The Right Triangle Model: Overcoming the Sparse Data Problem in Thermal/Optical Remote Sensing of Soil Moisture
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper succeeds in highlighting the benefits and rationale of the simplified right triangle approach -- for the estimation of the evaporative fraction (EF) and soil moisture (Mo) using a combination of remotely sensed observations of vegetation cover fraction and land surface temperature -- instead of more complex parameterizations, particularly in situations with sparse data.
Much of the content of the manuscript appears to have been previously published, namely Carlson (2020) and Carlson (2023), so its suggested that the author clarify and highlight the novel and/or original aspects of the work being presented here.
for reference:
Carlson, T. N., 2020: A brief analysis of the triangle method and a proposal for its operational implementation. Remote Sensing, 33212, 3832
Carlson, T. N., 2023: A critique of the triangle method and a version suitable for estimating soil moisture from satellite imagery, 334 J. Geography, Environment and Earth Science International. 27, 1-16. ISSN: 2454-7352)
One issue that stood out is around the statement (line 66) that "A salient feature of these images are well-defined edges to the pixel envelope." Qualitatively speaking this seems overwhelmingly true, but quantitatively, accurate placement of the lines at these bounding warm and cold edges seems to be a remaining challenging, and uncertainty in placement would seem to have significant impacts on the accuracy of the predictions. It would therefore be informative for potential users and those trying to gauge the efficacy of this approach to know how sensitive the predictions are to the placement of these warm and cold lines, both in theory and in practice.
On the latter point, the author notes (line 235) that the simplified right triangle approach requires only specification of the minimum and maximum surface temperatures (Tmax and Tmin) corresponding to minimum (NDVImin) and full (NDVImax) vegetation cover for a given area, from which the necessary equations defining the warm and cold edges can be determined. This clearly offers a practical solution to characterize the triangle, particularly in situations with sparse data. However, accurate determination of these values (Tmax at NDVImin and Tmin at NDVImax) seem to lie at the crux of the problem, since the simplified right triangle approach, as robust an approximation as it seems to be, still requires characterization of these few, and therefore most likely, critical values. The author only offers (line 236) that these values are "determined from the larger image, (Rahimzadah et al., 2012)". While it seems clear via the argument and evidence presented that a multitude of studies over many years have largely failed to produce results that warrant more complex models than a simple right triangle requiring only two temperatures (Tmax at 0 and Tmin at 100% cover), the challenge still remains to estimate these two temperatures in a reliable and routine fashion for even the much simpler right triangle. Given the importance of this problem, it seems appropriate to make this point clearer so as to help advance the field with clarity around the outstanding questions. If suitable methods already exists to estimate these values, it would help to reference them and/or briefly expand on the reference to the work by Rahimzahah et al. (2012).
Author Response
Thank you very much for your comments. Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsI have started reviewing the manuscript but could not complete it in time due to the heavy workload currently placed on academics. When I requested an extension to complete the review, the editor informed me that the academic editor had already made a decision, so I could decline the review invitation if I had not yet started. Since the academic editor has already made a decision, I see no point in continuing my review. However, I would like to provide my comments up to the point I have reviewed, as they may help improve the article. I apologise for not providing a systematic and refined version of the review due to the reason mentioned above.
It is a pleasure to review a paper by the author who first introduced the triangle model for estimating soil moisture using LST and vegetation index data. I highly regard this as a valuable contribution to the literature. However, I have some comments for the author to consider.
Firstly, I'm not sure if this paper fits under MDPI Remote Sensing's 'article' category. It does not present significant new data analysis or a structure that aligns with MDPI's guidelines for an article. MDPI Article Types. I believe it fits better as a 'Technical Note.'
- The author claims that the triangle method does not require ancillary data (external data) in several instances throughout the paper, including the abstract and introduction. However, this depends on how you define external/ancillary data in this context. One might argue that NDVI (or even LST data) is ancillary data when the focus is on soil moisture.
L34: Isn't the difficulty of being used as an algorithm applicable to a time series (or the scene dependency) another limitation?
L41: "This paper approaches the problem of remote sensing of soil water content based on 41 a right triangle model using remotely sensed optical/thermal measurements." Could you please refine this sentence to add more context and clarity or possibly combine it with the next sentence? A clearer explanation of the paper's objective would help readers.
L48: "Fr is derived from the normalized difference vegetation index (NDVI; Equation 2)." - Please move this sentence after Eq (1).
L48: Please explain whether Tmax and Tmin are the maximum and minimum pixel temperatures of a scene/image.
L58-60: References needed.
L63: Figure 1: How can T* have values < 0? For that to happen, Tmax should be less than Tir.
Fig1: What does the color coding in Figure 1 represent? A figure legend is needed.
- It would be beneficial to add more context on the objective and what you aim to address with the article, as readers may not be fully familiar with the triangle method.
There are several language errors throughout the manuscript. I have only listed the ones I noted up to the point I reviewed. I suggest checking the entire article for such issues.
Line 22: Change the comma to a full stop at the end of this sentence. "..literature (Carlson, 2023),"
Line 29: Change "...do soils (Piles et al., 2011)" to "...soils do (Piles et al., 2011)."
L42: ". measurements. In..." - Remove the extra space.
L61: Eq 2 appears twice. Remove the one at L61.
L72: Remove the extra space in "....of Fr. It is..."
There are several language errors throughout the manuscript. I have only listed the ones I noted up to the point I reviewed. I suggest checking the entire article for such issues.
Line 22: Change the comma to a full stop at the end of this sentence. "..literature (Carlson, 2023),"
Line 29: Change "...do soils (Piles et al., 2011)" to "...soils do (Piles et al., 2011)."
L42: ". measurements. In..." - Remove the extra space.
L61: Eq 2 appears twice. Remove the one at L61.
L72: Remove the extra space in "....of Fr. It is..."
Author Response
Thank you very much for your comments. Please see the attached file.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsInnovative:
In this paper, a right triangle model is proposed to solve the sparse data problem in the thermal/optical remote sensing of soil moisture. By further simplifying the triangle model with the use of right triangle shapes, the authors attempt to address the effect of data sparsity on soil water estimation and show the trend of right triangles over time, i.e. the migration direction of a point on the surface at scale surface radiative temperature (T*) and vegetation coverage (Fr), which is the first of its kind in the existing literature.
Theoretical basis:
In this paper, the theoretical basis of the right triangle model is fully explained, and how the model uses the relationship between the data to compensate for the problem of data sparsity is explained. The whole canopy temperature, surface temperature and soil moisture values at different vertical ground heights were analyzed.
Results and analysis:
The experimental results show that the right triangle model has a good performance in dealing with sparse data problems, and the conclusion is consistent with the evidence and arguments, and the quotation is appropriate. However, the analysis of the results in the paper can be more in-depth, and it is recommended to increase the quantitative evaluation of the model's performance and compare it with other existing methods to more fully demonstrate the advantages and limitations of the model.
Literature review:
The literature review part of the paper is relatively concise, and it is suggested to expand the literature review in related fields, especially the latest research on soil water estimation and sparse remote sensing data, so as to enhance the background background and research significance of the paper.
Language and format:
The language of the paper is generally clear, but there are some errors in details and inaccurate descriptions. For example, line 244 qqqq clerical error problem. It is recommended that the author proofread carefully during the revision process to ensure the accuracy and academicity of the language, while paying attention to the format specification of the paper to ensure the logical coherence between the various parts.
Overall, this paper presents an interesting model and validates its validity to a certain extent, but it still needs to further improve the theoretical elaboration, results analysis and literature review to enhance the overall quality of the paper and academic contribution. It is hoped that the author can fully consider these opinions in the process of revision and further improve the content of the paper.
Author Response
Thank you very much for your comments. Please see the attachment below.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThis paper presents an analysis and application of the right triangle model in the context of thermal/optical remote sensing for estimating soil moisture and evapotranspiration. The paper uses examples from Sentinel-3 images to illustrate the right triangle configuration, which is a strong way to demonstrate the model's applicability. The comparison between the right triangle model and the trapezoid model is insightful, highlighting the advantages of the former in terms of simplicity and data requirements. The paper acknowledges the limitations of the triangle method, such as the need for sufficient points to define the triangular shape and the subjectivity in visual construction. I have the follow comments.
1. While the paper discusses the potential of the model, it lacks a detailed statistical analysis comparing the right triangle model with existing methods, which would strengthen the argument.
2. While the right triangle model presented in this paper offers a promising approach for thermal/optical remote sensing of soil moisture, it would be beneficial to explore its applicability or adaptation to microwave-based soil moisture sensing. Microwave remote sensing has distinct advantages, particularly in its ability to penetrate through vegetation and provide measurements less affected by cloud cover and atmospheric conditions (or indicate as future works) .
3. L22, "m"any
Author Response
Thank you very much for your comments. please see the attachment below.
Author Response File: Author Response.pdf
