Markov Chain Monte Carlo (MCMC) is a powerful and promising tool for assessing the uncertainties in the Orbiting Carbon Observatory 2 (OCO-2) satellite’s carbon dioxide measurements. Previous research in comparing MCMC and Optimal Estimation (OE) for the OCO-2 retrieval has highlighted the issues of slow convergence of MCMC, and furthermore OE and MCMC not necessarily agreeing with the simulated ground truth. In this work, we exploit the inherent low information content of the OCO-2 measurement and use the Likelihood-Informed Subspace (LIS) dimension reduction to significantly speed up the convergence of MCMC. We demonstrate the strength of this analysis method by assessing the non-Gaussian shape of the retrieval’s posterior distribution, and the effect of operational OCO-2 prior covariance’s aerosol parameters on the retrieval. We further show that in our test cases we can use this analysis to improve the retrieval to retrieve the simulated true state significantly more accurately and to characterize the non-Gaussian form of the posterior distribution of the retrieval problem.

We analyzed the vertical distribution of atmospheric methane (CH ${}_4$ ) retrieved from measurements by ground-based Fourier Transform Spectrometer (FTS) instrument in Sodankylä, Northern Finland. The retrieved dataset covers 2009–2018. We used a dimension reduction retrieval method to extract the profile information, since each measurement contains around three pieces of information about the profile shape between 0 and 40 km. We compared the retrieved profiles against Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) satellite measurements and AirCore balloon-borne profile measurements. Additional comparison at the lowest tropospheric layer was done against in-situ measurements from a 50-m-high mast. In general, the ground-based FTS and ACE-FTS profiles agreed within 10% below 20 km and within 30% in the stratosphere between 20 and 40 km. Our method was able to accurately capture reduced methane concentrations inside the polar vortex in the Arctic stratosphere. The method produced similar trend characteristics as the reference instruments even when a static prior profile was used. Finally, we analyzed the time series of the CH ${}_4$ profile datasets and estimated the trend using the dynamic linear model (DLM).

Remote sensing of atmospheric carbon dioxide (CO₂) carried out by NASA's Orbiting Carbon Observatory-2 (OCO-2) satellite mission and the related uncertainty quantification effort involve repeated evaluations of a state-of-the-art atmospheric physics model. The retrieval, or solving an inverse problem, requires substantial computational resources. In this work, we propose and implement a statistical emulator to speed up the computations in the OCO-2 physics model. Our approach is based on Gaussian process (GP) regression, leveraging recent research on kernel flows and cross validation to efficiently learn the kernel function in the GP. We demonstrate our method by replicating the behavior of OCO-2 forward model within measurement error precision and further show that in simulated cases, our method reproduces the CO₂ retrieval performance of OCO-2 setup with computational time that is orders of magnitude faster. The underlying emulation problem is challenging because it is high-dimensional. It is related to operator learning in the sense that the function to be approximated maps high-dimensional vectors to high-dimensional vectors. Our proposed approach is not only fast but also highly accurate (its relative error is less than 1 %). In contrast with artificial neural network (ANN)-based methods, it is interpretable, and its efficiency is based on learning a kernel in an engineered and expressive family of kernels.

Quality filtering of satellite XCO ₂ retrievals is essential for every downstream science application, yet the community still grapples with the trade‐off between retaining data availability and suppressing biases. For the Orbiting Carbon Observatory‐2 (OCO‐2) record in particular, the long‐standing binary quality flag targets the single use case of global carbon flux inversion and is often too restrictive for small spatial scale analysis like quantifying emissions from coal‐fired power plants. To address the need for flexible quality filtering we introduce a data‐driven, ternary (three‐state) quality flag constructed from the agreement of three independent sub‐filters: two Random Forest classifiers trained on distinct “truth proxy” data sets and a third sub‐filter based on the uncertainty estimate from a non‐linear machine learning bias correction and the operational uncertainty product. We utilized a Bayesian multi‐objective optimization to tune the sub‐filters, balancing the competing goals of maximizing data throughput with minimizing error variance and retrieval uncertainty. The proposed ternary quality flag shows an improved reduction in root mean square error (RMSE) (22% for land and 53% for ocean) over the operational flag. This reduction is due in part to an improved ability to remove observations affected by 3D cloud biases. The flexible ternary flag can optionally increase data availability by 21% over land and 18% over ocean but is still competitive with the RMSE of the operational product. The proposed filter addresses the diverse needs of the science community and is generalizable to greenhouse gas monitoring missions such as GOSAT, CO2M and Carbon‐I.

Remote sensing of atmospheric carbon dioxide (CO₂) carried out by NASA’s Orbiting Carbon Observatory-2 (OCO-2) satellite mission and the related Uncertainty Quantification (UQ) effort involves repeated evaluations of a state-of-the-art atmospheric physics model. The retrieval, or solving an inverse problem, requires substantial computational resources. In this work, we propose and implement a statistical emulator to speed up the computations in the OCO-2 physics model. Our approach is based on Gaussian Process (GP) Regression, leveraging recent research on Kernel Flows and Cross Validation to efficiently learn the kernel function in the GP. We demonstrate our method by replicating the behavior of OCO-2 forward model within measurement error precision, and further show that in simulated cases, our method reproduces the CO₂ retrieval performance of OCO-2 setup with orders of magnitude faster computational time. The underlying emulation problem is challenging because it is high dimensional. It is related to operator learning in the sense that the function to be approximated is mapping high-dimensional vectors to high-dimensional vectors. Our proposed approach is not only fast but also highly accurate (its relative error is less than 1 %). In contrast with Artificial Neural Network (ANN) based methods, it is interpretable and its efficiency is based on learning a kernel in an engineered and expressive family of kernels.