A multiresolution spatial parameterization for the estimation of fossil-fuel carbon dioxide emissions via atmospheric inversions

Abstract

Abstract. The characterization of fossil-fuel CO 2 (ffCO 2 ) emissions is paramount to carbon cycle studies, but the use of atmospheric inverse modeling approaches for this purpose has been limited by the highly heterogeneous and nonGaussian spatiotemporal variability of emissions. Here we explore the feasibility of capturing this variability using a low-dimensional parameterization that can be implemented within the context of atmospheric CO 2 inverse problems aimed at constraining regional-scale emissions. We construct a multiresolution (i.e., wavelet-based) spatial parameterization for ffCO 2 emissions using the Vulcan inventory, and examine whether such a parameterization can capture a realistic representation of the expected spatial variability of actual emissions. We then explore whether sub-selecting wavelets using two easily available proxies of human activity (images of lights at night and maps of built-up areas) yields a low-dimensional alternative. We finally implement this low-dimensional parameterization within an idealized inversion, where a sparse reconstruction algorithm, an extension of stagewise orthogonal matching pursuit (StOMP), is used to identify the wavelet coefficients. We find that (i) the spatial variability of fossil-fuel emission can indeed be represented using a low-dimensional wavelet-based parameterization, (ii) that images of lights at night can be used as a proxy for sub-selecting wavelets for such analysis, and (iii) that implementing this parameterization within the described inversion framework makes it possible to quantify fossil-fuel emissions at regional scales if fossil-fuel-only CO 2 observations are available.

Quantification and attribution of urban fossil fuel emissions through atmospheric measurements

“…Previous CO 2 inverse modelling studies were mainly focused on estimating large-scale (grid spacing of 50 to several hundred kilometres) weekly to monthly mean ecosystem fluxes (Basu et al, 2016;Broquet et al, 2013;He et al, 2017;Liu and Bowman, 2016;Meesters et al, 2012;Ray et al, 2014;Rödenbeck et al, 2009;Schuh et al, 2010;Tolk et al, 2011). The observations used in these studies capture biospheric signals from a large domain dominated by daily to weekly variations.…”

“…It has been applied successfully to constrain biogenic fluxes of CO 2 by combining continental monitoring networks (like the Integrated Carbon Observation System) with regional to global transport models, leading to flux estimates at large spatiotemporal scales (0.5 to 10° and weeks to seasons) (e.g. (Basu et al, 2016;Broquet et al, 2013;Liu and Bowman, 2016;Meesters et al, 2012;Peters et al, 2007;Peters et al, 2010;Ray et al, 2014;Rödenbeck et al, 2009;Tolk et al, 2011;Van der Laan-Luijkx et al, 2015;Van der Laan-Luijkx et al, 2017)). However, most of the anthropogenic CO 2 emissions come from cities and therefore monitoring should be done at much smaller scales.…”

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.…”

“…Another method, which does not require the specification of regions in advance, instead uses empirical orthogonal functions (Hotelling, 1933;Lorenz, 1956;Pearson, 1901) to represent the fluxes, which again allows the covariance to be made diagonal (Zhuravlev et al, 2011(Zhuravlev et al, , 2013. Ray et al (2013) presents another method for reducing the memory and computational requirements for an inversion: use a wavelet transform (Daubechies, 1988;Mallat, 1989;Torrence & Compo, 1998) to decorrelate the fluxes, thereby changing to a basis where the covariance is again diagonal (Ray et al, 2014(Ray et al, , 2015. A contrasting method, Yadav and Michalak (2013), assumes that the dependencies of the prior error correlations on time and space were separable and showed that this assumption allows a reduction in the memory and computational requirements of the inversion (Gourdji et al, 2012;Hu et al, 2019).…”

A statistical approach for isolating fossil fuel emissions in atmospheric inverse problems

“…In Ray et al . [], the authors developed a parameterization of FF emission fields based on wavelets, and in Ray et al . [] they use a sparse reconstruction method to estimate FF emissions using their spatial model in a synthetic data test case.…”