Microphysical evolution and column loading drive nonlinear regional contrast in black carbon top-of-atmosphere forcing

Abstract. Black carbon (BC) aerosols remain among the most uncertain contributors to anthropogenic climate forcing, as their radiative impact depends sensitively on microphysical evolution and atmospheric loading. This study presents a physics-informed, machine learning (ML) approach to estimate clear-sky BC top-of-atmosphere direct radiative forcing (BCTOA) at high spatial-temporal resolution while retaining physical interpretability. The study derives necessary optical properties for radiative transfer modeling (RTM), by constraining them with multi-platform, multi-waveband observations and their associated uncertainties. The RTM outputs are then used to train the ML surrogates and applied over two contrasting urban agglomerates-Xuzhou, China, and Dhaka, Bangladesh. The ML framework closely reproduces physics-based regional climatological mean (–17.6 ± 2.2 W m^-2 versus –17.4 ± 2.6 W m^-2 over Xuzhou; –14.9 ± 1.1 W m^-2 versus –15.0 ± 1.2 W m^-2 for Dhaka), while achieving high predictive fidelity R² > 0.95; RMSE ~1.5–1.8 W m^-2 and strong cross-regional consistency (r > 0.9). Predictor decomposition reveals BCTOA is primarily modulated by BC aerosol optical depth (BCAOD), column number density, and mixing state, with their relative importance and influence varying non-linearly across cooling-to-warming regimes. Crucially, similar BC loading can yield contrasting absorption-scattering dynamics across region, which are not captured by simplfied forcing parameterization. Together, the physics-informed ML framework and the multi-domain evaluation provide an efficient and transferable tool for constraining BC radiative impacts across real-world heterogeneity. The analysis also offers new mechanistic insight into how regional properties reshape BC regional radiative forcing.