Hierarchical Structure of the Central Areas of Megacities Based on the Percolation Theory—The Example of Lujiazui, Shanghai

Round 1

Reviewer 1 Report

The paper is original, interesting and complete. The introduction is clear and very well done, frameworking the research.

The research questions are well posed.

The paper is very dense, too, and some concepts are like compressed in the available space, while some of them are repeated.

I suggest to improve the following in the abstract:

"This study is significant because it proposes a new method to study the hierarchical structure of urban central areas. The research on the hierarchical structure of urban central areas based on percolation theory also provides strategic support and guidance for the development of urban central areas from the perspectives of spatial connectivity, percolation transition, and scale control."

The main research methods and workflow of the study, depicted in Figure 1, can be improved by a wider description.

Please control English form in lines 89-91.

Most of the figures are too small and sometime illegible. This should be improved. It is a pity for such a work, because it highly damages the descriptions of the text. Also they could be better paginated in the paper.

The literary review at 5.1 is in an unusual position: I suggest to consider to present it at the beginning of the paper (even generating some more ideas) and then recall it in the conclusions.

Author Response

Point 1: I suggest to improve the following in the abstract:

"This study is significant because it proposes a new method to study the hierarchical structure of urban central areas. The research on the hierarchical structure of urban central areas based on percolation theory also provides strategic support and guidance for the development of urban central areas from the perspectives of spatial connectivity, percolation transition, and scale control."

Response 1: Thank you very much for your comment. This is a very good suggestion; we realized that the description of this sentence was not accurate, so we modified it to show that the focus of this study is to propose a new method for the delineation of the spatial structure of urban central areas.

Revised abstract: (Lines 10–20)

“The study of an urban center’s hierarchical structure is an important subject if one wishes to understand the city. Previous studies on urban hierarchical structure focused mostly on qualitative or quantitative research based on factors such as format, transportation, and economy, and lacked quantitative measurement from the perspective of street networks. This study examined the urban central area of Lujiazui, Shanghai, from the perspective of the percolation of the street network in the urban central area. Then, combined with the actual urban space function, the connotation and fractal nature of the hierarchical structure of the central area of the mega-city were obtained. The resulting nested hierarchies represent a reorganization of highly agglomerated urban centers that contribute to sustainability. The fractal results were verified by the box counting method. Finally, this study fulfills its main purpose, which is to propose a new method for the study of the hierarchical structure of urban central areas.”

Point 2: The main research methods and workflow of the study, depicted in Figure 1, can be improved by a wider description.

Response 2: Thank you very much for your careful reading and suggestions. We have made a broader description of the technical methods based on your suggestion.

Detailed modifications: (Lines 129–138)

“Percolation has three characteristics: threshold phenomenon, fractal phenomenon, and connectivity [28]. In fact, these three properties have a complementary relationship. The threshold phenomenon represents the morphological transition and critical phenomenon in the agglomeration process of street intersections; the fractal phenomenon ex-presses the morphological similarity and change process between different groups in the results of percolation analysis; and connectivity expresses the implicit relationship be-tween street intersections. In summary, we apply the percolation theory to street intersections in the city center to further understand the hierarchical structure of the city center at different scales. The main research methods and workflow of this study are depicted in Figure 1.”

Point 3: Please control English form in lines 89-91.

Response 3: Thank you very much for your careful reading and suggestions. I have had the entire manuscript proofread once again by a professional English-language editing company. In addition, I have edited these specific lines as shown below.

Modified part: (Lines 91–92)

“The main research question of this study is: Can percolation analysis at street intersections be used as a new method to study the spatial structure of urban central areas?”

Point 4: Most of the figures are too small and sometime illegible. This should be improved. It is a pity for such a work, because it highly damages the descriptions of the text. Also they could be better paginated in the paper.

Response 4: Thank you very much for your feedback. We have optimized all of the images and paginated them in the full text.

Point 5: The literary review at 5.1 is in an unusual position: I suggest to consider to present it at the beginning of the paper (even generating some more ideas) and then recall it in the conclusions.

Response 5:

Thank you very much for this comment. This helped us to become aware of this problem, which is related to our extended exploration in this research. Therefore, we have revised the description in the introduction and conclusion based on your suggestion. My detailed modifications are below.

Modified introduction: (Lines 58–65)

“At present, the research on the hierarchical structure in the field of urban planning mostly judges the entire city from the perspective of economic theory [13-14]. Zhang Xiaoyan [15] used the gravity model to study the hierarchical structure of urban hierarchy structure. Martin J. Beckmann [16] used a mathematical modeling approach to study the urban scale hierarchy. Hans Carol [17] qualitatively divided the hierarchical structure of the urban center through field research on commodity prices and services. There is currently a lack of quantitative hierarchical structure research at the level of urban central areas.”

Modified conclusion: (Lines 458–464)

It is worth noting that in the past, the urban hierarchy was mostly based on the macro-regional perspective [15] or the economic perspective [6-7] to discover the city-scale law, mainly including the discussion of the relationship between the market and the city and the selection of market locations. Research on the urban central area is slightly insufficient. Although this study mainly interprets the hierarchical structure from the perspective of urban functions, in terms of practical problems, the interpretation of urban location theory cannot be abandoned.

Reviewer 2 Report

The article presents a methodology that is suitable for both MDPI Sustainability and the special issue “Spatial Planning and Analysis in Urban Sustainability”. However, some major revisions are needed in order to be ready for publication:

Major revisions:

Overall the methodology is well presented and detailed on sections 3., 4. and 5.. However, the urban impact of its application is not.
The first line of the abstract reads: “The study of an urban center’s hierarchical structure is an important subject if one wishes to understand the city”; and the last line: “(…) also provides strategic support and guidance for the development of urban central areas (…)”, but there is not enough (if any) mention to how the methodology presented does in fact contributes to better understanding the city or how it can provide strategic support or guidance. I would suggest creating subsections on 4. and 5. that would take into consideration:

- For Lujiazui in specific, what does the methodology achieves in terms of the built environment and the urban planning so far? How can this methodology be used to help developing Luijiazui in the future?

- LINE 457 mentions that “percolation results obtained (…) is not universal”. Nevertheless, it would be interesting to add how a percolation analysis could help world-wide megacities to better understand their urban structure and how it could be used as a planning tool for future urban development. The results are not universal but the methodology should be.

- Finally, the article is being propose to be published in a special issued titled: “Spatial Planning and Analysis in Urban Sustainability” in MDPI Sustainability. The urban sustainability part is clearly missing, for both Lujiazui and in general. Not once the word sustainability is mentioned in the text. The presented methodology can be applied to spatial planning but it is important to understand how it can actually help to evaluate and achieve a more sustainable and resilient urban space.

Minor Revisions:

- English needs to be improved, mainly in the first two sections (1. Introduction and 2. Method and Dataset). Long phrases with too much information that are not straightforward to understand.

- Figures are too small with captions that are almost impossible to read.

- LINE 47 marks the end of the introduction and LINE 48 the start of the Review of Research. I would suggest a division into two sections or creating a new subsection at LINE 48.


In more detail:

- LINE 54: “resorts under the nested hierarchical structure”. Why was this model type chosen over the other three? Small description of what it consists based on literature would help readers that might not be familiarised with the method;


- LINE 61-63: Why is this conference taken as a starting point? I would be important to clarify what makes this conference so important as to be considered a starting point;

- LINE 89: I would suggest removing “finally” and creating a new paragraph for the “main research question”;


- LINE 177: I would say “that was imported to GIS”. There is no need to tell that ArcGIS PRO was used, or ArcGIS Maps or QGIS; The importance lays on using a Geographic Information System software;


- LINE 184-107 / Figure 3: If I’m understanding correctly what is being said is that the roads were classified according to their hierarchy. How does “arterial road-sub-arterial road-branch road” matches to what is shown on figure 3 (primary, secondary,…)? Additionally, how were they classified? And what classifies as a primary, secondary… road?
There are several road hierarchy classifications theories, considering between 3/4 up to 7 or more categories. Was this classification based on any of said theories? Some of the roads are classified as XXX_links. I think I understand why they were tagged as links but from my experience I would not make the division, as they act as part of road hierarchy they are connecting to. And, finally, on figure 3 it’s said “roughly 10 groups or type roads”. I don’t think roughly is an exact measure to be presented;


- LINE 180: Again, ArcScan can be left out. It was already mentioned that the network was obtained via OSM, so I would suggest just calling it “road network” from that point forward. Additionally, is it relevant that the image was exported in TIFF format?


- Figure 7 is not mentioned in the text and it is the first thing that appears on subchapter 2.2. I would suggest starting the chapter with the LINES 223-224 and mentioning the figure on that paragraph, presenting it after. Similar situation for figure 12 appearing first and then being mentioned at the end of the paragraph; It should be the opposite;


- Figure 11: Entertainment , financial and cultural function colours are too similar. I would suggest choosing a different set of colours for easier distinction and comprehension;

Author Response

Point 1: Overall the methodology is well presented and detailed on sections 3., 4. and 5.. However, the urban impact of its application is not.

The first line of the abstract reads: “The study of an urban center’s hierarchical structure is an important subject if one wishes to understand the city”; and the last line: “(…) also provides strategic support and guidance for the development of urban central areas (…)”, but there is not enough (if any) mention to how the methodology presented does in fact contributes to better understanding the city or how it can provide strategic support or guidance. I would suggest creating subsections on 4. and 5. that would take into consideration:

- For Lujiazui in specific, what does the methodology achieves in terms of the built environment and the urban planning so far? How can this methodology be used to help developing Luijiazui in the future?

Response 1: Thank you very much for your suggestion. Thanks to your feedback, we realized that this sentence was not very accurate, and so we modified it to show that the focus of this study is to propose a new method for the delineation of the spatial structure of the urban center.

Revised abstract: (Lines 10–20)

“The study of an urban center’s hierarchical structure is an important subject if one wishes to understand the city. Previous studies on urban hierarchical structure focused mostly on qualitative or quantitative research based on factors such as format, transportation, and economy, and lacked quantitative measurement from the perspective of street networks. This study examined the urban central area of Lujiazui, Shanghai, from the perspective of the percolation of the street network in the urban central area. Then, combined with the actual urban space function, the connotation and fractal nature of the hierarchical structure of the central area of the mega-city were obtained. The resulting nested hierarchies represent a reorganization of highly agglomerated urban centers that contribute to sustainability. The fractal results were verified by the box counting method. Finally, this study fulfills its main purpose, which is to propose a new method for the study of the hierarchical structure of urban central areas.“

Point 2: - LINE 457 mentions that “percolation results obtained (…) is not universal”. Nevertheless, it would be interesting to add how a percolation analysis could help world-wide megacities to better understand their urban structure and how it could be used as a planning tool for future urban development. The results are not universal but the methodology should be.

Response 2: Thank you very much for your careful reading and suggestions. This sentence was not very accurate. What I wanted to express was, "It is worth noting that the spatial structure of Lujiazui city center area obtained by percolation analysis is not common to other city center areas."
Detailed revisions: (Lines 384–388)

“What needs to be explained here is that the functions of different urban central areas differ, and the spatial structures reflected under the guidance of non-spatial attributes, such as policies, culture, and economy, also differ. Therefore, the hierarchical percolation results obtained in the urban central area of Lujiazui in Shanghai is not generalizable to other cities.”

Point 3: - Finally, the article is being propose to be published in a special issued titled: “Spatial Planning and Analysis in Urban Sustainability” in MDPI Sustainability. The urban sustainability part is clearly missing, for both Lujiazui and in general. Not once the word sustainability is mentioned in the text. The presented methodology can be applied to spatial planning but it is important to understand how it can actually help to evaluate and achieve a more sustainable and resilient urban space.

Response 3: Thank you very much for your suggestion; we did not notice this part of the instructions. Therefore, based on your suggestions, we have supplement the sustainability-related content in the Introduction and Conclusions.

Introduction revisions: (Lines 24–32)

“Goal 11 of the United Nations Sustainable Development 2030 Agenda proposes to “Make cities and human settlements inclusive, safe, resilient and sustainable” [1]. As the core zone for information, the economy, transportation, and other urban elements, the central area of the city is the starting point for many urban activities, and this can be the foundation for the “basic path focus” [2]. With explosive population growth, the problem of “overloading” appears in the urban central area. Therefore, the construction of efficient, intensive, and sustainable urban centers has gradually become an urgent problem. The optimization of the spatial structure is an important step in promoting the sustainable development of the urban central area.”

Conclusion revisions: (Lines 434–464)

I restructured the conclusion section and linked the conclusion to sustainability.

Point 4: - English needs to be improved, mainly in the first two sections (1. Introduction and 2. Method and Dataset). Long phrases with too much information that are not straightforward to understand.

Response 4: Thank you very much for your detailed reading and suggestions. We have reorganized and carefully optimized the paragraphs, sentences, grammar, and readability of the first two sections. In addition, we have hired a professional editing company to proofread the entire paper.

Point 5: - Figures are too small with captions that are almost impossible to read.

Response 5: Thank you very much for your suggestion. We have optimized all of the images in the full text.

Point 6: - LINE 47 marks the end of the introduction and LINE 48 the start of the Review of Research. I would suggest a division into two sections or creating a new subsection at LINE 48.

Response 6: Thank you very much for your detailed reading and suggestions. I have divided this into two subsections as you suggested and named the first section “1.1 Hierarchical structure and percolation analysis.”

Point 7: - LINE 54: “resorts under the nested hierarchical structure”. Why was this model type chosen over the other three? Small description of what it consists based on literature would help readers that might not be familiarised with the method;


Response 7: Thank you very much for your detailed reading and suggestions. Since the hierarchical structure is generally applied to object relationships in the computer field, this research chooses the most basic nested hierarchical structure that can express spatial object relationships. I have supplemented this part of the content accordingly.

Detailed modifications: (Lines 51–57)

“The nested hierarchy is a sorting structure with recursive properties, while the other three hierarchical structures are more specific extensions of the nested structure with different emphases, focusing on the relationship between object attributes in the computer field. Therefore, in this study, the nested hierarchical structure is used to express the implicit relatively primary inclusive relationship between urban block spaces so as to discover the interactive relationship between space and functional attributes.”

Point 8: - LINE 61-63: Why is this conference taken as a starting point? I would be important to clarify what makes this conference so important as to be considered a starting point;

Response 8: Thank you very much for your careful reading and suggestions. This sentence was inaccurate, so I removed this section.

Detailed modifications: (Lines 66–67)

“Percolation analysis at street intersections provides a new approach to the study of sustainable urban center hierarchies.”

Point 9: - LINE 89: I would suggest removing “finally” and creating a new paragraph for the “main research question”;


Response 9: Thank you very much for your detailed reading and suggestions. We have made changes based on your suggestion.

Detailed changes: (Lines 91–92)

“The main research question of this study is: Can percolation analysis at street intersections be used as a new method to study the spatial structure of urban central areas?”

Point 10: - LINE 177: I would say “that was imported to GIS”. There is no need to tell that ArcGIS PRO was used, or ArcGIS Maps or QGIS; The importance lays on using a Geographic Information System software;


Response 10: Thank you very much for your detailed reading and suggestions. We have revised this phrasing based on your suggestion.

Detailed changes: (Line 163–166)

First, the preliminary acquisition of OpenStreetMap (OSM) data and the definition of the central area of Lujiazui, Shanghai are as follows. This study obtained data from OSM (https://www.Openstreetmap.org/#map=6/46.449/2.210) to collect the street network data of the central area of Lujiazui, Shanghai, and imported it to GIS.

Point 11: - LINE 184-107 / Figure 3: If I’m understanding correctly what is being said is that the roads were classified according to their hierarchy. How does “arterial road-sub-arterial road-branch road” matches to what is shown on figure 3 (primary, secondary,…)? Additionally, how were they classified? And what classifies as a primary, secondary… road?
There are several road hierarchy classifications theories, considering between 3/4 up to 7 or more categories. Was this classification based on any of said theories? Some of the roads are classified as XXX_links. I think I understand why they were tagged as links but from my experience I would not make the division, as they act as part of road hierarchy they are connecting to. And, finally, on figure 3 it’s said “roughly 10 groups or type roads”. I don’t think roughly is an exact measure to be presented;


Response 11: Thank you very much for your detailed reading and suggestions. We have optimized the images you mentioned based on your suggestions and filtered out redundant road features.

Detailed changes: Figure 3

Point 12: - LINE 180: Again, ArcScan can be left out. It was already mentioned that the network was obtained via OSM, so I would suggest just calling it “road network” from that point forward. Additionally, is it relevant that the image was exported in TIFF format?


Response 12: Thank you very much for your detailed reading and suggestions. I apologize that the earlier version of this section was unclear. Since the roads obtained through OSM are still complex, further simplification is required. Therefore, the main purpose of this step is to vectorize the TIFF image and finally get the road centerline, that is, the “road network.”

Point 13: - Figure 7 is not mentioned in the text and it is the first thing that appears on subchapter 2.2. I would suggest starting the chapter with the LINES 223-224 and mentioning the figure on that paragraph, presenting it after. Similar situation for figure 12 appearing first and then being mentioned at the end of the paragraph; It should be the opposite;


Response 13: Thank you very much for your detailed reading and suggestions. We have adjusted the content of this section based on your suggestions.

Detailed changes: Line189-191 / Line361-364

Point 14: - Figure 11: Entertainment , financial and cultural function colours are too similar. I would suggest choosing a different set of colours for easier distinction and comprehension;

Response 14: Thank you very much for your detailed reading and suggestions. We have optimized the pictures you mentioned so that the different functional groups can be more clearly identified. My detailed modifications are as follows:

Detailed changes: Figure 11(Line337-338)

Round 2

Reviewer 2 Report

The authors have address all my concerns and suggestions making the necessary changes to the manuscript. I have nothing else to add.

Author Response

Dear Reviewer：

Thank you very much for your reply. We have made further minor revisions based on suggestions from academic editors. Adjust the limitations to the discussion section, and supplement other related studies from four aspects: research object, research method, research results, and generality of conclusion. Also in the Introduction, the rest of the Discussion has been slightly altered.

Main modifications: (Lines 391–417)

“This study has certain limitations. From the perspective of the research object, this study only conducts percolation analysis at street intersections, but in fact the complex and diverse composition of urban central areas still requires more diverse perspectives to interpret it. For example, Behnisch [31] applied percolation theory to quantify building connectivity to detect different urban boundaries. Arcaute [20] used commuting and population density to define the boundaries of urban systems and explored the relationship between urban indicators and scale. Cao [32] performed percolation analysis on population, roads, and nighttime lights to quantify urban extent. Montero  [33] found that MorphoLim method and percolation method obtained different morphological boundaries of urban agglomerations. From the perspective of research methods, this study only analyzes urban space, but lacks the consideration of location economy. At present, the research on the urban hierarchy is mostly based on the central place theory, from the perspective of microeconomics. For example, Hsu [7]  used the equilibrium model to obtain the urban spatial hierarchy from the perspective of microeconomics, which verified the central place theory. Tabuchi [34]  used the equilibrium method to provide a new economic research basis for the central place theory. Space and economy are both components of the spatial structure of urban central areas, and how to combine the two may be an important direction for future research. From the research results, this study obtains the static urban spatial structure at different scales through the percolation method but lacks the dynamic urban spatial evaluation. For example, Li  [35] conducted traffic congestion assessment from the nodes of dynamic traffic percolation transition. He [36] constructed a temporal hierarchical network through human movement data to control the spread of infectious diseases at multiple scales. In terms of the generality of the conclusions, the results of the division of the block-scale spatial structure in the central area of Lujiazui based on the percolation theory are not universal, and the block-scale and hierarchical structure of different types of urban central areas may need to be further discussed in the future.”

Sincerely

Author Response File: Author Response.docx