On Finding a Projected Coordinate Reference System

Round 1

Reviewer 1 Report

Dear Authors,

I found your research within this article very interesting and useful and hope that you'll continue this research in the near future.

Best regards!

Author Response

Response to Reviewer 1 Comments

Dear Authors, I found your research within this article very interesting and useful and hope that you'll continue this research in the near future. Best regards!

Dear reviewer, thank you very much for your appreciation and kind words. We will definitely continue our work and find your words very motivating to do so.

Reviewer 2 Report

This is a very valuable article. I only have a few minor comments.

• In the introduction after the sentence "Research pointed out that of the most principal concerns within the world of geographical data is the quality or reliability of the data [3]." I propose to give specific examples, e.g. from geomorphology. The credibility of the data was reported by, inter alia:
  • Hohensinner, S.; Egger, G.; Muhar, S.; Vaudor, L.; Piégay, H. What remains today of pre-industrial Alpine rivers? Census of
    historical and current channel patterns in the Alps. River Res. Appl. 2021, 37, 128–149.
  • Nardini, A.; Brierley, G. Automatic river planform identification by a logical-heuristic algorithm. Geomorphology 2021, 375, 107558.
• Write in the Materials and Methods why you chose these countries.
• In the discussion, refer to the Austrian maps available on mapire.eu. In their methodological guides, they described the problem you discussed.
• Browse through all the references and adapt to journal requirements. Especially items number 7, 10, 14, 15, 17-24, 26, 30-32.

Author Response

Response to Reviewer 2 Comments

Point 1: In the introduction after the sentence "Research pointed out that of the most principal concerns within the world of geographical data is the quality or reliability of the data [3]." I propose to give specific examples, e.g. from geomorphology. The credibility of the data was reported by, inter alia:

• Hohensinner, S.; Egger, G.; Muhar, S.; Vaudor, L.; Piégay, H. What remains today of pre-industrial Alpine rivers? Census of
  historical and current channel patterns in the Alps. River Res. Appl. 2021, 37, 128–149.
• Nardini, A.; Brierley, G. Automatic river planform identification by a logical-heuristic algorithm

Response 1: Thank you for pointing this out and providing these truly interesting references. We implemented the suggestion on line 78 instead of line 38: “(i.e., geology, archaeology, geomorphology), but refrained from adding specific use cases such as the ones provided since this would require an overload of examples from every application domain, which overarches the scope of the introduction. Besides, we believe the provided references are also outside of the scope of the paper in general, because the credibility of historical geomorphological map data is not assessed in this work (Hohensinner et al., 2021) or the issue on georeferencing maps is not addressed (Nardini & Brierley, 2021).

Point 2: Write in the Materials and Methods why you chose these countries.

Response 2: In section 2.1.7, we mention that “solutions for some Western European countries were found”, and the phrase “…notably Belgium and its neighboring countries” to specify this. We do realize that this is a limitative overview and that many other solutions can be presented. The selection for these specific countries is not based on any scientifically sound method and is rather arbitrary or random to illustrate the availability of information at national mapping agencies. We do not think that this requires further elaboration in the manuscript.

Point 3: In the discussion, refer to the Austrian maps available on mapire.eu. In their methodological guides, they described the problem you discussed.

Response 3: We would like to thank the reviewer for this suggestion. Although a reference to the mapire-project itself has not been added, we added the following phrase, with reference to two papers presented at this website: “In various of these cases, one could opt for the use of unambiguously identifiable features on the map itself, like large constructions or characteristic topographic shapes. However, this is a very time-consuming process and does not always benefit the geometrical quality of the georeferenced map. The quality of the georeferencing – especially when using features on the map – is hampered by various factors, like the positional accuracy and the scale of the map, mapping errors, but also scanning resolution and paper distortions [44] In order to obtain an acceptable result, a large series of ground control points will be required [45]. (…) Hence, especially for large systematic map series, the use of the corners of the map for both georeferencing and CRS determination is advised.“

Point 4: Browse through all the references and adapt to journal requirements. Especially items number 7, 10, 14, 15, 17-24, 26, 30-32.

Response 4: Thank you. The references are thoroughly revised in accordance with the journal’s guidelines.

Reviewer 3 Report

The authors propose an automatic method to find the „best“ coordinate reference system for spatial data assigned with an incorrect or a missing coordinate reference system. This is a highly relevant contribution in particular when working with geospatial data of disparate sources, time periods and acquisition methods. Well written and relevant. However, there are a few issues that should be fixed prior to publication (see below). I recommend major revision.

Abstract: The authors state: „They [CRS] are considered the ultimate binder for interoperability between geospatial data actors and stakeholders.“ : Not only this, but more importantly, for the visual and analytical integration of geospatial data from disparate data sources. --> Please add this to the sentence.

Abstract: the authors state „However, CRS are – for numerous reasons – often not in place.“ : I find this wording confusing. First, I would not say this happens „often“ – generally, professionally produced geospatial data does not suffer from such mistakes. It may happen in certain industries, often linked to changes in officiall used coordinate systems (e.g., change from GK to UTM in German cadastral data standards). Second, the term „not in place“ may suggest a „shift“ in the coordinates or somthing like that. I assume this is not what the authors mean. If I understand correctly, they refer to incorrect assignments of CRS (e.g., data is in NAD1983, but the assigned CRS is NAD1927).

 I would reword this to: „However, CRS may be – for numerous reasons – incorrectly assigned.“

Please define the acronym EPSG at first occurence in abstract and main text. In line 61, it would be interesting to read more about EPSG! Who created it, when, and why? Who maintains it? This would constitute interesting additional information.

Line 56: “..three-dimensional, two-dimensional or compound coordinate reference systems“: This is somewhat inaccurate and ambiguous. I understand what you are trying to get at, but this should be phrased more specifically. So would EPSG:4326 be considered two-dimensional? It actually has two dimensions, but describes a location in a 3d-space (on the WGS84 ellipsoid) – I would distiungish here between cartesian coordinates (X,Y) or (X,Y,Z) and spherical / ellipsoidal coordinates (Lat,Lon) – this would be more accurate. Moreover, if you add the height component here – would you consider an elevation reference system as 1d? And by compound systems you mean a CRS describing the planar component plus a vertical component? I would rather introduce the terms „horizonal“ vs „vertical“ CRS here first.

Line 57: The authors should mention here that there are basically two types of CRS: geographic and projected CRS – and describe their differences (spherical/ellips. Coordinates versus planar / Cartesian coordinates) and further break this down and add a few sentences to discuss the components that define a CRS: The geodetic datum, the reference ellipsoid / sphere, and, in the case of projected CRS, the cartographic projection rule that transforms from spherical / ellips. to planar coordinates, plus the coordinate system (i.e., orientation of the axis and location of the coordinate system origin (0,0). Also, the measurement unit (m, ft, degree) is considered part of the CRS as well.

Line 59: why the „and/or“ ? Are there any CRS that specify coordinates in both XYZ and Lat,Lon,h at the same time? I think this should just be „or“ here.

Line 64: „CRS or EPSG system“ - What is an EPSG system? I think you just mean CRS here.

Line 94: No need to define „CRS“ again – has been done in the Intro already.

Line 391: Should this be „NOT accompanied“ ?

Conclusion section: An obvious limitation is that this method only works for CRS that are based on projected reference systems (as you correctly state in the paper title!), but not for geographic reference systems (e.g., if we have NAD1927 lat,lon coordinates incorrectly declared as WGS84 or NAD1983 lat,lon) – this will result in systematic displacements of a up to a few 100m - in this case, would your method work ? Since your method is based on the CRS BBOX (which would be -90,90,-180,180 for a geographic CRS) would it still work?

Also, what is the role of the positional accuracy of the Nominatim geolocator API? If the displacement induced by the incorrect CRS assignment only causes slight offsets (< than the positional accuracy of the Nominatim API) – would your approach still work? Please elaborate on this and state such limitations clearly.

Other aspects of positional accuracy should be discussed – e.g. the positional accuracy in (scanned) historical maps may be affected by cartographic generalization, paper distortions, georeferencing inaccuracies, ...), how would this interfere with the proposed method?

Author Response

Response to Reviewer 3 Comments

General feedback: The authors propose an automatic method to find the „best“ coordinate reference system for spatial data assigned with an incorrect or a missing coordinate reference system. This is a highly relevant contribution in particular when working with geospatial data of disparate sources, time periods and acquisition methods. Well written and relevant. However, there are a few issues that should be fixed prior to publication (see below). I recommend major revision.

General response: We would like to thank reviewer 3 for providing clear remarks about elements concerning accuracy that should not be forgotten in a work like this. The proposed adaptations will contribute a lot to a clear and comprehensive work.

Point 1: Abstract: The authors state: „They [CRS] are considered the ultimate binder for interoperability between geospatial data actors and stakeholders.“ : Not only this, but more importantly, for the visual and analytical integration of geospatial data from disparate data sources. --> Please add this to the sentence.

Response 1: Thank you for this valuable suggestion. We implemented you suggestion accordingly.

Point 2: Abstract: the authors state „However, CRS are – for numerous reasons – often not in place.“ : I find this wording confusing. First, I would not say this happens „often“ – generally, professionally produced geospatial data does not suffer from such mistakes. It may happen in certain industries, often linked to changes in officiall used coordinate systems (e.g., change from GK to UTM in German cadastral data standards). Second, the term „not in place“ may suggest a „shift“ in the coordinates or somthing like that. I assume this is not what the authors mean. If I understand correctly, they refer to incorrect assignments of CRS (e.g., data is in NAD1983, but the assigned CRS is NAD1927). I would reword this to: „However, CRS may be – for numerous reasons – incorrectly assigned.“

Response 2: This is a valuable thought. The suggestions have been implemented in the abstract, as follows: “…CRS might be – for numerous reasons – incorrectly assigned or even missing”. We have added the possibility of a missing CRS, which is frequently the case when working with historical data. Furthermore, we extracted some useful aspects of this discussion and added the following phrases:
Section 1: “Thirdly, indistinctness might occur when officially used CRS are changes from one system to another (e.g. from Lambert 72 to Lambert 2008 in Belgium or from Gauss-Krüger to UTM in Germany).”

Point 3: Please define the acronym EPSG at first occurrence in abstract and main text. In line 61, it would be interesting to read more about EPSG! Who created it, when, and why? Who maintains it? This would constitute interesting additional information.

Response 3: We added some additional information about the dataset, accompanied with some references that will guide the reader towards more information: “EPSG stands for “European Petroleum Survey Group” and is frequently used to refer to the registry of CRS parameters originally developed and maintained by this organization since 1985 and is publicly accessible since 1993. Since 2005, the dataset is maintained by the Geomatics Committee of the International Association of Oil & Gas Producers (IAOGP), which describe the dataset as “a collection of definitions of coordinate reference systems and coordinate transformations which may be global, regional, national or local in application” [12]. CRS are update twice a year by the IAOGP and systems are described in accordance with the ISO 19111 standard [13]. Notwithstanding the widespread use of the dataset, it is not recognized as a standard sensu stricto [14].”

Point 4a: Line 56: “..three-dimensional, two-dimensional or compound coordinate reference systems“: This is somewhat inaccurate and ambiguous. I understand what you are trying to get at, but this should be phrased more specifically. So would EPSG:4326 be considered two-dimensional? It actually has two dimensions, but describes a location in a 3d-space (on the WGS84 ellipsoid) – I would distiungish here between cartesian coordinates (X,Y) or (X,Y,Z) and spherical / ellipsoidal coordinates (Lat,Lon) – this would be more accurate. Moreover, if you add the height component here – would you consider an elevation reference system as 1d? And by compound systems you mean a CRS describing the planar component plus a vertical component? I would rather introduce the terms „horizonal“ vs „vertical“ CRS here first.

Point 4b: Line 57: The authors should mention here that there are basically two types of CRS: geographic and projected CRS – and describe their differences (spherical/ellips. Coordinates versus planar / Cartesian coordinates) and further break this down and add a few sentences to discuss the components that define a CRS: The geodetic datum, the reference ellipsoid / sphere, and, in the case of projected CRS, the cartographic projection rule that transforms from spherical / ellips. to planar coordinates, plus the coordinate system (i.e., orientation of the axis and location of the coordinate system origin (0,0). Also, the measurement unit (m, ft, degree) is considered part of the CRS as well.

Response 4: We would like to address these two remarks in one run. On the one hand, we understand what the reviewer is trying to make clear. On the other hand, it must be noted that this part of the text was a literal quote from the INSPIRE guidelines. However, as our goal with this work is to provide a accessible tool which can also be used by a non-expert audience as well, it was chosen to write the text as to the point as possible. For this reason, we propose to remove the quote and to incorporate an adaptation adopting the terms “horizontal” and “vertical” CRS, with a compound CRS being a CRS providing both horizontal and vertical component. We shortly discuss geographical versus projected CRS, leaving out geocentric systems in order to remain comprehensible. We also added a reference to more specialized material, as we believe the text becomes incomprehensible for a layperson audience, when explaining the components of a CRS (and the many “special cases” to really come to a closed explanation/definition).

Point 5: Line 59: why the „and/or“ ? Are there any CRS that specify coordinates in both XYZ and Lat,Lon,h at the same time? I think this should just be „or“ here.

Response 5: The use of “and/or” was indeed confusing here. Thank you for the suggestion to remove this.

Point 6: Line 64: „CRS or EPSG system“ - What is an EPSG system? I think you just mean CRS here.

Response 6: Indeed. However, to clarify this section, we have added “…well-defined CRS definitions (like the aforementioned EPSG standardization in international specifications)”.

Point 7: Line 94: No need to define „CRS“ again – has been done in the Intro already.

Response 7: The definition was indeed redundant here and has been removed.

Point 8: Line 391: Should this be „NOT accompanied“ ?

Response 8: The word ‘NOT’ should be added here. Instead, we modified the following phrase: “…or when a raster dataset is accompanied by a regular ASCII-encoded world file instead of embedded data about the CRS)”. The world-file only contains the translation, rotation, and scale parameters, and no information about the actual CRS.

Point 9: Conclusion section: An obvious limitation is that this method only works for CRS that are based on projected reference systems (as you correctly state in the paper title!), but not for geographic reference systems (e.g., if we have NAD1927 lat,lon coordinates incorrectly declared as WGS84 or NAD1983 lat,lon) – this will result in systematic displacements of a up to a few 100m - in this case, would your method work ? Since your method is based on the CRS BBOX (which would be -90,90,-180,180 for a geographic CRS) would it still work?

Response 9: This issue is addressed in section 3.5, where the detection of the most appropriate CRS is illustrated for two examples. For some cases, our method indeed works for geographic CRS, but this is more an exception than a rule, and we tend to focus on projected coordinates. To integrate your correctly mentioned thought, we added the following phrase for sake of completeness: “For other examples where coordinates are expressed in a geographic CRS, like WGS84, NAD27, … the most probable CRS could not be selected due to the limited deviations be-tween the various systems.” Furthermore, a second phrase has been added to the conclusion: “Most of these CRS were projected systems, but some geographic systems were also successfully tested. For these systems, reservation is required on the final selection of the CRS, as difference between various systems will be limited.” Also, the initial distinction between projected and geographic CRS is clarified by adding the following sentence to section 2.2: “A preliminary selection of the CRS (projected or geographic) is based on the nature of the coordinates.”

Point 10: Also, what is the role of the positional accuracy of the Nominatim geolocator API? If the displacement induced by the incorrect CRS assignment only causes slight offsets (< than the positional accuracy of the Nominatim API) – would your approach still work? Please elaborate on this and state such limitations clearly.

Response 10: The Nominatim API returns a parameter “confidence” that represents the accuracy of the solution: “The confidence relates to how certain we are that the result corresponds to the input. For example, if you get a result for "10 street" and for "120 street", the confidence will be smaller than a result for "12 street". The accuracy relates to the returned location. If the data comes from GPS address point, it is very accurate. If it is extrapolated from a road segment min-max address, it is somewhat accurate. If it is extrapolated from the postal code is has a lower accuracy.” However, without trying to quantify the accuracy of the geocoding, the main influential elements are the input by the user (the extent of the inputted location: a city vs a street in a city) and the quality of the underlying data, which is the OpenStreetMap data in the case of the Nominatim-api. To give a clear answer on your question is not possible. However, it is indeed useful that we inform possible future users to try to be as precise as possible with the inputted location.

Point 11: Other aspects of positional accuracy should be discussed – e.g. the positional accuracy in (scanned) historical maps may be affected by cartographic generalization, paper distortions, georeferencing inaccuracies, ...), how would this interfere with the proposed method?

Response 11: These factors have a reasonable impact on the quality of the georeferencing process, but the influence on the CRS determination itself is limited. Still, we agree that it is important to mention this in the correct context of our work and we added the following phrase: “In various of these cases, one could opt for the use of unambiguously identifiable features on the map itself, like large constructions or characteristic topographic shapes. However, this is a very time-consuming process and does not always benefit the geometrical quality of the georeferenced map. The quality of the georeferencing – especially when using features on the map – is hampered by various factors, like the positional accuracy and the scale of the map, mapping errors, but also scanning resolution and paper distortions [44] In order to obtain an acceptable result, a large series of ground control points will be required [45]. These factors will have an influence on the georeferencing itself, but the impact on the detection of the most appropriate CRS, as presented in this work, is limited. Hence, especially for large systematic map series, the use of the corners of the map for both georeferencing and CRS determination is advised.”

Round 2

Reviewer 3 Report

The Authors addressed all of my comments. I think this is in good shape for publication.

One minor detail:

in line 73: please replace "without giving up correctness" with "without introducing distortion" - I would say the projection introduces distortion, but that does not make the coordinates in a projected CRS incorrect - they are correct with respect to the mathematical projection rule. "Correctness" has a different meaning in the uncertainty-related literature (e.g., correctness vs completeness).

Author Response

The Authors addressed all of my comments. I think this is in good shape for publication.

Point 2-1: One minor detail: in line 73: please replace "without giving up correctness" with "without introducing distortion" - I would say the projection introduces distortion, but that does not make the coordinates in a projected CRS incorrect - they are correct with respect to the mathematical projection rule. "Correctness" has a different meaning in the uncertainty-related literature (e.g., correctness vs completeness).

Response 2-1: Dear reviewer, thank you very much for your constructive feedback. We are happy to read that the previous series of remarks have been properly addressed in accordance with the interesting debate we had about the various points. It is a pleasure to inform you that the last remark has been implemented as suggested.