Hybrid transformer and physics-informed neural operator for correcting TEMPO NO2 biases over North America

Abstract Uncertainty in the Air Mass Factor (AMF) causes systematic biases in satellite-retrieved nitrogen dioxide (NO 2 ) vertical column densities (VCDs). We introduce the first physics-informed neural network that directly refines TEMPO’s AMF to improve the conversion of its slant columns to VCDs within a self-sufficient data pipeline. Our unique Transformer-Fourier Neural Operator hybrid architecture learns the dependencies among 2D and 3D radiative transfer features that govern AMF, using a Huber loss that enforces consistency between predicted AMF and radiative transfer theory. Trained on 74,919 TEMPO-Pandora observation pairs across North America from August 2023 to December 2024, our bias correction framework improves R 2 from 0.58 to 0.80 and reduces RMSE by 30%, with stable performance across all seasons. By incorporating an explicit physical constraint during training rather than relying on post-hoc bias fitting, our approach complements purely data-driven learning and provides a theory-consistent correction of AMF-driven biases in satellite VCD retrievals.