Preprints
https://doi.org/10.5194/gmd-2021-393
https://doi.org/10.5194/gmd-2021-393
Submitted as: development and technical paper
20 Jan 2022
Submitted as: development and technical paper | 20 Jan 2022
Status: this preprint is currently under review for the journal GMD.

Computationally efficient methods for large-scale atmospheric inverse modeling

Taewon Cho1, Julianne Chung2, Scot M. Miller3, and Arvind K. Saibaba4 Taewon Cho et al.
  • 1Department of Mathematics, Virginia Tech, Blacksburg, VA
  • 2Department of Mathematics and Computational Modeling and Data Analytics Division, Academy of Integrated Science, Virginia Tech, Blacksburg, VA
  • 3Department of Environmental Health and Engineering, Johns Hopkins University, Baltimore, MD
  • 4Department of Mathematics, North Carolina State University, Raleigh, NC

Abstract. Atmospheric inverse modeling describes the process of estimating greenhouse gas fluxes or air pollution emissions at the Earth's surface using observations of these gases collected in the atmosphere. The launch of new satellites, the expansion of surface observation networks, and a desire for more detailed maps of surface fluxes has yielded numerous computational and statistical challenges for standard inverse modeling frameworks that were often originally designed with much smaller data sets in mind. In this article, we discuss computationally efficient methods for large-scale atmospheric inverse modeling and focus on addressing some of the main computational and practical challenges. We develop generalized hybrid projection methods, which are iterative methods for solving large-scale inverse problems, and specifically we focus on the case of estimating surface fluxes. These algorithms confer several advantages. They are efficient, in part because they converge quickly, they exploit efficient matrix-vector multiplications, and do not require inverting any matrices. These methods are also robust because they can accurately reconstruct surface fluxes, they are automatic since regularization or covariance matrix parameters and stopping criteria can be determined as part of the iterative algorithm, and they are flexible because they can be paired with many different types of atmospheric models. We demonstrate the benefits of generalized hybrid methods with a case study from NASA's Orbiting Carbon Observatory 2 (OCO-2) satellite. We then address the more challenging problem of solving the inverse model when the mean of the surface fluxes is not known a priori; we do so by reformulating the problem, thereby extending the applicability of hybrid projection methods to include hierarchical priors. We further show that by exploiting mathematical relations provided by the generalized hybrid method, we can efficiently calculate an approximate posterior variance, thereby providing uncertainty information.

Taewon Cho et al.

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Efficient methods for large-scale atmospheric inverse modeling Taewon Cho, Julianne Chung, Scot M. Miller, and Arvind K. Saibaba https://doi.org/10.5281/zenodo.5772660

Taewon Cho et al.

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Short summary
Atmospheric inverse modeling describes the process of estimating greenhouse gas fluxes or air pollution emissions at the Earth's surface using observations of these gases collected in the atmosphere. The launch of new satellites, the expansion of surface observation networks, and a desire for more detailed maps of surface fluxes has yielded numerous computational and statistical challenges. This article describes computationally efficient methods for large-scale atmospheric inverse modeling.