A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

Ray, J.; Lee, J.; Yadav, V.; Lefantzi, S.; Michalak, A. M.; van Bloemen Waanders, B.

doi:10.5194/gmd-8-1259-2015

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

Journal Article · Wed Apr 29 00:00:00 EDT 2015 · Geoscientific Model Development (Online)

DOI:https://doi.org/10.5194/gmd-8-1259-2015· OSTI ID:1197811

Ray, J.; Lee, J.; Yadav, V.; Lefantzi, S.; Michalak, A. M.; van Bloemen Waanders, B.

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO₂ flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) and fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO₂ (ffCO₂) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO₂ emissions and synthetic observations of ffCO₂ concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.

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Research Organization:: Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States); Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories, Albuquerque, NM (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1197811

Alternate ID(s):: OSTI ID: 1214233
OSTI ID: 1182960

Report Number(s):: SAND--2014-15988J

Journal Information:: Geoscientific Model Development (Online), Journal Name: Geoscientific Model Development (Online) Journal Issue: 4 Vol. 8; ISSN 1991-9603

Publisher:: Copernicus Publications, EGUCopyright Statement

Country of Publication:: Germany

Language:: English

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