Experiences with the RTM Method in Local Quasi-Geoid Modeling
Round 1
Reviewer 1 Report
The manuscript presents relevant results in a well-organized way. Along with this review I am uploading an annotated version of the manuscript where I have included several comments and English language corrections. The authors should address my comments and make the necessary English language corrections as they prepare their revised manuscript.
I recommend publication after some revision.
Comments for author File: 
Comments.pdf
Along with this review I am uploading an annotated version of the manuscript where I have included numerous English language corrections and modifications. The authors should make the necessary English language corrections and modifications as they prepare their revised manuscript.
Author Response
Response to Reviewer #1
(1) Page 1, line 17:
“for well describing” à “to describe properly”
Response:
We have corrected this.
(2) Page 1, line 17:
“To our limited knowledge” à “To our knowledge”
Response:
We have corrected this.
(3) Page 1, line 18:
“albeit its importance is obvious” à “albeit its importance being obvious”
Response:
We have corrected this.
(4) Page 1, line 24:
“and keeping the accuracy” à “and maintaining the accuracy”
Response:
We have corrected this.
(5) Page 1, line 30:
“rugged terrains” à “rugged terrain”
Response:
We have corrected this.
(6) Page 1, line 31:
“moderate terrains” à “moderate terrain”
Response:
We have corrected this.
(7) Page 2, line 62:
“are usually used” à “may be used”
Response:
We have corrected this.
(8) Page 2, lines 64-66:
“To achieve this, the real Earth’s topography …… of the GGM”
There are some fine points related to the resolution of the smoothed topography and the resolution of the GGM. These are discussed in:
Rexer, M., Hirt, C., Bucha, B. et al. Solution to the spectral filter problem of residual terrain modelling (RTM). J Geod 92, 675–690 (2018). https://doi.org/10.1007/s00190-017-1086-y
You should cite this article here.
Response:
Thank you for your advice. The recommend reference has been added in the reference list and cited in the right place. Original statements have been modified accordingly in the revised manuscript.
(9) Page 2, line 67:
“The terrains” à “the terrain”
Response:
We have corrected this.
(10) Page 2, line 68:
“have actual masses” à “has actual masses”
Response:
We have corrected this.
(11) Page 2, line 75:
“several basic factors” à “several factors”
Response:
We have corrected this.
(12) Page 2, line 78:
“for well describing” à “to properly describe”
Response:
We have corrected this.
(13) Page 2, line 87:
“centered by” à “centered at”
Response:
We have corrected this.
(14) Page 2, lines 90-91:
“are divided” à “are selected”
Response:
We have corrected this.
(15) Page 2, line 95:
“usage” à “use”
Response:
We have corrected this.
(16) Page 3, line 104:
“keep our eyes on” à “focus on”
Response:
We have corrected this.
(17) Page 3, lines 114-116:
“To do so, ……, [31]”
You should definitely cite the following article here:
Rexer, M., Hirt, C., Bucha, B. et al. Solution to the spectral filter problem of residual terrain modelling (RTM). J Geod 92, 675–690 (2018). https://doi.org/10.1007/s00190-017-1086-y
The reference [31] that you cite here, as well as the reference [33] that you cite later are specifically discussing the harmonic correction (HC) that is needed for points located inside the reference topography. You have not discussed at all the HC up to this point, and your citations appear to confuse the harmonic correction with the spectral content of the reference topography.
Some clarification is necessary here.
Response:
Thank you for your advice. The statement has been modified in the revised manuscript. To avoid the confusion caused by citing reference [31] in this place, we have removed it from this citation in the revised manuscript.
(18) Page 3, lines 130-131:
“so as to the resulting residual terrains” à “and so the resulting residual terrain would also differ”
Response:
We have corrected this.
(19) Page 3, line 139:
“is to clearly investigate” à “is to systematically investigate”
Response:
We have corrected this.
(20) Page 4, line 142:
“The reminder of” à “The remainder of”
Response:
We have corrected this.
(21) Page 4, line 145:
“DEM combination effect” à “DEM resolution combination effect”
Response:
We have corrected this. Relevant corrections have been made over the whole manuscript.
(22) Page 5, line 169:
“occurred in the RTM reduction” à “occurring in the RTM reduction”
Response:
We have corrected this.
(23) Page 5, line 172:
“reference ellipsoidal” à “reference ellipsoid”
Response:
We have corrected this.
(24) Page 5, line 187:
“being analogue to” à “being analogous to”
Response:
We have corrected this.
(25) Page 5, line 191:
“the same formation as” à “the same form as”
Response:
We have corrected this.
(26) Page 6, line 206:
“the same formation as” à “the same form as”
Response:
We have corrected this.
(27) Page 6, line 219:
“their impacts” à “their impact”
Response:
We have corrected this.
(28) Page 6, lines 224-225:
“rugged terrains” à “rugged terrain”
Response:
We have corrected this.
(29) Page 6, lines 226-227:
“moderate terrains” à “moderate terrain”
Response:
We have corrected this.
(30) Page 7, line 239:
“deviate much”
How much? Specify.
Response:
Thank you for your advice. The threshold is specified as 100 m. We have modified this part in the revised manuscript.
(31) Page 7, lines 243:
“validation purpose” à “validation purposes”
Response:
We have corrected this.
(32) Page 8, line 254:
“SRTM DEM”
Why did you use the MERIT DEM in Colorado and the SRTM DEM in Auvergne? Explain.
Response:
Thank you for your advice. The reason of choosing two different DEMs in the two test areas is initially want to see whether the use of different DEMs can obtain similar guidelines for RTM correction computation. From the current results, it at least shows that the DEM resolution combination effect, integration radius effect, and the reference topography effect look quite similar in both test areas. And thus, the resulting guidelines can be considered as reasonable. For example, the guidelines can also be applied to the case of using the SRTM DEM in the Colorado test area and the MERIT DEM in the Auvergne test area.
(33) Page 8, line 258:
“the edge effect” à “edge effects”
Response:
We have corrected this.
(34) Page 8, line 263:
“proposed in” à “posed in”
Response:
We have corrected this.
(35) Page 8, line 272:
“reach to” à “be”
Response:
We have corrected this.
(36) Page 9, lines 289-290:
“” , “”
(a) What was the grid size of the elevation data used to estimate the elevation SH coefficients via harmonic analysis?
(b) Were the elevation data used in the harmonic analysis point or area-mean values?
(c) Was the same set of spherical harmonic coefficients used to create the 5' and 30' reference values? Was it truncated to d/o 2160 for the 5' values and d/o 360 for the 30' values?
(d) Were the synthesized reference values point or area-mean?
Specify.
Response:
Thank you for your advice. In the following we will answer the questions one by one:
(a) The grid size of the elevation data used to estimate the elevation SH coefficients via harmonic analysis is 15 arc-second. It should be noted that the 15” elevation data are averaged from the 3” elevation data.
(b) The elevation data used in the harmonic analysis is point values.
(c) Yes, the same set of spherical harmonic coefficients are used to create 5’ and 30’ reference values. Yes, it is truncated to d/o 2160 for the 5’ values and to d/o 360 for the 30’ values.
(d) The synthesized reference values are point values.
Relevant statements are added in the revised manuscript.
(37) Page 10, lines 315-316:
“are taken as the references” à “are taken as reference”
Response:
We have corrected this.
(38) Page 10, line 317:
“with respect to the references” à “with respect to the reference”
Response:
We have corrected this.
(39) Page 11, line 327:
“is reduced within” à “is less than”
Response:
We have corrected this.
(40) Page 11, line 329:
“the DEM is used” à “the DEM used”
Response:
We have corrected this.
(41) Page 12, line 356:
“are taken as the references” à “are taken as reference”
Response:
We have corrected this.
(42) Page 12, line 359:
“with respect to the references” à “with respect to the reference”
“An obvious feature can” à “An obvious feature that can”
Response:
We have corrected this.
(43) Page 12, lines 361-362:
“This is properly due to the fact that residual terrains contain more long-wavelength gravity field signals in the former case” à “This is due to the fact that the residual terrain contains more long-wavelength signal in the former case”
Response:
We have corrected this.
(44) Page 12, line 364:
“the RMS of differences is” à “the RMS of differences are”
Response:
We have corrected this.
(45) Page 12, line 365:
“The RMS difference become” à “The RMS difference becomes”
Response:
We have corrected this.
(46) Page 12, lines 370:
“It can also infer that, more attention …” à “We can also infer that more attention …”
Response:
We have corrected this.
(47) Page 12, lines 372:
“in the RCR procedure because” à “in the RCR procedure, because”
Response:
We have corrected this.
(48) Page 13, line 376:
“are taken as the references” à “are taken as reference”
Response:
We have corrected this.
(49) Page 13, line 379:
“go to see” à “consider”
Response:
We have corrected this.
(50) Page 13, line 382:
“are taken as the references” à “are taken as reference”
Response:
We have corrected this.
(51) Page 13, line 383:
“with respect to the references” à “with respect to the reference”
Response:
We have corrected this.
(52) Page 13, line 384:
“are almost same” à “are almost the same”
Response:
We have corrected this.
(53) Page 13, line 390:
“it is easy to find that” à “it is easy to see that”
Response:
We have corrected this.
(54) Page 14, line 395:
“are taken as the references” à “are taken as reference”
Response:
We have corrected this.
(55) Page 14, line 407:
“The RMS of differences is displayed” à “The RMS of differences are displayed”
Response:
We have corrected this.
(56) Page 15, line 412:
“may rely on” à “depends on”
Response:
We have corrected this.
(57) Page 15, lines 414-418:
“From the above experiment, …… to investigate this issue”
Yes, but the comparisons presented in Figure 10 do not provide any information about which reference topography is best for gravity anomalies.
One way to assess that would be to remove from the point gravity observations the RTM anomalies computed using different reference topographies, and then analyze the resulting values for smoothness, "edge" effects (e.g., for the DA case), etc.
This type of analysis should be presented here.
Response:
Thank you for your advice. The analysis of the smoothness of residual gravity anomalies obtained by removing the contributions of EIGEN-6C4 and RTM using different types of reference topographies from the observed gravity anomalies has been added in the revised manuscript. The results show the superiority of using the SH reference topography for gravity anomaly reduction.
(58) Page 15, line 429:
“are interpolated”
How?
What exactly is the interpolation method used here and why?
Specify and explain.
Response:
Thank you for your advice. The exactly used interpolation method is the bicubic spline interpolation. The reason of using this interpolation is that the residual gravity anomalies after removing the contributions from the GGM and RTM are quite smooth. And thus, the application of the bicubic spline interpolation is sufficient for accurate gridding over the computation area. A clarification is added in the revised manuscript.
(59) Page 16, line 460:
“a smaller SD. And then are the models” à “a smaller SD, followed by the models”
Response:
We have corrected this.
(60) Page 16, line 485:
“is highly recommended for high-frequency GGM augmentation”
You should also cite here the following two articles:
Pavlis, N.K., J.K. Factor, and S.A. Holmes (2007), Terrain-related gravimetric quantities computed for the next EGM, in Gravity Field of the Earth: Proceedings of the 1st International Symposium of the International Gravity Field Service (IGFS), Special Issue 18, edited by A. Kiliçoglu and R. Forsberg, pp. 318–323, Gen. Command of Mapp., Ankara, Turkey.
Hirt, C. (2010), Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data, J. Geod., 84(3), 179–190, doi:10.1007/s00190-009-0354-x
Response:
Thank you for your advice. As requested, we have cited the two articles in this place and added them in the reference list.
(61) Page 16, line 486:
“the adding of” à “the addition of”
Response:
We have corrected this.
(62) Page 17, line 491:
“is able to compute” à “is able to yield”
Response:
We have corrected this.
(63) Page 17, line 511:
“is rarely influenced” à “is not significantly influenced”
Response:
We have corrected this.
(64) Page 18, lines 522-524:
“When optimal values of the truncation degree …… in the Auvergne test area”
Interestingly though, both in Colorado and in Auvergne, the best results are obtained here using the DA reference topography, and not the SH one.
Do you have any comments about that?
Response:
Thank you for your advice. The result is actually out of our expectation because previous numerical results showed that smoother residual gravity anomalies are obtained when using the SH reference topography and better quasi-geoid models are computed in the case of using 30’ resolution SH reference topography. When the resolution of reference topography increases to 5’, the computed quasi-geoid models are actually at a similar accuracy level. The reason why the DA reference topography yields the slightly better results in terms of SD is still not clear to us at this moment. We have checked all steps in computing the quasi-geoid models. And nothing wrong is found. At least, the results demonstrated that the effect of the type of reference topography is not significant in quasi-geoid computation when the resolution of reference topography is high, such as 5’. In principle, the SH reference topography should be the most proper one. However, there are too many uncertainties to get the results what we want in practical computations. For the current results, one possible reason is that the GNSS/leveling benchmarks are located in flat area for the Auvergne test case and in the valleys for the Colorado test case, making the RTM corrections computed by different types of reference topographies to these points quite close to each other. And hence, the superiority of using the SH reference topography is not evident in this case. Maybe the SH reference topography is good at modeling in the mountainous area. However, this requires GNSS/leveling data in the mountainous region but now we do not have them. Therefore, further in-depth investigations are needed, especially when we have the right data.
A short comment has been added in the revised manuscript.
(65) Page 19, line 546:
“for well describing” à “for properly describing”
Response:
We have corrected this.
(66) Page 19, line 549:
“to be addressed” à “that were addressed”
Response:
We have corrected this.
(67) Page 19, line 560:
“the fully use of” à “the sole use of”
Response:
We have corrected this.
(68) Page 19, line 561:
“while keeping the accuracy and costing less time” à “while maintaining the accuracy and improving the efficiency”
Response:
We have corrected this.
(69) Page 19, line 575:
“are trivial no matter the reference topography” à “are insignificant no matter whether the reference topography”
Response:
We have corrected this.
(70) Page 20, line 595:
“is not sensitive in” à “is not critical in”
Response:
We have corrected this.
(71) Page 20, line 609:
“a similar frame” à “a similar structure”
Response:
We have corrected this.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This study mainly investigated impacts of three factors on RTM correction computation and local quasi-geoid modeling. Various numerical experiments can support their conclusions. Their conclusions are reasonable and their study can provide some useful information to the people in this field. Therefore, I reccomend to publish this manuscript after minor modificaitons.
(1) Are the conclusions are suitable for all the region in the whole Earth or only for the study areas in this manuscript, such as the point mentioned in the last sentence of the Abstract? I sugguest the authors explain this issue.
(2) Lines 549~555, the contents "More specifically, ....on local-geoid modeling be? To answer the two quesitons," should be removed, becasue these contents has been mentioned several times in this manuscript.
Lines 163~167, it seems these should be two sentences. Please check it.
Author Response
Response to Reviewer #2
Are the conclusions are suitable for all the region in the whole Earth or only for the study areas in this manuscript, such as the point mentioned in the last sentence of the Abstract? I suggest the authors explain this issue.
Response:
Thank you for your advice. In this paper, we have studied the DEM resolution combination effect, integration radius effect and reference topography effect on RTM correction computation and local quasi-geoid modeling in two test areas with typical topographic regimes. One is the Colorado test area with rugged terrain and the other is the Auvergne test area with moderate terrain. Rigorously speaking, the conclusions obtained from this study, such as how to combine DEM resolutions, how to choose integration radius, as well as which type of reference topography is preferred, can be directly used in those areas with less rugged terrain than the Colorado test area. For those regions with more rugged terrain, such as the Andes and Himalaya mountains, the current conclusions can be used as reference, or directly used although the parameter settings might not be optimal. To our knowledge, even in the above-mentioned mountains, the SH reference topography and the combination of 3” resolution DEM and the 30” resolution DEM should also work well. Only the inner and outer integration radii need to be selected with caution. As expected, larger values would be preferred.
To clarify this, a short comment has been added in the abstract in the revised manuscript.
Lines 549~555, the contents "More specifically, ....on local-geoid modeling be? To answer the two quesitons," should be removed, because these contents has been mentioned several times in this manuscript.
Response:
Thank you for your advice. As requested, we have removed this part in the revised manuscript.
Lines 163~167, it seems these should be two sentences. Please check it.
Response:
Thank you for your advice. We have divided it into two sentences in the revised manuscript.
Additional revisions made by the authors
All additional revisions made by the authors aim to improve the quality of this manuscript for possible publication in Remote Sensing. The main changes are:
1 The original personal email etlincat@126.com for Miao Lin has been replaced by his institutional email miaolin@xtu.edu.cn.
2 The fourth affiliation “College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, China” has been added.
Author Response File: Author Response.docx
