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1999
11ème Colloque Européen de Géographie Théorique et Quantitative, Durham, Royaume-Uni, 3-7 septembre 1999
132

Potential model application and planning issues

Le modèle de potentiel : un modèle d'interaction spatiale utilisable en aménagement

Christiane Weber et Jacky Hirsch

Résumés

Le modèle de potentiel a été et reste un modèle d'interaction spatiale utilisé pour diverses problématiques en sciences humaines, cependant l'utilisation qu'en ont fait Donnay (1997,1995,1994) et Binard (1995) en introduisant des résultats de traitement d'images comme support d'application a ouvert la voie à des applications novatrice par exemple, pour la détermination de la limite urbaine ou des hinterlands locaux. Les articulations possibles entre application du modèle de potentiel en imagerie et utilisation de plans de Système d'Information Géographique ont permis l'évaluation temporelle des tendances de développement urbain (Weber,1998). Reprenant cette idée, l'étude proposée tente d'identifier les formes de développement urbain de la Communauté urbaine de Strasbourg (CUS) en tenant compte de l'occupation du sol, des caractéristiques des réseaux de communication, des réglementations urbaines et des contraintes environnementales qui pèsent sur la zone d'étude.

L'état initial de l'occupation du sol, obtenu par traitements statistiques, est utilisé comme donnée d'entrée du modèle de potentiel afin d'obtenir des surfaces de potentiel associées à des caractéristiques spatiales spécifiques soit  : l'extension de la forme urbaine, la préservation des zones naturelles ou d'agricultures, ou encore les réglementations. Les résultats sont ensuite combinés et classés.

Cette application a été menée pour confronter la méthode au développement réel de la CUS déterminé par une étude diachronique par comparaison d'images satellites (SPOT1986- SPOT1998). Afin de vérifier l'intérêt et la justesse de la méthode les résultats satellites ont été opposés à ceux issus de la classification des surfaces de potentiel. Les zones de développement identifiées en fonction du modèle de potentiel ont été confirmées par les résultats de l'analyse temporelle faite sur les images. Une différenciation de zones en fonction des résultats du modèle et de l'intégration du réseau routier a pu être établie. L'intérêt de cette approche réside dans la possibilité de fournir une information spatiale, non accessible à partir de données couramment utilisées en aménagement et qui identifie des zones propices ou non au développement en fonction de choix ou de contraintes énoncées.

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Texte intégral

Introduction

1The aims of this studyhave their basements in the understanding of the relationships between urban social system and urban spatial system ; in other words how spatial characteristics do have an effect on social system, and in counterpart how social dynamics influence spatial urban shape ? This question is from long time debated but it is interesting replace in an urban modelling frame, where urban evolution interactions are studied. In fact, analysing the population mobility and its relationships with urban space production processes, one of the points to be defined is the capacity to foresee a site’s future design layout usable in simulation application. If Krafta (1999) denied this possibility, we think it is feasible to obtain such "qualification" on urban areas using potential model application. The interest here is the introduction of dynamical trend because designing a potential force "underlying interaction among places" (Abler et al., 1972). The spatial information extracted from satellite imagery allow us to attach information on urban spots, which might be introduced in a microsimulation approach.

2Considering that the initial estate compels the future development of a zone, it is interesting to attempt to define the probability of change according a previous spatial situation. So referring to the spatial configuration at time t, it is useful for further modelling application to get information of the influence of existing features and an idea of the orientations of spatial growth. We propose to use the power of interactions modelling to get this type of information through potential modelling.

3Potential models have been applied for long time in demographic, geographic or economic studies to define the interactions between located phenomena. The principle of interactions surface obtained using different locations is particularly interesting (J.Q. Stewart et W.Warntz (1968) and measures the reciprocal influence of each location inside a defined geographical surface. A lot of applications have been done performing usual data sets, but also more recently introducing spatial information extracted from imagery by Donnay (1997, 1995, 1994), and Binard (1995) who have promoted the application of such model on remote sensing products in order to obtain urban delimitation. Another use of potential model also dealing with remotely sensed product has been the integration of potential model principles and GIS capacities to evaluate development trends of an urban settlement over years (Weber, 1998). This study has for objectives to extract urban areas defined through urban evolution characteristics (availability, suitability, and proximity...) according to an initial estate. This situation might be evaluated comparing with the real urban development obtained some years later, with another remotely sensed image.

4The paper presents the different steps of the research, first the image processing treatments and the resulting land cover surfaces, after that the potential model application is developed and discussed. GIS layouts are also added to precise the quality of the sorted areas. The results are commented and confronted to an image classification result of 1998. These results is also analysed, in order to determinate if such development can be integrate in a dynamic modelling of urban growth.

The research steps

5The research is organised in different modules in order to get several layouts usable in the potential model application (Figure 1). These different steps are linked through the results obtained and the verifications done at each step.

Figure 1 : steps of  the study

Communauté urbaine de Strasbourg (CUS) presentation

6The research presented in this paper operated on the major urban community of Alsace (East of France Region). With about 480 000 inhabitants the Communauté urbaine de Strasbourg is one of the ten major urban poles in France (population and surface). The situation of this urban area is interesting because Strasbourg has been since 1945 a frontier city delimited by the Rhin River. These historical and geographical characteristics explain the results that have been obtained and the particular trends of growth that can be observed. The urban area is constrained on the West direction by very productive agricultural zones with large farms and intensive agricultural practices. On the South and Southwest directions the agricultural production is less important and some flooding problem occur regularly. The two big protected forest areas are remaining spots of the large Rhin alluvial forests with particular species of flora and fauna. All the major network infrastructures are designed with North-South axes and only one bridge crosses the river at Strasbourg location (Figure 2. color composite image).

Figure 2. Urban community of Strasbourg

Image processing treatments

  • 1  Remotely sensed data

7The application here focuses on the extraction of an initial estate of land-use/ land-cover situation (1986). In order to get spatial information different types of methods have been applied on the remotely sensed data1. Geometric correction has been done to get an image in Lambert II georeferenced system, which is used as the majority of the cartographic products on the region.

8Statistical methods (supervised classification) have been applied to get land-cover categories according to a general nomenclature (table1). The accuracy of the result classification is around 70%. This land-cover categories layout is used to obtain two types of results :

  • One is the surface of the built areas. This surface is obtained through morphologic processing methods in order to obtain only the urban continuous zones (Weber et Hirsch, 1997). It will be compared with the results of the 1998 SPOT image

  • The other is used by the potential model application to genrate suitable surface.

Names

Definition

Surfaces 1986 ha

Surfaces 1998 ha

Continuous Urban areas

Inner-city and continuous built areas

16,22 - 3,47%

10,10 - 2,16% *

High-densely building areas

Building with 3 and more dwellings areas

14,09 - 6,48%

23,29 - 7,14%

Residential area

Individual houses areas

43,12 - 9,22%

81,77 - 17,48%

Industrial area

Building, stores and parking in industrial or commercial areas

16,37 - 3,5%

19,49 - 4,17%

Agricultural area

Fields

215 - 45,9%

112 - 23,96% *

Forest area

Protected urban forest areas

63,65 - 13,6%

46,47 - 9,93%

Meadow areas

Natural or meadow areas

77,85 - 16,6%

123 - 26,29%

Water areas

River, ponds,

21,35 - 4,57%

20,39 - 4,36%

Table 1 : Urban nomenclature : 8 categories

9The difference is due to the lack of vegetation in May (98) in comparison with June 86. The distinction between inner city and densely buildings areas is more difficult to succeed. In the individual residential areas, such situation leads to an overestimation. In agricultural areas with winter cultivation fields, the mix with meadows or natural areas implies such results.

GIS Approach

10Some cartographic layouts have been digitised to introduce some other elements, which have an impact on urban growth. In fact the choice of infrastructure network (roads and highways) is based on accessibility studies done by Faller-Schaub and Schaub (1998) and Enaux (1998) on the daily mobility travels and the allotment development in the Strasbourg suburban areas during a decade (1970-1980). This reinforces for us the necessity to introduce in the area suitability extracting process the impact of the proximity (or not) of roads or of highway nodes. Buffers have been calculated for each feature type (500 meters for the roads and 2km for the nodes) in order to locate the areas sensitive to the presence of the infrastructure (Figure 3)

Figure 3. Network buffers : roads and highways.

Layouts created on topographic Maps 1/25 000e

Networks – 2 layers

Administrative limits (Urban Community Strasbourg) – Communes layers

11Administrative limits have been integrated too, to locate the features in the urban area and to perform some statistics over the communes.

12The resulting accessibility layouts have been integrated to potential model.

Potential model application

13The potential model is usually used to describe the amount of interaction energy at each point in a region (Abler et al., 1972). As such it considers places one at time with respect to interaction potential with all other locations. It is necessary to admit Meinke postulate (1970) to perform potential model application :

14There are some interactions between all elements characterised by their masses and their locations ;

  • the interaction probability is the same for all pair of elements ;

  • the intensity of the interaction is inversely proportional to the distance

15The model has been applied by the Surfaces laboratory in Liege (B) to define particularly the urban expansion, the hinterland of urban areas in a regional frame or residential areas identification (Nadasdi et al., 1991 ; Binard et al., 1995 ; Donnay 1994, 1995). It can be interpreted as the distance influence, or proximity measurements or also as a probability and intensity measure of interaction (Nadasdi, 1988). The interesting point is that using potential model we can get a potential surface where each pixel has a value according the objectives of the study. So the calculus of the masses needed in the potential formula is directly done on the remotely sensed result, which might be considered as a gradient decreasing from high potential values to low potential values.

16The potential model applied on different land-use types might be considered as a means too precise and represent the underlying interactions through a continuous surface. This type of use has been developed by Weber et al. (1998) to define suitability areas of development combining several potential surfaces extracted from satellite imagery data at one date, the ordered potential surface can be easily compare to another satellite image result.

17The application differs slightly from the original one because the measures are done on an imagery classification result where the potential is calculated as the sum of p potential (interaction between pixel i and all the others) and the self-potential value (mass of the pixel i).

18In order to diminish the calculus of the potential value (1) is run through a moving kernel (circle) all over the initial land-use estate. The auto-potential is thus recalculates for each step (diminishing its influence) and the exponent is based on Euclidean distance according to the resolution of the image. The obtained surface considered as the resulting interactions intensity, has a quantitative scale of the values between 0 to 200. The resulting surface might be used to discriminate urban space regarding the land-use characteristics and their interactions. The kernel has a large surface of 25 pixels of radius, which is large enough to take into account the pixels influencing the central pixel value. Regarding the size of the kernel, it has to be defined according the type of features which has been studied (the size of the urban elements for instance) and the variety of the urban fabric organisation to avoid uniformity. The exponent plays like filter smoothing the distance effect (less 1) or enhancing it (more than 1), but a value of 1 is still easier for the interpretation. Others parameter are sensitive, the weights affected to the land categories. They depend on the objectives of the study, if only one category is analysed, a bivariate surface will be obtained, if the weights are affected regarding a specific logic, ordered values give the best results (Nadasdi et Binard, 1997).

Discussion of the parameters :

19The limits of potential model have been early developed regarding the only two elements taken into account, the theoretical point of view and the mass interpretation could be reviewed in such application.

  • The reduction of the interaction to a bivariate schema : here the use of Land-use type to differentiate the studied space take into account the ontological principle of a location : its co-ordinates and its semantic definition. Distance is defined through Cartesian measures through a regular grid, and Mass reflect the land-use estate of space. To introduce variation of the interactions according to other factors (weights of political decision, resistance of agricultural areas, protection of natural zones...) some specific weights are attached to land-use types.

  • Another criticism can be applied on this model utilisation, the closure of the system (Isard, 1972). In fact the studied area is bounded by the layout used but as the application runs over the totality of the image, all the locations identified are input in the model. Of course this limit cannot be really pushed away in this application, but as we work on land-use results we may consider that it is of less importance with regard to demographic or economic application.

20The weights have been fixed according general principles regarding the existence of diverse development trends in the Strasbourg area.

  • The urban fabric has a general trend to expand the urban shape and to densify the empty places inside the continuous urban area

  • The agricultural areas are still exploited when the productivity is still interesting face to another exploitation process, for instance urbanisation ;

  • The surfaces considered both by expansion and agricultural exploitation could be designed as sensitive areas ;

  • The meadow areas can be associated to the agricultural areas for the behaviour rules ;

  • The forests are in this urban zone protected and as such they have not to afford some pressure from the urban fabric ;

  • Some planning directions regarding protected areas for instance might be introduced in the model with appropriated weights.

21The idea here is to integrate different potential surfaces in order to determine the possible development trends according to the initial estate constrains. Here an image composite is obtained combining 3 potential surfaces, urban, vegetation and development constrains realised according the weights of the table 2. It could be more using a multi-criteria decision support for instance. The urban surface potential is represented (Figure 4).

Figure 4 : potential results : urban surface

Name of the categories

URBAN

VEGE

DEVPT

1

Continuous Urban areas

9

1

1

2

High-densely building areas

8

2

2

3

Residential area

6

3

4

4

Industrial area

7

3

3

5

Agricultural area

0

8

5

6

Forest area

0

10

1

7

Meadow areas

0

8

5

8

Water areas

0

0

0

Table 2 : Potential weights

22The resulting image composite (Figure 5) shows the inner city core cohesion with some concentric halos. Strasbourg centre is identified with is larger suburb (Neudorf) ; peripheral communes like Schiltigheim, Bischheim or Geispolsheim are also detectable. Less densely built areas are recognisable inside the city perimeter, it concerns some parks, place or connected zone between more dense areas, like infrastructure network places, channels ruptures, harbour areas... Around this a very carved shape envelops the zone. Some interrogations still appear regarding some gravel extraction location, because of the difficulty to discriminate it properly on the image, they have the same spectral signature than the built area on the edges. What is impressive is the large agricultural which seems to resists to the urban expansion on the Northwest of Strasbourg adversely than the Southwest areas. The protected forest in the North and the South seem to resist correctly to development trends, and some vegetated areas can be observed in the south-west and south being identified as the "Buch de l’Andlau", and the "Ried de l’Ill", two yearly flooded areas. On the German part of the image, Kehl appear as a very little spot attached to Strasbourg by the harbour infrastructures.

Figure 5 : potential images composition

Results

23The ordered image of potential result split into 4 classes, (table 3) has been combined with the built areas image extracted from morphologic treatments on remotely sensed data of 1986. This has two functions the first to compare the location of built areas and the potential classes, and the second to prepare the confrontation with 1998 SPOT data.

Potential Classes

Urban

Vegetation

Development

1

0-0

150-200

150-200

2

1-25

150-200

150-200

3

1-25

25-75

50-150

100-150

100-200

150-200

4

25-75

75-150

50-100

100-200

100-200

100-200

Table 3 : Potential suitability Classes values

Images and potential results confrontation

24The confrontation of the dates allows defining where the real extension zones are located and to confirm that the changes have taken place inside the potential ordered bandwidth. It has to be noted that some misclassification results may confuse the interpretation, it is the reason why morphological treatments have been applied, but some still remain like field’s edges or channel banks or network tracks. Nevertheless the comparison between 1986-1998 (Figure 6) produces a rather successful result ; all the expansion and densification areas take place inside the identified suitability zones. The most noticeable features are industrial areas, which have a very strong development in the North and the Southwest direction, or along the highway and the allotment creation zones that increase in suburban areas. The stability of the agricultural area is interesting because it shows very well the resistance effect of this sub-region ; the fact that they have not really high value of suitability demonstrates also the compacity of the villages.

Figure 6 : confrontation potential classification and 1998 estate

25In addition the network buffers layout has been integrated to stress the accessibility of the studied zone (Figure 7 and 8). One first point is that there is only one link from France and Germany in this part of Alsace (another bridge is under construction), and this completely influences the representation of the layout turned toward the west. According to the buffers distance very few areas are out of connection (only the forest, some agricultural ills, or yearly flooded areas. What is noticeable here is the importance of highway nodes for industrial location, in the North and in the Southwest for instance.

Figure 7 : Accessibility and potential surfaces : 1998 built areas

Figure 7 : Accessibility and potential surfaces : 1998 built areas

Figure 8 : accessibility and potential surfaces : 1998 built surfaces

Conclusion

26This application has confirmed the interest of potential modelling approach in suitability development areas design. Of course this is strongly bounded with the hypotheses defined with the weights valuation. In this case the factors defined are linked with land-use categories and constraints are accessibility rules associated with the buffers and the combination of the weights itself.

27Some other weights might be integrated (land prices, risk areas delimitation….) to better fit with urban development reality.

28Another interesting point is the ease to reproduce such application on any land-use categories surface.

29The next step will be to integrate this type of suitability values surface as an element in an AC modelling or SMA zone valuation to get a feasible migration areas distribution regarding dwellings construction possibility in diverse areas. This information could be very interesting in the valuation of the installation zone in some residential migrations and linked spatial organisation modelling.

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Bibliographie

Abler, Adams & Gould, 1972, Spatial Organization. Prentice Hall International editions. 587 p.

Binard M. and all., 1995, Etudes multi-échelles : applications aux agglomérations du nord-ouest de l’Europe. in Télédétection des milieux urbains et péri-urbains. AUPELF. Presses de l’Université du Québec, 15-23.

Donnay J.P. et Lambinon M., 1997, Détermination des limites de l’agglomération par télédétection : discussion méthodologique et application au cas de Huy (Belgique). in Télédétection des milieux urbains et péri-urbains. AUPELF. Presses de l’Université du Québec, 239-246.

Donnay J.P., 1995, Délimitation de l’hinterland des agglomérations urbaines au départ d’une image de télédétection. Revue Belge de géographie. Vol 119, 325-331.

Donnay J.P., 1994, Agglomérations morphologiques et fonctionnelles, l’apport de la télédétection urbaine. Acta Geographica Lovaniensia. Vol 34, 191-199.

Enaux C., 1998, Essai de modélisation spatio-temporelle des flux de déplcements de travail. Exemple de la région urbaine strasbourgeoise de 1975 ) 1990. Thèse. Université Louis Pasteur. 266 p. + annexes.

Isard W , 1979, Strategic events of a theory of major structural change. Papers of Regional Sciences Association,1-14.

Krafta R., 1999, Spatial self-organization and the production of city. (http ://193.55.107.3)

Nadasdi I., 1971, Surface de potentiel de la population de la province de Liège. Exemple d’application de la transformation des champs géographiques discrets en champs continus. Bulletin de la Société Géogrraphique de Liège, 7, 51-60.

Nadasdi I., Binard M. and Donnay JP., 1991, Transcription des usages du sol par le modèle de potentiel. Mappemonde, 3, 27-31.

Rousselet C., 1998, Calibrage du modèle de potentiel aux images de télédétection. Applications urbaines et régionales. Université de Liège. Mémoire de licence. 90 p.

Faller-Schaub M. and Schaub G., 1998, Coalescence et lôtissements. In L’espace des villes. Pour une synergie multistrates. Anthropos, 49-60.

Stewart J.Q. and Warntz W., 1968, Physics of population distribution. Journal of Regional Science. Vol.1, 99-123.

Stouffer SA., 1940, Intervening opportunities a theory relating mobility and distance. Am.Sociological Review.Vol V. n°6., 845-867.

Weber C., 1998, La croissance urbaine de Kavala, évolution et perspectives. SFPT. n°151, 29-37

Weber C. et Hirsch J., 1997, Processus de croissance et limites urbaines.PHOTO-INTERPRETATION, Vol.1-2., 21-33.

Weber C., 1997. Croissance urbaine. Détermination des paramètres de croissance urbaine en vue d’une modélisation : le cas de KAVALA (Grèce). Rapport PNTS (95N71/1061). 50 p + figures.

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Notes

1  Remotely sensed data

SPOT XS - HRV1 1986 / Ref : KJ 50-252 / date 28/06/1986, spatial resolution : 20m

SPOT XS - HRV1 1998 /Ref : KJ 51-252 / date 11/05/1998, spatial resolution : 20m

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Table des illustrations

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Titre Figure 7 : Accessibility and potential surfaces : 1998 built areas
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Référence électronique

Christiane Weber et Jacky Hirsch, « Potential model application and planning issues  », Cybergeo : European Journal of Geography [En ligne], Dossiers, document 132, mis en ligne le 29 mars 2000, consulté le 21 novembre 2017. URL : http://cybergeo.revues.org/889 ; DOI : 10.4000/cybergeo.889

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Auteurs

Christiane Weber

IMAGE et VILLE UPRES-A 7011 CNRSchris@lorraine.u-strasbg.fr

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Jacky Hirsch

IMAGE et VILLE UPRES-A 7011 CNRSjacky@lorraine.u-strasbg.fr

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