Scale and Aggregation Effects of MAUP on Built-Up Area Concentration: Evidence from the Łódź Metropolitan Area
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe main problem of the article concerns the reliability of results derived from geographical studies of varying scales and spatial resolutions (i.e., in reference grids and spatial units differing in size and shape), using the example of issues related to the spatial differentiation of land cover in the areas of urbanization of the Łódź Metropolitan Area. The hypotheses being examined include the significance of how the choice of scale, shape, number, and size of spatial reference units affects the results of geographical research, as well as their sensitivity to changes in the degree of data aggregation and the characteristics of the basic spatial units of analysis. The discussion showed that the detail of the input data is very important for the results, as using less detailed data can make urban concentration seem higher than it really is. The study also confirms that larger computational units systematically underestimate the concentration level by smoothing out local differences. Ultimately, the work highlights the necessity of applying a multi-scale and multi-resolution approach in spatial planning to avoid errors in assessing the degree of concentration of urban built-up areas.
Author Response
Comments 1: The main problem of the article concerns the reliability of results derived from geographical studies of varying scales and spatial resolutions (i.e., in reference grids and spatial units differing in size and shape), using the example of issues related to the spatial differentiation of land cover in the areas of urbanization of the Łódź Metropolitan Area. The hypotheses being examined include the significance of how the choice of scale, shape, number, and size of spatial reference units affects the results of geographical research, as well as their sensitivity to changes in the degree of data aggregation and the characteristics of the basic spatial units of analysis. The discussion showed that the detail of the input data is very important for the results, as using less detailed data can make urban concentration seem higher than it really is. The study also confirms that larger computational units systematically underestimate the concentration level by smoothing out local differences. Ultimately, the work highlights the necessity of applying a multi-scale and multi-resolution approach in spatial planning to avoid errors in assessing the degree of concentration of urban built-up areas.
Response 1: Thank you very much for your comment. I'm pleased that the main points of the article and the importance of scale, resolution, and level of data aggregation in spatial analyses were well understood. I particularly appreciate the attention to the impact of data detail on assessing development concentration and the need for a multi-scale and multi-resolution approach, which I hope can provide significant support for spatial planning research and practice.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper investigates the impact of the Modifiable Areal Unit Problem (MAUP) on measuring the spatial concentration of built-up areas in the Łódź Metropolitan Area, Poland, which seems interesting.
Some suggestions have been given.
In general, there is repetition of the same content for e.g. 476 to 482, which was clearly mentioned in the introduction. Revise the entire manuscript by extracting such repetition.
Introduction has been well formulated with the justification that MAUP related studies are sufficient, but its effect on concentration analysis based on the Lorenz curve and systematic comparisons across unit types, data scales remain insufficient.
The paper focuses on data aggregation but how it affects data disaggregation remains lagging. Why has that author selected coarser scale data (1:100,000) and finer scale (1:10,000)? How can paper argue the scale effects by considering these two types? The multiscale and multi-dynamism seem missing
The grid shape of square and hexagonal has been selected. The basis of this selection type is missing. Although the result shows differences between square and hexagonal grids were minor for small and medium-sized units but noticeable at larger scales, it is not clear how MUAP affects the particular grid type. What type of study needed to select what type and size of grid? Although geometry does not influence an aggregated scale, up to what level of aggregation needed to concentrate to represents the built-up scenarios?
In Line 487-488 , the reference is missing.
The findings seem to have practical implications for urban planning and land use studies, advocating for cautious multiscale analysis, but how the MUAP effects can be seen in the concept of Degree of Urbanization ( DEGURBA) is suggested to elaborate.
In general, the attempt of a paper with the aim of analyzing the shape, size and geometry of the grid for analyzing built-up concentration is understandable, but the omission of other major land cover (green and blue) seems to pose a question about the selected methodology.
Author Response
I would like to sincerely thank the Reviewer for the assessment of the manuscript and for recognizing the relevance of the topic. I appreciate the time and effort devoted to reviewing my work and the constructive comments provided. All comments have been carefully considered, and detailed responses to each comment are presented below.
Comments 1: In general, there is repetition of the same content for e.g. 476 to 482, which was clearly mentioned in the introduction. Revise the entire manuscript by extracting such repetition.
Response 1: Thank you for pointing this out. The manuscript has been revised to eliminate unnecessary repetition of content already presented in the Introduction. In particular, the paragraph describing the purpose of the study, research questions (RQ1–RQ2), hypotheses (H1 - H3) and the overall methodological framework (4. Discussion and conclusions line 530) has been removed, as this information was clearly stated earlier in the manuscript. Furthermore, the repetitive description of the spatial units used in the analysis, namely the characteristics of the 835 cadastral districts and their aggregation into 33 higher-order units (former lines 172–174), has also been deleted. As a result, the manuscript is now more concise and avoids redundancy while preserving all essential methodological and contextual information.
Comments 2: Introduction has been well formulated with the justification that MAUP related studies are sufficient, but its effect on concentration analysis based on the Lorenz curve and systematic comparisons across unit types, data scales remain insufficient.
Response 2: I thank the reviewer for this insightful comment. Although MAUP has been widely discussed in the literature, I agree that its specific implications for Lorenz curve-based concentration measures, particularly in the context of systematic comparisons across different areal unit types and data scales, have not been sufficiently emphasized. To address this, the Introduction has been revised to more clearly position the study in this identified research gap (lines 80-88) .
Comments 3 The paper focuses on data aggregation but how it affects data disaggregation remains lagging. Why has that author selected coarser scale data (1:100,000) and finer scale (1:10,000)? How can paper argue the scale effects by considering these two types? The multiscale and multi-dynamism seem missing
Response 3: Thank you for this comment. The manuscript has been revised to clarify that the study focuses explicitly on aggregation-related MAUP effects and does not address data disaggregation or downscaling (lines 80-87). Additional text has been added to the Data section to justify the selection of land cover data at scales of 1:10,000 and 1:100,000 as two empirically relevant and methodologically contrasting reference levels (lines 161-169). It was also clarified that the multiscale character of the analysis arises from the systematic variation of areal unit size and configuration, rather than from the use of multiple source data resolutions (line 219-223). The study’s limitations and directions for future research have been explicitly acknowledged in the Conclusions (lines 642-651).
Comments 4: The grid shape of square and hexagonal has been selected. The basis of this selection type is missing. Although the result shows differences between square and hexagonal grids were minor for small and medium-sized units but noticeable at larger scales, it is not clear how MAUP affects the particular grid type. What type of study needed to select what type and size of grid? Although geometry does not influence an aggregated scale, up to what level of aggregation needed to concentrate to represents the built-up scenarios?
Response 4: Thank you for this comment. In response, I have revised the manuscript to clarify the rationale for selecting square and hexagonal grids, the role of grid geometry in MAUP effects, and the implications of aggregation level for representing built-up area concentration.
First, in Section 2.3 (Areal Units), I added a concise explanation of why square and hexagonal grids were selected, emphasizing their widespread use in spatial analysis and their contrasting geometric properties (lines 181-185).
Second, in Section 2.4 (Methods), I expanded the methodological description to clarify how MAUP-related effects are expected to arise from unit size (scale effect) and from boundary and edge alignment associated with grid geometry (zonation effect). It was explained that unit size controls the dominant aggregation effect, whereas geometry-related differences are expected to become most apparent at higher levels of aggregation (lines 246-254)
Third, in Section 3.3 (Results), I clarified the interpretation of the observed stabilization of concentration coefficients beyond intermediate unit sizes, emphasizing that this behaviour represents an empirical tendency specific to the study area rather than a universal threshold (lines 410-413).
Finally, in the Discussion, I added a short interpretative paragraph outlining how the choice of grid type and size should depend on the research objective, noting that small units are preferable for local pattern analysis, while at larger spatial extents aggregation dominates and differences between square and hexagonal grids become less critical (lines 565-569).
Comments 5: In Line 487-488, the reference is missing.
Response 5: Thank you for noting this omission. The missing reference has been added to support the statement regarding the effect of coarser spatial resolution on apparent concentration (line 534).
Comments 6: The findings seem to have practical implications for urban planning and land use studies, advocating for cautious multiscale analysis, but how the MUAP effects can be seen in the concept of Degree of Urbanization ( DEGURBA) is suggested to elaborate.
Response 6: A paragraph was added to the Discussion explicitly relating the observed MAUP effects to the Degree of Urbanization (DEGURBA) and highlighting the implications of scale and aggregation choices for urban classification (lines 635-641).
Comments 7: In general, the attempt of a paper with the aim of analyzing the shape, size and geometry of the grid for analyzing built-up concentration is understandable, but the omission of other major land cover (green and blue) seems to pose a question about the selected methodology.
Response 7: Thank you for this comment. The scope of the study was deliberately limited to built-up areas, as the primary objective was to assess how MAUP-related aggregation effects influence measures of spatial concentration for a highly clustered and spatially heterogeneous land cover class. Built-up areas constitute a discrete, object-based category with strong spatial concentration gradients, making them particularly suitable for isolating scale and zonation effects associated with areal aggregation. Including other major land cover types, such as green or blue areas, would introduce fundamentally different spatial structures and dispersion patterns, potentially obscuring the interpretation of MAUP effects on concentration measures. The methodological framework is designed to evaluate aggregation effects for built-up areas specifically, while the extension of this approach to other land cover classes remains an important direction for future research. To clarify this, I have revised the Conclusions to explicitly acknowledge this limitation and to indicate that extending the proposed framework to other land cover categories, such as green and blue infrastructure, represents an important direction for future research (lines 651-662).
Changes introduced according to reviewers' comments are marked in red in the text
Author Response File: 
Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsSummary and Contributions:
This manuscript reports on a systematic, comparative analysis of the scalar and zonal effects of MAUP on the concentration of built-up areas in the Łódź Metropolitan area. The Lorenz-based analysis leverages land cover data at two different resolutions aggregated to a combination of standardized grids (square and hexagonal) and irregular cadastral units to quantify the effects of MAUP on concentration measures across a range of scales and zoning configurations. The study provides both substantive empirical evidence to inform the ways in which MAUP manifests for a specific and relevant geographic phenomenon and a replicable framework for assessing other phenomena. Below I offer comments/questions/suggestions that I hope are helpful in enhancing the clarity of this work:
Introduction:
The Introduction section is overall focused and succinct (which is great) but given that there’s no formal background section, I suggest expanding the discussion, specifically on concentration analysis and providing a more formal introduction on, and definition of, the Lorenz method and how it works (not a technical detailing which is found in the methods section but a high level explanation for readers who may have limited familiarity) (lines 56-57).
Materials and Methods:
The study area is well qualified/contextualized, however, the data harmonization process (lines 127-132) is somewhat vague. Did the author implement the process or are they reporting on how it had been done in previous work? If the former, additional details are needed to help clarify and make the process reproducible (perhaps also including a workflow diagram).
Additional context needed on line 137 to define “Urban fabric (1.1)”.
Additional methodological details are needed to explain how data values depicted in Figure 2 maps were assigned to the various standardized grids and cadastral units. For example, what happens when a built up area only partially overlaps with a grid cell or unit?
Text on lines 174-176 appear redundant and should be removed.
The Gini coefficient equation (2) doesn’t appear to include an “n” as referenced in line 247.
Results:
The second sentence (lines 275-276) is somewhat difficult to follow: is “smaller scale” referring to map scale (i.e., larger area). Also, the term “patches” is only being introduced for the first time with no definition. Finally, table 1 suggests that the “share in area” is identical?
On line 281, there’s reference to “194 types of areal units” but it’s not clear exactly what this refers to… is it “types” or “different configurations” or both?
The table 3 description references “2012” but I think it should be 2018? Table 3 also reports a max value of 0.901 for data scale 1:100,000 but this doesn’t align with the max value range reported in table 2?
The claim made on lines 371-72 would be stronger if a couple citations were provided to qualify “related studies”.
The result reported on line 382-383 regarding degree of correlation and significance doesn’t quite track with the results reported in table 4, which suggests that the relationship was *statistically* significant for both units but the trend was much weaker for squares. Replacing the word “significant” with “strong” would improve clarity/accuracy.
The captions for the maps depicted in figures 9-11 should clarify what the dual legends are conveying. Is the bottom legend the distribution of values or area represented in each class? I don’t quite understand how the same color shade can be assigned to two different ranges of values in one map?
What exactly is meant by “reflecting the higher level of spatial aggregation” referenced on lines 468-70?
Discussion and Conclusions:
Lines 501-02 indicate that study results align with well-known aggregation effects, i.e., larger units smoothing local variability and measured inequality. Yet, this seems to be somewhat counterintuitive to the point above about coarser input data “amplifying” concentration values? Similar to larger spatial units, wouldn’t data at a coarser resolution tend to smooth variability in patterns?
Lines 531-532 make a connection between the irregular cadastral units and MAUP’s “zoning” effect but my interpretation is that effects are more likely attributable to “scale” effects given just how much smaller in size the sections are than the districts.
The paragraph beginning on line 536 reflects on findings specific to the irregular units. Does the author have any thoughts on the extent to which these units may (or may not) better align with the phenomenon being assessed, i.e., built up areas, as compared to regular grids which clearly don’t directly align with the underlying phenomenon being analyzed.
It would be valuable to extend the discussion on future work, particularly with regard to the role spatial autocorrelation plays with respect to the analysis of built up areas and ideation for how to harmonize concentration and autocorrelation analyses from global and local perspectives.
Author Response
I sincerely thank the Reviewer for the thorough and insightful assessment of the manuscript and for recognizing both the empirical contribution of the study and the replicable analytical framework it proposes. I appreciate constructive comments and suggestions that aim to improve the clarity and rigor of the work. All comments have been carefully considered and are addressed in detail below.
Comments 1: The Introduction section is overall focused and succinct (which is great) but given that there’s no formal background section, I suggest expanding the discussion, specifically on concentration analysis and providing a more formal introduction on, and definition of, the Lorenz method and how it works (not a technical detailing which is found in the methods section but a high level explanation for readers who may have limited familiarity) (lines 56-57).
Response 1: Thank you for this suggestion. In response, I have expanded the Introduction (lines 58–63) by adding a short, high-level explanation of spatial concentration analysis and the Lorenz curve, aimed at readers who may be less familiar with this method. The added text provides a conceptual overview of how the Lorenz approach characterises uneven spatial distributions.
Materials and Methods:
Comments 2: The study area is well qualified/contextualized, however, the data harmonization process (lines 127-132) is somewhat vague. Did the author implement the process or are they reporting on how it had been done in previous work? If the former, additional details are needed to help clarify and make the process reproducible (perhaps also including a workflow diagram).
Response 2: Thank you for this comment. I have clarified that the data harmonization procedure was implemented by the author in this study and expanded the methodological description to improve reproducibility. Additional details on the semantic alignment between BDOT10k and CLC classes have been provided, and the harmonization workflow is now explicitly documented in Table 1, which presents the class correspondence and inclusion criteria applied in the analysis (lines 136-138, 142–145).
Comments 3: Additional context needed on line 137 to define “Urban fabric (1.1)”.
Response 3: Thank you for this comment. Additional contextual information has been added in lines 143-145 to clarify the meaning of Urban fabric (1.1). The revised text now explicitly defines this category as built-up areas dominated by residential, service, and mixed-use buildings, consistent with the Corine Land Cover classification of artificial surfaces.
Comments 4: Additional methodological details are needed to explain how data values depicted in Figure 2 maps were assigned to the various standardized grids and cadastral units. For example, what happens when a built up area only partially overlaps with a grid cell or unit?
Response 4: Thank you for this comment. The additional methodological details were added to clarify how built-up areas were assigned to standardized grids and cadastral units (lines 260-267). The revised text now explicitly states that a GIS-based spatial intersection was used, whereby the built-up polygon layer was intersected with each grid configuration to obtain the exact built-up area within each unit, including cases of partial overlap.
Comments 5: Text on lines 174-176 appear redundant and should be removed.
Response 5: Thank you for this comment. The text in lines 174–176 (“The analysis was carried out for 835 cadastral districts with an average area of approximately 3 km² and for their aggregation into 33 higher-order units (cadastral districts), with an average area of 77.8 km². These units correspond to the basic territorial division of the municipalities comprising the Łódź Metropolitan Area”) has been removed from the revised manuscript
Comments 6: The Gini coefficient equation (2) doesn’t appear to include an “n” as referenced in line 247.
Response 6: Thank you for noting this inconsistency. Equation (2) has been corrected to explicitly include n as the upper bound of the summation and to follow the classical formulation of the concentration coefficient ensuring full consistency between the equation and the variable definitions (line 283).
Results:
Comments 7: The second sentence (lines 275-276) is somewhat difficult to follow: is “smaller scale” referring to map scale (i.e., larger area). Also, the term “patches” is only being introduced for the first time with no definition. Finally, table 1 suggests that the “share in area” is identical?
Response 7: Thank you for this comment. I have revised the text to explicitly clarify that “smaller scale” refers to a smaller map scale (1:100,000), i.e., a coarser spatial resolution. The term “patches” is now defined at its first occurrence as spatially contiguous built-up polygons. In addition, we clarified that the identical share of built-up area reported in Table 1 results from the harmonisation procedure, while differences between scales are expressed primarily in the number and size of built-up patches (Lines 315-317).
Comments 8: On line 281, there’s reference to “194 types of areal units” but it’s not clear exactly what this refers to… is it “types” or “different configurations” or both?
Response 8: Thank you for pointing this out. We agree that the term “types” was ambiguous. The text has been revised to clarify that the number refers to 194 different areal unit configurations, defined as unique combinations of unit geometry, size, and (for regular grids) orientation. The wording has been corrected accordingly in the manuscript line (line 325).
Comments 9: The table 3 description references “2012” but I think it should be 2018? Table 3 also reports a max value of 0.901 for data scale 1:100,000 but this doesn’t align with the max value range reported in table 2?
Response 9: Thank you for pointing out these inconsistencies. The reference to “2012” in the caption of Table 3 (now Table 4, line 336) was a typographical error and has been corrected to “2018”. The apparent inconsistency in Table3 resulted from rounding of the descriptive statistics in Table 3. The numerical precision of Table 3 has been increased to ensure consistency with the class intervals reported in Table 2.
Comments 10: The claim made on lines 371-72 would be stronger if a couple citations were provided to qualify “related studies”.
Response 10: Thank you for this suggestion. I have revised the statement in line 533 by adding specific citations to previously discussed studies that document similar MAUP-related effects on concentration and aggregation-sensitive measures (e.g., Briant et al. [64]; Salmivaara et al. [58]; Stępniak [63]).
Comments 11: The result reported on line 382-383 regarding degree of correlation and significance doesn’t quite track with the results reported in table 4, which suggests that the relationship was *statistically* significant for both units but the trend was much weaker for squares. Replacing the word “significant” with “strong” would improve clarity/accuracy.
Response 11: I Agree. The text was revised to distinguish between statistical significance and the strength of the correlation. The sentence now clarifies that the relationship was statistically significant for both unit types, while the correlation strength was much weaker for squares (432-434).
Comments 12: The captions for the maps depicted in figures 9-11 should clarify what the dual legends are conveying. Is the bottom legend the distribution of values or area represented in each class? I don’t quite understand how the same color shade can be assigned to two different ranges of values in one map?
Response 12: I have revised the maps in Figures 9–11 to improve the clarity of the dual legends by explicitly labelling their meaning. In addition, a short explanatory description has been added to the Methods section (lines 309–312) to clarify that the colour classes represent Lorenz-based cumulative contributions to the total built-up area rather than fixed numerical value ranges
Comments 13: What exactly is meant by “reflecting the higher level of spatial aggregation” referenced on lines 468-70?
Response 13: Thank you for this comment. I clarified this phrasing by explicitly stating that the “higher level of spatial aggregation” refers to the use of larger areal units, which smooth local variability in built-up area shares and reduce differences between data scales. The revised text now specifies the mechanism underlying this effect (lines 518-521)
Discussion and Conclusions:
Comments 14: Lines 501-02 indicate that study results align with well-known aggregation effects, i.e., larger units smoothing local variability and measured inequality. Yet, this seems to be somewhat counterintuitive to the point above about coarser input data “amplifying” concentration values? Similar to larger spatial units, wouldn’t data at a coarser resolution tend to smooth variability in patterns?
Response 14: Thank you for this insightful comment. I have clarified the text to clearly distinguish the aggregation effects operating at different stages of the analysis. The change (lines 548-550) clarifies that aggregating areal units smooths variability through averaging, while more detailed inputs amplify apparent concentration by generalizing spatial patterns and combining smaller clusters.
Comments 15: Lines 531-532 make a connection between the irregular cadastral units and MAUP’s “zoning” effect but my interpretation is that effects are more likely attributable to “scale” effects given just how much smaller in size the sections are than the districts.
Response 15: Thank you for this important clarification. I revised the interpretation to distinguish between scale and zoning effects more explicitly. The revised text (lines 582-584) emphasizes that the observed differences for irregular cadastral units are primarily driven by scale effects related to the substantial size differences between cadastral sections and districts, with zoning effects playing a secondary role.
Comments 16: The paragraph beginning on line 536 reflects on findings specific to the irregular units. Does the author have any thoughts on the extent to which these units may (or may not) better align with the phenomenon being assessed, i.e., built up areas, as compared to regular grids which clearly don’t directly align with the underlying phenomenon being analyzed.
Response 16: The discussion of irregular units was expanded to address their potential interpretative alignment with built-up areas (Lines 591-595). The revised text clarifies that while cadastral units may better reflect historically and administratively shaped urban structures and thus facilitate interpretation, they do not inherently reduce MAUP effects or provide a more accurate analytical representation compared to regular grids.
Comments 17: It would be valuable to extend the discussion on future work, particularly with regard to the role spatial autocorrelation plays with respect to the analysis of built up areas and ideation for how to harmonize concentration and autocorrelation analyses from global and local perspectives.
Response 17: Thank you for this valuable suggestion. In response the discussion was expanded of future research directions to explicitly address the role of spatial autocorrelation in the analysis of built-up areas. The revised manuscript now clarifies the complementary nature of Lorenz-based concentration measures and global and local spatial autocorrelation indicators, and outlines how these approaches could be harmonized to link global concentration patterns with local clustering and spatial dependence. These additions are included in the revised Discussion section (lines 644-663).
Changes introduced according to reviewers' comments are marked in red in the text
Author Response File: Author Response.docx
Reviewer 4 Report
Comments and Suggestions for AuthorsThis study addresses the classic challenge in Geographic Information Science—the Modifiable Areal Unit Problem (MAUP). Taking the Łódź Metropolitan Area in Poland as a case study, the authors designed and conducted a highly rigorous and systematic empirical analysis to examine the effects of data scale and areal unit configuration on the concentration of built-up areas (using the Lorenz curve method). The paper innovatively integrates harmonized multi-scale data, various regular and irregular spatial units, and refined sensitivity measurement methods, clearly quantifying the influence weights of each factor on the spatial concentration index of built-up areas. The research design is scientific, the analysis is thorough, and the conclusions are clear. The methodology and findings of this study hold significant academic reference value and meaning for related research in geographical spatial analysis and are commendable and recommendable.
Here are a few minor suggestions for the authors to consider when revising and improving the paper:
1.The main area for improvement in the paper might be to supplement the discussion of the study's limitations in the conclusion, particularly regarding the generalizability of the findings. The paper emphasizes the unique monocentric structure of the study area, but does this also imply that the applicability of the study's conclusions to metropolitan areas with different spatial structures and forms remains unverified? Examples include polycentric metropolitan areas or elongated urbanized regions. While the methodology has general applicability, I believe the conclusions require further validation through additional case studies. Secondly, I think the conclusion should appropriately mention that future research directions could also include exploring the interaction between data scale and unit size, which may be a promising direction for further investigation. For instance, examining whether differences persist for low-resolution data across different analytical unit scales.
2. Figure 4 requires re-examination. Panels (f) and (h) do not appear to differ significantly in orientation (angle), but rather seem to show a difference in cell size. The content presented in Figures 7 and 8 is not sufficiently intuitive. Using lines of different colors to connect data points of the same type might achieve a better visual presentation.
Author Response
I sincerely thank the Reviewer for this highly positive and insightful evaluation of our study. I greatly appreciate the recognition of the rigor of the research design, the methodological contributions, and the academic value of our findings. Below, we provide detailed responses to all comments and suggestions raised by the Reviewer.
Comments 1: The main area for improvement in the paper might be to supplement the discussion of the study's limitations in the conclusion, particularly regarding the generalizability of the findings. The paper emphasizes the unique monocentric structure of the study area, but does this also imply that the applicability of the study's conclusions to metropolitan areas with different spatial structures and forms remains unverified? Examples include polycentric metropolitan areas or elongated urbanized regions. While the methodology has general applicability, I believe the conclusions require further validation through additional case studies. Secondly, I think the conclusion should appropriately mention that future research directions could also include exploring the interaction between data scale and unit size, which may be a promising direction for further investigation. For instance, examining whether differences persist for low-resolution data across different analytical unit scales.
Response 1: Thank you for this valuable suggestion. In response to the reviewer's comment, I have expanded the "Discussion and Conclusions" section to explicitly address the limitations of generalizing the results. I have emphasized that the study area represents a strongly monocentric metropolitan structure and that, although well-suited to concentration analysis, this may limit the direct applicability of the empirical findings to metropolitan areas with different spatial forms, such as polycentric or elongated regions. Furthermore, I have clarified that while the proposed methodological framework is general in nature, the conclusions require further validation through comparative case studies in metropolitan areas with contrasting spatial structures. Finally, I have expanded the discussion on future research directions by emphasizing the need to examine the interaction between data scale and unit size, including whether scale-related differences persist for low-resolution data at different levels of aggregation (lines 612-623; 642-662).
Comments 2: Figure 4 requires re-examination. Panels (f) and (h) do not appear to differ significantly in orientation (angle), but rather seem to show a difference in cell size. The content presented in Figures 7 and 8 is not sufficiently intuitive. Using lines of different colors to connect data points of the same type might achieve a better visual presentation.
Response 2: Figures 7 and 8 have been revised for improved clarity and visual consistency, following the Reviewer’s suggestions. Figure 4 has also been corrected. Thank you for noting that in panel (f) a grid with a smaller cell size (15 km² instead of 20 km²) was used. This error has been corrected and the revised figures have been included in the article.
Changes introduced according to reviewers' comments are marked in red in the text
Author Response File: Author Response.docx
