Modelling of urban growth using spatial analysis techniques: a case study of Ajmer city (India

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Modelling of urban growth using spatial analysistechniques: a case study of Ajmer city (India)M. K. Jat a; P. K. Garg a; D. Khare aa Indian Institute of Technology Roorkee, Roorkee, 247667 India

First Published on: 25 October 2007To cite this Article: Jat, M. K., Garg, P. K. and Khare, D. (2007) 'Modelling of urbangrowth using spatial analysis techniques: a case study of Ajmer city (India)',International Journal of Remote Sensing, 29:2, 543 - 567To link to this article: DOI: 10.1080/01431160701280983URL: http://dx.doi.org/10.1080/01431160701280983

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, M. K

007 Modelling of urban growth using spatial analysis techniques: a case

study of Ajmer city (India)

M. K. JAT*, P. K. GARG and D. KHARE

Indian Institute of Technology Roorkee, Roorkee, 247667 India

(Received 13 May 2006; in final form 5 February 2007 )

The concentration of people in densely populated urban areas, especially in

developing countries like India and China, calls for the use of sophisticated

monitoring systems, like remote sensing and Geographical Information Systems

(GIS). Time series of land use/cover changes can easily be generated using

sequential satellite images, which are required for the prediction of urban growth,

verification of growth model outputs, estimation of impervious area, para-

meterization of various hydrological models, water resources planning and

management and environmental studies. In the present work, urban growth of

Ajmer city (India) in the last 29 years has been studied at mid-scale level (5–

25 m). Remote sensing and GIS have been used to extract the information related

to urban growth, impervious area and its spatial and temporal variation.

Statistical classification approaches have been used to derive the land use

information from satellite images of eight years (1977–2005). The Shannon’s

entropy and landscape metrics (patchiness and map density) are computed in

order to quantify the urban form (impervious area) in terms of spatial

phenomena. Further, multivariate statistical techniques have been used to

establish the relationship between the urban growth and its causative factors.

Results reveal that land development (200%) in Ajmer is more than three times

the population growth (59%). Shannon’s entropy and landscape metrics has

revealed the spatial distribution of the sprawl.

1. Introduction

Urbanization is an inevitable process globally, and an important topic for the

planners, managers and environmentalists. After economic liberalization in 1991,

urban centres in India have grown at a faster rate due to increased economic and

developmental activities. The extent of urbanization or its growth is one such

phenomenon that drives the changes in land use pattern. These changes may have an

adverse impact on ecology, especially on hydro-geomorphology, water resources

and vegetation. Information on accurate urban growth is of great interest in urban

and suburban areas for diverse purposes, such as urban planning, water and land

resource management, market analysis, service allocation, etc. Unfortunately, the

conventional surveying and mapping techniques are expensive and time consuming

for the estimation of urban growth. As a result, increased research interest is being

directed to the mapping and monitoring of urban growth using remote sensing and

GIS techniques (Epstein et al. 2002).

*Corresponding author. Email: mahesh.mnit@gmail.com

International Journal of Remote Sensing

Vol. 29, No. 2, 20 January 2008, 543–567

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2008 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160701280983

, M. K

Remote sensing is a cost effective, technologically sound and an increasingly used

technique for the analysis of urban growth (Sudhira et al. 2004, Yang and Liu 2005,

Haack and Rafter 2006). For nearly three decades, extensive research efforts have

been made for urban change detection using remotely sensed images (Toll 1985,

Royer et al. 1988, Singh 1989, Lo and Shipman 1990, Gomarasca et al. 1993, Green

et al. 1994, Yeh and Li 2001, Yang and Lo 2003, Haack and Rafter 2006). These

studies have been supported through either an image-to-image comparison or a

post-classification comparison. The post-classification comparison has the potential

to detect the nature of urban land use/cover changes (Jensen 1995). With the

availability of higher resolution images and the development of improved image

classification methods, greater details of urban land use/cover changes can be

mapped with a reasonable accuracy (Jensen and Cowen 1999).

The impervious area is generally considered as a parameter for quantifying the

urban growth (Torrens and Alberti 2000, Barnes et al. 2001, Epstein et al. 2002).

Here, impervious area includes residential, commercial and industrial complexes

along with paved ways, roads, markets, etc. Urban growth has been quantified by

considering the impervious area as the key feature, which can be obtained either

from physical survey or remotely acquired data.

There are a variety of techniques available to measure/estimate the area of

impervious surfaces. The time consuming and costly, but most accurate is manual

extraction of impervious surface features from remote sensing images through heads

up digitizing. Point sampling can be used as an alternative to digitizing, despite this

being time consuming and less accurate. Remote sensing pattern recognition

approaches, such as supervised, unsupervised and knowledge based expert system

approaches (Cibula and Nyquist 1987, Loveland et al. 1991, Franklin 1994, Harris

and Ventura 1995, Greenberg and Bradley 1997, Vogelmann et al. 1998, Stuckens

et al. 2000, Stefanov et al. 2001, Sugumaran et al. 2003, Lu and Weng 2005, Mundia

and Aniya 2005) have been used in the recent past to measure impervious area and

urban growth. These require both moderate to high resolution remote sensing data

as well as expertise to process and analyse. These data and analytical capabilities are

often beyond the reach of many planners and decision makers at a local level,

especially in developing countries.

Statistical techniques along with remote sensing and GIS have been used in many

urban growth studies (Lo 2001, Lo and Yang 2002, Weng 2001, Cheng and Masser

2003, Sudhira et al. 2004, Jat et al. 2006). Urban growth studies have been attempted

in several developed countries (Batty et al. 1999, Torrens and Alberti 2000, Barnes

et al. 2001, Epstein et al. 2002, Li and Weng 2005, Jantz et al. 2005, Yang and Liu

2005) and recently in developing countries like China (Yeh and Li 2001, Weng 2001,

Cheng and Masser 2003) and India (Lata et al. 2001, Sudhira et al. 2004, Jat et al.

2006). Statistical techniques like multivariate regression have been used to determine

the relationship between the percent impervious area and various urban develop-

ment parameters, such as road density, population density, land use type and size of

development units (Lo 2001, Lo and Yang 2002, Weng 2001, Cheng and Masser

2003, Sudhira et al. 2004). The convergence of GIS and database management

systems has helped in quantifying, monitoring, modelling, and subsequently

predicting the urban growth phenomenon. Characterizing urban growth patterns

involves detection and quantification with appropriate scales and statistical

summarization. There are scores of metrics available to describe the landscape

pattern. The landscape pattern metrics have been used for studying the forest

544 M. K. Jat et al.

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patches (Trani and Giles 1999, Civco et al. 2002) and detecting the urban growth

pattern in village clusters (Sudhira et al. 2004). Most of the indices are correlated

among themselves, because there are only a few primary measurements that can be

made from patches (patch type, area, edge and neighbour type). All metrics are then

derived from these primary measures. At the landscape level, GIS aids in calculating

the landscape metrics, like patchiness, density and diversity in order to characterize

the landscape properties in terms of spatial distribution and change (Trani and Giles

1999, Yeh and Li 2001, Civco et al. 2002, Sudhira et al. 2004). Such metrics have not

been determined yet for most of the urban centres of India (Sudhira et al. 2004).

Shannon’s entropy has been used in some of the studies to quantify the urban

forms, such as impervious area in terms of spatial phenomenon (Yeh and Li 2001,

Sudhira et al. 2004, Joshi et al. 2006). Shannon’s entropy is based on the concept of

information theory. It is a measure of uncertainty about the realization of a random

variable. Urban growth takes place in the form of impervious patches in newly

developed areas. A quantitative measure is required to monitor and identify this

fragmented urban growth. Developing this analogy, the mathematical representa-

tion of urban growth as a fragmented phenomena and the concept of entropy are

close (entropy is often used as a measure of dispersion) (Joshi et al. 2006). Shannon’s

entropy (Hn) is used to measure the degree of spatial concentration or dispersion

of geophysical variables (Xi) among n spatial units/zones. Entropy can also be used

to indicate the degree of urban growth/sprawl by examining whether the land

development in a city is dispersed or compact (Lata et al. 2001; Sudhira et al. 2004;

Joshi et al. 2006). Large value of Shannon’s entropy indicates the urban growth.

Despite these efforts, further research is needed in order to reinforce the absolute

and comparative relationship between the magnitude of change in landscape

imperviousness, type and intensity of urban land use/cover change and their

causative factors.

In India, currently 25.73% of the population (Census of India 2001) lives in urban

centres, while in the next 15 years it is projected to be around 33%. This indicates the

alarming rate of urbanization and the extent of urban growth that could take place.

Measurement and modelling of urban growth using satellite images have not been

well studied to date, especially in India (Sudhira et al. 2004). Such studies are vital

for the planning and management of urban infrastructure and water resources.

In this paper, an attempt has been made to investigate the usefulness of the spatial

techniques like remote sensing and GIS for urban growth detection and handling of

spatial and temporal variability of the same. The urban growth of Ajmer city

(situated in Rajasthan State of India) in the last 29 years has been estimated using

remote sensing images of eight different years ranging from 1977 to 2005. Remote

sensing and GIS techniques have been used to extract the information related to

urban growth, and its spatial and temporal variation is studied to establish a

relationship between urban growth (sprawl) and its causative factors. Statistical

image classification approach like Maximum Likelihood Classifier (MLC) has been

used for the analysis of satellite images obtained from Landsat MSS, TM, ETM +and IRS LISS-III sensor systems. Classified images have been used to understand

the dynamics of urban growth and to extract the area of impervious surfaces. In

order to quantify the urban forms such as impervious area in terms of spatial

phenomena, Shannon’s entropy (Yeh and Li 2001) and the landscape metrics

(patchiness, map density, etc.) are computed. The landscape metrics, normally used

in ecological investigations, are being extended to enhance understanding of the

Modelling of urban growth 545

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urban forms. Computation of these indices helped in understanding the process

of urbanization at a landscape level. Further, urban growth has been correlated

with its causative factors, like population, population density etc., using multivariate

regression analysis to arrive at a functional relationship. In addition, these

relationships are used to predict the future urban growth.

2. Study area

The study area is located between 26u209 N to 26u359 N latitudes and 74u339 E

to 74u459 E longitudes (figure 1). Ajmer is situated 132 km from Jaipur, the capital

of Rajasthan and flanked by Aravalli hills on two sides. Ajmer enjoys the status

of being one of the major centres of higher learning and specialized education

in Rajasthan, apart from having historic importance. The municipal limit of Ajmer

spreads over an area of 250 km2. The population of Ajmer was 0.49 million in

the year 2001, and it is expected to be 0.84 million in 2034, as per the present

growth rate.

3. Data used

The data have been collected from primary and secondary data sources. The data

collected from the primary sources include Survey of India (SOI) topo-sheets (scale,

1 : 25,000) (No. 45J/10/5, 6 and 45J/11/1, 2, 3, 4) and multi-spectral Landsat TM,

ETM + and Indian Remote Sensing (IRS) LISS-II and LISS-III images for the years

1977, 1989, 1991, 1994, 1997, 2000, 2002 and 2005. The data collected from

secondary sources include the demographic details (primary census abstracts for the

years 1961, 1971, 1981, 1991 and 2001) from the Directorate of Census Operations,

Census of India. Ward-wise population (year 2001) and urban settlement map of

Ajmer city (scale, 1 : 2500; year 2000) have been obtained from the Rajasthan Urban

Infrastructure Development Projects (RUIDP) Ajmer. Other maps of Ajmer city,

like ward map, municipal boundary map, drainage and master plan have been

obtained from the Town Planning Department, Ajmer.

Figure 1. Location of study area. Available in colour online.

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4. Methodology

Understanding dynamic phenomena such as urban growth requires land use change

analyses, urban growth pattern identification and computation of landscape metrics.

ERDAS (Leica) and ArcGIS software (ESRI) have been used to generate variousthematic layers like ward map, Ajmer municipal boundary map, roads, railway

network and administrative boundary map using the topo-sheets and other available

maps. Complete methodology has been described below, and also presented in figure 2.

Figure 2. Flowchart of methodology

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4.1 Image analysis

Standard image processing techniques in ERDAS Imagine software, such as image

extraction, rectification, restoration, and classification have been used for the

analysis of all eight images.

First of all, atmospheric correction has been applied using the improved dark

object subtraction method to ensure all the images have common reference spectral

characteristics. Water bodies available in the areas have been used as the dark

object. Further, these subtracted images have been stretched to complete 8-bit

digital number ranges. Images are further geo-referenced and geometrically

corrected corresponding to the polyconic projection system.

Satellite images and their respective range of reflectance values (DN values) have

been studied thoroughly to ascertain the probable land use classes. Spectral profiles

have been studied to ascertain the separability and relative difference in pixel values

of various land use classes in several spectral bands. Ten separable land use classes

have been identified, such as urban settlement, barren land, water, sandy soil, rocky

terrain, exposed rocks, shrubs, mix vegetation, fallow land, etc. Initially, MLC based

supervised classification has been used for the classification of various images, but the

knowledge based expert system was later used to enhance the classification accuracy.

Initially, the algorithm was trained by a supervised training process after

collection of parametric and non-parametric signatures (training samples). Each

training sample consisted of at least 90 image pixels to satisfy the 10 n criteria,

where n is the number of bands used for classification (Congalton 1991). Signatures

are further evaluated using three criteria to test whether these truly represent

pixels to be classified for each class: (i) histogram plots to examine various statistical

parameters, like standard deviation and unimodality of the histogram, (ii) signatures

separability using Transformed Divergence (TD), and (iii) contingency matrix,

which contains the number and percentage of pixels which are classified as expected.

Signatures are refined, deleted, renamed and merged to ensure the unimodality of

their histograms, statistical parameters, contingency matrix and TD values.

After evaluating the separability, spectral band combinations with good

separability (highest TD value) have been selected for final classification. Initially,

hill shadow is classified as a separate class, however after field verification it has

been merged with the shrub. Various techniques like ratio, subtraction etc., have

also been tried to remove the hill shadow, but no significant improvement is

observed. Results obtained from supervised classification are not found satisfactory

as misclassification has been observed for urban settlement, exposed rocks, and

rocky terrain, exhibiting lower overall accuracy. In the second stage, the knowledge

based expert system has been used for the post-classification refinement, i.e. the rule

based system is applied to the output from MLC in an attempt to modify and

improve the classification. Ancillary information from various sources (DEM,

municipal boundary map, location map of water bodies, soil map) has been

integrated with output from MLC for the preparation of knowledge base (rule base),

which is further refined from the ground truth collected by field visits. Finally,

classification is performed using the knowledge classifier module of ERDAS.

Classified images have been validated using the ground truth data and available

maps from various agencies (RUIDP and Ajmer Town Planning Department).

Results have been found satisfactory, and presented in figure 3.

Classification accuracy of results has been assessed using a reference dataset of

more than 300 randomly selected pixels. Land use for these pixels have been

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determined using an urban settlement map (prepared from the aerial survey carried

out in the year 2000), and data collected from other maps (municipal boundary map,

soil map, location map of water bodies, SOI topo-sheets and forest cover maps). The

original satellite images have also been used for accuracy assessment to avoid errors

in the reference dataset for temporally sensitive classes (such as vegetation). A

settlement map of the city and geographical locations of some important features,

like type of vegetation at a particular location, important buildings, play grounds,

water bodies and drains, collected during the field visits have also been used as

ground truth data. Further, an accuracy report and Kappa Coefficient have been

generated using the ERDAS Imagine’s accuracy assessment utility. Urban growth

over a period of three decades (1977–2005) has been determined from the classified

images, and results are compared with the settlement maps prepared by Ajmer

Town Planning Department.

4.2 Landscape metrics

Shannon’s entropy, patchiness and map density metrics have been determined to

understand the urban growth pattern at ward (different administrative zones

demarcated by Municipal authorities) level. Landscape metrics have been calculated

using the demographical and built-up area statistics.

Shannon’s entropy (Yeh and Li 2001) has been computed considering the urban

growth in different wards to detect the form of urban growth phenomena. The ward

boundary map, obtained from the Municipal Corporation of Ajmer, is taken as the

base for evaluation of the urban growth pattern from 1977 to 2005. Shannon’s

entropy (Hn) is given by:

Pi loge Pið Þ ð1Þ

Figure 3. Classified images of Ajmer fringe

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where, Pi is the proportion of the variable in the ith zone (ward), n is the total

number of zones. Pi refers to the impervious areas in ith wards, n represents total

number of wards (55) and log n refers to the upper limit of entropy (1.7403).

Shannon’s entropy has been calculated across all the wards considering each ward as

an individual spatial unit.

Patchiness or landscape diversity is the number of different land use classes within

the n6n window. It is a measurement of density of all land use class patches, or

number of heterogeneous land use/cover polygons over a particular area. The

greater the patchiness, the greater the heterogeneous landscape. In this study, the

density of patches among different land use categories has been computed by

moving a 565 size kernel on the classified image using the model maker utility of

the ERDAS Imagine software. Land use diversity in term of patchiness has been

determined using the respective classified images for years 1977, 1989, 1994, 2000

and 2005, which ranged from 1 to 8.

Map density values are computed by determining the number of impervious area

pixels out of total number of pixels in a 565 kernel. When this is applied to a

classified satellite image, it converts land use classes into 25 density classes. For

example, a density value of five for a pixel represents five impervious area pixels in a

565 kernel. Depending on the density levels, it is further classified into five

categories using the equal interval method, as very low, low, medium, high and very

high density classes, corresponding to the density values (number of built-up area

pixels out of 25 pixels) of 5, 10, 15, 20 and more than 20. Density landscape metrics

have been computed for all the five years (1977, 1989, 1994, 2000, and 2005).

Further, the relative percentage of each density category (percentage of total

impervious area in a particular category) has been computed, which enabled

identification of different urban growth centres and subsequently correlation of the

results with Shannon’s entropy.

4.3 Urban growth modelling

The population growth of Ajmer city has been evaluated using the demographic

data of four decades, i.e. 1961 to 2001 (Census of India). Population growth trends

are obtained for the decadal growth by studying different types of distribution, like

linear, logarithmic, exponential, power and polynomials. These distributions have

been tried to find out the best form of relationship representing the growth

phenomena. Such a relationship could be used for future prediction. The

distribution with the highest correlation coefficient has been chosen for further use.

Urban growth dynamics are analysed considering some of the basic causative

factors, like population (P), population density (PD) and population density for the

built-up area (a density, aD). The rationale behind this is to identify such factors

that play a significant role in the process of urbanization. Multivariate regression

analysis has been performed considering the urban growth in terms of percentage

impervious area (PB) as a dependent variable. Regression analysis has been

performed for two cases considering the urban area; (i) as a whole and (ii) at the

ward level (for year 2000 only). For other years, ward-wise population data are not

available.

The causative factors considered responsible for urban growth include P, aD, PD

and population growth rate (PAGR). The percentage impervious area of a ward is the

ratio of impervious to total area of ward (individual zone). The aD for a ward is the

ratio of the population in each ward to the impervious area of that ward. The PD for

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a ward is the ratio of population to the total area of ward. The population has been

accepted as a key factor of urban growth. In the present study, PB, aD and PD are

computed and analysed for the whole urban area (Case I) as well as ward-wise

(categorized as a sub-zone) (Case II). The PAGR has been used for Case I only.

Ward-wise impervious area has been obtained from the classified satellite image.

PAGR for the whole urban area is computed from the available population data

(1961 to 2001). Population of in-between years has been obtained by linear

interpolation and fitted regression equation.

In order to identify the probable relationship of PB (dependent variable) and

individual causative factors, different distributions (linear, quadratic, exponential

and logarithmic) have been explored for Case I only. The regression analyses reveal

the individual contribution of causative factors on urban growth.

To assess the cumulative effect of causative factors, stepwise multivariate

regression analysis has been performed. In multivariate regression, it is assumed

that the relationship is linear, which is supported by a higher correlation coefficient

for all individual causative factors. The multivariate regression gives the cumulative

relationship between the variables.

5. Results and discussion

5.1 Image analysis

Signature separability results are presented in the form of TD values (Table 1).

Values of TD for different land use pair lie within the satisfactory limits. Average

values of TD for different images vary between 1941 and 2000, which indicate a

good separation (TD.1900). Minimum values of TD for different images lie

between 1714 and 1993 (table 1). Lower values of TD for some land use classes

(1714) indicate that separation is fairly good. Best band combination, corresponding

to the highest value of TD, has been selected for the supervised classification. From

the two separability evaluation criteria, it can be concluded that signatures are good

enough for separability. However, these signatures may represent the narrow range

of reflectance values for each land use class, as these have been refined to satisfy

various evaluation criteria. Separability is slightly poor for the urban settlement as it

is mixed with rocky terrain, exposed rocks and wet alluvium soil landuse classes.

This mixing of urban settlement and rocky land use classes is due to the

heterogeneous character (different type of construction material and different type

Table 1. Transformed Divergence (TD) for supervised classification of various years.

Year SensorSpatial

resolution (m)

No. ofspectralbands

Spectralbands

considered

Transformeddivergence (TD)

Minimum Average

1977 Landsat MSS 57 4 2, 3, 4 1802 19411989 Landsat TM 28.5 7 1, 3, 4, 5 1748 19801991 IRS 1A LISS-II 36 4 1, 2, 4 1714 19781994 IRS 1B LISS-II 36 4 1, 2, 4 1875 19911997 IRS LISS-III 23 4 1, 3, 4 1879 19962000 Landsat ETM + 28.5 & 14.5 6 1, 2, 4, 6 1997 20002002 IRS 1D LISS-III 23 4 1, 3, 4 1993 20002005 IRS PVI LISS-III 23 4 2, 3, 4 1941 1998

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of impervious surfaces) of the urban area and surrounding hilly topography

(exposed rocks and hills, where reflectance is similar to the built-up areas).

For all images, results of accuracy assessment have been presented in table 2.Results of rule based post-classification refinement have been found to be

satisfactory with good overall accuracy. Both user and producer accuracies are

almost the same (table 2) which indicate consistent classification accuracy. Overall

classification accuracy has been found to be more than 90% for all the images

(table 2). Highest accuracy of 94.98% has been obtained for LISS-III image of the

year 2002, while 90.12% accuracy is achieved for the LISS-II image of the year 1994.

Mix vegetation land use/cover class represents different types of vegetation like

patches of plantations, small vegetable fields (but not regular feature) and patches of

natural trees within municipal limits, which have similar spectral characteristics.

After the field visit, this type of land cover has been classified as mixed vegetation.

This category is spectrally overlapping to the shrub land cover class at some

locations, in some images. Location of this land cover category is also not fixed, as

small agricultural activities are shifting as per the availability of water.

5.2 Population growth and built-up area

Quadratic distribution has been found to be best fitted for the population growth of

Ajmer city as compared to linear, exponential, logarithmic and power distributions.The following quadratic relationship of population growth has been adopted for

future projection of population, as it gives the highest correlation coefficient (0.97)

(figure 4):

P~1755:6 X 2z55087 Xz168220 ð2Þ

where P is the population and X is years in decade (1961 onwards). The lowestcorrelation has been found for the logarithmic distribution. Equation (2) has been

used for future population prediction. Values of the correlation coefficient for linear

(0.96) and exponential (0.96) relationships are also not significantly different, which

may be due to the small number of data sets used to form the relationship.

Urban growth for the years 1977 to 2005 has been estimated in the form ofimpervious areas, which are obtained from the classified satellite images. Built-up

area obtained from the classification may have some error due to mixed class pixels.

The classification algorithm designates a particular pixel to a particular land use

class, depending upon its reflectance characteristics (standard deviation and

Table 2. Overall accuracy of the image classification.

Classification accuracy

Overall classification accuracy

Overall Kappa statisticsProducers accuracy (%) Users accuracy (%)

1977 96.37 94.80 0.941989 93.75 94.00 0.931991 93.50 92.60 0.921994 90.90 90.12 0.901997 91.40 90.90 0.902000 93.90 94.08 0.942002 94.86 94.98 0.942005 92.54 92.45 0.91

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co-variance). Supervised classification used in this study does not deal with sub-pixel

classification. However, results are further refined using a knowledge based

approach by reducing the problem of mixed pixels. Urban area statistics for

Ajmer city are presented in table 3. The impervious area (built-up area) has

increased from 488.03 ha in year 1977 to 1463 ha in year 2005. Results in table 3

reveal that the rate of land development in Ajmer has outstripped the rate of

population growth. From the years 1977 to 2005, population in the region grew by

about 59%, while the amount of developed land grew by about 200% i.e. more than

three times the rate of population growth (figure 5 and table 3). This implies that the

land is being used for urbanization at a faster rate, which indicates that per capita

consumption of land has increased exceptionally over the last three decades. The per

capita land consumption refers to the utilization of all lands for development

Figure 4. Population growth of Ajmer and best fit distributions. y565.621x + 155.93,R250.968. y51.7561x2 + 55.084x + 168.22, R250.969.

Table 3. Urban growth statistics for Ajmer city.

YearBuilt-up area

(hectare)

Percentageincrease in

built-up area (%)Projected

populationPercentage growthin population (%)

1977 488.03 – 331073 –1989 838.41 71.79 397279 19.991991 909.01 8.42 402700 1.361994 979.12 7.71 428932 6.511997 1071.54 9.43 455163 6.112000 1139.38 35.89 481395 5.762002 1259.81 10.56 497160 3.272005 1463.00 16.12 525114 5.62

Note: population has been projected using piecewise linear interpolation based onhistorical data of the last four decades.

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initiatives, like commercial, industrial, educational, recreational and residential

establishments per person.

Spatial distribution of ward-wise urban growth (in the form of impervious area) inthe last 29 years is shown in figure 6. Here the impervious area (built-up area)

includes houses, industries, roads, etc. Urban growth is faster in the outer area

(ward number 1 to 6 and ward number 31 to 55) along the major roads as compared

to the central portion of the city, which is also substantiated by figures 6, 7 and

landscape metrics. Here the hypothesis is correct that improvement in economic

conditions relates to urban growth.

5.2 Metrics of urban sprawl

5.2.1 Shannon’s entropy (Hn). In the present investigation, Shannon’s entropy (Hn)

is used to measure the degree of spatial concentration or dispersion (homogeneity)

of a geophysical variable (impervious area) among n spatial units/zones (wards). In

the present study, ward-wise impervious area has been considered as the geophysicalvariable, which enables determination of urban growth. Entropy may range from 0

to log n, indicating a compact distribution of considered phenomena (urbanization)

for values closer to zero and dispersed distribution for the values closer to log n.

Values of entropy near to log n reveals the dispersion of the geophysical variable

(impervious area), which indicates the occurrence of urban growth.

Shannon’s entropy results for six years (1977, 1989, 1994, 2000, 2002 and 2005)

are presented in table 4. Entropy values have been calculated across all wards, and

are summed-up to represent the entropy for the whole urban area. Larger value ofentropy, more than 1.6 (table 4), reveals the occurrence and spatial distribution of

the variable (urban growth). Ward-wise results have not been presented here due to

Figure 5. Population and urban growth of Ajmer in the last 29 years.

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their large number (55 wards). The relatively lower value of Shannon’s entropy

(1.54) in the year 1977 indicates the compact and homogeneous distribution of the

impervious area (built-up area). This hypothesis is also proved from figures 3 and 6,

which show compact distribution of the urban area in 1977. Dispersed distribution

of the impervious area has been observed in recent years (figure 6), which is also

revealed by the results of Shannon’s entropy. Entropy value has increased from

1.541 in 1977 to 1.602 in 1989. Further value of Shannon’s entropy has increasedfrom 1.60 in 1989 to 1.628 in 2000. This increase in entropy indicates an increase in

dispersion of the impervious area, which reveals urban growth. The entropy values

Figure 6. Urban growth and its spatial distribution in last 29 years.

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obtained are 1.541 in 1977, 1.602 in 1989, 1.621 in 1994, 1.622 in 2000, 1.616 in 2002

and 1.616 in 2005. These are closer to the upper limit of log n, i.e. 1.7403, showing

the degree of dispersion of built-up areas in the region.

The higher value of overall entropy for the whole urban area represents higher

dispersion of the impervious area, which is a sign of urban growth. The increase in

dispersion is due to new areas being added to the municipal boundaries and some of

the new housing schemes implemented by the Government. The degree of dispersion

has reduced marginally from 2000 to 2005, which indicates an increase in

homogeneity of the impervious area. Ward-wise impervious areas in different years

(figure 7) further substantiate the entropy results. The value of entropy has increased

gradually from 0.15 (1977) to 0.58 (2005) for the wards located along the major

roads, like ward numbers 1, 2, 3, 4, 10, 11, 35, 36, 39, 40 and 53 to 55. The higher

values of entropy in outer areas indicate more urban growth as compared to central

Ajmer, indicating greater dispersion of impervious areas in outer wards.

Distribution is predominantly dispersed in outer areas, whereas it is compact in

areas surrounding central Ajmer. Hence, it can be concluded that Shannon’s

entropy is useful and effective in identifying the urban growth phenomena in terms

of dispersion of the impervious area.

Figure 7. Ward wise urban growth of Ajmer in the last 29 years.

Table 4. Overall Shannon’s entropy for the study area.

Year Overall value of Shannon’s entropy

1977 1.5411989 1.6021994 1.6212000 1.6282002 1.6222005 1.616

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5.2.2 Patchiness. Landscape diversity or patchiness is a measure of a number ofheterogeneous land use polygons over a particular area. Ward-wise landscape

diversity and its percentage distribution for the different years are presented in

figure 8 and table 5. Results reveal that diversity ranges from 1 to 7 land use class

Figure 8. Diversity (patchiness) of land use classes for different years.

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categories. One land use class category represents that only one land use class is

available within the kernel, two land use class category represents that any two land

use classes are available within the kernel, corresponding to the central pixel of the

kernel. For all the years, one and two heterogeneous land use classes categories are

highest, whereas five to eight heterogeneous class categories have been found to be

the minimum (table 5). However, one land use class category has gradually increased

from 36.6% to 55.18% and two land use class categories have reduced from 50.85%

to 17.54% (except 2000). Category three has increased from 11.77% to 19.137%,

which indicates the continuous process of urbanization in new areas. This reveals

that the percentage of homogeneous area has increased gradually since 1977, while

the remaining area which is heterogeneous with patch class ranging from two to six

has reduced. Results of the diversity analysis are in good agreement with Shannon’s

entropy results.

5.2.3 Map density. Map density is another index which can be used to examine the

homogeneity/dispersion of any spatial phenomena, like urbanization. Distribution

of impervious areas, which indicates urban growth, has been studied using density

metrics. Results of built-up/impervious area density metrics are presented in figure 9.

Re-classified categories of the densities (in terms of percentage of the total

impervious area) are presented in table 6. Very high and high density of the built-up

area refer to cluster or the more compact nature of the built-up theme, while

medium density refers to relatively lower compact built-up areas, and low and very

low density indicate loosely or sparsely spread built-up areas.

The percentage of high-density (built-up area) has gradually increased from

19.57% in 1977 to 24.47% in 2005. The percentage of very high-density built-up

areas is more than 40% until the year 1989, however it has reduced afterwards

(table 6). This revealed that percentage of more compact or highly dense built-up

areas is more up to 1989, and thereafter it has reduced on account of development of

new areas, which indicates dispersion. This reduction does not mean that impervious

areas have decreased since 1989. The relative share of very high compact built-up

areas has been reduced, though the total area under this category has not reduced.

In 1989, the area under very high density was 366.24 ha, which has increased to

376.14 ha in 2005. However, its percentage with respect to the total area under all

categories has been reduced. The increase in the value of very low, low, medium and

Table 5. Percentage distribution of patchiness for Ajmer urban area.

No. ofdiversityclass

Percentagedistribution

(1977)

(1989)

(1994)

(2000)

(2005)

1 36.604 31.234 52.883 53.102 55.1832 50.851 46.785 15.784 23.380 17.5413 11.771 18.699 14.961 14.960 19.1374 0.764 3.065 9.810 8.542 7.0855 0.009 0.213 5.001 0.015 0.9686 0.00 0.005 1.408 0.00 0.0827 0 0 0.149 0 0.0038 0 0 0.004 0 0

While deriving diversity of different landuse classes within Municipal boundary of the Ajmer,diversity function of the ERDAS Focal (Scan) model has been used considering 565 size ofkernel window.

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high density categories reveal urban growth and new developmental activities.

Figure 9 reveals that more land development has taken place in outer areas (wardnumbers 1, 2, 3, 4, 5, 35, 39, 40, 53, 54 and 55) along the major roads and railway

line. An important inference could be drawn here that high and medium density is

Figure 9. Density of impervious area in different years.

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Table 6. Different densities of built-up area and their percentage.

Modelling of urban growth using spatial analysis techniques: a case study of Ajmer city (India

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