Accuracy Evaluation of Geoid Heights in the National Control Points of South Korea Using High-Degree Geopotential Model

Round 1

Reviewer 1 Report

General comments and remarks:

Minor considerations and corrections:

Abstract: precise geoid heights are not so important to understand Earth’s gravity field, but they are important to Geodesy itself, since geoid is defined as the vertical reference, how much precise it is the better the vertical reference frame is defined. Sentence should be reviewed.

Section 1:

               Lines 39-41: The referred GGMs have authorship so references must be introduced here;

Lines 62 and 67: “goodness of fit” is not a scientific term, you must want to refer instead the “accuracy” and “precision”, corresponding to the mean or mean square root and the standard deviation of residuals;

               Lines 73-74: review the last sentence.

Line 98: Reference should be introduced in the Table legend.

Line 110: units should come after spaced numerical values (10 km)

Line 133: G is doubled and second definition is miss-referred, second G should be M, the Earth mass

Line 139: Please check Equation (2). There is no reason to present two similar equations, you can explain the limitation of an infinite series and its maximum degree of approximation without repeat a similar equation.

Line 150: information here is repeated, it has been mentioned before. Try to not repeat information.

Line 168: used a better word than “traditionally”, for instance “conventionally” since tradition comes from culture and not science. This equation should have some scientific references.

Line 180: used instead of “utilized”

Lines 180 – 185: You use 3 models (four, five and 7 parameter model) to fit geoid model to observed geoid undulation. They give you 3 different solutions of fitting, how you estimate accuracy? Each fitting model will return a different accuracy.

Lines 201-207: review English writing, you repeat to many times “Figures 2 and 3”. Since the paragraph is all about those figures it is not needed.

Lines 226 -237: references to minimum, maximum, mean and standard deviation to the Figures 4, but acronyms AR, AM and ASD are not defined in the legend of Figure and the respective correspondence is difficult to understand. Make references in the text to those acronyms and define them in the legend of Figure 4

Figures 4a – 4c: instead of equal maps, which seam no be any different, you should present surface maps of the residual. It would show the error spatial distributions, giving a better understanding of the model validation

Figure 5: the same as mentioned for Figure 4, the acronyms and surface map of resoduals

Lines 300-307: Review the English writing of this paragraph

               Lines 324-327: Differences in SD are not significant, they are all the same magnitude. 2 to 3 mm of difference do not represent a significant improvement, since the magnitude of SD is 10 cm.

Lines 351-355: What is a “stable result for standard deviation”? The results for all 3 GGM are similar. Differences are negligible. The supposed stability in the SD is supposedly observed in the 3 models. This conclusion should be reviewed.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This paper compares geometric (GNSS/levelling) geoid in Korea with gravimetric geoid and global geopotential geoid models.
It basically consist of the following parts:

- comparing geometric geoid at GNSS/ levelling points with interpolated gravimetric geoid at GNSS/ levelling points: This is the only part that in my view should be published.

- comparing geometric geoid at GNSS/ levelling points with global geopotential geoid models: the authors claim that, this comparison tell us which global model is suitable for Korea, but in page 1, they mention that in calculating gravimetric geoid KNGeoid13, EGM2008 has been used. The conclusion of the paper is also that EGM2008 is the best choice for Korea. So by comparing geometric geoid at GNSS/ levelling points with global geopotential geoid models, they do not reach any new conclusion.

- fitting a model to the geometric-gravimetric geoid difference, and the geometric-global geopotential geoid difference. I do not understand this part, and why and where these three 4, 5 and 7 parameters models could be useful. They conclude that 7 parameters model is the best fit; but where and how this model could be used?

Please see attached the PDF for the list of my technical comments.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have improved the article, but still my main concern is that the authors do not make a strong case for

1- comparing GNSS/ levelling geoid with global geopotential geoid models.
2- fitting models to the geoid differences

I also have two minor comments:

1- Comparing Figure 4 with Figure 6, there are not any zero contour lines in Figure 6. Could the authors provide a comment about this.
2- Equation 8 is not yet correct.

Author Response

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Author Response File: Author Response.docx

Round 3

Reviewer 2 Report

The authors have improved the article, but I believe the part about fitting models to the geoid differences is redundant and does not add any value to the paper.

For example, Table 5 already shows better statistics for EGM2008, and the least square adjustment makes no difference in this conclusion.
Also equation (8) has never been used and referred in the paper.

Author Response

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Author Response File: Author Response.docx