PSDefoPAT—Persistent Scatterer Deformation Pattern Analysis Tool

Round 1

Reviewer 1 Report

 

The paper describes a tool that automatically selects and fits a time series model to displacement data obtained from advanced DInSAR processing. The article presents a structured description of the methodology and the Matlab tool and its application to real cases.

Although the underlying methodology has already been presented and studied in previous works from the same authors (acknowledged as references 14 and 15 in the article), the topic of the paper is of practical relevance and could be interesting for the readers. The article is well structured and well presented. The motivation for the work is clearly stated and the background is thoroughly analyzed. The application cases are meaningful, varied and well illustrate the potential of the tool.

 

Specific comments and suggestions:

• Is the tool available? Is the tool accompanied by a technical documentation (possibly with working examples) for the users?
• Can you give the reader an idea of the computation time of the tool? Does the tool exploits parallel computing? If not, I suggest to consider the possibility to parallelize the computation.
• Are the plots shown in Section 4 (such as figures 7, 8, 9) automatically produced by the tool?
• In Section 3.1.1, it is not clear which data the WT is applied to. Is it applied to the whole time series or is it applied to each window of the moving average approach?
• The definitions of p-value and threshold α should be revised throughout the article. Indeed, the p-value is the probability of observing a value of the test statistics at least as extreme as the one computed from the data under the assumption that the null hypothesis H0 is true and the threshold α (the significance level of the test) is the probability of rejecting the null hypothesis H0 when it is true.
• I suggest to merge the outlier detection step into the components estimation step by adopting robust regression estimators (for example M-estimators or least trimmed squares estimators).
• I suggest to evaluate the possibility to include in the model external information (such as weather conditions) in the form of covariates.

 

The manuscript needs English proofreading as some minor errors are present in the manuscript.

Some examples are:

• various extend of the active deformation area
• They represent the amplitude β0, frequency β1 and temporal offset in respect to a usual sine function β2 of the modeled time series.
• segemnts
• Each case study was chosen do incorporate
• effected
• The dam body is not homogeneously build
• the Italian peninsular

Author Response

Dear Reviewer,
Thank you for taking the time to review our manuscript. Your comments and suggestions are 
appreciated. In the following, I want to answer your comments and suggestions individually. For that 
reason, I will first repeat your comment or suggestion and then reply to it. To ease handling the review 
process, I will mark the reply in blue.
Reply to the comments and suggestions
“Is the tool available? Is the tool accompanied by a technical documentation (possibly with working 
examples) for the users?”
Even though we would like to make the tool publicly available, it is currently not. Unfortunately, we 
have to comply with our company policies. However, we are currently working on a solution to provide 
the tool to a wide range of users.
“Can you give the reader an idea of the computation time of the tool?”
Thank you for asking this question. The computation time varies with the number of time series that 
need to be processed. For example, the data set of the Fehmarnsund bridge has 9,447 MPs and takes 
roughly a few of minutes to process. A more extensive data set, such as the one covering the area of 
Campi Flegrei with 324,228 MPs needs about a few days to compute.
We also included this information in the manuscript (see lines 459 - 462).
“Does the tool exploit parallel computing? If not, I suggest to consider the possibility to parallelize the 
computation.”
The tool already utilizes parallel computing. However, we are still working on further optimizing its 
performance.
“Are the plots shown in Section 4 (such as figures 7, 8, 9) automatically produced by the tool?”
The plots displayed in Section 4 are automatically generated with a separate Matlab script but not 
during the automatic usage of PSDefoPAT. We are currently working on an additional package that 
handles the visualization of the results. The plots in question will be included there. 
“In Section 3.1.1, it is not clear which data the WT is applied to. Is it applied to the whole time series or 
is it applied to each window of the moving average approach?”
Thank you for pointing out this uncertainty. The wavelet transformation is applied to the entire time 
series. Only extreme outliers are excluded from this step. Following your comment, we revised the
relevant paragraphs, hoping to describe the application of the wavelet transformation more clearly 
(see lines 231 & 274).
“The definitions of p-value and threshold α should be revised throughout the article. Indeed, the pvalue is the probability of observing a value of the test statistics at least as extreme as the one 
computed from the data under the assumption that the null hypothesis H0 is true and the threshold 
α (the significance level of the test) is the probability of rejecting the null hypothesis H0 when it is 
true.”
Thank you for pointing this out. We corrected the paragraph concerning the definition of the p-value 
(see lines 298 - 302, 322 - 323, 349 - 350, 361).
“I suggest to merge the outlier detection step into the components estimation step by adopting robust 
regression estimators (for example M-estimators or least trimmed squares estimators).”
Thank you for these suggestions. However, the choice to use wavelet transformation to suppress the 
noise of the observed signal was made based on the intention to design PSDefoPAT so that little a 
priori knowledge is necessary. Least trimmed squares, as we understood it, is a modified version of 
the ordinary least square (OLS) approach that takes outliers into consideration during processing. The 
amount of data points to be considered as outliers is determined by the trimming constant h, which is 
a parameter set by the analyst based on the suspected signal-to-noise-ratio (SNR) of the time series 
[1]. Thus, the trimming constant would need to be set for each time series individually and with a priori 
knowledge. The second approach suggested is the M-estimators approach. Here, the sum of squared 
residuals is replaced by an objective function, which needs to be minimized. It is our understanding 
that finding the right objective function is key to the M-estimator approach and depends on the data 
at hand, which implies a priori knowledge [2]. Due to the requirement of a priori knowledge and the 
need to provide user input, we concluded that both approaches do not meet the intentions for the 
design of PSDefoPAT and we decided to smooth the time series using wavelet transformation. 
Another aspect is, that a time series segmentation algorithm is used before a piecewise linear model 
is applied and the performance of this algorithm might suffer from the presence of outliers. 
“I suggest to evaluate the possibility to include in the model external information (such as weather 
conditions) in the form of covariates.”
This is a very interesting suggestion. If I have understood you correctly, you would like PSDefoPAT to 
provide the analyst with the option to include external data, such as ambient temperature or the 
amount of rainfall (weather conditions), during the modeling process. The challenge for the analyst 
would be that they would need to know precisely, which time series are affected by these conditions 
and which are not. However, PSDefoPAT was designed to require as little a priori knowledge as 
possible and to analyze the provided data without bias. Also, you run the risk of considering additional 
constraints during model selection for time series that are unaffected by these conditions. 
However, it might be interesting to use information, such as if snow fall occurred, to automatically 
exclude the displacement rates from dates, when snow fell. We are going to consider using additional 
data in such a manner for future versions of PSDefoPAT.
In addition, we also re-checked the entire manuscript for any spelling or grammatical errors, as was
suggested. For your convenience, we also included a change file in the Latex .zip folder.
Again, thank you for taking the time to evaluate the manuscript and for providing helpful commentary and 
suggestions.
Best Regards,
Madeline Evers, Antje Thiele, Horst Hammer & Stefan Hinz
Literature
[1] Čížek, P., Víšek, J.Á. (2000). Least Trimmed Squares. In: XploRe® — Application Guide. Springer, 
Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57292-0_2
[2] Gad, A. M., Qura, M. E. (2016). Regression estimation in the presence of outliers: A comparative 
study. International Journal of probability and Statistics, 5(3), 65-72

Author Response File: Author Response.pdf

Reviewer 2 Report

The Persistent Scatterer Deformation Pattern Analysis Tool or short PSDefoPAT was presented in detail to uncover the temporal feature embedded in deformation time series by this manuscript.  The processing chain of PSDefoPAT and the relevant fundamentals to determine the periodic and trend component of a time series model were introduced. Additionally, the capabilities of PSDefoPAT was demonstrated using four case studies characterized by different deformation mechanisms. Given the increasing availability of ground motion service over national and continental scale in recent years, the PSDefoPAT would be very attractive and widely applicable. Therefore, i strongly recommend to publish this manuscript.

 

There are several points needed to be strengthened or revised:

1. Page 7, line 253, how is the parameter c_j  defined? a formulation is needed here.

2.  Page 7, a colon maybe is missed in the sentence “There are two approaches hard and soft thresholding”.

3. The green line , which stands for the estimated best-fitting model, needs to be in bold to increase its visibility in Figures 4, 9, 13,17 and 21. Also, the font size of the captions for the x- and y- axis should be increased.

Author Response

Dear Reviewer,
Thank you for taking the time to review our manuscript. Your comments and suggestions are
appreciated. In the following, I would like to answer your comments and suggestions individually. 
Therefore, I will repeat your comment or suggestion and then reply to it. To ease handling the review 
process, my answer will be marked in blue.
Answers to the comments and suggestions
“Page 7, line 253, how is the parameter ?? defined? a formulation is needed here.”
Thank you for pointing this out. Following your comment, we extended the paragraph concerning 
thresholding with wavelet transformation, hoping to explain the origin of the parameters better (see 
lines 244 - 273). 
“Page 7, a colon maybe is missed in the sentence “There are two approaches hard and soft 
thresholding”. “
Thank you for point out this error. A colon was added to the sentences (see line 271).
“The green line, which stands for the estimated best-fitting model, needs to be in bold to increase its 
visibility in Figures 4, 9, 13,17 and 21. Also, the font size of the captions for the x- and y-axis should be 
increased.”
Thank you for bringing this to our attention. The figures were altered regarding the suggestions you 
and Reviewer 3 made to improve their quality and interpretability.
In addition, we also re-checked the entire manuscript for any spelling or grammatical errors, as was
suggested. For your convenience, we also included a change file in the Latex .zip folder.
Again, thank you for taking the time to evaluate the manuscript and for providing helpful commentary and 
suggestions.
Best Regards,
Madeline Evers, Antje Thiele, Horst Hammer & Stefan Hinz

Author Response File: Author Response.pdf

Reviewer 3 Report

In this work, a practical tool so-called PSDefoPAT was presented for the deformation pattern analysis. The case studies reveal that the isolated deformation contribution obey diverse deformation models are more informative than mean velocity rates. Absolutely, the MS is well structured and written. My general comments are in following: 1) the quality of figures can be further improved, such as using more large size fonts and/or bold annotations.  2) the causes for the diverse deformations (models) can be further discussed. Moreover, the promotion of this tool for other scenarios, such as landslides, can be further described. 3) Very few typos can be corrected after carefully checking and editing.

Author Response

Dear Reviewer,
Thank you for taking the time to review our manuscript. Your comments and suggestions are
appreciated. In the following, I will reply to your comments and suggestions individually. For that reason, 
I will first repeat your comment or suggestion and then reply to it. To ease handling the review process, 
my answer will be marked in blue.
Reply to the comments and suggestions
“The quality of figures can be further improved, such as using more large size fonts and/or bold 
annotations.”
Thank you for bringing this to our attention. The figures were altered concerning the suggestions you 
and Reviewer 2 made to improve their quality and interpretability.
“The causes for the diverse deformations (models) can be further discussed.”
Thank you for making this suggestion. We gladly extended the introduction of each use case to 
describe the underlying deformation in more detail (see lines 493 – 503, 559 – 565, 605 – 607, 655 -
656).
“Moreover, the promotion of this tool for other scenarios, such as landslides, can be further 
described.”
Following your comment, we included a paragraph concerning the application of PSDefoPAT for 
studying landslides in the Outlook (see lines 746 -751).
In addition, we also re-checked the entire manuscript for any spelling or grammatical errors, as you and 
the other reviewers suggested. For your convenience, we also included a change file in the Latex .zip folder.
Again, thank you for taking the time to evaluate the manuscript and for providing helpful commentary and 
suggestions.
Best Regards,
Madeline Evers, Antje Thiele, Horst Hammer und Stefan Hinz

Author Response File: Author Response.pdf