Unveiling urban area growth dynamics: insights from a comprehensive study of urban area growth curves

ABSTRACT

Amidst rapid global urbanization, comprehending urban area growth (UAG) dynamics is vital for urban planning and sustainability. Despite ample urban development research, the historical developmental patterns of UAG remain underexplored. Long-term UAG exhibits an initial acceleration followed by deceleration, thus, using 200-years UAG data from the U.S., we meticulously compare the S-shaped curve (Logistics and Gompertz models) with other time-series models, and unveil insights into UAG's intricacies by examining how S-shaped models perform across different urban stages. Notably, the Logistics model emerges as the more accurate modeling tool, boasting an RMSE of 0.019, which surpasses the Gompertz model's 0.032. Moreover, the parameters of the S-curve explicitly describe the fundamental properties of UAG, and we unveil the remarkable stability of the maximum growth rate in the S-shaped model through a thorough parameter analysis, which underscores its role as a reliable and universally applicable assessment tool for UAG. Fundamentally, this meticulously analytical research delves deep into the complexities of the UAG curve, robustly confirming the S-shaped trend as the ‘realistic’ consequence of UAG over time. Importantly, this enduring S-shaped trend remains consistent across historical and contemporary contexts. These findings significantly advance our understanding of UAG dynamics for informed urban planning and development.

KEYWORDS:

• Urban area growth
• S-shaped curve
• logistics model
• gompertz model
• maximum growth rate

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 42330103) and (No. 42271469), and also supported by the National Key Research and Development Program of China (No.2021YFE0117100 and No. 2022YFF1301102).