Simulating urban expansion by incorporating an integrated gravitational field model into a demand-driven random forest-cellular automata model

Interactions among cities are playing an increasingly significant role in driving urban expansion in urban agglomerations. Many studies have combined the gravitational field model (GFM) with the cellular automata (CA) model to analyze the impact of urban spatial interaction on urban agglomerations. However, previous studies have used threshold-based CA models, which cannot ensure that the amount of simulated urban land (an important control variable) of the proposed CA model and contrasting CA models are consistent during experiments. In addition, previous studies have applied only one or two indicators to represent spatial interactions among cities, which cannot fully reflect the urban spatial field intensity levels within city clusters. Furthermore, previous studies have tended to apply simple mining methods (e.g., logistic regression) to mine the transition rules of CA models. These methods cannot explore the complex relationships between urban growth and driving factors (including urban spatial field intensity). This study proposes an integrated gravitational field model (IGFM) by combining comprehensive economic indicators, time-cost distance and information flow intensity to quantify urban spatial field intensity. The random forest (RF) algorithm, a machine learning method with a strong fitting ability, is adopted to mine the complex transition rules of a demand-driven CA model, which the previously developed simple mining methods are unable to accomplish. The use of demand-driven CA ensures the consistency of urban demand between contrasting CAs, which can help generate more rigorous results. The proposed IGFM-RF-CA is applied to simulate urban growth in the Beijing-Tianjin-Hebei urban agglomeration (BTH). The IGFM-RF-CA can achieve high simulation accuracy not only for a whole area but also for most subdistricts, especially in relatively developed cities. We also find that the intensity of information flow in the simulation can significantly improve the performance of the CA model, particularly in small cities located along the periphery of the BTH, which are characterized by relatively low economic development but high Internet popularity. We suggest that some small cities (e.g., Zhangjiakou and Chengde) can promote their development by increasing their Internet popularity.