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The Potential of the Least-Squares Spectral and Cross-Wavelet Analyses for Near-Real-Time Disturbance Detection within Unequally Spaced Satellite Image Time Series

Remote Sens. 2020, 12(15), 2446; https://doi.org/10.3390/rs12152446

by Ebrahim Ghaderpour^1,*

and Tijana Vujadinovic²

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Remote Sens. 2020, 12(15), 2446; https://doi.org/10.3390/rs12152446

Submission received: 10 June 2020 / Revised: 14 July 2020 / Accepted: 29 July 2020 / Published: 30 July 2020

(This article belongs to the Section Forest Remote Sensing)

Round 1

Reviewer 1 Report

The manuscript “The potential of the least-squares spectral and cross-wavelet analyses for near-real-time disturbance detection within unequally spaced satellite image time series” describes a new method/technical solution for using unequally spaces remote sensing observation for detecting changes or breaks in remote sensing time-series monitoring approaches. It addresses a very important topic and challenge in time-series analysis and monitoring using remote sensing observations. Thus far most methods require evenly spaced and continuous observations throughout the year, conditions, which are often not feasible, particularly with optical data with higher resolution.

The presentation of the manuscript is very technical and mostly of theoretical nature and it is notable that authors have a strong mathematical background, but probably a lack of experience in remote sensing. This is favorable for the development of this method and thorough analysis of model simulations. As I am more an expert on the application side, rather that the theoretical background, I cannot safely judge the quality of the theoretical background.

However, the application part of this method on remote sensing data needs significant improvement. For readers, with a stronger background in the application of time-series methods (like me), rather than the development, it can be very hard to follow the content. The used study site is rather small and I consider adding more landscape variety and a larger variety of temporal changes (not only 2019). Furthermore, the validation of the real-world example is somehow unclear, e.g. how many samples did the authors use, what the results are, etc.

Overall this manuscript has potential for publication, but needs improvement, particularly on the application part and the validation of the real-world example. The language is good overall, but may need some smaller fixes. Specific remarks are stated below:

General positive and negative remarks (more detailed remarks below):

Positive:

The authors addressed a very important topic, which is essential for time-series analysis and near-real time monitoring especially with data of higher-spatial resolution and areas of challenging environmental conditions where temporally equally spaced data are unlikely.

The authors conducted several simulations and presented the advantages and limitations clearly.

Code is available.

Negative:

The practical application is rather limited and needs some improvement. The study site is too limited (spatially, land-cover diversity, fire dates), which limits the understanding of transferability and scalability. I suggest applying a broader analysis, across different sites and with disturbances in different periods.

The explanation of used data (real-world experiment), is rather limited and needs more detail.

Methods:

62: “Now the question is”. I think this sounds a bit sloppy and can get improved

Figure 3: The figure is good to understand the sensitivity of the method.

180: “Thousands of time series”. How many? Be precise.

182: You created random, normally distributed noise. Is noise in EVI Data randomly distributed or is it biased (negatively)? Please check if this is the case. If I remember correctly TIMESAT assumes non-normally distributed noise.

L: 263 ff. Geographical coordinates would be nice to have, to find the place more easily. Most readers will not know where High Level is located. A general overview map with the location would be helpful.

L 265: “storehouse”. This is a somehow strange formulation.

Figure 4: It is really hard to see the details of that figure. Overall this figure needs some improvement, e.g. more appropriate colormaps, better readability of text (A, B, C).

Figure 4: I suggest having panels A+B in a separate figure and an overview map.

Figure 4 c: Date of last change: This figure implies that the entire area has changed at some point after 2014. Is that really the case?

Figure 4 c-f are really hard to grasp due to strongly pixelated appearance. c and d may be removed completely as they are not highly important. Selecting a subset may help in that case or a resampling to better than 300m.

275: I think exact location names are irrelevant in this case.

278 ff. This part needs more information. Which Landsat sensors?, I guess it’s only L8. Why not the others? Did you apply some filtering before, e.g. by cloud cover?

283: I understand that you used EVI only, but I suggest that you also use NDVI 1) to have a comparison to EVI and 2) most readers expect to have NDVI included, as it’s still the most widely used index (although you mentioned its disadvantages).

284: Please provide more detail how you defined the uncertainties?

288: Results general: This part is quite descriptive, but I am missing quantitative validation, which you provided for the simulations.

289ff: I think this part should go to the Data section. How is the fire data structured? Is it from a report only or do they have vector/polygon datasets? These could help to properly validate your results.

301: better name the dataset

301: does this dataset include polygons to validate the entire area?

309: Table2: Caption “Some…” not the very best style.

309: Table2: Why is the lowest row separated from the others by a line? Is the area of that fire that large? The others were much smaller.

316: You say here that there is no disturbance in only 13 %. This is quite a small area and highly undersampled in a larger scale context. How did you chose your study area and is it representative for a larger area?

324: do they have proper geographic information rather than just points?

Figure 5: good to have an example where it is not working

339: “a few more”. Please be more precise

343ff: 4.2 temperature time-series might work for boreal forest and areas with very distinct seasonality, but is it also working for other land cover? I am not sure if you should keep it in here as the relation is not as simple, especially when it comes to more complex landcover. I keep it up to your discretion.

I think you should keep precipitation out. There are surely seasonal patterns, but the distribution is in my opinion way too inconsistent to relate it to spectral time-series.

378: First sentence is kind of strange

384 ff: What about a technical solution? E.g. choosing “recovery time series” from other, similar disturbance sites from previous years and using longer time-series.

398: You say that you achieved 87% accuracy. Is it stated in the results as well? Maybe I just missed it.

437: I think this part, particularly the numbers, could go into results. You mentioned that the method is rather light-weight. Reading the results I expected it to be stated there. Maybe you can have a short paragraph on the computational cost there.

440 ff. I guess it also depends on the hardware and implementation (parallelization?) If you move it to the results you can say a brief sentence about your configuration and that it took x amount of time on average. It would be interesting to have the comparison to “computationally expensive” algorithms to see if it is really that much different.

446: globally applicable. Maybe this is a bit too optimistic as this was

Author Response

Dear Reviewer,

We thank you very much for your comprehensive comments that we think they have significantly improved the presentation of our paper. We have tried to address them all and highlighted the changes in the manuscript. The structure and format of the manuscript have changed. Please see attached the responses in PDF format for your convenience.

General positive and negative remarks (more detailed remarks below):

Positive:

The authors conducted several simulations and presented the advantages and limitations clearly.

Code is available.

Negative:

The explanation of used data (real-world experiment), is rather limited and needs more detail.

We have provided further technical details in the manuscript according to your comments and checked the grammar and spelling. We have described why we selected this study region in Sections 2.1 and 2.2. We also added a flowchart describing the monitoring method (see Figure 3).

The line numbers in my answers correspond to the new version.

Methods:

62: “Now the question is”. I think this sounds a bit sloppy and can get improved

Line 157. For the near-real-time monitoring, however, the goal here is to determine whether the newly acquired observations …

Figure 3: The figure is good to understand the sensitivity of the method. Thank you!

180: “Thousands of time series”. How many? Be precise.

Line 272. The sensitivity (true-positive rate) and specificity (true-negative rate) of the proposed monitoring method are examined by simulating EVI time series.

Also, more details are provided in that paragraph.

Two independent random noises of the same type were added. One remains often after the cloud masking, and the other one can be used to define the statistical weights. Please see lines 279-291.

Figure 1 is added.

L 265: “storehouse”. This is a somehow strange formulation.

Line 84: The Canadian boreal forest stores approximately 11% of the world’s total carbon, purifies the air and water and regulates the climate [32].

Figure 4: It is really hard to see the details of that figure. Overall this figure needs some improvement, e.g. more appropriate colormaps, better readability of text (A, B, C).

Figure 4: I suggest having panels A+B in a separate figure and an overview map.

The former Figure 4 is now split into Figures 1 (contains panel a), 2 (contains panel b), and 7 (panels c-f).

Figure 4 c: Date of last change: This figure implies that the entire area has changed at some point after 2014. Is that really the case?

No. About 10% of the figure has not changed from 2013 to 2019 by our analysis.

Lines 351-354:

No significant historical changes are detected for approximately 10% of the study region, see the black pixels in Figure 7(a). Though SHPs for these areas can be longer than six years, the trend and seasonal components can still be approximated very well for the six-year period, effective for disturbance detection during MP.

Also, Lines 330-332:

Though SHP longer than six years may further improve the probability of disturbance detection, a six-year SHP is still pretty efficient.

It is described in detail in section 2.2.1 how the spatial resolution is set up and why we did it this way. Also, the quality of the images is improved.

275: I think exact location names are irrelevant in this case. Removed that sentence.

278 ff. This part needs more information. Which Landsat sensors? I guess it’s only L8. Why not the others? Did you apply some filtering before, e.g. by cloud cover?

Yes. It is Landsat 8. We added a paragraph (lines 108-111) explaining why:

To increase the temporal resolution, other sensor data may be included, such as Landsat 7 Enhanced Thematic Mapper (ETM+). However, since Landsat 8 Operational Land Imager (OLI) has improved calibration and signal-to-noise characteristics compared to Landsat 7 (ETM+) and with different sensitivity to surface reflectance and atmospheric state, it is difficult to properly link their EVI values [35]. This may cause undesired biases in the EVI time series which prevents rigorous testing of the proposed monitoring method. Therefore, the use of other sensor data is not in the scope of this research and is subject to future studies.

Figure 9 is added that targets the same per-pixel time series as Figure 8 but NDVI is used instead of EVI to compare the two indices for change detection (300m resolution). We do appreciate this comment which helps to reveal the challenges for monitoring land cover changes using different indices. For high latitude regions the canopy background noise (snow, ice) reduces NDVI significantly that can be detected as a change (increasing the false-positive rate). We added two paragraphs:

Lines 383-396:

To compare the change detection results using different vegetation indices, the weighted per-pixel NDVI time series are also calculated for pixels A, B, and C (300m resolution), and the monitoring results are illustrated in Figure 9. SHPs and the detected disturbances shown in Figure 9(a) and (c) agree with the ones shown in Figure 8(a) and (c). However, SHP is not correctly determined for pixel B. The ALLSSA season-trend model breaks down at the end of the historical time series, i.e., the model detects the observation pointed by the red arrow in Figure 9(b) as an outlier. This is mainly due to the presence of canopy background noise (e.g., snow and ice) that significantly reduces the NDVI value, and also the FMask algorithm has not properly identified the presence of clouds, snow, and ice on the 6th of November 2018, see a view of the clipped satellite image for pixel B in Figure 9(b). Therefore, the statistical weight defined from the FMask algorithm could not properly reduce the effect of this observation. EVI, however, did not have this issue mainly because EVI can attenuate canopy background and atmospheric noises and remain sensitive to canopy variations [16,37]. After ignoring this observation, ALLSSA provided a new season-trend fit, shown by the red dashed lines in Figure 9(b). Then, the disturbance in MP is currently detected.

Also:

lines 127-130:

For example, since NDVI values are usually higher than EVI values for healthy vegetation, cloud contamination can reduce the values of NDVI significantly more than EVI [16,37]. Thus, the statistical weights must be adjusted accordingly for better performance when using these indices.

Lines 266-267

… and a comparison is made between NDVI and EVI time series…

Lines 467-469

As shown in Figures 8 and 9, EVI time series appears to perform better than NDVI time series for near-real-time monitoring, yet both indices complement each other in global vegetation studies and improve upon the detection of vegetation changes.

284: Please provide more detail how you defined the uncertainties?

Lines 112-130 and lines 206-212 now describe more details of the uncertainties and statistical weights defined and used in this research.

288: Results general: This part is quite descriptive, but I am missing quantitative validation, which you provided for the simulations.

The simulation experiment had similar structures as the real-world EVI time series in the study region. Now the result section starts with the simulated examples and the real-world results are validated by the polygon shapefiles provided by the Natural Resources Canada and the Government of Alberta. Please see Figure 2 and lines 339-349.

301: better name the dataset

The data sets are now described in more detail in Section 2.2.2

301: does this dataset include polygons to validate the entire area?

Yes. Please see Figure 2 and lines 339-349. Please also see lines 143-151.

309: Table2: Caption “Some…” not the very best style. Fixed

309: Table2: Why is the lowest row separated from the others by a line? Is the area of that fire that large? The others were much smaller.

Lines 148-151:

The last row in Table 1 shows some information for the Chuckegg Creek Fire. An aerial view of this wildfire is also illustrated in Figure 2. No polygon shapefiles for the burned areas in 2019 are currently available for further comparisons and validations.

316: You say here that there is no disturbance in only 13 %. This is quite a small area and highly undersampled in a larger scale context. How did you choose your study area and is it representative for a larger area?

We have also described why we selected this study region in Sections 2.1 and 2.2. Further investigation of the effectiveness of our change detection method on other regions also show promising results. However, our main focus in this paper is analyzing vegetation time series within that particular region to show how the method treats inherently unequally spaced time series with long data gaps without any need for interpolation and gap fillings where most current change detection methods can fail.

324: do they have proper geographic information rather than just points?

Line 150: No polygon shapefiles for the burned areas in 2019 are currently available for further comparisons and validations.

Figure 5: good to have an example where it is not working

Figure 9(b) now shows an NDVI example that the automated method fails.

339: “a few more”. Please be more precise

Line 379: Four more observations..

I think you should keep precipitation out. There are surely seasonal patterns, but the distribution is in my opinion way too inconsistent to relate it to spectral time-series.

Yes. We agree with your comments, however, many researchers use far more questionable approaches to link the climate with vegetation, e.g., using manual gap fillings, simple box plots, simple correlation analysis, etc. Here, however, we show that the coherency analysis can provide phase difference information, coherency in the frequency domain which is a more robust analysis. To clarify the situation better and according to your comments, we added two sentences in Discussion:

Lines 476-479: However, note that the relationship between climate and vegetation may not always be straightforward especially when it comes to more complex land covers. LSCWA may help to investigate possible coherency between the components of two series, but it does not necessarily mean that such relationships must link different phenomena together.

378: First sentence is kind of strange

Edited:

Line 437: Based on the results in the previous section, the four questions raised in the introduction are discussed here.

384 ff: What about a technical solution? E.g. choosing “recovery time series” from other, similar disturbance sites from previous years and using longer time-series.

Added:

Line 443: For example, one may use the recovery time series from similar disturbance sites in previous years to use them for prediction

398: You say that you achieved 87% accuracy. Is it stated in the results as well? Maybe I just missed it.

Lines 340-349 now describe this stat in further details:

Twenty-seven hundred per-pixel EVI time series (30m resolution) are obtained within the known burned areas for model validation. From the PQA bands, all clear observations are selected to obtain these per-pixel EVI time series within all the seven numerically labeled locations shown in Figure 2 to test the SHP selection method without weights. Since the burned areas in locations 1, 2, 5, 6, and 7 are small, only four pixels (30m resolution) around the geographical coordinates of these locations are selected for the validation. The method could estimate the dates of disturbances caused by fire for 87% of these EVI time series within two-month accuracy. Furthermore, the weighted EVI time series (300m resolution) within the polygons are also analyzed separately using the weighted method, and the temporal accuracy of the detected changes was improved due to the inclusion of observations with higher uncertainties.

440 ff. I guess it also depends on the hardware and implementation (parallelization?) If you move it to the results you can say a brief sentence about your configuration and that it took x amount of time on average. It would be interesting to have a comparison to “computationally expensive” algorithms to see if it is really that much different.

We moved this paragraph to the end of section 3.2 lines 397-403 and added more details to it:

The computational complexity of the proposed method depends on several factors including the time-frequency resolution, covariance matrix (scale, diagonal, fully populated), hardware, and implementation. The entire process of the monitoring method including the downsampling of the clipped EVI images to obtain Figure 7 took approximately 15min in MATLAB on an average normal computer. The SHP selection process and monitoring a weighted time series of size 100 may take approximately 0.05s in MATLAB and 0.3s in Python. Also, only the monitoring (SHP is given) of a weighted time series of size 100 may take 0.001s in MATLAB and 0.006s in Python [59].

446: globally applicable. Maybe this is a bit too optimistic as this was

Of course, like many other change detection methods, this method needs further investigation for other land covers. However, we believe that the spectral method is one powerful method that can efficiently be used globally:

“If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration. We are just waves in time and space, changing continuously, and the illusion of individuality is produced through the concatenation of the rapidly succeeding phases of existence. What we define as likeness is merely the result of the symmetrical arrangement of molecules that compose our bodies” - Nikola Tesla

Thanks again for your constructive comments. Please kindly let us know if you have any further comments.

Best regards,

Ebrahim Ghaderpour

Author Response File: Author Response.pdf

Reviewer 2 Report

The investigation is relevant and offers a contribution to the analysis of time series generated from multispectral images. However, the manuscript must be restructured and better organized, in order to present methods and results with greater scientific rigor. Some general considerations about the manuscript are presented below.

- The Introduction has been confusing, fragmented, often inserting disconnected subjects in the same paragraph. Before addressing the issues to be investigated, it is necessary to clarify the general objective and some points that are recurrent in the manuscript, such as, what is a "consistent long gap".

- In the Methods section there is also an alternation of subjects within the same paragraph, making it difficult to follow the methodological development and analyzes. The structure of the topics in this section needs to be reviewed. The inclusion of one or more flowcharts showing the chain of activities would facilitate, not only the understanding of the methods proposed by the reader, but also a more appropriate definition and description of the topics by the authors.

- The experiments carried out with real and simulated data are consistent, but their presentation is very disordered. There is no problem in leaving the results of tests performed with simulated time series in the method section, but there must be a clear and linear narrative of their development.

- Sections 3 (Study area and data sets) and 4 (Results) deal exclusively with the time series obtained from real data (EVI values extracted from images and/or from climatic variables), but both mix presentation of data sets with development methodology and results. This experiment needs to be better systematized, perhaps by creating a more general section that includes sections 3 and 4. It is necessary to reorganize the content of sections 3 and 4 to ensure that results are not entered prematurely, before describing how they were generated (case of Figure 4), or that tables characterizing data appear in the middle of the analysis of results (such as the Table 2).

- The discussion section (which would become section 4, in this new structure) would continue to address the results obtained with real and simulated data, but in the same way that the conclusion needs to be better elaborated.

In addition to the general issues, some specific aspects deserve to be highlighted:

Line 35 – The main factor that must be considered when acquiring optical images is the cloud cover.

Line 56 – What is a "consistent long gap"? This is a definition that appears repeatedly in this work.

Line 66 – It is necessary to elaborate this aspect better. Which previous questions will be answered based on the simulated time series and which are treated with real data?

Line 85 – One or more flowcharts showing the methodological development would not only facilitate a more immediate understanding of the proposed approach, but would also help the authors to define more appropriate titles for the subsections of the method.

Line 135 – If the first step in the proposed change detection is the definition of an appropriate SHT, would it not be consistent to present first how SHT is specified and then show how it is used in monitoring near-real-time disturbances?

Line 159 – How was this simulated time series built? This is presented later in item 2.2. Shouldn't the procedure for creating the time series BEFORE you adopt one as an example?

Line 189 – Figure 2 is presented in another session (2.2). Presentation of the method is very disordered, which makes it difficult to follow the methodological development.

Line 211 – What is the purpose of reviewing this method in the context of this study? This section is not limited to reviewing the LSCWA and the title of this subsection should be consistent with the subject matter. It would be more appropriate to use the questions raised in the introduction as a reference to divide the subsections of the method (which could be something like: Analysis of coherence between time series using LSCWA ...).

Line 262 – Results with simulated time series were presented in the method. Sections 3 and 4 refer to time series obtained from real data and, again in these two sections, data, method and results are all mixed. It would not be better to create a more comprehensive section (3. EVI time series experiment, for example) and subdivides it into: 3.1- Study region and data sets integration and 3.2 - Results. Section 4 would continue to be a general discussion of the results.

Line 263 – A map indicating the geographic location of the study area is very efficient in showing the spatial distribution of the features of interest on the Earth's surface. I strongly suggest its inclusion.

Line 269 – Figure 4 needs to be subdivided and / or moved to another part of the manuscript. So far, only the image shown in Fig. 4 (a) has been included in the text. The explanation in the text of how the subsequent images were obtained and the meaning of the numbers and letters inserted, only appear in another section: results (in the text that is between pages 289 to 307, but that should be placed next to this figure 4).

Line 298 – This entire paragraph (between lines 289-298) refers to processing performed on the image. It doesn't stick very well to results.

Line 303 – Table 2 presents the characteristics of another set of data used. It certainly doesn't fit with the results!

Line 304 – This point needs to be further elaborated. Time series were generated from which spatial reference? The average of the EVI values of all pixels included in the burned areas, defined by A, B and C in the images (c) - (f) of figure 4?

Line 318 – What are the criteria used to define these three locations?

Were the time series generated for A, B and C constructed from the average EVI of the pixels included in the burned area? Why show location, if the information on how the reference areas of the analysis were defined is not present?

Line 360 – Figure 6 should be enlarged or divided into 3. It contains a lot of information and, for a proper interpretation, the details should be better understood.

Line 384 – Contains a placement that goes beyond the scope of the work developed. Propositions for other applications for the method fit better in the conclusion.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

We thank you very much for your comprehensive comments that we think they have significantly improved the presentation of our paper. We have tried to address them all and highlighted the changes in manuscript. The structure and format of the manuscript have changed. We also addressed all your comments in the PDF file that you included. Please see the attached PDF file the "Response to Reviewer 2 comments" for your convenience.

The line numbers in my answers correspond to the new version.

The structure of the paper is changed according to your comments and MDPI guidelines:

Introduction
Materials and Methods
- Study region
- Data sets and preprocessing
  - Satellite imagery
  - Validation data sets
- Monitoring method
  - Stable history period selection
  - Near-real-time disturbance detection
- Least-squares cross-wavelet analysis as an assessment method
Results
- Simulation experiment for validation of the monitoring method
- Disturbance detection in the study region
- Assessment of the results using the coherency analyses
Discussion
Conclusions

We have modified the introduction based on your comments and the changes are highlighted in the new version.

The structure of the manuscript is changed according to your comments. We added a flowchart describing the monitoring method (see Figure 3) where we describe the monitoring method.

The simulation experiment is now in the result section. We have checked several published papers in remote sensing journals and concluded that the new structure and formatting are more fluent.

Table 2 moved to Materials and Methods. Lines 262-270 in Results:

This section demonstrates the results of applying the proposed monitoring method to vegetation time series including assessments. First, the effectiveness of the method is evaluated by simulating EVI time series that have similar structures as the real-world EVI time series for the study region. Then, the method is tested by applying it to the collection of real-world EVI time series with a spatial resolution of 300m as described in the previous section, and a comparison is made between NDVI and EVI time series. The SHP selection results are also validated by the per-pixel EVI time series of resolution 30m, affected by the historical wildfires (see the details in Table 1). Finally, the monitoring results of three EVI time series, each corresponding to a square area of 9ha, are assessed by LSCWA, also showing the possible coherency between the EVI time series and temperature/precipitation time series.

The discussion and conclusion parts follow your comments now.

In addition to the general issues, some specific aspects deserve to be highlighted:

Line 35 – The main factor that must be considered when acquiring optical images is the cloud cover.

Line 38: First, the cloud cover is the main factor that must be considered when acquiring optical images.

Line 56 – What is a "consistent long gap"? This is a definition that appears repeatedly in this work.

Line 43: i.e., no valid observations are available in a certain season (e.g., November to April) every year due to the availability of satellite imagery, cloud cover, snow, etc.

Line 66 – It is necessary to elaborate this aspect better. Which previous questions will be answered based on the simulated time series and which are treated with real data?

Lines 69-71: The proposed monitoring method will be tested using simulated EVI time series to provide general solutions to the first three questions raised above. Then, using real-world time series these four questions will be discussed further.

Figure 3 shows the flowchart of the proposed monitoring method.

Indeed. Now in the Results (section 3.1) we first show one example of the simulated EVI time series used to obtain the probability of disturbance detection. First example is the SHP Figure 4 and then it comes Figure 5 for the monitoring part using LSSA. Then Figure 6 shows the probability of the disturbance detection against noise level.

Line 159 – How was this simulated time series built? This is presented later in item 2.2. Shouldn't the procedure for creating the time series BEFORE you adopt one as an example?

Yes. Fixed it now.

Line 189 – Figure 2 is presented in another session (2.2). Presentation of the method is very disordered, which makes it difficult to follow the methodological development.

Yes. Fixed it now. The simulation experiment is in Results (section 3.1) that now clearly links the reordered figures.

The title is changed to 2.4. Least-squares cross-wavelet analysis as an assessment method.

We have searched many other articles and follow the MDPI guidelines to define the sections.

Figure 1 is added.

The former Figure 4 is now split into Figures 1 (contains panel a), 2 (contains panel b), and 7 (panels c-f).

Line 298 – This entire paragraph (between lines 289-298) refers to processing performed on the image. It doesn't stick very well to results.

Modified and moved to Section 2.1 and 2.2

Line 303 – Table 2 presents the characteristics of another set of data used. It certainly doesn't fit with the results!

Moved to section 2.2.2 Validation data sets

Line 112-130 describe the pre-processing of the imagery:

Lines 115-118: … Herein, the EVI images are downsampled to a resolution of 300m for the sake of visualization purposes and computational efficiency. The downsampling of images is an optional process and should not be considered as a limitation of the proposed monitoring method…

For validation purposes, EVI time series with 30 m resolution are also used. We indicate them using parentheses (30m resolution) or (300m resolution) in the manuscript.

Line 318 – What are the criteria used to define these three locations?

Line 138-142: Three pixels A, B, and C (300m resolution) with known characteristics, according to the information at https://wildfire.alberta.ca/, are selected to assess the results of the monitoring method, displayed in Figure 2. Pixels A and B are in forested areas impacted by the Chuckegg Creek Fire and a wildfire started in August 2019, respectively. Pixel C is also in a forested area where no change is reported during 2019.

Section 2.2.2 describes in detail the validation data sets now.

Line 360 – Figure 6 should be enlarged or divided into 3. It contains a lot of information and, for a proper interpretation, the details should be better understood.

We enlarged it and enhanced its quality.

Line 384 – Contains a placement that goes beyond the scope of the work developed. Propositions for other applications for the method fit better in the conclusion.

The highlighted lines are moved to the last paragraph in Conclusions.

Thanks again for your constructive comments. Please kindly let us know if you have any further comments.

Best regards,

Ebrahim Ghaderpour

Author Response File: Author Response.pdf

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The Potential of the Least-Squares Spectral and Cross-Wavelet Analyses for Near-Real-Time Disturbance Detection within Unequally Spaced Satellite Image Time Series

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