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Aerosol optical quantities have been widely employed as the proxy variables of cloud condensation nuclei concentration to study aerosol indirect effects (AIE). Due to the aerosol swelling effect, cloud condensation nuclei and aerosol optical quantities do not vary in harmony, leading to a bias in the estimation of the AIE. To identify and quantify this artifact, we employ extensive measurements of aerosol and cloud properties made at four sites in different continents that have distinct aerosol properties in terms of size and composition. One-unit enhancement in aerosol scattering coefficient by swelling effect is found to lead to a systematic underestimation of the first indirect effect (FIE) by about 23% that can result in an underestimation in the FIE-related radiative forcing by several W/m(2) depending on aerosol properties and relative humidity. This likely contributes significantly to the systematic difference between satellite-based estimates of the FIE and those simulated by general circulation models. Recommendations are made to make more sound comparisons of the AIE estimated from observations and model simulations.

Plain Language Summary Due to the limited measurements of cloud condensation nuclei concentration, the aerosol optical quantities such as aerosol optical depth have been widely employed to study the aerosol first indirect effect (FIE), which is one of the largest sources of uncertainties in climate studies. Aerosol optical quantities are significantly influenced by aerosol swelling effect, but cloud condensation nuclei are not, which can lead to a bias in the estimation of the FIE. Here we employed extensive measurements of aerosol and cloud properties made at four Atmospheric Radiation Measurement sites that have distinct aerosol types to identify and quantify this artifact. Our results reveal that one-unit enhancement in aerosol scattering coefficient due to aerosol swelling can result in underestimating the FIE by similar to 23%, which will lead the significant underestimation on the FIE-related radiative forcing. The finding helps account for the systematic differences between observation-based and modeled simulated FIE, especially for those derived from satellite-based measurements. It may also help explain some observed positive aerosol indirect effects values.