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As the physical manifestation of these transformations, urban form provides a key basis for examining its connections with urban outcomes. While previous studies have primarily focused on two-dimensional (2D) measures, cities are inherently three-dimensional (3D), and the increasing availability of spatial data has recently enabled more detailed 3D analyses. However, comprehensive frameworks that integrate both horizontal and vertical dimensions remain limited. Here, we analyze building height data for 296 Chinese prefecture-level cities in 2019, proposing a volume-constrained framework to explore cross-sectional scaling relationships of urban 3D form with transport emissions, building operation emissions, and GDP. Our results suggest that, conditional on comparable total building volumes, cities characterized by greater vertical development and smaller horizontal extent are statistically associated with lower transport and building operation emissions and higher GDP. We further examine heterogeneity in these associations across cities with different levels of economic development, population size, energy transition, and spatial structure. Additionally, we decompose building operation emissions by end use and show that the height-emission association varies substantially across regional contexts and energy structures, particularly in reliance on heating. This framework provides a systematic approach for incorporating 3D urban form into cross-city scaling analyses, highlighting the diversity of spatial configurations and their associations with urban performance.<\/jats:p>","DOI":"10.1021\/acs.est.6c06830","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T21:38:49Z","timestamp":1788471529000},"page":"26397-26407","source":"Crossref","is-referenced-by-count":1,"title":["Scaling\nof Urban 3D Form with Emissions and GDP in\nChinese Cities"],"prefix":"10.1021","volume":"60","author":[{"given":"Peiran","family":"Zhang","sequence":"first","affiliation":[{"name":"Beijing Jiaotong University , , ,","place":["Beijing, China, 100044"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4005-0339","authenticated-orcid":true,"given":"Liang","family":"Gao","sequence":"additional","affiliation":[{"name":"Beijing Jiaotong University , , ,","place":["Beijing, China, 100044"]},{"name":"Beijing Jiaotong University , , ,","place":["Beijing, China, 100044"]},{"name":"Beijing Jiaotong University , , ,","place":["Beijing, China, 100044"]},{"name":"Lanzhou Jiaotong University , , ,","place":["Lanzhou, China, 730070"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rafael","family":"Prieto-Curiel","sequence":"additional","affiliation":[{"name":"Complexity Science Hub , ,","place":["Vienna, Austria, 1030"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chaoyang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Lanzhou Jiaotong University , , ,","place":["Lanzhou, China, 730070"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daqing","family":"Li","sequence":"additional","affiliation":[{"name":"Beihang University , , ,","place":["Beijing, China, 100191"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4050-2868","authenticated-orcid":true,"given":"Yupeng","family":"Liu","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences , , ,","place":["Xiamen, China, 361021"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lulu","family":"Song","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences , , ,","place":["Xiamen, China, 361021"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Jia","sequence":"additional","affiliation":[{"name":"Beijing Jiaotong University , , ,","place":["Beijing, China, 100044"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7686-2331","authenticated-orcid":true,"given":"Wei-Qiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences , , ,","place":["Xiamen, China, 361021"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ziyou","family":"Gao","sequence":"additional","affiliation":[{"name":"Beijing Jiaotong University , , ,","place":["Beijing, China, 100044"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,3]]},"reference":[{"key":"2026092210110357100_cit1","doi-asserted-by":"publisher","first-page":"1067","DOI":"10.1007\/s11430-016-9022-2","article-title":"Chinese urbanization\n2050: SD modeling\nand process simulation","volume":"60","author":"Gu","year":"2017","journal-title":"Sci. China Earth Sci."},{"key":"2026092210110357100_cit2","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1080\/04353684.1971.11879355","article-title":"Urban allometric\ngrowth. Geografiska Annaler: Series B","volume":"53","author":"Nordbeck","year":"1971","journal-title":"Human\nGeography"},{"key":"2026092210110357100_cit3","doi-asserted-by":"publisher","first-page":"7301","DOI":"10.1073\/pnas.0610172104","article-title":"Growth, innovation, scaling, and the pace of life in\ncities","volume":"104","author":"Bettencourt","year":"2007","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2026092210110357100_cit4","doi-asserted-by":"publisher","first-page":"198702","DOI":"10.1103\/PhysRevLett.111.198702","article-title":"Modeling the\nPolycentric Transition of Cities","volume":"111","author":"Louf","year":"2013","journal-title":"Phys. Rev.\nLett."},{"key":"2026092210110357100_cit5","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.aar4644","article-title":"Toward\ncities without slums: Topology and the spatial evolution of neighborhoods","volume":"4","author":"Brelsford","year":"2018","journal-title":"Sci. Adv."},{"key":"2026092210110357100_cit6","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abb4112","article-title":"Deconstructing\nlaws of accessibility and facility distribution in cities","volume":"6","author":"Xu","year":"2020","journal-title":"Sci. Adv."},{"key":"2026092210110357100_cit7","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2214254120","article-title":"Scaling of the morphology of African\ncities","volume":"120","author":"Prieto-Curiel","year":"2023","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2026092210110357100_cit8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s44284-025-00338-3","article-title":"Urban sprawl\nis associated with reduced\naccess and increased costs of water and sanitation","volume":"2","author":"Prieto-Curiel","year":"2025","journal-title":"Nat. Cities"},{"key":"2026092210110357100_cit9","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1016\/j.enpol.2016.01.015","article-title":"City density\nand CO2 efficiency","volume":"91","author":"Gudipudi","year":"2016","journal-title":"Energy Policy"},{"key":"2026092210110357100_cit10","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-019-11184-y","article-title":"Effects\nof changing population or\ndensity on urban carbon dioxide emissions","volume":"10","author":"Ribeiro","year":"2019","journal-title":"Nat.\nCommun."},{"key":"2026092210110357100_cit11","doi-asserted-by":"publisher","first-page":"106185","DOI":"10.1016\/j.scs.2025.106185","article-title":"Quantifying\ncontributions of geographical features to urban GDP outputs\nvia interpretable machine learning","volume":"121","author":"Zhang","year":"2025","journal-title":"Sustainable\nCities Society"},{"key":"2026092210110357100_cit12","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2214813119","article-title":"Satellite mapping of urban built-up heights reveals\nextreme infrastructure gaps and inequalities in the Global South","volume":"119","author":"Zhou","year":"2022","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"2026092210110357100_cit13","doi-asserted-by":"publisher","DOI":"10.1016\/j.rse.2023.113578","article-title":"A first Chinese building\nheight estimate at 10m resolution (CNBH-10m) using multi-source earth\nobservations and machine learning","volume":"291","author":"Wu","year":"2023","journal-title":"Remote Sens.\nEnviron."},{"key":"2026092210110357100_cit14","doi-asserted-by":"publisher","first-page":"105635","DOI":"10.1016\/j.scs.2024.105635","article-title":"Refining urban morphology: An explainable machine learning\nmethod for estimating footprint-level building height","volume":"112","author":"Chen","year":"2024","journal-title":"Sustainable Cities Society"},{"key":"2026092210110357100_cit15","doi-asserted-by":"publisher","DOI":"10.1016\/j.rse.2024.114108","article-title":"Remote\nsensing of\ndiverse urban environments: From the single city to multiple cities","volume":"305","author":"Chen","year":"2024","journal-title":"Remote Sens. Environ."},{"key":"2026092210110357100_cit16","doi-asserted-by":"publisher","DOI":"10.1088\/1748-9326\/ab59bf","article-title":"Building up or spreading\nout? Typologies\nof urban growth across 478 cities of 1 million+","volume":"14","author":"Mahtta","year":"2019","journal-title":"Environ. Res. Lett."},{"key":"2026092210110357100_cit17","doi-asserted-by":"publisher","first-page":"113225","DOI":"10.1016\/j.rse.2022.113225","article-title":"Three decades\nof\nglobal trends in urban microwave backscatter, building volume and\ncity GDP","volume":"281","author":"Frolking","year":"2022","journal-title":"Remote Sens. Environ."},{"key":"2026092210110357100_cit18","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1038\/s44284-024-00100-1","article-title":"Global\nurban structural growth shows a profound shift from spreading out\nto building up","volume":"1","author":"Frolking","year":"2024","journal-title":"Nat. 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Cities"},{"key":"2026092210110357100_cit22","doi-asserted-by":"publisher","DOI":"10.1016\/j.buildenv.2022.109588","article-title":"Frontal area index: A review of calculation methods\nand application\nin the urban environment","volume":"224","author":"Xu","year":"2022","journal-title":"Building Environ."},{"key":"2026092210110357100_cit23","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1080\/01431161.2012.714509","article-title":"Spatial variability\nof frontal area index and its relationship\nwith urban heat island intensity","volume":"34","author":"Wong","year":"2013","journal-title":"Int. J. Remote\nSensing"},{"key":"2026092210110357100_cit24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s44284-025-00254-6","article-title":"The form of China\u2019s urban commercial expansion\nin the digital era","author":"Zhang","year":"2025","journal-title":"Nat. Cities"},{"key":"2026092210110357100_cit25","doi-asserted-by":"publisher","DOI":"10.1016\/j.compenvurbsys.2022.101800","article-title":"Urban morphological regionalization based on 3D building\nblocksA\ncase in the central area of Chengdu, China","volume":"94","author":"Yang","year":"2022","journal-title":"Computers, Environ. Urban Systems"},{"key":"2026092210110357100_cit26","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1057\/s41289-018-0072-1","article-title":"Measuring\nthe complexity of urban form and design","volume":"23","author":"Boeing","year":"2018","journal-title":"Urban\nDesign Int."},{"key":"2026092210110357100_cit27","doi-asserted-by":"publisher","DOI":"10.1016\/j.scitotenv.2022.159502","article-title":"Scaling of Chinese urban CO2 emissions and multiple dimensions\nof city size","volume":"857","author":"Yang","year":"2023","journal-title":"Sci. Total Environ."},{"key":"2026092210110357100_cit28","unstructured":"Shalizi, C. R. S.\n          \n          Scaling\nand Hierarchy in Urban Economies, 2011, arXiv:1102.4101. arXiv.org e-Print archive https:\/\/arxiv.org\/abs\/1102.4101."},{"key":"2026092210110357100_cit29","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0705","article-title":"How the geometry of cities determines\nurban scaling\nlaws","volume":"18","author":"Molinero","year":"2021","journal-title":"J. R. Soc., Interface"},{"key":"2026092210110357100_cit30","doi-asserted-by":"publisher","DOI":"10.1177\/23998083251332324","article-title":"How buildings change\nthe fundamental allometry","author":"Ribeiro","year":"2024","journal-title":"Environ. Planning\nB: Urban Analytics City Sci."},{"key":"2026092210110357100_cit31","first-page":"923","volume-title":"Climate Change\n2014","author":"Seto","year":"2014"},{"key":"2026092210110357100_cit32","doi-asserted-by":"publisher","first-page":"6283","DOI":"10.1073\/pnas.1315545112","article-title":"Global\ntypology of urban energy use and potentials for an urbanization mitigation\nwedge","volume":"112","author":"Creutzig","year":"2015","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026092210110357100_cit33","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1177\/00420980211017817","article-title":"Urban scaling in rapidly\nurbanising China","volume":"59","author":"Lei","year":"2022","journal-title":"Urban Stud."},{"key":"2026092210110357100_cit34","doi-asserted-by":"publisher","first-page":"959","DOI":"10.5194\/essd-11-959-2019","article-title":"EDGAR v4.3.2 Global\nAtlas of the three major greenhouse gas emissions for the period 1970\u20132012","volume":"11","author":"Janssens-Maenhout","year":"2019","journal-title":"Earth Syst. Sci. Data"},{"key":"2026092210110357100_cit35","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1038\/s41597-020-0462-2","article-title":"High resolution temporal profiles\nin the Emissions Database for Global Atmospheric Research","volume":"7","author":"Crippa","year":"2020","journal-title":"Sci. Data"},{"key":"2026092210110357100_cit36","author":"Crippa","year":"2022","journal-title":"CO2 emissions\nof all world countries"},{"key":"2026092210110357100_cit37","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1038\/s41597-024-02971-4","article-title":"City-level building operation and\nend-use carbon emissions dataset from China for 2015\u20132020","volume":"11","author":"Yu","year":"2024","journal-title":"Scientific Data"},{"key":"2026092210110357100_cit38","doi-asserted-by":"publisher","first-page":"912","DOI":"10.1038\/467912a","article-title":"A unified theory of\nurban living","volume":"467","author":"Bettencourt","year":"2010","journal-title":"Nature"},{"key":"2026092210110357100_cit39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2023.02.002","article-title":"Mathematical models\nto explain the origin of urban\nscaling laws","volume":"1012","author":"Ribeiro","year":"2023","journal-title":"Phys. Rep."},{"key":"2026092210110357100_cit40","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1086\/260489","article-title":"The Cobb-Douglas\nproduction function once again: its history, its testing, and some\nnew empirical values","volume":"84","author":"Douglas","year":"1976","journal-title":"J. Political Economy"},{"key":"2026092210110357100_cit41","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-021-02327-7","article-title":"Commuting\nnetwork effect on urban\nwealth scaling","volume":"11","author":"Alves","year":"2021","journal-title":"Sci. Rep."},{"key":"2026092210110357100_cit42","first-page":"367","article-title":"Transcendental logarithmic\nutility\nfunctions","volume":"65","author":"Christensen","year":"1975","journal-title":"Am. Econ. Rev."},{"key":"2026092210110357100_cit43","doi-asserted-by":"publisher","first-page":"906","DOI":"10.1038\/s41597-023-02815-7","article-title":"A dataset of low-carbon\nenergy transition index for\nChinese cities 2003\u20132019","volume":"10","author":"Shen","year":"2023","journal-title":"Scientific\nData"},{"key":"2026092210110357100_cit44","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1111\/gean.12002","article-title":"Urban centrality:\na simple index","volume":"45","author":"Pereira","year":"2013","journal-title":"Geographical Anal."},{"key":"2026092210110357100_cit45","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1038\/s42949-024-00172-x","article-title":"Scaling laws\nof CO2 emissions during global urban expansion","volume":"5","author":"Yang","year":"2025","journal-title":"npj Urban Sustainability"},{"key":"2026092210110357100_cit46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41893-024-01271-4","article-title":"Co-benefits\nof transport demand reductions from compact\nurban development in Chinese cities","volume":"7","author":"Fu","year":"2024","journal-title":"Nat. Sustain."},{"key":"2026092210110357100_cit47","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1038\/s44284-024-00119-4","article-title":"A universal framework\nfor inclusive 15-minute cities","volume":"1","author":"Bruno","year":"2024","journal-title":"Nat. Cities"},{"key":"2026092210110357100_cit48","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1038\/s41562-023-01770-y","article-title":"The 15-minute\ncity\nquantified using human mobility data","volume":"8","author":"Abbiasov","year":"2024","journal-title":"Nat. Human\nBehaviour"},{"key":"2026092210110357100_cit49","doi-asserted-by":"publisher","DOI":"10.1016\/j.cities.2025.106516","article-title":"Vertical 15-minute city: Modeling\nurban density and functional mix with multi-source geospatial data","volume":"169","author":"Chen","year":"2026","journal-title":"Cities"},{"key":"2026092210110357100_cit50","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.cities.2017.08.010","article-title":"Does compact development\nincrease\nor reduce traffic congestion?","volume":"72","author":"Ewing","year":"2018","journal-title":"Cities"},{"key":"2026092210110357100_cit51","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1080\/01441649108716787","article-title":"Transport\nand urban form in thirty-two of the world\u2019s\nprincipal cities","volume":"11","author":"Newman","year":"1991","journal-title":"Transport Rev."},{"key":"2026092210110357100_cit52","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s44284-025-00342-7","article-title":"Metros reduce\ncar use in European cities but trams do not","volume":"2","author":"Prieto-Curiel","year":"2025","journal-title":"Nat. Cities"},{"key":"2026092210110357100_cit53","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41893-025-01615-8","article-title":"Revealing building\noperating carbon dynamics for multiple cities","volume":"8","author":"Yap","year":"2025","journal-title":"Nat. Sustainability"},{"key":"2026092210110357100_cit54","doi-asserted-by":"publisher","first-page":"5985","DOI":"10.1073\/pnas.1504315112","article-title":"Energy\nand material\nflows of megacities","volume":"112","author":"Kennedy","year":"2015","journal-title":"Proc. National Academy\nSci."},{"key":"2026092210110357100_cit55","doi-asserted-by":"publisher","first-page":"1438","DOI":"10.1126\/science.1235823","article-title":"The\nOrigins of Scaling in Cities","volume":"340","author":"Bettencourt","year":"2013","journal-title":"Science"},{"key":"2026092210110357100_cit56","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms2961","article-title":"Urban characteristics\nattributable to density-driven tie formation","volume":"4","author":"Pan","year":"2013","journal-title":"Nat. Commun."},{"key":"2026092210110357100_cit57","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1038\/s41586-023-06757-3","article-title":"Human mobility\nnetworks reveal increased\nsegregation in large cities","volume":"624","author":"Nilforoshan","year":"2023","journal-title":"Nature"}],"container-title":["Environmental Science &amp;\nTechnology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.est.6c06830","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/esthag\/article-pdf\/60\/37\/26397\/68300322\/acs.est.6c06830.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/esthag\/article-pdf\/60\/37\/26397\/68300322\/acs.est.6c06830.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T14:49:11Z","timestamp":1790088551000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/esthag\/article\/60\/37\/26397\/5414729\/Scaling-of-Urban-3D-Form-with-Emissions-and-GDP-in"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,3]]},"references-count":57,"journal-issue":{"issue":"37","published-online":{"date-parts":[[2026,9,3]]},"published-print":{"date-parts":[[2026,9,22]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.est.6c06830","relation":{},"ISSN":["0013-936X","1520-5851"],"issn-type":[{"value":"0013-936X","type":"print"},{"value":"1520-5851","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,3]]}}}