Leguijt et al. present a comprehensive analysis of carbon monoxide emissions from iron and steel plants over Europe. They performed both analytical inversions and cross-sectoral flux estimates using TROPOMI observations, which are further compared against the facility-level reports. They have shown reasonably good agreement in the flux estimates across different approaches, considering error bars. They also investigated if TROPOMI could detect changes in emissions between years.

Overall, the manuscript is well written and most of the results are straightforward. The authors did a great job of providing background about the iron and steel industry and the different approaches used. I enjoy reading this paper and thereby recommend its publication after providing clarifications for a few minor comments:

P1L14 –regarding year-to-year variability: what about temporal variability across different months or overpasses? Can the authors resolve or constrain the emissions at a finer temporal resolution beyond one year? Also, see below comments relating to P8L186-188.

P3L87-88: What prevents the authors from extending the flux estimates for 2020 for all iron and steel production? Lack of observed data or reported data from E-PRTR? Because only 4 of the total plants see substantial changes in emissions between years?

P4L96-100: I may miss this, but does the E-PRTR provide uncertainty estimates to either their measurement or calculation as well, e.g., in Fig. 5?

P6: When inverting emissions using WRF, would there be any nearby emission sources apart from the individual iron and steel plants? How would the authors deal with those non-iron and steel emission sources, e.g., as in the background? In other words, were most of the plants relatively isolated?

P6L123: How have injection height and plume height been considered in WRF simulations? I suppose those are taken care of by the “sector-specific vertical profiles”?

P7:163- 165: The choice of uncertainties seems a bit arbitrary (e.g., 20% for prior, 50% for transport? etc), even though the authors later performed a set of sensitivity tests of the impact of uncertainties on flux estimates. I would suggest at least providing a few more references or reasoning to those numbers.

P7L174: It seems that the spatial mismatches between modeled and observed plumes can likely be minimized by a plume-rotation algorithm, while the authors rely on an ensemble of model plumes (Fig.2 right) for “best” alignment. What if none of the ensembles match the observed plumes perfectly (e.g., a near-field bias in wind direction, esp when the plume is curving)?

P8L186-188: I am a bit confused by the aggregation of inversion results here. For example, how many days of TROPOMI have been combined to optimize an annual flux rate? Were the authors able to resolve for a posteriori that is spatially resolved (e.g., posterior flux rate per emission grid) or just one number per plant per year? Were there any possible sampling biases across seasons given cloud interference? I would suggest the authors provide more info on the number of TROPOMI overpasses being examined and whether those overpasses are representative of an annual average (if they have not done that).

These lines also relate to the other comment – could the authors try to resolve the emissions from individual plants at a finer resolution beyond just one year?

P9L196-197: Interesting - I was especially intrigued by the co-assimilation of background values with the fluxes! Could the authors provide more info or reference on such inversion construction? For example, any error correlation between the background (mean + gradient) and the fluxes? How much adjustment was made to background vs. plume signals using TROPOMI observations? Relating to the 10% error in background assumed on L163 – what would be prior errors for background mean and background gradients? Providing some supplementary details on the prior error and the Jacobian, particularly for the background optimization would be very helpful for readers.

P12L263-268: Glad that the authors also reported the averaging kernel (Eq.5) of their inversion. Very minor point - I would probably differentiate the word choices since TROPOMI also has its own “averaging kernel” from the retrieval.

Sect. 3.4 – the 2020 analysis: I am slightly confused by these comparisons and their implications. What drives the smaller year-to-year changes in TROPOMI-constraint emissions compared to E-PRTR reports? Were the authors implying that the wind directional biases may be the driver? Does TROPOMI sampling differ greatly between years as well?

P18L340: A more general, clarification question – Do the authors “trust” more of the report from E-PRTR or the inversion results from TROPOMI (yet, E-PRTR and TNO inventory are used as priors)? Were E-PRTR reports in turn used as a dataset to validate the TROPOMI-based inversion (e.g., many figures in the results)? Or both the reports and TROPOMI-based posteriors are not treated as “truth”?