Constructing Efficient Mesh-Based Global Grid Systems with Reduced Distortions
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper proposes an Efficient Mesh-Based Global Grid Systems with Reduced Distortions, which is a complete data organization architecture and achieve good results. The article is interesting and well-structured, I think MBD can achieve a certain position in the DGGS framework. While, a minor revision is still needed before accepted. Below is the suggestions for modifying this paper:
The first and second sections of this paper are too long and some parts are repetitive descriptions. It is recommended that the author reduce the length of the paper.
Some formulas have insufficient explanations, and some formulas are hidden in the main text without numbering.
The experimental results need to highlight the key points.
If possible, it would be better to compare quadrilateral DGGS methods and grid types.
Author Response
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Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper describes a way to approximate the spherical Earth with a polyhedron. This polyhedron is then used to create a planar grid system with very low distortions.
A general remark is that the method proposed gives so little distortion with respect to the sphere, it is possible that the ca. 20 km flattening of the Earth significantly influence the accuracy of the claimed results. I admit that this is mentioned at multiple places (esp. in section "Future work"). However, until a directly ellipsoidal solution is found, one should convert between the ellipsoid and the sphere using, e.g., an auxiliary latitude.
I also wonder if the increase in polyhedron faces would not result in problems emerging from separating nearby points to different (maybe not even neighbouring) faces, which may result in computation of, e.g., distance even more complicated than it would be using spherical geometry directly.
While the paper is, in general, well-written, I found some minor problems in the understanding of map projections.
Multiple places: "area-preserving"
Please consider to use proper terminology. Equal-area, equivalent, or authalic are all accepted terms for this concept.
l. 141: The WGS84 ellipsoid is the most accurate approximation of the shape of Earth
In my opinion, a geoid would be a more accurate approximation—although way too coplicated for any practical usage.
l. 659: The formula is wrong. The multiplication by two should appear before function arcsine.
"This quantity represents the maximum difference in angle between a point on the spherical circle and a point on the planar ellipse."
Please correct it to, e.g., This quantity represents the maximal difference between a spherical angle and its corresponding mapped image.
"The circle’s radius is set to the minimum distance to one of the cell edges minus a small epsilon. This ensures that none of the sample points of the circle fall into a neighboring base-cell. Then, to approximate the major and minor axis, we sample each circle with 1000 points, project each point, and find the furthest and closest points from the projected center point. Mean, maximum, and minimum distortion values are calculated from these samples."
This probably works and gives approximately acceptable results, but it is very strange to use such an overly complicated method, if closed-form simple textbook formulae have been available to calculate the same quantity for a few centuries. (You can bet that |a|=c/cos^3(d) and |b|=c/cos(d), where c is the distance between the polyhedron face and the centre of the unit sphere, d is the subtended angle between the vector ponting to our point and the vector pointing to the centre of the polyhedron face.) You know, the simpler method you use, the less likely to make an error.
Section 4.4: Please consider to use another term for the ratio between the area of a cell and its spherical counterpart. "Areal distortion" is reserved for a quantity measured at an infinitesimal scale (i.e., the product of the two semi-axes of the infinitesimal distortion ellipse).
l. 886: "Additionally, extending this method to achieve efficient operations with an ellipsoidal spatial domain"
It will not work without significant adjustments: The gnomonic projection of the sphere maps geodesics to straight lines. You used this fact in your algorithm. Unfortunately, the gnomonic projection of the ellipsoid does not map geodesics to straight lines… Furthermore, it has been demonstrated long ago, that it is definitely impossible to map all geodesics of an ellipsoid to straight lines.
Author Response
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Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsI find the article interesting and worth publishing, and I suggest minor corrections.
Page 1, line 26
"… which often result in distortions …" should be changed to ""… which always result in distortions …"
Page 2, line 68
"Area-preserving projections are often used to reduce areal distortion" should be changed to "Area-preserving projections are used to provide zero areal distortion
Page 7
Be careful when citing [9] because there are errors in that paper. For example, the caption below Figure 1 in that paper is wrong.
Page 8, line 327
When you use the abbreviation CG for the first time, it is necessary to explain it.
Page 9, lines 368, 370, 372, 373
Instead of "a index", it should be "an index"
Page 16, line 628
"slice-and-dice" is not a map projection. See [60].
Page 16, line 656
For the definition of angle distortion, you refer to the literature from 2006 [60]. However, this term was known from 1881 (Tissot, A., 1881, Memoire sur la representation des surfaces et les projections des cartes geographiques: Paris, Gauthier Villars) and was later mentioned in all textbooks and manuals on map projections).
Page 17, line 682
Skipepd ?
Page 17, line 684
It would be good to explain the formula for calculating the ideal area of each face.
Page 20
It would be good to explain the meaning of compactness. What does it mean and what is it for?
Pages 26-40
Appendices with a bibliography are mixed in.
The paper is too long. I suggest leaving out all appendices.
Author Response
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Author Response File: Author Response.docx
