Comparing mass balance and adjoint methods for inverse modeling of nitrogen dioxide columns for global nitrogen oxide emissions

Abstract

Satellite observations offer information applicable to top‐down constraints on emission inventories through inverse modeling. Here we compare two methods of inverse modeling for emissions of nitrogen oxides (NOx) from nitrogen dioxide (NO2) columns using the GEOS‐Chem chemical transport model and its adjoint. We treat the adjoint‐based 4D‐Var modeling approach for estimating top‐down emissions as a benchmark against which to evaluate variations on the mass balance method. We use synthetic NO2 columns generated from known NOx emissions to serve as “truth.” We find that error in mass balance inversions can be reduced by up to a factor of 2 with an iterative process that uses finite difference calculations of the local sensitivity of NO2 columns to a change in emissions. In a simplified experiment to recover local emission perturbations, horizontal smearing effects due to NOx transport are better resolved by the adjoint approach than by mass balance. For more complex emission changes, or at finer resolution, the iterative finite difference mass balance and adjoint methods produce similar global top‐down inventories when inverting hourly synthetic observations, both reducing the a priori error by factors of 3–4. Inversions of simulated satellite observations from low Earth and geostationary orbits also indicate that both the mass balance and adjoint inversions produce similar results, reducing a priori error by a factor of 3. As the iterative finite difference mass balance method provides similar accuracy as the adjoint method, it offers the prospect of accurately estimating top‐down NOx emissions using models that do not have an adjoint.

Comparison and evaluation of anthropogenic emissions of SO<sub>2</sub> and NO<sub><i>x</i></sub> over China

“…The smearing length is around 50 km over China in summer (assuming wind speed 5 m s −1 , NO 2 lifetime 3 h), comparable to the model grid size, implying weak effects upon the inversion of horizontal mass transport between grids. Compared to the basic mass-balance method described in Martin et al (2003), the FDMB method reduces the errors from nonlinearity of NO x -OH-O 3 chemistry (Gu et al, 2016;Cooper et al, 2017). A unitless scaling factor β was introduced to represent the sensitivity of fractional modeled NO 2 columns to the fractional anthropogenic emission changes for each grid.…”

“…Furthermore, daily data of SO 2 and NO 2 vertical column density were developed after allocating the OMI pixels to model grids (0.667 • × 0.5 • ) based on area weights. Top-down NO x emissions were developed following the finite difference mass balance (FDMB) methodology (Lamsal et al, 2011;Cooper et al, 2017). We used the summer data to develop the top-down emissions because of the stronger relationship between local emissions and grid columns.…”

Comparison and evaluation of anthropogenic emissions of SO<sub>2</sub> and NO<sub>x over China

“…We apply 15% perturbation to emissions, simulate the NO 2 column changes, and calculate β following Eq. (1) (Lamsal et al, 2011;Cooper et al, 2017).…”

“…In this work, top-down emission inventories are developed following the Finite Difference Mass Balance (FDMB) methodology (Lamsal et al, 2011;Cooper et al, 2017). We use the summer data to develop the top-down emissions because of the stronger relationship between local emissions and grid columns.…”

“…Following Cooper et al (2017), we limit β within 0.1-10, to avoid biases in regions with negligible low anthropogenic emissions or columns. The absolute error in the retrieved NO 2 columns is estimated at 1 × 10 15 molecules/cm 2 (Martin et al, 2003 (expressed in Tg-NO 2 hereafter); 1% and 16% less than MIX, respectively.…”