26 Spatial Gradient Analysis
Dr. Madhushree Das
1. Introduction
Some of the geographical characteristics show a declining relationship with distance. For example in a city the density of population is found to be highest at the centre of a city and as we move away from the centre it keeps on declining up to the periphery of the city where it is found to be the minimum. This kind of spatial relationship is also known as “Distance Decay Function”. The rate of the decline of any phenomenon with respect to distance or any other characteristics is known as its gradient. Thus the decline in the population density in a city from its “Central Business District” (CBD) to its peripheryis measured in terms of population density gradient. Thus, population density gradient can be defined as a spatial variation in population density with respect to area within a city. In considering the study of population, the density gradient has been referred as the change in population density of an urban area from the city center to its periphery. The principle of “distance decay” also operates on phenomenon such as: volume of migration from an origin to a destination keeps on declining as distance between them increases and altitude of an area falls down as we move closer to the Sea level etc. The study of the distance decay function assumes an special significance in geography as it highlights the underlying impact of geographical force on the society. The intensity of the distance decay relationship is evaluated by the corresponding gradient with which it operates under different situations. Thus the distance decay function will show a high gradient in areas where Central Business District areais highly developed but out side it there may be big vacuum of urban facilities. On the contrary in another situation of a city with balance urban facilities through out the city may show a moderate gradient in distance decay function.
Collin Clark, an economist in 1951, based on a study of 36 cities, first proposed a formula to describe the pattern of population density in any city.In order to simplify the study of urban population density and the comparison of its results, Colin Clark (1951) established two general hypotheses:
(i) In almost all cities of developing worldexcluding areas of cities dedicated to business and commerce, the central part of a cityexists with high population density, which decreases when moving away from the center. This phenomenon is typical in most of the developing cities across the world.As an explanation of the decline of population density between city center and its suburbs it has been suggested that ‘the activities closer to the city center occupy vertical space on expensive land consuming little spaceby a household and the activities at the periphery of a city consume much space at cheaper land rent. Since the land consumed by each household increases with distance from the city centre, population density therefore must drop’ (B.J.L.Berry, J.W.Simmonds and R.J.Tennant). The urban density may be seen as a logical extension of the urban land use theory.
(ii) In most of the cities in developed world with time, the density becomes constant in the central areas and increases in the suburbs. Thus city expands its territory.This is because of the fact that in recent years there has been a larger growth of population in the suburban parts of the urban areas because of the rapid use of land for residential and other urban purpose as the urban amenities at low prices are available in comparison to the city center. Thus cities are becoming more ‘flat’ and the spatial pattern of population density tends toward unification when peripheral areas of cities accommodating more population. Figure 1 shows a fast decrease ofpopulation density in developing countries giving a fairly higher value of the gradient of population density with respect to distance , while this curve becomes more curvilinear for the developed countries where rate of decline of population density with respect to distance is found to be slow and will give a moderate gradient of population density with respect to distance.
Figure-1: Spatial Gradient of Population in Developing and Developed Countries
On the basis of the first hypothesis, there exists a negative relationship between the distance from the urban centre ‘x’ and the density of the population ‘y’. As the distance increases away from the city centre, the density of population decreases. For the purpose of density gradient analysis, a functional model of space known a Distance Decay Model is used. It shows that the spatial interaction falls off with distance. It is represented as F = aD-2 ( Pareto’s Model). In this model F shows the interaction between two places and D shows the distance between them. The negative exponent of 2 shows inverse relationship between the interactions and the distance. In general, Distance Decay is a geographical term which describes the decreasing effect of distance on economic, cultural or spatial interactions between places. The distance decay effect states that the interaction between two locales declines as the distance between them increases.
With the advent of faster travel, distance has less effect than it did in the past, except where places previously well-connected by railroads, for example, have fallen off the beaten path. Advances in communications technology, such as phones, radio and television broadcasts, and internet, have further decreased the effects of distance.
Distance decay is graphically represented by a curving line that swoops concavely downward as distance along the x-axis increases. Distance decay can be mathematically represented by the expression I=1/d², where I is interaction and d is distance, among other forms. It also weighs into the decision to migrate, leading many migrants to move less far than they originally contemplated.
2. Distance decay is also evident in town/city centres. It can refer to:
The number of pedestrians getting further from the centre of the Central Business District(CBD), the street quality decreasing as distance from the centre increases as well, the quality of shops decreasing as distance from the centre also increases the height of buildings decreasing as distance from the centre increases the price of land decreasing as distance from the centre increases
3. Features of Density Gradient Analysis
- Pattern of relationship is negative.
- Working Principle Model is the Distance Decay Model
i.e.
d(x) = doe-bX,
Where, ‘d(x)’ represents population density ‘d’ at distance ‘x’ from the city centre, ‘do’ is the central density, ‘e’ an exponent of distance and ‘b’ is the density gradient or the rate of diminishing of population density with distance from the centre, a negative exponential decline.
The model shows a non-linear relationship between the distance and population density. In order to find out a linear relationship, a logarithmic transformation of the distance- decay equation is necessary. Thus we get,
loged(x) = loge (doe-bX)
Or
loged(x) = logedo–bXlogee(since logee = 1)
Thus, loged(x)=logedo– bX.
If loged(x) is written as ̂and loge do= a, then
̂= a-bX,it is a linear form of distance decay equation.
3.1 Example:
In order to understand the spatial gradient of population in Guwahati city, the gradient analysis is pursued for which ward wise population data were collected from Guwahati Municipal Corporation for 2001.
Figure-2: Spatial Pattern of population Density in Guwahati City (2001)
3.2 Calculation:
Given ward wise data of area and population of Guwahati city
Table 1: Area and Population of Wards in Guwahati City
Table 2: Population density in Different Wards in Guwahati city
Table 3: Calculation for the Distance Decay Model
| Distance from the city center (X axis) | Population Density (dx) Y-axis | log dx (Y axis) | xy | x2 | ̂ | Antilog of ̂ |
| 0 | 21705 | 4.336 | 0 | 0 | 4.211 | 16255 |
| 0.9 | 14388 | 4.158 | 3.742 | 0.81 | 4.112 | 12942 |
| 2.4 | 7316 | 3.864 | 9.273 | 5.76 | 3.949 | 8892 |
| 4.0 | 6125 | 3.787 | 15.148 | 16.00 | 3.775 | 5957 |
| 5.2 | 3340 | 3.523 | 18.310 | 27.04 | 3.644 | 4405 |
| 6.8 | 1913 | 3.281 | 22.310 | 46.24 | 3.469 | 2944 |
| 8.0 | 2436 | 3.386 | 27.088 | 64.00 | 3.339 | 2183 |
| 9.6 | 2197 | 3.341 | 32.073 | 92.16 | 3.169 | 1459 |
The plots of population density and its log transformed values subject to distance from the central part of city were made to show the trend of density decay in Guwahati city (Figure-3).
Figure 3: Population Density Gradient Analysis of Guwahati city, 2001
The graph indicates that from the observed values of population density, it is seen that the location of population density in the city is quite significant. It ranges between 21705 persons per square km in the city and 1913 persons per square km in the periphery. The value of b is very less that shows steep slope of distance decay curve in Guwahati city. An overall pattern in decline of population density in respect to distance from the city centreshows verysteepness within a radius of about 2.4 km from 21705 persons per square km to 7316 persons per square km. It then becomes moderate up to a distance of about 4 km (6125 persons per square km) and then it falls gently towards the periphery.
Analysis of the Distance-Density Relationship reveals that the gradient is very steep. The observed central density is found to be significantly higher than the expected one. Likewise, the peripheral density also deviates positively from the trend line, because of the new residential areas gradually coming up here. However, in the extensive portion of the middle area, the observed density is significantly lower than the expected density. This is because of the presence of the low lying areas, swampy land and forested regions and so on. This middle area of the city in particular, together with the peripheral ancillaries need further development for balanced and sustainable development of the urban area like Guwahati Municipal Corporation.
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References
- Clark, C. (1951): “Urban Population Densities”, Journal of Royal Statistical Society, Vol. 114, No. 4, pp. 490 – 496.
- Knowles, R. and Wareing, J. (1986): Economic and Social Geography, Rupa, New Delhi – 110002.
- Muth, R, F. (1967): “The Distribution of Population within Urban Areas”, Determinants of Investment Behavior,NationalBureau of Economic Research, pp. 269 – 300