Modeling urban growth using spatially heterogeneous cellular automata models: Comparison of spatial lag,spatial error and GWR

Many methods can be used to construct geographical cellular automata (CA) models of urban land use, but most do not adequately capture spatial heterogeneity in urban dynamics. Spatial regression is particularly appropriate to address the problem to reproduce urban patterns. To examine the advantages and disadvantages of spatial regression, we compare a spatial lag CA model (SLM-CA), a spatial error CA model (SEM-CA) and a geographically-weighted regression CA model (GWR-CA) by simulating urban growth at Nanjing, China. Each CA model is calibrated from 1995 to 2005 and validated from 2005 to 2015. Among these, SLM and SEM are spatial autoregressive (SAR) models that consider spatial autocorrelation of urban growth and yield highly similar land transition probability maps. Both SAR-CA and GWR-CA accurately reproduce urban growth at Nanjing during the calibration and validation phases, yielding overall accuracies (OAs) exceeding 94% and 85%, respectively. SAR-CA is superior in simulating urban growth when measured by OA and figure-of-merit (FOM) while GWR-CA is superior regarding the ability to address spatial heterogeneity. A concentric ring buffer-based assessment shows OA valleys that correspond to FOM peaks, where the ranges of valleys and peaks indicate the areas with active urban development. By comparison, SAR-CA captures more newly-urbanized patches in highly-dense urban areas and shows better performance in terms of simulation accuracy; whereas, GWR-CA captures more in the suburbs and shows better ability to address spatial heterogeneity. Our results demonstrate that spatial regression can help produce accurate simulations of urban dynamics featured by spatial heterogeneity, either implicitly or explicitly. Our work should help select appropriate CA models of urban growth in different terrain and socioeconomic contexts.     

How much can temporally stationary factors explain cellular automata-based simulations of past and future urban growth?

Driving factors are usually assumed temporally stationary in cellular automata (CA) based land use modeling, hence the persistence of their relationships. Therefore, major questions as to how much do the temporally stationary factors explain the past and future urban growth, and how long can these factors justify the projection of urban scenarios in the future, are worth further study. We selected seven explanatory driving factors to calibrate a DE-CA (differential evolution-based CA) model to simulate urban growth in Ningbo of China during 2000–2015 and project nine scenarios of urban growth from 2015 to 2060. We evaluated the effects of factors on urban growth using generalized additive models (GAM) based on fitting statistics such as accumulative deviance explained (ADE). Our results show remarkably temporal change in factor effects on the future urban growth – the ADE peaks with 34.7% in 2045 for the total projected urban growth since 2015 while that for every five years decreases continuously from 26.5% during 2000–2005 to 1.9% during 2050–2055, but slightly increase to 3.0% during 2055–2060. These indicate that the stationary factors have less strong explanatory power to the new urban areas that are farther away from the existing built-up areas. The results suggest that a 30-year period in the future is most suitable to project the urban growth scenarios, where the new urban area approximates the initial urban area. The specific best period for scenario projection elsewhere can then be identified using the method presented in this study.     

A method to analyse neighbourhood characteristics of land use patterns

Neighbourhood interactions between land use types are often included in the spatially explicit analysis of land use change. Especially in the context of urban growth, neighbourhood interactions are often addressed both in theories for urban development and in dynamic models of (urban) land use change. Neighbourhood interactions are one of the main driving factors in a large group of land use change models based on cellular automata (CA).This paper introduces a method to analyse the neighbourhood characteristics of land use. For every location in a rectangular grid the enrichment of the neighbourhood by specific land use types is studied. An application of the method for the Netherlands indicates that different land use types have clearly distinct neighbourhood characteristics. Land use conversions can be explained, for a large part, by the occurrence of land uses in the neighbourhood.The neighbourhood characterization introduced in this paper can help to further unravel the processes of land use change allocation and assist in the definition of transition rules for cellular automata and other land use change 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.     

Modeling urban growth in Atlanta using logistic regression

This study applied logistic regression to model urban growth in the Atlanta Metropolitan Area of Georgia in a GIS environment and to discover the relationship between urban growth and the driving forces. Historical land use/cover data of Atlanta were extracted from the 1987 and 1997 Landsat TM images. Multi-resolution calibration of a series of logistic regression models was conducted from 50 m to 300 m at intervals of 25 m. A fractal analysis pointed to 225 m as the optimal resolution of modeling. The following two groups of factors were found to affect urban growth in different degrees as indicated by odd ratios: (1) population density, distances to nearest urban clusters, activity centers and roads, and high/low density urban uses (all with odds ratios < 1); and (2) distance to the CBD, number of urban cells within a 7 × 7 cell window, bare land, crop/grass land, forest, and UTM northing coordinate (all with odds ratios > 1). A map of urban growth probability was calculated and used to predict future urban patterns. Relative operating characteristic (ROC) value of 0.85 indicates that the probability map is valid. It was concluded that despite logistic regression’s lack of temporal dynamics, it was spatially explicit and suitable for multi-scale analysis, and most importantly, allowed much deeper understanding of the forces driving the growth and the formation of the urban spatial pattern.     

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.     

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.     

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.     

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.     

基于多智能体与GIS城市土地利用变化仿真研究*

摘要：为动态模拟城市土地利用变化,以复杂适应系统理论为基础,通过集成多智能体、GIS和元胞自动机建立城市发展模型,并以Repast和 ArcGIS为基础设计实现了城市土地利用动态模拟系统,并以广州市番禺区为例进行了仿真实验。仿真结果表明,该方法是一种模拟土地利用变化的有效方法,可以为城市建设、管理和规划工作提供辅助决策支持。     

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.     

Modeling urban growth by coupling localized spatio-temporal association analysis and binary logistic regression

Understanding and forecasting the dynamics of urban growth can be helpful for making sustainable land-use policies. Computing models can simulate urban growth but many require extensive data input, which cannot be always met. Here we proposed coupling localized spatio-temporal association (LSTA) analysis and binary logistic regression (BLR) to model urban growth from historical land cover configurations. An indicator called neighborhood aggregation index (NAI) was defined first to measure configuration enrichment for any land cover type under spatial-and-temporal contexts. Multiple NAIs for different land cover types were taken into the proposed LSTA-BLR model to project future urban growth. A case study was selected in Wuhan, China where land covers were classified for each year during 2014–2017 based on the Landsat Imagery from Google Earth Engine. Urban growth from the year 2016 to 2017 was extracted from the classified land cover maps as the dependent variable which was modeled by the LSTA-BLR using predictors of the NAIs from the previous years. The LSTA-BLR models were tested under different neighborhood sizes (3 × 3, 5 × 5, 7 × 7, 9 × 9, and 11 × 11) and time windows (2016, 2015–2016, and 2014–2016). Results indicated that the best accuracy of the modeled urban growth reached 72.9% under the setting of 5 × 5 neighborhood size and time window 2014–2016. Urbanization was most likely to occur close to previously urbanized areas and unlikely near the neighborhood of enriched forest and water bodies. The neighborhood size affected the modeled result and the time window defining the NAIs had the most significant impact on model performance. We conclude that prior land cover configurations should be integrated for mapping future urban growth and the proposed LSTA-BLR model can serve as a useful tool to understand the near-future urbanization process based on the historical land cover configurations.     

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.     

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.     

Modeling different urban change trajectories and their trade-offs with food production in Jiangsu Province,China

Urban areas in China have expanded rapidly in recent decades, which mainly resulted in the conversion of fertile cropland. As the growth of urban areas is likely to continue in the next decades, there is a need for detailed assessments of urbanization impacts on food production. However, most land use models cannot simulate different types of urban change trajectories, such as expansion and densification, which constrains their capacity to inform such assessments with sufficient detail on the patterns of urbanization. In this paper, we present a land use model that represents multiple types of settlements, which allows to simulate multiple different urban change trajectories. We applied this model to Jiangsu Province, China, and assess the impact of projected urban development between 2015 and 2030 on cropland area and crop production. Results show that population growth is accommodated by different urban change trajectories, depending on the absence or presence of land use policies to maintain food security. In the absence of policies, population growth mainly leads to urban expansion, yielding losses in both cropland area and crop production. Implementing strict cropland protection policies leads to more urban densification and all population can be accommodated without a net loss of cropland. Yet, crop production decreases in this scenario as the most productive croplands are still converted and compensated by less productive areas. Protecting crop production instead leads to a small loss in cropland area combined with cropland intensification and different types of urban change, but maintains the total crop production. These results show the relevance of more nuanced representation of urban development in land use models in order to inform land use policies.     

Simulation models as a tool for urban planning

Computer-simulation models are a useful tool in planning in general. They can be of particular use in the areas of urban planning such as land use, choice of residential locations, problems of transport, etc. A general utility simulation system (GUSS) has been developed that can be applied in a multitude of problems. This system, GUSS, a module of UPFAR (Utility Program for the Analysis of Risk), has been applied successfully for the evaluation of risk in investment alternatives. An effort is made in this paper to illustrate how GUSS can be used in simulating urban planning problems. The preliminary model presented in the paper combines different factors of importance to the urban planning decisions.     

Land suitability and urban growth modeling: Development of SLEUTH-Suitability

Land suitability is one of the important variables influencing urbanization and needs to be considered in urban growth simulation and modeling. The present study is aimed to introduce land suitability which is a function of a few important urbanization explanatory drivers into an urban growth model for realistic urban growth simulation. Development of SLEUTH-Suitability, an improved version of the SLEUTH urban growth model has been presented in which land suitability has been integrated as an additional urban growth decision variable. The model development includes land suitability assessment, Multi-Criteria Evaluation (MCE) based Analytical Hierarchy Process (AHP) framework and its integration in the urban growth simulation process of the existing SLEUTH model, writing programming code, and verification of SLEUTH-Suitability version. The performance of the SLEUTH-Suitability version has been quantified in terms of relative improvement in the best fit value of the Optimal SLEUTH Metric (OSM), spatial and statistical measures while simulating urban growth of Ajmer City in the Rajasthan state of India as compared to existing SLEUTH version. Both versions i.e., SLEUTH and SLEUTH-Suitability models were parameterized and calibrated using a required dataset of 05 years over a period of 18 years i.e., 1997, 2000, 2008, 2013, and 2015. Performance of the SLEUTH-Suitability has been found to be better in terms of improved calibration as indicated by better OSM values and improved capturing of different urban growth forms like fragmented and scattered growth. Furthermore, using the SLEUTH-Suitability, urban growth is forecasted up to the year 2040 in Ajmer city to understand the growth pattern.     

基于GIS的城市土地利用分析与建模框架研究

本文针对城市土地利用数据的时空特性,依托地理信息系统(GIS)丰富的空间分析工具以及对海量空间数据的高性能计算优势,围绕城市土地利用研究有关数据的处理、分析、建模等方面问题设计了一个基于GIS的城市土地利用分析与建模框架;框架主体结构中有关城市土地利用变化的驱动力机制建模方法选取逻辑回归模型,对地理数据的空间自相关性处理则根据Getis自相关系数构建滤波模型;具体应用则结合深圳市国土资源局的"城市土地利用虚拟政策实验室"项目,取得良好效果     

基于空间信息多级网格的CA模型研究

具备时空计算特征的元胞自动机(CA)模型与GIS集成极大促进了GIS对地理过程的模拟能力。论文简要介绍了空间信息多级网格(SIMG)——一种既能适合网格计算环境又充分考虑到地球空间的自然特征和社会属性的差异性及经济发展不平衡的特点的空间信息表示新方法。充分研究了SIMG与CA之间的联系,分别讨论了在SIMG上CA元胞及状态的确定、元胞空间的确定、规则的定义、时间粒度确定等,提出了空间信息多级网格元胞自动机模型(SIMGCA),并提出了SIMGCA模型在土地利用/覆被变化中的应用框架。     

High-resolution urban change modeling and flood exposure estimation at a national scale using open geospatial data: A case study of the Philippines

Many developing countries in Asia are experiencing rapid urban expansion in climate hazard prone areas. To support climate resilient urban planning efforts, here we present an approach for simulating future urban land-use changes and evaluating potential flood exposure at a high spatial resolution (30 m) and national scale. As a case study, we applied this model to the Philippines – a country frequently affected by extreme rainfall events. Urban land-use changes were simulated to the year 2050 using a trend-based logistic regression cellular automata model, considering three different scenarios of urban expansion (assuming low/medium/high population growth). Flood exposure assessment was then conducted by overlaying the land-use simulation results onto a global floodplain map. We found that approximately 6040–13,850 ha of urban land conversion is likely to be located in flood prone regions between 2019 and 2050 (depending on the scenario), affecting approximately 2.5–5.8 million additional urban residents. In locations with high rates of future urban development in flood prone areas (Mindanao Island, in particular), climate resilient land-use plans should be developed/enforced, and flood mitigation infrastructure protected (in the case of “nature-based” infrastructure) or constructed. The data selected for our land-use change modeling and flood exposure assessment were all openly and (near-)globally available, with the intention that our methodology can potentially be applied in other countries where rapid urban expansion is occurring. The 2050 urban land-use maps generated in this study are available for download at https://www.iges.or.jp/en/pub/ph-urban2050/en to allow for their use in future works.