A Solar Trajectory Model for Multi-Spectral Image Correction of DOM from Long-Endurance UAV in Clear Sky

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors address an important issue in generating reflectance data from long-endurance UAV flights. They present the Solar Trajectory Model (STM) approach, which is interesting, I have some concerns regarding its overall applicability.

The proposed STM approach corrects only for the variation in solar elevation angle over time. While i believe this approach effectively adjusts for solar irradiance under clear skies with stable aerosol conditions, I would have appreciated a discussion on how the method's accuracy might be affected under overcast or variable cloud conditions.

Minor Comments:

1. Introduction:
   “Experimental results demonstrated that the RMSE (Root Mean Square Error) for the STM-based method decreased by 37% and 51% in Shanghai, and by 16% and 56% in Tianjin, respectively.”
   This sentence is unclear. What is the difference between the 37% and 51% reductions? If these figures refer to RMSE, the numbers suggest an increase instead of  a decrease. Please clarify.
2. Equation (3):
   The parameters used in Equation (3) should be specified directly after the equation.
3. Line 119:
   “In equation (3), the diffuse radiation component was neglected because it accounts for only 5% to 15% of the total radiative energy.”
   As UAVs are also used under overcast conditions, is this assumption still  true in such scenarios? Please discuss in more detail.
4. Line 186:
   “First, perform radiometric correction, georeferencing, geometric correction, and image mosaicking on the UAV and CRP images to obtain the DOM image while also calculating approximate.... The code for correction, mosaicking, and other processes can be found in the open-source code provided by MicaSense.”
   Please provide more details about these processing steps instead of just referring to a code. 
5.  

5.      Figure 5:
The figure is unclear. Not clear which processing steps have been applied in traditional and DLS approach  Please revise the figure to make the applied steps much clearer.

 

6.     Figure 6:
Please add a plot showing the Beta correction over time  

7.     Figure 6 c and 6d

Please adjust the X-axis to cover the same time period (e.g., from 11:50 to 16:10) in both plots to enable better comparison. Include a discussion on the causes of the differences observed in the variations between the two plots.

 

8.     Figure 6d:
Please discuss the observed variation in the DLS data. Could this be due to UAV platform instability? Is there any  attitude information (pitch, roll, yaw) available that could help explain these variations? If so, please plot the attitude data as well.

 9.     Inconsistency between Figure 6d and Figure 10:

There appears to be an inconsistency between the DLS data shown in Figure 6d and Figure 10. In Figure 6d, significantly less DLS data is presented, which seems to be limited to the exact times of UAV data acquisition. Peaks or dips observed at these specific times could be artifacts of UAV platform instability. These fluctuations could have been smoothed  if the full set of DLS data were included. Please clarify this discrepancy and consider using all available DLS data for consistency and more robust analysis.

 

 

 

 

 

Author Response

1. Introduction:
   “Experimental results demonstrated that the RMSE (Root Mean Square Error) for the STM-based method decreased by 37% and 51% in Shanghai, and by 16% and 56% in Tianjin, respectively.”
   This sentence is unclear. What is the difference between the 37% and 51% reductions? If these figures refer to RMSE, the numbers suggest an increase instead of  a decrease. Please clarify.

   Response: Thank you for pointing this out. I agree with your comment, and I have revised the relevant sentences in both the Introduction and Abstract to clarify the comparison. The percentages now clearly indicate the performance improvement of our method compared to two different baseline methods. Specifically, the 37% and 51% reductions refer to the RMSE decrease compared to Method A and Method B, respectively. The revised text can be found in lines 17-22 on the first page.

2.  Equation (3):
   The parameters used in Equation (3) should be specified directly after the equation.

   Response: Thank you for your comment. We have revised the manuscript to address this concern. The parameters used in Equation (3) are now clearly specified and explained immediately after the equation, ensuring that the meaning of each parameter is well-defined for readers.

3. “In equation (3), the diffuse radiation component was neglected because it accounts for only 5% to 15% of the total radiative energy.”
   As UAVs are also used under overcast conditions, is this assumption still  true in such scenarios? Please discuss in more detail.

   Thank you for your insightful comment. Due to limitations in the available data, our current study primarily focuses on clear-sky conditions, as most UAV operations are typically conducted under sunny and less cloudy conditions. Therefore, the assumption in Equation (3) is reasonable for the scope of this work. However, we acknowledge that overcast conditions present a more complex scenario, and we plan to address this in future research once sufficient data is collected. We appreciate your suggestion and will consider it as an important direction for our subsequent studies. Thank you.

4. “First, perform radiometric correction, georeferencing, geometric correction, and image mosaicking on the UAV and CRP images to obtain the DOM image while also calculating approximate.... The code for correction, mosaicking, and other processes can be found in the open-source code provided by MicaSense.”
   Please provide more details about these processing steps instead of just referring to a code. 

   Response: Thank you for your valuable suggestion. We agree with your point and have thoroughly revised Section 3.3, "Validation Experiments," on page 7 (lines 231–252). The updated text now provides a detailed explanation of the specific steps involved in radiometric correction and geometric correction, rather than simply referring to the code. We believe these clarifications will help readers better understand the processing workflow. Thank you for your feedback, which has significantly improved the clarity of our manuscript.

5. Figure 5:
   The figure is unclear. Not clear which processing steps have been applied in traditional and DLS approach  Please revise the figure to make the applied steps much clearer.

    Response: Thank you for your feedback, which is very helpful. We have rewritten Section 3.3, "Validation Experiments," and replaced both the text and the figure to provide a clearer explanation of the processing steps applied in the traditional and DLS approaches. The revised version now explicitly highlights the differences and steps for each method, making it much easier to understand. We appreciate your suggestion, which has significantly improved the clarity of our manuscript.

6. Please add a plot showing the Beta correction over time  

   We have updated Figure 6 to include a plot showing the variation of the Beta correction over time during the operation of the STM method.

7. Please adjust the X-axis to cover the same time period (e.g., from 11:50 to 16:10) in both plots to enable better comparison. Include a discussion on the causes of the differences observed in the variations between the two plots.

   Response: You are absolutely correct. We have adjusted the X-axis in Figures 6(c) and 6(d) to cover the same time period (from 11:50 to 16:10) with identical coordinate values. This modification allows for a more accurate and meaningful comparison between the two plots. Additionally, we have included a discussion on the causes of the observed differences in the variations between the plots, providing further insights into the underlying factors. Thank you for your valuable suggestion, which has significantly improved the clarity and interpretability of Figure 6.

8.  Please discuss the observed variation in the DLS data. Could this be due to UAV platform instability? Is there any  attitude information (pitch, roll, yaw) available that could help explain these variations? If so, please plot the attitude data as well.

   Response: Thank you for your comment. The DLS data we used already includes Horizontal Irradiance, which is angle-compensated data calibrated using directional light sensors in the DLS. This means the data inherently accounts for any attitude information (pitch, roll, yaw). We apologize for not clearly explaining the source of the DLS data in the previous version. We have revised Section 4.1, "Comparison of CRP Reflectance Calculated by the Different Methods," in lines 268–277 to provide a clearer explanation of the DLS data and its processing. We appreciate your feedback, which has helped us improve the clarity of our manuscript.

9. There appears to be an inconsistency between the DLS data shown in Figure 6d and Figure 10. In Figure 6d, significantly less DLS data is presented, which seems to be limited to the exact times of UAV data acquisition. Peaks or dips observed at these specific times could be artifacts of UAV platform instability. These fluctuations could have been smoothed  if the full set of DLS data were included. Please clarify this discrepancy and consider using all available DLS data for consistency and more robust analysis. 

   Thank you for pointing out this inconsistency. The difference in the number of DLS data points between Figure 6d and Figure 10 is intentional. Figure 6d specifically shows the DLS data for the blue band at the exact moments of CRP image capture, which corresponds to the instantaneous DLS data during the reference panel acquisition. In contrast, Figure 10 includes all available DLS data to provide an overall trend and identify potential issues in the DLS measurements. This approach allows us to better compare the DLS data with the STM method. We appreciate your attention to detail and hope this clarification addresses your concern.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposed a solar trajectory model for multi-spectral image correction of DOM from long-endurance UAV. There are some issues that need to be carefully addressed.

1.       In the introduction section, the latest research advances in multi-spectral image correction of DOM from UAV should be added.

2.       The innovation and contribution of the paper should be clearly stated in the introduction section.

3.       The methodology section of the paper needs to be elaborated in more detail. And it is suggested to add a flowchart of the proposed method.

4.       In the experiment Section, it is suggested to add the efficiency comparison experiment of three algorithms to further verify the progressiveness of the proposed method.

Author Response

1. In the introduction section, the latest research advances in multi-spectral image correction of DOM from UAV should be added.

   Response: Thank you for your suggestion. We have revised the introduction section and incorporated the latest research advances in multi-spectral image correction of DOM from UAVs. The updated content can be found in lines 45–103. These additions provide a more comprehensive background and highlight recent developments in the field. We appreciate your feedback, which has strengthened the foundation of our work.

2. The innovation and contribution of the paper should be clearly stated in the introduction section.
   

   Response: Thank you for your valuable suggestion. We have revised the introduction section to clearly highlight the innovation and contribution of our paper. The updated content can be found in lines 113–131. We appreciate your feedback, which has helped us better articulate the significance of our work. Thank you again for your insightful comment.

3. The methodology section of the paper needs to be elaborated in more detail. And it is suggested to add a flowchart of the proposed method.

   Response: Thank you for your constructive suggestion. We have elaborated on the methodology section and revised Figure 5 in Section 3.3 to provide a clearer explanation of the proposed method. The updated Figure 5 now better illustrates how the STM, Traditional Method, and DLS are individually calculated and compared. We appreciate your feedback, which has significantly improved the clarity and detail of our methodology.

4.  In the experiment Section, it is suggested to add the efficiency comparison experiment of three algorithms to further verify the progressiveness of the proposed method.

   Response: Thank you for your valuable suggestion. To compare the computational efficiency of the three methods, we have designed a new experiment, as described in line 325, and added Table 2. This table compares the computation time and efficiency of the three methods for processing a single image and a strip of 1,594 images. Your feedback has greatly enhanced the robustness of our experimental analysis, and we sincerely appreciate your insightful comment.

Reviewer 3 Report

Comments and Suggestions for Authors

The research carried out by the authors is well developed in terms of equipment, methodology and procedure. As an evaluator I only find a comment regarding the current situation to the state of the art and initial references since there are solutions on the market in various software programs, I didn't find these references in the paper. Pix4DMapper (Sun angle compensation) or its option Pix4DFields have algorithms that perform this process. It is therefore a well-developed study but there are already solutions on the market, however it is interesting work developed and openly puts a properly executed work for assessment of the scientific community.

I believe that the authors should include a study of existing solutions in the introductory section. It would also have been very interesting if the authors had contrasted their proposal with results obtained from existing applications in order to evaluate them. Both proposals would make the study more impactful.

I believe that this work of comparison with existing solutions is a priority in order to publish the article.

Author Response

The research carried out by the authors is well developed in terms of equipment, methodology and procedure. As an evaluator I only find a comment regarding the current situation to the state of the art and initial references since there are solutions on the market in various software programs, I didn't find these references in the paper. Pix4DMapper (Sun angle compensation) or its option Pix4DFields have algorithms that perform this process. It is therefore a well-developed study but there are already solutions on the market, however it is interesting work developed and openly puts a properly executed work for assessment of the scientific community.

I believe that the authors should include a study of existing solutions in the introductory section. It would also have been very interesting if the authors had contrasted their proposal with results obtained from existing applications in order to evaluate them. Both proposals would make the study more impactful.

I believe that this work of comparison with existing solutions is a priority in order to publish the article.

Response: Thank you for your thorough review and valuable feedback. We greatly appreciate your suggestion and have carefully addressed it by expanding the introduction section (lines 45–80) to include a detailed discussion of existing solutions, such as Pix4DMapper and Metashape. Specifically, we have analyzed the capabilities and limitations of these software tools in terms of sun angle compensation and radiometric correction.

Regarding the experimental comparison, we would like to clarify that the reflectance calculation methods used by commonly adopted UAV processing software, such as Pix4DMapper and Metashape, are essentially the same as the "Traditional Method" described in our paper. Therefore, the comparison results between the STM model and the Traditional Method directly reflect the differences between the STM model and the results obtained from Pix4DMapper, Metashape, and similar software. This comparison effectively demonstrates the superiority of the STM model over these existing software-based approaches.

We believe these revisions and clarifications have strengthened the impact of our study and addressed your concerns. Thank you again for your insightful comments, which have significantly improved the quality of our manuscript.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors The authors have sufficiently addressed my concerns and comments.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have well addressed all my comments. I have no more concerns.

Author Response

The authors have well addressed all my comments. I have no more concerns.

Response:  Thank you very much for your positive feedback and for taking the time to review our manuscript. We greatly appreciate all the insightful comments and suggestions you provided during the review process, which have significantly improved the quality of our work.We are pleased to hear that our revisions have addressed your concerns.

Reviewer 3 Report

Comments and Suggestions for Authors

I appreciate your effort including a reference of the current most professional uses of DLS and Panel Reflectances for radiometric calibration. I agree the text and references included in the introduction are right.

I am not sure and you probably have studied in your research.

Traditional softwares have several options to include the radiometric calibration. Reflectance Panels, Sun angle and DLS or any combinations of them. When you include in the introduction the reference of these applications, I don't know if you refer to Sun angle the capability of them to make the radiometric calibration. Even you told as traditional method the uses and comparison of the Panel Reflectation.

Could it be possible that the applications uses some of them: Panel + DLS to determine the initial sun angel and ilumination and them DLS during the flight to include possible sun or ilumination change in long flights?. Of course they can do it in a different method that yours and this could be the really interest of the paper. Your improve will include new options and put in value this new procedures or equation in the process.

For sue, it is possible that you have told all these comments in your paper but I didn't understand this in the document. I would suggest the inclusion if not.

I think it is also possible that a reference that you have included the comparison or study of these applications with your research could be something to include in the discussion because this will help to remark your new proposal of methodology over the current traditional ones.

Author Response

I appreciate your effort including a reference of the current most professional uses of DLS and Panel Reflectances for radiometric calibration. I agree the text and references included in the introduction are right.

I am not sure and you probably have studied in your research.

Traditional softwares have several options to include the radiometric calibration. Reflectance Panels, Sun angle and DLS or any combinations of them. When you include in the introduction the reference of these applications, I don't know if you refer to Sun angle the capability of them to make the radiometric calibration. Even you told as traditional method the uses and comparison of the Panel Reflectation.

Could it be possible that the applications uses some of them: Panel + DLS to determine the initial sun angel and ilumination and them DLS during the flight to include possible sun or ilumination change in long flights?. Of course they can do it in a different method that yours and this could be the really interest of the paper. Your improve will include new options and put in value this new procedures or equation in the process.

For sue, it is possible that you have told all these comments in your paper but I didn't understand this in the document. I would suggest the inclusion if not.

I think it is also possible that a reference that you have included the comparison or study of these applications with your research could be something to include in the discussion because this will help to remark your new proposal of methodology over the current traditional ones.

Response: First of all, I would like to express my sincere gratitude for your valuable comments. Your suggestions are highly practical and reasonable.

Secondly, I would like to provide some clarification regarding the paper. You are absolutely correct that "traditional software typically offers several options for radiometric calibration, including reflectance panels, sun angle, and DLS, or any combination of them." In our preprocessing, we do take solar elevation angle into consideration. Our preprocessing workflow references the open-source code provided by MicaSense at https://github.com/micasense/imageprocessing. This website addresses the processing of DLS data by taking into account UAV flight attitude issues and also considers the combination of CRP and DLS. The DLS data used in our paper were processed using the same approach.

Traditional software such as Pix4DMapper and Metashape can directly read the energy from metadata. However, their workflows still assume that the incident radiation energy remains constant, which is similar to the "Traditional Method" described in our paper. Of course, traditional software can also utilize DLS data, and they do correct the DLS data based on flight attitude. However, errors still occur, such as when the propellers or the aircraft body reflect part of the energy to the DLS, causing extreme values in the readings. Additionally, some sensors or aircraft, such as the DJI Zenmuse X4S and DJI Zenmuse X5S, are not equipped with DLS capabilities.

Regarding how to make DLS data more accurate and eliminate the effects of flight attitude and external factors, this involves the cleaning and correction of DLS data. Existing methods generally take aircraft attitude into account, but errors still persist, as shown in Section 5.1 ("Comparison of downwelling radiation obtained using the STM and DLS") and Figure 6(d) of our paper. Therefore, in our next research, we will take your suggestions into consideration and explore ways to further improve the accuracy of the data.

As for your second point, we humbly accept your feedback. Indeed, some methods, such as the combination of reflectance panels and DLS, have already been applied, and we have highlighted this in the second paragraph of the introduction (lines 92–112). Additionally, I have highlighted the processing workflow after installing DLS in the introduction and listed the relevant parts where we compare the DLS and reflectance panel methods with our STM model: lines 268–280 and 298–307 in Section 4.1 ("Comparison of CRP Reflectance Calculated by the Different Methods"), lines 368–371 in Section 4.3 ("Reflectance of Typical Features"), and lines 422–443 in Section 5.2 ("Comparison of STM and Histogram Matching Method"). Please kindly review these sections.

Once again, thank you very much for your comments and suggestions, which have been extremely helpful to us.

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

Congratulations to authors for the effort revising the comments I tried to sugestivo to this interesting paper.

Hope our conversation could help to include some diferent help to the readers