Volumetric urban Sprawl: Horizontal and vertical growth in two metropolitans

The escalating complexities of rapid urbanization necessitate a paradigm shift in urban form evaluation, moving beyond traditional horizontal analyses to incorporate the crucial dimension of vertical growth. This study pioneers a volumetric approach, integrating 3D and 2D spatial analyses, to dissect compactness, sprawl, and their underlying drivers across two contrasting metropolitan regions: the Tehran Metropolitan Region (TMR) and the Greater Sydney Region (GSR) over a 40-year period (1980s–2020s). Our findings reveal a striking dichotomy: TMR exhibits pronounced ‘vertical sprawl,’ characterized by the haphazard proliferation of high-rises in peripheral areas like Karaj, coupled with a dramatic 43 ​% decline in volumetric efficiency and a tripling of built-up area, signifying uncoordinated expansion. Conversely, GSR demonstrates ‘strategic polycentric verticality,’ effectively balancing a 40 ​% horizontal growth with the development of clustered, high-density hubs, such as Parramatta, resulting in stable volumetric density. Employing the Weighted Urban Proliferation (WUP) metric and the Inverse S-Curve Model, we quantify the profound impact of policy frameworks: TMR's regulatory voids fuel inefficient 3D sprawl, evidenced by a 203 ​% increase in WUP vertical sprawl, while GSR's integrated planning fosters resource-efficient growth. This research underscores the indispensable role of multidimensional urban form assessments in guiding sustainable urban development. By bridging the contextual gap between developing and developed cities, this study delivers a universally applicable framework for policymakers to harmonize vertical densification with infrastructure, equity, and environmental sustainability, crucial in an era of intensifying vertical urban expansion.