From κ to χ: Evaluating Hygroscopicity-Based Mixing State Estimates with a Particle-Resolved Model

Abstract. Aerosol mixing state strongly influences how particles interact with clouds, radiation, and atmospheric chemistry, but it remains difficult to quantify from routine observations. The aerosol mixing state index (χ) typically requires detailed single-particle composition data, available only from particle-resolved models or advanced measurements. Yuan and Zhao (2023) proposed estimating χ from in-situ hygroscopicity (κ) measurements using a hygroscopicity tandem differential mobility analyzer (HTDMA), offering a promising observational pathway. However, their method assumes a binary system of more- and less-hygroscopic components, which may not represent aerosol populations containing intermediate-hygroscopicity species. Here, we systematically evaluate this κ-based χ retrieval using the stochastic particle-resolved model PartMC-MOSAIC. We generated a large ensemble of aerosol populations from urban plume simulations spanning a wide range of emissions, aging conditions, and meteorology. For each population and particle diameter (50–250 nm), we compared the “true” mixing state index from per-particle composition (χ^PMC) with the χ inferred from κ distributions (χ^YZ). The retrieval performs well for many aerosol populations, but systematically overestimates χ when externally mixed intermediate-hygroscopicity components violate the binary assumption. By quantifying the error distributions across particle sizes, we derive uncertainty bounds for the retrieval and apply them to long-term HTDMA datasets from urban, continental, and coastal sites, providing a first multi-site assessment of seasonal variability in χ inferred from hygroscopicity measurements.