Evaluation of the Accuracy of the Remote Determination of the Brewster Angle When Measuring Physicochemical Parameters of Soil

Round 1

Reviewer 1 Report

Dear Authors, 

The manuscript "Evaluation of the Accuracy of the Remote Determination of the 2 Brewster Angle when Measuring Physicochemical Parameters 3 of Soil " is very good and scintific. I think minor changes need to implemented to improve paper quality further. All of them are as mention:

1) Figure 3, 5 7, 8, 10(b,c), 11(a,c), 12, and13 have annoying line below. please remove that. Its frustating.

2) Referencec are fewer. I would like to suggest to add few more.

3) Authors please mention novelty in your work.

4) Comparative study is missing. I suggest to add comparative study.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

1) Figure 3, 5 7, 8, 10(b,c), 11(a,c), 12, and13 have annoying line below. please remove that. Its frustating.

All unnecessary lines have been removed in indicated figures. All figures in the text of the manuscript are presented in vector format.

2) Referensec are fewer. I would like to suggest to add few more.

The following resources have been removed from References

15. Nagib, N.N.; Abdallah, A.; Bahrawi, M.; Mousa, E. Novel polarimetric method for determination of the Brewster angle of a dielectric. Results in Optics 2020, 1, 100006. https://0-doi-org.brum.beds.ac.uk/10.1016/j.rio.2020.100006. (duplicate);
16. Xu, Z.; Ferraro, D.; He, Y.; Zaltron, A.; Galvanetto, N.; Sun, L.; Wang, Y.; Wu, J.; Dong, J.; Yang, P.; Zhang, Y.; Liu, Z.; Merano, M. Pseudo-Brewster angles for monolayer-MoS2 and graphene immersed in a dielectric medium. Thin Solid Films 2022, 761, 139491. https://doi.org/10.1016/j.tsf.2022.139491).

Publications were analyzed and four more sources were added to the list of cited sources (the text highlighted in red, after agreement with you, will be added to the manuscript):

5. Srivastava, P.K.; Prasad, R.; Kumar, S.C.; Yadav, S.A.; Sharma, J.; Suman, S.; Pandey, V.; Singh, R.; Gupta, D.K. Chapter 20 - Challenges in Radar remote sensing. Radar Remote Sensing, 2022, 377-387. https://0-doi-org.brum.beds.ac.uk/10.1016/B978-0-12-823457-0.00020-3.

6. Zajícová, K.; Chuman, T. Application of ground penetrating radar methods in soil studies: A review. Geoderma, 2019, 343, 116-129. https://0-doi-org.brum.beds.ac.uk/10.1016/j.geoderma.2019.02.024.

9. Shakya, A.K.; Ramola, A.; Kandwal, A.; Vidyarthi, A. Soil moisture sensor for agricultural applications inspired from state of art study of surfaces scattering models & semi-empirical soil moisture models. Journal of the Saudi Society of Agricultural Sciences, 2021, 20(8), 559-572. https://0-doi-org.brum.beds.ac.uk/10.1016/j.jssas.2021.06.006.

17/ Thomson, L.I.; Osinski, G.R.; Pollard, W.H. Application of the Brewster angle to quantify the dielectric properties of ground ice formations. Journal of Applied Geophysics 2013, 99, 12-17. https://0-doi-org.brum.beds.ac.uk/10.1016/j.jappgeo.2013.08.015.

26. Kookhyun Kim, K.; Kim, J.-H.; Cho, D.-S. Radar cross section analysis of marine targets using a combining method of physical optics/geometric optics and a Monte-Carlo simulation. Ocean Engineering 2009, 36(11), 821-830. https://0-doi-org.brum.beds.ac.uk/10.1016/j.oceaneng.2009.05.005.

27. Khmelinin, A.P., Konurin, A.I., Denisova, E.V.: Simulation of electromagnetic high-frequency wave propagation processes in multilayer geo-structures. Geohazard Mechanics 2023. https://0-doi-org.brum.beds.ac.uk/10.1016/j.ghm.2023.04.001

28. Kawanishi, T. The shift of Brewster's scattering angle. Optics Communications 2000, 186 (4-6), 251-258. https://0-doi-org.brum.beds.ac.uk/10.1016/S0030-4018(00)01075-0.

3) Authors please mention novelty in your work.

In order to directly indicate the novelty of the results of scientific research, the text of the Abstract has been modified.

For the first time, it is proposed to use the phase shift between the oscillations of the interference waves with vertical and horizontal polarization to measure the Brewster angle.

4) Comparative study is missing. I suggest to add comparative study.

Thank you for your comment by responding to which we will improve our understanding of our article. It is proposed to make the following changes:

in Abstrast add :

A comparative evaluation of the accuracy of Brewster's angle determination by known amplitude methods and the proposed phase method has been performed.

Instead of: «Based on the developed model of the process of interference wave formation under oblique irradiation of a planar-layered lossy dielectric, we have estimated the accuracy of determining the Brewster angle using the amplitude method. The factors that influence the accuracy of determining the Brewster angle are identified. It is proposed to use the phase shift between the oscillations of vertically and horizontally polarized interference waves to measure the Brewster angle.».

Suggested: Based on the solution of the Helmholtz wave equation for a three-layered structure of the propagation medium (air, upper fertile soil layer, soil layer below the groundwater level), a model of the process of forming an interference wave under oblique irradiation of a planar layered dielectric with losses has been developed. Using the developed model, factors influencing the accuracy of determining the Brewster angle have been identified. For the first time, it is proposed to use the phase shift between the oscillations of the interference waves with vertical and horizontal polarization to measure the Brewster angle. A comparative assessment of the accuracy of determining the Brewster angle using known amplitude methods and the proposed phase method has been carried out.

in Results add :

A comparative assessment of the accuracy characteristics was conducted for the four methods of measuring the Brewster angle: ...

Thank you for your attention to our article.

Reviewer 2 Report

Remote radar sensing techniques are able to measure soil moisture and other parameters. When incidence angle is close to the Brewster’s angle under vertical-polarization, the penetration of electromagnetic waves through the "air-surface" interface shows a minimum reflection coefficient. The reflection coefficient (strictly speaking, scattering coefficient) of "air-surface" interface as well as Brewster’s angle depend on the complex dielectric permittivity of the surface soil layer, as well as roughness. As a matter of fact, the scattering mechanism of electromagnetic wave from "air-surface" interface is extremely complicated. Consequently, it is not easy to determine the Brewster’s angle for rough soil surface. In this manuscript, it is proposed to use the phase shift between the oscillations of vertically and horizontally polarized interference waves to measure the Brewster angle. The adequacy of the method was experimentally confirmed.

Specific comments are as follows:

1. The influence of soil surface’s roughness on the accuracy of measuring the Brewster’s angle should be discussed.

2. In this manuscript, Fresnel formula are used for measuring complex reflection coefficients for the vertically and horizontally polarized waves. The validity region of Fresnel formula should be checked.

3. For measuring Brewster’s angle, a comparison between calculated and measured results should be given and discussed.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

1. The influence of soil surface’s roughness on the accuracy of measuring the Brewster’s angle should be discussed.

The authors agree with the reviewer's opinion about the significant influence of soil roughness on the accuracy of Brewster's angle determination, so the roughness coefficient was introduced when modeling the process of reflected signal formation. This coefficient takes into account the reduction of the signal amplitude from the degree of diffuseness of the reflection. Initially, for the developed method, the requirements for the size of irregularities were determined from the Rayleigh condition h<λ/8cosφ, not explicitly presented in the paper. Then, according to the results of varying the standard deviation of roughness sizes, the conclusion about the limiting value of this parameter was made.

Suggest the following adjustments to the manuscript  (the text highlighted in red, after agreement with you, will be added to the manuscript.) :

Instead of:  «The influence of soil irregularities, surface roughness on the nature of reflection is as-sessed on the basis of the Rayleigh criterion [25].»

Suggested: The irradiation of the Earth's surface is intended to be carried out in accordance with the Rayleigh criterion [29]: 

h<λ/8cosφ.

2. In this manuscript, Fresnel formula are used for measuring complex reflection coefficients for the vertically and horizontally polarized waves. The validity region of Fresnel formula should be checked.

The process of reflection and refraction of electromagnetic waves at the air-surface interface is considered in the paper in a general form and is represented by analytical expressions in complex form without limiting assumptions (the boundary surface is smooth enough, the roughness dimensions satisfy the Rayleigh condition; the media are isotropic within the layer; the first and second Snellius laws are satisfied). Therefore, there are no restrictions on validity region of the Fresnel formulas.

3. For measuring Brewster’s angle, a comparison between calculated and measured results should be given and discussed.

Unfortunately, the permissible length of the article did not allow us to cite the results of experimental studies available to us beyond what is illustrated in Figure 4 and Table 1.  The results obtained under other conditions also showed good convergence of experimental and theoretical data.  We are ready to present the results of comparative studies in other conditions on request.

Thank you for your attention to our article. 

Reviewer 3 Report

Reviewer(s)' Comments to Author:

In this paper, the authors measure the Brewster angle by using the phase shift between the oscillations of vertically and horizontally polarized interference waves. The findings demonstrate that information about the Brewster angle lies not only in the minimum amplitude of a vertically polarized interference signal, but also can be provided by phase difference between vertically and horizontally polarized interference waves. The boundary conditions determining the applicability of different methods for estimating the Brewster angle have been examined. Furthermore, the adequacy of the method is experimentally confirmed.

In general, the idea of this paper technically makes sense; and the manuscript is easy to follow. Hence, I may suggest a minor revision for this work. However, the following issues should be addressed:

Detailed comments: 

1-    There is a need to strengthen the Abstract. The author should improve the abstract to include the following in its body: a brief background, brief description of methods and results.

2-    The author doesn’t mention the actual problem statement, what are the specific questions that the author is going to answer?

3-    Provide the article structure at the end of the introduction section.

4-    The introduction should briefly indicate the main contributions of this paper in bullets, before the article structure at the end of the introduction section.

5-    The paper does not provide any insights into the interpretability of the obtaining results.

6-    The quality of the figures 4-10 are not good enough. Kindly, insert high-quality figures.

7-    The references are sufficient, recent and within the field of specialization associated with the title of the paper.

8-    How did the authors set the parameters? Please explain why the settings of the parameters are picked.

9-    The authors did not discuss the limitations of the proposed approach, and the potential future directions for improvement.

10- Errors in using the singular and plural forms of nouns Errors in the singular and plural forms of nouns.

11- Language in the whole manuscript requires improvements. There are some grammatical issues throughout the paper.  Some grammatical errors and expressions need to be further improved.

English language fine. Just, some minor editing is required

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

1    There is a need to strengthen the Abstract. The author should improve the abstract to include the following in its body: a brief background, brief description of methods and results.

We fully agree with your comments and suggest adding the following text to the Abstract section (the text highlighted in red, after agreement with you, will be added to the manuscript.)

Based on the solution of the Helmholtz wave equation for a three-layered structure of the propagation medium (air, upper fertile soil layer, soil layer below the groundwater level), a model of the process of forming an interference wave under oblique irradiation of a planar layered dielectric with losses has been developed. Using the developed model, factors influencing the accuracy of determining the Brewster angle have been identified. For the first time, it is proposed to use the phase shift between the oscillations of the interference waves with vertical and horizontal polarization to measure the Brewster angle. A comparative assessment of the accuracy of determining the Brewster angle using known amplitude methods and the proposed phase method has been carried out.

2    The author doesn’t mention the actual problem statement, what are the specific questions that the author is going to answer?

We fully agree with your comments and suggest that the following text be added to the manuscript (Introduction section):

A contradiction arises between the active use of remote sensing methods for measuring the physico-chemical parameters of soil, including the use of the Brewster effect, and the lack of a scientific and methodological apparatus that sufficiently allows for the evaluation of the influences of different factors on the accuracy of determining the Brewster angle and other parameters based on it.

To achieve the set goal, it is necessary:

• to develop a mathematical model of electromagnetic wave interference;
• to carry out an experimental verification of the adequacy of the developed model;
• to conduct a study of the mathematical model to identify the factors influencing the accuracy of determining the Brewster angle;
• to develop recommendations for the use of the known amplitude and proposed phase methods for measuring the Brewster angle under various conditions;
• to demonstrate how, by measuring the Brewster angle, we can estimate the physical and chemical parameters of the soil using the example of determining its volumetric moisture content.

3    Provide the article structure at the end of the introduction section.

And 

4    The introduction should briefly indicate the main contributions of this paper in bullets, before the article structure at the end of the introduction section.

In response to comments 3 and 4, it is suggested that the following terms be added at the end of the Introduction section:

The solution to the first two problems is presented in the Research Methodology section. The section Results is dedicated to the study of the mathematical model of interference and the evaluation of its accuracy. The recommendations for using the known amplitude and newly proposed phase measurement methods for estimating the physical and chemical parameters of soil are given in the Discussion section.

5    The paper does not provide any insights into the interpretability of the obtaining results.

The authors fully agree with your comments and suggest adding the following text to the manuscript (Conclusions section)

The obtained results of mathematical modeling, theoretical and experimental research enable remote measurement of the soil’s physical and chemical parameters such as moisture content with an accuracy sufficient for the rational crop management using precision farming technology.

Timely remote determination of soil moisture at different stages of development of agricultural plants will allow a reasonable choice of rational agrotechnical measures. Further research will aim to evaluate the cation exchange capacity, the particle size distribution (granulometric composition) and the humus content of soil by measuring the Brewster angle and the complex dielectric constant of soil.

6    The quality of the figures 4-10 are not good enough. Kindly, insert high-quality figures.

We have changed the format of presentation of figures, after which, we hope, their quality has become sufficient.

7    The references are sufficient, recent and within the field of specialization associated with the title of the paper.

Thank you for this assessment of the research we have done on the state of the issue.

8    How did the authors set the parameters? Please explain why the settings of the parameters are picked.

The set of parameters selected for mathematical modeling is typical corresponding to real conditions in which the developed method is supposed to be applied. In particular, the characteristics of electrical conductivity correspond to the parameters of soil cover of different soil types and different percentages of moisture content. The set of parameters given in the article is not the only one at which good coincidence of theoretical and experimental data is observed.

It is proposed to supplement the text of the article  (Research Methodology section, page 3) as follows:

The input data used for modeling correspond to the typical conditions of remote sensing techniques used to determine the physical and chemical parameters of agricultural soils.

9    The authors did not discuss the limitations of the proposed approach, and the potential future directions for improvement.

We thank you for the opportunity to eliminate the mistake that we made, related to the absence of the statement of the prospects of application of the developed method. It is proposed to add the following lines to the Conclusion section:

The authors associate the prospects for further research on the accuracy of the Brewster angle measurement with the combination of amplitude and phase methods, as well as with the application of digital processing of interference signals.

10  Errors in using the singular and plural forms of nouns Errors in the singular and plural forms of nouns.

and

11 Language in the whole manuscript requires improvements. There are some grammatical issues throughout the paper.  Some grammatical errors and expressions need to be further improved.

Additional analysis of grammatical errors has been performed. The changes made are highlighted in the text of the manuscript.

Thank you for your attention to our article.

Round 2

Reviewer 2 Report

I have no further questions, you have answered to all my questions.