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

2026-06-15

AI Summary

This work addresses the high computational cost and difficulty in accurately quantifying uncertainties inherent in traditional OCO-2 satellite–based CO₂ retrieval methods. The authors propose a multi-branch deep neural network framework trained on high-fidelity simulation data, integrating Laplace approximation with normalizing flows to enable rapid probabilistic inversion of atmospheric column-averaged CO₂ concentrations. By leveraging amortized inference, the method dramatically accelerates computation, robustly models systematic errors, and effectively captures non-Gaussian, asymmetric posterior distributions. Compared to conventional full-physics inversions, the approach achieves speedups of several orders of magnitude while yielding more accurate point estimates and better-calibrated uncertainty quantification.

Abstract

Space-based monitoring of atmospheric carbon dioxide (CO2) is essential for constraining the global carbon budget. NASA's Orbiting Carbon Observatory-2 (OCO-2) estimates column-averaged dry-air mole fractions of CO2 (XCO2) using high-resolution spectra. However, current operational retrieval algorithms are computationally expensive and do not properly quantify uncertainties. We present a novel deep learning framework that addresses these challenges. Due to the difficulties of ground-truth data for real satellite observations, we develop and validate our approach using a high-fidelity simulation dataset. This dataset, created to support OCO-2 uncertainty quantification (UQ), incorporates realistic forward model errors. Our architecture encodes spectral bands using a multi-branch neural network and estimates posteriors of the full CO2 column or desired summaries thereof using two scalable UQ methods: Laplace approximations and normalizing flows. Our approach has five key advantages relative to operational "full-physics" solvers: (1) Amortization: Inference is orders of magnitude faster, enabling real-time processing of massive data streams; (2) Model error robustness: By training on simulations that explicitly include model discrepancies, our method accounts for systematic errors often neglected by standard inversions; (3) Point estimate accuracy: We achieve superior predictive accuracy compared to baseline methods; (4) Improved UQ: The probabilistic outputs yield better-calibrated uncertainty estimates; and (5) Non-Gaussian posteriors: When utilizing normalizing flows, our framework successfully models complex, asymmetric posterior distributions, overcoming the limitations of the Gaussian assumption. These results suggest that simulation-based deep learning is a viable path toward next-generation operational processing systems.

Problem

• atmospheric CO2 retrieval
• uncertainty quantification
• OCO-2
• computational efficiency
• satellite remote sensing

Innovation

• amortized inference
• uncertainty quantification
• normalizing flows
• Laplace approximation
• deep learning for remote sensing