arXiv subjects

Jonathan Hobbs

Publications and source records attributed to Jonathan Hobbs.

7 recordsLinked to original sources

arXiv2026

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) 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.

cs.LG↗

arXiv2025

An Error Model for Evaluating the Accuracy of Satellite-Based XCO$_2$ Products

Several satellites (e.g., OCO-2 & 3) and their derived products now provide spatially extensive coverage of the abundance of carbon dioxide in the atmospheric column (XCO$_2$). However, the accuracy of the XCO$_2$ reported in these products needs to be carefully assessed for any downstream scientific analysis; this involves comparison with reference datasets, such as those from the Total Carbon Column Observing Network (TCCON). Previously, systematic and random errors have been used to quantify differences between satellite-based XCO$_2$ measurements and TCCON data. The spatiotemporal density of satellite observations enables the decomposition of the error variability into these components. This study aims to unify the definitions of these error components through a hierarchical statistical model with explicit mathematical terms, which enables a formal definition of the underlying assumptions and estimation of each component. Specifically, we focus on defining model elements, like global bias and systematic and random error, as part of this framework. We use it to compare OCO-2 XCO$_2$ v11.1 data (both original scenes from the `Lite' files and 10-sec averages) and gridded Making Earth System Data Records for Use in Research Environments (MEaSUREs) products to TCCON data. The MEaSUREs products exhibit comparable systematic errors to other OCO-2 products, with larger errors over land versus ocean. We describe the methodology for creating the MEaSUREs products, including their prior and posterior error covariances, with information on spatial correlation for efficient incorporation into scientific analysis.

stat.AP↗

arXiv2025

A Bayesian hierarchical framework for fusion of remote sensing data: An example with solar-induced fluorescence

Solar-induced chlorophyll fluorescence (SIF) has emerged as an effective indicator of vegetation productivity and plant health. The global quantification of SIF and its associated uncertainties yields many important capabilities, including improving carbon flux estimation, improving the identification of carbon sources and sinks, monitoring a variety of ecosystems, and evaluating carbon sequestration efforts. Long-term, regional-to-global scale monitoring is now feasible with the availability of SIF estimates from multiple Earth-observing satellites. These efforts can be aided by a rigorous accounting of the sources of uncertainty present in satellite SIF data products. In this paper, we introduce a Bayesian Hierarchical Model (BHM) for the estimation of SIF and associated uncertainties from Orbiting Carbon Observatory-2 (OCO-2) satellite observations at one-degree resolution with global coverage. The hierarchical structure of our modeling framework allows for convenient model specification, quantification of various sources of variation, and the incorporation of seasonal SIF information through Fourier terms in the regression model. The modeling framework leverages the predictable seasonality of SIF in most temperate land areas. The resulting data product complements existing atmospheric carbon dioxide estimates at the same spatio-temporal resolution.

stat.AP↗

arXiv2022

Bayesian Latent Variable Co-kriging Model in Remote Sensing for Observations with Quality Flagged

Remote sensing data products often include quality flags that inform users whether the associated observations are of good, acceptable or unreliable qualities. However, such information on data fidelity is not considered in remote sensing data analyses. Motivated by observations from the Atmospheric Infrared Sounder (AIRS) instrument on board NASA's Aqua satellite, we propose a latent variable co-kriging model with separable Gaussian processes to analyze large quality-flagged remote sensing data sets together with their associated quality information. We augment the posterior distribution by an imputation mechanism to decompose large covariance matrices into separate computationally efficient components taking advantage of their input structure. Within the augmented posterior, we develop a Markov chain Monte Carlo (MCMC) procedure that mostly consists of direct simulations from conditional distributions. In addition, we propose a computationally efficient recursive prediction procedure. We apply the proposed method to air temperature data from the AIRS instrument. We show that incorporating quality flag information in our proposed model substantially improves the prediction performance compared to models that do not account for quality flags.

stat.AP↗

arXiv2021

A Geospatial Functional Model For OCO-2 Data with Application on Imputation and Land Fraction Estimation

Data from NASA's Orbiting Carbon Observatory-2 (OCO-2) satellite is essential to many carbon management strategies. A retrieval algorithm is used to estimate CO2 concentration using the radiance data measured by OCO-2. However, due to factors such as cloud cover and cosmic rays, the spatial coverage of the retrieval algorithm is limited in some areas of critical importance for carbon cycle science. Mixed land/water pixels along the coastline are also not used in the retrieval processing due to the lack of valid ancillary variables including land fraction. We propose an approach to model spatial spectral data to solve these two problems by radiance imputation and land fraction estimation. The spectral observations are modeled as spatially indexed functional data with footprint-specific parameters and are reduced to much lower dimensions by functional principal component analysis. The principal component scores are modeled as random fields to account for the spatial dependence, and the missing spectral observations are imputed by kriging the principal component scores. The proposed method is shown to impute spectral radiance with high accuracy for observations over the Pacific Ocean. An unmixing approach based on this model provides much more accurate land fraction estimates in our validation study along Greece coastlines.

stat.AP↗

arXiv2020

Computer Model Emulation with High-Dimensional Functional Output in Large-Scale Observing System Uncertainty Experiments

Observing system uncertainty experiments (OSUEs) have been recently proposed as a cost-effective way to perform probabilistic assessment of retrievals for NASA's Orbiting Carbon Observatory-2 (OCO-2) mission. One important component in the OCO-2 retrieval algorithm is a full-physics forward model that describes the mathematical relationship between atmospheric variables such as carbon dioxide and radiances measured by the remote sensing instrument. This forward model is complicated and computationally expensive but large-scale OSUEs require evaluation of this model numerous times, which makes it infeasible for comprehensive experiments. To tackle this issue, we develop a statistical emulator to facilitate large-scale OSUEs in the OCO-2 mission with independent emulation. Within each distinct spectral band, the emulator represents radiances output at irregular wavelengths via a linear combination of basis functions and random coefficients. These random coefficients are then modeled with nearest-neighbor Gaussian processes with built-in input dimension reduction via active subspace. The proposed emulator reduces dimensionality in both input space and output space, so that fast computation is achieved within a fully Bayesian inference framework. Validation experiments demonstrate that this emulator outperforms other competing statistical methods and a reduced order model that approximates the full-physics forward model.

stat.AP↗

arXiv2020

Objective frequentist uncertainty quantification for atmospheric CO$_2$ retrievals

The steadily increasing amount of atmospheric carbon dioxide (CO$_2$) is affecting the global climate system and threatening the long-term sustainability of Earth's ecosystem. In order to better understand the sources and sinks of CO$_2$, NASA operates the Orbiting Carbon Observatory-2 & 3 satellites to monitor CO$_2$ from space. These satellites make passive radiance measurements of the sunlight reflected off the Earth's surface in different spectral bands, which are then inverted in an ill-posed inverse problem to obtain estimates of the atmospheric CO$_2$ concentration. In this work, we propose a new CO$_2$ retrieval method that uses known physical constraints on the state variables and direct inversion of the target functional of interest to construct well-calibrated frequentist confidence intervals based on convex programming. We compare the method with the current operational retrieval procedure, which uses prior knowledge in the form of probability distributions to regularize the problem. We demonstrate that the proposed intervals consistently achieve the desired frequentist coverage, while the operational uncertainties are poorly calibrated in a frequentist sense both at individual locations and over a spatial region in a realistic simulation experiment. We also study the influence of specific nuisance state variables on the length of the proposed intervals and identify certain key variables that can greatly reduce the final uncertainty given additional deterministic or probabilistic constraints, and develop a principled framework to incorporate such information into our method.

stat.AP↗