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The development of cities in the vertical dimension is important in valley-type cities where physical growth is limited by terrain. However, little research has focused on three-dimensional urban expansion of valley-type cities. Lanzhou is a typical valley-type city in China and Chengguan District is the core area of Lanzhou City. This research is aimed at understanding the development of valley-type cities through the analysis of the three-dimensional urban expansion of Lanzhou Chengguan District and providing a reference for urban planning. We extracted five periods of architectural contours and height information between 1975 to 2018 with the support of multi-source remote sensing and network data. We used overlay analysis and mathematical statistical methods to analyze urban horizontal expansion and used the building density, floor area ratio, vertical expansion speed, fluctuation degree, and skyline to analyze urban vertical expansion. We found that the mode of horizontal expansion of Chengguan District shifted from adjacency to enclave through mountain area reclamation. The area with the fastest vertical expansion speed first appeared in the horizontal expansion completed area, and then in both the rapid horizontal expansion area and in the horizontal expansion completed area. Before 2007, the speed of horizontal expansion increased and reached its peak while the vertical expansion speed was relatively stable. After that, the former decreased, and the vertical expansion increased rapidly and dominated the urban development. The vertical expansion of the valley-type city gradually dominates urban development. Urban planning should consider the three-dimensional expansion, especially in the vertical dimension.

Rapid urban expansion has seriously threatened ecological security and the natural environment on a global scale, thus, the simulation of dynamic urban expansion is a hot topic in current research. Existing urban expansion simulation models focus on the mining of spatial neighborhood features among driving factors, however, they ignore the over-fitting, gradient explosion, and vanishing problems caused by the long-term dependence of time series data, which results in limited model accuracy. In this study, we proposed a new dynamic urban expansion simulation model. Considering the long-time dependence issue, long short term memory (LSTM) was employed to automatically extract the transformation rules through memory units and provide the optimal attribute features for cellular automata (CA). This study selected Lanzhou, which is a semi-arid region in Northwest China, as an example to confirm the validity of the model performance using data from 2000 to 2020. The results revealed that the overall accuracy of the model was 91.01%, which was higher than that of the traditional artificial neural network (ANN)-CA and recurrent neural network (RNN)-CA models. The LSTM-CA framework resolved existing problems with the traditional algorithm, while it significantly reduced complexity and improved simulation accuracy. In addition, we predicted urban expansion to 2030 based on natural expansion (NE) and ecological constraint (EC) scenarios, and found that EC was an effective control strategy. This study provides a certain theoretical basis and reference value toward the realization of new urbanization and ecologically sound civil construction, in the context of territorial spatial planning and healthy/sustainable urban development.

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