Inversion Approach for Inferring Mixing State and Improving Optical Estimation of Coated Black Carbon Using Bulk-Volume Variables and Number-Size Distributions

Black carbon (BC) exerts a strong warming effect on the climate system, which is significantly influenced by its mixing state with nonabsorbing materials. Large-scale models typically simplify BC mixing state representation due to computational constraints, often resulting in substantial overestimations of light absorption. Under the steady-state assumption, we present a physically grounded inversion approach to infer the mixing state of coated BC (CBC) particles by mapping bulk volume and volume fraction of BC cores to the total number concentration and coating thickness distribution parameter ( k ), based on preset number-size distributions of BC core diameter. By introducing the k -value, we reconstruct the two-dimensional distribution of CBC particles for calculating key optical properties through efficient lookup tables. The inversion approach is validated against both particle-resolved model simulations and field observations, yielding mean relative errors of below 5% for optical properties. Compared to traditional assumptions of uniform composition, our approach accounts for coating thickness heterogeneity among CBC particles, improving optical evaluation in models with a negligible additional computational cost. This work provides a practical and scalable solution to represent the BC mixing state in atmospheric models, facilitating more reliable assessments of BC radiative effects in air quality and climate studies.