5

Laboratory Studies of Cirrus Cloud Processes

PAUL J. DEMOTT

A number of processes that play a role in the formation, evolution of microphysical properties, and radiative characteristics of cirrus clouds are amenable to investigation in a laboratory setting. These laboratory studies provide fundamental data for quantifying and validating theoretical concepts and help guide investigations involving direct and remote measurements of cirrus. Laboratory data also may be used for formulating parameterizations for numerical cloud models, especially where information is incomplete or full descriptions are not possible. This chapter reviews results from laboratory studies of ice formation, ice crystal growth, radiative transfer, and aerosol scavenging and transformation in the cirrus environment. Emphasis is placed on ice formation in cirrus conditions. The related topic of contrail formation is covered separately in this book. The formation mechanisms of lower stratospheric clouds are reviewed elsewhere (e.g., Tolbert 1994; Peter 1996; Carslaw et al. 1997; Koop et al. 1997a).

5.1 Ice Formation Processes in Cirrus

5.1.1. Overview

Laboratory studies of cirrus ice formation are at a rapidly developing stage, so it is useful to provide significant background bases for current and needed studies. Key issues are aerosol composition, ice nucleation mechanisms, and the synergy between theory and laboratory measurements. Vali (1996),Baker (1997) and Martin (2000) discuss some of these issues in review papers.

Upper tropospheric aerosols

Upper tropospheric aerosol particles play an important catalytic role in the formation of cirrus. The nucleation process is important in determining the microphysical properties of cirrus. Numerical modeling studies (e.g., Jensen and Toon 1994; DeMott et al. 1994; 1997; Heymsfield and Sabin 1989) indicate that variation in the factors that drive the nucleation of ice and variations in the physical and chemical characteristics of aerosol particle populations lead to the formation of cirrus with different microphysical characteristics. 

Knowledge of the physics and chemistry of aerosols in the upper troposphere and lower stratosphere has evolved at a rapid pace. A detailed accounting of this topic is beyond the scope of this chapter. For the purpose of the present discussion, it is sufficient to note that the aerosol from which cirrus nucleate may vary significantly from place to place. Differences in aerosol properties in time and space occur because particles can arrive to the upper troposphere in so many ways and from so many sources. For example, cumulus convection can loft boundary-layer air into the upper troposphere that is rich in particles that derived from surface generation, combustion processes (over continents), and boundary-layer chemical processing. Many of these particles may be sulfates, but their composition may transform depending on the concentrations of trace gas species. For example, an abundance of ammonia in air could favor the formation of ammonium sulfate from an initial population of sulfuric acid particles. Convection also introduces large amounts of insoluble matter to the upper troposphere. Thus, although sulfates have sometimes been observed to dominate the aerosol (Sheridan et al. 1994), insoluble inorganic species can be found in a large proportion of aerosols on other occasions (Chen et al. 1998; Talbot et al. 1998; Buseck and Posfai 1999). The insoluble components of mixed particles can act as heterogeneous nucleants for crystallizing liquid to dry solute or liquid to ice under conditions that are quite different than for a pure solute particle. 

The ubiquitous nature of organic components of sulfates and other aerosol particles throughout the troposphere has been determined (Novakov et al. 1997 Murphy et al. 1998). These organics may alter chemical and cloud formation processes in ways that are not yet fully understood. 

Where cirrus clouds have been present in the upper troposphere, aerosols are collected, modified by chemical reactions on ice crystals, and redistributed through sedimentation to lower levels. The particles remaining after cloud dissipation may have quite different physical, chemical, and cloud-nucleating properties. This cloud "processing" may also leave large regions or layers of the atmosphere depleted of aerosol particles. The reduction of particle surface area for condensation of gases makes these locations favored areas for the nucleation of new particles, sulfuric acid in particular. This appears to be a primary mechanism for maintaining the upper tropospheric aerosol populations (e.g., Schröder and Ström 1997; Clarke et al. 1999). 

Other local- or regional-scale impacts on upper tropospheric aerosol properties are produced by the exchange of air with the lower stratosphere and the direct injection of particulates by jet aircraft. Lower stratospheric air is typically dominated by sulfuric acid aerosols and tends to contain less insoluble matter (Pueschel et al. 1992; Sheridan et al. 1994; Murphy et al. 1998). Aircraft exhaust has been implicated in enhancing black carbon concentrations in cirrus (Petzold et al. 1998; Ström and Ohlsson 1998). The role of exhaust particles as potential nuclei for cirrus formation is the subject of current study (e.g., DeMott et al., 1999).

The relation between aerosol composition and ice-nucleating properties is not well understood (see, e.g., Pruppacher and Klett 1997). Figure 5.1 provides a summary in schematic form of the various potential pathways to ice formation. Ice nucleation at cirrus conditions may occur homogeneously in liquid aerosol particles or heterogeneously on particles that may or may not already contain water as a component. 

Homogeneous ice nucleation

Homogeneous freezing nucleation, analogous to that which occurs in pure water droplets, may occur in concentrated solution (haze) droplets at below about -40°C (pathway A in fig. 5.1). This mechanism can occur at relative humidities that are below 100% with respect to water. The presence of solute has the effect of lowering the freezing rate compared to an equal-sized pure droplet, but the freezing rate also increases sharply with decreasing temperature. An increase in relative humidity with respect to water (RH_w) leads to an increase in the equilibrium size of solution droplets, thus diluting the solute to a condition (depending on temperature) where freezing occurs. Other phase transition behaviors of aerosol particles complicate homogeneous freezing in cirrus conditions. For example, the transformation of a solid (anhydrous) soluble particle to a saline droplet occurs spontaneously at the deliquescence relative humidity. The temperature dependent solubility characteristics of aerosols determine the humidity of deliquescence (Tang and Munkelwitz 1993). This RH_w for deliquescence usually increases with decreasing temperature for salt particles, potentially imposing a limitation on freezing (pathway B in fig. 5.1). The deliquescence humidity also increases for smaller particle sizes (Chen 1994). Once a particle has become liquid, it must dry significantly below the deliquescence RH_w in order to crystallize again as an anhydrous particle of the same composition. This complete crystallization, also known as efflorescence, is a nucleation phenomenon and so requires the solute to supersaturate. The particle in pathway A in figure 5.1 has not undergone efflorescence, but the particle in pathway B has. Consequently, the particle in B is limited from freezing until it deliquesces. When aerosols are already in a liquid state, chemical phase transitions may alter the compositional makeup of haze particles at lower temperatures. Consequently, the expected conditions where freezing will occur may be altered (pathway C1 in fig. 5.1). For example, (NH₄)₃H(SO₄)₂ (letovicite) may crystallize in NH₄HSO₄ (ammonium bisulfate) solutions. The freezing conditions of the remaining acidified solution may be quite different from the original bisulfate solution.

Figure 5.1.Hypothesized pathways to ice formation in cirrus clouds. The particle types and phase are indicated, and the size of particles is intended to indicate their relative growth or dilution. The vertical position indicates (higher) humidity, (lower) temperature, and the height of formation of the cirrus cloud as indicated by ice particle formation. The nucleation pathways are A, homogeneous freezing of solution droplets; B, homogeneous freezing limited by deliquescence requirement; C1, homogeneous freezing limited by secondary phase crystallization; C2, heterogeneous freezing induced by secondary phase crystallization; D, heterogeneous freezing of solution droplets; E1, deposition nucleation on an insoluble particle; E2, deposition nucleation on an anhydrous (dry) soluble particle; F, contact freezing nucleation.

A common basis for quantifying ice formation processes in cirrus for use in numerical models has been classical nucleation theory (e.g., Pruppacher and Klett 1997; Khvorostyanov and Sassen 1998). The limitations of classical theory and its application of macroscopic attributes to microscale ice embryo formation must be acknowledged at the outset of any discussion of its use. Nevertheless, the theory is intellectually appealing, and there is evidence that it can be applied to explain measurements of ice formation by homogeneous freezing in pure water droplets. The fundamental relation that describes the steady-state nucleation rate, J_hf (1/cm³/ s) of ice embryos in a liquid drop may be written as (see, e.g., Pruppacher and Klett 1997),

(1)

In equation 1, DF_act is the activation energy for movement of water molecules from the solvent to the ice phase, DF_g is the energy of formation of the critical embryo, k is Boltzmann’s constant, and T is temperature. The pre-exponential factor, C, is 

(2)

where N_c is the monomer concentration (»5x10¹⁴ for pure water), r_w is the density of water, r_i is the density of ice, h is Planck’s constant, and s_i/s is the interfacial energy of the ice-solution interface. The energy of formation in the spherical cap model of an ice embryo may be formulated as

(3)

where r_gis the germ radius. Khvorostyanov and Sassen (1998) have derived

(4)

where the temperature-dependent “effective” latent heat of formation (L_ef) replaces the average latent heat of freezing from previous classical treatments. T₀ is the triple point of water (approximately the melting temperature), S_w is the water saturation ratio, and G = RT/(L_efM_w) in equation 4, M_w being the molecular weight of water and R the universal gas constant. Mackenzie et al. (1998) offered an alternative form of r_g.

Equations 1 - 4 are generalized here for any solution droplet composition. For particles in equilibrium with the vapor phase, the Köhler equation relates S_w to aerosol composition via the aerosol water activity. Thus, equations 1 - 4 and the Köhler equation provide a set of equations for calculating J_hf as a function of ambient temperature, humidity, and aerosol size distribution. At infinite dilution, S_w tends to 1, which is the case for a pure water droplet. Expressions for the temperature dependencies of r_w, r_i, L_ef, and DF_act for pure water are found in Khvorostyanov and Sassen (1998), Jensen et al. (1994), and Pruppacher (1995). Solute particles may freeze at S_w < 1. The most obvious consequence of this is to suppress the melting point temperature, T₀ in equation 4. However, this simplistic view belies other dependencies that solutes may introduce.

Two of the most problematic quantities in applying homogeneous nucleation theory to solutions are DF_act and s_i/s. These quantities are sometimes treated to depend on temperature alone (e.g., Khvorostyanov and Sassen 1998), but clearly they must depend also on solution composition (e.g., Luo et al. 1992; Tabazadeh et al. 1997). One approach to determining DF_act has been to equate it to the measurable energy for viscous flow (e.g., Jeffery and Austin 1997; Tabazadeh et al. 1997). In the viscous flow approximation, DF_act always increases monotonically toward low temperature. Pruppacher (1995) proposed that, for pure water, this term decreases with decreasing temperature below -30°C, reflecting that transfer across the ice-water interface may involve increasingly larger clusters of water molecules for which the hydrogen bonds are broken only at the cluster periphery. In contrast, Jeffery and Austin (1997) point out that a correct derivation of the activation energy from water self-diffusivity data provides the lower values of DF_act that were required by Pruppacher (1995) to bring theory into agreement with experiment for pure water. This issue will likely remain a point of contention among theoreticians.

The determination of s_i/s by experimental techniques is difficult, and measurements even for pure water show a spread of as much as 25% over the temperature range from 0 to -40°C (Pruppacher and Klett 1997).In the context of the above equations, huge differences in nucleation rate can result from this uncertainty in s_i/s. Indirect methods exist for estimating s_i/s for aqueous solutions. One may apply what Antonoff’s rule to conject that s_i/s is equal to the absolute difference of the individual surface tensions of ice and solution against air (see, e.g., Tabazadeh et al. 1997). Alternatively, s_i/s is estimated to be the fusion heat required to change the hydrogen bonds from the oriented solid state to the aqueous state (e.g., Luo et al. 1992; Pruppacher and Klett 1997). At very low temperatures where crystal growth rates are much slower than embryo formation rates, it is possible to derive DF_act from crystallization kinetics and then use this estimate to determine s_i/s from nucleation rate measurements at warmer temperatures (see, e.g., Disselkamp et al. 1996). The more common scenario is that freezing rate measurements are used to determine DF_act or s_i/s, assuming that the other quantity can be estimated (see, e.g., Hagen et al. 1981; DeMott and Rogers 1990). This has always compromised somewhat the comparison of classical theory with experiments.

Homogeneous nucleation is a stochastic process. Thus, the fraction, F_hf, of droplets with volume V_d that freeze homogeneously in a small time interval, Dt, is given by

(5)

This expression for F_hf serves as the basis for calculating J_hf from laboratory measurements of the Poisson statistics of homogeneous freezing (Hagen et al. 1981; DeMott and Rogers 1990; Krämer et al. 1996; Disselkamp et al. 1996; Koop et al. 1997b; Shaw and Lamb 1999). Equation 5 also serves as the basis for making numerical model calculations of ice formation in cirrus, starting from a specified aerosol size distribution and chemical composition. Both J_hf and V_d depend on aerosol properties. The droplet volume depends on the water uptake of aerosol particles, which is a function of their solute composition. Approximations may permit an analytical solution to be obtained for the fraction of the total aerosol nucleating ice that depends only on (model) grid point conditions and moment parameters of the aerosol size distribution. The validity of such simplifications, which allow details of the nucleation process to be incorporated into mesoscale and global scale models, are testable in the laboratory.

Numerical studies of cirrus that included ice formation by homogeneous freezing of solution droplets have offered some tantalizing insights into the roles of aerosol properties and cloud forcing in determining cirrus properties.For example, for one assumed aerosol composition, the concentration of ice crystals is largely controlled by the balance between vapor production by cloud updraft and vapor depletion by ice crystal growth (e.g., Heymsfield and Sabin 1989; Sassen and Dodd 1989; Jensen and Toon 1994; DeMott et al. 1997). If updrafts are sustained until vapor depletion dominates, then higher concentrations of ice crystals are predicted to form at higher updrafts. Only extreme changes in particle size distribution, such as occur after volcanic eruptions (Jensen and Toon 1992), can temporarily alter the predicted relationship by more than some tens of percent. A potentially more important way that solution composition could alter cirrus is by changing the humidity required for cloud initiation (DeMott et al. 1997). Lowering the humidity required for formation might alter the water vapor balance toward favoring lower ice crystal concentrations, but larger ice crystals and more widespread cirrus. Nevertheless, these numerical studies were done without detailed information on the low temperature hydration and freezing behavior of different relevant compositions of solution droplets. It is likely that a range of sulfate particle compositions exist in regions of the upper troposphere; depending on transport processes from source regions and the thermodynamic conditions along the transport pathway (Tabazadeh and Toon 1998). Detailed thermodynamic models of the phase and composition of soluble aerosol particle systems at low temperatures now exist (e.g., Clegg et al. 1998), but necessarily require extrapolation in the much of the cirrus temperature and humidity regime. Laboratory studies can provide the fundamental data required. One could also envision laboratory cloud chamber simulations being used to validate model predictions of the relation between cloud forcing and cloud properties.

Heterogeneous ice nucleation

There are at least four different mechanisms hypothesized to lead to heterogeneous ice nucleation by aerosol particles (Vali 1985). Direct deposition of ice to an insoluble surface is indicated as pathway E1 in figure 5.1. It is also possible that soluble but dry (anhydrous) sulfate particles may form ice at low temperatures in this same manner (Martin 1998; Tabazadeh and Toon 1998). This is indicated as pathway E2 in figure 5.1. Contact freezing nucleation may occur after a solid particle collides with a liquid haze particle (pathway F in fig. 5.1). In condensation freezing (pathway D in fig. 5.1), the soluble component of a mixed particle causes condensation, and the insoluble component catalyzes freezing instantaneously. The nucleation process is referred to as immersion freezing if the insoluble component catalyzes ice formation at a much later time (lower temperature or greater droplet dilution) following either collision or condensation. Figure 5.1 indicates that immersion freezing might also occur when a new crystalline phase forms within a haze droplet upon cooling (pathway C2). The importance of the deposition mechanism anywhere is an open question due to the low likelihood of finding completely insoluble particles. Most scrutiny has focused on the potential roles of condensation and immersion freezing nucleation. Nevertheless, knowledge of the importance of the different pathways in figure 5.1 is poor.

The role of heterogeneous nucleation in cirrus is the subject of renewed attention in laboratory studies. Knowledge of the presence of insoluble particulates in the upper troposphere and advent of improved capabilities to measure heterogeneous ice nuclei concentrations and compositions there (e.g., DeMott et al. 1998; Rogers et al. 1998) provide motivation for new laboratory studies. Numerical simulations suggesting that heterogeneous nucleation could dominate in cirrus formed by the widespread, slow ascent of air (DeMott et al. 1997; Jensen and Toon 1997) also motivate laboratory studies. 

The theoretical basis for quantifying heterogeneous nucleation is much less certain than for homogeneous freezing. Theoretical descriptions require information on surface properties for innumerable substances that could act as ice nuclei, and these properties could depend on aerosol processing effects. For example, the free energy of formation for heterogeneous freezing nucleation may be written

(6)

where f(m_i/n,x) is a geometric factor (Pruppacher and Klett 1997) that depends in the simplest case (spherical cap embryo on a curved and uniform substrate) on the cosine of the contact angle between the ice embryo and substrate nucleus (m_i/n = cosq_i/n) and the ratio of the nucleus to ice embryo radius (x = r_n/r_g).Effective freezing nuclei have higher values of m_i/n and this value determines a nearly temperature-independent ice saturation ratio at which a nucleation rate of 1 event per particle per second occurs. For example, using equation 6 in the model of Tabazadeh et al. (1997), even a relatively ineffective freezing nucleus (e.g., m_i/n = 0.1) of 100 nm size is calculated to instantly freeze a 400 nm sulfuric acid solution droplet once the ice saturation ratio exceeds 1.25 (ice relative humidity RH_i = 125%).

5.1.2. Laboratory Methodologies for Studying Cirrus Ice Formation

New data are needed on the chemical phase, water activity, and ice-phase transition conditions of bulk and dispersed phase (wet and dry aerosol) particulates at cirrus temperatures. These data will come from studies using a variety of methods.

Methods for studying cirrus ice formation in the laboratory may be placed into various categories. At the most basic are studies of the freezing of relatively large volumes of solutions (e.g., Gable et al. 1950; Ohtake 1993; Chelf and Martin 1999). These studies provide the equilibrium freezing temperature as a function of composition for a solute-water system, a fundamental piece of information concerning ice nucleation. Relevant secondary data come from measurements of water vapor pressure over solutions at low temperature (e.g., Zhang et al. 1993; Massucci et al. 1996). A second category of experiments examines the behavior of small dry particles or solution droplets dispersed in air or in another medium.Subcategories of experiments on dispersed-phase particles focus on the behavior of particle populations or on the behavior of individual particles.

Devices to study the freezing of populations of liquid droplets were some of the first to give inferences to the homogeneous and heterogeneous freezing behavior of small liquid aerosol particles at cirrus conditions. Populations of solution droplets have been observed optically while supported on a chilled surface or at the interface of two surfaces of differing density (Pruppacher and Neiberger 1963; Koop et al. 1998). Other experiments involved creating droplet emulsions that were monitored, using calorimetric techniques, for ice formation during cooling and for melting conditions on warming (Rasmussen and Luyet 1970; Ganguly and Adiseshaiah 1992). The unknown effect of instrument surfaces or surface interaction with the mother phase in emulsions on nucleation is always a concern in such studies.

The concept of flow tubes is to expose freely suspended particles of known composition to a known temperature for a defined time. A large number of studies have used flow tubes to study the infrared spectroscopic changes of populations of aerosol particles at compositions and temperatures representative of the upper troposphere and lower stratosphere. These studies seek to determine the nonequilibrium- phase transitions of deliquescence, efflorescence, chemical crystallization in drops (e.g., Cziczo et al. 1997; Onasch et al. 1999) and the freezing of water in particles of differing compositions (e.g., Bertram et al. 1996; Clapp et al. 1997; Cziczo and Abbatt 1999). Composition is fixed in such studies by flowing high concentrations of liquid aerosol particles rapidly through a constant temperature tube. The principle is that the water in the particles exceeds the gas phase water by such a large amount that the composition of the particles does not readjust to the ice saturation conditions in the tube during the residence time. Definition of the composition of particles at the point of freezing is an experimental issue. Composition is usually determined based on extrapolation of relationships between composition and the area under certain FTIR (Fourier transform infrared spectroscopy) spectroscopic bands. These relationships are determined from studies of thin films of known composition, usually conducted at temperatures that are warmer than cirrus (e.g., Anthony et al. 1995). Particle size measurements support composition determinations, but inferences by way of Mie theory require optical constant data as a function of composition at low temperature. Refractive indices as a function of temperature and composition in the stratospheric regime have been determined recently from infrared aerosol extinction spectra obtained in flow tube (Niedzela et al. 1998), and thin film studies (Tisdale et al. 1998). Improvements in defining particle composition have also been made by coupling tunable diode laser hygrometers to the same sample volume where FTIR measurements are made (Niedzela et al., 1998) or by using a second FTIR spectrometer to measure the composition of evaporated haze particles.

In an ice-thermal diffusion chamber, the goal is for particles to adjust in size, in a natural manner, toward equilibrium with set temperature and humidity conditions. The relative humidity condition of ice nucleation is thereby measured and composition is determined by application of diffusional growth equations. Equilibrium conditions are achieved by varying the temperature of two parallel ice surfaces (e.g., Rogers 1988; Rogers et al. 1998). These devices may be oriented horizontally to develop a static gradient of temperature (warm over cold) and vapor density (high over low) into which aerosol particles are drawn. Alternately, aerosols flow through the systems in a horizontal or vertical orientation. A flow system permits continuous measurements and helps assures that vapor is not depleted by ice particle growth. Definition of the conditions to which particles are exposed is aided by focusing the aerosol into a lamina (e.g., by surrounding it with particle-free flows). Detection of ice formation is aided by the fact that, under most conditions, ice particles will grow rapidly to sizes that can be distinguished in some way (e.g., optically) from haze particles. This also yields information on ice particle growth rates.

Nucleation studies can also be done in larger volume chambers. Aerosols can be observed over long time periods or during slow cooling at ice saturation in such devices (e.g., Disselkamp et al. 1996). Other cloud chambers are capable of processing aerosols through realistic thermodynamic trajectories and repeated cloud formation events (e.g., White et al. 1987; DeMott and Rogers 1990). Such methods could provide validation of other laboratory results for conditions that mimic the real atmosphere, yet they are easier to control and observe. 

In the area of single particle experiments, the modern development of great promise involves the isolation of aerosol particles from surfaces by optical, acoustic, or electrodynamic levitation (see review of Davis 1997). The electrodynamic levitation method has been used most commonly for phase change and growth studies (Tang and Munkelwitz 1994; Wyslouzil et al. 1994; Lamb et al. 1996; Carleton et al. 1997; Bacon et al. 1998, Xu et al. 1998). A particle is balanced in space horizontally by applying an alternating current to a ring electrode. The particle is balanced against gravity by applying a direct current to the end caps of the cylinder around the particle. The resulting electrostatic field confines the charged particle to a stable position in space. The growth of particles is determined from relationships among the DC current required to produce the levitating field, particle charge, and mass. Particle composition is calculated based on particle growth from a known initial composition. Changes in mass reflect nucleation or changes in particle composition. Observations of light scattering by, or infrared emission from, larger particles (5-100 mm) may be made to better define composition and phase transitions or to determine how particles depolarize light. A useful capability that has not been generally implemented with the levitation techniques is control on water vapor pressure. Anders et al. (1996) and Roth and Frohn (1998) describe a low-temperature optical levitation device that permits particle exposure to an ice supersaturated airflow, but the precision of humidity control is not yet sufficient for accurate study. Swanson et al. (1999) describe a combination electrodynamic balance and ice-thermal diffusion chamber. This system has thus far been operated only at very low ice supersaturations.

5.1.3. Results of Laboratory Studies of Ice Formation in Cirrus

Homogeneous ice nucleation

Pruppacher (1995) summarized nearly 40 years of efforts to measure the homogeneous freezing nucleation rate of pure water by various methods. These included measurements of droplets cooled on surfaces or thermocouples, within (as emulsions) or at the interface of liquids, or suspended in the air. Some measurements on the freezing temperature of pure or highly dilute droplets free of surface contact or surfactants are plotted in figure 5.2 along with the theoretical nucleation rate curves proposed by Pruppacher (1995) and by Jeffery and Austin (1997). The data include measurements in slow (DeMott and Rogers 1990) and rapid (Hagen et al. 1981) expansion cloud chambers, as well as the first measurements made on levitated droplets (Krämer et al. 1996). It is possible to bring standard classical theory into good agreement with the existing experimental data. In one case, this requires an appeal to some proven and some hypothesized critical behaviors of water at -45°C (Pruppacher 1995) which, nevertheless, do not explain the observation of freezing (as cubic ice) of clusters of water molecules at temperatures of around -70°C (Huang and Bartell 1995). Jeffery and Austin (1997) got classical theory to agree with the standard data and the very low temperature results by employing a new analytical equation of state that accounts for the role of strong hydrogen bonds in determining the properties of water (Jeffery and Austin 1999). Some authors suggest that many of the results in figure 5.2 reflect heterogeneous nucleation and so are a high-temperature limit for homogeneous freezing conditions (e.g.,Granasy, 1995).

Figure 5.2. Homogeneous freezing nucleation rate of pure water versus temperature. The theoretical results of Pruppacher (1995) and Jeffery and Austin (1997) are given by the dashed and solid lines, respectively. Pruppacher’s curve does not extend below -45°C because he deemed this to be a critical temperature below which pure liquid water could not exist. Selected data for freely suspended dilute or pure water droplets are from DeMott and Rogers (1990), given by ´ symbols with error bars, from Hagen et al. (1981), given by triangles with error bars, and for Kramer (1998), given by open circles. The results of Huang and Bartell (1995), shown as the diamonds, are for cubic ice formation in minute water clusters at 550 bars.

Most early studies of the freezing of solutions at temperatures in the warmer part of thecirrus regime were done on populations of droplets, sometimes quite large ones, suspended in oil. In cases where heterogeneous nucleation was determined not to play a role, Pruppacher and Neiberger (1963) showed that 2000-mm solution droplets froze at progressively lower temperatures as solute concentration increased. This tendency is expected theoretically. Nevertheless, the temperature depression of the freezing point compared to pure water droplets of equivalent sizes exceeded the equilibrium melting point depression by up to a few degrees at solution molalities up to 1 mole/kg. Hoffer (1961) noted a similar effect for different solutions with molality up to about 3 mole/kg. Pruppacher and Neiberger (1963) speculated that the extra amount of supercooling required for freezing was a reflection of the effects of ion size or ion charge on ordering of ice molecules in solutions. Nevertheless, no consistent picture has emerged from studies that have attempted to resolve the nature of the ionic hindrances to ice formation in solutions (Hoffer 1961; Pruppacher and Neiberger 1963; Ganguly and Adiseshaiah 1992). 

During the 1970s, researchers with interests in cryobiological applications noted a more patterned behavior to the effects of solutes and other cryoprotective liquids on homogeneous freezing conditions. Working with emulsions of droplets of a few microns in size, Rasmussen and Luyet (1970), Rasmussen and Mackenzie (1972), and Mackenzie (1977) showed that both ionic and nonionic liquids displayed freezing-point depressions that increased in direct proportion to melting-point depressions measured in the same experiments. Figure 5.3 integrates some of the results from this group along with the emulsion data of Ganguly and Adiseshaiah (1992) and data on the freezing of larger solution droplets from Hoffer (1961) and Pruppacher and Neiberger (1963). Individual solutions were found to obey the expression

(7)

whereDT_n and DT_m are the depressions of the freezing (or nucleation) and melting point temperatures, respectively. The coefficient l ranges from 1.4 to 2.2 for different solutions. Khvorostyanov and Sassen (1998) have suggested that some part of the reason that l is typically so much greater than 1 may be due to the temperature dependence of the latent heat of freezing. Rasmussen (1982a,b) has pointed out previously that this relationship between nucleation and melting temperatures cannot be easily derived from classical nucleation theory if the expected dependencies ofs_i/s andDF_act on solution properties are included. Koop et al. (2000) recently proposed that the typical l is a consequence of nucleation depending primarily on water activity by way of the hydrogen bonding structures required for freezing. This hypothesis does not explain the range of l observed.

Figure 5.3.Summary of the relationship between the measured depression of the nucleation temperatures (DT_n) of solution droplets below those of pure water droplets and the measured (in same experiments) or tabulated (from data on bulk solutions) melting point depressions. All data are from studies of the freezing of captive droplets ranging in size from 1 mm (emulsions) to a few hundred microns.Particular solutes are denoted by squares (NH₄Cl), diamonds (KCl), triangles (LiCl), circles (NaCl), plus signs (KCl) and asterisks (CaCl₂). Data for these solutes are from Rasmussen (1982a) and Rasmussen and Mackenzie (1972) (filled symbols), Pruppacher and Neiberger (1963) (open symbols), and Ganguly and Adiseshaiah (1992) (shaded symbols). The ´ symbols indicate data for a variety of other solutes examined by these authors and by Hoffer (1961). The solid lines indicate 1:1 and 2:1 relationships between the two temperature depressions. The dashed line is a fit to the numerous data points of Koop et al. (1998) for H₂SO₄/H₂O droplets.

Sassen and Dodd (1988, 1989) proposed that a simple means of parameterizing the nucleation temperatures (e.g., the temperatures at which J_hfV_d» 1/s) of solution droplets for cirrus conditions was to define an effective freezing temperature (T_eff), given by

(8)

This expression may be substituted for temperature (T) in the classical theoretical equations for J_hf or simply within a polynomial function that describes the results for J_hf shown in figure 5.2. Using l = 1.7, Sassen and Dodd (1989) used a microphysical model to estimate the relative humidity for cirrus formation (RH_wnuc). RH_wnuc could be described by

(9)

with coefficients a = -0.276, b = 5.36x10^-3, and c =0. DeMott et al. (1994, 1997) also used equations 7 and 8 substituted either into a polynomial equation for J_hf or into equation 1 to investigate the critical sensitivities and uncertainties in predicting homogeneous freezing in cirrus. Figure 5.4 explores the validity of this parametric approach to using laboratory data, and the parameterization of Koop et al. (2000), as compared to using classical theory. The nucleation rates versus temperature by the parametric methods agree in form with classical theoretical treatments of homogenous freezing of H₂SO₄ solution droplets. The agreement of the Khvorostyanov and Sassen (1998) model with l = 1 is interesting, but may be fortuitous because this theoretical model ignores the compositional dependencies in s_i/s and DF_act. The theoretical calculations based on Tabazadeh et al. (2000) include these dependencies, but predict a different position and slope to the nucleation rate curve. The position of this curve is reasonably close to the position predicted by l = 1.7 (suggested by fig. 5.3) and by the Koop et al. (2000) parameterization. The slope difference may indicate a deficiency of the parametric approaches, or it may be an artifact of the manner in which Tabazadeh et al. determined s_i/s (Antonoff’s rule) and DF_act (adjusted to obtain agreement of J_hf with the laboratory data of Koop et al. 1998). More laboratory data could help to resolve this issue and reduce the uncertainty in the temperature and composition at which a solution droplet is predicted to freeze. According to figure 5.4, this uncertainty is as large as several degrees Celsius.

Figure 5.4.Comparison of methods for calculating the homogeneous freezing nucleation rate of 15 weight % (~93% relative humidity at equilibrium) sulfuric acid droplets versus temperature. All methods compared here have an explicit or implicit basis in laboratory studies. The solid curves labeled l = 1 and l = 1.7 were obtained by substituting T_eff (equations 8 and 9) for temperature in a polynomial fit for J_hf of pure water (solid line, based on Jeffery and Austin, 1997). The filled square points are based on the theoretical model of Khvorostyanov and Sassen (1998) that extends the classical theory of Pruppacher (1995) to solutions. The thin, dotted curves are from substituting T_eff (at l = 1 and l = 1.7) for temperature in solution-dependent quantities in the theoretical equations for homogeneous freezing of pure water given in Jensen et al. (1994). The filled triangles are based on the classical theory model of Tabazadeh et al. (2000) that was constrained by the measurements of Koop et al. (1998). The thick, dashed curve is the water activity-dependent parameterization proposed by Koop et al. (2000).

The relationship between DT_m and DT_n shown in figure 5.3 has not, until very recently, been investigated for soluble particles that are particularly relevant to ice formation in cirrus. A simplified consideration of the soluble components of upper tropospheric aerosols has led to the greatest recent experimental focus on the H₂SO₄/H₂O/(NH₄)₂SO₄ ternary liquid aerosol system. This system encompasses all compositions of sulfate aerosols, from H₂SO₄ through the 1:1 ratio of ammonia and sulfate ion (ammonium bisulfate) to the completely neutralized form ((NH₄)₂SO₄).

Figure 5.5 summarizes some measurements of ice formation in sulfuric acid aerosols. Various details are given in the figure caption. Experimental results are given as different threshold conditions for ice formation and are shown on thermodynamic-phase diagrams in temperature-composition and/or temperature-humidity space. This jump from a discussion primarily of nucleation rates to one of freezing conditions is done to simplify and conceptualize the implications for cirrus cloud formation and to enable comparison of varied experimental techniques. Nevertheless, one must recognize that all the techniques have kinetic limitations that imply different sensitivities to nucleation rate. Therefore, the definition of threshold freezing conditions differs in each case. Additional fundamental kinetic limitations to ice formation may also exist that are not yet understood.

The most apparent feature in figure 5.5 is the large variability in current results on where H₂SO₄/H₂O particles freeze. The FTIR/flow tube measurements of Bertram et al. (1996) provided the first low-temperature measurements of freezing conditions of small (~400 nm diameter), free-flowing sulfuric acid particles as a function of composition. The Bertram et al. data suggest l» 1 for their stated onset conditions for ice formation. Koop et al. (1998) observed ice formation in populations of ~10 mm H₂SO₄ droplets placed on a chilled hydrophobic surface. These larger drops needed to supercool a great deal more compared to the freezing of small, free-flowing drops (e.g., l» 1.9), as shown in figures 5.4 and 5.5. Measurements of levitated single droplets of up to 50 mm diameter by Krämer (1998) support the Koop et al. results. Both data sets on larger drops are consistent with the freezing versus melting point depression relations for other solutions (figure 5.4) and with laboratory observations of how difficult it is to freeze stratospheric (> 35 weight percent composition) H₂SO₄ aerosols (e.g., Song 1993; Anthony et al. 1995; Carleton et al. 1997; Koop et al. 1997b). 

Figure 5.5. Experimental results on the freezing conditions for sulfuric acid/water aerosols plotted on (a) temperature/composition and (b) temperature/water saturation ratio (= RH_w/100) (b) phase diagrams.Interpolations from one diagram to the other were made on the assumption of equilibrium and using low temperature vapor pressure data. Flow tube results of Bertram et al. (1996) for 400 nm (mean) diameter polydisperse aerosols are given by the filled circles. The data given by open circles are based on the droplet freezing device data of Koop et al. (1998) for 5 - 12 mm particles. The squares are based on studies of levitated 40mm particles by Krämer (1998). The filled diamonds are for approximately 100 nm droplets from continuous flow diffusion chamber studies (Chen et al., 2000). The melting point curve (ice saturation), indicated as "T₀-DT_melt," is based on Gable et al. (1950). T_hf0 is the homogeneous freezing temperature of pure water (235 K used). The curves indicated as "T_hf0-DT_melt" and "T_hf0-2*DT_melt" are equivalent to assuming l =1 and 2, respectively, in equation 8 for 5-mm droplets. The observed conditions for cirrus formation summarized by Heymsfield and Miloshevich (1995) are shown by the shaded line in panel b.

More recent measurements of small H₂SO₄ solution droplets by Chen et al. (2000) are also included in figure 5.5. These measurements, made with a continuous flow diffusion chamber (CFD), agree with the large drop studies. The CFD measurements indicated that different fractions of particles nucleated ice at different sets of temperature and humidity conditions, when provided with a set residence time. The CFD results for 1% of approximately 100-nm (size after water uptake) particles nucleating in about 12 s are plotted in figure 5.5. Chen et al. (2000) used equations 7 and 8, the Köhler equation (to infer droplet composition and thereby DT_m), and a polynomial for J_hf of pure water to find that these data are consistent with an average value of l» 2.0. This information is not readily determined by comparison to the constant l lines in figure 5.5, since those lines areplotted for a specific (large) droplet size. The nucleated fraction is not easily discerned in all types of studies. In flow tube studies, a transition of FTIR spectra showing some ice to one that no longer changes and is presumed to be all ice is observed. This transition can occur over many degrees Celsius (Bertram et al. 1996; Clapp et al. 1997; Cziczo and Abbatt 1999) and may reflect inhibition of complete freezing or simply the successive nucleation of larger fractions of a polydisperse particle population. Future studies should strive to determine nucleation rates by measuring the percentages of particles of known sizes nucleating. Comparisons of data can then be made on plots such as figure 5.4.

Figure 5.5b also indicates the conditions for ice formation in continental cirrus clouds, based on Heymsfield and Miloshevich (1995). These authors inferred the onset conditions (RH_wnuc) of cirrus and orographic wave clouds from the maximum RH_w measured in clear air around clouds. Heymsfield and Miloshevich (1995) matched the measured RH_wnuc to equation 9, finding a = 1.8892, b = 0.0281 and c = 1.3336x10^-4. It is apparent that these conditions for the formation of ice in continental cirrus clouds are not satisfied by assuming that cirrus haze particles are composed of sulfuric acid that freezes by homogeneous nucleation. Sulfuric acid solution droplets require a degree of dilution for freezing that is only achieved above 90% relative humidity at all temperatures warmer than -60°C. Even with l = 1, the threshold freezing conditions of sulfuric acid aerosols require higher RH_w than Heymsfield and Miloshevich’s (1995) RH_wnuc for cirrus formation. Complete freezing in a real updraft scenario might require even higher ambient RH_w. More recently, Heymsfield et al. (1998) found no dependence of RH_wnuc (~95%) on temperature in selected sampling around cirrus over oceans. These authors also found the Heymsfield and Milosevich (1995) parameterization to generally underestimate RH_wnuc at temperatures below -55°C, independent of air mass source region. Both of these more recent observations may reflect the role of sulfuric acid aerosols in ice formation in some cirrus.

A compilation of measurements of deliquescence, efflorescence, and freezing of ammonium sulfate aerosols is shown in figure 5.6. These results indicate the potential importance of the phase states of the ammoniated sulfates under different atmospheric conditions. There is good agreement (data not shown) obtained in levitation experiments (Xu et al. 1998) and flow tube studies (Cziczo and Abbatt 1999; Onasch et al. 1999) on the weak temperature and compositional dependence of the deliquescence line. These results on deliquescence are consistent with the calculations of thermodynamic models (Clegg et al., 1998). Likewise, good agreement on the compositions along the ice (saturation) equilibrium line has been obtained by different methods. Considerable disagreement exists between flow tube and levitation experimental results on conditions for efflorescence of liquid (NH₄)₂SO₄ droplets (Onasch et al. 1999). Nevertheless, this disagreement may be partly explained by the much longer observation time and lower nucleation rates observed in the levitation experiments or by heterogeneous nucleation.

Figure 5.6 includes flow tube, diffusion chamber and droplet freezing results on the ice formation conditions of ammonium sulfate aerosols. The CFD measurements of Chen et al. (2000) are for monodisperse, submicron-sized, liquid ammonium sulfate aerosol particles. The phase state of particles was not known in the static diffusion chamber measurements of Detwiler (1980), but they were probably liquid. Chen et al. (2000)determined an average value of l = 1.75 ± 0.35 for their data. This value is close to that inferred from recent studies of freezing of micron-sized emulsified ammonium sulfate droplets (Bertram et al. 2000). Data from Bertram et al. (2000) can be shown to correlate with l» 2.1.The flow tube results of Cziczo and Abbatt (1999) are for the onset or very first ice formation in polydisperse liquid particles. In contrast to the other studies, these results indicate that some (unknown) fraction of ammonium sulfate solution droplets can freeze in a very (solute) concentrated state in the atmosphere. Most interesting is the fact that the experimental freezing conditions agree well with the observed RH_wnuc conditions needed for ice formation in continental cirrus (Heymsfield and Miloshevich 1995). This result suggests a case where l < 1. Since l < 1 suggests enhancement of homogeneous freezing by the solute in small solution droplets, these results need to be confirmed and explained. Estimations of nucleation rates in the various studies are underway and should help in evaluating results. 

Chen et al. (2000) also noted that dried (NH₄)₂SO₄ required higher RHw (by at least 5%) for ice formation to occur as compared to initially liquid aerosols. Dry solutes could nucleate ice formation by deposition nucleation or by first deliquescing and then freezing. The extrapolation of the deliquescence line below the eutectic temperature is educated conjecture, but deviation of this line to higher saturation ratios at low temperatures could explain the Chen et al. (2000) observations.

Figure 5.6. Experimental results on freezing conditions for ammonium sulfate aerosols plotted on (a) temperature/composition and (b) temperature/water saturation ratio (= RH_w/100) (b) phase diagrams. The data given by the filled circles are the onset conditions for ice formation in the flow tube studies of Cziczo and Abbatt (1999). The open circles are based on the emulsion droplet-freezing data (Bertram et al., 2000). The diamonds are the conditions for nucleating 1% of liquid particles as ice in continuous flow diffusion chamber (CFD) studies (Chen et al., 2000). The square symbols are for ice nucleation of 1% of particles in the static diffusion chamber studies of Detwiler (1980). Particle sizes of around 200 nm (dry size prior to water uptake) were used in diffusion chamber and flow tube studies, while drops of sizes 5-20 mm were used in Bertram et al. (2000). Particles were monodisperse only in the CFD studies. The curve defining conditions for deliquescence and the equilibrium melting point curve are based on Clegg et al. (1998). These curves are extrapolated below their point of intersection ("eutectic"). The efflorescence curves (see text) in panel a are based on (1) Xu et al. (1998) and (2) Cziczo and Abbatt (1999). Other lines are as defined in Figure 5.5.

The first measurements of the low-temperature phase states of ammonium bisulfate particles in an electrodynamic trap (Imre et al. 1997) were in substantial disagreement with thermodynamic model (Clegg et al. 1998) calculations of conditions for deliquescence and the equilibrium compositions at ice saturation (see Tabazadeh and Toon 1998). Experiments by Chelf and Martin (1999) and Yao et al. (1999) using larger solution volumes suggest that the levitation measurements require reevaluation. These authors performed measurements of solution composition upon freezing and measured the vapor pressures over NH₄HSO₄ solutions at low temperatures. These more recent and standard measurements agree well with the thermodynamic model of Clegg et al. (1998). It was demonstrated that under most tropospheric conditions, letovicite ((NH₄)₃H(SO₄)₂) would be the first substance to crystallize from liquid bisulfate solutions. Imre et al. (1997) found a possible exception to this rule at around -31°C, where they noted the formation of the hydrate NH₄HSO₄·8H₂O, but this result requires new validation in light of the other discrepancies with bulk solution studies. When letovicite does crystallize from NH₄HSO₄ solutions, the remaining solution maintains an excess of H⁺ ions (acidifies) and may only effloresce at very low humidity. FTIR studies conducted at room temperature were unable to demonstrate any phase transitions or efflorescence of wet bisulfate aerosols down to 2% RH_w (Cziczo et al. 1997). In contrast, Chen et al. (2000) noted indirect evidence of partial crystallization (as letovicite) in the process of drying NH₄HSO₄ aerosols. The reasons for this discrepancy are under study.

Figure 5.7 shows the first measurements of ice nucleation conditions for ammonium bisulfate aerosol particles. The Chen et al. (2000) results are from continuous flow diffusion chamber studies of submicron, liquid solution droplets while Koop et al. (1999) studied emulsified micron-sized droplets. Data points from the polynomial provided by Koop et al. (1999) to describe the median freezing temperature of droplets are plotted in figure 5.7 and correlate with l» 2.3. Chen et al. (2000) inferred l» l.4 for bisulfate droplet freezing, but the uncertainty of the measurements did not allow for them to be distinguished from the freezing conditions of either ammonium sulfate or sulfuric acid. Bertram et al. (2000) likewise concluded that there was no significant difference in the average freezing conditions of various sulfate aerosols.

Figure 5.7. Experimental results on freezing conditions for ammonium bisulfate aerosols plotted on (a) temperature/composition and (b) temperature/water saturation ratio (= RH_w/100) (b) phase diagrams. The filled diamond data points indicate conditions for 1% of 200 nm (prior to water uptake) particles freezing in continuous flow diffusion chamber studies (Chen et al., 2000). The deliquescence line is plotted for letovicite, because it was determined that letovicite crystallized in bisulfate solution droplets when they were dried following generation by Chen et al. (2000). The open circle symbols are based on the results of emulsion (3-12 mm droplets) freezing studies (Koop et al., 1999).

Much work still remains on resolving the freezing behavior of droplets of specific compositions in cirrus conditions. Many other species such as nitrates may play an important role in ice formation in cirrus (e.g., Tabazadeh and Toon 1998). The impact of HNO₃ on enhancing water uptake in ternary solutions with sulfuric acid is well known (e.g., Molina et al. 1993; Lamb et al. 1996). The potential impacts of organic components on the growth and freezing of haze particles must also be considered.

Heterogeneous nucleation of ice

The discussion of laboratory results on heterogeneous ice nucleation given here will largely focus on cirrus clouds at temperatures below -35°C. This reflects the definition of cirrus, as ice clouds, given at the beginning of this book. It must be acknowledged that this omits some cirrus-like clouds, at temperatures between -25 and -35°C, where heterogeneous ice nucleation processes are the only primary mechanisms for generating ice crystals.

Laboratory studies have demonstrated that certain insoluble particulates will cause solution drops to freeze in more concentrated form than they do homogeneously (e.g., Hoffer 1961; Reischel and Vali 1975). Some results are adapted from Hoffer (1961) in figure 5.8. Hoffer observed approximately 100 mm pure water droplets freeze at -36.5°C. The freezing point lowering by solution droplets of MgCl₂ plus Na₂SO₄ closely followed equation 7 with l = 2. Pure water droplets seeded with different clay particles froze heterogeneously at the higher median temperatures indicated in the caption for figure 5.8. The separation of the data points for seeded solution droplets from those for unseeded droplets may be partly the consequence of plotting the median freezing temperatures of populations of droplets in figure 5.8. Heterogeneous freezing occurred over a broader range of temperatures than for freezing pure solution droplets. Nevertheless, it is probably valid to note that the DT_n-solute concentration relationship for seeded solution droplets approximately parallels the one for homogeneous freezing. A careful examination of figure 5.8 indicates that heterogeneous freezing may become even more difficult as a droplet becomes saturated with solute. This inference is supported by the observations of Koop et al. (1995, 1997b) and Biermann et al. (1996) on the sulfuric acid system. These authors have shown that various micrometeorites, metal oxides, silicates, and even AgI nuclei do not crystallize hydrate or ice formation in concentrated sulfuric acid drops at stratospheric temperatures. A reasonable conclusion from figure 5.8 would be that l_het£l_hom. It will be of interest to extend measurements of heterogeneous freezing to conditions of high solute concentration (>0.1 - 1 saturation of solute) that exceed those existing at the point where homogeneous freezing will occur.

Figure 5.8.Depression of the median heterogeneous freezing temperature of approximately 100mm droplets as a function of the composition (given as a fraction of saturated) of solutions of MgCl₂ and Na₂SO₄. The ice nuclei used in droplets were illite (squares, median freezing T = -24°C), montmorillonite (triangles, median freezing T = ?24°C), hallyosite (diamonds, median freezing T = -32.5°C), and kaolinite (crosses, median freezing T = -32.5°C). The median freezing temperature for pure water droplets was ?36.5°C, and the homogeneous freezing point depressions of pure solution droplets are given by the circles. These latter values are shown to approximately agree with l = 2. Adapted from Hoffer (1961).

Limited data also indicate that soot particles will freeze water at low temperatures (DeMott 1990; Diehl and Mitra 1998; DeMott et al. 1999). The ice-nucleating properties of soot aerosols are of interest due to the contribution of combustion processes (jet fuel combustion in particular) to the upper tropospheric aerosol. DeMott (1990) nucleated micron-sized cloud droplets on soot particles produced from burning acetylene and observed ice formation from the suspended droplets during simulated adiabatic cooling. That study found that only a few percent of 80 to 120 nm soot particles froze micron-sized water droplets at temperatures down to -34°C. Freezing fraction was also found to directly relate to particle surface area, as is expected theoretically for a uniform surface. The observation that not all particles of one size froze at the same temperature is not explainable by theory, but is a frequent finding in studies of heterogeneous freezing. 

Diehl and Mitra (1998) observed the freezing of large droplets (~200 to 400 mm) formed from a liquid suspension containing particles produced from burning jet fuel. In this case, more than one particle may have been placed within each droplet. Diehl and Mitra (1998) found that 100% of their droplets froze when suspended in a wind tunnel below about -28°C. A much lower freezing efficiency is obtained from the Diehl and Mitra data when the calculation is referenced to the total particle surface area within the “dirty” drops, more consistent with DeMott’s (1990) results.

DeMott et al. (1999) report the first experiments on freezing of small soot particles in cirrus conditions. They showed that polydisperse (240 nm average diameter) black carbon particles coated by sulfuric acid would act as heterogeneous freezing nuclei when the acid coating exceeded a few weight percent of particle mass and temperature was below -53°C. 

Numerical calculations indicate the potential importance of the heterogeneous freezing nucleation mechanism to cirrus formation conditions. Jensen and Toon (1997) used a classical theoretical approach to demonstrate that existing concentrations of soot particles acting as freezing nuclei should lower ice crystal concentrations in cirrus compared to the singular homogeneous freezing scenario. Jensen and Toon assumed a contact parameter of m_i/n = 0.8 in their analyses. Kärcher et al. (1996) measured m_i/n = 0.57 on a larger graphite surface. The laboratory data of DeMott (1990) suggest that some soot aerosols probably act with m_i/n < 0.1. DeMott et al. (1997) used the empirical approach embodied in equation 8 to extrapolate the soot freezing fractions of DeMott (1990) to the case of H₂SO₄ solution droplets freezing at low temperatures. Despite the differences in the assumed ice nucleating properties of soot particles, DeMott et al. (1997) showed the same functional effect of heterogeneous ice nuclei abundance on cirrus crystal concentrations as did Jensen and Toon (cf. Jensen and Toon 1997: fig. 4 with DeMott et al. 1997: fig. 7). Both numerical studies suggest that freezing nuclei would have the greatest impact on cirrus crystal concentrations for low updraft rates (<20 cm/s) and in warmer cirrus. DeMott et al. (1997) also emphasized that the other critical role of heterogeneous ice nuclei was to lower the threshold humidity for cirrus formation. In the absence of detailed information on the ice nucleating properties of soot particles at temperature below -40°C, these are only qualitative inferences.

Few data exist on heterogeneous ice-nucleation mechanisms besides freezing at low temperatures. A common misconception is that ice formation by deposition nucleation should ensue at very low ice supersaturations. Detwiler and Vonnegut (1981) measured the need for steadily increasing ice supersaturation with decreasing temperature in order to activate deposition nucleation on AgI particles. An ice supersaturation of 20% was needed at -60°C, even though AgI has m_i/n = 0.96 for deposition. More common atmospheric nuclei might be expected to have much lower m_i/n and thus would require exceedingly high ice supersaturations for ice formation by this mechanism.

Although laboratory and modeling studies suggest the potentially important role of heterogeneous ice nuclei in cirrus, their role is critically tied to the abundance of insoluble particulates. As noted previously, different data sets differ in the observed abundance of insoluble particulates in the upper troposphere (Hagen et al. 1994, Sheridan et al. 1994; Chen et al. 1998; Murphy et al., 1998). The presence of insoluble cores within haze particles lofted to cirrus levels also will likely affect how readily such particles effloresce (e.g., Oatis et al. 1998; Han and Martin 1999). Ultimately, more may be learned about these issues by applying some of the laboratory techniques to the atmosphere after sufficient refinement.

5.2 Other Cirrus-related Laboratory Studies

5.2.1. Ice Crystal Morphology, Growth, and Evaporation in Cirrus

The radiative effects of cirrus ice particles depend not only on their concentrations, but also on their subsequent growth or evaporation and their shapes. A number of laboratory studies have been performed to determine the growth habits, growth rates, and evaporation rates of ventilated or freely falling ice particles existing at temperatures higher than -30°C.These studies used an assortment of laboratory devices, including diffusion chambers, cloud chambers, and supercooled cloud tunnels (e.g., Ryan et al. 1976; Oraltay and Hallett 1989; Takahashi et al. 1991; Song and Lamb 1994a). Kobayashi (1965) conducted studies in the temperature regime from -40 to -90°C, but these were of epitaxial growth on large substrate surfaces at standard pressure. Gonda (1983) studied the growth of artificially nucleated crystals in free fall in a cold chamber (-40 to -140°C) at standard pressure. The increased diffusivity of water molecules in air at lower cirrus pressures should lead to faster crystal growth rates and could affect crystal habit and morphology. Bailey and Hallett (1998) map out growth rates and ice crystal morphology at low temperatures, reduced pressures and variable ice saturation ratios for crystals held on drawn glass threads in a thermal diffusion chamber. Some of these results have been mentioned in a previous chapter. These experiments validate the pressure effect on growth rate. Bailey and Hallett (1998) have also found a high frequency of occurrence of crystals with nonhexagonal symmetry and scalene-hexagonal shapes in cirrus conditions. Crystal polycrystallinity has been found to increase toward lower temperatures at the low to moderate ice supersaturations often found in cirrus. 

Emphasis has been given to the study of levitated single ice crystals. Bacon et al. (1998) used electrodynamic isolation to investigate evaporation rates of frost crystal structures at temperatures from 0 to -30°C.The ratios of crystal dimensions along different growth axes increased as crystals evaporated. This result increased the likelihood of crystal fracture, suggesting that fracture is a potentially important secondary ice production process for complex ice crystals. One ice crystal could spawn many particles in regions of evaporation.Swanson et al. (1999) used the same levitation device to examine ice crystal growth rates at low ice supersaturations and temperatures as low as -30°C. Crystal growth and sublimation rates were in agreement with recent theoretical formulations. It can be expected that much data on ice crystal habit transitions, growth, and evaporation rates in the cirrus regime will be obtained through single particle studies of these types. 

A question of particular interest regarding cirrus clouds is the influence of ice crystal surfaces on chemical processing and the effects of surface chemistry on the lifetimes of cirrus crystals. Studies of HNO₃ and HCl uptake and desorption on ice at cirrus conditions have been performed using ion chromatography of frost crystals grown in a diffusion chamber (e.g., Diehl et al. 1995; 1998) and FTIR spectroscopic probing of thin films (e.g., Zondlo et al. 1997; Warshawsky et al. 1999). Current results do not support inhibition of cirrus crystal evaporation because typical HNO₃ partial pressures are too low to lead to liquid surface coverage.

Ice crystal studies must be extended to lower temperatures, higher ice saturation ratios, and varied orientations of crystals to address processes in cirrus conditions. All ice crystal studies should ultimately investigate the effect that the underlying nucleation process may have on the initial form that ice crystals take.

5.2.2. Radiative Properties of Cirrus Ice Crystals

Laboratory studies provide fundamental data on the interaction of radiation with cirrus clouds, validating theories and practical information for interpreting active and passive remote sensing data. A handful of laboratory studies have been performed to measure the scattering properties of cirrus ice crystals. Most of these have been performed in the warmer segment of the cirrus regime. The conduct of increasingly detailed theoretical calculations of scattering by complex cirrus crystals (see Chapter13) and the development of optical array nephelometers for directly measuring scattering phase function in cirrus clouds (e.g.. Gayet et al. 1998; Lawson et al. 1998) have helped motivate new laboratory studies. Some groups have used cloud chambers that contained a light source (e.g., diode laser) and a means for focusing and collecting scattered light (Nikiforova et al. 1978; Volkovitskiy et al. 1980; Sassen and Liou 1979a,b; Rimmer and Saunders 1997; Saunders et al. 1998). Particle imaging nephelometers have also been used to measure the scattering properties of laboratory clouds (Lawson et al. 1998). These laboratory investigations have validated the optical phenomena expected theoretically for certain ice crystal habits, but not for others. Lawson et al. (1998) also noted the close reproduction of natural cirrus crystal habits to -42°C in laboratory clouds formed by controlled expansion. However, many of the expected halo phenomena for different crystal types were smoothed out in the phase function measurements (Lawson et al. 1998). Smooth phase functions may indicate the effect of surface roughness properties (Yang and Liou 1998). Could roughness be induced by the nature of the nucleation process? Issues for cloud chamber studies that require future consideration include the range of crystal sizes that can be investigated and understanding the influence of multiple scattering, background liquid droplets, and non-monodisperse ice-crystal size distributions on interpreting phase function measurements. Saunders et al. (1998) made some progress on these issues.

Scattering and depolarization measurements are also being integrated with single particle (electrodynamic) isolation techniques (Roth and Frohn, 1998; Swanson et al. 1999; Bacon and Swanson 2000). Chapter 13 discusses these measurements. The impact of the complex nucleation processes on scattering and depolarizing properties is a consideration for future investigations in the laboratory.

5.2.3. Collection and Transformation of Aerosols by Cirrus

Nucleation processes are only one means for particles to be collected (scavenged) in cirrus. Ice crystal growth and cirrus cloud dynamics can be expected to lead to the redistribution of aerosol particles after nucleation. Additionally, cirrus crystals can scavenge atmospheric aerosols from the interstitial air. Some laboratory data have been obtained on this process in the warm temperature regime of cirrus. Bell and Saunders (1991; 1995) produced hexagonal plate ice crystals in a cloud chamber and allowed these to settle through an aerosol chamber at -27°C. These authors found high scavenging efficiencies (0.1 to 1) for supermicron aerosols by crystals smaller than 150mm. The noted decrease in scavenging efficiency with increased crystal size was not to the extent necessary to give agreement with extrapolations from theoretical calculations at larger crystal sizes (Martin et al. 1980). Song and Lamb (1994b) studied scavenging of submicron aerosol particles by columnar and plate crystals down to -14°C in a continuous flow cloud chamber. Their measurements agreed with theoretical calculations of scavenging efficiency for 100 to 400 mm plates (Martin et al., 1980) and columns (Miller and Wang 1989). The measurements of Song and Lamb (1994b) suggest that actual scavenging efficiencies may exceed theoretical values for crystals smaller than 100mm. Ice crystals smaller than 100 mm are commonly found in cirrus and contrails. 

The reaction of gas-phase chemical species on cirrus ice crystals or on the various phases of aerosols that may be present in the upper troposphere is a topic only recently explored. Laboratory studies of HNO₃ uptake by cirrus crystals and the effect on crystal evaporation have been mentioned. Other species may also be taken up on cirrus, and the presence of one or another condensate could alter the reactivity of the particles for other species. These chemical reactions can lead to transformations of aerosols in and around cirrus clouds. This is a topic of laboratory investigation, particularly among the researchers who have studied reactions on polar stratospheric clouds.

Due to aerosol and chemical scavenging processes, the aerosols remaining after evaporation of cirrus clouds may be greatly modified compared to the particles that were present before cloud processing. This processing of aerosols may affect their ice nucleation properties at later times. These complex issues deserve greater study.

5.3. Summary

Numerous scientific problems related to understanding cirrus clouds are now being addressed through laboratory studies. This should continue to be an area of vigorous study in the future. Already, field and laboratory programs focusing on cirrus clouds and ice formation processes are in the planning stages. More and more, these efforts will involve participants from many disciplines. The need for validation of remote sensing measurements and model development should also persist.

Acknowledgments.A large number of colleagues, referenced throughout this chapter, deserve thanks for responding to requests for information. Jon Abbatt, Matt Bailey, Alann Bertram, Yalei Chen, Daniel Cziczo, Thomas Koop, Sonia Kreidenweis, Scot Martin, David Rogers, Tony Prenni, Azadeh Tabazadeh, and Vitaly Khvorostyanov provided additional helpful discussions and specific material. Special thanks to Andrew Detwiler and Gabor Vali for their thorough reviews, and to the National Science Foundation (NSF ATM-0071321 ) and the National Aeronautics and Space Administration (NAG 5-9308) for their support while I was writing this chapter.

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