Models in Spatial Analysis

Lena Sanders is a senior scientist in geography at the CNRS (Centre National de la Recherche Scientifique), France, specializing in urban geography, spatial analysis and dynamic modeling. She is Director of Géographie-cités, a research laboratory of CNRS-University Paris 1-University Paris 7, France.

• Preface xiiiIntroduction xvChapter 1. Modeling Concepts Used in Spatial Analysis 1François DURAND-DASTÈS1.1. Introduction 11.2. Modeling universals 21.2.1. Logical frames for modeling 21.2.2. The language of models 61.2.2.1. Material or physical model languages 61.2.2.2. The language of images: iconic models 71.2.2.3. Modeling in mathematical language 91.3. A few specific features of spatial models 111.4. Spatial models: a study grid 161.4.1. Sequencing and explanation 161.4.2. The group and the individual 181.4.3. The random and the determined 201.4.4. Movement and balance 211.5. Conclusion 251.6. Bibliography 26Chapter 2. Geographical Scales and Multidimensional Statistical Methods 29Hélène MATHIAN and Marie PIRON2.1. Introduction 292.2. Scaling issues 312.2.1. The consideration of different geographical levels: two possible approaches 312.2.2. Formalization of relations between two levels 332.2.2.1. Nested relations and partition graph 332.2.2.2. Neighborhood relations and proximity graphs 352.2.3. Processing of multilevel information 372.2.3.1. Multilevel structure and attributes 372.2.3.2. Multidimensional statistical methods 392.3. Change of levels, change of structures 402.3.1. Scale and variability 412.3.2. Exploratory analysis of the scale system 412.3.2.1. Analysis of aggregated levels or interclass analysis 432.3.2.2. Transition analysis between two levels or intraclass analysis 452.3.3. Application of outlying Ouagadougou space to the social and spatial organization 462.4. Integration of the different levels 512.4.1. The scale: a set of territorial and spatial references 512.4.2. The analysis of local differences 552.4.3. Other local analysis methods 582.5. Multilevel models 592.5.1. Contextual effects and regression models 602.5.2. Multilevel modeling 652.6. Conclusion 682.7. Bibliography 69Chapter 3. Location of Public Services: From Theory to Application 73Dominique PEETERS and Isabelle THOMAS3.1. Introduction 733.2. The modeling approach 753.2.1. A typology of public services: an attempt 763.2.2. Estimating demand 773.2.3. Analyzing supply 783.2.4. Adjusting supply to demand 793.2.5. Evaluating the solutions 823.2.6. Methodological perspectives 833.3. A prototype location model: the k-median 843.4. An example: recycling centers 863.4.1. The problem: the optimal location of recycling centers 863.4.2. Results of the model 883.5. Conclusion 913.6. Bibliography 92Chapter 4. Time-geography: Individuals in Time and Space 97Sonia CHARDONNEL4.1. Introduction: why integrate “time” when we analyze space? 974.1.1. The study of spatio-temporal processes 974.1.2. For a time-integrated geography 984.2. The foundations of time-geography 994.2.1. The premises 994.2.2. A certain vision of the world 1004.3. The conceptual framework of time-geography 1024.3.1. The creation of a “notation system” 1024.3.2. Tools to decrypt daily life 1034.3.2.1. Trajectory, station, project: basic concepts 1034.3.2.2. Different types of constraints 1054.3.2.3. A transversal analysis of the “three worlds” 1094.4. Time-geography in practice 1104.4.1. Simulation of individual activity programs: public transport possibilities in the city of Karlstad – an application by Bo Lenntorp 1114.4.1.1. General features of the simulation model 1114.4.1.2. The application of Karlstad 1114.4.1.3. New implementations and operational methods in time-geographic research 1154.4.1.4. Partial conclusion 1184.4.2. Daily lives of women: adaptation strategies in time and space – the Tora Friberg method 1184.4.2.1. From Højrup’s life forms to Friberg’s three women life forms 1194.4.2.2. Relation with time-geography 1204.5. Conclusion 1214.6. Bibliography 122Chapter 5. The Process of Spatial Diffusion and Modeling Change 127Thérèse SAINT-JULIEN5.1. Introduction 1275.2. The manifestations of diffusion in space 1285.2.1. Elements and levels of approach of a spatial diffusion process 1295.2.2. Distances and propagation channels 1315.2.3. Spatial diffusion in time 1365.3. Simulating a spatial diffusion process: Hägerstrand’s pioneer approach 1375.3.1. A probabilistic model 1385.3.2. The rules of the basic model 1395.3.2.1. Diffusion in a homogenous space 1395.3.2.2. Diffusion in a heterogeneous space 1395.3.3. Simulation procedure 1415.4. Analysis models, interpretative models 1435.4.1. References 1435.4.2. Models of form 1455.4.3. Explanatory models 1495.5. Conclusion 1535.6. Bibliography 153Chapter 6. Spatial Microsimulation Models 159Einar HOLM and Lena SANDERS6.1. Introduction 1596.2. Choosing the aggregation level for modeling 1606.2.1. “Micro-objects” and spatial analysis 1616.2.1.1. Arguments for choosing a modeling level 1616.2.1.2. Individuals as the favored micro-objects in spatial microsimulation 1646.2.2. Theoretical point of view: interactions and emergence phenomena 1696.2.3. Thematic point of view: the driving role of the inter-individual diversity 1706.2.4. Technical point of view: management of information tables 1716.3. The elements of a dynamic microsimulation model .1726.3.1. The different sources of microdata: comprehensive information, samplings, artificial worlds 1726.3.2. Statistical procedures or agent type autonomy: the different ways to formalize individual change 1766.4. National forecasts and simulation of individual biographies with the SVERIGE model 1786.4.1. Classical aggregate outputs 1796.4.2. The biography of Kristina 1816.5. A simulation of population spatial dynamics with MICDYN 1856.5.1. Operation of the MICDYN model 1856.5.2. Determining workplaces and places of residence of migrants 1876.5.3. Simulating the population evolutions 1990-2040 1886.5.4. Perspectives 1916.6. Conclusion 1926.7. Bibliography 193Chapter 7. Multi-agent Simulations of Spatial Dynamics 197Jean-Pierre TREUIL, Christian MULLON, Edith PERRIER and Marie PIRON7.1. Introduction 1977.2. The multi-agent approach 1997.2.1. Multi-agent systems 2007.2.2. Multi-agent simulation of natural and social phenomena 2047.3. Modeling of spatial dynamics 2067.3.1. Computer models and simulation of spatial dynamics 2077.3.1.1. An example: modeling of the ecosystem of the interior delta of the river Niger 2077.3.1.2. The concepts of a computer model of spatial dynamics 2107.3.2. Mathematical models of spatial dynamics 2127.3.2.1. Eulerian and Lagrangian approaches 2127.3.2.2. An example on water runoff modeling 2167.3.3. Computer and mathematical models of spatial dynamics toward convergence 2197.3.3.1. A common duality: Eulerian point of view and Lagrangian point of view 219 7.3.3.2. Source and necessity of the comparison: simulation and its limits 2207.4. The multi-agent approach in spatial dynamics modeling: a point of view 2227.4.1. The methodology 2227.4.2. Hierarchy of choices and the place of agents: an example 2237.5. Conclusion 2247.6. Bibliography 225Chapter 8. From Image to Model: Remote Sensing and Urban Modeling 231Françoise DUREAU and Christiane WEBER8.1. Introduction 2318.1.1. A modeling of urban reality 2328.1.2. Objectives of the chapter 2338.2. The satellite image in the demographic information production 2378.2.1. The different phases of information production from satellite imagery 2388.2.2. Area sampling method on satellite image: general principles 2398.2.3. Application in Bogota in 1993 2408.3. The use of imagery in urban modeling 2428.3.1. The potential model and satellite data 2428.3.2. Application of the model to satellite imagery 2448.3.3. Application in Bogota 2478.4. Spatial information and dynamic modeling 2538.4.1. Towards a dynamic multilevel model 2558.4.2. Application in Bogota: a preliminary simulation 2558.5. Conclusion 2578.6. Bibliography 258Chapter 9. Mathematical Formalization for Spatial Interactions 261Alain FRANC9.1. Introduction 2619.2. Formalizations 2649.3. Notion of perfect aggregation of variables 2679.4. Mean field 2699.5. Example of the Ising model 2719.6. Use of mean field notion in ecology 2739.7. Reaction-diffusion models 2759.8. Conclusion 2779.9. Bibliography 278Chapter 10. Fractals and Geography 281Pierre FRANKHAUSER and Denise PUMAIN10.1. Introduction 28110.2. Fractality and structuring of the geographical space 28210.2.1. Density: a traditional but unsuitable measure 28210.2.2. The fractals: references adapted to the space of human societies 28410.3. Fractal models of spatial structures 28610.3.1. Surface models 28610.3.2. Line models 28810.3.3. Multifractal models 29010.3.4. Stochastic models 29010.4. Measuring fractality 29010.4.1. Notion of fractal dimension 29110.4.2. Global analysis methods 29210.4.2.1. The grid analysis 29210.4.2.2. The correlation analysis 29310.4.3. Local methods of analysis 29310.4.3.1. Radial analysis 29310.4.3.2. The curve of scaling behavior 29410.5. The morphology of contours 29510.6. The morphology of land occupation 29610.6.1. Form of occupied surfaces 29610.6.2. Intensity of land occupation 30010.7. The morphology of hierarchies: population and systems 30210.7.1. Urban hierarchies 30210.7.2. Measuring the morphology of networks 30210.8. Towards dynamic models 30410.9. Conclusion 30610.10. Bibliography 308List of Authors 313Index 317