General Comments:

The study “Quantifying particulate matter optical properties and flow rate in industrial stack plumes from PRISMA hyperspectral imager” by Calassou et al. addresses the issue of industrial stacks plumes retrieval by means of PRISMA satellite data. The topic is scientifically relevant and the paper is well structured and written. I recommend the manuscript for publication after addressing the following points and clarifications.

• Is it the first time that PRISMA data have been used for this type of research? If yes it would be valuable to highlight that, if not you should provide references in literature.
• Have you checked if other studies on the same test sites have been conducted in literature?
• Have you considered the issue of clouds influence? Are the images you’ve taken into account (both PRISMA and L2/MSI) free of clouds?
• Have you considered the possibility to provide an independent validation of the presented results? Maybe with existent satellite products/derived satellite products/other ground truth sources; in line 354-357 you mention that the validation with in situ measurements remains virtually impossible. Have you investigated if there are satellite products that provide the same parameters you estimated?

Specific Comments:

• Line 100: do you mean only detection or also retrieval?
• 1 -> Is there a reference in literature?
• 2 -> Is there a reference in literature?
• Line 128: Is there a reference in literature to the COMANCHE software?
• 3 -> Is there a reference in literature? -> Could you clarify why there is no direct component of the solar irradiance related to δ?
• Line 165: “the uncertainties due to the water vapor concentration are empirically fixed to 10%” -> Is there a reference in literature for the uncertainty due to the water vapor concentration?
• Line 166: “the uncertainties of the background aerosol visibility is set to 5 km” -> -> Is there a reference in literature for the uncertainty of the background aerosol visibility?
• Line 227: LM acronym has not been defined previously.
• Line 236: “the combined plume mask based on DOF and iteration number (Figure 5c)” -> Could you clarify how DOF and iteration number are combined to get the plume mask (ex.: “pixels corresponding to DOF threshold of ... and?/or? pixels corresponding to number iteration of ... are taken into account...”)
• Caption of Figure 5: OEM acronym has not been defined previously.
• Line 238: “The initial value of AOT is set to 0.5 with an uncertainty of 1.0. The retrieved AOT map (Figure 6a) reflects[...]” -> Could you mention/briefly recall the process to retrieve the parameters in Figure 6 (how to obtain Figure 6 from Figure 5 basically). Is the process mentioned in line 192-193 (“The aerosol optical properties are simulated using the MOPSMAP T-matrix algorithm (Gasteiger and Wiegner, 2018)”) ?
• Line 256: “The median radius of the accumulation mode is on average equal to 0.11 ± 0.02 μm in the pixels present in the plume mask.” -> The plume mask (as well as the DOF and Number of iterations) have been shown only for case 1 (Gas flaring, Fig. 5), I suppose the procedure is exactly the same for all the sites, is that correct?
• Line 262-263: “The partial detection can be due to a poor reconstruction of the vegetated soils[...]” -> May be the partial detection caused also by the fact that the plume may be less thick/more dispersed in that areas?
• Line 263-264: “Further downstream, an artifact due to the sunglint on a water retention bassin can observed” -> Where the artifact/water retention bassin is located in the map?
• Figure 8: May the point B be a false positive?
• Line 290-291: “The relative error on the surface reflectance reaches 60% at 550nm for this particular cases” -> Could you specify which case? In the previous sentence the coal-fired plant has been mentioned while from Figure 10 it seems that the flaring site exhibits a relative error of 60% at 550nm. Could you clarify that and check the correspondence between text and Figure 10 from 285 to 291 lines?
• Line 292: “The error associated to the surface reflectance estimation and to the aerosol properties retrieval process”-> Could you provide a reference in the text on where in the manuscript the error associated with the aerosol properties retrieval process is computed? Is the 3.3 section?
• Line 330: “There are several limitations (low revisit time, cloud cover, ...)”-> Could you specify limitations of the “applicability of the proposed framework to monitor the air quality around the facilities”

Technical Comments:

• Line 26: stationnary -> stationary
• Line 30: developped -> developed
• Line 47: impletation -> implementation
• Line 50: betwen -> between
• Line 116: space after the point “[...] m²).For a flat, [...]”
• Line 165: visibily -> visibility?
• Line 271: “The radius is equal to 0.20 μm” -> Do you mean the radius of the point B? Could you specify?
• Line 290: “dractic”->drastic
• Line 302: “contribution contribution”-> contribution
• Line 311:” dominated by the error on large error”-> Could you review this part of the sentence?

The reviewed manuscript focuses on the development of an inversion framework using spaceborne PRISMA hyperspectral imager to estimate particulate matter emissions from industrial stacks. It addresses the challenges associated with aerosol plume retrieval over continental surfaces, considering, e.g. surface interference and particle characteristics. The study presents a methodology that incorporates surface reflectance estimation, radiative simulations, and an optimal estimation framework to retrieve aerosol properties and emission flow rates. The reliable retrieval of aerosol properties is of vital importance for correct estimate of the ecological footprint of a given factory or country as well as for the public health, so any effort improving our knowledge is laudable, and I think that the manuscript is topical. It is well organized and the presentation is clear. There are few things in the methodological part, though, which I’d like to see improved or clarified, so I’ve selected “major revision”, but the changes I propose below are easy to implement.

General comments:

• The authors did a good job by presenting their model and by providing the optimal estimation formalism. But, the method lacks such an important validation step as a self-consistency study, which would both assure the reliability of the proposed method and estimate its uncertainty. Let me explain: if one has a forward model and the inversion algorithm for some instrument, one should be able to take the initial state of the atmosphere (some synthetic image or a retrieved one, with some prescribed aerosol size distribution), name it a “reference”, run the forward simulation and obtain the “would be” multispectral image. Then, this information should be fed to an inversion algorithm, which should be run for several times, each time starting with a different guess state. The retrieved aerosol properties should be compared with the reference ones and the biases and root-mean-square values should be estimated. Presumably, a purely theoretical noise-free retrieval will give the result close to the reference. This will tell us about the reliability of the method. In the next step, the simulated radiances should be modified using some realistic noise and the retrieval should be repeated. The biases and r.m.s. values got at this step would tell us about the real uncertainty of the data presented in the manuscript and obtained from real observations using the suggested method. I saw the discussion of the uncertainties in Section 3.3, but as far as I understand, this does not clarify the self-consistency issues outlined above.
• Another validation step I did not find in the manuscript is the comparison with existing observations. All three test cases happened in the period when the CALIOP/CALIPSO lidar was still operable, and the corresponding aerosol information retrieved from CALIOP observations should be available. Another space-borne lidar observing the Earth in the same period was ALADIN/Aeolus, but the comparison of PRISMA retrievals with Aeolus L2A optical data might be difficult due to its long averaging along the track (in this case, the apples-to-apples comparison would require averaging the PRISMA data along the same 87km length). I understand that a good overlapping for a given date is not guaranteed, but I believe that one can pick up another day, which would give the same image as in the figures provided in the manuscript, and at the same time the image would be overlapped with the CALIPSO track. Such a comparison would be a good validation both for the method and for the measurement itself. I do not suggest to redo the whole study, but at least one collocation and one comparison plot for one site are needed.

Minor comments and technical corrections

The title mentions only the PRISMA hyperspectral imager whereas the authors use a synergy of PRISMA and S2/MSI multi-spectral observations, and it looks like the results shown in the article would not be achievable using only the PRISMA instrument. Wouldn’t it be better to mention this synergy right in the title?

Line 12 and elsewhere: normally, each number should be accompanied with its uncertainty. I hope that the uncertainties will be available after the first general comment above is addressed.

Line 43: “though” -> “through”

Line 47: “impletation” -> “implementation”

Line 49: it would be better to use “smaller than” instead of “less than”

Line 105 and elsewhere: the spectral channels are mentioned, but no information on the kernels is given, whereas it would be interesting to see where does the information on aerosols come from.

Line 148 and the whole section: the regularized solution implies that there is a certain “safe” solution, around which we try to retrieve the result. How heavily is the solution regularized? What happens if the regularization coefficient is set to zero? Is the task so ill-conditioned that it won’t converge at all? It would be interesting to compare the number of equations with number of unknowns

Line 232: it is not surprising that the farther the guess from the real solution is, the longer the iterative process is, but what is the link between the number of iterations and the footprint size, given that the pixels are treated individually?

Line 238: does the solution depend on the initial AOT value?  

Line 293: “to estimated” -> “to estimate”