Geographical Modeling

Cities and Territories

Denise Pumain

• Publisher: Wiley-ISTE
• Year: 2019
• ISBN:
  9781119687269
• Edition: 1
• Topic: Matemáticas
• Subtopic: Matemáticas general

The modeling of cities and territories has progressed greatly in the last 20 years. This is firstly due to geographic information systems, followed by the availability of large amounts of georeferenced data – both on the Internet and through the use of connected objects. In addition, the rise in performance of computational methods for the simulation and exploration of dynamic models has facilitated advancement. Geographical Modeling presents previously unpublished information on the main advances achieved by these new approaches. Each of the six chapters builds a bibliographic review and precisely describes the methods used, highlighting their advantages and discussing their interpretations. They are all illustrated by many examples. The book also explains with clarity the theoretical foundations of geographical analysis, the delicate operations of model selection, and the applications of fractals and scaling laws. These applications include gaining knowledge of the morphology of cities and the organization of urban transport, and finding new methods of building and exploring simulation models and visualizations of data and results.

1
Complexity in Geography

The last three or four decades have completely renewed the modeling practices of geographers. Two major changes, one epistemological and the other technical, are at the origin of these transformations. Technological change is the tremendous expansion of information processing capabilities, which has made work that could previously only be sketched as thought experiments possible, or work that has been carried out wholly incompletely due to a lack of powerful computing resources. This technical change has made it possible since about the 2000s to fully implement a major epistemological change that occurred sometime earlier in the 1970s and 1980s. This is the introduction of paradigms and models from the natural sciences into geography, whose keywords are self-organization (the dissipative structures of Prigogine and Nicolis (1971)), synergetics (Haken 1977; Weidlich 2006), and complexity and the notion of emergence (Bourgine et al. 2008). We will not recall here those filiations that are already mentioned in several works (e.g. Dauphiné 2003; Pumain et al. 1989; Sanders 1992). We want to show not so much how these forms of modeling can be applied in geography, but how to proceed for real model transfers, since many theories of the discipline had already largely anticipated the need for the newly proposed formalizations.

Transferring scientific language, concepts, methods, and instruments from one discipline to another is only a fruitful operation if it meets an expectation, a real need for innovation. In this case, it is not so much the paradigm of complexity as such that has been the novelty for the human and social sciences since they have always been confronted with the irreversibility of the trajectories of their objects, the near impossibility of prediction, and the phenomena of emergence in the systems studied. It is because complexity sciences provide complementary methods, means to process information and to formalize knowledge. Many geographers have adopted these references to work on their models. These have contributed to building cumulative knowledge when previously acquired intuitions could benefit from the transfer. This is why it seemed useful in this introductory chapter to remind geographers as well as readers trained in other sciences of the disciplinary fundamentals on which geography modeling can be based, particularly to deal with the complex objects that are cities and territories. We quickly retrace the successive postures of geographers faced with the possibilities of modeling, and then, we outline a set of regularities that can be more easily modeled among the objects that geography studies. These regularities partly lead to specific modeling practices by geographers, which are largely motivated by the multiplicity of observation scales, but also practices that have been much more in demand over the past two decades by the influx of geolocalized data, which opens up considerable development opportunities.

The general idea is that the complexity of the objects and processes observed by geographers is always constructed, not so much in formulating universal “laws”, but more often by including spatiotemporal elements, like in other human and social sciences, which are fundamentally “historical sciences” (Passeron 1991). These disciplines share with the natural sciences certain forms of nonlinear relationships, processes of self-organization, morphogenesis, dynamics oriented by attractors, or emergence phenomena characteristic of complex systems, which are formalizable on specific case subsets or segments of their trajectory. Geography adds to this complexity of nonlinear processes the specific feature of being interested in a very wide diversity of variables and levels of observation, including natural and social elements, in an attempt to formalize the evolution of landscapes, cities, and territories, which gives an additional dimension to the complexity of the systems that geography models¹.

1.1. A first bifurcation in the epistemology of geographic modeling

Geography appears among the humanities and social sciences as one of the most practiced in modeling (Banos 2013; Sanders 2001). Geography has often been identified as a pioneer in the use of digital tools. It is no coincidence that a philosopher has chosen to test his conceptions of modeling with this discipline (Varenne 2018).

This is a paradox: indeed, until recently, geography seemed to be a “soft science”, insofar as it does not assert theories as powerfully unitary as the so-called mainstream economy, and does not export its concepts as much as sociology, if we think, for example, of the French theory in vogue in the United States for at least 30 years. However, the theoretical and quantitative “revolution” that began in the 1950s in Sweden and the United States and then developed in France in the 1970s (Cuyala 2014; Pumain and Robic 2002), probably explains, to a large extent, why a certain “spatial turn” took place in most human and social sciences in the 1990s. Concepts and methods, software tools such as geographic information systems (GIS), and research questions brought by geographic space modeling practices (Banos 2016; Bonhomme et al. 2017) have been successfully imported into almost all disciplines.

However, in everyday language as in many representations of common sense, the “geography” or description of the Earth sometimes seems to be summed up in terms of nomenclatures, knowledge of locations (latitude, longitude, and altitude), and place names, the toponyms that societies have associated with them, whether they are mountain ranges, rivers, islands, or cities. However, academic geographic science – once the era of exploratory journeys and the “discoveries” of the regions of indigenous peoples by colonizers had passed – relied in the late 19th Century on questions designed to unpack the reasons for the diversity of the imprints shaped by societies on the Earth’s surface. Agrarian landscapes and forms of habitats, the exploitation of mining resources and industrial production, arrangements of villages and cities, traffic routes, and tangible or intangible flows have been examined at all scales, in a diverse range of geographical environments and according to their evolution over the course of history. Two main types of explanation successively dominated the research. In the first half of the 20th Century, the main focus was on the relationship between a society and its environment, speculating on the more or less favorable or constraining nature of natural conditions and the social capacity to develop them, according to a somewhat “vertical” interpretation of its relationship with the resources offered locally by the planet. In the second half of the 20th Century, another, more “horizontal” way of producing explanations emerged, which tends to interpret the characteristics of a territory or a city from its situation in the world, i.e. from its relations with other territories and other cities. In truth, these two explanatory forms, which lead to very different models, are complementary and are necessarily articulated in any geographical interpretation of a particular city or territory.

1.1.1. “Vertical” explanations for the “science of places, not people”²

In its academic history, geography has long been at the interface between the natural and human sciences. Taking into account the description of the planet (Robic et al. 2006) and its transformation into environments and landscapes by societies (Robic 1992), it had built a few general models. The relationship between the material organization of societies and natural resources, mediated by climatic and altitudinal zones, had been well observed and described, revealing some regularities. In particular, they highlighted the fairly close interdependence between ancient societies and the local character of mineral and plant resources used in housing and agriculture, which did not, however, exclude long-distance trade in less common commodities. When such regularities were systematized to excess (e.g. “limestone votes left, granite votes right” to caricature the positions of André Siegfried, founding geographer of electoral sociology in the 1930s, who actually linked the hydrography of these environments to their form of habitat, grouped, or dispersed and to the degree of dependence of the inhabitants on the domination of landowners), the corresponding statements were quickly rejected on the grounds of “determinism”. Conversely, noting the great diversity of selections and combinations of resources made by societies under more or less equivalent physical conditions could also, on the contrary, lead to “exceptionalism” (Schaefer 1953). This expression covers Schaefer’s criticism, both of the claims, which was frequent at the time, of a specificity of the geographical explanation, based on the genetics of the places, and of its consequence consisting in highlighting the uniqueness of the places. Regional idiosyncrasies have been the subject of numerous demonstrations denying the possibility of a rise in generality, the authors insisting sometimes on the strong constraint exerted by local resources and sometimes on the social free will with regard to how using and transforming them, as well as to the diversity of their creations in terms of the forms of their political, social, and cultural organizations. In the early days of academic geography, it was, therefore, physical geography in the fields of geomorphology or climate, which allowed modeling. Thus, since the early 1960s, the English geographer Richard Chorley (1962) advocated the transposition of von Bertalanffy’s general theory of systems into geomorphology and advocated the design of open systems, both for physical and human geography³. In such systems, the second law of thermodynamics does not apply and evolutions are not directed toward the maximum entropy and homogeneity, but other processes generate all kinds of configurations, formalized in models, which were listed five years later in a book written with Peter Haggett about these two branches of geography (Chorley and Haggett 1967).

1.1.2. “Horizontal” explanations for the science of the spatiality of societies

Some other types of regularities had indeed been observed since at least the early 19th Century in the organization of cities and territories and gave rise to various attempts at formalization, through mathematical models or iconic representations. The regularities of the spacing of cities, the hierarchy of their functions, and the interlocking of their catchment areas had been described since 1841 by the Saint-Simonian Jean Reynaud as “the general system of cities” strongly constrained by the use of the nearest service and thus generating forms of circular or hexagonal service areas, interlocking according to a hierarchy of rarity of urban services (Reynaud 1841; Robic 1982). This concept and the derived spatial models had little immediate impact, but the principles of a theory associating the size of cities with the rarity of their economic functions and the extent of their clientele in the surrounding region were rediscovered and systematized by the German geographer Walter Christaller (1933) in a “central place theory”, which was the subject of multiple tests in all parts of the world (Berry and Pred 1961). This theory actually included the previous model known as the “Reilly law of retail gravitation” (Reilly 1931), which explained the location of commercial activities by competition between businesses and services frequented by consumers under the constraint of proximity. In both the Reilly and Christaller models, travel costs are borne by the consumer and are added to the price of goods, encouraging people to buy from the nearest place. This determines, in the cartographic representations, more or less circular-shaped catchment areas, which fit together in the form of hexagons in the spatial diagrams drawn by Christaller.

In fact, these early geographic models validate what American cartographic geographer Waldo Tobler (1970) later referred to as “the first law of geography” (“everything interacts with everything, but two close things are more likely to interact than two distant things”). This law summarizes many of the previous observations made about the movement of people in space. The first formalizations can be attributed to the geographer Ernst Georg Ravenstein (1885), who published several articles from 1885 onward which summarized the main characteristics of population movements in a period of high rural exodus under the title “Migration laws” in a British statistical journal.

It was the American geographer Edward Ullmann who, in 1954, proposed defining geography as the science of spatial interactions. In his work Geography as Spatial Interaction, he certainly introduces the same “physical” model as the astrophysicist Stewart (1948), namely, a “gravitation” model (the flows between two geographical units are proportional to the product of their masses and inversely proportional to the distance that separates them) but he truly transposes this idea to the social sciences. He specifies the geographical conditions that are likely to explain the exchange and the movement: there must be a complementarity between a demand for a given product from a certain place of origin and the resources available in a place of supply, and travel must be possible, and therefore not too costly, for the exchange to take place. The characteristic principle that organizes geographical space is, therefore, the constraint of proximity; it includes the “sociological” principle that puts it into practice, stipulating that the nearest destination is chosen. There must also be no closer places offering the same product, or intermediate locations, which the sociologist Stouffer (1940) calls intervening opportunities.

The geography that is built on these foundations (Abler et al. 1977) is then conceived as a science of the organization of space. This expression was coined by the French geographer Jean Gottman (1961) about the Northeast megalopolis, the group of cities that stretches from Boston to Washington. Although it is made up of distinct urban entities, whose urban structure is not continuous, this large reg...

Table of contents

• Cover
• Table of Contents
• Introduction
• 1 Complexity in Geography
• 2 Choosing Models to Explain the Dynamics of Cities and Territories
• 3 Effects of Distance and Scale Dependence in Geographical Models of Cities and Territories
• 4 Incremental Territorial Modeling
• 5 Methods for Exploring Simulation Models
• 6 Model Visualization
• References
• List of Authors
• Index
• End User License Agreement