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

Geoscientific Model Development (2014) 7(5) 1901-1918
DOI: 10.5194/gmd-7-1901-2014
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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 CO2inverse problems aimed at constraining regional-scale emissions. We construct a multiresolution (i.e., wavelet-based) spatial parameterization for ffCO2emissions 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 CO2observations are available.

Figures

  • Figure 1. 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. N te the different color maps; ffCO2 emissions can as ume only non-negative values.
  • Figure 1. Differences in the spatial distribution of biospheric (top) and fossil-fuel (bottom) CO2 fluxes. The biospheric fluxes are sta ionary, whereas ffCO2 emissions are non-stationary and correlated with human habitation. The fluxes/emissions cover June 1 - June 8, 2002. The biospheric fluxes are obtained
  • Figure 2. Sparsity of representation at scale s = 4 (left) and s = 6 (right) for a combination of wavelet families and orders. We find that Haar provide the sparsest representation.
  • Figure 4. Variation of sparsity, reconstruction error , and the Pearson correlation between the true and reconstructed fV, i.e., ρ(fV, fV ′ ) as a function of α.
  • Figure 3. We plot the average value of the non-zero coefficients (solid lines) and their standard deviation (dashed line), at different scales s, when fV is subjected to wavelet transforms using Haar, Daubechies 4 and 6, and Symlet 4 and 6 wavelets. We find that while Haar may provide the sparsest representation (Fig. 2), the non-zero values tend to be large and distinct.
  • Figure 5. Annually averaged Vulcan emissions fV are modeled using Haar wavelets on scales 1, 2, 4, 5, and 6. The figure at the top (left) plots fV, and the rest its decomposition across wavelet scales. Note that we have displayed only the relevant part of the dyadic 2M ×2M grid on which wavelets are described.
  • Figure 6. Top row: maps of nightlight radiances (left) and BUA percentage (right), for the US. Middle row: the sparsity of representation, the correlation between X and fV and the normalized error f between the Vulcan emissions fV and the sparsified form obtained by projecting it on X. These values are plotted for nightlights (left) and the BUA maps (right). Bottom row: plots of (fpr − fV) obtained from nightlights (left) and BUA maps (right).
  • Figure 7. CDF of emissions inR, before and after the imposition of non-negativity, as described in Sect. 4. We see that the CDF of the emissions without non-negativity imposed contains a few grid cells with negative fluxes; further, the magnitude of the negative emissions is small. Thus the spatial parameterization, with sparse reconstruction, provides a good approximation of the final, non-negative emissions.

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APA

Ray, J., Yadav, V., Michalak, A. M., Van Bloemen Waanders, B., & McKenna, S. A. (2014). A multiresolution spatial parameterization for the estimation of fossil-fuel carbon dioxide emissions via atmospheric inversions. Geoscientific Model Development, 7(5), 1901–1918. https://doi.org/10.5194/gmd-7-1901-2014

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