Comparison of non-local metrics towards the assimilation of pollutant plumes without thedouble penalty
Authors: Vanderbecken Pierre , Farchi Alban , Bocquet Marc , Dumont le Brazidec Joffrey , Roustan Yelva , Broquet Grégoire , Potier Elise 
Published: March 2022

&lt;p&gt;&lt;span&gt;In the future, spectral image monitoring instruments from ESA missions will&lt;/span&gt;&lt;br&gt;&lt;span&gt;provide&lt;/span&gt; &lt;span&gt;spatial&lt;/span&gt; &lt;span&gt;observations&lt;/span&gt; &lt;span&gt;of&lt;/span&gt; &lt;span&gt;pollutants&lt;/span&gt; &lt;span&gt;(CO&lt;/span&gt;&lt;span&gt;2&lt;/span&gt;&lt;span&gt;,&lt;/span&gt; &lt;span&gt;CH&lt;/span&gt;&lt;span&gt;4&lt;/span&gt;&lt;span&gt;,&lt;/span&gt; &lt;span&gt;...).&lt;/span&gt; &lt;span&gt;Like&lt;/span&gt; &lt;span&gt;TROPOMI,&lt;/span&gt;&lt;br&gt;&lt;span&gt;these&lt;/span&gt; &lt;span&gt;instruments&lt;/span&gt; &lt;span&gt;have&lt;/span&gt; &lt;span&gt;a&lt;/span&gt; &lt;span&gt;large&lt;/span&gt; &lt;span&gt;swath&lt;/span&gt; &lt;span&gt;allowing&lt;/span&gt; &lt;span&gt;the&lt;/span&gt; &lt;span&gt;monitoring&lt;/span&gt; &lt;span&gt;of&lt;/span&gt; &lt;span&gt;city&lt;/span&gt; &lt;span&gt;plumes.&lt;/span&gt;&lt;br&gt;&lt;span&gt;Currently,&lt;/span&gt; &lt;span&gt;the&lt;/span&gt; &lt;span&gt;resulting&lt;/span&gt; &lt;span&gt;plume&lt;/span&gt; &lt;span&gt;images&lt;/span&gt; &lt;span&gt;are&lt;/span&gt; &lt;span&gt;assimilated&lt;/span&gt; &lt;span&gt;(i)&lt;/span&gt; &lt;span&gt;either&lt;/span&gt; &lt;span&gt;with&lt;/span&gt; &lt;span&gt;quick&lt;/span&gt; &lt;span&gt;in-&lt;/span&gt;&lt;br&gt;&lt;span&gt;verse&lt;/span&gt; &lt;span&gt;methods&lt;/span&gt; &lt;span&gt;relying&lt;/span&gt; &lt;span&gt;on&lt;/span&gt; &lt;span&gt;simplifying&lt;/span&gt; &lt;span&gt;hypotheses&lt;/span&gt; &lt;span&gt;for&lt;/span&gt; &lt;span&gt;the&lt;/span&gt; &lt;span&gt;transport&lt;/span&gt; &lt;span&gt;and&lt;/span&gt; &lt;span&gt;fate&lt;/span&gt; &lt;span&gt;of&lt;/span&gt;&lt;br&gt;&lt;span&gt;the pollutants, or (ii) with rigorous inverse methods using observation operators&lt;/span&gt;&lt;br&gt;&lt;span&gt;and local metrics based on pixel-wise comparisons.&lt;/span&gt; &lt;span&gt;Local metrics are, however,&lt;/span&gt;&lt;br&gt;&lt;span&gt;prone&lt;/span&gt; &lt;span&gt;to&lt;/span&gt; &lt;span&gt;heavily&lt;/span&gt; &lt;span&gt;penalyse&lt;/span&gt; &lt;span&gt;small&lt;/span&gt; &lt;span&gt;offsets&lt;/span&gt; &lt;span&gt;between&lt;/span&gt; &lt;span&gt;images&lt;/span&gt; &lt;span&gt;which&lt;/span&gt; &lt;span&gt;is&lt;/span&gt; &lt;span&gt;known&lt;/span&gt; &lt;span&gt;as&lt;/span&gt; &lt;span&gt;the&lt;/span&gt;&lt;br&gt;&lt;span&gt;double penalty issue.&lt;/span&gt; &lt;span&gt;This makes local metrics not always well suited for plume&lt;/span&gt;&lt;br&gt;&lt;span&gt;comparison within an emission inversion framework.&lt;/span&gt;&lt;br&gt;&lt;span&gt;Therefore, we propose to use non-local metrics inspired by optimal transport&lt;/span&gt;&lt;br&gt;&lt;span&gt;and the Wasserstein distance.&lt;/span&gt; &lt;span&gt;Such metrics have the advantage to treat plumes&lt;/span&gt;&lt;br&gt;&lt;span&gt;as&lt;/span&gt; &lt;span&gt;coherent&lt;/span&gt; &lt;span&gt;objects&lt;/span&gt; &lt;span&gt;and&lt;/span&gt; &lt;span&gt;hence&lt;/span&gt; &lt;span&gt;avoid&lt;/span&gt; &lt;span&gt;the&lt;/span&gt; &lt;span&gt;double&lt;/span&gt; &lt;span&gt;penalty&lt;/span&gt; &lt;span&gt;issue.&lt;/span&gt; &lt;span&gt;Furthermore,&lt;/span&gt;&lt;br&gt;&lt;span&gt;these new metrics developed here are split into several terms that can be related&lt;/span&gt;&lt;br&gt;&lt;span&gt;to&lt;/span&gt; &lt;span&gt;errors&lt;/span&gt; &lt;span&gt;in&lt;/span&gt; &lt;span&gt;source&lt;/span&gt; &lt;span&gt;location,&lt;/span&gt; &lt;span&gt;wind&lt;/span&gt; &lt;span&gt;field,&lt;/span&gt; &lt;span&gt;emission&lt;/span&gt; &lt;span&gt;rate,&lt;/span&gt; &lt;span&gt;and&lt;/span&gt; &lt;span&gt;whose&lt;/span&gt; &lt;span&gt;respective&lt;/span&gt;&lt;br&gt;&lt;span&gt;contributions to the global metric can be evaluated.&lt;/span&gt;&lt;br&gt;&lt;span&gt;A sensitivity study towards these error sources is made for each metric.&lt;/span&gt; &lt;span&gt;To&lt;/span&gt;&lt;br&gt;&lt;span&gt;this end, a large catalogue of realistic tracer plumes is built.&lt;/span&gt; &lt;span&gt;The ultimate goal&lt;/span&gt;&lt;br&gt;&lt;span&gt;here&lt;/span&gt; &lt;span&gt;is&lt;/span&gt; &lt;span&gt;to&lt;/span&gt; &lt;span&gt;discuss&lt;/span&gt; &lt;span&gt;which&lt;/span&gt; &lt;span&gt;metrics&lt;/span&gt; &lt;span&gt;is&lt;/span&gt; &lt;span&gt;the&lt;/span&gt; &lt;span&gt;best&lt;/span&gt; &lt;span&gt;suited&lt;/span&gt; &lt;span&gt;for&lt;/span&gt; &lt;span&gt;updating&lt;/span&gt; &lt;span&gt;anthropogenic&lt;/span&gt;&lt;br&gt;&lt;span&gt;emission inventories.&lt;/span&gt;&lt;/p&gt;