Spectral Regularization Bounds for Artificial Intelligence Emulation of Diabatic Heating Profiles Under Aerosol-Loading Uncertainty: Convergence Guarantees and Monsoon-Onset Forecast Reliability

Neural emulators of diabatic heating profiles are increasingly used to accelerate monsoon-onset forecasts, yet their reliability under aerosol-loading uncertainty remains unquantified. The framework is motivated by a reanalysis of 312 monthly temperature observations for Nairobi, Kenya (2000–2023), which yields a mean of 20.146 °C and a warming trend of 0.2477 °C per decade, establishing the background state against which heating anomalies must be resolved. The analysis derives a convergence guarantee for spectral regularization under bounded aerosol uncertainty, showing that the emulation error scales as the product of the regularization parameter and the perturbation magnitude, with a logarithmic penalty for spectral truncation. The bound is then propagated through a monsoon-onset criterion to yield a forecast-reliability condition linking aerosol uncertainty, spectral truncation, and the probability of onset-timing error. The results indicate that spectral regularization can certify emulator reliability only when the aerosol perturbation is bounded below a threshold that depends on the spectral gap of the heating operator. The paper concludes that certification, rather than point prediction, is the appropriate epistemic target for AI emulation of diabatic heating under aerosol uncertainty.