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

Abstract. The characterization of fossil-fuel CO₂ (ffCO₂) 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 non-Gaussian 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 CO₂ inverse problems aimed at constraining regional-scale emissions. We construct a multiresolution (i.e., wavelet-based) spatial parameterization for ffCO₂ 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 CO₂ observations are available.