Real-Time Water Level Monitoring Based on GNSS Dual-Antenna Attitude Measurement

Round 1

Reviewer 1 Report

This paper presents a technique and associated experiment for measuring water level from using groundbased GNSS-R. The approach is based on double-difference carrier-phase measurements.
Apart from the interesting months long experiment, that was spoiled by how the in-situ comparison data was recorded but still holds valuable information, the novelty and overall interest of the paper is difficult to appreciate. In particular, it is unclear how the dual-antenna attitude measurement, highlighted in the title, is of importance in the proposed approach, which only seems to rely on double-difference carrier phase measurements.
I thus suggest that major corrections should be applied to the current paper.

Here is a list of things that have to be fixed/explained before a further, more detailed review of the paper could be performed before publication:

1. The word "resolution" seems to often be confused with "coverage": line 12, water level gauges actually have very high spatial resolution (but low coverage). Line 15, the authors claim that GNSS-R requires extended signal recording durations while saying beforehand that it has high temporal resolution, which is contradictory - here again I would guess the correct word to use was coverage. The same confusion appears several times in the paper and has to be fixed for the paper to be understandable. There are several proper occurences of the word "resolution" too, so the authors have to be careful where to replace it with "coverage".

2. The abstract claims that the proposed technique enhances the accuracy and temporal resolution of water level measurements in GNSS-R, but the authors never present the accuracy and temporal resolution that has already been achieved in GNSS-R in previous works. Several references listed by the authors (e.g. [27-30]) achieve centimeter level accuracy or better with measurement rates up to the Hertz level. Phase measurements can be realized at a 1000Hz rate, meaning that once the ambiguity is solved such a rate could be reached for GNSS-R altimetry. The announced accuracy of around 2.5cm RMSE for 10mn averaging of the water level measurements thus doesn't seem highly resolved in time. A comparison of the presented accuracy and time resolution with previous works on GNSS-R carrier-phase altimetry should be presented. Also, an explanation on why the averaging duration is of 10mn, or a study of the accuracy as a function of the averaging duration, should be provided.

3. The abstract indicates the development of a model for inverting water level based on the "baseline vector". This model is actually quite lightly presented in the paper. Equation (6) should be more clearly explained and its terms should be fully defined through formulas for the model to be properly described.

4. How is section 2.4 useful for the proposed technique? How are y and p used in the height retrieval process?

5. The proposed approach implies using signals from several satellites that reflect on the same water surface, so that the baseline would be the same for all of them and the double-difference computation would hold water level information. The canal where the experiment took place seems to be about 20m large and the position of the antenna made it only possible to get reflections from South-East or East. In this context, how could the receiver provide water level measurements continuously (figure 8)? Also, how are the satellites selected as having useful GNSS-R data from reflections over the canal? The discussion indicates 30 to 40 satellites involved in the calculation at all times. How could 30 to 40 satellite signals possibly simultaneously reflect on only the eastern side of a 20m large canal surface?

6. Why only use data at three different hours of the day? Why 7:25, 15:25 and 18:25 and not, say, 9:25 and 11:25 as well? The amount of results and temporal coverage suffer from this choice and I don't see how the lack of timestamp information for the in-situ measurements explains this choice.

7. What are the reasons for the water level to change in the canal? The increase between two instants can be of up to 50cm, it seems very large for an inland canal.

8. As for section 2.4, I don't understand what section 4.2 provides to the paper. How would the attitude angle be related to the occurence of waves on the canal? This angle depends only on the positions of the antennas, not on the reflected signal paths. Also, or a pitch angle close to -90° (vertical antennas axis), it is to be expected that the heading angle is random, as there is no horizontal distance between the antennas and thus no actual heading angle.

Further general comments:

9. It should be made clear that the first paragraph of section 2 is an overview of what will be described in the section. References should be provided when using techniques defined in other works (GDOP satellite selection algorithm, LAMBDA algorithm...). Line 119-120 indicates that an integer ambiguity can be obtained and the next lines are again for obtaining a fixed integer ambiguity. Figure 1 has typo ("ambiguitie") and is cut at the bottom.

10. j,k,s,m should be defined for equations 4 and 5. s was already used before in equation 3. If it's a different variable, then a different letter should be chosen.

11. The idea of having a signal clapboard for avoiding interferences of direct/reflected signals in the LHCP/RHCP antenna data is not as new as the authors seem to believe (see e.g. figure 5.27 of the PhD thesis of Dallas Masters (2004)).

12. The reasons for the data losses in June and on July 19 and 20 (lines 259-264) don't have to be this extensively provided as they add no relevant information for the paper. Figure 9 and the associated text hold much less information than figure 8 and the RMSE results. In my opinion, Figure 9 can be removed.

13. In the conclusion, what is a "satellite altitude angle"? The elevation angle?

As pointed in the general list of comments, some words are not properly used. Several sentences also suffer from grammatical errors. Listing them while the paper requires extensive modifications would not be efficient.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, the authors introduce a water level monitoring method based on GNSS dual-antenna. The method is validated with field tests. Finally, the authors tried to analyze the effect of the roughness of the water surface through the defined attitude angle of the double-antenna system. The authors have done a lot of work, but there are still many problems that need to be answered. The specific questions are as follows,

1.Title problem: The name of the proposed method to determine water level height is defined as ‘GNSS dual-antenna attitude measurement, it seems NOT CORRECT. The water level height is calculated by using double-difference carrier phase method consistent with the previous ground-based dual-antenna method. Carefully propose new concepts and modify ALL related expressions.

2.Abstract problem: One goal of the proposed method is to enhance the temporal resolution; however, the test results are smooth results with only a time resolution of 10 mins. such as the Kalman filter method, inverse modeling method, and even some neural network-based SNR methods, have reached this temporal resolution. Suggest modifying the corresponding expression or giving a reliable explanation.

3.Abstract problem: A single-epoch calculation method is proposed to optimize cycle jump detection, and what is the single-epoch calculation method? There is no explanation and no corresponding results in the text. 

4.Line 158: Incorrect equation number reference. 

5.Line 160, 168, etc.: Correct ‘Where’ to ‘where’.

6.Equation (6): Please add the specific form of the A and B matrices, which is important to know the method presented in this text.

7.Section 2.4: The attitude measurement method listed here is actually based on the local horizontal coordinate system, the name defined as ‘attitude measurement method’ is unsuitable. 

8.Section 3: Please add more information about experimental equipment, such as the receiver, the LHCP, and RHCP antennas.  

9.Line 267-270: Why can you choose water level data from 07:25 to 07:35, 15:25 to 15:35, and 18:25 to 18:35 each day as a reference?

10.Section 4: the results of the original sampling rate (1 Hz) are not given in the text, and it is recommended to supplement the corresponding results.

11.Section 4.2: The defined body-fixed coordinate system is based on the RHCP antenna and the virtual LHCP antenna, and the defined coordinate system will change continuously with the position of the virtual LHCP antenna. How to deal with this problem? How to delineate the relationship between the roughness of the water surface and the defined body-fixed coordinate system? 

12.Section 4.2: Still the above problem, figure 10 is hard to relate with the geometry of the double-antenna method, please make a new figure. How to delineate the relationship between the heading and pitch angles with equations (10) and (11)?

13.Section 4.2: Figure 11 depicts the heading and pitch angles, and the heading angles are almost evenly distributed between 0 and 360 degrees. The authors consider the multi-path of reflected signals as the main reason, there is no further clarification and explanation. In fact, the heading angle is very sensitive to calculation errors, and the errors could be affected by many factors. How to determine the change of the heading angles related to the multi-path of reflected signals. Please give a reliable explanation.

Moderate editing of the English language.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors answered most of my questions and the originality/contribution of the paper is much easier to understand. The paper can be considered for publication. However, three of my original questions are still left without proper answer:

1- The authors indicate that their aim is to improve the temporal resolution of GNSS-R (abstract line 17). However, the measurement rate of the proposed technique is announced to be of 1Hz, with displayed RMSE being computed after 10mn pre-averaging. Several of the referenced works have better time resolution with accuracy reaching the cm level without such long averaging. Also, the announced contribution of the paper is the use of GNSS dual-antenna attitude measurement for correcting double difference observations. The aim of this correction is actually to improve the accuracy, leaving the time resolution obtained from double difference observations unchanged. In itself, the accuracy of the proposed approach and the information on time resolution displayed in the paper is fair.

The sentence "To enhance the temporal-resolution and accuracy of GNSS-R technology for practical applications" should be removed from the abstract and the abstract should also indicate what time resolution is achieved (measurement rate of 1Hz).

2- The amount of satellites that have their signal reflecting on a water surface in coastal or river/canal GNSS-R altimetry is very often limited by where the antenna is fixed (as in this work where North and West reflections are not available), not to mention how large waves affect high elevation reflections. In a double-difference approach based on the resolution of equations 4/5/13 with 3 parameters to estimate using a least squares approach, at least 3 independent double-difference measurements should be available at all times. The paper barely discusses this aspect. Also, the information on which satellites are available based on their azimut is unclear (75° to 225° according to line 289, 45° to 250° according to figure 4). 75° to 225° seems reasonable, but looking at figure 4, for azimut angles between 170° and 225° an additional cutoff would have to be put on the elevation angle.

The actual cutoff for azimut has to be made clear (same information in the text and figure) and the question of the number of available reflections on water has to be discussed more (at least, amount of simultaneous reflection events necessary for inverting the double difference system of equations, number of satellites used for the GNSS-R calculation during the experiment, which could be added to figure 12).

3- The additions in section 4.2 help a lot in understanding the paper, but several sentences are still unclear/unjustified:

- "The heading angle of the baseline vector between the two antennas is 0°" (line 400). When the antennas are one above the other, there is no value for the heading angle, the heading angle can only be defined if there is a difference in the horizontal positions of the antennas.

- The meaning for "actual" and "ideal" values of the angles/antennas positions is unclear. As I understand, what authors mean by "actual" is "computed by double difference" (which in fact may not be the actual values) and "ideal" is the values in case the antennas are perfectly one above the other (which is most certainly not completely true either). Please make it clearer what "actual" and "ideal" mean throughout this section.

- There is few justification for the list of main factors depicted starting line 403. The authors claim that multipath "effect is the primary reason why the actual position of the virtual antenna differs from its ideal position". There is no proof to this sentence. A 4th main factor on the error on the estimated pitch angle could be the noise on the data (induced by the thermal noise, the local oscillator, etc) and the errors from the least square estimation.

- As I understand, the heading and pitch angle are estimated from the relative positions of the antennas as obtained by the least square approach. Line 421 and figure 11 say the exact opposite: "the position of the virtual antenna determined using the pitch angle"?

Other comments:

- Line 73: "By combining data from multiple stations and signals, water level inversion with millimeter to centimeter accuracy was achieved for the first time [22]". This is not true, centimeter accuracy was already achieved in GNSS-R altimetry before 2021, including in works already included in the references.

- Line 89: "Scholars have proposed methods to avoid calculating the integer ambiguity [27-29], but these methods require long recording times [30], limiting their real-time applicability." Again, this is not true. The works cited there have measurement rates close or even better than that of the proposed approach.

- Added equations in section 2.3:

Why have equation (6) with error terms dx, dy, dz if it's for completely ignoring them later on? Equation (6) can be removed.

Why have two different notations for dx, dy, dz / Deltax, Deltay, Deltaz in (9) and (11)-(13)? Only use one notation.

Please define the h^{jk} terms in equation (13).

- Most of the information in the paragraph starting line 294 don't seem relevant as the water level changed over time during the experiment.

- The sentence from line 310 to 312 is vague/unclear and is not very relevant in this paper.

- Please make clear in the caption and associated text (line 340) that the results displayed in Figure 7 is that of the double-difference approach detailed before. Why are the results from May 12 to June 8 not displayed (figure 7 and 12 as well)?

- As I understand, there is no reason to seperate the results from the two periods of the experiment as nothing changed in the equipment/approach used. Figure 8 and 9 could be united, and the RMSE could be provided as a single value.

- Figure 12 could use doted lines and/or different markers in order for the reader to be able to differentiate the data.

Please check grammar on lines 63, 68 and 69 (both start and end of that sentence), 228, 396 (depicts)

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The author gave revisions based on the comments of the previous round of review, explained the relevant issues, and I think the manuscript can be published, only the following improvements are needed:

1. Figure 7 is not very clear, it is recommended to replace it with a clear result graph;

2. Why are the results in the Figure 7 segmented (with some definite steps)? 

Author Response

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Author Response File: Author Response.pdf