| 09 Sep 2026
Theory for Optically Observing Cloud Aerosol Critical Activation Diameter
Abstract. Aerosol activation is the fundamental microphysical process governing cloud droplet formation. The critical activation diameter, π·π, is a key parameter that characterizes cloud supersaturation and aerosol activation and serves as a fundamental variable in simulations of aerosol–cloud interactions. Kuang et al. (2025) proposed a machine-learning framework for the instantaneous retrieval of π·π from spectral scattering measurements of interstitial and activated aerosols. However, the lack of a rigorous theoretical foundation has limited the understanding of the method's physical basis, applicability, and limitations in field observations. Here, we establish the missing theoretical foundation by integrating aerosol activation theory with Mie scattering theory to derive a unified closed-form solution linking optical scattering to the π·π. The resulting theory provides the first analytical explanation for the approximately linear relationship between π·π and the scattering fraction of interstitial aerosols reported by Kuang et al. (2025), while also revealing the strongly nonlinear behavior near the limiting scattering regimes. Furthermore, the theoretical detection limit of the optical approach is quantified, and its potential applicability to different cloud types is evaluated. Overall, this work provides a rigorous theoretical foundation for optical observations of cloud aerosol activation. The unified analytical solution bridges all limiting regimes, clarifies the physical basis of optical retrievals of the critical activation diameter, and offers theoretical guidance for the design and optimization of future optical instruments for cloud activation measurements.
This work presents a theoretical foundation for retrieving the aerosol cloud condensation nuclei critical diameter Da from spectral light scattering measurements of interstitial and activated aerosols. The research is a follow-up to the Kuang (2025) paper, and combines aerosol activation theory with Mie scattering theory to derive a unified closed-form solution linking optical scattering to the Da to the scattering ratio fsp of interstitial aerosols divided by the total sub-micron scattering. The theoretical basis is solidly outlined in Sect. 2.1, leading to an explicit relationship between fsp and critical activation diameter Da (Eq.16). The authors acknowledge the practical difficulties in using this equation and further derived approximations, including a linear approximation between Da and fsp that was shown to work over a large fsp range (~0.20-0.80) that often occurred during the field campaign conditions in the North China Sea. Measured and calculated Da demonstrated a fairly strong correlation (R2=0.57) when the linear approximation was used to calculate Da. The correlation between measured and calculated Da was improved upon (R2=0.83) when the machine learning model (Kuang, 2025) was used. The machine-learning framework developed by Kuang et al. (2025) provides a practical implementation by incorporating the nonlinear and multidimensional dependencies revealed by the theory, including the effect of scattering Angstrom exponent on the relationship between Da and fsp. The paper provides a thorough summary of the physical limitations and applicability of the optical retrieval of Da from aerosol light scattering measurements, discussed by (Kuang et al., 2025). I believe that the paper could contribute to improved understanding of CCN activation in/near clouds and recommend publication. I would like to see some discussion of the measurements used to train and evaluate the ML model to predict Da would be helpful, even if in the Supplement. The authors cite the Kuang (2018) and Kuang (2025) papers so only a brief section is needed.