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A parameterization of the activation of a lognormal size distribution of aerosols to form cloud droplets is extended to a sectional representation of the aerosol size distribution. For each section, number concentration and chemical composition are uniform functions of particle radius. The parameterization is applied by calculating an effective critical supersaturation of all sections from which the maximum supersaturation of the air parcel is calculated using the previously derived parameterization. The Köhler theory is used to relate the aerosol size distribution and composition to the number activated for each section as a function of maximum supersaturation. For most cases, parametric results are within 10% of those obtained by detailed numerical computations for both idealized and measured aerosol size distributions. The parameterization thus provides an accurate method of treating the activation process for models that use a sectional representation of the aerosol size distribution.
Abdul‐Razzak et al. (Fri,) studied this question.