Comparison of non-local metrics towards the assimilation of pollutant plumes without thedouble penalty

In the future, spectral image monitoring instruments from ESA missions will
provide spatial observations of pollutants (CO2, CH4, ...). Like TROPOMI,
these instruments have a large swath allowing the monitoring of city plumes.
Currently, the resulting plume images are assimilated (i) either with quick in-
verse methods relying on simplifying hypotheses for the transport and fate of
the pollutants, or (ii) with rigorous inverse methods using observation operators
and local metrics based on pixel-wise comparisons. Local metrics are, however,
prone to heavily penalyse small offsets between images which is known as the
double penalty issue. This makes local metrics not always well suited for plume
comparison within an emission inversion framework.
Therefore, we propose to use non-local metrics inspired by optimal transport
and the Wasserstein distance. Such metrics have the advantage to treat plumes
as coherent objects and hence avoid the double penalty issue. Furthermore,
these new metrics developed here are split into several terms that can be related
to errors in source location, wind field, emission rate, and whose respective
contributions to the global metric can be evaluated.
A sensitivity study towards these error sources is made for each metric. To
this end, a large catalogue of realistic tracer plumes is built. The ultimate goal
here is to discuss which metrics is the best suited for updating anthropogenic
emission inventories.