A Covariance-Based Approach to Merging InSAR and GNSS Displacement Rate Measurements
Round 1
Reviewer 1 Report
Dear Editor, Dear Authors
This manuscript proposed a framework to integrating the deformation velocity measurements derived from time-series InSAR images and from GNSS network, based on their error variance and covariance. Particularly, the covariance of InSAR APS is proposed to be estimated from short temporal baseline interferograms, and then applied to better interpolate and remove the atmospheric residues in the velocity map. They tested their method on simulated datasets to show that the method can retrieve the absolution motion from InSAR with a reduced set of GNSS stations. They also applied their method to two real datasets: One covering the whole Netherland, the other from North Anatolian Fault. After integrating the InSAR and GNSS measurements, the low-frequency errors in the InSAR velocity maps has been significantly reduced.
The work present here is very promising and interesting. The description of the method is clear and the results and interpretation are sound. I only have a few comments for authors to consider before publishing:
1, For Figure 2. Could you please provide more information regarding to this variograms, namely how many interferograms are used, how their temporal baseline distributed?
2, Line 209. The removal of solid tide and continental drift is very interesting and important for large-scale deformation studies. Could you please show the removed solid tide and continental drift signal along with Figure 6-8? You can make them a four sub-plate figure to include these two large-scale components, so that readers can better understand how this signal will affect the interpretation of the results.
3, Some minor comments:
Line 22 bigger -> larger Line 29, add e.g., before inter-seismic Line 49, it seems should be it can avoid, not can be avoided Line 153, let -> by Line 156 Sentinel -> Sentinle-1 Line 238, add e.g., before Eurasian Please color code the dots in Fig 6-8 to indicate the differences between GNSS and InSAR rates
Regards
Author Response
Dear Editor,
Dear Reviewer,
The authors would like to thank you for the help in improving the manuscript.
I copied the comments provided by the reviewer and I tried to answer them point per point.
With my best Regards
Alessandro Parizzi
Dear Editor, Dear Authors
This manuscript proposed a framework to integrating the deformation velocity measurements derived from time-series InSAR images and from GNSS network, based on their error variance and covariance. Particularly, the covariance of InSAR APS is proposed to be estimated from short temporal baseline interferograms, and then applied to better interpolate and remove the atmospheric residues in the velocity map. They tested their method on simulated datasets to show that the method can retrieve the absolution motion from InSAR with a reduced set of GNSS stations. They also applied their method to two real datasets: One covering the whole Netherland, the other from North Anatolian Fault. After integrating the InSAR and GNSS measurements, the low-frequency errors in the InSAR velocity maps has been significantly reduced.
The work present here is very promising and interesting. The description of the method is clear and the results and interpretation are sound. I only have a few comments for authors to consider before publishing:
1, For Figure 2. Could you please provide more information regarding to this variograms, namely how many interferograms are used, how their temporal baseline distributed?
Yes, I added another example in order to fulfill also the requirements of Reviewer 2. The Variograms shown corresponds to two of the stacks in the NAF test site. Information about them ( #images, time span…) is then available in the table.
2, Line 209. The removal of solid tide and continental drift is very interesting and important for large-scale deformation studies. Could you please show the removed solid tide and continental drift signal along with Figure 6-8? You can make them a four sub-plate figure to include these two large-scale components, so that readers can better understand how this signal will affect the interpretation of the results.
Sure, the removed continental drift patterns are now shown for all the 3 considered datasets. Unfortunately for the Solid Earth Tides Corrections it was not possible since the correction has been computed at interferogram level.
3, Some minor comments:
Line 22 bigger -> larger Line 29, add e.g., before inter-seismic Line 49, it seems should be it can avoid, not can be avoided Line 153, let -> by Line 156 Sentinel -> Sentinle-1 Line 238, add e.g., before Eurasian Please color code the dots in Fig 6-8 to indicate the differences between GNSS and InSAR rates
Thanks, the corrections have been done and the color-coded plot added to the results.
Reviewer 2 Report
The authors propose an approach for merging InSAR and GNSS displacement rates aimed at improving the accuracy of the final displacement rate measurements. Basically the residual atmospheric contribution and the reference point velocity are estimated by using the displacement values derived from GNSS, the known noise affecting the GNSS measurements, and an estimation the covariance matrix of the difference measurements.
The paper is interesting and well written. In particular, the section devoted to simulations clearly shows the performances of the proposed approach according to the GNSS measurements number and accuracy.
The paper is worth for publication, but there are some issues that need to be revised. In the following, my specific suggestions.
Issue 1
Section 2, which introduces the methodology, suffers of lack of details and it is hard to read. I would suggest improving the description of the equations presented in the section by: 1) by clearly introducing each term; 2) showing each term of matrixes and vectors (at least the first time); 3) clearly indicating the terms coming from the measurements and terms coming from estimation.
Issue 2
Moreover there are references to results from literature that should be reported with more details.
Example 1
Row 46-48: “After such corrections the mean variograms of the error on the interferometric measurements shows a stationary behavior that can be well approximated by a covariance function.” Row 112-113: “Results of the analysis in [8 ] have shown that, if the phase correction using ECMWF models are performed [22 ] [23 ], the residual atmospheric effects after the processing show a quite good stationary behavior.” It could be useful to provide an example of such variograms and to show their stationary behavior.
Example 2
Row 123-124: “according to the theory this can be obtained imposing the orthogonality between interpolation/prediction error and data [24 ].” Add more details.
Issue 3
Section 4.2: the results presented in this section should be commented highlighting the improvements provided by the proposed approach.
Author Response
Dear Editor,
Dear Reviewer,
The authors would like to thank you for the help in improving the manuscript.
I copied the comments provided by the reviewer and I tried to answer them point per point.
With my best Regards,
Alessandro Parizzi
The authors propose an approach for merging InSAR and GNSS displacement rates aimed at improving the accuracy of the final displacement rate measurements. Basically the residual atmospheric contribution and the reference point velocity are estimated by using the displacement values derived from GNSS, the known noise affecting the GNSS measurements, and an estimation the covariance matrix of the difference measurements.
The paper is interesting and well written. In particular, the section devoted to simulations clearly shows the performances of the proposed approach according to the GNSS measurements number and accuracy.
The paper is worth for publication, but there are some issues that need to be revised. In the following, my specific suggestions.
Issue 1
Section 2, which introduces the methodology, suffers of lack of details and it is hard to read. I would suggest improving the description of the equations presented in the section by: 1) by clearly introducing each term; 2) showing each term of matrixes and vectors (at least the first time); 3) clearly indicating the terms coming from the measurements and terms coming from estimation.
Issue 2
Moreover there are references to results from literature that should be reported with more details.
Example 1
Row 46-48: “After such corrections the mean variograms of the error on the interferometric measurements shows a stationary behavior that can be well approximated by a covariance function.” Row 112-113: “Results of the analysis in [8 ] have shown that, if the phase correction using ECMWF models are performed [22 ] [23 ], the residual atmospheric effects after the processing show a quite good stationary behavior.” It could be useful to provide an example of such variograms and to show their stationary behavior.
Example 2
Row 123-124: “according to the theory this can be obtained imposing the orthogonality between interpolation/prediction error and data [24 ].” Add more details.
I try to address the first two issues jointly. Section 2 has been revised.
A section that specifically describes how the residual atmospheric error covariance is computed has been added in order to better separate what is estimated from what it has been assumed.
A more accurate description of Equation 2 has been introduced and Equation 8 has been described more in detail.
A footnote stating the use of “widehat” to indicate the estimated variable has been also added.
Two different variogram examples are displayed referring also to the specific test site that they represent
Issue 3
Section 4.2: the results presented in this section should be commented highlighting the improvements provided by the proposed approach.
The presentation of the results and the comments has been enhanced. The zero mean offsets and the continental drift screens are now displayed and discussed in the Results Section.
