28 Measurement and Analysis of Spatial Interaction

Dr. Madhushree Das

1.0 Introduction:

Spatial interaction is the interaction between places on the basis of movement of products, people, services, etc in response to localized supply and demand. It is a dynamic flow process from one location to another. It is a transportation supply and demand relationship that is often expressed over a geographical space. In other words, it can be described as a realized movement of people, freight or information between an origin and a destination. Spatial interaction covers a wide variety of movements such as journey to work, migration, tourism, the usage of public facilities, the transmission of information or capital, the market areas of retailing activities, international

trade and freight distribution. Economic activities are generating (supply) and attracting (demand) flows. The simple fact that a movement occurs between an origin and a destination, underlines that the costs incurred by a spatial interaction are lower than the benefits derived from such an interaction. As such, a commuter is willing to drive one hour because this interaction is linked to an income, while international trade concept such as comparative advantage underlines the benefits of specialization and the ensuing generation of trade flows between distant locations. Spatial interaction usually includes a variety of movements such as travel, migration, transmission of information, journeys to work or shopping, retailing activities, or freight distribution. Thus, it is a transport demand/supply relationship expressed over a geographical space.

In addition, most spatial interaction models attempt to predict the movement of people or goods in terms of two basic factors, although some models incorporate additional explanatory variables. These two basic factors are:

the distance, travel time or more generally, impedance between the two locations and the size or some measure or prediction of the total amount of people or goods attracted to each candidate destination

Additional explanatory variables that have been incorporated in more complex models include:

• Accessibilities, to capture spatial autocorrelation and/or agglomeration effects, convenience or centrality,
• Psychological Boundaries, such as rivers, ridge lines, railroad tracks or even major highways which decrease the probability of interaction,
• Demographic Attributes, such as the income, age or employment status of travelers,
• Destination Qualities (other than its size or the number of attractions) such as its walkability, diversity of land uses, etc., and
• K-Factors and Other Spatial Bias Factors, which are not explanatory variables, but fixed factors to account for unexplained patterns.

It may be stated that transportation and communication systems are created or improved only after there is a demand which the new systems will satisfy.Improvement intransport systemfostered the increased interactions, but they were not solely responsible for them. The leading geographers Edward L. Ullmanwho worked ontransport geography in the twentieth century,postulated three conditions affecting transportation development.Which are the Fundamental conditions governing all forms of spatial interaction.

They are therefore: complementarity, intervening opportunity, and transferability. Let us examine each condition in turn.

1.1: Complementarity(the actual or potential relationship between two places, usually referring to economic interactions. Clearly demonstrated in the movement of crude / refined petroleum in int’l trade)

Traditionally, it was assumed that interaction between the places developed because of areal differentiation in their socio economic conditions and different geographical background – the fact that places differed from one another. This is true to some extent of course, but mere differentiation never produces interaction by itself. For two places to interact, there must be a differentiation in demand and the supply of goods between the places. Since the demand and the supply must be specifically complementary to each other, interaction among them takes place. To take an absurd example as an illustration, if there is a shortage of meat in place A, it makes little  difference that there is a marketable surplus of pulpwood in place B. The two commodities are not substitute to each other, and a flow of wood from B to A will not come about because of A’s meat requirements. The two places lack specific Complementarity (Abler, Adam and Gould)

Complementarity is so important as a basis for spatial interaction that many very low value bulk commodities can move thousands of kilometres if complementarity conditions are properly satisfied. Grain from continental interiors move to sea ports, and from the ports moves by inexpensive ocean transport to markets of the other side of the world. Crude and refined petroleum products –commodities of relatively low value per unit of bulk – move enormous distances, from oil fields in the Middle East, the Canadian Prairies, and Venezuela to industrialized areas of Europe, Japan and North America. When steel mills were built in the Chicago region, the need for coking coal was great enough to draw supplies from West Virginia despite the relatively low value of the coal and a distance overland of more than eight hundred kilometres. Without the specific complementarity of each supply and demand regions, the movement and interaction would never have taken place.

1.2: Intervening Opportunity (the presence of a nearer opportunity that greatly diminishes the attractiveness of sites farther away)

Complementarily between places can generate interchange only in the absence of intervening opportunities. If we are considering the potential for a movement of goods from place A to place B,we have to consider any place C between them which might act as an intervening origin or an alternative destination. For example, Sikkim is closer to Guwahati than to Simla in Himachal Pradesh, so for Guwahateans anxious to take a summer holiday to a hill station, Sikkim constitutes an intervening opportunity between Guwahati and Simla.

Intervening opportunities do not always curtail long distance interactions. It is entirely possible that a sequence of such opportunities can help to create interactions between widely separated areas by making immediate transport links profitable and thereby paying part of the costs of the link between distant places. In a sense, intervening opportunities are like spatial sponges soaking up potential interaction between complementary places.

1.3: Transferability(the ease or difficulty in which a good may be transported from one area to  another. It is a function of 3 conditions: value/characteristic of the product, distance measured in  time & money, and ability of the item to bear the cost of movement. if the time / cost of moving over distance is too much, exchange cannot occur)

Besides complementarities and intervening opportunity, the third condition under which spatial interaction occurs is transferability – the friction of distance. Transferability is measured in real time and money costs. If the time and money costs of traversing a distance are too large, the movement will not take place despite of perfect complementarity and the absence of intervening opportunities. Instead of reaping the benefits of interaction, people will stay where they are and continue unchanged the life that they know. If goods cannot move because of their high cost of their movement, other goods will be substituted if possible or people will just go without. Transferability differs between places, between classes of movements and between modes of movement and even changes with time.

Thus, spatial interaction systems are influenced by three factors: (1) complementarity, depending on areal differentiation, which results in a supply at one place meeting a specific demand at another place; (2) the intervening opportunities between places; (3) transferability measured in time and money costs. When spatial interactions occur, it is because each of these conditions has been satisfied. If two places have no interaction with each other, we can usually point to one or more of these factors as the reason.Thus, the amount of interaction (migration, travel,) between two places depends upon: the distance between two places, the attractiveness of each place and the availability of “intervening opportunities.

2.0 There are two basic types of Interaction Model

Gravity  model.  Measures  interactions  between  all  the  possible  location  pairs.A mathematical formula that describes the level of interaction between two places, based on the size of their populations and their distance from each other.

Potential model. Measures interaction of one location with remaining other locations.It provides an estimate of the interaction opportunities available to a center of a network

2.1 Gravity model: (The gravity model is the most common spatial interaction model in travel forecasting).

Gravity model as a measure of interaction has been derived from Newton’s Law of Gravitation in physics. This principle of Gravity model was first introduced in geography by Stewart, a social scientist. As applied in geography, it states that the interaction between two places (iand j) is directly proportional to the product of their population and inversely proportional to the distance between them

It is exemplified by taking case of interaction of the literate population of Guwahati city with its surrounding towns located in the part of Brahmaputra plains. It is assumed that literacy determines the intensity of people interaction in the towns in this region.

As per given model (Equations- 1and 2),the data of two attributes, namely the size of population and distance between the towns are required to find out the intensity of population interaction of Guwahati city with the neighbouring urban centres and of Dibrugarh town of Upper Brahmaputra Valley for the purpose of comparison of interaction pattern.It is to note that Brahamaputra plain is ahomogeneous tract of land and formed with the new alluvial soils. The economy of the plain is largely dependent on agricultural activities. However, these towns having historical impact on their economies and petroleum products and oil refineries are non-agricultural activities performed in this region and have implicit impact on spatial interaction among towns. The emerging pattern of spatial interaction is comparable to search the causes of such emerging phenomena in the region. Two examples are taken for the purpose.

2.1.1: Example-1: the Middle part of Brahmaputra plain: Data of the magnitude of literate population and their distance of seven urban centres of Kamrup district that is located in the middle part of the plains are collected from government offices. It is given below:

Table-1: Literates of different towns in Kamrup District

Table -2: Road distance (in kilometres) among the towns

2.1.2: Use of Spatial Interaction model:Quantitative form of the model with respect to the present case of seven towns and for simplicity assuming b=1 and G=1 is as given below:

    Where P1,…,P7 are the size of town population and d is distance between them.

Interaction between the pairs of points was calculated in the following manner:

As we know,

Guwahati  literate  population = 412.733  thousand personsRangia literate  population =

13.690 thousand persons

Distance between Rangia and Guwahati = 52 km.

In the same way the interaction between all the other urban centres with Guwahati town have been calculated as given below.

Fig.-1 Population interaction of Guwahati city with neighbouring urban centers, 1991.

2.2: Example-2: the Upper part of Brahmaputra plains: Data of two attributes, population and distances of all 4 towns of Dibrugarh district were collected (Table-3 and 4)

Table-3: Population of different towns in Dibrugarh District, 1991

Table-4: Road distance (in kilometres) among the towns.

and interactionbetween Dibrugarh and remaining three towns of Dibrugarh district were shown(Figs.- 3 and4). Applying Gravity model, the following population interaction were calculated as given below:

DIBRUGARH

Fig.-2: Population interaction map of Dibrugarh town with neighbouring urban centres, 1991

2.4: Interpretation:

In the middle part of Brahmaputra plains, a general spatial pattern of population interaction shows that Rangia and North Guwahati towns have maximum interaction with Guwahati- a regional centre of the North Eastern part of India. Noonmati oil refineryof the north Guwahati and military centre located in Rangia are major reasons behind interaction in this area.

On the other hand, in the Upper part of Brahmaputra plains, petroleum products and oil refinery are major activities located in Dibrugarh town that attract the population of nearby towns. Dhuliajan – a closely located town, has highest degree of interaction with Dibrugarh. Distance and good transport connectivity are main reasons of higher degree of interaction in this region.

3.0: Use of Potential model:

An important point to note here is that, for every Vi there is a term involving dii i.e. d11 , d22 , …..relating to the interaction of an area with itself. Since dii is always = 0, it is replaced by half of its distance with the nearest. Thus for V1 we have the following:

Fig.-3: Population Potential map of Kamrup district, 1991.

value for Rangia. In the same way, population potential values for other centres of Kamrup District were calculated as:

Following the same method the population potential values for Dibrugarh town and other centres are calculated.

     On the basis of the above calculated population potential values,the urban potential maps of Kamrupand Dibrugarh districts have been prepared using iso-potential lines joining places with equal population potential values (Figs.-3)

Fig.-4: Population potential map of Dibrugarh district, 1991

The potential values as shown from the above figures indicates a much larger potential at Guwahati – the capital city with a population potential value of 56613 persons/km2. It is followed by Amingaon and North Guwahati with the potential value of 31301.37 and 27429 persons/km2. Distance has a great impact on the values of population potential. In Dibrugarh District, it is interesting to note that population potential value is highest in Duliajan town (6444persons/km2)as it is an oil township attracting heterogeneous population from North East and all over India,followed by Dibrugarh 6251,Naharkatia 5334 and Namrup 3261 persons/km2.

4.0: Summary:

Spatial interaction among the townsis described by measuring it into two ways using Gravity model and population potential model. These models are mainly dependent on two attributes of urban places: the functional/population size of town which accelerates the process of attraction provided town functions (goods and services) are complementary among the towns, and the distance among towns that generally is considered in its physical term but transport costs and travel times are also scales of distance measurement. In the model, the relationship of these attributes is established by considering its logarithmic form. In fact, mode generalises that in aregion, spatial interaction is positively related to town size and negatively dependent on distance. This relationship seems true in the case of Brahmaputra plains as Guwahati has more interaction with North Guwahati and Rangia towns and Dibrugarh located in Upper Brahmaputra plainhas implicit interaction with the towns surrounded in its close vicinity.

Although the experimental validation of spatial interaction techniques is gaining interest, many virtual reality researchers still consider it an ‘art’ rather than a ‘science’. In the design cycle of spatial interaction techniques, the evaluation part is most often addressed in a qualitative way, rather than being based on firm quantitative evidence. This multi-disciplinary project has two main objectives. First, to develop a more quantitative approach to the design of spatial interaction techniques. Second, to apply and test this quantitative approach in the design of new spatial interaction techniques.

References

• Davis, P. (1988): Science in Geography 3, Data description and presentation, Oxford University Press, Hong Kong, pp 42 – 49.
• Smith. David, M. (1975): Patterns in Human Geography, Penguin Books Limited, Auckland, New Zealand.