The particle-to-particle heterogeneity in aerosol hygroscopicity is crucial for understanding aerosol climatic and environmental effects. The hygroscopic parameter κ, widely applied to describe aerosol hygroscopicity for aerosol populations both in models and observations, is a probability distribution highly related to aerosol heterogeneity due to the complex sources and aging processes. However, the heterogeneity in aerosol hygroscopicity is not represented in observations and model simulations, leading to challenges in accurately estimating aerosol climatic and environmental effects. Here, we propose an algorithm for quantifying particle-to-particle heterogeneity in aerosol hygroscopicity, based on information-theoretic entropy measures, by using the data that comes only from the in-situ measurement of the hygroscopicity tandem differential mobility analyzer (H-TDMA). Aerosol populations in this algorithm are assumed to be simple binary systems consisting of the less hygroscopic and more hygroscopic components, which are commonly used in H-TDMA measurement. Three indices, including the average per-particle species diversity D_α, the bulk population species diversity D_γ, and their affine ratio χ, are calculated from the probability distribution of κ to describe aerosol heterogeneity. This algorithm can efficiently characterize the evolution of aerosol heterogeneity with time in the real atmosphere. Our results show that the heterogeneity varies much with aerosol particle size and large discrepancies exist in the width and peak value of particle number size distribution (PNSD) with varied heterogeneity after hygroscopic growth, especially for conditions with high relative humidity. This reveals a vital role of the heterogeneity in ambient PNSD and significant uncertainties in calculating the climate-relevant properties if the population-averaged hygroscopicity is applied by neglecting its heterogeneity. This work points the way toward a better understanding of the role of hygroscopicity in evaluating aerosol climatic and environmental impacts.

aerosol,hygroscopicity,heterogeneity