Multi-GNSS Combination Multipath Reflectometry Based on IVMD Method for Sea Level Retrieval

Round 1

Reviewer 1 Report

The authors used a robust regression solution strategy based on multi-GNSS sea-level retrieval and an improved variational mode decomposition (IVMD) algorithm to process the sea-level retrieval. The authors consider the energy entropy mutual information (EEMI) as an indicator and the sum of two EEMI modal functions as objective functions to develop the VMD algorithm. The insufficient decomposition or over-decomposition problems in traditional VMD are overcome by the present method to accurately determine the number of decomposed modal functions (IMF) and the value of penalty factors in the denoising process. The results of this study show that the IVMD method based on multi-GNSS sea level retrieval can further improve the accuracy to <10 cm and can achieve 10-minute equal interval sampling. Hence, the present method is a suitable approach to detecting sea-level height and monitoring sea-level change GNSS-MR retrievals. The manuscript is well-written, and the results are convincing.

I may suggest acceptance of the manuscript after minor revision as per the following comments.

Comments:

 In Abstract

Line 21-22 It is not clear what these station symbols are. It should be revised to let the readers understand which station, what recordings and where it is situated. Was it a campaign mode observation or a permanent station?

 In Introduction

In the very beginning, the authors should elaborate about the traditional techniques like Tide gauge and other modern techniques like GNSS-R and GNSS-MR, etc. techniques for sea level heights, etc. as they are mentioned in the literature review in the subsequent paragraphs. 

There are recent studies confirming that the KELM-based estimates from multi GNSS-R observations comprising QZSS-R and other complementary measurements from GPS-R, and GLONASS-R, providing alternative unbiased estimations to the traditional tide-gauge (TG) measurement (Ansari et al., 2022). I suggest the authors to refer and cite the same available at https://doi.org/10.1038/s41598-022-25994-6

The figure axis and labels are not visible clearly, please enhance the figure quality for better visibility.

 Line 200 Typo Equqtion

I suggest the authors to add the following either in the present form or in their own words at the beginning of description of VMD by appropriately referring and citing the following article that discusses VMD is one of the recently established multi-resolution techniques for adaptive and non-recursive signal decomposition into different IMFs (Dabbakuti et al., 2020; https://doi.org/10.1049/iet-rsn.2019.0394 ).

Line 299 The authors are expected to interpret the IMF components variation pattern and physical reasons. The reason for a dissimilar pattern for IMF6 at two stations could have been elucidated.

 Line 303 Incomplete sentence “To distinguish useful information from the mixed-signal component.”

 Line 337 Avoid frequent use of word retrieval in “The retrieval results of this study show that the sea level retrieval” and subsequent sentences.

Reference #2 Missing YEAR, Reference #3 DOI is not opening, Reference #18 Wrong volume and page information. The authors are suggested to verify other such instances.

Author Response

Thank you very much for your appreciation and valuable suggestions for this study, In response to your suggestions, we have made corresponding amendments.

 

#Abstract:

1. Line 21-22 It is not clear what these station symbols are. It should be revised to let the readers understand which station, what recordings and where it is situated. Was it a campaign mode observation or a permanent station?

Thanks for your valuable suggestions, we have added more details about the two stations in the abstract and have rewritten the corresponding sentences. “BRST and HKQT stations are located on the west coast of France and the north coast of Hong Kong. Two station both can received satellite observation data from the four satellite systems. Through the data experiment from the retrieval of the BRST and HKQT station, the results of this study show that the IVMD method based on multi-GNSS sea level retrieval can further improve the accuracy to <10 cm, …”

 

#Introduction:

2. In the very beginning, the authors should elaborate about the traditional techniques like Tide gauge and other modern techniques like GNSS-R and GNSS-MR, etc. techniques for sea level heights, etc. as they are mentioned in the literature review in the subsequent paragraphs.

Thanks for your valuable suggestions, we have added corresponding description: “Traditionally, sea level monitoring by the tide gauge (TG) [1], the emergence of satellite altimetry technology has made it possible to detect the sea level of the global oceans , playing a key role in the study of sea level changes [2]. With the development of global navigation satellite systems (GNSS), the applications of GNSS have expanded continuously. The multipath effect, which has been considered as an error source, has been demonstrated to be suitable for estimating sea level [3]”

 

3. There are recent studies confirming that the KELM-based estimates from multi GNSS-R observations comprising QZSS-R and other complementary measurements from GPS-R, and GLONASS-R, providing alternative unbiased estimations to the traditional tide-gauge (TG) measurement (Ansari et al., 2022). I suggest the authors to refer and cite the same available at https://doi.org/10.1038/s41598-022-25994-6

Thanks for your valuable suggestions, we have added corresponding description: “Ansari et al confirmed that the KELM-based estimates from multi GNSS-R observations comprising QZSS-R and other complementary measurements from GPS-R, and GLONASS-R, providing alternative unbiased estimations to the traditional tide-gauge measurement [12].”

 

4. The figure axis and labels are not visible clearly, please enhance the figure quality for better visibility.

Thanks for your valuable suggestions, We have thickened the coordinate axis of the Figure, marked the name of the station on the figure to make it easier to distinguish the difference between the data changes of the two stations.

 

5       Line 200 Typo Equqtion

Thanks for your remind, we have corrected the corresponding Equqtion.

 

6       I suggest the authors to add the following either in the present form or in their own words at the beginning of description of VMD by appropriately referring and citing the following article that discusses VMD is one of the recently established multi-resolution techniques for adaptive and non-recursive signal decomposition into different IMFs (Dabbakuti et al., 2020; https://doi.org/10.1049/iet-rsn.2019.0394 ).

Thanks for your valuable suggestions, we have added corresponding references and described them in the manuscript. “VMD is one of the recently established multi-resolution techniques for adaptive and non-recursive signal decomposition into different IMFs, can be used to reduce the non-stationary of data [36]. The basic principle of VMD is to decompose the original signal  into  modal element with center frequency , and reconstruct it”

(Reference #36: Dabbakuti J , Jacob A , Veeravalli V R , et al. Implementation of IoT analytics ionospheric forecasting system based on machine learning and ThingSpeak. IET Radar, Sonar & Navigation, 2020, 14(2),341-347. DOI: 10.1049/iet-rsn.2019.0394.)

 

7       Line 299 The authors are expected to interpret the IMF components variation pattern and physical reasons. The reason for a dissimilar pattern for IMF6 at two stations could have been elucidated.

Thanks for your valuable suggestions, we have added the reason for a dissimilar pattern for IMF6 at two stations: “Due to the different data time lengths and data differences between the two stations, the resulting VMD decomposition is also different”

 

8       Line 303 Incomplete sentence “To distinguish useful information from the mixed-signal component.”

Thanks for your valuable suggestions, we have rewritten the corresponding sentences: “In order to distinguish useful information from the mixed-signal component, we used the composite evaluation index  ”

 

9       Line 337 Avoid frequent use of word retrieval in “The retrieval results of this study show that the sea level retrieval” and subsequent sentences.

Thanks for your valuable suggestions, we have rewritten the corresponding sentences: “The results of this study show that the sea level retrieval”; “The results were in agreement with the measured data from the tide-gauge station”; “affect the final accuracy of the overall retrieval”

 

10    Reference #2 Missing YEAR, Reference #3 DOI is not opening, Reference #18 Wrong volume and page information. The authors are suggested to verify other such instances.

Thanks for your remind, We have corrected the corresponding wrong references.

(Reference #2: “ Larson, K.M. ; Löfgren, J.S.; Haas, R. Coastal sea level measurements using a single geodetic GPS receiver. Adv. Space Res. 2013,51, 1301–1310. DOI:10.1016/j.asr.2012.04.017”

Reference #3: “Small EE, Larson KM, Braun JJ. Sensing vegetation growth with reflected GPS signals. Geophys . Res. Lett. 2010,37, L12401. DOI: 10.1029/2010GL042951”

Reference #18: “Wang X, Zhang Q, Zhang S. Water levels measured with SNR using wavelet decomposition and Lomb–Scargle periodogram. GPS Solut. 2018, 22, 01, 22 ”)

Reviewer 2 Report

The manuscript proposed an improved variational mode decomposition (IVMD) algorithm to process the sea level retrievals from multi-GNSS combination. The EEMI method is used to determine the key parameter K and a in the traditional VMD method. The method shows better improvement than the before study. However, there are still some problems to be handled.

 

General remarks:

 

The robust regression solution strategy is the method in section 3.1.2 or not? The title and the expression in the manuscript can be replaced to that.

 

The IVMD method is used to filter the sea level retrieval time series using multi-GNSS combination. The detailed procedure is unclear. Please descripe figure 3 more clearly in the manuscript.

 

The accuracy is better than 10 cm, which can be seen in Table 3. However, 10-minute equal interval sampling is not fully demonstrated in the manuscript.

 

Please check the manuscript to ensure that there are not many unnecessary format and grammar problems.

 

Specific comments:

 

The figures are not clear and well explained. Some pictures have the same legend. So the sites name can be added in the figures.

In 177 and 208, “robust refression solution” should be robust regression solution.

In 225, “Eq. Equation (6)” is Eq.(6). And all the writings need to be the same style.

Figure 5 is not necessary in the manuscript.

The sites name in Figure 7 are all BRST.

In eq.(3), the subscript “l” is not clear, and can be replaced with another one.

Comments for author File: Comments.pdf

Author Response

Thank you very much for your appreciation and valuable suggestions for this study, In response to your suggestions, we have made corresponding amendments.

1. The robust regression solution strategy is the method in section 3.1.2 or not? The title and the expression in the manuscript can be replaced to that.

Thanks for your valuable suggestions, the robust regression solution strategy is the combination method mentioned in section 3.1.2 of the manuscript. We used the robust regression solution strategy to combine the multi-GNSS sea level retrieval, so “Combination method for multi-GNSS sea level retrieval” was used as the title of section 3.1.2 here. We have replaced the title of section 3.1.2 with “Multi-GNSS combination method using robust regression solution strategy”

 

2. The IVMD method is used to filter the sea level retrieval time series using multi-GNSS combination. The detailed procedure is unclear. Please descripe figure 3 more clearly in the manuscript.

Thanks for your valuable suggestions, we have added a description about Figure 3 in the manuscript, “ The specific steps of IVMD Algorithm based on multi-GNSS combination sea level retrieval are as follows:

Step1: Set the range of VMD algorithm parameters, and initialize GOA algorithm parameters. according to the literature [36-39] and the fact that this study focused on VMD appling to the multi-GNSS combination sea level retrieval. We set the modal component , and the penalty factor . For the population number of the GOA algorithm, we set , the maximum cycle number we set .

Step2: Select the optimal parameters of the VMD method using the method described in Section 3.2.2, and select the VMD method with the optimal parameters to decompose the multi-GNSS combination sea level retrieval.

Step3: Using the composite evaluation index T [40]. Each modal component is sequentially accumulated to form a reconstructed signal, and the composite evaluation index T value of each reconstructed signal is calculated. When the T value is the lowest, the corresponding reconstructed time series was a denoising time series, while the remaining IMF components are considered high-frequency noise. Using denoising time series to contain the final sea level height value.”

 

3. The accuracy is better than 10 cm, which can be seen in Table 3. However, 10-minute equal interval sampling is not fully demonstrated in the manuscript.

Thanks for your valuable suggestions, we have added the explanation about the10-minute equal interval sampling in the manuscript, “In this study, we applied 10-min combined time as the width of windows for the sampling rate of the BRST and HKQT stations, and we can contain 10-minute equal interval multi-GNSS combination sea level retrieval to process IVMD Algorithm, so that we can receive 10-minute equal interval sampling.”

 

4. Please check the manuscript to ensure that there are not many unnecessary format and grammar problems.

Thanks for your valuable suggestions, we have checked the manuscript and deleted Figure 5, made corresponding correction in this manuscript.

 

5. The figures are not clear and well explained. Some pictures have the same legend. So the sites name can be added in the figures.

Thanks for your valuable suggestions, We have thickened the coordinate axis of the Figure, marked the name of the station on the figure to make it easier to distinguish the difference between the data changes of the two stations.

 

6. In 177 and 208, “robust refression solution” should be robust regression solution.

Thanks for your remind, we have made corresponding correction.

7. In 225, “Eq. Equation (6)” is Eq.(6). And all the writings need to be the same style.

Thanks for your remind, we have deleted the word “Equation” and made corresponding correction in this manuscript.

8. Figure 5 is not necessary in the manuscript.

Thanks for your valuable suggestions, In order to make the algorithm process more clear, we retained the Figure 5, and added the corresponding explanation: “From the Figure 5, it can be seen that after two iterations of the objective function, the optimal solution of the parameter tends to be stable, and the conclusion can be drawn: for the two stations, two iterations are needed to get the optimal result.”

9. The sites name in Figure 7 are all BRST.

Thanks for your remind, we have made corresponding correction in the description of the Figure 7.

10. In eq.(3), the subscript “l” is not clear, and can be replaced with another one.

Thanks for your remind, we changed the font of eq.(3) to highlight the difference between the letter “l”, and the modified eq.(3) can be seen more clearly than in the past.

 

Reviewer 3 Report

The authors present an interesting method to deal with data gaps and data noise in sea level retrieved from GNSS-R. The method is sound and they provide proof that it works and also improves upon a standard regression (smoothing) method. This is worthwhile publishing and only needs minor revision.

minor issues:

see anotated pdf

 

Comments for author File: Comments.pdf

Author Response

Thank you very much for your appreciation and valuable suggestions for this study, In response to your suggestions, we have made corresponding amendments.

1. Line 159: ? probably should be skipped.

Thanks for your remind, we have deleted the word “and”.

2. Line 165: put a comma after hdot

Thanks for your remind, we have put a comma after hdot.

3. Line 172: is notation correct, I don’t exactly understand

Thanks for your remind, We have added subscripts to the corresponding notation to ensure the correctness of the notation, “A_i=(M_i 1)"

4. Line 177: regression

Thanks for your remind, we have made corresponding correction.

5. Line 189: maybe choose different font for caption to make it stand out from the main text, or put more space between caption and the main text.

Thanks for your remind, we have put more space between caption and the main text.

6. Line 200: (also: leave a bit of space between equation set 4 and the subsequent text (a bit difficult to see where the dots belong to)

Thanks for your remind, we have made corresponding correction.

7. Line 208: regression

Thanks for your remind, we have made corresponding correction.

8. Line 225: skip

Thanks for your remind, we deleted the word “Equation”.

9. Line 252: describing the method requires a bit more referencing?

Thanks for your valuable suggestions, we have added the specific steps about the method and cited some references to explain the specific process.

(Reference #36: Zhou, C.; Ma, J.; Wu, J.; Yuan, X. An adaptive VMD method based on improved GOA to extract early fault feature of rolling bearings. Int. J. Innov. Comput. Inf. Control 2019,15, 1485–1505.

Reference #37: Li, C.; Liu, Y.; Liao, Y. An Improved Parameter-Adaptive Variational Mode Decomposition Method and Its Application in Fault Diagnosis of Rolling Bearings. Shock Vib. 2021, 2021, 2968488.

Reference #38: He, X.; Bos, M.S.; Montillet, J.P.; Fernandes, R.; Melbourne, T.; Jiang, W.; Li, W. Spatial Variations of Stochastic Noise Prop-erties in GPS Time Series Remote Sens. 2021, 13, 4534.

Reference #39: Silva, L.K.J.; Ramarakula, M. An efficient interference mitigation approach for NavIC receivers using improved variational mode decomposition and wavelet packet decomposition. Trans. Emerg. Telecommun. Technol. 2021, 32, e4242.

Reference #40:Zhu, J.; Zhang, Z.; Kuang, C. A Reliable Evaluation Indicator of Wavelet Denoising. Geomat. Inf. Sci. Wuhan Univ. 2015, 40, 688–694.)

10. Line 273: in the diagram: Paramter should read Parameter

Thanks for your valuable suggestions, we have added the specific steps about the method and discussed specific parameter settings.

11. Line 283: because what do we actually see here? Is this some sort of Pareto front?

Thanks for your valuable suggestions, it is not a sort of Pareto front, we have added an explanation for Figure.4, “The best combination of parameters can be obtained through VMD decomposition and GOA algorithm. As shown in the Figure.4, historical search results are obtained using GOA algorithm and objective function, …”

 

12. Line 292: are you referring to Figure 5? Please introduce the Figure and explain what we .. does it mean that only 2 iterations are needed to get the optimal result?

Thanks for your valuable suggestions, we have added a description of the iterative convergence of functions: “From the Figure 5, it can be seen that after two iterations of the objective function, the optimal solution of the parameter tends to be stable, and the conclusion can be drawn: for the BRST and HKQT stations, two iterations are needed to get the optimal result.”

        

13. Line 299: so is this comparable to a kind of EOF/SVD analysis?

Thanks for your valuable suggestions, it is not a kind of EOF/SVD analysis, we just used the VMD method with the optimal parameter to decomposition the multi-GNSS sea level retrieval. In order to better distinguish high-frequency noise from low-frequency useful signals, a composite evaluation index T is used. We have added corresponding explantion in the manuscript.

 

14. Line 311: i=1…3 i think, see my other comment)

Thanks for your remind, we have made corresponding correction

 

15. Line 319: Is Table 2 for HKQT station? But here minimum is reached for i=1-3 so you have to change that in the main text!

Thanks for your remind, we have made corresponding correction