In this manuscript, the authors report on the first application of COBRA, a new algorithm to the retrieval of SO₂ columns from measurements of the TROPOMI instrument. The algorithm is briefly explained and results for a full year of data are compared to columns from existing algorithms for SO₂ retrievals (DOAS, PCA). The performance of the new algorithm is further demonstrated by a comparison to modelled SO₂ fields (CAMS regional) and MAX-DOAS measurements in two locations. Long-term averages of the new SO₂ product are shown together with existing SO₂ source lists and emission estimates based on the new data are compared to those based on the operational product. Finally, an example is shown for a multi-source emission estimate of a weak source.

The topic of the manuscript fits into the scope of ACP although, in my opinion, it would have been a better match for AMT. The article is clearly structured and well written, the algorithm described and the nice results shown a clear improvement over existing data and certainly worth reporting, and overall, I have only minor comments and suggestions. The only general point I would like to make is, that this being the first report of the method, a more detailed discussion of the implementation and the tests performed would be appropriate.

Page 3, line 21: Not sure, if TROPOMI is the first mission with a tropospheric focus – I guess instruments like OMI, MOPITT or TES could also be seen as having this focus.

Page 6, line 18: Maybe that is obvious, but can you please explain a bit more, what the difference is between the uncertainty in the SO₂ free spectrum and the measurement noise? Isn’t in your method measurement noise one of the contributions to ε_bg?

Page 7, line 5: Can you please elaborate on how equation 6 follows from equation 5?

Page 7, line 25: How is wavelength calibration being dealt with in your method? Is there any analogue to shift and squeeze or are you assuming that wavelength calibration and stability of the spectra is so good that this is not needed?

Page 8, line 17: As this is the first report of an application of COBRA on UV/vis data, it would be good to add some discussion on the results of your tests and justification for the choice of parameters.

Page 9, line 1: The need for SO₂ free spectra in each orbit, row, and latitude segment can be an important limitation of this method in the case of volcanic SO₂ plumes reaching the stratosphere. Please add some discussion on this point here, including some numbers on how many measurements you had to skip in your data set because of this constraint.

Page 10, line 13: Was the background correction applied by row? If so, why do we see the low-frequency variations in the results? If not, why not?

Figure 2: To make this a bit more quantitative, it would be good to add scatter plots between the different existing products and the new COBRA data.

Page 15, line 16: is likely not reflecting => is likely reflecting

Figure 5: It would be interesting to add similar figures for the operational DOAS product, maybe in the supplement

Page 19, line 1: I could not find any link or other means to access this file

Figure 7: What does the size of the markers in the left panel stand for?

Figure 7: On which of the two emission estimates is the size of the marker in the right panel based on?

Page 28, line 14: “fairly consistent” – this is a vague formulation! Why not check if the values agree within their reported uncertainties? Why not add error bars to the left panel of Figure 7? It is an interesting piece of information for users of the existing emission values whether they are still valid (within their uncertainties) or if numbers will change with the new product. If the latter is the case, this would warrant some discussion.

Page 28, line 18: For some of the emission estimates, COBRA has smaller ratios. Have checked why?

Page 29, line 17: I agree that this indicates that COBRA is good in exploiting the gain in spatial resolution provided by TROPOMI; if it is optimal in doing so I wouldn’t know.

This manuscript describes a new optimal estimation algorithm for UV SO2 which puts all the variability in the covariance matrix. It has been developed for use with TROPOMI data and shows reduced variability in the residuals as well as lower limits of detection. These improvements enable changes in source strength to be more readily observed and for weaker sources to be monitored. It is good work which should be published after minor corrections.

I agree with all Referee 1’s comments and think they should be made.

It would be good if you can address the comment about ACP vs AMT. One way of making it more ‘ACP’ is to add a bit more on the interpretation of the new estimates of SO2 emissions and what the implications are for model studies using existing inventories. I was surprised to see that lower detection limits did not lead to more SO2 emissions being estimated overall. Does that mean even smaller sources are unimportant? Such a discussion would also strengthen the broader conclusions.

Two other comments:

1. How does the type of land surface, and particularly its spectral signature, affect the retrieval? You mention particular land surfaces in respect to a couple of examples of less good agreement. Is that related to a retrieval issue or to possible emissions from that land surface? Similarly for aerosol loading.
2. Could the potential error sources / limiting factors be mentioned as well as the advantages? Is this the perfect algorithm which is limited by measurement characteristics?

Minor comments

Page 29, line 19 – delete ‘actually’

Page 30, line 11 – ‘spatial distributions: the emissions’