Pith. sign in

REVIEW 4 major objections 4 minor 63 references

The third dimension of cities - relating building height, urban area, and population

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Building height shows almost no association with city population size once built area is counted.

desk verdict Valuable new dataset and a sharp question, but the central claim rests on standardized regression coefficients being read as elasticities, so 'height doesn't matter' is not currently supported. read the letter →

arxiv 2508.20114 v1 pith:4SNVQQLG submitted 2025-08-21 physics.soc-ph

Peiran Zhang , Liang Gao , Fabiano L. Ribeiro , Bin Jia , Ziyou Gao , Diego Rybski This is my paper · ORCID
classification physics.soc-ph
keywords urbanscalingbuildingheightCobb-Douglasmodelhorizontalexpansionverticaldevelopmentfunctionalareaspopulationaccommodationcross-sectionalanalysis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that, when city population is related at the same time to the total footprint of its buildings and to their average height, the height term contributes almost nothing. Fitting the two-factor multiplicative relation P ~ A^αA h^αh separately for 42 national urban systems (2,903 functional urban areas in 2015), the authors find αA is positive and usually below 1, while αh is near zero in most countries and even negative in a few. The consequence, if true, is that today's cities accommodate people mainly by spreading out horizontally, and building taller has not, on average, been an effective way to increase population capacity. A reader should care because this challenges a standard intuition behind high-rise urban policy and attaches a concrete number to how strongly each dimension tracks population.

What carries the argument

The Cobb-Douglas production form P ∼ A^αA h^αh—a two-factor multiplicative power-law relation—estimated by ordinary least squares on log-transformed, standardized variables is the central object. Its exponents are read as marginal products: how much population changes with a 1% change in total building area, holding average height fixed, and vice versa. The ratio σ = −αh/αA converts the pair of exponents into the slope of a constant-population isoquant, giving three regimes (complementary, independent, substitutive). A geometric identity V = A·h ties the model to the one-dimensional scaling laws and yields the predicted negative relationship between αA and αh.

What would settle it

Re-run the country-level Cobb-Douglas regression without standardizing, i.e., on raw log(P), log(A), and log(h); if for a country like Poland the raw height coefficient is clearly positive and stable, the claim that height contributes nothing fails for that country. Alternatively, a within-city panel that follows cities after large additions of tall residential buildings would contradict the cross-sectional null if population grows with added vertical floor area.

Watch

Extended reading notes

Core claim

The paper's central claim is that the Cobb-Douglas relation P ~ A^αA h^αh, fit city by city within each country, separates horizontal and vertical contributions to population in a way the one-dimensional scaling laws cannot. For most countries the vertical exponent αh is statistically indistinguishable from zero, so taller average building height does not track larger population once area is accounted for; the horizontal exponent αA is positive and typically between 0 and 1, meaning population grows less than proportionally with built footprint. A few countries (Egypt, Morocco, Bangladesh, the Philippines) show negative αh, and some (Germany) show positive αh. The paper also reports a negati

Load-bearing premise

The result that height does not matter hinges on treating the coefficients of standardized (z-scored) log regressions as structural elasticities; if height varies little across a country's cities, standardization can drive αh toward zero even when vertical space would house people at the margin.

Editorial extensions

If this is right

  • If the cross-sectional result is right, vertical development should not be justified chiefly by its population capacity; whatever high-rises deliver has to be measured in other outcomes.
  • Horizontal built-up area is the dimension that tracks population, but sublinearly (αA < 1), so each added square meter of footprint is associated with proportionally fewer additional residents.
  • In countries where population is concentrated in a few large cities (high ζ), horizontal expansion is the dimension tied to population; those urban systems may need land-use and density policies different from more evenly distributed countries.
  • Countries with positive αh, such as Germany, already constrain horizontal growth; the pattern suggests height can contribute where policy forces compactness, while height restrictions elsewhere may push growth into horizontal expansion.
  • The same P–A–h framework can be applied to other urban quantities (e.g., energy use, emissions, economic output), giving a systematic way to separate horizontal and vertical contributions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the regressions are run on standardized variables, the 'height contributes nothing' headline is partly a statement about within-country variance in average height; where all cities have similar heights, αh cannot be large even if vertical space matters at the margin. Re-fitting on raw logs or computing elasticities at the mean would tell how much of αh≈0 is real and how much is a scaling a
  • The cross-section compares cities at one time, so it cannot distinguish whether population follows height or height follows population; a longitudinal test on cities that add substantial residential tower stock would help decide.
  • Using average height hides the distribution of building heights. It could be that the top of the height distribution (a few very tall buildings) matters little while moderate mid-rise density matters a lot; decomposing height into floors or per-capita floor area would be a natural extension.
  • The country-level association between αA and the population-concentration exponent ζ is ecological: it does not say that concentrated countries should expand horizontally, only that their current stock lines up that way. Testing within countries over time would separate national hierarchy from local land-use decisions.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This paper proposes a Cobb-Douglas scaling model P ∼ A^αA h^αh linking population to total building footprint area and average building height, and fits it to 2903 Functional Urban Areas in 42 countries using the 3D-GloBFP dataset. The authors report that αA is positive and typically below one, while αh is approximately zero for most countries, which they interpret as evidence that vertical development does not significantly contribute to population accommodation. They further compute a substitution rate σ = −αh/αA, relate αA and αh to country-level metrics (Global North/South, ζ-exponent, GDP, urbanization) via Lasso regression, and run a building-type classification robustness check (Germany, Philippines, Spain).

Significance. The question of whether cities accommodate population through horizontal expansion or vertical density is of broad urban-science and policy relevance, and the paper brings a new global dataset to bear on it. The authors have made data and code available, and the cross-country design is more comprehensive than earlier single-country or single-city studies. If the quantitative results were correct, the finding that height contributes little to population accommodation would challenge a common policy intuition. However, the central estimates are currently not the quantities they are claimed to be because of standardization; this must be resolved before the paper's conclusions can be evaluated. The paper's strongest asset is the dataset and the multivariate formulation; its current quantitative evidence for the headline claim is not valid.

major comments (4)
  1. [§2.1, Eqs. (3)-(4)] The paper states 'we standardize all variables before regression' and then reports the coefficients as αA and αh, defined in Eq. (4) as ∂lnP/∂lnA and ∂lnP/∂lnh. These are not the same. If lnP, lnA, and lnh are z-scored before fitting, the OLS coefficients are standardized betas βA and βh, related to the raw partial elasticities by αA = βA·sP/sA and αh = βh·sP/sh. No conversion is reported. Consequently, the headline αh≈0 may simply reflect a small cross-city variance of lnh relative to lnP within countries, rather than an absence of structural association. The claim that building height does not contribute to population accommodation is therefore not supported by the reported statistics. Please re-estimate in raw log-log space or report converted elasticities together with the within-country standard deviations.
  2. [§2.3, Eq. (5), Fig. 3] The substitution rate σ = −αh/αA is used to classify countries into complementary, no-interaction, and substitution regimes. When computed from standardized coefficients, the quantity is actually −βh/βA · sA/sh, not the slope of the constant-population isoquant derived in Eq. (14). Thus the regimes in Fig. 3 and the associated interpretation of how area and height trade off are variance-scaled artifacts of the standardization. The isoquant plots (Figs. 3d-e) should be based on the raw model, and σ must be recomputed from the raw elasticities.
  3. [§4.2, Eq. (13), Fig. 2d] The derivation of the negative αA–αh relationship imposes consistency between the Cobb-Douglas model and the bivariate scaling laws A∼P^βA and V∼P^βV, which are fitted on the same data. Eq. (13) is therefore an algebraic consistency condition, not an independent theoretical constraint. The negative correlation in Fig. 2d is partly a mathematical consequence of this identity and of the estimation procedure, so it should not be presented as independent evidence of a volume-constrained trade-off. If the standardization issue is corrected, this relationship may change and should be re-examined.
  4. [§4.1.1] The data-cleaning procedure excludes countries with fewer than 30 FUAs, applies a population threshold cut-off, and then excludes countries with fewer than 10 remaining FUAs. These choices are not justified, and truncating the city-size distribution can bias the estimated scaling exponents. Because the country-level αA and αh are the paper's main outputs, the sensitivity of the results to the threshold choices should be reported (e.g., varying the minimum number of FUAs and the population cutoff).
minor comments (4)
  1. [§2.1] 'Variance Inflation Factor' should be 'the variance inflation factor'. Also, the text refers to Supplementary Figure S1 for all countries, but only example countries are shown in the main text; please clarify what the supplementary figure contains.
  2. [Discussion] In the final paragraph of the Discussion, 'approch' should be 'approach'.
  3. [Fig. 4 caption] The caption has grammatical issues: 'the white horizontal line represent' should be 'represents', and 'with the color denote' should be 'with the color denoting'.
  4. [References] Reference [40] is cited without a year or volume/page information; please provide the full publication details.

Circularity Check

2 steps flagged · score 4.0 of 10

Model form leans on a self-citation and the αA–αh trade-off is a same-data algebraic consequence, but the central αh≈0 finding remains an independent estimation.

  1. self citation load bearing [Section 2.1, Eq. 3]
    "Theoretically, as demonstrated in our previous study [40], integrating horizontal and vertical dimensions offers a natural approach to reconcile the opposing forces of urban growth. Accordingly, to capture the multivariate characteristics of urban development, we propose a Cobb-Douglas production function of the form P ∼ A^{αA} h^{αh} , (3)"

    Ref. [40] is Ribeiro, Zhang, Gao, Rybski, i.e., the present authors. The Cobb-Douglas form is the central premise from which all αA and αh estimates are obtained. However, the model is also empirically fitted and tested on an external dataset, so the self-citation is not the only load-bearing support; it is a minor self-citation rather than a complete reduction.

  2. fitted input called prediction [Section 4.2, Eq. 13 (referenced in Section 2.2)]
    "αh = − βA/(βV−βA) αA + 1/(βV−βA). (13) ... Empirical evidence consistently shows that βV − βA = βh > 0 (Supplementary Figure S2), reflecting a negative relationship between αA and αh"

    The negative αA–αh relationship is presented as theoretically supported by Eq. 13, but βA and βV are fitted from the same (A,V,P) dataset that yields αA and αh. Given h=V/A and the Cobb-Douglas form, Eq. 12 is a conservation identity; the sign of the correlation is a mathematical consequence of the fitted scaling exponents, not an independent confirmation. This partially reduces the trade-off finding to its own inputs, though the central αh≈0 result is an independent estimate.

full rationale

The paper's headline result—that αh is approximately zero for most countries—is an OLS estimation on an external global building dataset (3D-GloBFP), not a back-fit of the model's own parameters, so it has independent empirical content. The main circularity concerns are secondary. First, the Cobb-Douglas model form is justified by a citation to the authors' own prior work (Ref. 40), though the present paper's fits and robustness checks stand independently. Second, the theoretical derivation of the negative αA–αh trade-off (Eq. 13) uses βA and βV fitted on the same data, so the 'reflecting' relationship is partly an algebraic consequence rather than an independent prediction. The standardization of variables before regression (Section 2.1) is a serious validity concern—standardized betas are not raw elasticities—but it is a correctness/interpretation issue, not circularity, because the small αh is not forced by construction. Overall, the central claim remains independent; score 4.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper adds a Cobb-Douglas regression as the main model, but the exponents are fitted, and the standardization step introduces an additional transformation that is not standard for scaling law estimation. The theoretical relation between αA and αh is derived from the same dataset's scaling fits, limiting its independence. No new entities are invented.

free parameters (4)
  • αA (per country) = Varies; e.g., most 0<α<1, Japan, Egypt, Morocco >1
    OLS coefficient of ln A in standardized log-log regression; central parameter.
  • αh (per country) = Varies; mostly ≈0, negative for Egypt, Morocco, Bangladesh, Philippines
    OLS coefficient of ln h in standardized log-log regression; central parameter.
  • Population threshold cut-off = Not specified in the paper
    Applied to filter cities for power-law city size distributions; threshold value not disclosed.
  • Country inclusion thresholds = 30 FUAs initially, 10 after filtering
    Arbitrary cutoffs to ensure statistical robustness; not justified or robustness-tested.
assumptions (4)
  • domain assumption Cobb-Douglas functional form P ~ A^αA h^αh
    Postulated as the model; not derived from first principles.
  • ad hoc to paper Standardization before regression preserves the meaning of coefficients as elasticities
    Standardization changes coefficients to standardized betas; not standard for scaling law estimation and not justified.
  • domain assumption The bivariate scaling laws A ~ P^βA and V ~ P^βV hold and are estimated from the same data
    Used to derive Eq. (13); if these fits are noisy or not power laws, the theoretical relation is not applicable.
  • domain assumption The 3D-GloBFP dataset provides accurate building heights and footprints for all cities
    Central data source; the paper does not validate the dataset.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The third dimension of cities - relating building height, urban area, and population." pith.science (2026). https://pith.science/paper/4SNVQQLG

@misc{pith2026250820114,
  author       = {Pith},
  title        = {Pith review of: The third dimension of cities - relating building height, urban area, and population},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4SNVQQLG}},
  note         = {Machine review of arXiv:2508.20114}
}
read the original abstract

For decades, urban development was studied on two-dimensional maps, largely ignoring the third dimension. However, building height is crucial because it dramatically potentiates the interior space of cities. Here, using a newly released global building height dataset of 2903 cities across 42 countries in 2015, we develop a Cobb-Douglas model to simultaneously examine the relationship between urban population size and both horizontal and vertical urban extents. We find that, contrary to expectations, the residents of most urban systems do not significantly benefit from vertical dimension, with population accommodation being primarily driven by horizontal extent. The associations with country-level external indicators demonstrate that the benefits of horizontal extent are more pronounced in urban systems with more extreme size distribution (most population concentrated in few cities). Moreover, building classification tests confirm the robustness of our findings across all building types. Our findings challenge the intuition that building height and high-rise development significantly contributes to urban population accommodation, calling for targeted policies to improve its efficiency.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 48 canonical work pages

  1. [1]

    Habitat International 34(2), 236–243 (2010) https://doi.org/10.1016/j.habitatint.2009.09.008

    Zhao, P.: Sustainable urban expansion and transportation in a growing megacity: Consequences of urban sprawl for mobility on the urban fringe of Beijing. Habitat International 34(2), 236–243 (2010) https://doi.org/10.1016/j.habitatint.2009.09.008

    work page doi:10.1016/j.habitatint.2009.09.008 2010

  2. [2]

    PloS ONE 6(8), 23777 (2011) https://doi.org/10.1371/journal.pone.0023777

    Seto, K.C., Fragkias, M., G¨ uneralp, B., Reilly, M.K.: A meta-analysis of global urban land expansion. PloS ONE 6(8), 23777 (2011) https://doi.org/10.1371/journal.pone.0023777

    doi:10.1371/journal.pone.0023777 2011

  3. [3]

    Proceedings of the National Academy of Sciences109(40), 16083–16088 (2012) https://doi.org/10.1073/pnas.1211658109

    Seto, K.C., G¨ uneralp, B., Hutyra, L.R.: Global forecasts of urban expansion to 2030 and direct impacts on biodiversity and carbon pools. Proceedings of the National Academy of Sciences109(40), 16083–16088 (2012) https://doi.org/10.1073/pnas.1211658109

    work page doi:10.1073/pnas.1211658109

  4. [4]

    Nature Sustainability 2(8), 755–763 (2019) https://doi.org/10.1038/s41893-019-0340-0

    Vliet, J.: Direct and indirect loss of natural area from urban expansion. Nature Sustainability 2(8), 755–763 (2019) https://doi.org/10.1038/s41893-019-0340-0

    work page doi:10.1038/s41893-019-0340-0 2019

  5. [5]

    Urban Studies 57(4), 731–747 (2020) https: //doi.org/10.1177/0042098019873796

    Lobo, J., Bettencourt, L.M., Smith, M.E., Ortman, S.: Settlement scaling theory: Bridging the study of ancient and contemporary urban systems. Urban Studies 57(4), 731–747 (2020) https: //doi.org/10.1177/0042098019873796

    work page doi:10.1177/0042098019873796 2020

  6. [6]

    Lincoln Institute of Land Policy, Cambridge, MA, ??? (2012)

    Angel, S., Blei, A.M., Civco, D.L., Parent, J.: Atlas of Urban Expansion. Lincoln Institute of Land Policy, Cambridge, MA, ??? (2012)

    work page 2012

  7. [7]

    submitted (2025)

    Victor, V., Lemoy, R.: Removing Population Size, World Cities Leave on Land a Footprint of Wealth. submitted (2025)

    work page 2025

  8. [8]

    Nature Communications 11(1), 2647 (2020) https://doi.org/10.1038/ s41467-020-16461-9

    Li, Y., Schubert, S., Kropp, J.P., Rybski, D.: On the influence of density and morphology on the Urban Heat Island intensity. Nature Communications 11(1), 2647 (2020) https://doi.org/10.1038/ s41467-020-16461-9

    work page 2020

Show all 63 references
  1. [9]

    Nature Cities 1(8), 522–532 (2024) https: //doi.org/10.1038/s44284-024-00091-z

    Yang, M., Ren, C., Wang, H., Wang, J., Feng, Z., Kumar, P., Haghighat, F., Cao, S.-J.: Mitigating urban heat island through neighboring rural land cover. Nature Cities 1(8), 522–532 (2024) https: //doi.org/10.1038/s44284-024-00091-z

    2024 doi

  2. [10]

    Environmental Research 215, 114387 (2022) https://doi.org/10.1016/j.envres.2022.114387

    Nieuwenhuijsen, M.J., Dadvand, P., M´ arquez, S., Bartoll, X., Barboza, E.P., Cirach, M., Borrell, C., Zijlema, W.L.: The evaluation of the 3-30-300 green space rule and mental health. Environmental Research 215, 114387 (2022) https://doi.org/10.1016/j.envres.2022.114387

    2022

  3. [11]

    Science Advances 8(27), 0095 (2022) https://doi.org/10.1126/sciadv.abo0095

    Zhang, L., Yang, L., Zohner, C.M., Crowther, T.W., Li, M., Shen, F., Guo, M., Qin, J., Yao, L., Zhou, C.: Direct and indirect impacts of urbanization on vegetation growth across the world’s cities. Science Advances 8(27), 0095 (2022) https://doi.org/10.1126/sciadv.abo0095

    2022 doi

  4. [12]

    Nature Communications 14(1), 6460 (2023) https://doi.org/10

    Wu, S., Chen, B., Webster, C., Xu, B., Gong, P.: Improved human greenspace exposure equality during 21 st century urbanization. Nature Communications 14(1), 6460 (2023) https://doi.org/10. 1038/s41467-023-41620-z

    2023

  5. [13]

    Nature Cities, 1–11 (2024) https://doi.org/10.1038/s44284-024-00162-1

    Bakhtsiyarava, M., Moran, M., Ju, Y., Zhou, Y., Rodriguez, D.A., Dronova, I., Pina, M., Matos, V.P., Skaba, D.A.: Potential drivers of urban green space availability in Latin American cities. Nature Cities, 1–11 (2024) https://doi.org/10.1038/s44284-024-00162-1

    2024 doi

  6. [14]

    Nature Reviews Physics 1(6), 406–415 (2019) https://doi.org/10.1038/s42254-019-0054-2

    Barthelemy, M.: The statistical physics of cities. Nature Reviews Physics 1(6), 406–415 (2019) https://doi.org/10.1038/s42254-019-0054-2

    2019 doi

  7. [15]

    Energy Policy 91, 352–361 (2016) https://doi.org/10.1016/j.enpol.2016.01.015

    Gudipudi, R., Fluschnik, T., Ros, A.G.C., Walther, C., Kropp, J.P.: City density and CO2 efficiency. Energy Policy 91, 352–361 (2016) https://doi.org/10.1016/j.enpol.2016.01.015

    2016 doi

  8. [16]

    Nature Communications 10(1), 3204 (2019) https://doi.org/10.1038/ 19 s41467-019-11184-y

    Ribeiro, H.V., Rybski, D., Kropp, J.P.: Effects of changing population or density on urban carbon dioxide emissions. Nature Communications 10(1), 3204 (2019) https://doi.org/10.1038/ 19 s41467-019-11184-y

    2019

  9. [17]

    Nature Sustainability 7(3), 294–304 (2024) https://doi.org/10.1038/s41893-024-01271-4

    Fu, X., Cheng, J., Peng, L., Zhou, M., Tong, D., Mauzerall, D.L.: Co-benefits of transport demand reductions from compact urban development in Chinese cities. Nature Sustainability 7(3), 294–304 (2024) https://doi.org/10.1038/s41893-024-01271-4

    2024 doi

  10. [18]

    Nature Communications 15(1), 6456 (2024) https://doi.org/ 10.1038/s41467-024-50840-w

    Qiu, L., He, J., Yue, C., Ciais, P., Zheng, C.: Substantial terrestrial carbon emissions from global expansion of impervious surface area. Nature Communications 15(1), 6456 (2024) https://doi.org/ 10.1038/s41467-024-50840-w

    2024 doi

  11. [19]

    Lippincott’s Magazine 57, 403–409 (1896)

    Sullivan, L.H.: The tall office building artistically considered. Lippincott’s Magazine 57, 403–409 (1896)

  12. [20]

    American Quarterly 9(9), 316–324 (1957) https://doi.org/10.2307/2710531

    Buitenhuis, P.: Aesthetics of the skyscraper: The views of sullivan, james and wright. American Quarterly 9(9), 316–324 (1957) https://doi.org/10.2307/2710531

    1957 doi

  13. [21]

    Journal of Urban Economics 129, 103419 (2022) https://doi.org/10.1016/j.jue.2021.103419

    Ahlfeldt, G.M., Barr, J.: The economics of skyscrapers: A synthesis. Journal of Urban Economics 129, 103419 (2022) https://doi.org/10.1016/j.jue.2021.103419

    2022

  14. [22]

    Ahlfeldt, G.M., Baum-Snow, N., Jedwab, R.: The skyscraper revolution: Global economic develop- ment and land savings (2023) https://doi.org/10.2139/ssrn.4649000

    2023 doi

  15. [23]

    Nature Cities, 1–12 (2024) https://doi.org/10

    Frolking, S., Mahtta, R., Milliman, T., Esch, T., Seto, K.C.: Global urban structural growth shows a profound shift from spreading out to building up. Nature Cities, 1–12 (2024) https://doi.org/10. 1038/s44284-024-00100-1

    2024

  16. [24]

    Cities 158, 105682 (2025) https://doi.org/10.1016/j.cities.2024.105682

    Xiao, W., Ruan, L., Wang, K., Xu, S., Yue, W., He, T., Chen, W., Li, X., Zhang, Y.: Measuring three-dimension urban expansion using multi-source data and change detection algorithm: A case study of Shanghai. Cities 158, 105682 (2025) https://doi.org/10.1016/j.cities.2024.105682

    2025

  17. [25]

    Land Use Policy 153, 107542 (2025) https://doi.org/10.1016/j.landusepol.2025.107542

    Yin, C., Chen, R., Xiao, X., Qin, Y., Meng, F., Yao, Y., Pan, L., Zheng, L.: Spatio-temporal evolution of vertical urban growth in China’s Yangtze River Delta from 1990 to 2020. Land Use Policy 153, 107542 (2025) https://doi.org/10.1016/j.landusepol.2025.107542

    1990

  18. [26]

    Nature Cities, 1–9 (2024) https://doi.org/10.1038/ s44284-024-00120-x

    Wu, S., Chen, B., An, J., Lin, C., Gong, P.: The interplay of cloud cover and 3D urban structures reduces human access to sunlight. Nature Cities, 1–9 (2024) https://doi.org/10.1038/ s44284-024-00120-x

    2024

  19. [27]

    Proceedings of the National Academy of Sciences 119(46), 2214813119 (2022) https://doi.org/10.1073/pnas

    Zhou, Y., Li, X., Chen, W., Meng, L., Wu, Q., Gong, P., Seto, K.C.: Satellite mapping of urban built- up heights reveals extreme infrastructure gaps and inequalities in the Global South. Proceedings of the National Academy of Sciences 119(46), 2214813119 (2022) https://doi.org...

    2022 doi

  20. [28]

    Com- puters, environment and urban systems 54, 32–46 (2015) https://doi.org/10.1016/j.compenvurbsys

    Broitman, D., Koomen, E.: Residential density change: Densification and urban expansion. Com- puters, environment and urban systems 54, 32–46 (2015) https://doi.org/10.1016/j.compenvurbsys. 2015.05.006

    2015 doi

  21. [29]

    PLoS ONE 11(6), 0156808 (2016) https://doi.org/10.1371/journal.pone.0156808

    Biljecki, F., Arroyo Ohori, K., Ledoux, H., Peters, R., Stoter, J.: Population estimation using a 3D city model: A multi-scale country-wide study in the Netherlands. PLoS ONE 11(6), 0156808 (2016) https://doi.org/10.1371/journal.pone.0156808

    2016 doi

  22. [30]

    Geografiska Annaler: Series B, Human Geography 53(1), 54–67 (1971) https://doi.org/10.1080/04353684.1971.11879355

    Nordbeck, S.: Urban allometric growth. Geografiska Annaler: Series B, Human Geography 53(1), 54–67 (1971) https://doi.org/10.1080/04353684.1971.11879355

    1971

  23. [31]

    Physics Reports 1012, 1–39 (2023) https://doi.org/10.1016/j.physrep.2023.02.002

    Ribeiro, F.L., Rybski, D.: Mathematical models to explain the origin of urban scaling laws. Physics Reports 1012, 1–39 (2023) https://doi.org/10.1016/j.physrep.2023.02.002

    2023 doi

  24. [32]

    Proceedings of the National Academy of Sciences 104(17), 7301–7306 (2007) https://doi.org/10.1073/pnas.0610172104

    Bettencourt, L.M., Lobo, J., Helbing, D., K¨ uhnert, C., West, G.B.: Growth, innovation, scaling, 20 and the pace of life in cities. Proceedings of the National Academy of Sciences 104(17), 7301–7306 (2007) https://doi.org/10.1073/pnas.0610172104

    2007 doi

  25. [33]

    SAGE Publications Sage UK: London, England (2011)

    Batty, M., Ferguson, P.: Defining city size. SAGE Publications Sage UK: London, England (2011). https://doi.org/10.1068/b3805ed

    2011 doi

  26. [34]

    Frontiers in Conservation Science 3, 879934 (2022) https://doi.org/10.3389/fcosc.2022.879934

    Burger, J.R., Okie, J.G., Hatton, I.A., Weinberger, V.P., Shrestha, M., Liedtke, K.J., Be, T., Cruz, A.R., Feng, X., Hinojo-Hinojo, C., et al.: Global city densities: Re-examining urban scaling theory. Frontiers in Conservation Science 3, 879934 (2022) https://doi.org/10.3389/...

    2022

  27. [35]

    Nature Cities, 1–9 (2025) https://doi.org/10.1038/s44284-025-00208-y

    Xu, G., Zhu, M., Chen, B., Salem, M., Xu, Z., Cobbinah, P.B., Li, X., Sumari, N.S., Zhang, X., Jiao, L., et al.: Underlying rules of evolutionary urban systems in Africa. Nature Cities, 1–9 (2025) https://doi.org/10.1038/s44284-025-00208-y

    2025 doi

  28. [36]

    arXiv preprint (2015) https://doi.org/10.48550/arXiv.1512.00946

    Schl¨ apfer, M., Lee, J., Bettencourt, L.: Urban skylines: building heights and shapes as measures of city size. arXiv preprint (2015) https://doi.org/10.48550/arXiv.1512.00946

    2015 doi arXiv

  29. [37]

    Earth System Science Data 2024, 1–28 (2024) https://doi.org/10.5194/essd-2024-217

    Che, Y., Li, X., Liu, X., Wang, Y., Liao, W., Zheng, X., Zhang, X., Xu, X., Shi, Q., Zhu, J., et al.: 3D-GloBFP: the first global three-dimensional building footprint dataset. Earth System Science Data 2024, 1–28 (2024) https://doi.org/10.5194/essd-2024-217

    2024 doi

  30. [38]

    arXiv preprint (2011) https://doi.org/10

    Shalizi, C.R.: Scaling and hierarchy in urban economies. arXiv preprint (2011) https://doi.org/10. 48550/arXiv.1102.4101

    2011 doi arXiv

  31. [39]

    arXiv preprint (2013) https://doi.org/10.48550/arXiv.1301.5919

    Bettencourt, L., Lobo, J., Youn, H.: The hypothesis of urban scaling: formalization, implications and challenges. arXiv preprint (2013) https://doi.org/10.48550/arXiv.1301.5919

    2013 doi arXiv

  32. [40]

    Environment and Planning B https://doi.org/10.1177/23998083251332324

    Ribeiro, F.L., Zhang, P., Gao, L., Rybski, D.: How buildings change the fundamental allometry. Environment and Planning B https://doi.org/10.1177/23998083251332324

    doi

  33. [41]

    Remote Sensing of Environment 240, 111705 (2020) https://doi.org/10.1016/ j.rse.2020.111705

    Li, X., Zhou, Y., Gong, P., Seto, K.C., Clinton, N.: Developing a method to estimate building height from Sentinel-1 data. Remote Sensing of Environment 240, 111705 (2020) https://doi.org/10.1016/ j.rse.2020.111705

    2020

  34. [42]

    Journal of Urban Economics 132, 103507 (2022) https://doi.org/10.1016/j.jue.2022.103507

    Jedwab, R., Barr, J., Brueckner, J.K.: Cities without skylines: Worldwide building-height gaps and their possible determinants and implications. Journal of Urban Economics 132, 103507 (2022) https://doi.org/10.1016/j.jue.2022.103507

    2022

  35. [43]

    Mapping and the Citizen Sensor, 37–59 (2017) https://doi.org/10.5334/bbf

    Mooney, P., Minghini, M., et al.: A review of OpenStreetMap data. Mapping and the Citizen Sensor, 37–59 (2017) https://doi.org/10.5334/bbf

    2017 doi

  36. [44]

    Nature Communications 14(1), 3985 (2023) https://doi.org/10.1038/s41467-023-39698-6

    Herfort, B., Lautenbach, S., Albuquerque, J., Anderson, J., Zipf, A.: A spatio-temporal analysis investigating completeness and inequalities of global urban building data in OpenStreetMap. Nature Communications 14(1), 3985 (2023) https://doi.org/10.1038/s41467-023-39698-6

    2023 doi

  37. [45]

    Physica A: Statistical Mechanics and Its Applications 560, 125162 (2020) https://doi.org/10.1016/j.physa.2020.125162

    Xu, G., Xu, Z., Gu, Y., Lei, W., Pan, Y., Liu, J., Jiao, L.: Scaling laws in intra-urban systems and over time at the district level in Shanghai, China. Physica A: Statistical Mechanics and Its Applications 560, 125162 (2020) https://doi.org/10.1016/j.physa.2020.125162

    2020

  38. [46]

    Cities 131, 103919 (2022) https://doi.org/10.1016/j.cities.2022.103919

    Chakraborty, S., Dadashpoor, H., Novotn` y, J., Maity, I., Follmann, A., Patel, P.P., Roy, U., Pra- manik, S.: In pursuit of sustainability–Spatio-temporal pathways of urban growth patterns in the world’s largest megacities. Cities 131, 103919 (2022) https://doi.org/10.1016/j....

    2022

  39. [47]

    Landscape and Urban Planning 139, 26–39 (2015) https://doi.org/10.1016/j.landurbplan.2015.02.017

    Jiao, L.: Urban land density function: A new method to characterize urban expansion. Landscape and Urban Planning 139, 26–39 (2015) https://doi.org/10.1016/j.landurbplan.2015.02.017

    2015 doi

  40. [48]

    Environment and Planning B: Urban Analytics and City Science 47(5), 870–888 (2020) https://doi.org/10.1177/ 21 2399808318810532

    Lemoy, R., Caruso, G.: Evidence for the homothetic scaling of urban forms. Environment and Planning B: Urban Analytics and City Science 47(5), 870–888 (2020) https://doi.org/10.1177/ 21 2399808318810532

    2020

  41. [49]

    Scientific Reports 11(1), 22044 (2021) https://doi.org/10.1038/s41598-021-01477-y

    Lemoy, R., Caruso, G.: Radial analysis and scaling of urban land use. Scientific Reports 11(1), 22044 (2021) https://doi.org/10.1038/s41598-021-01477-y

    2021 doi

  42. [50]

    submitted (2025)

    Laziou, G., Lemoy, R.: The three-dimensional structure of population density in world cities. submitted (2025)

    2025

  43. [51]

    The Journal of Law and Economics 48(2), 331–369 (2005) https://doi.org/10.1086/ 429979

    Glaeser, E.L., Gyourko, J., Saks, R.: Why is Manhattan so expensive? Regulation and the rise in housing prices. The Journal of Law and Economics 48(2), 331–369 (2005) https://doi.org/10.1086/ 429979

    2005

  44. [52]

    Proceedings of the National Academy of Sciences 119(38), 2201780119 (2022) https: //doi.org/10.1073/pnas.2201780119

    Wicki, M., Hofer, K., Kaufmann, D.: Planning instruments enhance the acceptance of urban den- sification. Proceedings of the National Academy of Sciences 119(38), 2201780119 (2022) https: //doi.org/10.1073/pnas.2201780119

    2022 doi

  45. [53]

    Land Use Policy 30(1), 485–495 (2013) https://doi.org/10.1016/j.landusepol.2012.04.016

    Ding, C.: Building height restrictions, land development and economic costs. Land Use Policy 30(1), 485–495 (2013) https://doi.org/10.1016/j.landusepol.2012.04.016

    2013 doi

  46. [54]

    submitted (2025)

    Jehling, M., Kr¨ uger, T., Behnisch, M., Rybsk, D.: Tackling the net-zero land-take question. submitted (2025)

    2025

  47. [55]

    Nature Cities 1(10), 642–653 (2024) https://doi.org/10.1038/ s44284-024-00118-5

    Wang, L., Saiz, A., Li, W.: Natural fragmentation increases urban density but impedes trans- portation and city growth worldwide. Nature Cities 1(10), 642–653 (2024) https://doi.org/10.1038/ s44284-024-00118-5

    2024

  48. [56]

    Physical Review Letters 111(19), 198702 (2013) https://doi.org/10.1103/PhysRevLett.111.198702

    Louf, R., Barthelemy, M.: Modeling the polycentric transition of cities. Physical Review Letters 111(19), 198702 (2013) https://doi.org/10.1103/PhysRevLett.111.198702

    2013 doi

  49. [57]

    Nature Communications 15(1), 4507 (2024) https://doi.org/10.1038/s41467-024-48909-7

    Zhao, P., Wang, H., Liu, Q., Yan, X.-Y., Li, J.: Unravelling the spatial directionality of urban mobility. Nature Communications 15(1), 4507 (2024) https://doi.org/10.1038/s41467-024-48909-7

    2024 doi

  50. [58]

    Nature Communications 8(1), 1841 (2017) https://doi.org/10.1038/ s41467-017-01882-w

    Li, R., Dong, L., Zhang, J., Wang, X., Wang, W.-X., Di, Z., Stanley, H.E.: Simple spatial scaling rules behind complex cities. Nature Communications 8(1), 1841 (2017) https://doi.org/10.1038/ s41467-017-01882-w

    2017

  51. [59]

    Nature 593(7860), 522–527 (2021) https://doi.org/10.1038/s41586-021-03480-9

    Schl¨ apfer, M., Dong, L., O’Keeffe, K., Santi, P., Szell, M., Salat, H., Anklesaria, S., Vazifeh, M., Ratti, C., West, G.B.: The universal visitation law of human mobility. Nature 593(7860), 522–527 (2021) https://doi.org/10.1038/s41586-021-03480-9

    2021 doi

  52. [60]

    Computers, Environment and Urban Systems 95, 101809 (2022) https://doi.org/10.1016/j.compenvurbsys.2022.101809

    Biljecki, F., Chow, Y.S.: Global building morphology indicators. Computers, Environment and Urban Systems 95, 101809 (2022) https://doi.org/10.1016/j.compenvurbsys.2022.101809

    2022

  53. [61]

    Technical report, JRC Technical Report (2019)

    Schiavina, M., Moreno-Monroy, A., Maffenini, L., Veneri, P.: GHSL-OECD Functional Urban Areas. Technical report, JRC Technical Report (2019). https://www.adrmuntenia.ro/downloadfile/ document/1239/Functional-Urban-Areas-2019-OECD-Report.pdf

    2019

  54. [62]

    Delineation and population trends

    Moreno-Monroy, A.I., Schiavina, M., Veneri, P.: Metropolitan areas in the world. Delineation and population trends. J. Urban Econ. 125, 103242 (2021) https://doi.org/10.1016/j.jue.2020.103242

    2021

  55. [63]

    PLoS ONE 16(1), 0245771 (2021) https://doi.org/ 10.1371/journal.pone.0245771 22

    Ribeiro, H.V., Oehlers, M., Moreno-Monroy, A.I., Kropp, J.P., Rybski, D.: Association between population distribution and urban GDP scaling. PLoS ONE 16(1), 0245771 (2021) https://doi.org/ 10.1371/journal.pone.0245771 22

    2021 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.