# Constraining surface emissions of air pollutants using inverse modeling:
method intercomparison and a new two-step two-scale regularization
approach

## Task 3c, principal investigator: CEREA/CLIME.

When constraining surface emissions of air pollutants using
inverse modeling one often encounters spurious corrections to the
inventory at places where emissions and observations are co-located,
referred to as the co-localization problem.
Several approaches have been used to deal with this problem:
coarsening the spatial resolution of emissions; adding spatial correlations
to the covariance matrices; adding constraints on the spatial derivatives
into the functional being minimized; and multiplying the emission error covariance matrix by
weighting factors.
Intercomparison of methods for a carbon monoxide inversion over a city
shows that even though all methods diminish the co-localization problem
and produce similar general patterns, detailed information can greatly change according to
the method used ranging from smooth, isotropic and short range modifications to not so smooth,
non-isotropic and long range modifications. Poisson (non-Gaussian) and Gaussian
assumptions both show these patterns, but for the Poisson case the emissions are naturally
restricted to be positive and changes are given by means of multiplicative correction
factors, producing results closer to the true
nature of emission errors. Finally, we have proposed and tested a new two-step,
two-scale, fully Bayesian approach that deals with the
co-localization problem and can be implemented for any prior density distribution.

Time average difference between the a priori (official) carbon monoxide
inventory and the optimized inventories after assimilating real
observations using Gaussian estimates: grid-cell values and smoothed
contours. (a) Using no
modifications. (b) Using correlations with a radius of influence
r=2.5 cells. (c) Adding a constraint on the derivative in the
functional. (d) Using weighting factors over ** B **. (e) Performing a two
step multiscale inversion on a coarse grid of 3X3 for one of the
possible grid positions and (f) the same as (e) after averaging the nine possible
placements of the 3X3 grid. Note that positive values represent a decrease over the background
emissions and negative values represent an increase over the
background emissions. See the text for details. Units are in micro grams
per square meter per second.