How do cities grow? A mathematical model to predict urban development

Where will future cities be built? A joint study by a team of researchers from the University of Bologna and the Ca' Foscari University of Venice have attempted to answer this question by developing a mathematical model to predict future urban development based on historical urban lighting data observed from space. By analysing a large area around Beijing, research has shown that urban districts develop preferentially towards lowlands and where water resources are present. The study was published in the scientific journal Earth's Future.

Urbanisation, understood as the physical expansion of urban areas through the construction of new buildings and infrastructure, is a growing global phenomenon. Demographic projections indicate that by 2050, 66% of the world's population will reside in urban areas. This expansion will profoundly transform the landscape and will have environmental and socio-economic consequences, including the loss of natural habitats and biodiversity, alteration of water and biogeochemical cycles, air and environmental pollution, urban heat island phenomena, and increased demand for essential resources such as water, energy and food.

"Although scientific literature recognises the role of multiple factors – environmental, hydroclimatic, socioeconomic, political and institutional – in controlling urban growth, key information on the spatial and temporal dynamics governing the process is still lacking. Our model offers an initial answer, laying the foundations for projections on possible future urban developments worldwide," explains Serena Ceola, associate professor at the Department of Civil, Chemical, Industrial and Materials Engineering at the University of Bologna and co-author of the study alongside Giulia Grandi and Enrico Bertuzzo of the Ca' Foscari University of Venice.

HOW TO PREVENT URBAN EXPANSION

The study proposes a probabilistic model that represents, in spatial terms, the dynamics of urban expansion, specifically in a square area measuring 1000 kilometres per side in North-East China. This area encompasses Beijing and has seen significant urban growth in recent decades. The urbanisation data was obtained from satellite images of night lights, acquired at a spatial resolution of 1 kilometre, during the period between 1992 and 2013. Each square kilometre in the area was then classified as urban or non-urban according to the intensity of its night-time brightness.

The model predicts that, in subsequent years, each cell may make the transition from non-urban to urban status with a probability determined by geomorphological variables (altitude, land slope, proximity to rivers and the sea) and climatic variables (average temperature and rainfall). The model also takes into account the likelihood of urban sprawl moving towards areas that are already urbanised, closer to the city suburbs.

A MATHEMATIC APPROACH TO SUPPORT DECISION-MAKERS
The mathematical model accurately reproduced the actual distribution of urbanised areas, faithfully rendering the shape and size of the new urban clusters that developed after 1992. The data collected indicates that the main factors influencing urban sprawl in the area in question are geomorphological in nature, in particular, altitude, land slope and proximity to waterways and the coastlines. The result is consistent with historical evidence: human settlements have traditionally been concentrated in the lowlands and near water resources.

"The strength of our approach," concludes Enrico Bertuzzo, Professor of Hydrology at the Ca' Foscari University of Venice, "lies in its ability to provide a formal assessment of the main factors driving urban expansion, as well as in its flexibility, which makes it suitable for application in various areas of the world. With its ability to identify areas of preferential urban development, the model could be useful in supporting sustainable urban planning and hydrogeological risk management, especially in a context marked by an increasing frequency in extreme events linked to climate change".