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Peer-Review Record

Noise Analysis and Combination of Hydrology Loading-Induced Displacements

Remote Sens. 2022, 14(12), 2840; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14122840

by Chang Xu¹

, Xin Yao¹ and Xiaoxing He^2,*

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Remote Sens. 2022, 14(12), 2840; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14122840

Submission received: 16 April 2022 / Revised: 30 May 2022 / Accepted: 8 June 2022 / Published: 14 June 2022

(This article belongs to the Special Issue Modelling Geodetic Time Series and Applications for Earth Science and Environmental Monitoring)

Round 1

Reviewer 1 Report

this paper discusses the noise characterization and combination of the vertical displacements predicted by different hydrology models. It can be published after some improvements.

the abrreviation should be given the full name for the first time.
the precise imporvement of the model should be clearly defined and presented.
The figures such as figure 5 is too coarse to be seen.
the importance of the physical mechanisms should be highlight in your introduction part.
the present form fo the paper is only based on mathematical considerations. there should some comparision between yours with the popular used physcial mechanisms.

Author Response

Responses to the reviewer’s comments: Reviewer #1: Comments 1: the abbreviation should be given the full name for the first time. Response: Corrected accordingly. Comment 2: the precise improvement of the model should be clearly defined and presented. Response: Corrected accordingly. Statistical indices (e.g., mean overlapping Hadamard variance, Nash-Sutcliffe efficiency, and variance reduction) shows that our proposed algorithm has an overall good performance and seems to be potentially feasible for performing correction on geodetic GPS heights. Comment 3: The figures such as figure 5 is too coarse to be seen. Response: Corrected accordingly. Comment 4: the importance of the physical mechanisms should be highlight in introduction part. Response: Corrected accordingly. The surface mass loading is currently predicted by using the numerical procedures (e.g, spherical harmonic function and Green's function) based on the status of Earth models and the existing surface load data (e.g., atmosphere, ocean, land hydrosphere and cryosphere) (for details, see [3]). Varying model parameters (e.g., land/sea mask, ocean response, love numbers, and earth model) as well as input data choose have great impacts on displacement modeling [7,8]. Comment 5: the present form of the paper is only based on mathematical considerations. there should some comparison between yours with the popular used physical mechanisms. Response: We should point that the error analysis of mass loading models has not been well solved yet. Large uncertainties still exist in available hydrology loading prediction models (e.g., MERRA, GLDAS/Noah, GEOS-FPIT, and ERA interim), and currently no consensus is reached on which loading model is superior. As such, the question of how to validate the model predictions is not straight forward to answer. It has to be clear that validation does not mean verification. Following Oreskes et al. (1994) we emphasize that verification using current physical mechanisms is not possible and that validation is a process of reaching a consensus on which model appears to represent nature (or the modelled aspect of nature) in a satisfactory way. In view of these considerations, we resort to mathematical methods.

Reviewer 2 Report

Review of the manuscript ID: remotesensing-1707812

Title: Noise Analysis and combination of hydrology loading-induced displacements

Authors: Chang Xu, Xin Yao, Xiaoxing He

General comments

This paper presents a noise analysis of hydrological loading signal for the vertical component at 70 worldwide GPS sites from 1 January 2011 to 31 December 2014. The authors used the deformation time series from various models individually as well as time series they computed from a combination of the models. They also compared the model signals to GPS observations. They used different statistic indicators to determine the model that fits better the observations. In the first section, they present the state of the art on loading effect, of their correction on GPS time series and the need for a combined solution. In a second section, they present the methods used (Principal Component Analysis and overlapping Hadamard variance). In the third section, they present the hydrological models and services used to provide the loading deformation time series. In the results section, they present the noise analysis of the different hydrological loading models and the comparison to GPS positioning time series provided by JPL/SOPAC. Finally, they conclude summarising the results.

The paper is written in relatively good English but there are English mistakes, misspellings, confusion of terms and unclear sentences. There are repeated words in some sentences, easily identifiable with a careful read. There are too many acronyms in some sentences, which makes the paper difficult to read. A sentence of the template was not removed (l. 239-240).

The study is interesting and I think that the authors have done a rigorous job. Nevertheless, some key aspects need to be enhanced. The state of the art needs a major update adding important and recent publications relevant to their study, as suggested in the detailed comments, and not only from the co-authors of this submitted paper (they cited only 6 references newer than 2019 including 3 written by one of the co-authors). The objectives need to be more clearly exposed in the introduction. It is very surprising that the authors make no mention of GRACE missions, whereas is seems unavoidable when studying hydrological loading effects. Even if they don’t use GRACE dataset in their analysis, it should at least be mentioned in the introduction and they need to justify properly their choice. The authors also need to explain the selection criteria of the 70 GPS sites and of the time span considered for their analysis (2011-2014). The term “superior” is, from my point of view, not an appropriate term and they need to explain more on what criteria they qualify a model as “superior”. Moreover, in Section 2. Materials and Methods, the method is not enough clearly explained. I strongly suggest the authors to clarify some key points to increase the reader understanding. In section 4. Results, they should keep the same colour legend for all the figures to avoid confusing the reader. Some units are missing. Some essential points are missing such as the reference frame in which the time series are expressed as well as the accuracy of the GPS time series used. They never compare their results to the GPS measurement accuracy, which has to be considered in such analysis. I suggest performing this comparison to reinforce the value of the results. I also advise to add some numerical values and use more precise terms when possible rather than e.g. “great impact” (l. 28), “mostly higher” (l. 135), “large quantities” (l.225), “current precision” (l.226). Moreover, when they quantify the results I advise to add some comments for instance to underline their reliability and significance and not only listing numbers. It is not clear why the noise analysis is not performed on the combined time series in section 4.1. A spatial analysis of the results should have been interesting. Finally, I recommend that the authors comment, discuss the results more thoroughly, including a perspective of the results in relation to recent publications, and add prospects.

Recommendation

Despite the interest and the quality of this work, some aspects of the study need improvements and clarifications to be enough convincing and to better value the results. I strongly recommend the authors to clarify the explanations of the method. They also have to update the state of the art in the introduction and to complete the discussion of their results by adding recent relevant references. I suggest ensuring the consistency between the colours used in the different figures, when possible, for a better readability of the results. With these revisions, I’m sure that the paper will reach the standard of this journal. I consequently recommend a major revision for this paper, expecting that the authors will be able to provide the necessary improvements within a reasonable time for revision.

Detailed comments

Hereafter are some detailed comments and remarks to improve the paper. L. refers to line. I didn’t corrected English mistakes.

Abstract

Add the fact that the considered GPS sites are worldwide distributed
Add the time span considered
20-21: “we find that our proposed algorithm seems to be potentially feasible from applications perspectives”: be more specific

Section 1. Introduction

General comment: Even if the state of the art is based on many papers, it needs an important update. I highly recommend the authors to add some recent major publications relevant to the subject that are missing, including at least:

Chanard, K., Fleitout, L., Calais, E., Rebischung, P., and Avouac, J.-P. (2018). Toward a global horizontal and vertical elastic load deformation model derived from GRACE and GNSS station position time series. Journal of Geophysical Research: Solid Earth, 123, 3225– 3237. https://0-doi-org.brum.beds.ac.uk/10.1002/2017JB015245

Mémin, A., J.-P. Boy, and A. Santamaría-Gómez (2020), Correcting GPS measurements for non-tidal loading, GPS Solutions, 24(2), 45. https://0-doi-org.brum.beds.ac.uk/10.1007/s10291-020-0959-3

Michel, A., A. Santamaría-Gómez, J.-P. Boy, F. Perosanz and S. Loyer, 2021. Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models, Remote Sensing, 13, 4523. https://0-doi-org.brum.beds.ac.uk/10.3390/rs13224523.

Nicolas, J., J. Verdun, J.-P. Boy, L. Bonhomme, A. Asri, A. Corbeau, A. Berthier, F. Durand, and P. Clarke (2021), Improved Hydrological Loading Models in South America: Analysis of GPS Displacements Using M-SSA, Remote Sensing, 13(9), 1605. https://0-doi-org.brum.beds.ac.uk/10.3390/rs13091605

Scanlon, B. R., et al. (2018), Global models underestimate large decadal declining and rising water storage trends relative to GRACE satellite data, Proceedings of the National Academy of Sciences, 115(6), E1080. https://0-doi-org.brum.beds.ac.uk/10.1073/pnas.1704665115

Zhong, D., S. Wang, and J. Li (2021), A Self-Calibration Variance-Component Model for Spatial Downscaling of GRACE Observations Using Land Surface Model Outputs, Water Resources Research, 57(1), e2020WR028944. https://0-doi-org.brum.beds.ac.uk/10.1029/2020WR028944

27 reference 5: this reference seems at the wrong place with respect to the text
28 “great impact”: quantify
37 “in previous studies”: add references
38, l. 51 “superior”: express the idea differently to be more precise
52 “a combined series”: from what dataset?
53 “Koot et al. [18]”: does not correspond to the reference 18 (Liang et al.2021)
55-56 “only those … from this approach”: why? Explain in few words.
63 “array”: I suggest to use network
What about the comparison with GRACE missions?
Explain more clearly the objectives of the study

Section 2. Materials and Methods

Improve the clarity of this section
Many English errors
89 “loading”: I assume the authors wanted to say weight
100: How M is defined? What is its physical meaning?

Section 3. Modeling Hydrology Loading Displacements

Add references for ERA Interim, GEOS-FPIT, NCEP models
Clearly indicate the notations used
108-120: I suggest to put a table with all the models characteristics to improve the clarity and the comparison
124: Explain in few words what the package MALO computes
129-130 “in the center of Earth’s figure (CF)”: Justify why in CF instead of Center of Mass.
Explain in few words the differences between the various models

Section 4. Results

4.1 Noise Analysis

34 « from 1 January 2011 to 31 December 2014”: explain the choice of this period, justify why this time span is long enough to perform the noise analysis
35 “mostly higher”: quantify
137 “70 GPS sites”: How these sites were selected?
139 “~1.8”: unit?
Figure 1: unit? Why considering MERRA as a reference?
150 “circle per year”: I assume the authors refer to cycle per year. Same remarks for each time “circle” is used.
154-155: Justify the selection of these 4 examples instead of others. Are they specific or do they illustrate a general behaviour pattern seen in all the stations of the network?
157 “noise level is variable in time and site-by-site”: quantify
159-162: justify the addition of a white noise in each case whereas in L. 156 it is written “WH turns to be unlikely to exist”. Better argue these points so as not to lose the reader
What about random walk and flicker noises mentioned in Equation 6 (l.105)?
164: Explain in few words what represents the Akaike criteria
165-166: Why using Hector package and MLE? On which parameter the model selection is based? As far as I know, Hector package performs noise analysis but does not perform model selection. Clarify the different steps of the method used to select the model.
169-171: I suggest to add a figure to illustrate these results
Figure 2: “stacked periodogram”: specify in the main text the stacked aspect and justify why it is appropriate to do so. Clearly indicate the arbitrary shift of each individual solution and its value. Add the units in the zoom part of the figure.
Figure 3: If possible, keep the same colour legend for each figure to increase the clarity. Add more comments on these results in the main text. Explain and justify “variation fits near 1,… cpy are removed” in the text. “Error bars are omitted for clarity”: give an order of magnitude. It is not clear since in L. 140 “the accuracy of the surface load … are impossible to determine”. How the error bar on the loading displacement was computed?
Figure 4: Add more comments in the main text. Clarify the text of the legend.
Why the noise analysis is not performed on the combined time series?
Are they geographical patterns? Do the results apply for all types of geographical area? A spatial analysis would be interesting.

4.2 Data Combining ans analysis

Some repetitions
188 “more than 90% of cumulative variance explained”: by what?
190-194: not clear
199 “Nash-Sutcliffe Efficiency”: Why using this criterion?
206-208: Justify the use of MERRA for ATML and of ECCO for NTOL. What impact on the analysis can it have if we use another model?
What is the quality of these GPS time series? What loading correction and models are included? In which reference frame are the solutions expressed?
210-216: Add mode comments on the results. Are they significant with respect to the GPS accuracy?
Figure 5: If possible use the same colour legend as before. Unit?
Figure 6: same comment on the colours.
Again, is there a geographical pattern? It is not easy to see with sites alphabetically sorted.

Section 5. Conclusion

225-226 : Quantify "large uncertainties", "current precision"
Some repetitions
Add some discussion of the results with respect to recent references.
239-240: remove

Acknowledgments

Add a reference for all the used datasets and packages as well as the corresponding website when available, some are missing

References

Some references are incomplete
Add more recent publications
Add the doi when available
255 reference 1: year? Does a paper exists instead of an EGU abstract?
271 reference 10: replace "et al." by the relevant author names
273 reference 11: same remark
276 reference 12: year?
305 reference 26: same remark as for reference 10

Author Response

Reviewer #2:

Comment 1: The study is interesting and I think that the authors have done a rigorous job. Nevertheless, some key aspects need to be enhanced. The state of the art needs a major update adding important and recent publications relevant to their study, as suggested in the detailed comments, and not only from the co-authors of this submitted paper (they cited only 6 references newer than 2019 including 3 written by one of the co-authors). The objectives need to be more clearly exposed in the introduction.

Response: Corrected accordingly. We have update added some important and recent publications relevant to our study.

Comment 2: It is very surprising that the authors make no mention of GRACE missions, whereas is seems unavoidable when studying hydrological loading effects. Even if they don’t use GRACE dataset in their analysis, it should at least be mentioned in the introduction and they need to justify properly their choice.

Response: Corrected accordingly. It is worth noting that the GRACE is also a popular technology to study the water storage trends (Scanlon et al., 2018; Zhong et al., 2020). However, the fundamental temporal and spatial resolution of the GRACE data is 10 days and 400 km (Rowlands et al., 2005). As such, GRACE may be insufficient to study the hydrological loading effects at a specific GPS site. Additionally, the computation strategy is completely different from the above four HYLD models, so we tentatively do not use the GRACE dataset in our analysis.

Comment 3: Figure 3: If possible, keep the same colour legend for each figure to increase the clarity. Add more comments on these results in the main text. Explain and justify “variation fits near 1,… cpy are removed” in the text. “Error bars are omitted for clarity”: give an order of magnitude. It is not clear since in L. 140 “the accuracy of the surface load … are impossible to determine”. How the error bar on the loading displacement was computed?

Response: We have explained and justified “variation fits near 1,… cpy are removed” in the text. The error bars omitted in Figure 3 is the error bars of Hadamard variance not the loading displacement.

Comment 4: Figure 2: “stacked periodogram”: specify in the main text the stacked aspect and justify why it is appropriate to do so. Clearly indicate the arbitrary shift of each individual solution and its value. Add the units in the zoom part of the figure.