Constraining the Global Direct Radiative Forcing of Black Carbon via the Chemical Aerosol Mixing State Index

Black carbon (BC) is an important climate forcing agent, yet its direct radiative forcing (DRF) remains highly uncertain at the global scale, largely due to simplified representations of particle morphology and chemical mixing state in numerical models. Despite advances in particle-scale studies, global assessments still commonly assume fully internal mixing. Here, we present an implementable modelling framework that characterises particle-scale chemical heterogeneity using the mixing state index (χ) and coating volume ratio (VR). Particle-resolved simulations are employed to quantify the effects of χ and VR on BC optical properties. Machine learning is then used to map this particle-scale information onto variables accessible in Earth system models, enabling the estimation of BC radiative forcing under more realistic mixing state conditions. This framework provides a practical pathway to improve global assessments of BC radiative effects.