An Algorithm Developed for Smallsats Accurately Retrieves Landsat Surface Reflectance Using Scene Statistics

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

General Comments:

This manuscript excels in presenting an Atmospheric Correction (AC) software that tackles the challenges associated with sensor radiometry and the availability of ancillary data, commonly limiting real-time AC. The software demonstrates comparable or even superior performance to radiative transfer (RadTran) methods like the Landsat Surface Reflectance Code (LaSRC) for the Landsat program and Sen2Cor for the Sentinel 2 (S2) program. Nevertheless, a few minor suggestions and questions for improving the manuscript are needed to be solved.

 

Major Comments:

The major comments are organized by section of the text and include line numbers where appropriate.

 

Introduction

Page 1: While this manuscript diverges from the traditional Introduction format, which typically includes the introduction of research significance, previous work, limitations, and innovations, it's worth noting that this manuscript builds upon the foundation laid in paper 1. In light of this, certain sections can be streamline. In my perspective, a clearer structure for the introduction would adjust to start with the research's significance, followed by an overview of the LaSRC and Sen2Cor methods, highlighting their limitations, and then present the Closed-form Method for Atmospheric Correction (CMAC) approach along with its advantages (Directly comparing the merits and drawbacks of LaSRC, Sen2Cor, and CMAC, ranging from sensor radiometry and ancillary data to radiance calibration, is also a good choice.), workflow, and improvement in the future. Finally, I recommend adding a section summary at the end of the Introduction, akin to Paper 1. This addition will aid the readers in swiftly identifying the information they seek. 

Materials and Methods

Lines 177-179: I presume this is a crucial step for Surface Reflectance (SR) retrieval, but certain aspects are unclear. Could you please elaborate on how you construct the statistical model after extracting top-of-atmosphere reflectance (TOAR) spectral data from index plots and subplots? Additionally, how do you derive the “Atm-I” response to the atmospheric effect from this model? Specifically, could you explain how you modeled by multiple linear regression and assuming a negative binomial distribution as mentioned in the point (10) of the workflow from paper 1? Furthermore, could you please clarify the independent and dependent variables in this modeling process, or alternatively, present the formulas?

Lines 242-244: Additionally, I consider that this is another crucial step for SR retrieval, and I am curious about the details of translating the “Atm-I” grayscale brightness into slopes and offsets.

 

Lines 344-345: Here, you mentioned a linear function used to adjust the S2 Atm-I model output for Landsat 8 and 9 (L8/9). Could you please provide detailed information on this process? If you have employed a method proposed by other researchers, kindly provide the reference. Alternatively, if you have devised a new method, please share the specifics. On another note, if the intention is to generalize this AC method to other smallsats, how do we perform cross-calibration through wavelength interpolation? Your insights on this matter would be appreciated.

 

Lines 349-356: Also, how did you determine the slopes and offsets for L8/9 and extrapolate the single values of the Atm-I and proxy slope and offset to enable the new L8/9 CMAC version? Could you please provide a formalization or graphical representation of these processes?

 

Results

The comprehensive comparison between CMAC and LaSRC across low, moderate, and extreme Atm-I conditions clearly demonstrates a significantly superior software capable of accurately translating TOAR to SR—a crucial parameter for many studies. With this success, are you considering applying this method to other satellites, such as MODIS and VIIRS? If so, what are the crucial points that need attention?

Comments on the Quality of English Language

Title: It is advisable to avoid abbreviating proper nouns in the title, such as “CMAC”, unless widely recognized in the field, and opt for a noun phrase rather than a complete sentence for the title.

 

Page 1, Line 16: Please change “LaSRC” to “Land Surface Reflectance Code (LaSRC)”.

 

Page 2, Line 62: Please give the full name of “R&D”, I guess it maybe “Research and Development”.

 

Page 3, Line 106: Please change “[7}” to “[7]”.

 

Page 4, Line 148: Please give the full name of “ASD”, I guess it maybe “Analytical Spectral Devices”.

 

Page 8, Line 280: Please give the full name of “WRS2”.

Page 9, Line 340: Please add a bracket and change “relative spectral response RSRs” to “relative spectral response (RSRs)”.

 

Page 20, Line 694: For picture 11, please remove “Horizontal (Value) Axis” in row 1.

Author Response

General Comments:

This manuscript excels in presenting an Atmospheric Correction (AC) software that tackles the challenges associated with sensor radiometry and the availability of ancillary data, commonly limiting real-time AC. The software demonstrates comparable or even superior performance to radiative transfer (RadTran) methods like the Landsat Surface Reflectance Code (LaSRC) for the Landsat program and Sen2Cor for the Sentinel 2 (S2) program. Nevertheless, a few minor suggestions and questions for improving the manuscript are needed to be solved.

 

Major Comments:

The major comments are organized by section of the text and include line numbers where appropriate.

 

Introduction

Page 1: While this manuscript diverges from the traditional Introduction format, which typically includes the introduction of research significance, previous work, limitations, and innovations, it's worth noting that this manuscript builds upon the foundation laid in paper 1. In light of this, certain sections can be streamlined. In my perspective, a clearer structure for the introduction would adjust to start with the research's significance, followed by an overview of the LaSRC and Sen2Cor methods, highlighting their limitations, and then present the Closed-form Method for Atmospheric Correction (CMAC) approach along with its advantages (Directly comparing the merits and drawbacks of LaSRC, Sen2Cor, and CMAC, ranging from sensor radiometry and ancillary data to radiance calibration, is also a good choice.), workflow, and improvement in the future. Finally, I recommend adding a section summary at the end of the Introduction, akin to Paper 1. This addition will aid the readers in swiftly identifying the information they seek. 

Though a cogent suggestion, an overview of LaSRC and Sen2Cor in relationship to CMAC is both beyond the scope of this paper and especially our expertise for these two RadTran methods, its length is presently excessive, plus I suspect that there are undoubtedly many small steps in the RadTran application that are not explained in the papers that document them. I appreciate why this request was made but leave it to someone more knowledgeable than us to take this up. As requested, we revisited and rearranged the order of information presented in this section and we have added a final paragraph to summarize the paper’s sections to assist the reader.

 

Materials and Methods

Lines 177-179: I presume this is a crucial step for Surface Reflectance (SR) retrieval, but certain aspects are unclear. Could you please elaborate on how you construct the statistical model after extracting top-of-atmosphere reflectance (TOAR) spectral data from index plots and subplots? Additionally, how do you derive the “Atm-I” response to the atmospheric effect from this model? Specifically, could you explain how you modeled by multiple linear regression and assuming a negative binomial distribution as mentioned in the point (10) of the workflow from paper 1? Furthermore, could you please clarify the independent and dependent variables in this modeling process, or alternatively, present the formulas?

These lines, now 187-189 have been expanded to better described the modeling. Furthermore, the modeling steps used linear regression that was expressed as the negative binomial. This is a well-known procedure that encodes the index values as natural logs so that they are normally distributed. The regression then fits a relationship and to decode the natural logs, the calculation of the regression relationship is exponentiated.   

 

Lines 242-244: Additionally, I consider that this is another crucial step for SR retrieval, and I am curious about the details of translating the “Atm-I” grayscale brightness into slopes and offsets.

(These lines are now 187-189.) The text is expanded through addition of new Lines 258-260 that briefly describe the calibration process. This is expanded in the original lines 349-356 that prompted the additional comment below.

 

Lines 344-345: Here, you mentioned a linear function used to adjust the S2 Atm-I model output for Landsat 8 and 9 (L8/9). Could you please provide detailed information on this process? If you have employed a method proposed by other researchers, kindly provide the reference. Alternatively, if you have devised a new method, please share the specifics. On another note, if the intention is to generalize this AC method to other smallsats, how do we perform cross-calibration through wavelength interpolation? Your insights on this matter would be appreciated.

(These lines are now 359-361) As I understand and applied it, cross calibration pairs two sensor responses or their derivative output with sensor 1 on the x-axis and sensor 2 on the y-axis. Regression is then used to fit a relationship that translates the sensor 2 to the sensor 1. As described, we used the Sentinel 2 derived model as a sensor 1 and the bandwise inputs from Landsat (sensor 1) to fit a curve that make the Atm-I model outputs equivalent. This scales the Landsat output to emulate the Sentinel 2 scaling.

 

Lines 349-356: Also, how did you determine the slopes and offsets for L8/9 and extrapolate the single values of the Atm-I and proxy slope and offset to enable the new L8/9 CMAC version? Could you please provide a formalization or graphical representation of these processes?

(These lines are now 365-374) Revisiting the CMAC equation at (original) Line 246, you can see that each slope and offset combination describing a single atmospheric condition must balance in order to correctly predict SR. These are balanced iteratively so that the TOAR is adjusted to be equivalent to the known surface reflectance of target. The families of curves of the master satellite are used as a standard, introduced at Line 143 and expanded upon at Lines 329-336. Additional language was added at old line 331 (new line 346) that better defines the families of curves.

 

Results

The comprehensive comparison between CMAC and LaSRC across low, moderate, and extreme Atm-I conditions clearly demonstrates a significantly superior software capable of accurately translating TOAR to SR—a crucial parameter for many studies. With this success, are you considering applying this method to other satellites, such as MODIS and VIIRS? If so, what are the crucial points that need attention?

Responding to this questions. No, our focus is to enhance surface reflectance retrieval for smallsats that have resolution of say, 30m or better. There are fundamental changes to reflectance distributions through downscaling to much larger pixels in the application of the CMAC workflow because the opportunity to find low blue reflectance is severely decreased. We have seen relationships in our study that support that the quality of the corrected images increases through the CMAC workflow as resolution increases. I think that the RadTran approach for MODIS and VIIRS may be the more appropriate.

 

Comments on the Quality of English Language

Title: It is advisable to avoid abbreviating proper nouns in the title, such as “CMAC”, unless widely recognized in the field, and opt for a noun phrase rather than a complete sentence for the title.

 Agreed: CMAC now changed in the Title to “An Algorithm Developed for Smallsats Accurately retrieves Landsat Surface Reflectance”

Page 1, Line 16: Please change “LaSRC” to “Land Surface Reflectance Code (LaSRC)”.

 Done

Page 2, Line 62: Please give the full name of “R&D”, I guess it maybe “Research and Development”.

Done

 Page 3, Line 106: Please change “[7}” to “[7]”.

 Done

Page 4, Line 148: Please give the full name of “ASD”, I guess it maybe “Analytical Spectral Devices”.

 Done

Page 8, Line 280: Please give the full name of “WRS2”.

 Done

Page 9, Line 340: Please add a bracket and change “relative spectral response RSRs” to “relative spectral response (RSRs)”.

  Done

Page 20, Line 694: For picture 11, please remove “Horizontal (Value) Axis” in row 1.

  Done

Reviewer 2 Report

Comments and Suggestions for Authors

The authors verified a new AC model called “CMAC” described in previous work through Landsat 8/9 scenes processing and LaSRC SR comparison. Compared with the previous work focused on Sentinel-2, current work on Landsat 8/9 verification showed the extension efforts of the original CMAC. It seems CMAC has the potential, as claimed by authors, to apply numerous VNIR satellite data, especially for ones with only 4 bands and without rigorous radiometric calibration. Although the whole structure of the manuscript, validation and result description is good, I still look forward to seeing improvements of this work by additional clarification and explanation before acceptance for publication.

 

1．To my understanding, the key points of CMAC includes prior knowledge of alfalfa spectral reflectance, Atm-I index estimation based on the blue band, and inversion of the empirical slope (m) and offset (b) from Atm-I. I followed the original paper but did not find the Atm-I definition and how to get the slope and offset at each spectral band from Atm-I. I suggest the author adds a flow chart to describe it in the part of “Materials and Methods”. Furthermore, at the beginning of the second paragraph of section 2.1, it is mentioned that the VNIR band is used as the input for the model, but the corresponding details are not mentioned in this section. It is suggested to provide a brief supplement to this.

 

 

2. Related to 1. Figures 2 and 3 has been illustrated in Paper 1 and they are not necessarily to repeat here. However, the description (part 2.4) of calibration transfer from Sentinel-2 to Landsat 8/9 should moved before part 2.3 because it is a basis to set up Landsat 8/9 Atm-I. More details should be added to describe the calibration transfer process.

 

3. The general idea of CMAC is the spatial variation of empirical line method as described in the first paragraphs of Section 4. I suggest putting them in the introduction section to help readers understand its main principle without reading the original paper.

 

4. The CMAC is a promising AC model by LaSRC comparison. The CMAC method has similarities in principle with the DDV algorithm, both are based on vegetation regions for fitting atmospheric effects. In addition, this method utilizes Sen2Cor data for training. I would like to inquire if there is any difference in the accuracy of surface reflectance between vegetation and non vegetation areas using this method? Is there a correlation between its results and Sen2Cor's results? Have you conducted any relevant experiments on these issues?

 

5. The CMAC has the advantage to remove haze compared with LaSRC results in Figure 5. However, LaSRC did not consider haze compensation process in its original algorithm design. Another AC module called “ATCOR” has such function to process haze and then conduct AC as following steps. The whole work did not cite the work of ATCOR and showed the comparison of ATCOR inversion for Landsat 8/9.

 

6. It should be adding the response curve of Landsat 9 in Figure 7. And Figure 13 makes no sense and I suggest removing it.

 

7. The introduction section has some unclear logic. I suggest reorder the description of CMAC and other relevant AC methods, summarizing the other’s work first and then describing the CMAC and its extension (Lines 62~80) at the end of this section.

 

Author Response

The authors verified a new AC model called “CMAC” described in previous work through Landsat 8/9 scenes processing and LaSRC SR comparison. Compared with the previous work focused on Sentinel-2, current work on Landsat 8/9 verification showed the extension efforts of the original CMAC. It seems CMAC has the potential, as claimed by authors, to apply numerous VNIR satellite data, especially for ones with only 4 bands and without rigorous radiometric calibration. Although the whole structure of the manuscript, validation and result description is good, I still look forward to seeing improvements of this work by additional clarification and explanation before acceptance for publication.

 

1．To my understanding, the key points of CMAC includes prior knowledge of alfalfa spectral reflectance, Atm-I index estimation based on the blue band, and inversion of the empirical slope (m) and offset (b) from Atm-I. I followed the original paper but did not find the Atm-I definition and how to get the slope and offset at each spectral band from Atm-I. I suggest the author adds a flow chart to describe it in the part of “Materials and Methods”. Furthermore, at the beginning of the second paragraph of section 2.1, it is mentioned that the VNIR band is used as the input for the model, but the corresponding details are not mentioned in this section. It is suggested to provide a brief supplement to this.

We revised the description to include iterative fits of slope and offset that are balanced using the CMAC equation. Yes, the VNIR bands are used to assess atmospheric index Atm-I, first through development of a statistical model and in routine application from spatial sampling of band values that result from the statistical model. 

 

2. Related to 1. Figures 2 and 3 has been illustrated in Paper 1 and they are not necessarily to repeat here. However, the description (part 2.4) of calibration transfer from Sentinel-2 to Landsat 8/9 should moved before part 2.3 because it is a basis to set up Landsat 8/9 Atm-I. More details should be added to describe the calibration transfer process.

Though we agree, we have included these figures for the convenience of readers who may not be inclined to study the original Paper 1.

 

3. The general idea of CMAC is the spatial variation of empirical line method as described in the first paragraphs of Section 4. I suggest putting them in the introduction section to help readers understand its main principle without reading the original paper.

Done

 

4. The CMAC is a promising AC model by LaSRC comparison. The CMAC method has similarities in principle with the DDV algorithm, both are based on vegetation regions for fitting atmospheric effects. In addition, this method utilizes Sen2Cor data for training. I would like to inquire if there is any difference in the accuracy of surface reflectance between vegetation and non vegetation areas using this method? Is there a correlation between its results and Sen2Cor's results? Have you conducted any relevant experiments on these issues?

Excellent question: we have begun a process of checking whether the results for different environments are giving different answers.

• Firstly, the warehouse QIAs that we used for calibration and others that we used for testing are not vegetated environments and by definition give excellent results.
• So far, our investigations have not shown that there is a loss of accuracy for natural environments that are very different from the warehouse QIAs. Verification has been determined from the match of CMAC surface reflectance for equivalent S2 TOAR values at the same Atm-I in a comparison of spreadsheet values used for S2 analysis in Paper 1. These were a few percent either side of zero difference between the two sets and yes, the CMAC results are tighter than Sen2Cor. This investigation has been carried out for images that have elevated Atm-I but not above what would be routinely expected for correction.
• This investigation is continuing and will be the subject of a white paper that is under development.

 

5. The CMAC has the advantage to remove haze compared with LaSRC results in Figure 5. However, LaSRC did not consider haze compensation process in its original algorithm design. Another AC module called “ATCOR” has such function to process haze and then conduct AC as following steps. The whole work did not cite the work of ATCOR and showed the comparison of ATCOR inversion for Landsat 8/9.

Removal of haze as a separate step from surface reflectance retrieval is not something I have considered specifically because if true surface reflectance is delivered then there is no haze by definition. Compensation in this regard is a telling admission that the image may look clearer but can’t be verified to be true surface reflectance

 

6. It should be adding the response curve of Landsat 9 in Figure 7. And Figure 13 makes no sense and I suggest removing it.

Re: Figure 7 – the L9 response curve has been verified to be virtually identical to L9 as cited in the paper by Gross et al., 2022 and is a point made in the paper. This figure is intended to show, qualitatively, that there is a systematic difference between S2 and L8 (and, in the context provided in the paper, also ~representing 9) bands.

Re: Figure 13. Removed.

 

7. The introduction section has some unclear logic. I suggest reorder the description of CMAC and other relevant AC methods, summarizing the other’s work first and then describing the CMAC and its extension (Lines 62~80) at the end of this section.

The paragraphs in the introduction were reordered in view of this and Reviewer 1’s comments to the best that we could do for this very complex subject.

Reviewer 3 Report

Comments and Suggestions for Authors

Closed-form Method for Atmospheric Correction (CMAC) using a closed-form linear model is shown to accurately retrieve smallsat surface reflectance data post application of the atmospheric effect across the image as an index (Atm-I) from scene statistics. It is compared with LaSRC software. This follows in the wake of the author's previous paper which compared CMAC with Sen2Cor but the authors may consider adding some three-way comparison (CMAC, Sen2Cor, LaSRC) at least in supplementary files or as appendix.

 

The main optimization is obtained by avoiding a radiance-based workflow like RadTran - substituting an empirically derived mathematical model for the observed effect of atmospheric transmission upon reflectance.

This empirical nature may vitiate interpretation when CMAC encounters non-conforming scene statistics leading to improper Atm-I indexing as (the authors have noted) groundtruth sampling lacks in real-time precision. If possible, it is suggested that sensitivity analysis for the robustness against Atm-I parameter may be performed.

Author Response

Closed-form Method for Atmospheric Correction (CMAC) using a closed-form linear model is shown to accurately retrieve smallsat surface reflectance data post application of the atmospheric effect across the image as an index (Atm-I) from scene statistics. It is compared with LaSRC software. This follows in the wake of the author's previous paper which compared CMAC with Sen2Cor but the authors may consider adding some three-way comparison (CMAC, Sen2Cor, LaSRC) at least in supplementary files or as appendix.

A three-way comparison is a great suggestion and will be a consideration of future white papers. This paper and the one preceding it are the beginning of a series of investigations into accuracy and robustness. As stated in this paper in the error analyses in the results section, LaSRC provided a more accurate results in the investigations here.

 

The main optimization is obtained by avoiding a radiance-based workflow like RadTran - substituting an empirically derived mathematical model for the observed effect of atmospheric transmission upon reflectance. This empirical nature may vitiate interpretation when CMAC encounters non-conforming scene statistics leading to improper Atm-I indexing as (the authors have noted) groundtruth sampling lacks in real-time precision. If possible, it is suggested that sensitivity analysis for the robustness against Atm-I parameter may be performed.

First, to respond to the non-conforming scene statistics, the way CMAC is calibrated and applied renders it capable of working with any condition of scene statistics. However, as we have discovered and for which we are pursuing a fix: at high levels of atmospheric effect, there becomes a mismatch between the calculated irradiance based solely upon top-of-atmosphere measurements, and the illumination of ground targets beneath the resulting severe haze. Because of this, the CMAC surface reflectance estimates for the upper limb of the reflectance distribution are incorrect. It is a problem that is well illustrated in Figure 10 of paper 1. While CMAC can be calibrated for the lower limb to be correct in extreme levels of Atm-I, the upper limb of reflectance requires additional adjustment to assure the reflectance of the entire distribution is correct. As you will note in that figure, this is an issue for Sen2Cor as well (and all other optical satellite VNIR sensors). Our study of this phenomenon has indicated that it is the result of diffuse shading by aerosol particles. It will be reversed through a secondary function to be called forth by the magnitude of Atm-I. Note, though, that even though there is a shift in color balance, the corrected image appears clear visually, the curve for Atm-I = 1743 in Figure 10 is the same image that is shown in Figure 16 of Paper 1