Cloud Droplet Formation and Khler Theory

In the Earth's atmosphere, cloud droplets do not generally form by homogeneous nucleation of supersaturated water vapor (i.e., condensation of water molecules from the gas phase in the absence of a preexisting condensation nucleus). This would require the initial formation of droplet embryos (clusters of water molecules) with a very small radius of curvature. Because of surface tension, however, the equilibrium vapor pressure over such a strongly curved surface is much greater than over a flat surface ("Kelvin effect" or "curvature effect"). Thus water-vapor supersaturations (the relative difference between the actual vapor pressure and the equilibrium vapor pressure over a flat surface) of several hundred percent are needed for homogeneous nucleation of water droplets (Pruppacher and Klett 2000; Andreae and Rosenfeld 2008).

In the atmosphere, such large supersaturations are not reached, because aerosol particles facilitate the condensation of water vapor. The equilibrium water-vapor pressure over an aqueous solution is generally lower than over pure water ("Raoult effect" or "solute effect"; reduction of water activity), and thus water vapor can condense and form solution droplets on particles composed of soluble material (deliquescence and hygroscopic growth). Insoluble, but wettable particles can also facilitate droplet formation by decreasing the curvature effect for water adsorbed on the surface (depending on hydrophilicity and contact angle), and the uptake of water vapor on insoluble particles can be enhanced by soluble materials that are ubiquitous in the atmosphere (e.g., sulfuric acid).

By accounting for curvature and solute effects, Köhler theory describes the hygroscopic growth and CCN activation of soluble aerosol particles as a function of relative humidity or water-vapor supersaturation, respectively (Seinfeld and Pandis 1998; Pruppacher and Klett 2000; McFiggans et al. 2006): For a given dry particle diameter, it enables the critical water-vapor supersaturation to be calculated; that is, the minimum supersaturation required to form an aqueous droplet that can freely grow by further condensation (cloud droplet).

For a given water-vapor supersaturation, it permits the critical dry particle diameter to be determined; that is, the minimum dry particle diameter required to form a cloud droplet.

A wide range of different Köhler models have been applied in experimental and theoretical studies of aerosol-cloud interactions. Depending on the equations, parameterizations, and approximations used to quantify the Raoult effect and describe water activity in the aqueous solution droplet, they can be broadly classified as activity parameterization models, osmotic coefficient models, van't Hoff factor models, effective hygroscopicity parameter models, and analytical approximation models. Some of these, however, yield substantially different results even for simple and well-defined standard aerosols and reference substances (Rose et al. 2008a).

Figure 3.12 illustrates the range of critical supersaturations calculated as a function of dry particle diameter (20-200 nm) with different Köhler models for ammonium sulfate and sodium chloride. As discussed by Rose et al. (2008a), activity parameterization models based on the Aerosol Inorganics Model (AIM; Clegg et al. 1998a, b) can be regarded as the most accurate Köhler models available for these substances. The relative deviations of alternative models range up to 20% for ammonium sulfate and 10% for sodium chloride.

As outlined below, such deviations may be negligibly small compared to other uncertainties in current investigations of the interactions between aerosol, cloud, and climate using regional and global atmospheric models. For detailed mechanistic studies of cloud processes, however, and compared to the high precision of state-of-the-art measurement techniques (e.g., CCN counters), the

Figure 3.12 Critical supersaturations (Sc) calculated for ammonium sulfate and sodium chloride particles with dry particle mass or volume equivalent diameters (Ds) in the range of 20-200 nm at 298 K using selected Köhler models: an activity parameterization model based on the AIM (AP3, black); a van't Hoff factor model (VH4, red); and an analytical approximation model (AA1, blue). For details see Rose et al. (2008a).

Cobalt Sulfate Van Hoff

Figure 3.12 Critical supersaturations (Sc) calculated for ammonium sulfate and sodium chloride particles with dry particle mass or volume equivalent diameters (Ds) in the range of 20-200 nm at 298 K using selected Köhler models: an activity parameterization model based on the AIM (AP3, black); a van't Hoff factor model (VH4, red); and an analytical approximation model (AA1, blue). For details see Rose et al. (2008a).

deviations between different Köhler models can be very substantial and exceed other sources of uncertainty. To ensure that measurement and model results can be properly compared, CCN studies should always report exactly which Köhler model equations and parameters have been applied.

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