GeoPrior-Mamba: Structured Process Priors with Mamba for Fine-Resolution XCO2 Reconstruction

Space-based monitoring of atmospheric carbon dioxide (CO$_2$) constrains the global carbon budget. NASA's Orbiting Carbon Observatory-2 (OCO-2) estimates column-averaged dry-air mole fractions of CO$_2$ (XCO$_2$) 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 CO$_2$ 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 XCO$_2$ 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 XCO$_2$ 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.

Eddy-covariance (EC) flux towers provide in situ measurements of $CO_2$ flux and serve as the ground-truth data for predictive `upscaling' models derived from satellite products. However, many satellites now resolve spatial scales smaller than an EC tower's footprint. We show theoretically that upscaling models trained on high-resolution data in heterogeneous landscapes must account for an EC tower's footprint to avoid bias in pixel-level predictors. To address this problem, we introduce Footprint-Aware Regression (FAR), a deep-learning framework that simultaneously predicts spatial footprints and pixel-level estimates of $CO_2$ flux, and show it yields unbiased pixel-level predictions given sufficient training data. We demonstrate FAR on our AMERI-FAR25 dataset, which combines 205 site-years of tower data with corresponding Landsat scenes, and show that FAR outperforms non-footprint-aware models. FAR increased half-hourly $R^2$ from approximately 0.575 to 0.634 and reduced RMSE by about 7% relative to the best fixed-footprint baseline on a dataset of withheld sites. Gains are larger for monthly and yearly averages relative to a coarser 990 m baseline. Site-level analyses show that these gains extend across multiple ecosystem types. These performance gains are observed whether footprints are learned jointly or estimated independently using an established footprint model, despite substantial variation in footprint size between methods. In a regional comparison over the Western Cascades, FAR produces flux estimates with a distribution comparable to that of existing high-resolution process-based models.

Commercial Microwave Links (CMLs) offer dense spatial coverage for rainfall sensing but produce path-integrated measurements that make accurate ground-level reconstruction challenging. Existing methods typically oversimplify CMLs as point sensors and neglect line integration relating rainfall to signal attenuation, resulting in degraded performance under heterogeneous precipitation. In this work, we view rain field reconstruction as a Bayesian inverse problem with Diffusion Models (DMs) as high-fidelity spatial priors. We show that diffusion models better preserve key rainfall statistics compared to censored Gaussian processes. Framing rainfall estimation as a Bayesian inverse problem with a DM prior enables training-free posterior sampling using a broad family of methods, including Plug-and-Play, Sequential Monte Carlo, and Replica Exchange methods. Experiments on synthetic and real-world datasets demonstrate consistent improvements over established CML-based reconstruction baselines.