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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.
Wang et al. (Tue,) studied this question.