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 (BC TOA) 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). SHAP based predictor attribution indicates that BC TOA estimates are strongly associated with BC aerosol optical depth (BCAOD), column number density, and mixing state, with their relative contributions 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 simplified forcing parameterization. To test transferability, the combined ML model (trained in Xuzhou, China and Dhaka, Bangladesh) was evaluated zero-shot on two additional regions with contrasting aerosol microphysical conditions represented by Delhi, India (urban and agricultural burning sources) and Mongu, Zambia (strong savanna fires). While transference to Delhi is reasonable (Adj. R2=0.91, RMSE = 2.3 W m−2), there is a systematic underestimate at Mongu (Adj. R2=0.83; MBE = −4.2 W m−2). Feature-space overlap analysis attributes this degradation to a distributional mismatch in key microphysical predictors. Retraining on an expanded dataset including all four regions preserves urban performance while reducing Mongu RMSE by 68 % and bias from −4.2 to −0.8 W m−2. 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 study also offers new mechanistic insight into how regional properties reshape BC radiative forcing.