Mathematical derivation and physical interpretation of particle size-resolved activation ratio based on particle hygroscopicity distribution: Application on global characterization of CCN activity

Size-resolved particle activation ratio (SPAR), the size-dependent ability of aerosol particles to form cloud condensation nuclei (CCN), is generally parameterized by a formula with sigmoidal shape with three key parameters. However, our understanding about the intrinsic relationship between the sigmoidal shape function and aerosol hygroscopicity distribution remains incomplete. In this study, the relationship between SPAR and particle hygroscopicity distribution is mathematically derived and relationships between key parameters for SPAR and particle hygroscopicity distribution are manifested, making it clear for the physical understanding of key CCN spectral characteristics. On the basis of the mathematically derived SPAR parameterization, a simplified method to calculate SPAR parameters (including maximum activation fraction (MAF), critical diameter and its heterogeneity of CCN-active particles) based on hygroscopicity distribution data is proposed. This simplified method is applied to Hygroscopicity Tandem Differential Mobility Analyzer (HTDMA) field measurement datasets around the world for the meta-analysis of regional and seasonal characteristics of CCN activity. It was found that, for CCN-active particles in polluted regions, the MAF can reach lower values, and the variations of both hygroscopicity and its heterogeneity can be larger, compared with those in clean regions. In summer, the MAF and the hygroscopicity of CCN can reach higher values than those in winter. In addition, the variations of SPAR parameters among different campaigns are large and thus measurements of CCN Counter or HTDMA are needed to specify the SPAR parameters at a specific site during a specific period. The bulk CCN activity at different SSs are also calculated based on the calculated SPAR by considering the measured particle number size distribution. The mathematical derivation and physical interpretation of SPAR parameterization in this study can further the understanding of CCN activity based on particle hygroscopicity distribution. The proposed simplified method to calculate SPAR parameters based on HTDMA measurements allows meta-analysis of SPAR parameters and helps expand the CCN activity datasets around the world. •Relationship between Size-resolved particle activation ratio and hygroscopicity distribution is mathematically derived.•A simplified method to calculate SPAR parameters based on hygroscopicity distribution data is proposed.•Meta-analysis of CCN activity is c