Offline-Online Change Detection for Sentinel-1 InSAR Time Series

Round 1

Reviewer 1 Report

The study propose a simple statistical approach for detecting offsets and gradient changes in InSAR time series. The article presents interesting research and very well prepared. The test procedure is clear and justified. The study data are rightly chosen and sufficient. The authors of the article correctly described the study; it is important that the test procedure can be reproduced by other researchers. Below I have listed comments and suggestions for Authors.

A. General comments:

1. For the introduction section of this article, I suggest to reduce them to max. 5 paragraphs.

2. In the discussion part, regarding spatial filtering and window size used in gradient change detection, I suggest to remove it to the related content in section 2, otherwise the logic of the article is not clear.

3. It is very meaningful for Hatfield Moors to be selected as the test area for natural gas extraction and storage. However, the study did not conduct a further analysis on the results of the deformation during the monitoring period, and lacks of the external data to confirm the accuracy of the method. I suggest that this part should be improved.

B. Specific Comments:

1. Line 127: why has only 90% of the data been used? How to determine the selection of the data？

2. Please add the time unit in Fig. 3.

3. Please add the displacement unit in Fig. 4.

4. Line 189-193: please explain why choose the 6 points from ‘a to f’ for time series analysis?

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 2 Report

The present work addreses the question how incidences of non-linear deformation in large InSAR data sets can be detected. Given the availability of ever bigger amounts of data this is a relevant research question. Unfortunately, the submitted text suffers from severe shortcomings. The description of methods is insufficient and the text contains even several wrong statements. The authors seem to assume implicitely that MintPy provides correct time-series also in case of offsets. This is unusual and requires to explain in some detail how this is achieved. Irritating in this regard is the statement in lines 107-108 that they "intentionally did not correct unwrapping errors in our processing as these are useful change points in the time series that we can detect". How could an error be usefull? If it is not an error, how do they know? There is no discussion of that. Furthermore, in lines 247-248 they state "Atmospheric noise-induced peaks in the time series are the main source of false positives in our offset detector.". Why are there significant peaks stemming from atmosphere left in the signal? All InSAR time-series algorithms that want to detect deformation try to get rid of the atmospheric signal. It is surprising that significant peaks shouldn't have been removed. Accordingly, the signals displayed in Figure 6 show offsets and peaks that look rather unusual. Moreover, the spatial distribution of offsets presented in Figure 7b) seems arbitrary. A corresponding map of detected gradient changes is missing. Finally, results are neither validated nor do the authors try to give an explanation of the observed patterns. Therefore, I recommend to reject the paper.

Why are formulas not enumerated?

line 33: ISRO=?
line 36: "for example [e.g. ..." -> I would suggest to omit "e.g.".
line 39: I would suggest to omit "responsible".
line 79: Reference [26] should also appear in the text.
Figure 1.: Please use a larger font size.
Figure 2.: Please use a larger font size for labelling.
Figure 2.a): It is an odd choice to display maximum and minimum using a histogram plot. I would suggest to use e.g. a boxplot. Furthermore, the minimum coherences seem rather large. Please explain in the text how the coherence has been determined and how pixels are selected that have been evaluated for this plot.
Figure 2.b): Something is wrong here. According to the color bar red means average coherence lower than 0.45. I would infer that in this case the minimum coherence is lower than 0.45 as well. But you say that minimum
coherence lower than 0.45 is indicated by dashed lines. Why are there red lines that are not dashed?
lines 102-103: Here you state that all interferograms with an average coherence less than 0.45 are removed, while according to the text of Figure 2 you used minimum coherence?
lines 107-108: Please explain this in more detail. How could an error be usefull?
InSAR Processing and time series analysis, lines 97-108: Usually InSAR time-series analysis makes assumptions on the signal, e.g. temporal or spatial smoothness of the displacement field. In your work you seem to assume
implicitely that MintPy provides correct time-series also in case of offsets. This is unusual and requires that you explain in some detail how this is achieved.
line 111: "offsets in displacement and changes in displacement gradients"
-> "offsets and changes in displacement gradients"
line 111: Why are offsets retained? How do you discerne offsets from unwrapping errors?
Figure 3: Case "Offset with changes in linear gradients": The first difference should in average be larger than zero where the displacement is going up and in average be negative where the displacement is going down. Why is this not visible?
line 118-119: Are the time differences between successive acquisitions all equal? You should discuss the applicability of your method in case of irregularly sampled acquisitions. What is the benefit of considering higher differences?
line 121-122: Why should a first, second or third difference of a seasonal pattern be stationary? Why is the assumption that the first, second and third difference of the time series are stationary meaningful for InSAR data? Please state clearly your mathematical model/assumptions and justify why it is appropriate for the investigated data.
First formula below line 128: This is no proper notation. To denote this set I would suggest to use e.g. {y^k_t:t\in T}, where T is the set of acquisition dates.
Second formula below line 128: The sum should run up to N.
line 132: Maybe you want to justify your use of Student's t-statistic by stating that you assume the noise to be i.i.d. Gaussian?
Formula below line 135: What is t? In the case n>1 this formula is wrong.
line 137-138: This statement is wrong. The mean of the first difference will be unequal zero if there was a trend in the original series. In consequence, the derivation of the formula below line 138 is not justified.
Formula below line 153: To make the paper more self-contained it should be explained how the second derivative is actually calculated.
Figure 4, text: smoothed with window of width 15 days or rather smoothed with window of width 15 acquisitions?
Figure 4, time axes: One would expect that the detected change intervals are associated with the peaks of the second derivative. Possibly this is not visible because the time axes have not been appropriately positioned for the derivatives. Please shift the time axes for the derivatives and explain this proceeding to the reader.
Figure 5: It would be helpful if the marked pixels were assigned to their land cover class.
Figure 6: Why are there moderate peaks that have been detected as change points while more significant ones have not? As in Figure 4, the change intervals are not positioned in a plausible way.
line 194-197: Please improve the language.
Figure 7b: Can you say anything about the validity and physical causes of the detected pattern?
lines 247-248: Usually, multi-temporal InSAR algorithms mitigate the atmospheric signal. Why does it here still cause significant peaks? You should explain in detail how the data were processed that were the input to your detector (cp. comment to paragraph "InSAR Processing and time series analysis").
line 289-290: The following text should be deleted: "For research articles with several authors, a short paragraph specifying their individual contributions must be provided. The following statements should be used".

A relevant reference that is lacking is
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 58, NO. 2, FEBRUARY 2020
Individual Scatterer Model Learning for Satellite Interferometry
Bas van de Kerkhof, Victor Pankratius, Ling Chang, Rob van Swol, and Ramon F. Hanssen

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 3 Report

This is an interesting paper focused on the detection of changes in time series of deformation using a huge stack of SAR (Sentinel-1) images.

The approach is innovative and the results and conclusion are supprted by the data.

I have only a suggestion. The presentation of the results is very short. I suggest to improve this part showing more example given the limited widening of the study area.

Author Response

This is an interesting paper focused on the detection of changes in time series of deformation using a huge stack of SAR (Sentinel-1) images.

The approach is innovative and the results and conclusion are supprted by the data.

I have only a suggestion. The presentation of the results is very short. I suggest to improve this part showing more example given the limited widening of the study area.

- Thank you very much for your positive review. We have additional text in the Results section of the manuscript and added a further two time series detection examples in Figure 7 and updated Figure 6 accordingly. The Results section now has 3 important Figures, which we believe is sufficient to show the breadth of results in this study.

Round 2

Reviewer 2 Report

Although the authors improved the presentation with regard to the first version, the main caveats are still valid. The statistical assumptions of the paper are insufficiently justified. The mathematical derivation of the method contains an error. There is no validation of the approach, merely processing results are presented. The data that are used are problematic for InSAR analysis and would require a detailed analysis to make sure that results are meaningful. The more, as results seem doubeous.
In conclusion, I recommend the rejection of the paper.

p. 5, formula (1): Usually difference time series are defined in analogy with derivation (see e.g. equations (2.30) and (2.32) in [33]). For k>1 your definition is not in agreement with the usual definition found in literature. Please give the correct definition.
p. 5, lines 113+114: To which time series has the ADF test been applied? You should spend more care on proving that these assumptions are relevant for time series stemming from InSAR deformation analysis and present your analysis to the reader. The more the ones depicted later in the paper are rather peculiar.
p. 5, Figure 3: If the first difference is stationary the second and third should also be stationary. How do you explain that your test says they are not?
p. 6: According to formula (2) y^k_t is a set. In formula (3) it is a number. Please use consistent notation.
p. 6, lines 137-139: As in the first version, this is wrong for k=1. If your time series has the form x_t=s*t+w_t, where t is time, s is a constant unequal zero and w_t is i.i.d. Gaussian with expectation value m, then the first difference series has expectation unequal zero:
E[x_t-x_(t-1)]=s*(t-(t-1))+m-m=s
p. 9, lines 206-209: There is no evidence that your results are meaningful and reason to doubt it:
a) The mathematical derivation of your method contains an error (line 139).
b) The displayed time series do not look at all as if caused by injection and withdrawal of gas. All time series over gas storage sites I have seen show a seasonal pattern stemming from the larger consumption of gas in winter 
and refilling the storage in summer. In particular, they do not show sharp peaks. Over a peatbog it would make sense to look if records of groundwater levels are available to check if there is any correlation. 
c) You apply InSAR over an area, where it usually has problems. Over peatbogs analysis is sometimes possible, but requires methods capable of dealing with distributed scatterers. In your cover letter you state that no 
spatial averaging has been performed but that MintPy "does use SNAPHU connected components as a guide". Yunjun et al. explain that these "regions usually have moderate to high spatial coherence". But this will not be the case in vegetated areas or peatbogs. So I am still wondering how you could have obtained meaningfull results in this area?
Over cultivated areas a continous monitoring seems not possible. The jumps visible in the time series of Figure 7 possibly are arbitrary because of lack of coherence. It is problematic to enforce connectivity of the baseline graph by 
using low coherence interferograms. Better would be to allow instead for larger baselines. 

Author Response

Thank you very much for your comments and suggestions. We have responded to each point raised (in red). The line numbers correspond to the track_change version of the manuscript.

Author Response File: Author Response.docx