Round 1

Reviewer 1 Report

General comments:

Aerosol is very important to impact atmospheric cycle and climate system by direct and indirect effects, a hot issue of scientific researches internationally. Also, atmospheric pollutions from anthropogenic activities cause adverse harm to human health, such as, aerosols and gases. Aerosols are known to originate from direct emission and secondary formation, namely, POA and SOA. The organic aerosol (OA) is a very important part of aerosols, including BC and OC. Inorganic ions are important compositions of aerosols. Aerosol is so complex that the people understands it with large challenge and difficult, i.e. physical, chemical, optical, hygroscopity etc. Remote sensing is crucial to detect aerosol, cloud, even atmospheric, acted as an efficient tool, although some uncertainty existing in part of region in the world. This paper development a theory to analyze and estimate the uncertainty caused by aerosol microphysical model selected in retrieval of satellite processing, in order to quantify uncertainty and rise retrieval accuracy, and test the availability of theory using the products of DSCOVR/EPIC. The topic of this paper is of common interest within the scientific community, the manuscript includes some important theory and method.

Author Response

Please see the attachment.

Reviewer 2 Report

The topic is suitable for Remote Sensing but I am wondering if the content is. There are so many equations and so much mathematical notation. I can't imagine the readers of Remote Sensing making it through more than 2 pages of this. I have to reject this paper as I feel that almost no one would be interested in deciphering it.

General comments

The abstract should tell the reader how the retrieval becomes more accurate when model uncertainty is taken into account. It must be that the retrieval is tending toward the a priori value of some state parameter when model uncertainty is high.

Specific comments

L6: This sentence is repetitive (“solution” appears twice)

L12: bayesian -> Bayesian

L25: This statement does not belong in the introduction. It seems like a conclusion.

L28: A comma should appear after any leading prepositional phrase (see L31 for correct punctuation).

L31: I don’t think a new paragraph should start. This paragraph is too closely related to the previous one (“these tools” on L32).

L32: I don’t think it is acceptable to have “[3] [4]” as the subjects of the sentence. The editor can weigh in. I would suggest using authors’ names here, as well as “[3] [4]”. Also, I believe “[3] [4]” should be written as “[3-4]”. The editor can clarify here also.    

L37: The editor can weigh in again on whether it is OK to refer to Eq. 8 before Eq. 1 appears. If it is not OK, the authors can simply write “see below”).

L63: Place “λ” after “wavelength”.

L64: Define “N”

L64: Layer height is not an element of real numbers. Layers heights cannot be negative infinity. I find the authors are lost in their notation. The readers of Remote Sensing do not even need to see to which set of numbers “x” belongs. I suggest the authors tailor this paper to the readers, or else most of them will find it indigestible.  

L64: Why is it necessary to have R raised to the power N?

L65 (Eq. 1): Why is this nonlinear? 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Review of "Model selection in atmospheric remote sensing with application to aerosol retrieval from DSCOVR/EPIC. Part 1: Theory"

Summary

This paper reports an aerosol retrieval technique to improve the solution accuracy by considering the modeling uncertainty, where there is not enough information on the aerosol model. In sections 2 to 6, the manuscript clearly describes the theoretical framework for aerosol retrieval. In section 7, the authors demonstrate this technique for the EPIC instrument onboard on the DSCOVR platform. Synthetic measurements simulated at 660 nm for different optical thickness and aerosol layer height are used for the performance test of this retrieval algorithm. This manuscript is very well written without skipping any steps. However, I have some concerns/questions regarding their application of this algorithm for EPIC measurements. These concerns/questions are listed in the general comments section.

My recommendation to the authors is to redo section 7. using at least two spectral bands and see how the results are improved.

General comments

1. Why authors are doing a single band aerosol retrievals for EPIC instruments, while the instrument has 10 spectral bands ranging from 317 to 780 nm?

2. Why not use another spectral band so that aerosol layer height information can be driven from the spectral difference in Rayleigh scattering?

3. What is the assumption of BRDF of the surface? Is it a Lambertian surface?

   1. As per the Test example #3, a weight for constraining surface as w_A = 10^3wA​=103, basically means that the surface albedo is over-constrained to a priori assumption of the surface albedo value. When surface albedo is retrieved along with the $\tau$ and H, MMLE and MLMMLE perform better compared to GCV and MLGCV technique. For the case of Test example #1, and #2 it was vice versa. Is there any explanation for this change in the relative error?.

4. If you use only one spectral band for the aerosol retrieval, the radiance measured by the instrument is a combination of light scattered by aerosol ( diffused and direct), surface reflection, and rayleigh scattering. Are you trying to retrieve 2 parameters from 1 equation (for the case of Test example #1 and #2)?. When you are retrieving surface albedo along with the $\tau$, and H. You are using 1 equation and retrieving 3 unknowns. Am I interpreting this wrong?.

5. Another assumption is that the Covariance matrix has only diagonal elements, what if there are some off-diagonal elements (say there is a correlation between the spectral bands). Can this technique be customized or modified to accommodate this correlation?

6. Describe what kind of forward model RT code is used? Is it an in-house or other RT code?

7. Is this proposed method mainly for the application of high aerosol loading conditions?. How does the retrieval perform for $\tau$ < 0.25?

Specific comments

1. Line #198: It should be "go to step 10" rather than "step 11"?

2. Line #200: It should be "go to step 12" rather than "step 11"?

3. Line #209: It should be "Appendix 3", instead of Appendix 4 in the text.

4. Line #233: SNR given is for the 660 nm channel?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Re-review of Sasi et al. (submitted to Remote Sensing)

The authors need to keep things simpler so they don’t get confused themselves. L64 says F is a model, but a model is not a real number. Perhaps F is a model estimate?  

I strongly encourage all six authors to carefully read the paper and make sure they understand every line of it. I feel that it is unlikely that the six authors have carefully read this paper with some of the sloppy or careless errors that are present. The authors really need to try to take “a step back” and find all the undefined terms that limit what most readers can get out of this overly theoretical paper. I stopped reading at L87. I feel the manuscript is not in a state to be submitted to Remote Sensing (let alone published).

I have been developing remote sensing algorithms for almost 20 years and have worked on aerosol layer height retrieval for the past 8 years. I have not heard of “maximum solution estimate” (L12). The authors claim it is “frequently used in the literature”. A Google search for this term produced only 1 unique hit and the following response from Google:

It looks like there aren't many great matches for your search

Do you the authors mean “maximum likelihood estimation solution”?

L19: Add a space after “example,”

L28: Put a comma after leading prepositional phrases such as “By model selection,” as you correctly do on L22. See also L61.

L34. Add a space after the end of the sentence.

L35: I don’t think it is acceptable to have “[3] [4]” as the subjects of the sentence. The editor can weigh in. I would suggest using authors’ names here, as well as “[3] [4]”. Also, I believe “[3] [4]” should be written as “[3-4]”. The editor can clarify here also.   

L40: The editor can weigh in again on whether it is OK to refer to Eq. 8 before Eq. 1 appears. If it is not OK, the authors can simply write “see below”).

L64: Once again, the authors are sloppy or confused. M is a number of dimensions in “R^M” but two lines later M is the number of wavelengths.  

L74: M’ and mesi’ are not defined. Also, it appears that M is not the number of wavelengths here. So is M the number of dimensions?

L75: The c_mes on the left and the right hand side of the equation are very similar looking. This may be the intent, but I could see many readers not realizing the c_mes from the right hand side is on the left hand side in the subsequent equation.

L75: Before Equation 5, write something like “and the scaling matrix P is given by”. It helps the reader to understand what P represents. Currently, P is first referred to as a “scaling matrix” on L86.

L87: M is the number of wavelengths again.

Reviewer 3 Report

I would like to congratulate the authors of the paper. My concerns and questions have been addressed by the authors. I would like to recommend this paper for publication.