Modelling multi-regional urban growth with multilevel logistic cellular automata

Simulation models based on cellular automata (CA) are useful for revealing the complex mechanisms and processes involved in urban growth and have become supplementary tools for urban land use planning and management. Although the urban growth mechanism is characterized by multilevel and spatiotemporal heterogeneity, most existing studies focus only on simulating the urban growth of singular regions without considering the heterogeneity of the urban growth process and the multilevel factors driving urban growth within regions that consist of multiple subregions. Thus, urban growth models have limited performance when simulating the urban growth of multi-regional areas. To address this issue, we propose a multilevel logistic CA model (MLCA) by incorporating a multilevel logistic regression model into the traditional logistic CA model (LCA). In the MLCA, multilevel driving factors are considered, and the multilevel logistic model allows the transition rules to not only vary in space, but also change when the subregional level factors change. To verify the MLCA's validity, it was applied to simulate the urban growth of Tongshan County, located in China's Xuzhou Prefecture. The results were compared with three comparative models, LCA1, which only considered grid cell-level factors; LCA2, which considered both grid cell- and subregional-level factors; and artificial neural network CA. Urban growth data for the periods 2000–2009 and 2009–2017 were used. The results show that the MLCA performs better on both visual comparison and indicators for accuracy verification. The Kappa of the results increased by <5%, but the improvement was significant, while increases for the accuracy of urban land and figure of merit were much higher than 5%. In addition, the results of MLCA had the smallest mean absolute percentage error when allocating new urban land areas to the various subregions. The results reveal that higher-level (e.g., town level) factors either strengthened or weakened the effects of grid cell-level factors on urban growth, which indirectly affected the spatial allocation of new urban land. The MLCA model is an effective step towards simulating nonstationary urban growth of multi-regional areas, using the comprehensive effects of multilevel driving factors.     

A comparative analysis of cellular automata models for simulation of small urban areas in Galicia,NW Spain

Urban growth models developed in the second half of the 20th century have allowed for a better understanding of the dynamics of urban growth. Among these models, cellular automata (CA) have become particularly relevant because of their ability to reproduce complex spatial and temporal dynamics at a global scale using local and simple rules. In the last three decades, many urban CA models that proved useful in the simulation of urban growth in large cities have been implemented. This paper analyzes the ability of some of the main urban CA models to simulate growth in a study area with different characteristics from those in which these models have been commonly applied, such as slow and low urban growth. The comparison of simulation results has allowed us to analyze the strengths and weaknesses of each model and to identify the models that are best suited to the characteristics of the study area. Results suggest that models which simulate several land uses can capture better land use dynamics in the study area but need more objective and reliable calibration methods.     

Assessing cellular automata model behaviour using a sensitivity analysis approach

Rapid advances in computer and geospatial technology have made it increasingly possible to design and develop urban models to efficiently simulate spatial growth patterns. An approach commonly used in geography and urban growth modelling is based on cellular automata theory and the GIS framework. However, the behaviour of cellular automaton (CA) models is affected by uncertainties arising from the interaction between model elements, structures, and the quality of data sources used as model input. The uncertainty of CA models has not been sufficiently addressed in the research literature. The objective of this study is to analyze the behaviour of a GIS-based CA urban growth model using sensitivity analysis (SA). The proposed SA approach has both qualitative and quantitative components. These components were operationalized using the cross-tabulation map, KAPPA index with coincidence matrices, and spatial metrics. The research focus was on the impacts of CA neighbourhood size and type on the model outcomes. A total of 432 simulations were generated and the results suggest that CA neighbourhood size and type configurations have a significant influence on the CA model output. This study provides insights about the limitations of CA model behaviour and contributes to enhancing existing spatial urban growth modelling procedures.     

Improving spatial accuracy of urban growth simulation models using ensemble forecasting approaches

This paper aims to improve the spatial accuracy of urban growth simulation models and clarify any associated uncertainties. Artificial Neural Networks (ANNs), Random Forest (RF), and Logistic Regression (LR) were implemented to simulate urban growth in the megacity of Tehran, Iran, as a case study. Model calibration was performed using data between 1985 and 1999 whereas the data between 1999 and 2014 was used for model validation. First of all, Transition Index Maps (TIMs) were computed by means of each model to assess the potential of urban growth for each cell. Using the standard deviation, consensus between the TIMs was evaluated. Because the TIMs of the individual models manifested discrepancies, they were combined using a number of ensemble forecasting approaches including median, mathematical average, principle component analysis, and weighted area under the total operating characteristic. The individual and combined TIMs were then put into Cellular Automata (CA) to simulate the future pattern of urban growth in Tehran. The results were evaluated in two stages. At first, the TIMs were evaluated by means of Total Operating Characteristics (TOC), and then a set of statistical indices was used to evaluate the spatial accuracy of the simulated urban growth maps. The best result was obtained by median ensemble forecasting, whereas the LR model showed the lowest level of accuracy. In similar studies, it is recommended to implement and compare different ensemble methods when integrating individual models.     

Patch-based cellular automata model of urban growth simulation: Integrating feedback between quantitative composition and spatial configuration

Urban land use change modeling can enhance our understanding of processes and patterns of urban growth that emerge from human-environment interactions. Cellular automata (CA) is a common approach for urban land use change modeling that allows for discovering and analyzing potential urban growth pathways through scenario building. Fundamental components of CA such as neighborhood configuration, transition rules, and representation of geographic entities have been examined in depth in the literature. However, trade-offs in the quantitative composition that urban gains from different non-urban land types and their dynamic feedback with the spatial configuration of urban growth are often ignored. The urban CA model proposed in this study links the quantitative composition with the spatial configuration of urban growth by incorporating a trade-off mechanism that adaptively adjusts the combined suitability of occurrence for non-urban land types based on analysis of transition intensity. Besides, a patch growing module based on seeding and scanning mechanisms is used to simulate the occurrence and spreading of spontaneous urban growth, and a time Monte Carlo (TMC) simulation method is employed to represent uncertainties in the decision-making process of urban development. Application of the model in an ecologically representative city, Ezhou, China, reveals improvement on model performance when feedback between the quantitative composition and spatial configuration of urban growth is incorporated. The averaged figure of merit and K-fuzzy indices are 0.5354 and 0.1954 with respect to cell-level agreement and pattern similarity, indicating the utility and reliability of the proposed model for the simulation of realistic urban growth.     

Partial validation of cellular automata based model simulations of urban growth: An approach to assessing factor influence using spatial methods

Cellular Automata (CA) based models have a high aptitude to reproduce the characteristics of urban processes and are useful to explore future scenarios. However, validation of their results poses a major challenge due to the absence of real future data with which to compare them. A partial validation applied to a CA-based model for the Madrid Region (Spain) is presented as a proposal for determining the influence of given factors on the results and testing their spatial variability. Several simulations of the model were computed by different combinations of factors, and results were compared using flexible map comparison methods in order to study spatial pattern matches and similarities between them. Main and total effects of these factors were calculated for each method, by applying a simplified Global Sensitivity Analysis approach. Frequency maps showing the most frequent cells with changed land use in the results were generated.     

Modeling of urban growth dynamics and its impact on surface runoff characteristics

Modeling urban growth and generating scenarios are essential for studying the impact and sustainability of an urban hydrologic system. Urban systems are regarded as complex self-organizing systems, where the dynamic transitions from one form of landuse to another occur over a period of time. Therefore, a modeling framework that captures and simulates this complex behavior is essential for generating urban growth scenarios. Cellular Automata (CA)-based models have the potential to model such discrete dynamic systems. In this study, a constraint-based binary CA model was used to predict the future urban growth scenario of the city of Roorkee (India). A hydrologic model was applied on the simulated urban catchment to study its hydrologic response. The Natural Resources Conservation Service Curve Number (NRCS-CN) method, which is suitable for ungauged urban watersheds, was adopted to determine the impact of urban growth on the quantity of storm water runoff over a period of time. The results indicate that urban growth has a linear relationship with peak discharge and time to peak for the catchment under investigation.     

Integrating spatial nonstationarity into SLEUTH for urban growth modeling: A case study in the Wuhan metropolitan area

Accurate forecasting of future urban land expansion can provide useful information for policy makers and urban planners to better plan for the impacts of future land use and land cover change (LULCC) on the ecosystem. However, most current studies do not emphasize spatial variations in the influence intensities of the various driving forces, resulting in unreliable predictions of future urban development. This study aimed to enhance the capability of the SLEUTH model, a cellular automaton model that is commonly used to measure and forecast urban growth and LULCC, by embedding an urban suitability surface from geographically weighted logistic regression (GWLR). Moreover, to examine the performance of the loosely-coupled GWLR-SLEUTH model, a layer with only water bodies excluded and a layer combining the former with an urban suitability surface from logistic regression (LR) were also used in SLEUTH in separate model calibrations. This study was applied to the largest metropolitan area in central China, the Wuhan metropolitan area (WMA). Results show that the integrated GWLR-SLEUTH model performed better than either the traditional SLEUTH model or the LR-SLEUTH model. Findings demonstrate that spatial nonstationarity existed in the drivers' impacts on the urban expansion in the study area and that terrain, transportation and socioeconomic factors were the major drivers of urban expansion in the study area. Finally, with the optimal calibrated parameter sets from the GWLR-SLEUTH model, an urban land forecast from 2017 to 2035 was conducted under three scenarios: 1) business as usual; 2) under future planning policy; and 3) ecologically sustainable growth. Findings show that future planning policy may promise a more sustainable urban development if the plan is strictly obeyed. This study recommended that spatial heterogeneity should be taken into account in the process of land change modeling and the integrated model can be applied to other areas for further validation and forecasts.     

A segment derived patch-based logistic cellular automata for urban growth modeling with heuristic rules

Cellular automata (CA) models are extensively applied in urban growth modeling in different forms (i.e., pixel or patch). Studies have reported that the patch-based approach can achieve a more realistic urban landscape. However, they are subjected to uncertainties due to a variety of stochastic processes involved, which weakens their effectiveness on urban planning or decision making. Here, we propose a new patch-based urban growth model with heuristic rules that employed logistic CA model with a watershed segmentation algorithm (Segmentation-Patch-CA). The segment objects derived from features of urban CA model were regarded as potential patches for conversion, through defining a utility function that considered both the suitability and heterogeneity of pixels within the patch. Thereafter, two different urban growth types, i.e., organic growth and spontaneous growth, were identified and simulated separately by introducing a landscape expansion index (LEI) that built on neighborhood density analysis. The proposed Segmentation-Patch-CA was applied to Guangzhou City, China. Our results revealed that the proposed model produced a more realistic urban landscape (96.00% and 97.38%) than pixel-based (45.14% and 74.82%) for two modeling periods 2003–2008 and 2008–2012, respectively, when referring to an assembled indicator that closely related to urban patterns (e.g., shape, size, or distribution). Meanwhile, it also achieved a good performance when comparing to other patch-based urban CA models but with less uncertainty. Our model provided a very flexible framework to incorporate patches using segments or self-growth based on pixels, which is very helpful to future urban planning practices.     

A grid-based spatial data model for the simulation and analysis of individual behaviours in micro-spatial environments

As crowd simulation in micro-spatial environment is more widely applied in urban planning and management, the construction of an appropriate spatial data model that supports such applications becomes essential. To address the requirements necessary to building a model of crowd simulation and people–place relationship analysis in micro-spatial environments, the concept of the grid as a basic unit of people–place data association is presented in this article. Subsequently, a grid-based spatial data model is developed for modelling spatial data using Geographic Information System (GIS). The application of the model for crowd simulations in indoor and outdoor spatial environments is described. There are four advantages of this model: first, both the geometrical characteristics of geographic entities and behaviour characteristics of individuals within micro-spatial environments are involved; second, the object-oriented model and spatial topological relationships are fused; third, the integrated expression of indoor and outdoor environments can be realised; and fourth, crowd simulation models, such as Multi-agent System (MAS) and Cellular Automata (CA), can be further fused for intelligent simulation and the analysis of individual behaviours. Lastly, this article presents an experimental implementation of the data model, individual behaviours are simulated and analysed to illustrate the potential of the proposed model.     

Incorporation of extended neighborhood mechanisms and its impact on urban land-use cellular automata simulations

Urban cellular automata (CA) models are broadly used in quantitative analyses and predictions of urban land-use dynamics. However, most urban CA developed with neighborhood rules consider only a small neighborhood scope under a specific spatial resolution. Here, we quantify neighborhood effects in a relatively large cellular space and analyze their role in the performance of an urban land use model. The extracted neighborhood rules were integrated into a commonly used logistic regression urban CA model (Logistic-CA), resulting in a large neighborhood urban land use model (Logistic-LNCA). Land-use simulations with both models were evaluated with urban expansion data in Xiamen City, China. Simulations with the Logistic-LNCA model raised the accuracies of built-up land by 3.0%–3.9% in two simulation periods compared with the Logistic-CA model with a 3 × 3 kernel. Parameter sensitivity analysis indicated that there was an optimal large window size in cellular space and a corresponding optimal parameter configuration.     

Calibration of cellular automata urban growth models from urban genesis onwards - a novel application of Markov chain Monte Carlo approximate Bayesian computation

Cellular Automata (CA) models are widely used to study spatial dynamics of urban growth and evolving patterns of land use. One complication across CA approaches is the relatively short period of data available for calibration, providing sparse information on patterns of change and presenting problematic signal-to-noise ratios. To overcome the problem of short-term calibration, this study investigates a novel approach in which the model is calibrated based on the urban morphological patterns that emerge from a simulation starting from urban genesis, i.e., a land cover map completely void of urban land. The application of the model uses the calibrated parameters to simulate urban growth forward in time from a known urban configuration.This approach to calibration is embedded in a new framework for the calibration and validation of a Constrained Cellular Automata (CCA) model of urban growth. The investigated model uses just four parameters to reflect processes of spatial agglomeration and preservation of scarce non-urban land at multiple spatial scales and makes no use of ancillary layers such as zoning, accessibility, and physical suitability. As there are no anchor points that guide urban growth to specific locations, the parameter estimation uses a goodness-of-fit (GOF) measure that compares the built density distribution inspired by the literature on fractal urban form. The model calibration is a novel application of Markov Chain Monte Carlo Approximate Bayesian Computation (MCMC-ABC). This method provides an empirical distribution of parameter values that reflects model uncertainty. The validation uses multiple samples from the estimated parameters to quantify the propagation of model uncertainty to the validation measures.The framework is applied to two UK towns (Oxford and Swindon). The results, including cross-application of parameters, show that the models effectively capture the different urban growth patterns of both towns. For Oxford, the CCA correctly produces the pattern of scattered growth in the periphery, and for Swindon, the pattern of compact, concentric growth. The ability to identify different modes of growth has both a theoretical and practical significance. Existing land use patterns can be an important indicator of future trajectories. Planners can be provided with insight in alternative future trajectories, available decision space, and the cumulative effect of parcel-by-parcel planning decisions.     

Residual-based specification of a hidden random field included in a hierarchical spatial model

A method for specifying a hidden random field (HRF) included in a hierarchical spatial model is proposed. In hierarchical models of interest the first stage describes, conditional on a realization of the HRF, a response variable which is observable on a continuous spatial domain; the second stage models the HRF which reflects unobserved spatial heterogeneity. The question which is investigated is how can the HRF be modeled, i.e. specified. The method developed to address this question is based on residuals obtained when the base model, i.e. the hierarchical model in which the HRF is assumed constant, is fitted to data. It is shown that the residuals are linked with the HRF, and the link is used to specify the HRF. The method is applied to simulated data in order to assess its performance, and then to real data on radionuclide concentrations on Rongelap Island.     

A stochastically constrained cellular model of urban growth

Recent approaches to modeling urban growth use the notion that urban development can be conceived as a self-organizing system in which natural constraints and institutional controls (land-use policies) temper the way in which local decision-making processes produce macroscopic patterns of urban form. In this paper a cellular automata (CA) model that simulates local decision-making processes associated with fine-scale urban form is developed and used to explore the notion of urban systems as self-organizing phenomenon. The CA model is integrated with a stochastic constraint model that incorporates broad-scale factors that modify or constrain urban growth. Local neighborhood access rules are applied within a broader neighborhood in which friction-of-distance limitations and constraints associated with socio-economic and bio-physical variables are stochastically realized. The model provides a means for simulating the different land-use scenarios that may result from alternative land-use policies. Application results are presented for possible growth scenarios in a rapidly urbanizing region in south east Queensland, Australia.     

Residual-based specification of a hidden random field included in a hierarchical spatial model

A method for specifying a hidden random field (HRF) included in a hierarchical spatial model is proposed. In hierarchical models of interest the first stage describes, conditional on a realization of the HRF, a response variable which is observable on a continuous spatial domain; the second stage models the HRF which reflects unobserved spatial heterogeneity. The question which is investigated is how can the HRF be modeled, i.e. specified. The method developed to address this question is based on residuals obtained when the base model, i.e. the hierarchical model in which the HRF is assumed constant, is fitted to data. It is shown that the residuals are linked with the HRF, and the link is used to specify the HRF. The method is applied to simulated data in order to assess its performance, and then to real data on radionuclide concentrations on Rongelap Island.     

Explore for a day? Generating personalized itineraries that fit spatial heterogeneity of tourist attractions

Recommender systems are widely adopted by firms as an innovative personalization tool across various industries. Most of the existing tour recommender systems treat the spatial structure of tourist attractions as a single type, which neglects the spatial heterogeneity among these attractions. This study attempts to address this problem by modeling the spatial heterogeneity in the design of personalized trips. We propose a two-phase heuristic approach, which involves an improved artificial bee colony algorithm and a differential evolution algorithm. The results of a field experiment confirm that our new model outperforms the benchmark models in maximizing customer utilities.     

Spatially varying coefficient models in real estate: Eigenvector spatial filtering and alternative approaches

Real estate policies in urban areas require the recognition of spatial heterogeneity in housing prices to account for local settings. In response to the growing number of spatially varying coefficient models in housing applications, this study evaluated four models in terms of their spatial patterns of local parameter estimates, multicollinearity between local coefficients, and their predictive accuracy, utilizing housing data for the metropolitan area of Vienna (Austria). The comparison covered the spatial expansion method (SEM), moving window regression (MWR), geographically weighted regression (GWR), and genetic algorithm-based eigenvector spatial filtering (ESF), an approach that had not previously been employed in real estate research. The results highlight the following strengths and limitations of each method: 1) In contrast to SEM, MWR, and GWR, ESF depicts more localized patterns of the parameter estimates and does not smooth local particularities. 2) ESF is less affected by multicollinearity between the local parameter estimates than MWR, GWR, and SEM. 3) Even though the in-sample explanatory power and prediction accuracy of ESF is superior compared to the competitors, repeated sampling indicates a limited out-of-sample fit and prediction accuracy, suggesting over-fitting tendencies. 4) The application of ESF is less intuitive than MWR and GWR, which are available off-the-shelf.     

Cellular automata for simulating land use changes based on support vector machines

Cellular automata (CA) have been increasingly used to simulate urban sprawl and land use dynamics. A major issue in CA is defining appropriate transition rules based on training data. Linear boundaries have been widely used to define the rules. However, urban land use dynamics and many other geographical phenomena are highly complex and require nonlinear boundaries for the rules. In this study, we tested the support vector machines (SVM) as a method for constructing nonlinear transition rules for CA. SVM is good at dealing with nonlinear complex relationships. Its basic idea is to project input vectors to a higher dimensional Hilbert feature space, in which an optimal classifying hyperplane can be constructed through structural risk minimization and margin maximization. The optimal hyperplane is unique and its optimality is global. The proposed SVM-CA model was implemented using Visual Basic, ArcObjects^®, and OSU-SVM. A case study simulating the urban development in the Shenzhen City, China demonstrates that the proposed model can achieve high accuracy and overcome some limitations of existing CA models in simulating complex urban systems.     

Effects of agent heterogeneity in the presence of a land-market: A systematic test in an agent-based laboratory

Representing agent heterogeneity is one of the main reasons that agent-based models become increasingly popular in simulating the emergence of land-use, land-cover change and socioeconomic phenomena. However, the relationship between heterogeneous economic agents and the resultant landscape patterns and socioeconomic dynamics has not been systematically explored. In this paper, we present a stylized agent-based land market model, Land Use in eXurban Environments (LUXE), to study the effects of multidimensional agents’ heterogeneity on the spatial and socioeconomic patterns of urban land use change under various market representations. We examined two sources of agent heterogeneity: budget heterogeneity, which imposes constraints on the affordability of land, and preference heterogeneity, which determines location choice. The effects of the two dimensions of agents’ heterogeneity are systematically explored across different market representations by three experiments. Agents’ heterogeneity exhibits a complex interplay with various forms of market institutions as indicated by macro-measures (landscape metrics, segregation index, and socioeconomic metrics). In general, budget heterogeneity has pronounced effect on socioeconomic results, while preference heterogeneity is highly pertinent to spatial outcomes. The relationship between agent heterogeneity and macro-measures becomes more complex when more land market mechanisms are represented. In other words, appropriately simulating agent heterogeneity plays an important role in guaranteeing the fidelity of replicating empirical land use change process.     

Coupling machine learning,tree-based and statistical models with cellular automata to simulate urban growth

This paper compares six land use change (LUC) models, including artificial neural networks (ANNs), support vector regression (SVR), random forest (RF), classification and regression trees (CART), logistic regression (LR), and multivariate adaptive regression splines (MARS). These models were used to simulate urban growth in the megacity of Tehran Metropolitan Area (TMA). These LUC models were integrated with cellular automata (CA) and validated using a variety of goodness-of-fit metrics. The results showed that the percent correct metrics (PCMs) varied between 54.6% for LR and 59.6% for MARS, while the area under curve (AUC) ranged from 67.6% for LR to 74.7% for ANNs. The results also showed a considerable difference between the spatial patterns within the error maps. The results of this comparative study will enable decision makers and scholars to better understand the performance of the models when reducing the number of misses and false alarms is a priority.