Amortized Probabilistic Retrieval of Atmospheric CO2 from OCO-2 Spectra Using Deep Learning with Laplace Approximations and Normalizing Flows

Space-based monitoring of atmospheric carbon dioxide (CO2) constrains the global carbon budget. NASA's Orbiting Carbon Observatory-2 (OCO-2) estimates column-averaged dry-air mole fractions of CO2 (XCO2) from high-resolution spectra, but operational retrievals are computationally expensive and impose stringent Gaussianity assumptions on the retrieved posterior. We present a deep learning framework that addresses both through amortized probabilistic inference. Lacking ground truth for real observations, we train and evaluate on a high-fidelity OCO-2 simulation ensemble with calibrated forward-model errors, comparing against the version-10 ACOS full-physics retrieval on the same radiances. Our architecture encodes each spectral band separately and estimates posteriors of the full CO2 column, or summaries thereof, with Laplace approximations and conditional normalizing flows. Once trained, inference costs milliseconds per sounding rather than minutes, and calibrated posteriors are attainable at that cost. Trained on simulations that explicitly include forward-model discrepancy, our retrievals are more accurate than the operational one for XCO2 on both data partitions we consider, and competitive on profiles. The flow represents asymmetric posteriors that a Gaussian cannot, a gain attributable to shape rather than scale, and its advantage in predictive density persists where its accuracy advantage does not. These results are established on a land-only ensemble against one configuration of the operational algorithm. On reference soundings withheld from training and on two unseen months the XCO2 and density advantages persist while calibration degrades under sparsely sampled observing conditions, pointing to the diversity of the simulated scene population rather than the method as the main obstacle.