“…The target vector x includes the variables to be optimized by the inversion; it includes the main variables of interest, such as the surface fluxes, but also variables relating to atmospheric chemical sources and sinks, background concentrations in the case of limited-area transport models, model parameters, etc., which are required to make the inversion physically consistent. The observation operator H mainly includes the computation of atmospheric transport and chemistry (if relevant) by numerical Eulerian global circulation models (e.g., LMDZ, Chevallier et al 2010;TM5, Houweling et al 2014;GEOS-Chem, van der Laan-Luijkx et al 2017;Liu et al 2015;Palmer et al 2019;Feng et al 2017;NICAM, Niwa et al 2017), regional Eulerian chemistry-transport models (e.g., CHIMERE, Broquet et al 2011;Fortems-Cheiney et al 2019;WRF-CHEM, Zheng et al 2018;COSMO-GHG, Mizzi et al 2016;LOTOS-EUROS, Curier et al 2012) or Lagrangian Particle Dispersion models (e.g., FLEXPART, Thompson and Stohl 2014;STILT, Bagley et al 2017;Brioude et al 2013;Trusilova et al 2010). It also includes pre-and post-processing operations required to project the target vector to a format compatible with the model input and the model outputs to the observation vector; these operations can be the applications of e.g., averaging kernels in the case of satellite operations, or interpolation of the target vector to higher resolution model inputs.…”