空间分析模型综述：理论与应用探讨

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《空间分析中的模型》由Lena Sanders编著，于2001年在法国出版，原书名为"Modèles en analyse spatiale"。此书提供了对空间分析中广泛存在的各种模型以及形成这些模型背后不同思维方式的深入探讨。作者们拥有广泛的学术背景，涵盖了地理、经济、水文学、生态学等多个领域，并运用了数学、统计学、计算机科学和物理学等多种方法论，体现了跨学科的研究视角。书中分为两类章节，一类是从主题角度审视空间分析，另一类则聚焦于关键概念或特定的空间分析方法论领域。作者们的目的是为读者提供一个全面的问题概述，并通过实例应用来支持理论阐述。为了便于读者间的交流和各章之间的关联性，法语版采用了交叉引用的阅读系统。作者团队的无私合作、出版社的翻译工作、François Durand-Dastès在审稿方面的帮助，以及Eugénie Dumas和Malika Madelin在项目完成阶段的支持，都是本书顺利出版的重要因素。版权方面，根据1988年的《版权、设计与专利法》，除非出于研究、私人学习、批评或评论目的，否则未经书面许可，任何形式的复制、存储或传输都必须获得出版商的许可，或者在复制图形作品时遵循CLA（Copyright Licensing Agency）的条款和许可。《空间分析中的模型》不仅是一本理论性的参考书籍，还是一本实用的工具书，为研究者、专业人士和学生提供了深入理解空间分析模型及其在实际问题中的应用的宝贵资源。通过阅读这本书，读者将能够洞悉空间组织原则、定位逻辑、空间互动的形式及其在空间动态中的作用，从而提升自己在这个领域的专业技能。

xvi Models in Spatial Analysis

In order to illustrate the diversity of meanings that come with the word “model”

in a given application, in the following sections we will rely for the most part on two

concrete examples. In the first, the goal is to model the evolution of the spatial

distribution of the population over a few decades and, in the second, of the land use .

From a methodological perspective, each of these two examples involves dealing

with and modeling “spatial dynamics”. However, modeling spatial dynamics can

take on several different meanings: it can consist of describing changes as clearly as

possible, or of finding causality underlying the type and speed of the observed

evolution. These two approaches, the former used to describe and the latter to

explain, should logically complement each other and be conducted one after the

other. In practice, however, the line between the two is not always clear, and the

structure of the information itself leads to different attitudes in research. If this

structure is complex, the first step can constitute the entire work of modeling.

Indeed, the objective is then to provide a simplified picture, in the form of a map, for

example, of a complex information obtained from several sources. If, on the other

hand, the information is described by a simple and relatively regular structure, such

as in the case of statistical information, the first step is short and most of the

modeling work is done in the second. In order to study spatial differentials in

population growth, the geographer will build an explanatory model based on

mechanisms he knows are fundamental, the role of rent, the effects of competition

for space, urban polarization, the deterring effect of distance, etc. In order to study

the evolution of land use, the agriculture scientist will develop a model involving the

modes and structures of farming, the specializations and quality of soil.

In any case, the first step consists of identifying the elementary objects that give

the level at which the information has to be collected. These objects can be cells or

pixels (image analysis), households or firms (surveys or census results), or spatial

entities (morphological or administrative units). When studying a settlement system,

the elementary entities can be municipalities or agglomerations. When analyzing

land use, plots or farms can be used. This identification becomes more complicated

in a dynamic framework, since there can be changes in the object’s semantics (when

a given agglomeration “absorbs” another, for example), identifier (a plot can be

divided in two) or its spatial extent (expansion of a farm) [CHE 95]. Once the

objects are identified, we have to come up with ways of measuring changes that

make sense in regards to the topic, and which are compatible with the spatial scale.

Already, throughout this entire process of formalizing information, we are dealing

with models. These are, on the one hand, conceptual models concerning the meaning

of the chosen indicators, particularly the link between the phenomenon being studied

(which refers to a theoretical framework) and the set of data obtained from its

measurements (which refers to what is observable), given the observation levels that

were chosen. These are, on the other hand, models of data that are necessary to

organize thematic and geometric information in order to process them (relational ,

object-oriented, vector/raster, etc.).

Introduction xvii

Once the thematic model has been designed and the gathered information has

been organized, it is necessary to formalize the model in order to validate it, to test

hypotheses and, sometimes, to establish scenarios to conduct prospective studies or

to help decision making. Different approaches are then possible, each one associated

with a specific set of skills.

If we choose a geomatics approach, we would develop and use the functionalities

of a geographic information system (GIS) in order to connect layers of information

related to different aspects of the phenomenon being studied and to find evidence of

possible spatial regularities. We can construct, for example, requests designed to

pinpoint plots located at a certain distance from a freeway interchange and that have

undergone a specific change in land use. If we choose a statistical framework, a

typical method consists of identifying the variables that have to “be explained”

(dependent variables), quantitative (population growth rate, variations in the number

of jobs) or qualitative (changes in land use, changes in the economic profile), and

“explanatory” variables that refer to the features of the agglomerations or land plots

and express the hypotheses set out in the thematic model. For the statistician the

discussion will focus on the choice of a statistical model, linear, loglinear,

exponential, etc., depending on the statistical nature of the variables and on their

relations. Facing the same question, researchers trained in mathematics or physics

will develop a dynamic model in the framework of complex systems (for example, a

non-linear prey-predator model) that includes bifurcation properties. These will be

particularly useful if we consider that the parameters that characterize the general

environment of the system being studied are governed by threshold effects that may

cause a qualitative change in the behavior of settlement dynamics. Formalizing the

model within the framework of computer sciences will lead to the use of cellular

automata or multi-agent systems and to focusing on interaction and emergence

properties. Such models work by conducting simulations, and these are particularly

useful when trying to establish the effect that the set of local interactions has on the

evolution of spatial structures at a higher level [WHI 97, BEN 04, POR 04].

To the thematician, these different approaches represent a series of methods that

are useful to formalize and test his thematic model, each one leading to different and

complementary possibilities. His choice will depend on his abilities, his

collaborations or, better, on the adequacy between his hypotheses on the why and

the how of the change he is interested in and the properties of the available

statistical, physical, geomatics or computer model. In some cases, he may have to

use a series of models: a GIS to create spatial indicators; a statistical model to test

the relevance of the relationship between some of the variables used, or also to

estimate missing information; a differential equation model to deal with the overall

evolutions of a certain number of state variables; a cellular automata model to

simulate the local spatial interactions; a multi-agent system to account for the effects

of a cooperation between several agents. In order to implement a thematic model, it

xviii Models in Spatial Analysis

thus becomes necessary to string together, to couple and to integrate models

originating from different fields, and confusions of course can occur when the same

word “model” is used without being associated with a complement that specifies its

meaning.

Each of these groups of methods has its specific advantages and integrates in its

own way the spatial dimension of the phenomena being studied. The statistical

approach emphasizes the covariation mechanisms of the phenomena, and space can

be included in the analysis by means, first, of the type of statistical individuals

considered (spatial entities, location pairs) and, second, of the variables (distances,

shapes of spacings or types of neighborhoods, for example). In dynamic models,

space can, in the same way, intervene as a frame for the studied objects (spatial

entities), and also through an interaction term, connecting the dynamics of the

entities with each other (the distance or the commuting cost between two entities, for

example). If the cellular automata are used to represent geographic space, the very

driving force of the change is spatial, since any change can be determined based on

the neighborhood configuration. Each of these methodological frameworks can be

used with the goal of describing, exploring or explaining. The lines that separate

these approaches are not always clear and depend more on how the researcher

designs his methodological device than on the methods themselves.

The question can be stated in similar terms for spatial analysis. Depending on

the contexts and the authors, different meanings are bound to this concept in the case

of geography alone. Some give the phrase a strong thematic meaning: “Formalized

analysis of the configuration and properties of the geographic space, as it is

produced and experienced by human societies” [PUM 97]. Others emphasize the

spatial aspect of the phenomenon being studied: “Searching, within the features of

spatial entities, what is relevant to their geographic positions, particularly their

relative geographic positions, making it necessary to model the spatial structure”

[CHA 95]. Others, finally, insist on the methodological aspects, and spatial analysis

refers to the “set of mathematical and statistical methods designed to specify the

nature, the quality, the quantity related to places and to their relations – all of this

defining space – by studying both attributes and localizations” [BRU 92], or also, in

a similar approach, a “whole cluster of techniques and models which apply formal,

usually quantitative, structures to systems in which the prime variables of interest

vary significantly across space” [LON 96]. GIS users, on the other hand, when they

use the phrase spatial analysis, refer to a set of functionalities, such as superposition

techniques, topological and geometric functions, interpolation techniques, network

analysis, etc.

Again, there can be some confusion between thematicians, such as geographers,

who see spatial analysis as a conceptual framework in which the effects of position,

neighborhood and co-occurrence play a key role in helping to make clear the

Introduction xix

interactions between space and society, associated with elementary spatial models

referring to gravity, potential, diffusion and to the tools of spatial statistics (for

example, spatial autocorrelation, variogram), and GIS users for whom the phrase

spatial analysis sometimes means the same thing as the geometric and superposition

functionalities of GISs.

Thus, a computer scientist and a thematician do not share the same meaning for

the phrase “models in spatial analysis”. We will not discuss in detail in this book the

differences in points of view, but instead we will adopt the following statement. The

idea is to describe the approaches concerned with thematic modeling, and to give an

idea of the diversity of the methodological choices made in practice by those whose

object of study is strongly rooted in space. Any modeling requires geographic

information to be formalized, but the emphasis does not rest explicitly on this

question, but rather on how the hypotheses are formalized. The goal is to

understand, explain and simulate spatial organizations, special localizations, the

emergence or the end of certain phenomena in certain locations, and the types of

interactions between different places.

Geographic information plays a central role in all of the studies detailed in this

book, even if there are few explicit references to GISs. Despite going unnoticed in

these modeling studies, they have nonetheless a strong implicit presence and are

essential tools in some processing steps. Certain spatial analysis methods useful for

developing a thematic spatial model exist in the GIS, or can easily be internalized,

while others are used in completely independent ways or are coupled. Geographers

have produced remarkable advances over the last decade in coupling and integrating

tools of spatial analysis, simulation models and GIS ([MAG 06]).

Each chapter in this book shows the relationship between a conceptual

framework of spatial analysis and a set of methods and models. The frameworks are

related to the questions of localizations and interactions in space, of geographic

scales and levels of observation, of spatial dynamics. Some authors favor the

contribution of a group of methods originating from statistics, mathematics, and

computer science, while others base their presentations on theories deeply rooted in

geography or economics. All of them attach a key importance to the connection

between the thematic meaning of their studies and the properties of the tools they

have chosen. Space is present both as an object – the objective being to describe,

understand and predict localizations, spatial configurations and their evolution – and

as a part of the explanation – the objective being to assess the effects of location and

neighborhood on these localizations, configurations and changes.

xx Models in Spatial Analysis

Two central and recurring concepts: spatial interactions, levels of observation

Every chapter in this book deals with situations where space plays a key role,

sometimes as a passive frame but most often as an active function. On the other

hand, the various chapters are very diverse in terms of the phenomena being studied

(for example, water run-off, localization of public services, population mobility), of

the analysis tools (for example, multivariate analysis, differential equations, multi-

agent systems), of spatial scales (from a square foot cell to the national level) and

time scales (from a minute to a century). This book thus illustrates the diversity of

questions and practices in spatial analysis modeling. Beyond this diversity, there are

recurring concepts that are unavoidable in any approach in terms of spatial analysis.

These concepts are spatial interactions and levels.

Modeling spatial interactions

The concept of spatial interactions is used in most chapters, and is in fact at the

core of the spatial analysis approach. When the locations have been characterized,

when the intensity and the types of spatial differentiations have been determined,

and when the similarities and contrasts have been brought to light, the next task

consists of finding the relationship between these features of spatial organization

and the exchanges these locations maintain among each other, as well as the mutual

influences they have on each other. These influences and exchanges originate from

the disparities of space; in fact Alain Franc uses the phrase “interactions driven by

spatial organization” (Chapter 9). The other way round, these interactions, in turn,

contribute to producing disparities. Thus, spatial interactions reflect relations of

complementarity and/or competition between the locations and act as a driving force

in the transformation and the dynamics of spatial systems. The interaction between

these locations can either be the object of research itself (when trying to explain why

some flows are more or less significant between certain pairs of locations), or

represent a constraint (movement from one location to another is viewed as a

constraint on achieving a task for a given agent), or also constitute the explanatory

element of a dynamic (the start of or an increase in a phenomenon in a location

brought about by exchanges with other locations).

As a result, spatial interactions take on various forms, operate on several levels,

and their analyses lead to different formalizations. In the following sections, we will

attempt to express the major aspects of this diversity that are dealt with throughout

the different chapters.

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