Data-driven models have been extensively employed in urban CA modeling. Various sampling methods have been used to extract driving mechanisms of urban growth. Based on whether the sampling relies on single or two-period land use data and whether negative samples are drawn from unchanged urban areas, we identified the three predominant approaches of ‘M-1’, ‘M-2’, and ‘M-3’. Both model selection and sampling methods influence the modeling outcomes, yet most studies focused on the application of advanced data-driven models in CA modeling, with limited attention paid to the effect of sampling methods. Consequently, we evaluated how sampling methods influenced different stages of CA modeling. Driving mechanisms derived from each approach differ significantly, which resulted in spatially distinct development suitability maps. Notably, the samples obtained from M-2 contained pronounced non-linear characteristics, which resulted in substantial differences between the training results of linear and non-linear models. We found that the ‘‘land use change rules’ extracted from two-period maps were more beneficial for achieving high-precision simulations than rules derived from a single map. M-2 may represent a more robust approach with non-linear models because it incorporates unchanged urban land as negative samples, and provides richer non-linear land use change characteristics than M-1 or M-3.

Due to spatial heterogeneity and temporal non-stationarity, urban expansion models are often only applicable locally. However, changes in urban expansion strategies will deplete the advantages of urban expansion models trained on local historical data, and there is a need to transfer reliable urban expansion models to improve their ability to simulate future scenarios. This paper proposes a similarity law-based method for transferability of urban expansion model. By leveraging geographic similarities, the proposed approach selectively transfers transition rules between cities, promoting predictive consistency across diverse local contexts. To test this approach, transition rules from Beijing were applied within the city and then transferred to other cities in the Beijing-Tianjin-Hebei region. While models with transferred transition rules showed no clear advantages in the calibration period, they performed better in the validation period compared to models using artificial neural network (ANN) or geographic weighted regression (GWR). Additional tests showed that cities benefited more from transition rules adapted from cities with comparable land use policies. These findings suggest that this approach is useful for future scenarios simulation under policy shifts and expansion strategy changes.

The neighborhood effect, a pivotal element within the realm of Geographic Cellular Automata (GCA) modeling, has garnered significant attention in research. However, no research has yet investigated GCA modeling based on varying neighborhood sensitivity for different land use types. In this study, we sought to bridge this gap by integrating the First Law of Geography with diverse sensitivities of different land use types, thus introducing a novel approach termed Adaptive Spatially Heterogeneous Neighborhood (ASHN) for GCA modeling. By applying this innovative framework to three regions, namely Beijing, Wuhan, and the Pearl River Delta, we elucidated the implementation process and conducted comprehensive land use change simulations. The calibration period spanned from 2000 to 2010, followed by the validation period from 2010 to 2020. The results demonstrated that the ASHN-GCA model outperformed both the Adaptive Homogeneous Neighborhood Geographic Cellular Automata (AHN-GCA) model and the Homogeneous Neighborhood Geographic Cellular Automata (HN-GCA) model, yielding superior Overall Accuracy (OA), kappa, fuzzy kappa, and Figure of Merit (FoM) scores. Furthermore, the ASHN-GCA model provided more nuanced and detailed insights into landscape patterns, further highlighting its efficacy and potential for advancing GCA modeling in land use dynamics.

Spatiotemporal modeling has long been a major concern of geographic information science. Even though previous research has shown the importance of temporal and spatial information in quantifying the neighborhood effects of urban cellular automata (CA) models, constructing a spatiotemporal non-stationary neighborhood remains a challenge, due to the complexity of the spatiotemporal models. In this study, we introduced spatiotemporal modeling into the neighborhood of an urban CA model and constructed a geographically and temporally weighted neighborhood (GTWN). A corresponding approach to optimizing the bandwidth of the GTWN was also developed. Taking Beijing and Wuhan in China as examples, the GTWN-CA model was employed to simulate their urban expansion. The experimental results indicate that the GTWN-CA model has a better and performance than other CA models whose neighborhood is constructed based on the assumption of temporal or spatial stationarity, highlighting the advantages of spatiotemporal modeling in quantifying the neighborhood effect. Compared with the commonly used CA model with a homogeneous neighborhood (HON-CA), in terms of the figure of merit (FoM), the calibration accuracy of the GTWN-CA model was improved by 0.87% in Beijing and 5.4% in Wuhan, and the validation accuracy was improved by 7.9% in Beijing and 8.9% in Wuhan.

Spatial heterogeneity is an essential feature of land use change. It is important for cellular automata (CA)-based urban expansion modeling to consider the spatial heterogeneity of neighborhood effect. According to the first law of geography, there exists a distance decay effect in the neighborhood space of the urban CA models. But no research has ever been able to accurately quantify the neighborhood decay effect and apply it to models. In this study, we propose a methodology to accurately quantify the neighborhood decay effect of CA models with large neighborhood size, including the design of neighborhood configuration and the selection and optimization of decay strategies. Taking Wuhan and Guangzhou as examples, we show the implementation process of the methodology and simulate urban expansion of two areas for the periods 2000–2010 and 2010–2015 by CA models with distance decay neighborhood to reveal the advantages and characteristics of modeling the neighborhood decay effect. The results show that the simulation accuracy of CA models with the spatial heterogeneous neighborhood and the hybrid neighborhood (HYN) is higher than that of CA models with homogeneous neighborhood, and in most cases, the HYN can more accurately describe the neighborhood decay effect.

This study investigates the effects of sample size and sample prevalence on cellular automata (CA) simulation of urban growth. We take the CA models based on an artificial neural network (ANN), logistic regression (LR), and support vector machine (SVM) as examples, to simulate the urban growth of Wuhan city in China and the Wuhan Metropolitan Area under different sampling schemes. The results of the CA models based on the ANN, LR, and SVM methods are generally consistent. The sampling scheme with a small sample size and a low sample prevalence should be discarded because of the high uncertainty. Sample size determines the robustness of a CA model, whereas sample prevalence affects the performance of a CA model when there are sufficient samples. In particular, the closer the sample prevalence is to the population prevalence, the higher the simulation accuracy and the lower the shape complexity and fragmentation of the simulated urban patterns. We suggest that the optimal sampling scheme has a sample rate of 1% and a sample prevalence that is the same as the population prevalence. The selection of the optimal sampling scheme is independent of the population sizes represented by different study areas.

The stochastic perturbation of urban cellular automata (CA) model is difficult to fine-tune and does not take the constraint of known factors into account when using a stochastic variable, and the simulation results can be quite different when using the Monte Carlo method, reducing the accuracy of the simulated results. Therefore, in this paper, we optimize the stochastic component of an urban CA model by the use of a maximum entropy model to differentially control the intensity of the stochastic perturbation in the spatial domain. We use the kappa coefficient, figure of merit, and landscape metrics to evaluate the accuracy of the simulated results. Through the experimental results obtained for Wuhan, China, the effectiveness of the optimization is proved. The results show that, after the optimization, the kappa coefficient and figure of merit of the simulated results are significantly improved when using the stochastic variable, slightly improved when using Monte Carlo methods. The landscape metrics for the simulated results and actual data are much closer when using the stochastic variable, and slightly closer when using the Monte Carlo method, but the difference between the simulated results is narrowed, reflecting the fact that the results are more reliable.

Simulating urban landscape dynamics in metropolitan areas has attracted much attention lately, but the difficulty remains. Although large-scale urban simulation studies consider spatial interaction as an important factor, spatial interaction cannot be accurately measured based on a single element flow, and its effects may not strictly follow a distance decay function. Furthermore, different cities may require different transition rules. In this study, we combined bidirectional flows of population and information and an improved gravitational field model to model the urban spatial interaction, and we then integrated a partitioned cellular automata (CA) model to simulate the urban growth for different cities in the Yangtze River middle reaches megalopolis. It was found that the simulation results generated by the CA model considering spatial interaction are significantly improved. Furthermore, partitioned conversion thresholds can effectively improve the model performance. The proposed model showed a much better performance in the simulation of subordinate cities surrounding the core cities, than for the core cities and fringe cities. We suggest that large-scale urban simulation should pay more attention to the development of partitioned transition rules. The effects of intercity urban flows should also be considered in the simulation of small- and medium-sized cities near the regional cores.