A team led by Yiwei Yang of BOKU University in Vienna, together with colleagues at the Complexity Science Hub, Trier University, and the Max Planck Institute of Geoanthropology, took a radical methodological step. Instead of treating each city as a single data point—the so-called one-city-one-value approach—they chopped the entire contiguous United States into more than five million grid cells of one square kilometer each and treated every cell as an observation. Onto this lattice they layered some of the most detailed geospatial datasets ever assembled for the purpose: ten-meter-resolution maps of every building and piece of mobility infrastructure in the country, one-kilometer gridded greenhouse gas emissions from the Vulcan and DARTE inventories, and census-block population counts from 2020.

The mathematical heart of the study is the scaling law, a power relationship of the form Y = Y0 P^β, where an urban attribute Y grows with population P at an exponent β. When β exceeds one, the attribute grows super-linearly—doubling population more than doubles the attribute, as with income and patents. When β falls below one, growth is sub-linear: bigger populations need disproportionately less of the thing being measured. The researchers simply swapped cities for grid cells, asking how eighteen indicators—building footprints, floor areas, material masses, street areas, and emissions from residential, commercial, industrial, and on-road sources—scale with the population living in each cell.

The results are strikingly consistent. Residential building footprints, useful floor area, and material stocks scale moderately sub-linearly, with exponents between roughly 0.82 and 0.89. Non-residential buildings and mobility infrastructure scale far more steeply sub-linear, with exponents between 0.42 and 0.74. In practical terms, a grid cell with twice the population of its neighbor contains only about 1.9 times the building material, but just 1.5 times the mass of mobility infrastructure and roughly 1.35 times the street area. Roads, it turns out, are where density pays its biggest dividends: people packed closely together simply need far less pavement between them.

Greenhouse gas emissions follow the same logic, with an important sectoral twist. Residential building emissions and on-road transport emissions scale sub-linearly, at an average exponent of about 0.75, meaning a cell with double the population emits only around 1.7 times the carbon from homes and cars. The authors attribute this to the geometry of compact buildings—which have higher volume-to-surface ratios and therefore lower heating and cooling demand per unit of floor space—along with shorter trips and better public transport options. Commercial and industrial emissions, by contrast, scale nearly linearly, reflecting the fixed, energy-hungry operations of factories and offices that do not shrink much when surrounded by more people.

Translated into per capita terms, the findings become a blunt statement about the American landscape. Using benchmarks of roughly 50 people per square kilometer for rural areas, 600 for suburbs, and 1,800 for urban cores, the researchers calculate that residents of high-density urban cells need only 58 percent of the building footprint and a mere 17 percent of the mobility infrastructure area required by rural residents. Their combined building and infrastructure material stock is just 37 percent of the rural figure, and their residential and on-road emissions are 41 percent. Suburbanites sit in between, at roughly half to two-thirds of rural per capita levels. In short, people living in dense urban areas use half or less, per person, of nearly everything the built environment demands.

The study’s robustness checks are unusually thorough. The team tested sensitivity to grid placement, to assumptions about residential building heights and floor counts, and to spatial autocorrelation by comparing ordinary least squares with spatial lag and spatial error models—all with negligible changes to the estimated exponents. They subdivided the country into 15,600 windows of 30 by 30 kilometers and ran the regressions locally, finding that the exponents are distributed approximately normally around the national averages. A handful of anomalous windows, mostly in sparsely populated mountainous or rural terrain, showed super-linear or negative scaling, but these carried weak statistical reliability and did not disturb the overall pattern. Regional differences across the Northeast, South, Midwest, and West were statistically detectable but modest in practical magnitude.

Perhaps the most intellectually satisfying part of the paper is its explanation of why all this happens. Drawing on a fractal framework proposed by Molinero and Thurner, the authors interpret the scaling exponent as the ratio of the fractal dimension of infrastructure to that of population—essentially, how fully each occupies space across scales. Sub-linear scaling emerges when population fills space more completely than infrastructure does. This also explains why the exponents depend on scale: as grid cells grow larger, they capture more of the spatial complexity of the built environment, and the exponents drift upward toward city-level values. The team even found a compensatory trade-off—across all grid sizes, the exponents for street area and building footprint sum to a nearly constant value, a consequence of buildings and streets being forced to share the same finite two-dimensional land.

The comparison with conventional city-based analysis is where the study delivers its sharpest critique. Depending on which of four urban boundary definitions is used—compact urban centers, Census urban areas, morphological footprints, or functional commuting zones—city-level scaling exponents for emissions can flip from sub-linear to super-linear regimes, a long-standing embarrassment for the field. The grid-based approach sidesteps this arbitrariness entirely. It also reveals that the apparent per capita equality of building demand across cities of different sizes is an illusion produced by aggregation: city averages blend together low per capita demand in dense cores with high per capita demand in sprawling fringes, canceling each other out.

The policy implications are hard to escape. Because rural areas contain 1.7 times the total material mass, 3.2 times the mobility infrastructure area, and 1.3 times the on-road emissions of high-density urban areas despite a smaller total population, sustainability strategies aimed only at city cores will miss where much of the material and carbon burden actually sits. The authors argue that where, and at what density, new residents are accommodated is the decisive variable: prioritizing infill development, compact renewal, and efficient land use is central to any credible path toward lower material throughput and emissions. At the same time, they caution that material efficiency does not automatically translate into carbon efficiency—the transport sector’s emissions scale less favorably than its infrastructure, meaning that compactness must be paired with broader technological and social change. Whether these intra-settlement laws hold over time, and whether they generalize beyond the United States, remain open questions. But the message of this study is already clear: the greenest square kilometer in America is not the one with the biggest city around it, but the one with the most people sharing what has already been built.

Subject of Research: Scaling relationships between population density, built environment material stocks, service provisioning, and greenhouse gas emissions across the urban–rural continuum of the contiguous United States

Article Title: Intra-settlement scaling across the urban–rural continuum: material stocks, service provisioning, and greenhouse gas emissions in the contiguous United States

Article References: Intra-settlement scaling across the urban–rural continuum: material stocks, service provisioning, and greenhouse gas emissions in the contiguous United States. (n.d.). https://doi.org/10.1007/s44498-026-00125-w

Image Credits: AI Generated

DOI: 10.1007/s44498-026-00125-w

Keywords: urban scaling laws, material stocks, greenhouse gas emissions, population density, built environment, mobility infrastructure, grid-based analysis, urban–rural continuum, fractal cities, sustainable urban development, industrial ecology, remote sensing

The scale of the existing system is staggering. The team estimates that in 2024 the world’s mobility infrastructure contained roughly 355 billion metric tons of materials, with an uncertainty range of 255 to 455 billion tons. Aggregates such as sand and gravel account for 74 percent of that mass, followed by concrete and asphalt. Lower-class roads, the local and rural routes that rarely attract attention, hold nearly half of all the material, while high-class roads such as motorways hold another 37 percent. Rail-based infrastructure, including subways, trams, bridges and station buildings, represents only 6 percent of the total mass but consumes a remarkable 68 percent of all the steel embedded in mobility networks. Parking, fueling stations and airport runways contribute less than 3 percent.

What makes the study politically explosive is its mapping of inequality. Per-capita infrastructure stocks range from about 5 metric tons in densely populated, low-income regions such as Sub-Saharan Africa and South Asia to nearly 500 tons in affluent, low-density regions of North America and Western Europe. In length terms, that spans from less than one meter of infrastructure per person to more than 230 meters. The researchers point to earlier work suggesting that well-being gains from mobility infrastructure saturate at around 100 tons per capita, a threshold already exceeded by roughly 20 percent of countries. If the rest of the world converged on that decent-mobility level, global stocks would triple to about 1,037 billion tons by 2060, with South Asia seeing an eightfold increase and Sub-Saharan Africa a sevenfold increase.

Methodologically, the study is a marriage of two modelling traditions that rarely speak to each other. The team first mapped global infrastructure at a resolution of 10 by 10 meters using OpenStreetMap data, which earlier research has shown to be more than 80 percent complete for roads, and harmonized the features into 37 infrastructure classes. They converted lines and points into areas using region-specific average widths validated against satellite imagery, then multiplied each class’s area by material intensity factors covering ten materials from steel and copper to timber and plastics. This produced the baseline stock for 2024. Future stocks were projected by matching each country’s infrastructure to vehicle-kilometer trajectories from the MESSAGEix-Transport integrated assessment model across 12 world regions and seven transport modes, under the Shared Socioeconomic Pathway ‘middle of the road’ scenario.

The second half of the workflow is what gives the study its carbon teeth. Annual material inflows were calculated from the net change in stocks plus maintenance flows derived from class-specific lifetimes, using a ‘leaching’ approach in which infrastructure gradually wears out rather than disappearing at a single end-of-life date. These flows then feed into MESSAGEix-Materials, an economy-wide model that tracks materials from extraction through industrial processing to recycling and waste, and computes the embodied carbon dioxide of producing concrete, asphalt, iron and steel, and aluminum. In the reference scenario, annual material flows reach 23 billion tons by 2060, split roughly equally between expansion and the maintenance and replacement of existing networks, with about 69 percent of maintenance concentrated in higher-income countries whose stocks are already saturated.

The headline numbers on carbon are sobering. Cumulative embodied emissions from 2024 to 2060 amount to about 11 gigatons of carbon dioxide in the reference scenario, equivalent to roughly 1.0 to 6.2 percent of the remaining carbon budget for holding warming to 2 degrees or 1.5 degrees respectively. Under the global convergence scenario, emissions climb 76 percent to 19 gigatons. Most striking is the rail paradox: a worldwide modal shift from road to rail, often promoted as a climate solution, would push embodied emissions up 241 percent to 37 gigatons of carbon dioxide, because railways are extraordinarily hungry for steel, concrete, aluminum and copper. In that scenario, rail infrastructure stocks grow fourteenfold to 300 billion tons, with copper stocks increasing 21-fold and timber, largely for railway sleepers, growing 14-fold.

Not every demand-side measure moves the needle. Halving the vehicle fleet through car sharing, and fully electrifying the passenger fleet, change total stocks by less than 1 percent, because parking and charging infrastructure are a trivial share of total mass. The single most powerful lever is reducing mobility demand itself, particularly in high-income countries. An income-tiered global mobility reduction holds 2060 stocks to 520 billion tons, well below the reference trajectory, and cuts cumulative embodied emissions by 44 percent to 6 gigatons. The researchers are careful to frame their projections as exploratory ‘what-if’ scenarios rather than forecasts, noting that the relationship between demand and infrastructure is non-linear; sensitivity tests in which high-intensity regions utilize infrastructure more intensively before expanding yield stocks 10 to 35 percent below reference levels.

Supply-side measures alone disappoint. Bundles of circular economy and decarbonization options, including material substitution, higher recycling rates, fuel switching in heavy industry and carbon capture and storage, reduce embodied emissions by only 4 to 8 percent when deployed without broader climate policy. But the picture changes dramatically when they are combined with economy-wide climate policy consistent with a 67 percent chance of staying below 2 degrees. Pairing that policy package with the reference or convergence scenarios cuts cumulative emissions by 40 to 47 percent. Most importantly, the fully integrated scenario, combining mobility reduction, rail expansion, enhanced recycling and industrial decarbonization, delivers a 63 percent reduction in embodied emissions while still providing adequate infrastructure for a growing and urbanizing world, helping to offset the carbon cost of building the public transport systems needed to slash operational emissions.

The study’s authors argue that the decisive question is not how much infrastructure gets built but what kind and where, and that urban form is the hidden variable. Decentralized, car-oriented development entrenches automobile dependence, while dense, well-planned cities enable efficient public and active transport with far lower infrastructure requirements per person served. Urban mobility already accounts for 40 percent of global passenger transport carbon emissions, and the urban fabric laid down in South Asia and Sub-Saharan Africa over the coming decades will lock in mobility patterns for a century. The researchers point to empirical evidence from Vienna and scenario analyses for Indian cities showing that shifts toward public and non-motorized transport can substantially reduce resource use and emissions, and to concepts such as Barcelona-style ‘superblocks’ and transit-oriented development as spatial strategies that make car-free life convenient rather than coercive.

There is also a deeper tension the study forces into the open. Operational emissions from vehicles, estimated at roughly 260 to 300 gigatons of carbon dioxide cumulatively through 2060, dwarf infrastructure’s embodied emissions by nearly thirty times, which is why the latter has been ignored. Yet infrastructure and operations are coupled: every new kilometer of road stimulates the very traffic that makes decarbonization harder, a dynamic known as induced demand, vividly illustrated by the Belt and Road initiative opening new freight corridors across Eurasia. The authors stress that replacing motorized trips with walking and cycling in dense urban settings requires comparatively little material investment and delivers public health co-benefits through cleaner air and more physical activity. Their bottom line is that neither demand reduction nor cleaner production alone can reconcile the coming infrastructure boom with climate goals; only an integrated strategy, planned jointly with land use, can deliver mobility for all without mortgaging the carbon budget.

Subject of Research: Global material stocks and embodied carbon emissions of future road and rail mobility infrastructure expansion

Article Title: Material and carbon implications of future mobility infrastructure expansion around the world

Article References: Baumgart, A., Ünlü, G., Grammer, B., Javaid, A., Maczek, F., Krausmann, F., Krey, V., & Wiedenhofer, D. (2026). Material and carbon implications of future mobility infrastructure expansion around the world. Journal of Industrial Ecology, 30(4), 1935-1949. https://doi.org/10.1007/s44498-026-00132-x

Image Credits: AI Generated

DOI: 10.1007/s44498-026-00132-x

Keywords: mobility infrastructure, material stocks, embodied emissions, carbon budget, railways, roads, circular economy, decarbonization, urban form, OpenStreetMap, integrated assessment modelling, Global South