Urban sprawl modelling _ A methodological approach

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Cybergeo : European Journal of Geography

12me Colloque Europen de Gographie Thorique etQuantitative, St-Valry-en-Caux, France, 7-11 septembre 2001

Jean-Philippe ANTONI

Urban sprawl modelling : Amethodological approach

Modlisation de l'talement urbain : une approche mthodologique

[@article] 207

ABSTRACT/RSUM

The urban sprawl is usually associated with the idea of unsuitable development. It depends on numerous simultaneous processeswhich make it difficult to deal with. Its modelling appears then an interesting means to understand it and to run simulations, according

to different scenarios of urban development, for making planning decisions. The methodological approach presented here combinesthree steps. Each one corresponds to a model : the first step deals with the quantification of the sprawl (transition model), the secondwith its location (potential model), and the third one with its differentiation (cellular automata). These three steps are associated to aspatio-temporal database, using a grid to store the needed information within a GIS.

Ltalement urbain est gnralement considr comme peu profitable au dveloppement des villes. Il associe plusieurs processusqui agissent simultanment et qui le rendent di fficile matriser. Sa modlisation apparat alors comme un outil intressant pourmieux le comprendre et pour simuler diffrents scnarii de dveloppement utiles lamnagement. Lapproche mthodologiqueprsente ici combine trois tapes. Chacune des tapes correspond un modle : la premire quantifie ltalement (modle de

transition), la deuxime le localise (modle de potentiel), et la troisime le diffrencie (automate cellulaire). Les trois tapessassocient une base de donnes spatio-temporelle qui utilise le carroyage pour stocker lintgralit des informations ncessairesdans une couche SIG unique.

PLAN

Processing the data structure

Collecting raw data

Storing the information

Thematic and technical criteria to reach a pertinent scale

Three steps for modeling the urban sprawl

To quantify the urban sprawl : a transition model

To locate the urban sprawl : a potential model

Conclusion : towards the third step

TEXTE INTGRALPDF

Urban sprawl is frequently associated with the idea of an unsuitable development, leading to increasing

economic, social and environmental problems. Moreover, its control is difficult because it combines

multiple overlapping patterns relaying on numerous traditional urban planning fields. So, considering

urban sprawl usually demands to take into account several patterns including numerous

sociodemographic indicators, as density or family size. Here, it will only be considered in itsmorphological aspects, as a combination between built and non-built areas. Thus, urban sprawl process

will be defined as the spatial expansion of the built areas of a city through time. Modelling appears a

useful means to understand and manage its complexity. The urban area of Belfort (North-East of

France, approximatively 80000 inhabitants in 1999) seems an interesting area for measuring the sprawl

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an sprawl modelling : A methodological approach http://cybergeo.revues.org/4188

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quantification of the urban expansion caused by the urban sprawl process (question "how

much ?")

location of the expansion according to the geographic characteristics of the peri-urban outskirts

(question "where ?")

differentiation of the located expansion in order to determine which kind of land use will be

generated in each location (question "what ?") 1. However, first of all, a solid database isneeded in order to apply the models described in each step (fig. 1).

Figure 1 :Three methodological steps to construct a global model

to collect and store data taking into account the sprawl process scale

to develop a tool in order to query and analyse data in a spatio-temporal way.

Processing the data structure

Collecting raw data

Urban sprawl has to be considered within a temporal dimension to be understood as a process.

The Belfort Agency proposes to study it from the 50s, considering the rural depopulation

(1954-1968) and the massive peri-urbanization (1968-1999) statistically measured by the French

statistics institute (INSEE) 2 for the Belfort area, and more generally for France ;

Measuring the urban sprawl requires to consider space at the urban-block scale or at the

individual house scale, and not at the community scale as in the available censuses : the land use

process since the 50s, and simulate scenarios of expansion towards 2015. The model is developed

within a three-year collaboration with the Agence durbanisme du Territoire de Belfort (urban planning

agency). Their aim is to collect data and test the models operational feature, according to their planning

issues. Concerning the urban sprawl and the planning problems, the model must answer to three

questions about the future urban growth to help decision-making : how much ? where ? what ?

The aim of this paper is then to present a methodological approach to model the urban sprawl process.

It deals with the construction of a global model based on three successive steps. Each step

corresponds to a model with a precise goal :

2

Constructing such a database will allow to achieve two important goals :3

The construction of the database stresses different questions which have to be answered and validated.

The first one is about collecting raw data : what kind of information is needed ? How to get it ? The

second one is about storing the data : is there a database structure allowing to organize it in order toprocess easily and quickly ? At last, we will assess the technical and thematic uses of the database :

which criteria should we favour ? Is it possible to find a compromise according to both uses ? Of

course, the answers to these questions must be included in a Geographical Information System (GIS)

approach, considered as a generic tool for collecting, storing and analyzing spatial data.

4

According to the goal of the model, two important facts have to be considered :5


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changes introduced by peri-urbanization cannot by visualized at a small scale and demand to use

precise indicators. To find information corresponding to these major goals, three data sources

can usually be used : satellite imagery, aerial photographs and topographic maps.

Figure 2 : Land use categories 4The Ct row corresponds to the codage in the database. It will be described in section 1.2.

Storing the information

Satellite images, with high (or very high) spatial resolution, appear like one of the most interesting data

source (Puissant, 2000). But, in our case, they do not exist before the 70s and do not allow to consider

the early time of the process. Aerial photographs exist since the beginning of the century, but only a few

photographic coverages are available on the study area : we have a first coverage in 1954 and a

second one in 1992. No coverage is available between these dates. Then, the more complete sourcesof information for considering urban sprawl through time seem to be the different topographic maps

produced at three dates (1955, 1975 and 1995) 3 by the French national geographic institute (IGN).These maps cover regularly the study area : one map a twenty-year period. Nevertheless, with only

these sources, the thematic choice of the data is strongly determined by its representation on the map.

The discrimination of the land use categories related to the urban sprawl process is then a delicate

operation : they must be represented on each map in order to be regularly considered for the encoding.

According to the map keys, thirteen land use categories only appear systematically for the three dates.

For the more recent date (1995), they have been checked and completed by field surveys. The chosen

land use categories include natural areas, built areas, and networks (fig. 2) :

6

In order to study the urban sprawl process, we must be able to visualize the land use transformations of

urban and peri-urban areas, and to compare these transformations from one location to another and

from one date to another. So, the problem is how to harmonize this disparate raw data for obtaining

comparable information in space and time. Using a tessellation appears an interesting solution for

collecting and storing the information.

7

Tessellation consists in transforming continuous original mapped data into discreet spatial data within

regular (squares, hexagons) or irregular polygons (Thiessen polygons). In our case, a regular mesh

seems adapted and square cells appear the simplest geometric form to generate it. The result of the

tessellation is a lattice. To make it easier, we call it a grid. Such a grid makes it possible to consider the

geographic information inside the cells, whatever its date and its source. Through the grid, the threegeoreferenced maps allow to visualize the land use for each cell at the three dates (1955, 1975 and

1995). A rasterization (vector to raster conversion) could then be an interesting solution. But, technically,

considering that the only software used during our collaboration with theAgence durbanisme is a vector

GIS, this operation must be processed in a vector mode. Then, we have to think about creating vector

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create cells as small as possible (thematic criterion)

reduce their number (technical criterion).

Thematic and technical criteria to reach a pertinent scale

square cells and using vector GIS structure for the tessellation. We chose to manage spatial information

in polygons S (a regular grid of square cells covering continuously the study area) associated with

temporal information (stored in a table of attributes Ctcorresponding to each polygon) :

S (x, y, Ct1,

, Ctn

)9

x,y : geographical coordinates10

n = 3, t1 = 55, t2 = 75, t3 = 9511

After digitising the maps, the grid encoding (space) for each date (time) is automatically done by a

spatial request (GIS request). The cells geographic location is given by their coordinates (x,y), and their

land use for each date is given by their attributes (Ct). Each polygon is associated with three attributes,

C55

, C75

and C95

corresponding to their land use category in 1955, 1975, and 1995. The consequence

of using such a vector structure is that the whole data is stored in a unique GIS layer, while a raster

technique would need one layer for each date. The disadvantage is that the structure is heavier than

raster and can quickly lead to technical data-processing problems.

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Nevertheless, using vector or raster mode, the tessellation stresses the important question of the cells

size : the efficiency (and also consistency and quality) of the database depends on it. On the one hand,the smaller the cells are, the more precise and efficient the database will be. But, on the other hand, if

the cells are very small, they are numerous and they make the database less easy to consult (this is one

of the major problems induced by the vector GIS structure). The database may quickly need too much

computing resources and finally it may be difficult to handle in a prospective way. This is why we chose

to determine the optimal size of the cells according to the following objectives :

13

Four spatial resolutions have been tested on a test-field : 200, 100, 50, and 25 meters corresponding

respectively to 4 ha, 1 ha, 0,25 ha and 0,0625 ha for each cell. The fifty-meters resolution seems the

more interesting. It reproduces the urban morphology in a correct way and produces 160000 cells. Of

course, the test results depend very much on the test fields distinctive features. We are presently

reproducing the same exercise on other test fields, in order to eliminate these features and to validate

the choice of a fifty-meters resolution. The first results seem to confirm it. Then, with such a resolution,

the amount of cells is important but may still be handled with a GIS set up on a powerful computer. So,

this choice is based on a thematic criterion (characterization of the morphological urban area) but also

on a technical criterion (construction of a database easy to handle). It appears as a compromise linking

the thematic analysis of the sprawl process and the optimization of calculations and simulations speed

processes. This choice should lead to construct a tool allowing both to improve urban sprawl knowledge

and to run quickly useful simulations for making planning decisions. With thirteen land use categories and

a fifty-meters resolution, the grid database allows to quantify the importance of each category for each

date within cells of 0,25 ha. For example, it shows with a rather good precision that the built area of

Belfort grows constantly (fig. 3) :

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Figure 3 : Morphological growth of Belfort

Figure 4 : Evolution of the urban morphology

Three steps for modeling the urban sprawl

Processing the database allows then to map the urban morphology through t ime (fig. 4) and grid

mapping appears an interesting method to quantify the built-area limits and to represent the evolution of

the built / non-built ratio. This operation consists of a simple GIS request, searching for the residential

and non-residential built cells, (Ct= 4, 5, 6, 7, 8 and 9 for each date, cf. fig. 2).

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To quantify the urban sprawl : a transition model

Figure 5 : Contingency tableN : number of cells which changed from one category to another between t and t+1

The whole information concerning the land use changes can then be queried through space and time

within a unique GIS layer. But, the vector structure which has been used at the beginning in order to

harmonize data, offers now an interesting grid to run different models. We can use it to apply

successively three models, based on principles as different as gravity or Artificial Distributed

Intelligence. Each one will be applied to approach a particular part of the urban sprawl global model.

16

If we systematically reproduce the request described in the section 1.3, the quantification of every land

use changes is easy. For example, we can search the cells containing forest areas in 1955 (c55

= 2),

considered as open spaces in 1975 (c75

= 1) and occupied by individual houses in 1995 (c95

= 4). Such

an exercise leads quickly to the construction of two contingency tables, displaying the transformations

between 1955 and 1975 and between 1975 and 1995. It consists in counting cells which changed during

the two periods and storing the results within two 13*13 tables linking the land use categories at the

date t and t+1 (fig. 5) :

17

These land use changes can be visualized through a graphic, showing the complexity of past transitions

(fig. 6). Apart from particular cases as highway nodes (Ct

= 12), there are few transition impossibilities.

The non-symmetry of the two parts indicates that changes have a tendency to stabilize in the second

period : the possibilities of transition are less important during 1975-1995 than during 1955-1975. To

make it easier, it is now possible to reduce this complexity by considering the transitions in relation to

their occurrence probability, and not only in relation to their presence (in a binary way). From the

frequencies extracted from the database, it is possible to calculate the probability of each cell to movefrom one category to another, in order to create two transition matrices. The importance of the

probabilities shown by the diagonal of the matrices demonstrates that a significant inertia force exists

and that it is most important in the second period than in the first one (fig. 6). Although almost all land

use transformations are possible, the majority of the cells do not change from 1975 to 1995.

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Figure 6 : Graphic of observed transitions through time and transition matrices(Blank cells correspond to null probabilities)

Figure 7 : Generation of a homogeneous matrix of transition and simulation in 2015

From the two transition matrices, it is possible to estimate the transitions corresponding to the Belforturban morphology towards 2015. This operation requires the use of a transition model, taking into

account the stabilization of the transformation probabilities observed over the graphic and the second

transition matrix diagonal (1975-1995). For example, we can test linear regressions and other methods

relying on Markov processes (Collins, 1975). The comparison and the interpretation of the results

obtained with these models depend strongly on the related hypotheses, but each one predicts precisely

the land use categories which will increase or decrease. Then for instance, by summing up the two

transition matrices weighted by their effectives on each line (Berchtold, 1998), we can create a

homogeneous matrix representing the general trend of changes (fig. 7).

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Figure 8 : Estimation of the future urban expansion (brought down to 1)

To locate the urban sprawl : a potential model

urban expansion creates an interaction between new and old urban spaces which can be

considered as complementary spaces

urban expansion is based on the minimization of the mathematical distances between the

concerned cells

urban expansion favors the best solutions by testing all the possibilities of complementarities and

distances.

Of course, this method is based on the assumption that the changes follow a trend which is similar

through time (1955-2015), and that it can be determined from the two previous periods (1955-1975,

1975-1995). Using this general trend, we can then calculate the probable transitions between 1995 and

2015, and determine the number of cells of each category that will compose the study area in 2015

(fig. 7). This method seems quite interesting to estimate the future land use changes (fig. 8) but does

not bring any information about the location of the cells that will be built. This is why to consider the

changes, we have to complete this first step with a second one introducing spatial dimension, in order to

locate the areas involved in urban sprawl.

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Different spatial models can be used to locate the n cells that will be built in 2015 (n being defined in the

first step). For instance, we can use a potential model (cf. Weber, 1997, 1998). It takes simultaneously

into account the complementarities between each cell and the rest, their respective distances, and the

intervening opportunities existing on the area, as it usually appears in spatial interaction models (Abler

and al., 1972). This way, the potential model assumes that :

21

In order to better explain, we will take an example using one of the most simple equations of the

potential model, and will consider only the open space cells (Ct= 1) 5 :

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P

i= potential value of the cell i,

mj = mass value of the cell j,

dij = distance from i to j

Figure 9 : Locations obtained by the potential modelm values used for calculation (from Ct=1 to Ct=13) : 0 0 0 3 2 2 2 2 0 2 4 0 0 ; radius of calculation : 300 meters

Conclusion : towards the third step

Calibrating such a model means defining the mass values m corresponding to the land use category of

each cell j. Empirically, we will use intuitive values according to the presumed attractiveness of each

category and we will try to validate them by running the model on the known past periods : from the

initial state 1975, we will try to find the initial state 1995. So, the last map shows the location of the n

cells corresponding to the most important potential values for the 1975-1995 period obtained by

modeling (fig. 9). These n cells should correspond to the ones which have been built during the same

period. The results are quite relevant : about 25% of the simulated cells are located in the same location

as observed cells, and about 90% are located within a radius of 200 meters.

23

A method based on multiple-correspondence analysis (Lebart and al., 1997) is currently under

development to measure the nature of neighbor cells around the cells built between 1955 and 1975, and

between 1975 and 1995, within different radii. This should help to determine the mass values m.

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At this stage, the approach allows to locate the n cells that should change from a non-built category to a

built category, but we cannot describe more precisely the changes. For instance, we cannot know if the

n (step 1) located (step 2) cells concerned with urban sprawl will be residential-, industrial units or

facilities. This discrimination remains to be done. The recent works in urban geography, using techniques

issued from Artificial Distributed Intelligence, offer a new conceptual framework to approach this kind of

problems (Langlois, Phipps, 1997). Here, cellular automata seem an interesting tool to determine the

land use category of the cells located in step 2. Cellular automata should assume that the category of

the cells is determined by its neighborhood, actually by the categories of the neighbor cells. In fact, the

analysis of the neighborhood should allow to define some transition rules that could be applied to thenon-defined cells to choose their category. Of course, the biggest problem is the definition of pertinent

rules. At first, they can be determined by empirical tests, according to the users estimation. Then, a

statistical method should be developed to construct a set of rules firmly relying on quantified

observations (it could be quite similar to the method developed for the calibration of the potential model,

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BIBLIOGRAPHIE

Abler R, J.S. Adams, Gould P., 1972, Spatial organization : the geographers view of the world,

Prentice Hall International, 587 p.

Berchtold A., 1998, Chanes de Markov et modles de transition. Application, aux sciences sociales,

Hermes, 284 p.

Collins L., 1975,An introduction to Markov chain analysis, Catmog, n1, 36 p.

Langlois A., Phipps M., 1997, Automates cellulaires. Application la simulation urbaine. Herms, 197

p.

Lebart L., Morineau A., Piron M., 1997, Statistique exploratoire multidimensionnelle, Dunod, 439 p.

Puissant A., Weber C, 2000, Potentialities of very high spatial resolution image to identify urban

fabrics, Geocarto International, 12 p (in press)

Weber C., 1998, La croissance urbaine de Kavala. Evolutions et perspectives, 11 pages. In : Socit

franaise de photogrammtrie, n151, 1998, pp. 29-39.

Weber C., Hirsch J., 1997, Potential model applications in planning issues, 11th European Colloquium

on Quantitative and Theoretical Geography. Cybergeo n158, 5 May 2000 :

http://www.cybergeo.presse.fr/teldschu/weber/weber.htm

NOTES

1 At this time, the third step uses cellular automata, but leaves other ways open to answer the question "what ?".

2 The dates correspond to the French censuses.

3 Actually, the mapped information for 1955 is based on 4 sheets drawn between 1954 and 1957 by the IGN ; the mapped

information for 1975 is based on 4 sheets drawn between 1974 and 1977 by the IGN. The information for 1995 is a numeric file (IGNscan25) updated in 1995.

4 The names of some categories are very difficult to translate from French into English : they often correspond to an administrativehierarchy which has no strict equivalent in English-speaking countries (e.g. roads). Concerning the residential built areas, individualhousing (Ct = 4) corresponds to individual houses surrounded by gardens, urban buildings (Ct = 5) correspond to traditional urban

continuous buildings, and estate housing (C t = 6) correspond to high rise buildings with high density of population. We can note here

that highways and rai ls are considered as punctual elements, and measured using highway accesses and railways stations only. Thisstructure has been studied in order to take into account the real accessibility offered by the networks : roads are usually accessible

from any part of their linear implantation ; but highways are only reachable via punctual connections (as stations or nodes). Thisconsideration will be interesting for using the potential model which considers the attractiveness allowed by each network.

5 This calculation is computed in a software developed by Olivier Klein in Image et Ville laboratory, and named P2C2 (Programme Potentiel Calcul Carroyage). This program can be fed with several parameters, such as local weighting for the mass values and

local weighting taking into account the regulations issued by the code de lurbanisme. It can also locally block or promote the urban

sprawl model. These options have not been used in the example presented here.

6 The first matrix (initial state) contains only the land use information. That means that to take into account other kind of data, thecellular automata must be able to read information stored in a second, perhaps a third or a fourth (etc.) matrix. Such a prototype ofcellular automaton is currently developed by the Image et Vi lle laboratory.

cf. section 2.2). Finally, it will be interesting to integrate administrative information or legislation (that

means information not directly concerning the land use) so as to refine the transition rules 6.

By associating these three steps, the methodological approach presented here can be associated to an

imbrication of models. The final global model is not yet completed but should correspond to an

interesting solution allowing to understand the urban sprawl and the role of the neighborhood (and its

attractiveness) in the process. It should allow to run simulations easily. The parameters needed for

these simulations can be modified at each step, according to the hypotheses given by the scenarios :

modification of the general trend (step 1), of the global attractiveness (step 2), of the neighborhoodsrole (step 3). In any case, the use of a grid database developed within GIS allows every possible

continuation in modeling. From collecting to encoding spatio-temporal data to calculating complex

simulations, grid mapping can be used efficiently at every step.

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POUR CITER CET ARTICLE

Jean-Philippe ANTONI, Urban sprawl modelling : A methodological approach , Cybergeo : European Journal of Geography, 12th

European Colloquium on Quantitative and Theoretical Geography.St-Valery-en-Caux, France, September 7-11, 2001. St-Valery-en-Caux, France, September 7-11, 2001, article 207, mis en ligne le 01 mars 2002, modifi le 21 fvrier 2007.URL : http://cybergeo.revues.org/4188. Consult le 07 mars 2011.

AUTEUR

Jean-Philippe ANTONI

Laboratoire Image et Ville, CNRS UMR 7011 Universit Louis Pasteur, Strasbourg I

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Urban sprawl modelling _ A methodological approach

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