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Figure 1. Köhler curves: variation of the equilibrium drop size with the saturation ratio. All curves are for droplets formed from ammonium sulfate particles, with the dry radius labeled in units of micrometers. The dashed curve represents the curvature effect for pure water droplets. (From Chen, 1994.)

have a lower critical Seq, and thus the advantage of easier activation.

It is important to recognize that hygroscopic aerosols have a broad size range, and very large CCNs may play very different roles in cloud and precipitation formation than the smaller ones. In addition, the sizes of aerosols might be much more important than their chemical composition, which normally has smaller variability, in determining their ability to activate into cloud drops (Rosenfeld, 2006; Dusek et al., 2006), unless the aerosols have large insoluble fractions.

2.1.1. Twomey's indirect effects

Twomey in 1974 first pointed out that increasing anthropogenic pollution would result in higher CCN and cloud drop number concentrations. Note that traditionally we discuss Twomey's effects with a focus on hygroscopic CCNs, but other types of aerosols may also contribute to such effects. The relationship between the number concentrations of CCNs and cloud drops during the activation process (at the cloud base) can be seen through the calculations from a detailed parcel model, as shown in Fig. 2, in which the CCN size distribution assumes the empirical expression Nccn = CASk, as derived by Twomey (1959), where Nccn is the number concentration of CCNs (outside the cloud) or cloud drops (inside the cloud), C is a coefficient that roughly represents the total number of condensation nuclei, AS is the supersaturation, and k represents the gradient by which the number density (in log scale) varies with the CCN size (note: CCN size is connected with the supersaturation AS, following the Köhler theory). Observation evidences also concur with

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