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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/amt-2020-451
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-2020-451
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  16 Nov 2020

16 Nov 2020

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This preprint is currently under review for the journal AMT.

Reduced-Cost Construction of Jacobian Matrices for High-Resolution Inversions of Satellite Observations of Atmospheric Composition

Hannah Nesser1, Daniel J. Jacob1, Joannes D. Maasakkers2, Tia R. Scarpelli3, Melissa P. Sulprizio1, Yuzhong Zhang4, and Chris H. Rycroft1 Hannah Nesser et al.
  • 1School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
  • 2SRON Netherlands Institute for Space Research, Utrecht, the Netherlands
  • 3Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA
  • 4School of Engineering, Westlake University, Hangzhou, Zhejiang Province, China

Abstract. Global high-resolution observations of atmospheric composition from satellites can greatly improve our understanding of surface emissions through inverse analyses. Variational inverse methods can optimize surface emissions at any resolution but do not readily quantify the error and information content of the posterior solution. In fact, the information content of satellite data may be orders of magnitude lower than its coverage suggests because of failed retrievals, instrument noise, and error correlations that propagate through the inversion. Analytical solution to the inverse problem provides closed-form characterization of posterior error statistics and information content but requires the construction of the Jacobian matrix that relates emissions to atmospheric concentrations. Building the Jacobian matrix is computationally expensive at high resolution because it involves perturbing each emission element, typically individual grid cells, in the atmospheric transport model used as forward model for the inversion. We propose and analyze two methods, reduced-dimension and reduced-rank, to construct the Jacobian matrix at greatly decreased computational cost while retaining information content. Both methods begin from an initial native-resolution estimate of the Jacobian matrix constructed at no computational cost by assuming that atmospheric concentrations are most sensitive to local emissions. The reduced-dimension method uses this estimate to construct a Jacobian matrix on a multiscale grid that maintains high resolution in areas with high information content and aggregates grid cells elsewhere. The reduced-rank method constructs the Jacobian matrix at native resolution by perturbing the leading patterns of information content given by the initial estimate. We demonstrate both methods in an analytical Bayesian inversion of GOSAT methane satellite data with augmented information content over North America in July 2009. We show that both methods reproduce the results of the native-resolution inversion while achieving a factor of 4 improvement in computational performance. The reduced-dimension method produces an exact solution at lower spatial resolution while the reduced-rank method solves the inversion at native resolution in areas of high information content and defaults to the prior estimate elsewhere.

Hannah Nesser et al.

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Hannah Nesser et al.

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Short summary
Analytic inversions of satellite observations of atmospheric composition can improve emissions estimates and quantify error but are computationally expensive at high resolution. We propose two methods to decrease this cost. In an inversion of GOSAT satellite methane observations, the methods reproduce high-resolution results at a quarter of the cost. The reduced-dimension method creates a multiscale grid. The reduced-rank method solves the inversion where information content is highest.
Analytic inversions of satellite observations of atmospheric composition can improve emissions...
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