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

J. Ray, V. Yadav, A.M. Michalak, B. van Bloemen Waanders and S.A. McKenna


As the world explores avenues for climate change mitigation, it is becoming increasingly important to be able to evaluate the magnitude and spatial distribution of CO2 emissions from fossil fuel burning. Atmospheric observations of CO2 provide one key piece of the puzzle, as these observations reflect emissions at upwind locations. The strong spatial heterogeneity of fossil fuel emissions makes it challenging to disentangle signals coming from different geographic regions, however. This manuscript presents a wavelet-based approach for tackling this problem. The approach leverages the information content of atmospheric observations, as well as the localized nature of fossil fuel emissions.

Figure: Differences in the spatial distribution of biospheric (top) and fossil-fuel (bottom) CO2 fluxes. The biospheric fluxes are stationary, whereas ffCO2 emissions are non-stationary and correlated with human habitation. The fluxes/emissions cover 1–8 June 2002. The biospheric fluxes are obtained from CASA-GFED (http://www. globalfiredata.org/index.html). The post-processing steps to obtain the fluxes as plotted are described in Gourdji et al. (2012). The units of fluxes/emissions are μmol s−1 m−2 of C. The ffCO2 emissions are calculated by spatiotemporal averaging of the Vulcan inventory. Note the different color maps; ffCO2 emissions can assume only non-negative values.


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.

Ray, J., V. Yadav, A.M. Michalak, B. van Bloemen Waanders, S. A. McKenna (2014) “A multiresolution spatial parameterization for the estimation of fossil-fuel carbon dioxide emissions via atmospheric inversions”, Geoscientific Model Development, 7, 1901-1918, doi:10.5194/gmd-7-1901-2014.