Projecting future populations of urban agglomerations around the world and through the 21st century

The study addresses the need for accurate, long-term projections of urban agglomeration populations to inform planning, risk assessment, and sustainability policies. Rapid urban population growth, particularly in developing countries, strains infrastructure and services and has implications for SDGs and climate adaptation. Many global research applications (e.g., flood risk, heat waves, disease spread, biodiversity, and water availability) require spatially explicit, long-run projections. Existing approaches either lack global coverage, do not map naturally to real cities, fail to reproduce empirically observed city-size distributions (Zipf’s law), or lack robust uncertainty quantification across socioeconomic scenarios. The research question is how to produce global, city-level projections to 2100 that are consistent with SSP narratives, validated against historical data, respect observed power-law city-size distributions, and provide uncertainty estimates.

Past work includes city morphology and land-use/transport interaction models (Alonso–Muth–Mills) that typically assume given total city populations and are difficult to scale globally. Demographic projections such as cohort-component methods and ARIMA models are effective subnationally but require detailed age-structured panel data not available worldwide. Global grid-based downscaling (heuristic functions, gravity models, cellular automata) can generate large-scale projections but often do not align with administrative or functional cities and may violate Zipf’s law in city-size distributions. Random growth frameworks (Simon, Gibrat) produce power-law distributions but are stochastic, complicating validation for individual cities. Recent work also models urban land cluster sizes with stochastic simulations yielding power-law footprints; however, such approaches are not directly applicable to projecting city populations. There is a gap for methods that: operate globally; project at the level of real agglomerations; reproduce power-law size distributions; validate historically; and incorporate SSPs for uncertainty.

Data: The study synthesizes multiple sources to build a 2010 baseline of urban agglomerations and settlements. Urban populations and coordinates at 5-year intervals (1950–2035) are from UN World Urbanization Prospects 2018 (WUP). Gridded Population of the World v4 (GPW) Population Count (PC, 30 arc-second raster) and Administrative Unit Center Points (AUCP; 8,342,421 locations with 2000–2020 populations) provide spatial populations and settlement points. GeoNames and World Gazetteer lists seed locations. GDP per capita for agglomerations (OECD.stat, Global Metro Monitor) and national averages (World Development Indicators) are compiled. OpenStreetMap (OSM) major roads (motorway, trunk, primary) are used to infer urban extents. SSP national scenario inputs (IIASA-SSP database) provide 2010–2100 population and GDP per capita by 5-year steps. Workflow to construct 2010 urban dataset and extents: For each WUP agglomeration, a maximum road-travel time T determines its urban extent. OSM links are rasterized to 30 arc-second cells; assumed speeds are 50 km/h on road cells and 10 km/h off-road. From the WUP city center, travel times to surrounding cells are computed and the maximum included time t_max is chosen so that the sum of GPW-PC population within the time contour equals the observed WUP population. Where WUP centers and GPW grids are inconsistent, a 2-hour worst-case T is used. Maximum road-time model: Following Makse et al., T ≈ a0 N^{a1} G^{a2} R^{a3}, where N is population, G is GDP per capita, and R is the major-road grid area ratio. Parameters are estimated by log-linear regression across 1,816 cases, yielding R^2 = 0.82. Estimated coefficients: ln(a0) = −6.167, a_N = 0.321, a_G = 0.167, a_R = −1.210. As expected, T increases with N and G, and decreases with higher road coverage. Merging and settlement selection: If a smaller agglomeration’s center lies within the time contour of a larger one, the smaller is merged with the larger. This reduces WUP agglomerations to 1,794 entities. Applying the same procedure to GeoNames, World Gazetteer, and GPW-AUCP yields 415,886 settlements. A subset of 89,620 settlements (population ≥5,000) is selected for modeling, covering 6.6 billion people (~95% of GPW-AUCP’s 2010 total). Country-specific thresholds for minimum urban population N_mc are set so that the modeled 2010 urban share matches observed national urbanization; settlements above the threshold are treated as urban, others as rural. Random-growth urban model (deterministic allocation with Pareto property): The model is based on preferential attachment and yields an asymptotic Pareto city-size distribution. A continuous form relates the rate of change to national urban growth n and a geographic fitness term; the tail probability scales as Pr(N) ~ N^{-(1+ω m/n)}. For projections, a discrete formulation updates city populations at 5-year steps using national urban totals from SSPs and the 2010 city-size distribution as the baseline. When national urban populations increase, additional urban residents are allocated proportionally to existing cities’ sizes, and new cities are admitted by increasing the rank threshold until the minimum urban size N_mc is respected. When national urban populations decline, the number of cities contracts by lowering the rank threshold. If the sum of modeled city populations exceeds the SSP national total at any step, smallest cities are sequentially zeroed until totals match. The model assumes fixed 2010 urban extents (no spatial expansion), does not simulate the emergence of entirely new settlements (only promotion of existing rural seeds), and keeps the total set of seed settlements fixed. Uncertainty model (APE): Absolute percent errors are regressed against city size and time horizon using historical comparisons to WUP (1736 agglomerations, 1950–2035, excluding 2010). The model is log(APE) = β0 + β_N log(N) + β_τ log(T), with estimates: ln(β0) = 1.530, β_N = −0.451, β_τ = 0.728 (N=30,495 observations; R^2 = 0.386). This yields expected APEs that decrease with city size and increase with projection horizon (e.g., for N=1 million: ~5% at 10 years, ~24% at 90 years; for N=10 million: ~1.7% at 10 years, ~8.6% at 90 years). Validation: Postdiction from 2010 back to 1950 for 1,794 agglomerations (with WUP histories) and projection comparisons against WUP forward to 2035 provide model accuracy assessment and error characteristics. The model shows strong positive correlation for 98% of agglomerations, with notable failures in cities with abrupt growth or decline due to policy/economic shocks (e.g., Shenzhen, Glasgow).

- Validation: Backcasts to 1950 show large MAPEs for all cities due to small-population right-skew, but for agglomerations ≥100,000, MAPEs are reasonable (e.g., 37% in 1950, 24% in 1990, 11% in 2000). Forward comparisons to UN WUP through 2035 yield MAPEs of ~5% (2015), 10% (2020), 13% (2025), 14% (2030), 16% (2035); MALPE is positive (up to 13% by 2035), indicating the model tends to underestimate populations when urban extents are fixed. - Uncertainty: Expected APE scales down with city size and up with horizon. For a 1-million city, ~5% (10 years) and ~24% (90 years); for a 10-million city, ~1.7% and ~8.6%. Across SSP projections, for agglomerations ≥100,000, MAPE ~24–25% in 2050 and ~42–44% in 2100; restricting to ≥1 million, ~10% (2050) and ~18% (2100). - Global projections to 2100 (SSPs): Urban populations increasingly concentrate in larger agglomerations in all SSPs. The number of megacities (≥10 million) rises steadily to 2100 in all scenarios except SSP1; SSP1 and SSP5 both have rapid urbanization but differ by fertility/migration storylines, affecting city counts in OECD countries. - Regional patterns: Strong urban expansion in South Asia and sub-Saharan Africa. India (notably the Ganges basin) shows growth in megacities and 1–5 million cities; sub-Saharan Africa (e.g., Nigeria, DRC) sees growth in 1–5 million cities and megacities under SSP4. SSP5 projects numerous megacities in North America as well. - City rankings and sizes: The most populous cities vary by scenario, but large developing-country cities dominate. Delhi is often ranked first by 2050 and 2100. In SSP5, New York and Los Angeles enter the top 10 by 2100, with New York approaching ~49 million. In all scenarios, the largest 2100 agglomerations exceed 40 million; by 2050, the largest also generally surpass 2010’s Tokyo (36.86 million) except in SSP3. - City number and size distribution: From 2010 to 2050, the count of cities ≥100,000 increases across SSPs; from 2050 to 2100 it decreases in most scenarios except SSP3. Despite differing trajectories for small/mid-size cities, the share of population in larger agglomerations rises toward 2100, most prominently in SSP5.

The study demonstrates that a simple, globally scalable, deterministic urban-growth allocation consistent with Zipf’s law can reproduce historical trajectories for most cities and generate long-run, SSP-specific city-level projections. Population itself functions as the dominant driver (reflecting agglomeration economies and labor-market scale effects). Using an agglomeration-based spatial unit facilitates validation and policy relevance compared to purely grid-based models. Differences among SSPs imply distinct policy challenges: SSP4 concentrates large-city growth in high-fertility, lower-income countries (notably Africa), heightening risks of acute urban crises; SSP5 suggests very large megacities in developed countries due to high migration and economic growth; SSP1 yields more moderate concentration despite fast early urbanization. Results point to heavy future demands on housing, transport, water, sanitation, and waste systems in megacities. The model’s tendency to underestimate compared to WUP highlights the importance of accounting for spatial expansion of urban footprints. Although rank changes are constrained by the deterministic allocation, the approach still fits most historical trends, suggesting it captures core mechanisms. Integrating a spatial-expansion module could allow modeling of city mergers and changing rankings domestically and internationally. Scenario-based analysis captures uncertainty across socioeconomic futures, aiding long-term urban policy planning.

This work provides the first global, city-level projections to 2100 that explicitly enforce empirically observed power-law city-size distributions while aligning with SSP national trajectories. It assembles a harmonized 2010 baseline for 89,620 settlements, validates against historical WUP data, and projects SSP-specific urban futures showing increasing concentration into large agglomerations, with the largest cities surpassing 40 million (and up to ~50 million in some pathways). The projections and uncertainty estimates offer actionable insights for planning infrastructure, housing, transportation, and climate adaptation under alternative socioeconomic futures. Future research should incorporate dynamic urban extents (geographical expansion and mergers), enrich drivers beyond population (economic, technological, environmental, and policy factors), allow for the creation of entirely new settlements, and reassess urban definitions as urban life evolves (including post-pandemic dynamics).

- Fixed spatial extents: Urban boundaries are held at 2010 contours; real cities typically expand, which likely contributes to underestimation versus WUP and may bias concentration metrics. - Simplified drivers: The model omits explicit political, economic, technological, and environmental shocks; it cannot capture city-specific booms or declines (e.g., Shenzhen’s explosive growth, Glasgow’s industrial decline). - Deterministic allocation and rank rigidity: Preferential allocation based on current size limits rank changes absent spatial merger modeling. - No emergence of brand-new settlements beyond 2010 seeds: Only promotion of existing rural settlements is allowed, affecting the lower tail of the distribution. - Uncertainty higher for small cities and long horizons: Errors are right-skewed for small populations; MAPEs rise toward 2100, especially below 1 million population. - Dependence on UN’s agglomeration definition and thresholding: National minimum urban-size thresholds and the urban concept may vary across contexts and over time.