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.     

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.     

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.     

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.     

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.     

Quantifying how landscape composition and configuration affect urban land surface temperatures using machine learning and neutral landscapes

The urban heat island effect is an important 21st century issue because it intersects with the complex challenges of urban population growth, global climate change, public health and increasing energy demand for cooling. While the effects of urban landscape composition on land surface temperature (LST) are well-studied, less attention has been paid to the spatial arrangement of land cover types especially in smaller, often more diverse cities. Landscape configuration is important because it offers the potential to provide refuge from excessive heat for both people and buildings.We present a novel approach to quantifying how both composition and configuration affect LST derived from Landsat imagery in Southampton, UK. First, we trained a machine-learning (generalized boosted regression) model to predict LST from landscape covariates that included the characteristics of the immediate pixel and its surroundings. The model achieved a correlation between predicted and measured LST of 0.956 on independent test data (n = 102,935) and included predictors for both the immediate and adjacent land use. In contrast to other studies, we found adjacency effects to be stronger than immediate effects at 30 m resolution. Next, we used a landscape generation tool (Landscape Generator) to alter landscape configuration by varying natural and built patch sizes and arrangements while holding composition constant. The generated neutral landscapes were then fed into the machine learning model to predict patterns of LST.When we manipulated landscape configuration, the average city temperature remained the same but the local minima varied by 0.9 °C and the maxima by 4.2 °C. The effects on LST and heat island metrics correlated with landscape fragmentation indices. Moreover, the surface temperature of buildings could be reduced by up to 2.1 °C through landscape manipulation.We found that the optimum mix of land use types is neither at the land-sharing nor land-sparing extremes, but a balance between the two. In our city, maximum cooling was achieved when ~60% of land was left natural and distributed in 7–8 patches km⁻² although this could be location dependent and further work is needed. Opportunities for urban cooling should be required in the planning process and must consider both composition and configuration at the landscape scale if cities are to build capacity for a growing population and climate change.     

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.     

Establishing the relationship between urban land-cover configuration and night time land-surface temperature using spatial regression

Studies suggest that urban form can influence microclimate regulation. Remote sensing studies have contributed to these findings through analysis of high-resolution land cover maps, landscape ecology metrics, and thermal imagery. Collectively, these have been referred to as land cover configuration studies. There are three objectives to this study. The first is to assess the relationship between nighttime land surface temperatures (LST) and land cover configuration and composition. The second objective is to outline a comprehensive methodology that includes ordinary least squares (OLS), spatial regression, variable selection, and multicollinearity analysis. Our last objective is to test three hypotheses about the relationship between LST and land cover, which can briefly be described as: 1) the importance of land-use regimes in modeling LST from land cover composition and configuration variables; 2) the strength of the correlation between LST and roads, buildings, and vegetation; and 3) the improved quality of models using landscape metrics in modeling the relationship between LST and land cover. Based on 16 different models (8 OLS, 8 spatial regression) we could confirm the above hypotheses, but we found that the configuration of buildings, roads, and vegetation have a complex relationship with LST. Our interpretation of this complexity, combined with the strength of composition variables, is that parsimonious models, for now, are more useful to urban planners because they are more generalizable. Finally, spatial regression models of land cover configuration and LST demonstrated an improvement over non-spatial linear models (OLS). Spatial regression models reduced heteroskedasticity and clusters of residuals, and tempered coefficients, suggesting that the OLS models could be biased. OLS models were still found to be a valuable tool for exploratory analysis.     

Understanding the drivers of sustainable land expansion using a patch-generating land use simulation (PLUS) model: A case study in Wuhan,China

Cellular Automata (CA) are widely used to model the dynamics within complex land use and land cover (LULC) systems. Past CA model research has focused on improving the technical modeling procedures, and only a few studies have sought to improve our understanding of the nonlinear relationships that underlie LULC change. Many CA models lack the ability to simulate the detailed patch evolution of multiple land use types. This study introduces a patch-generating land use simulation (PLUS) model that integrates a land expansion analysis strategy and a CA model based on multi-type random patch seeds. These were used to understand the drivers of land expansion and to investigate the landscape dynamics in Wuhan, China. The proposed model achieved a higher simulation accuracy and more similar landscape pattern metrics to the true landscape than other CA models tested. The land expansion analysis strategy also uncovered some underlying transition rules, such as that grassland is most likely to be found where it is not strongly impacted by human activities, and that deciduous forest areas tend to grow adjacent to arterial roads. We also projected the structure of land use under different optimizing scenarios for 2035 by combining the proposed model with multi-objective programming. The results indicate that the proposed model can help policymakers to manage future land use dynamics and so to realize more sustainable land use patterns for future development. Software for PLUS has been made available at https://github.com/HPSCIL/Patch-generating_Land_Use_Simulation_Model     

Validating land change models based on configuration disagreement

Land change models are increasingly being employed to predict future landscapes and influence policy and decision-making. To ensure the highest model accuracy, validation methods have become commonplace following a land change simulation. The most common validation method employed uses quantity and allocation disagreement. However, these current measures may not account for differences in the configurations of land change, placing them in potential conflict with the principals of heterogeneity and spatial patterning of landscape ecology. We develop a new metric, termed configuration disagreement, designed to focus on the size, shape, and complexity of land change simulations. Using this metric, we demonstrate the value of including errors of configuration disagreement – in addition to quantity and allocation error – in the assessment of land change models. Four computational experiments of land change that vary only in spatial pattern are developed using the FUTURES land change model. For each experiment, configuration disagreement and the traditional validation metrics are computed simultaneously. Results indicate that models validated only with consideration of quantity and allocation error may misrepresent, or not fully account for, spatial patterns of landscape change. The research objective will ultimately guide which component, or components, of model disagreement are most critical for consideration. Yet, our work reveals why it may be more helpful to validate simulations in terms of configuration accuracy. Specifically, if a study requires accurately modeling the spatial patterns and arrangements of land cover. Configuration disagreement could add critical information with respect to a model's simulated changes in size, shape, and spatial arrangements, and possibly enhance ecologically meaningful land change science.     

Applicability and calibration of an irregular cellular automata model for land use change

Cellular automata (CA) models of spatial change have been developed and applied in the context of large regional or metropolitan areas and usually use regular cells, with spatial interactions and transition rules operating within fixed-size neighbourhoods. Model calibration has also been an area of intensive research with many models still using expert-based input to ensure visual calibration of modelled land use maps. In this paper, we present an innovative CA model where irregular cells and variable neighbourhoods are used to better represent space and spatial interaction. Calibration is based on an optimisation procedure that uses particle swarm (PS) to determine the optimal set of parameters of the CA model. Hypothetical test instances are used to assess the CA model and its calibration to small urban areas. Our conclusion was that the use of PS ensures calibration results for the CA model that compare very well with results obtained through other approaches reported in the literature.     

超大城市土地覆盖与热环境的随机森林回归模型研究

目前对于超大城市土地覆盖和热环境定量模型研究报道不足,这主要是因为大城市地表温度和地表生物物理组分之间存在复杂的潜在非线性关系,这使得准确评估城市热环境情况遇到了严峻的技术挑战。研究选取中外6个典型超大城市（北京、上海、广州、伦敦、纽约和东京）为研究对象,以Landsat遥感影像为主要数据源,利用单通道算法反演各城市地表温度,采用随机森林回归模型（RFR）建立土地覆盖类型与城市热环境定量关系模型（LCT）,综合分析城市土地覆盖因子与热环境间的多维定量关系。土地覆盖与地表温度的定量关系显示,城市地表热场的空间结构在很大程度上被下垫面用地类型所左右,不透水面会导致高温热场的聚集,而植被和水体则有降温作用。6个超大城市地表覆盖结构变化产生的升温/降温效应有所差异,北京、上海、纽约和东京等城市区域的植被和水体降温效应较广州和伦敦显著。基于随机森林回归方法建立了NDVI、MNDWI和NDISI等3种土地覆盖类型与城市热环境的综合定量关系模型（LCT）,模型得到的精度高于基于多元线性回归方法建立的模型。LCT＿RF模型的R2值在0.623～0.826之间,比LCT＿MLR模型高0.021～0.07...     

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.     

Modeling and simulating residential mobility in a shrinking city using an agent-based approach

Shrinking cities are characterized by a huge oversupply of dwellings and resulting residential vacancies. Discussions among urban planners and policymakers in Europe have focused on the consequences of urban shrinkage following demographic transition, fertility decline and individualization. In this study, the shrinking city of Leipzig in Eastern Germany is singled out as a case basis for the study of residential mobility and land use change using agent-based modeling techniques, in which social scientists developed a concept of household types based on empirical data that form a unique base; these techniques were used to construct a data-driven, agent-based model. The spatially explicit simulation model RESMOBcity presented here ‘translates’ these empirical data via behavioral rules of households. It computes spatially explicit household patterns, housing demands and residential vacancies. Based on three scenarios, population growth, stagnation and shrinkage, we show that population might stabilize within the coming years. The number of households is expected to further increase. We demonstrate that a selective demolition of vacant housing stock can counteract the enormous oversupply of dwellings and better balance housing demand and the number of available flats. Scenario simulation shows that the model can reproduce observed patterns of population, inner-urban migration and residential vacancy in a spatially explicit manner and thus can be applied to the analysis of scenarios of demographic change in urban regions. The presented model acts as a tool supporting the testing of hypotheses in social science research and allowing the quantification of land-use scenarios in urban regions based on household choices.     

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.     

Developing a cellular automata model of urban growth to inform spatial policy for flood mitigation: A case study in Kampala,Uganda

Urban growth may intensify local flooding problems. Understanding the spatially explicit flood consequences of possible future land cover patterns contributes to inform policy for mitigating these impacts. A cellular automata model has been coupled with the openLISEM integrated flood modeling tool to simulate scenarios of urban growth and their consequent flood; the urban growth model makes use of a continuous response variable (the percentage of built-up area) and a spatially explicit simulation of supply for urban development. The models were calibrated for Upper Lubigi (Kampala, Uganda), a sub-catchment that experienced rapid urban growth during 2004–2010; this data scarce environment was chosen in part to test the model's performance with data inputs that introduced important uncertainty. The cellular automata model was validated in Nalukolongo (Kampala, Uganda). The calibrated modeling ensemble was then used to simulate urban growth scenarios of Upper Lubigi for 2020. Two scenarios, trend conditions and a policy of strict protection of existing wetlands, were simulated. The results of simulated scenarios for Upper Lubigi show how a policy of only protecting wetlands is ineffective; further, a substantial increase of flood impacts, attributable to urban growth, should be expected by 2020. The coupled models are operational with regard to the simulation of dynamic feedbacks between flood and suitability for urban growth. The tool proved useful in generating meaningful scenarios of land cover change and comparing their policy drivers as flood mitigation measures in a data scarce environment.     

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。