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

Abstract

Abstract. Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 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 CO 2 (ffCO 2 ) 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 multiresolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 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.

Atmospheric inverse modeling via sparse reconstruction

“…Martinez-Camara et al (2013) used a sparse reconstruction approach to estimate emissions of radioactive substances for the Fukushima accident, and Ray et al (2015) analyzed fossil fuel carbon dioxide emissions in an idealized, synthetic data setup.…”

Atmospheric Inverse Modeling via Sparse Reconstruction

“…A greater value forces the solution to stay close to the a priori solution x a , while a small value results in a better model-data fit. A number of methods are available to automatically choose a balancing regularization parameter (see, e.g., Reichel and Rodriguez, 2012). We use Morozov's discrepancy principle (see Eq.…”

Development of a Mesoscale Inversion System for Estimating Continental‐Scale CO2 Fluxes

“…While the methods of Ray et al (2013Ray et al ( , 2014Ray et al ( , 2015 are a promising avenue of investigation, those papers apply the method to anthropogenic carbon dioxide fluxes and do not suggest how to apply wavelet methods to the existing body of research on biogenic flux error correlations (e.g., Chevallier et al, 2006Chevallier et al, , 2012Hilton et al, 2013;Kountouris et al, 2015). Given the result of Ray et al (2013Ray et al ( , 2015) that the assumed correlation structure is more important to the quality of the final result than even the prior mean estimate, this study opted to use spectral methods (Dietrich & Newsam, 1993;Nowak et al, 2003) to represent the spatial correlations, which are much simpler to use with a specified correlation function (section 3.1), and the methods of Yadav and Michalak (2013) to produce the full spatio-temporal error correlation matrix.…”

“…While the methods of Ray et al. (2013, 2014, 2015) are a promising avenue of investigation, those papers apply the method to anthropogenic carbon dioxide fluxes and do not suggest how to apply wavelet methods to the existing body of research on biogenic flux error correlations (e.g., Chevallier et al., 2006, 2012; Hilton et al., 2013; Kountouris et al., 2015). Given the result of Ray et al.…”