucleation, d ln k / d lnD^ = -3, indicating that the same critical supersaturation can be maintained for a particle if a 10% decrease in Ddry is compensated by a 30% increase in k.

Liquid drop nucleation

dry

K

T t

s/a

D dry

1

-3

-1

1

K

-1/3

1

-1/3

1/3

T

-1

-3

1

1

°s/a

1

3

1

1

| Sensitivity to temperature was evaluated assuming that k is independent of temperature and that the surface tension of pure water is constant. In reality, surface tension increases with decreasing temperature, introducing some cross-correlation into the sensitivity table.

| Sensitivity to temperature was evaluated assuming that k is independent of temperature and that the surface tension of pure water is constant. In reality, surface tension increases with decreasing temperature, introducing some cross-correlation into the sensitivity table.

The intrinsic sensitivities in Table 13.1a must be combined with typical variations in each variable in order to rank their relative importance. Let us consider now excursions in each parameter of Equation 13.5 and list the selected ranges, d ln X. (see Table 13.1b). For diameter, we consider both a large variability in submicrometer size, 0.01-1 p.m, and a smaller excursion of 0.08-0.2 p.m, intended to capture typical variations in the median diameter of the accumulation mode. Andreae and Rosenfeld (2008) summarize many published estimates of aerosol composition and hygroscopicity in terms of equivalent k values. They suggest that continental particles, with more significant mass fractions of non- and less-hygroscopic components, can be well represented by k=0.3 ± 0.1 and marine particles by k = 0.7 ± 0.2. We note that close

Table 13.1b Range in parameters considered for estimation of sensitivities (see Tables 13.1c and 13.3b). acc: accumulation mode; mar: marine; cont: continental; dil: dilute.

dlnDdry

dln k

d ln T

dln o, s/a

Range of Ddry, all sizes 0.01-1 ^m

4.6

Range of Ddry, acc 0.08-0.2 ^m

0.92

Range of k, all 0.01-1.2

4.8

Range of k, mar 0.2-0.4

0.69

Range of k, cont 0.5-0.9

0.59

Range of T 240-303 K / 210-240 K

0.23/0.13

Range of osM, all 0.025-0.075 N m 1

1.1

Range of osM, dil 0.06-0.075 N m 1

0.22

to sources, on urban and smaller scales and in the boundary layer, the mixing processes (such as coagulation and condensation), which serve to homogenize composition as well as to move the aerosol particles toward a single mode in the accumulation size range, have not had sufficient time to operate. Thus particles observed at such scales may exhibit larger variability in k values; that is, the aerosols may contain multiple modes with possible k values 1.2 > k> 0.01, suggesting a maximum range of d ln k ~ 4.8. For liquid drop formation, the relevant temperature range is 240-303 K. Finally, we consider variations in surface tension which span the wide range of values for atmospheric aerosols that have been speculated in the literature (approximately 0.025 N m-1, up to the value for water, 0.075 N m-1) and a smaller range, 0.06 N m-1 to the pure water value, which is likely more representative of surface tensions for dilute solutions in particles near the point of activation.

Table 13.1c combines the intrinsic sensitivities with the range estimates to produce an estimate of the sensitivities between two parameters, X. and X:

sensitivity =

J /intrinsic

From Table 13.1c, it is clear that T, k, and os/a have comparable influences on CCN activity, if excursions in T, k, and ash are limited to smaller ranges, as appropriate for well-mixed marine or continental aerosols exhibiting minimal surface tension suppression. If small temperature changes of a few degrees, such as might be associated with climate change, are considered, then the relative influence of T on critical supersaturation is very small. Whether sensitivity of critical supersaturation is higher for k or Dáry depends to a large part on the ranges of variations one wishes to consider reasonable for the various parameters. The sensitivities of sc to variations in diameter are almost

Table 13.1c Relative sensitivities, of column with respect to row variables, limiting allowed variations to those observed in the atmosphere, as shown in Table 13.1b. To obtain the values shown, the excursions in Table 13.1b have been multiplied by the absolute values of the intrinsic sensitivities, as given in Table 13.1a (see text for definition). The temperature range 240-303 K has been applied, appropriate for liquid drop nucleation.

Table 13.1c Relative sensitivities, of column with respect to row variables, limiting allowed variations to those observed in the atmosphere, as shown in Table 13.1b. To obtain the values shown, the excursions in Table 13.1b have been multiplied by the absolute values of the intrinsic sensitivities, as given in Table 13.1a (see text for definition). The temperature range 240-303 K has been applied, appropriate for liquid drop nucleation.

Liquid drop nucleation

^ an

Ddry, acc

k, all

k, mar

k, cont

T

k, all

2.9

0.58

k, mar

20

4.0

k, cont

23

4.7

T

20

4.0

7.0

1.0

0.86

<v„, aU

4.2

0.84

1.5

0.21

0.18

0.21

aM> dil

21

4.2

7.3

1.01

0.89

1.1

always the largest, except for the case of accumulation-mode particle sizes with large variations in k, which might occur for an externally mixed aerosol. This observation highlights the importance of aerosol mixing state, which can result in large particle-to-particle excursions in k within a size range, exerting a large influence on variability of critical supersaturations in the accumulation mode aerosol.

In addition to the direct role of temperature in Equation 13.5 evaluated above, temperature variations also modify particle thermodynamic properties, including hygroscopicity, surface tension, and phase state. It is generally assumed that variations in solution water activity (and hence in k) with temperature are small, and that aw-composition relationships obtained at room temperature can be extrapolated to all tropospherically relevant temperatures. For individual inorganic compounds, calculations which include temperature variations show that k is within a few percent of that computed when ignoring the temperature effects (Clegg et al. 1998), as demonstrated in Figure 13.2. However, the ther-modynamic data on which the calculations are based is sparse, and the validity of this assumption is unknown for more complex particle types including those dominated by organic constituents.

The initial phase state of a particle can significantly raise the critical supersaturation required for activation, if supersaturated conditions are required to initiate dissolution (e.g., Bilde and Svenningsson 2004). However, many atmospheric particles are mixtures of a number of constituents, and thermo-dynamic arguments suggest they can retain water to very low RH (Marcolli et al. 2004), which implies that in the atmosphere, solid-to-liquid phase transitions only infrequently influence CCN activity. In Figure 13.3 we explore the

Temperature (K)

Figure 13.2 The hygroscopicity parameter computed as a function of temperature from the water activities predicted by the Aerosol Inorganics Model (AIM), Model II (Clegg et al. 1998), evaluated at aw=0.9985, corresponding approximately to the dilution at CCN activation.

Temperature (K)

Figure 13.2 The hygroscopicity parameter computed as a function of temperature from the water activities predicted by the Aerosol Inorganics Model (AIM), Model II (Clegg et al. 1998), evaluated at aw=0.9985, corresponding approximately to the dilution at CCN activation.

effect of a related property, solubility (C), on predicted CCN activity. Here solubility is expressed as the volume of compound per unit volume of water in the saturated solution. For C. > 10-1, the initial particle or component phase state has no impact on CCN activity. For Ct < 5 x 10-3, the particle or component may be treated as effectively insoluble. In the intermediate regime, the effects are more complex and lead to enhanced sensitivity of CCN activity to Ddry (i.e., sc- Ddry relationships that do not follow K-isolines; see Petters and Kreidenweis 2008). We note, however, that this highly sensitive regime applies to a limited region of solubilities, and only a few studies (Hori et al. 2003; Bilde and Svenningsson 2004) have observed solubility-limited behavior for laboratory-generated, single-component organic proxy aerosols. Thus, despite the sensitivity of CCN activity to solubility, we argue that in practice, it may be sufficient to know if a constituent or entire particle falls into the effectively insoluble or effectively infinitely soluble regime, and assign only moderate importance to this parameter.

We close this section with a brief discussion of the broader picture; namely, factors that influence the activation of a population of particles to cloud drops (see also Feingold and Siebert, this volume). In some cases in clean regions

Insoluble Sparingly Soluble soluble

Insoluble Sparingly Soluble soluble

Solubility

Figure 13.3 Variation of critical supersaturation with solubility C t (volume of compound per unit volume of water in the saturated solution) for particles having assumed K = 0.6 and dry diameters of 30, 50, and 120 nm (solid lines). The dashed line represents a 50 nm particle of mixed composition, with 95% by volume of a substance with k j = 0.6 and 5% of an infinitely soluble substance with k2 = 0.3. The plot delineates three solubility regimes that impact CCN activity in the size range 30 < D, < 500 nm: (1) Cj < ~5 x 10 3, where solubility of that compound is negligible, regardless of the value of k, and the compound may be treated as insoluble (k = 0). (2) Ct > ~10 ', where solubility is large enough so the compound may be treated as infinitely soluble. (3) ~5 x 10 3 < C j < ~10 ', where solubility can strongly impact CCN activity, and the compound's CCN behavior, either as a pure compound or in a mixture, must be treated as discussed in Petters and Kreidenweis (2008).

Solubility

Figure 13.3 Variation of critical supersaturation with solubility C t (volume of compound per unit volume of water in the saturated solution) for particles having assumed K = 0.6 and dry diameters of 30, 50, and 120 nm (solid lines). The dashed line represents a 50 nm particle of mixed composition, with 95% by volume of a substance with k j = 0.6 and 5% of an infinitely soluble substance with k2 = 0.3. The plot delineates three solubility regimes that impact CCN activity in the size range 30 < D, < 500 nm: (1) Cj < ~5 x 10 3, where solubility of that compound is negligible, regardless of the value of k, and the compound may be treated as insoluble (k = 0). (2) Ct > ~10 ', where solubility is large enough so the compound may be treated as infinitely soluble. (3) ~5 x 10 3 < C j < ~10 ', where solubility can strongly impact CCN activity, and the compound's CCN behavior, either as a pure compound or in a mixture, must be treated as discussed in Petters and Kreidenweis (2008).

and/or in the presence of strong updrafts, virtually all of the available particles may be nucleated to drops, and any variations in Table 13.2 parameters are much less important than total aerosol number concentrations in influencing total drop number concentrations. If excess numbers of particles are available, then drop number concentrations also depend on the spectrum of the individual particles' critical supersaturations as well as on the competition in the forming cloud between generation and consumption of water supersaturation, which determines the peak supersaturation achieved in each cloud element. For a single choice of input aerosol properties, Figure 13.4 demonstrates the effects of variations in surface tension on the spectrum of critical supersaturations, hygroscopicity, temperature, particle number median diameter, geometric standard deviation of the particle population, and total particle number concentration. The complexity of the response of critical supersaturation to

0.01 0.1 1 Supersaturation (%)

0.01 0.1 1 Supersaturation (%)

0.01 0.1 1 Supersaturation (%)

0.01 0.1 1 Supersaturation (%)

Figure 13.4 Variation of CCN activation spectrum, expressed as the normalized number concentration of particles active as a function of the supersaturation (abscissa). The calculations were performed for a log-normal aerosol distribution having a geometric number mean diameter of 100 nm and geometric standard deviation of 1.8, with the following assumed properties and environmental variables: k=0.3; osaa = 0.065 N m '; and T = 280 K. In (a), the shaded region indicates the effect of a ±10% excursion in surface tension (response is opposite in sign to the others in this panel), temperature, or median diameter, or a ±30% excursion in k. Panels (b) and (c) indicate the effects of ±10% excursions in geometric standard deviation and total aerosol number concentration, respectively.

0.01 0.1 1 Supersaturation (%)

Figure 13.4 Variation of CCN activation spectrum, expressed as the normalized number concentration of particles active as a function of the supersaturation (abscissa). The calculations were performed for a log-normal aerosol distribution having a geometric number mean diameter of 100 nm and geometric standard deviation of 1.8, with the following assumed properties and environmental variables: k=0.3; osaa = 0.065 N m '; and T = 280 K. In (a), the shaded region indicates the effect of a ±10% excursion in surface tension (response is opposite in sign to the others in this panel), temperature, or median diameter, or a ±30% excursion in k. Panels (b) and (c) indicate the effects of ±10% excursions in geometric standard deviation and total aerosol number concentration, respectively.

various perturbations for this single case gives an indication of the difficulty in generalizing sensitivities. Nevertheless, it is immediately obvious from Figure 13.4 that at high supersaturations, where almost all particles are able to activate, there is sensitivity only to the total number concentration of particles. At intermediate supersaturations, all of the other variables can modify the number concentration active at a selected supersaturation, with approximately similar influences on changes in number concentration for similar percentage excursions (except for k, which is three times less influential, as discussed above), as noted already in Table 13.1a for surface tension, diameter, and temperature. Finally, we wish to highlight two additional, important points. First, when cloud dynamics are taken into account, sensitivities of drop number concentrations to all of the variables considered here are lower than the sensitivities computed for the response of CCN concentrations to those variables. The lower sensitivity arises because the number concentration of activated droplets is tied to the peak supersaturation achieved in an updraft, which changes in response to changes in the input aerosol. Second, particle dissolution kinetics (Asa-Awuku et al. 2008; Taraniuk et al. 2007) and reduction of mass accommodation coefficients, and thus drop growth rates (Chuang et al. 1997; Nenes et al. 2001), can also alter peak supersaturations. Thus, it is not possible to use Figure 13.4 to evaluate directly the effect of a parameter perturbation on drop number concentration. These issues are discussed in detail by McFiggans et al. (2006), who also summarize many recent modeling and observational studies aimed at CCN-drop number concentration closure. Even more complexity exists at scales larger than a single updraft, where factors controlling cloud formation and maintenance are not well understood and may prove to be of more importance to the global radiation balance than perturbations induced by changes in the atmospheric aerosol (for further discussion on cloud-controlling factors, see Bretherton and Hartmann; Stevens and Brenguier; Grabowski and Petch; Kârcher and Spichtinger; and Feingold and Siebert, all this volume).

Relevant Properties: Ice Cloud Particle Precursors

In discussing the particle properties relevant to ice formation in the atmosphere, the first distinction that must be made is with respect to freezing mechanism. Homogeneous freezing (i.e., nucleation of an ice crystal from solution and subsequent freezing of the particle) is important at temperatures colder than about -38°C and can occur either in supercooled, dilute droplets or in aqueous solution droplets. Heterogeneous freezing can proceed via several processes, all requiring the presence of a solid surface with properties that catalyze ice nucleation either from the gas phase or in a cloud drop. Added complications are that ice crystal nucleation is strongly temperature dependent and, unlike cloud drop formation, stochastic (i.e., there is a probability per unit time for nucleation to take place in a given volume; Vali 2008). Nevertheless, the onset conditions for nucleation in individual particles can be identified with characteristic supersaturations and temperatures: since nucleation rates vary so dramatically across small changes in these variables, they can often be approximated as step functions.

Heterogeneous Freezing

Heterogeneous ice nuclei (IN) can play important roles in determining cloud particle phase state, for supercooled clouds between 0°C and -38°C. It is the onset of freezing that determines when such clouds transition into a colloidally unstable regime. With the appearance of ice crystals in clouds, precipitation and lightning processes become greatly accelerated. This highlights the importance of onset freezing temperatures associated with the nuclei, in addition to their number concentrations. Some bacterial IN can nucleate ice at temperatures as warm as -2°C, whereas observed onset temperatures for dust IN range from -8° to -25°C. Typical number concentrations of IN in the atmosphere range from ~0.001 to 0.01 cm-3, although values up to 1 cm-3 have been observed in dust plumes (DeMott et al. 2003b). Their very low number concentrations, compared with that of the total ambient aerosol, which even in extremely clean conditions of 10 cm-3 is four orders of magnitude larger, present unique measurement and modeling challenges.

For T > -38°C, most ice nucleation mechanisms require the presence of a formed, or forming, cloud droplet. The droplets are usually sufficiently dilute to ignore the presence of a dissolved solute. Effective heterogeneous freezing nuclei often have a component with a crystallographic near-match to the structure of hexagonal ice (Vonnegut 1947); however, crystal polarity (Gavish et al. 1992) also plays a role. Ice germs are thought to form on surface irregularities, or active sites (Vali 1994; Marcolli et al. 2007). It appears that the presence of an aqueous solution can deactivate sites for germ formation for heterogeneous nucleation of haze at cirrus temperatures (Möhler et al. 2005; Koehler 2007; Zobrist et al. 2008), perhaps implying that coatings of hygroscopic solutes may reduce ice nucleation efficiency of dusts in dilute cloud droplets also. In the atmosphere, however, hygroscopic coatings may be necessary to activate the particle into a cloud droplet and thus a necessary condition for immersion freezing to proceed (Vali 1994; Andreae and Rosenfeld 2008). Mineral dusts, some strains of bacteria, and certain organic compounds have been found to initiate ice in laboratory studies at temperatures warmer than -20°C. Ice crystal residuals collected in field study sampling of clouds in this temperature regime have not been investigated to date because the ice crystals must be separated reliably from the cloud droplet population. Recently developed ice counterflow virtual impactors (Mertes et al. 2007) may fill this gap. Electron microscopy analyses of residual particles from ice crystals formed inside continuous flow diffusion cloud chambers (DeMott et al.

2003a) at warmer temperature regimes will also provide new information on composition. Those studies that have characterized composition of ice-forming particles in the atmosphere, mostly limited to ice crystal residuals collected at cirrus temperatures, show salts, crustal materials, carbonaceous particles, and bacteria (Jayaweera and Flanagan 1982; Heintzenberg et al. 1996; DeMott et al. 2003a; Twohy and Poellot 2005; Targino et al. 2006). Little, however, is known about the specific sources, their seasonality, and their strength, the combination of which apparently drive the global IN budget.

Homogeneous Freezing

Cloud droplets freeze spontaneously when cooled below ~ -38°C (Jeffery and Austin 1997). In the presence of dissolved solutes, the freezing point is depressed, and metastable liquid phases can exist even at much colder temperatures. Nevertheless, ice germ nucleation may occur in submicrometer solution particles at relative humidities subsaturated with respect to liquid water. The most widely applied parameterization for computing homogeneous freezing nucleation rates in such aqueous haze particles is that of Koop et al. (2000), who reviewed a large body of experimental data and showed that freezing temperature was associated with a unique solution water activity. Koop et al. provide empirical fits for computing nucleation rates, if the solution water activity-composition relationship is known; variations in these relationships and in dry particle densities among compounds lead to small changes in the computed aqueous particle volume that can affect nucleation rates, which are based on the volume of solution. Thus, particle hygroscopicity and surface tension of the solution, as discussed above with respect to CCN activity, are again relevant parameters.

Sensitivity of Ice Cloud Particle Formation to Particle Properties

We now estimate the sensitivity of ice crystal formation to relevant particle properties (see also Karcher and Spichtinger, this volume, who consider dynamic controls on cirrus formation in addition to aerosol influences). Figure 13.5 demonstrates the relationships between homogeneous freezing relative humidity (FRH), dry diameter, temperature, and hygroscopicity, as calculated from the Koop et al. (2000) parameterization. As expected, the lowest RH onset is associated with the coldest temperature (i.e., the largest supercooling). Large dry particle size and particle hygroscopicity lead to more favorable conditions for freezing because the available droplet volumes are larger, because of the action of the Kelvin effect, which increases solution concentration in equilibrium at the specified RH for smaller particles. The results in Figure 13.5 have been used to estimate numerically sensitivities to Ddxy, k, T, and asa, which are displayed in Table 13.2a. Freezing rates are, by far, most sensitive to

1.00

0.95

Hygroscopicity (k)

0.90

0.85

Hygroscopicity (k)

1.00

0.95

0.90

0.85

0.01

Dry diameter (|jm)

Figure 13.5 Calculated relative humidity, using the parameterization of Koop et al. (2000), for 0.1% of particles to freeze homogeneously within 5 s at two different temperatures (-43° and -60°C) and three different hygroscopicities (k = 1, 0.1, 0.01). Gray lines demonstrate evaluation of the sensitivity of freezing relative humidity to T, Ddry, and k at Ddry = 1.0 ^m.

0.01

Dry diameter (|jm)

Figure 13.5 Calculated relative humidity, using the parameterization of Koop et al. (2000), for 0.1% of particles to freeze homogeneously within 5 s at two different temperatures (-43° and -60°C) and three different hygroscopicities (k = 1, 0.1, 0.01). Gray lines demonstrate evaluation of the sensitivity of freezing relative humidity to T, Ddry, and k at Ddry = 1.0 ^m.

temperature. Weighting by the typical excursions in dlnx, as discussed above for warm clouds (Table 13.1b), we find the sensitivities presented in Table 13.2b. We have modified the unique matrix elements shown, from those selected for presentation in Table 13.1c, to more clearly demonstrate the strong sensitivity to temperature above all other variables. In general, the next most important variable is Ddry, and sensitivity to k and to surface tension is minimal.

Because of the low temperatures and sometimes low relative humidities in the mid to upper troposphere, particle phase state may be a more important factor in influencing conditions for onset of homogeneous freezing than it is in influencing warm cloud formation: for some particle types and sizes, it is possible that no aqueous phase exists until water supersaturation conditions. However, the deliquescence relative humidities for ammonium sulfate (Onasch et al. 1999), some organic compounds (Brooks et al. 2002), and some mixed particle types (Brooks et al. 2002; Marcolli et al. 2004; Parsons et al. 2004) have been examined at low temperatures in the laboratory, and results suggest thus far that in most cases freezing processes would not be inhibited because of high deliquescence RHw. Further, since ice cloud formation can occur for such a low number concentration of particles, even if only a small fraction of available particles are deliquesced, these will be sufficient to initiate ice formation. We have therefore estimated that homogeneous freezing nucleation is only somewhat sensitive to initial phase state of individual

Table 13.2a As in Table 13.1a, but for homogeneous freezing nucleation. The intrinsic sensitivities have been evaluated numerically, using the formulae recommended by Koop et al. (2000).

Homogeneous freezing nucleation

Ddry

k

T +

°S/a

Ddry

1

—4

0.024

~2

k

—1/4

1

0.006

~1/2

T

42

156

1

-83

~1/2

~2

-0.012

1

| Sensitivity to temperature was evaluated assuming that k is independent of temperature and that the sur face tension of pure water is constant. In reality, surface tension increases with decreasing temperature, introducing some cross-correlation into the sensitivity table.

| Sensitivity to temperature was evaluated assuming that k is independent of temperature and that the sur face tension of pure water is constant. In reality, surface tension increases with decreasing temperature, introducing some cross-correlation into the sensitivity table.

particles. Before homogeneous freezing can set in, a particle must take up water to dilute its content until a minimal level of temperature-dependent water activity is reached. Consequently, we estimate some sensitivity to the composition mixing state, which determines the distribution of hygroscopic material and thus of k.

All of the sensitivities of heterogeneous freezing onset conditions to particle properties were estimated using qualitative arguments, since no definitive theoretical treatments exist to date. It is reasonable to assume that surface properties, which control the number of active sites, are the most important variable, and that Ddry assumes importance because active sites may scale with surface area (Vali 1994; Marcolli et al. 2007). It is expected that the probability of ice germ formation on an active site immersed inside a cloud droplet increases exponentially with decreasing temperature (e.g., Vali 1994 and references therein); surprisingly, however, some atmospheric observations do not follow

Table 13.2b Sensitivities, of column variable with respect to row variable, limiting allowed variations to those observed in the atmosphere, as shown in Table 13.1b. To obtain the values shown, the excursions in Table 13.1b have been multiplied by the absolute values of the intrinsic sensitivities, as given in Table 13.3a (see text for definition). The temperature range 210-240 K has been applied, appropriate for homogeneous freezing.

Homogeneous freezing nucleation k, all k, mar k, cont T vs/a, all asJa, dil

Ddry, an

0.26

0.04

0.03

1.18

0.12

0.02

D. , acc dry'

1.30

0.19

0.16

5.89

0.60

0.12

k, all

4.51

0.46

0.09

k, mar

31.40

3.19

0.64

k, cont

36.72

3.73

0.75

T

0.10

0.02

this trend (Gultepe et al. 2001; Prenni et al. 2007a). In fact, deposition nuclei at cirrus temperatures also freeze at constant ice supersaturation with no sensitivity of freezing onset RH. to temperature for T<-40°C (Koehler et al. 2007). Nevertheless T is likely to be important in heterogeneous freezing processes; thus we have assigned a moderate sensitivity to this variable. Coatings of soluble material degrade freezing activity for deposition nuclei under cirrus conditions (Möhler et al. 2005; Koehler 2007), so we expect there to be strong sensitivity to initial phase state and composition mixing state, and some sensitivity to solubility; the exact value of hygroscopicity of the soluble material, in contrast, is not so important. The importance of phase state is also highlighted by recent observations that the water soluble compounds ammonium sulfate and oxalic acid can nucleate ice via deposition if they are in their crystallized form (Abbatt et al. 2006; Zobrist et al. 2006).

Future Changes in Cloud Particle Precursor Types, Properties, and Concentrations

For purposes of understanding the effects of past and future changes in aerosol populations on cloud particle precursor concentrations, we separate the problem into two parts: factors that affect particle properties, such as hygroscopic-ity, and additional factors that affect particle residence times, although clearly these are related (e.g., through effects of hygroscopicity on precipitation scavenging). As a basis for discussing the impacts of past and future changes in aerosol burden and composition on CCN number concentrations, we use the differences in preindustrial and present-day aerosols as simulated by Tsigaridis et al. (2006). Those authors found a nonlinear response of global annual average aerosol burdens (expressed in Tg) to emissions (expressed in Tg y-1): while emissions of inorganic aerosol precursors increased by factors of 3-6, burdens of corresponding aerosol species increased by factors of only 2.6-2.9. Dust and sea salt were kept constant for all simulations, and represented nearly the same fractions of total aerosol burden in both cases (see their Figure 13.3). The main differences are that increased contributions of inorganic aerosol components in present-day aerosols create "more acidic and hygroscopic aerosols," with significantly higher associated aerosol water contents. Their model does not simulate aerosol mixing state, but since many secondary inorganic aerosol species partition to the particle phase via condensation, it is implied that more internal mixing occurs in the present day, as indicated by significantly shorter simulated times for primary organic aerosol and black carbon to transform from hydrophobic to hydrophilic. Table 13.3 shows the modeled preindustrial and present-day relative mass fractions of constituents other than dust and sea salt. We choose representative k values for each component (e.g., k soa=0.1; k poa=k bc = 0; all other k=0.7) and compute the volume-weighted mixture k, assuming that the aerosol particles are internally mixed (at some distance

Table 13.3 Present and preindustrial mass fractions (excluding contributions from dust and sea salt) for secondary organic aerosol (SOA), primary organic aerosol (POA), black carbon (BC), sulfate, ammonium, nitrate, and methanesulfonic acid (MSA), as presented by Tsigaridis et al. (2006). Overall k values were calculated by weighting the assumed component hygroscopicities with the modeled volume fractions; we assumed that the mass and volume fractions are identical.

Table 13.3 Present and preindustrial mass fractions (excluding contributions from dust and sea salt) for secondary organic aerosol (SOA), primary organic aerosol (POA), black carbon (BC), sulfate, ammonium, nitrate, and methanesulfonic acid (MSA), as presented by Tsigaridis et al. (2006). Overall k values were calculated by weighting the assumed component hygroscopicities with the modeled volume fractions; we assumed that the mass and volume fractions are identical.

K

Present

Preindustrial

SOA

0.1

0.31

0.46

POA

0.0

0.24

0.19

BC

0.0

0.04

0.02

Sulfate

0.7

0.13

0.09

Ammonium

0.7

0.13

0.09

Nitrate

0.7

0.12

0.09

MSA

0.7

0.02

0.25

overall k

0.32

0.28

from the source). We find that the difference in mixture k between the two time periods is less than ~15%. Of greater consequence would be the persistence of unmixed aerosols farther from source regions in preindustrial times, because of lower condensation rates for sulfate, nitrate, and ammonium. However, if less condensation onto primary organic aerosol (POA) and black carbon (BC) produced fewer internally mixed particles, the results would be two populations: one, containing POA and BC, with smaller k than the computed average, and one, containing only secondary species, characterized by a larger k. Unless the particle size in the two modes varied significantly from that of the completely mixed aerosol, the net effect on CCN spectra would be small. In summary, past and future changes in composition alone are probably insufficient to have a large impact on CCN activity.

From the sensitivities estimated in Table 13.1c, changes in lifetime that might affect mean particle size (and total number concentrations) are probably more important influences on CCN populations than changes in overall composition. Indeed, we have shown here that a small change in particle size has as much impact on CCN activity as a much larger change in that particle's composition. Tsigaridis et al. (2006) used present-day meteorology in their preindustrial simulations, so that computed changes in the aerosol were entirely driven by the applied changes in emissions. If past and future climates are associated with significant changes in spatial and temporal patterns of precipitation, the main removal mechanism for aerosols, particle lifetimes will change from their present-day values. Similarly, if future climates are associated with more frequent and persistent high-pressure systems over regions having significant particle precursor emissions, we can expect enhanced condensation and growth of the accumulation mode. An unresolved question is whether the increases in global aerosol mass burden from the preindustrial era to the present day, and any changes in meteorology, were associated with similar increases in global aerosol number concentrations, so that mean aerosol size was not greatly affected. Since coagulation processes tend to reduce aerosol number concentrations rapidly, and process ambient submicrometer size distributions toward a single, accumulation-mode peak, we speculate that number and mass increases were not proportional, and that the mean diameter of the accumulation mode (again, at some distance from primary sources) is probably larger in the present day than in preindustrial times. For the extreme assumption that preindustrial number concentrations were similar to those in the present day, the modeled increase in the atmospheric burden of non-sea salt, non-dust aerosol over this period reported by Tsigaridis et al. (2006), 2.7 to 4.8 Tg, would result in a ~20% increase in mean particle size, equivalent in its effects on CCN activity to a ~60% increase in k, much larger than the effect of varying chemical composition alone. Assuming that homogeneous ice nucleation follows the predictions of Koop et al. (2000), neither the projected changes in hygroscopicity nor in mean accumulation-mode particle size have the potential to affect homogeneous freezing processes substantially. In contrast, however, any changes in dust and biological particle emissions strength, transport patterns, and lifetimes could play a strong role in frequency and altitude of ice cloud formation. Although Tsigaridis et al. (2006) assumed dust emissions were unchanged, other studies have considered the impacts of land use change, prolonged drought, and other climate variables. To date there is no consensus on the past or future changes in dust global cycles, and emissions estimates of biological particles active in cloud formation are virtually unknown for even the present day. Both are needed to develop estimates of future aerosol-cloud precursor relationships.

Status of "Closure" and Recommended Research Directions Warm Cloud Formation

CCN closure studies evaluate the consistency between measured CCN number concentrations at a certain supersaturation and predictions based on measured particle size distributions and chemical composition or hygroscopicity. McFiggans et al. (2006) summarized several closure studies which show that predicted CCN number concentrations, while generally within ~20% of observations, are almost always biased high compared with direct measurements. This bias, with exception of the Vestin et al. (2007) result, is also evident in more recent studies (Broekhuizen et al. 2006; Mochida et al. 2006; Medina et al. 2007; Stroud et al. 2007). Although the closure studies are often within experimental uncertainties, the consistent overprediction is troubling and not easily explained. Many of the suggested modifications to Köhler theory, such as surface tension depression effects by aerosol organic components, lead to even greater predicted CCN concentrations. It is important to point out that Equation 13.1 is an equilibrium expression, and this has motivated some investigators to search for non-equilibrium effects, related to particle growth kinetics, that may reduce the closure bias. Reduced growth rates may prevent particles expected to activate under equilibrium conditions from forming supermicrometer droplets and being detected as CCN in instruments with finite growth times. At least two mechanisms have been identified to explain such a phenomenon: (a) it has been hypothesized that organic films are ubiquitous on atmospheric particles (Gill et al. 1983); (b) if the dry soluble mass in a particle is unable to dissolve during the particle's exposure to supersaturated conditions, then the s required for activation is increased over the equilibrium value. Results from laboratory experiments have been interpreted as exhibiting the latter effect (e.g., Hegg et al. 2001).

In the laboratory, the presence of a film at the gas/liquid interface has been shown to reduce the rate of condensational growth (e.g., Chuang 2003, and references therein). Mass accommodation coefficients as low as 10-5 have been measured for a single component film. However, in the atmosphere, where the organic fraction comprises numerous species, it is unclear to what extent reductions in mass accommodation occur. Recent measurements of the growth rate of atmospheric particles by Ruehl et al. (2008) have found that particles that grow only one-half and one-tenth as quickly as ammonium sulfate particles were commonly found at four sites ranging from rural to urban, representing up to 80% and 20% of all particles, respectively. Some recent studies address also the possibility that dissolution kinetics may play a role in droplet activation in the atmosphere (Asa-Awuku et al. 2008; Taraniuk et al. 2007).

A significant problem with the interpretation of CCN data is introduced by the need to calibrate the supersaturation in the CCN instruments, since calculated supersaturations, based on temperature and vapor gradients, do not agree with inferred supersaturations, based on ammonium sulfate test aerosol and Köhler theory. This disagreement is found in both static (Snider et al. 2006) and continuous flow (Rose et al. 2008) CCN instruments. Further, no universally accepted relationship between critical supersaturation and dry particle diameter exists for ammonium sulfate, the typical calibration aerosol, and assumed k values for calibrations ranging from 0.45 to 0.7. Thus, reported sc - Ddry relationships for even the same particle types may vary between studies using different calibration assumptions: the 0.45 < k < 0.7 range represents up to a 50% bias in the sc - Ddry relationship that is added to the measurement uncertainties. To achieve equivalence of datasets, it may be better to adopt the suggestion of Roberts et al. (2006) to report all Ddry measurements at a particular supersaturation relative to the Ddry assumed for ammonium sulfate at that supersaturation, although this method still leaves uncertain the precise relationship between particle size and actual critical supersaturation.

Accurate measurements of particle size distributions and CCN number concentrations are prerequisites for achieving closure. Additionally, closure studies must often rely, at least in part, on assumptions about aerosol mixing state, solution surface tension, particle shape, density, or refractive index, particle phase state during sizing, organic component hygroscopicity, insoluble fractions, and mass accommodation coefficient, which can be difficult to constrain well. Thus, even successful closure does not necessarily indicate predictive power: it should be viewed as a test for consistency within a reasonable parameter space. In several studies, consistency could not be demonstrated, even by this less stringent standard, suggesting biases in the sizing, number concentration, and CCN measurements themselves.

As discussed above, cloud droplet activation is sensitive to the dry volume-equivalent diameter, which must be inferred from optical, aerodynamic, or mobility-based measurement systems. Basic sizing and number concentration errors stemming from uncertainties in instrument operation parameters (e.g. flow rates, electric fields, laser strength, binning, counting) are usually on the order of 10-20%, and are worse for particles larger than about 500 nm, which are present in relatively low number concentrations; however, these largest particles generally activate at the lowest sc, and are thus very important contributors to the CCN budget at low supersaturations. Even insoluble, large particles, when coated with small amounts of hygroscopic material, may readily serve as CCN at low supersaturations. This is seen from Figure 13.1, which shows that a 500 nm particle activates at a supersaturation of 0.1% of its hygroscopicity k> 0.01. This value of k corresponds to ammonium sulfate comprising just 1.7% of the volume of an otherwise nonhygroscopic particle. Conversion uncertainties from operationally defined size to volume-equivalent size are often 10% and sometimes as large as 100%, adding to the uncertainties. In contrast, overall particle hygroscopicity can usually be measured within ~30% (Petters and Kreidenweis 2007) using either H-TDMA or size-resolved CCN measurements. Although these techniques are difficult to apply to particles larger than 500 nm, the sc of those particles is generally low enough that accurate characterization of their number concentrations is likely a more important issue than determination of their hygroscopicity in evaluating their role in CCN budgets. The many unidentified, semivolatile organic species present in tropospheric particulate matter are often cited as problematic in attempting to characterize completely the chemical composition of particulate matter, and are implicated as primary causes of the inability to model accurately observed CCN spectra from measurements of particle properties (e.g., McFiggans et al. 2006). However, we believe this situation is not so dire, because thus far experience has shown that variations in the hygroscopicity of typical ambient organic aerosols are not so large. Further, in mixtures, if the volume fraction of very hygroscopic (generally inorganic) material dominates, then the k of those constituents dominates the volume-weighted k for the particle, and the volume fr

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