A GtoG Direct Coding Mapping Method for Multi-Type Global Discrete Grids Based on Space Filling Curves

Round 1

Reviewer 1 Report

This manuscript aims at a direct mapping method for converting one DGGS encoded data to another one. This is an important problem related to interoperability among different grid systems. The manuscript has an excellent introduction to surveying various global grid systems and summarizing in an informative table ( 1-to 2 DGGS system should be added (One-to-two digital earth, Amiri et al.)).

Comparisons: The manuscript provides a good motivation for mapping codes between different systems without the use of the lat-long and spherical intermediate domains:

“The longitude-latitude is a floating-point format and lacks hierarchical features, which will lead to 58

a huge computing cost and low efficiency in the integrated analysis and interoperability 59

of multi-source data in DGGS. “

Several experimental comparisons in Section 4 have supported this claim. However, the base for Long-lat comparisons has not been clarified. While the proposed method seems to have a good effeicency ratio,  this kind of mapping is usually used in preprocessing and off-line scenarios. One of the main advantages of DGGS over traditional lat-long is its ability to handle uncertainty resulting from floating-point; however it is unfortunate to see the result of this work will generate uncertainty.

 

The scope and limitations:  As evident in Table 1 and also the introduction of the manuscript, there are many variations of DGGS, including the type of initial polyhedron, cell type, refinement and the employed indexing. An elegant mapping should work for many of these. The proposed method only works with icosahedron as the initial polyhedron, and one type of refinement (1 to 4), and some specific types of indexing. Also, the mapping is done only at the same resolution. These limitations make the significance of the proposed method low. I would appreciate it if the authors put the effort into expanding the scope of this work by addressing some of the limitations.

 

 

Missing related work: Hierarchical grid conversion (Amiri et al.):  some of the mappings between different cell types are a simple form of methods covered in the above paper. This manuscript assumes that cells have the same resolution, while in that paper, the mapping between grids is described for all resolutions. Obviously, they do not aim at the mapping between indices, but their mapping can also be used for this purpose.

Author Response

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Reviewer 2 Report

Overall this is a very interesting paper that provides a good basis for further work developing DGGS index schema mapping across different DGGS implementations. That said, the approach described in the paper will only work effectively if each DGGS is aligned to each other. If the orientation of the base polyhedron between different DGGS implementations is different then a different approach will need to be taken. This paper does, however, acknowledge this challenge.

There are some very minor typographical/gramatical errors in the manuscript described below.  

Line 38 - "...foundation of modern digital earth..." should read "...foundation of a modern digital earth..."

Line 50-51 - "...and planning analyze..." should read "...and planning for analysis"

Line 141 - "On each triangular surface of icosahedron..." should read "On each triangular surface of the icosahedron..."

Line 352-353 - "Since both hexagonal and diamond grid adopt quadtree partition structure..." should read "Since both the hexagonal and diamond grids adopt a quadtree partition structure..."

Line 519 - "...than the average diameter of grid cells at corresponding level..." should read "...than the average diameter of grid cells at the corresponding level..."

Line 542 - "...Attribute uncertainty of discrete line is the length..." should read "...The attribute uncertainty of a discrete line is the length..."

Line 543 - "...position offset of discrete line..." should read "...position offset of a discrete line..."

Line 576 - "...In addition to icosahedron, regular polyhedron also includes..." should read "...In addition to the icosahedron, regular polyhedrons also includes..."

 

 

Author Response

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Reviewer 3 Report

Dear colleagues, 

thank you for your effort and wonderful results with your GtoG coding mapping method for multi-type global discrete grids. The topic on grid systems gains importance in a common data space. Therefore any mapping and its quality constraints become important. 

Your contribution starts with listing discrete global grid systems and their index structure, introduces into the indexing of different grid systems, evaluates a direct mapping for diamond, triangular and hexagonal grid code, compares and analyses the mapping in an experimental way by its efficiency and accuracy and (most importantly) discusses the three observed dimensions of uncertainty (position, attribute and topological relationship). From my point of view the comparison and discussion touches the most important topics that need to be considered when dealing with grid systems. 

There are some minor changes that I recommend: 

(1) The tables 3 to 15 are important, but influence the reading flow. Could these tables be moved to an appendix?

(2) There is an editorial in line 120: gird should be grid

(3) The list of discrete global grid subdivisions in table 1 is extensive. There is one famous grid, the "Open Location Code" (https://plus.codes/), that is missing and could enhance understanding to the importance of grid systems. Doesn`t it fit in your observation?

Thank you a lot for your work.

 

Author Response

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Round 2

Reviewer 1 Report

The scope and limitations:  As evident in Table 1 and also the introduction of the manuscript, there are many variations of DGGS, including the type of initial polyhedron, cell type, refinement and the employed indexing. An elegant mapping should work for many of these. The proposed method only works with icosahedron as the initial polyhedron, and one type of refinement (1 to 4), and some specific types of indexing. Also, the mapping is done only at the same resolution. These limitations make the significance of the proposed method low. I would appreciate it if the authors put the effort into expanding the scope of this work by addressing some of the limitations.

 Response 4: In the Discussion 5.2, it is explained that the mapping rule base in this paper can also be directly applied to tetrahedra, octahedron and hexahedron. The extensibility of this article's mapping library is also added in line 595-597. In future work, we will continue to improve the mapping library, hoping to be applicable to various polyhedra and subdivision types.

This is the new text concerning this comment:” Although the mapping rule base in this paper can not be directly used for other aperture and coding grid conversion, but the idea of this paper can still be used, the corresponding mapping rule base needs to be slightly changed.”

 

 

This comment was the main reason why I decided on a major revision (low ranking in Significance of Content). Unfortunately, the authors have not put any effort into addressing this comment. At least, it is expected to have a more in-depth discussion of the scenarios in that they can modify the proposed rule-based methods for other grid types. Also, I think with the help of Hierarchical grid conversion (Amiri et al.) the authors may be able to use a broader method for other grid types.

Author Response

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Round 3

Reviewer 1 Report

The authors have added new parts to Section 5 that address my primary comment.