Rapid urban population growth has significant societal, environmental, and economic consequences, particularly in developing nations. Accurate population projections are crucial for effective urban planning and addressing the UN's Sustainable Development Goals (SDGs), especially Goal 11, which aims to make cities inclusive, safe, resilient, and sustainable. Long-term projections are also needed to assess risks associated with climate change, flooding, heat waves, and other phenomena. Existing methods for projecting urban populations face limitations: some are localized, others don't readily scale globally, and many fail to accurately represent the power-law distribution of city sizes (Zipf's law). This study addresses these limitations by proposing a novel method that operates globally, predicts individual city populations, reproduces observed population distributions, and incorporates SSP scenarios to quantify uncertainties.

Numerous studies have investigated urban morphology and spatially detailed population distribution within cities. However, these studies typically assume given total populations for target urban agglomerations and do not readily extend to global scales. Other approaches use grid-based methods, heuristic functions, gravity-type models, or cellular automata, but may be suboptimal as they might not map readily onto actual cities and may not reproduce the well-known power-law distribution observed for real cities (Zipf's law). Many lack validation against historical trends and fail to incorporate uncertainties stemming from varying socioeconomic conditions. The current study aims to overcome these limitations.

This study uses a novel method that satisfies several criteria: global scope, individual city population projections, realistic distribution of urban populations (obeying Zipf's law), and incorporation of SSP scenarios for uncertainty quantification. The method uses an urban-growth model based on the Simon model, assuming that a city's population itself drives further growth. The model is seeded with data from World Urbanization Prospects (WUP) 2018, Gridded Population of the World (GPW) v. 4, and OpenStreetMap, encompassing population and location information for ~20,000 urban agglomerations in 151 countries in 2010. The model is validated by comparing its postdictions (backward projections) and projections (forward projections) to WUP data. Mean absolute percent errors (MAPEs) are calculated to assess accuracy. A model for absolute percentage errors (APEs) is developed to estimate uncertainty, accounting for factors like population size and time horizon. Finally, using country-specific SSP data from the International Institute for Applied Systems Analysis (IIASA), the model projects future populations under five different SSP scenarios (SSP1-SSP5) until 2100.

Model validation showed reasonable MAPEs, comparable to those of other empirical prediction models. MAPEs for all cities grew extremely large at long times in the past. However, restricting the analysis to cities with populations of 100,000 or more yielded acceptable MAPEs. For future projections, MAPEs were lower than for postdictions (10% for 10-year projections and 16% for 25-year projections). The model tends to underestimate urban populations compared to UN WUP projections, possibly due to the assumption of fixed spatial extent for urban agglomerations. Projections show that populations will continue to concentrate in larger agglomerations, with the largest reaching at least 40 million residents by 2100. Significant urban expansion is predicted in South Asia and sub-Saharan Africa. The number of megacities (populations exceeding 10 million) will continue to increase under all scenarios, except possibly SSP1. Table 3 shows the projected number of cities and total population in various population classes for 2050 and 2100 under different SSPs. Figures 1 and 2 show the spatial distribution of urban agglomerations for 2010 and projected for 2100 under the five SSP scenarios. Table 4 lists the populations of the world's ten most populous cities in 2010 and projected for 2050 and 2100 under the five SSPs. MAPE values for SSP-specific population projections range from 24-25% in 2050 to 42-44% in 2100 for agglomerations of 100,000 or more, but are lower for larger agglomerations.

The model, despite its simplicity, successfully captures key drivers of urbanization. The dominant driver of urban growth is population itself, implicitly assuming urbanization mechanisms of the knowledge-based economy. The study's projections are based on the UN's traditional definition of urban agglomeration. The model's simplicity implies that relative city rankings cannot change; however, it still accurately reproduces historical trajectories for many agglomerations, suggesting it captures essential growth mechanisms. Future research could incorporate spatial expansion of cities, considering mergers and accounting for factors like transportation improvements. The projections highlight the possibility of unprecedented urbanization in developing countries and show that different SSP scenarios require diverse urban policy strategies.

This study provides long-term projections of urban populations, showing a continued trend toward concentration in larger agglomerations, particularly in developing countries. The findings highlight the substantial challenges facing rapidly growing cities, necessitating investment in infrastructure and urban planning. Future research should focus on incorporating factors like spatial expansion and the impact of events like the COVID-19 pandemic.

The model's simplicity is a limitation. It assumes fixed geographical footprints for urban agglomerations and does not explicitly account for various factors influencing urban growth, such as political, economic, technological, and environmental changes. The model also does not account for the potential emergence of entirely new cities. The uncertainty estimates rely on a model for APEs fitted to existing data, introducing potential bias. The definition of 'urban' may also evolve, potentially affecting the interpretation of the results.