Assessment of differential urbanization using spatial entropy model for Tiruchirappalli urban and tier towns, India

Urban sprawl is associated with many urban centres across the world; many times, the impacts are found to be negative on living organisms and the natural environment. Quantification of urban has been a valuable field of study to understand its various factors like dispersion, density, diversity, dimension, and many others. To be resilient and sustainable, many of these cities need to be physically restructured, which is quite an impossible task, especially in developing countries like India; Although, instead of restructuring established urban centres, plans can be developed to focus on the growth of the surrounding tier urban centres. The objectives of the present study are to, (1) assess the changes in the urban growth and built-up density; (2) assess the urban diversity of the Tiruchirappalli Municipal Corporation and the tier urban centres on a temporal scale for the years 1996, 2008 and 2020. The study has been carried out with the use of Landsat 5 and 8 satellite images. The hierarchical unsupervised image classifier technique is used to classify the image and the study area has been split into eight zones in which, Batty’s spatial entropy method was used to assess the diversity index. The study results are comparable to understanding the relative spatial growth and patterns among the select urban centres across the zones. Like many Class–II cities, Tiruchirappalli Municipality Corporation has mostly recorded inward developments during the periods from 1996 to 2008; while from 2008 to 2020 they have recorded outward fringe developments leading to expansion of the city.


Introduction
Urbanization is not a uniform process thus the degree of urbanization varies from each urban centre (Zeng et al. 2016;Rahman et al. 2018).At a particular urban scale, the degree of urbanization is different within the urban itself.The term 'entropy' has different meanings in various contexts.There are several studies carried out using the concept of entropy, such as thermodynamics, statistical mechanics, information theory etc. Entropy in geographical studies was broadly applied to investigate urban and its growth.Claude Shannon's entropy model laid the foundation for the use of entropy models in geographical studies.Wilson A developed the first entropy model for investigating geographical items and their spatial interactions in the year 1970 ;Batty M (1974) developed the spatial entropy model with the potential to study urban growth dynamics at varying spatial intervals.The spatial entropy model is so far the most sophisticated method to study urban growth dynamics in detail; however, few methodological changes in the application of the model have been made during the past decade; for example, an urban area can be investigated through consecutive rings or cross sections of the urban.
Urban development in developing countries like India is experiencing rapid urban explosion which needs to be studied and monitored with modern techniques to quantify and impose sustainable practices to withstand future urban challenges (Sudhira et al. 2003a(Sudhira et al. , 2003b)).Urbanization is now commonly regarded as one of the most important social processes, having an enormous impact on the ecology at local, regional, and global scales (Turner 1990), controlled by the physical, social, and economic factors that influence population growth, policies, and economic development (Saravanan et al. 2012;Rimal et al. 2017).
According to the United Nations-Department of Economic and Social Affairs (UNDESA 2021), 55% of the world's population was reported from urban areas during the year 2018.The report also estimated that urban areas are about to accommodate 66% of the total population by the year 2050; of which 90% of the urban growth will be reported from the Asian and African countries, especially China, India, and Nigeria.
For many years, demographic explosion and rural-to-urban migration have been the fundamental factors for rapid urbanization in developing countries leading to radical land use conversion which causes problems like loss of natural habitat and biodiversity (He et al. 2014), poverty, over-population, employment, unhealthy housing conditions, inadequate infrastructure, hygiene and sanitation, poor water quality and pollution (UN-Habitat 2010; Mohabir et al. 2017;Bhagat 2017).To a larger extent, urbanization is a good sign of development; however, there are meticulous sustainable urban plans based on quantitative urban analysis and implementation strategies are required to get the benefits of urbanization (Gisbert et al. 2017;Meijering 2018;Munier 2011).
Urbanization is an irreversible dynamic process at varying rates of expansion; the rate of expansion depends on the physical, social, economic, and infrastructure of the urban area (Li et al. 2003;Solon 2009;Aljoufie et al. 2011).Although, the physical conditions determine the establishment of the urban areas, to sustain the urban growth, three fundamental factors are necessitated viz (1) Function (2) Demography and (3) Economy (Batty 1974b).In situations related to the decay of the urban centres or the collapse of an urban centre, it could impart serious problems to the living and non-living systems.It is also noteworthy for urban planners to enable urban centres to continue functioning by satisfying (1) efficient production and delivery of quality goods and (2) resilient and flexible urban systems in certain catastrophic events (Cabral et al. 2013;Preston et al. 2021;Brandão 2017).
Given the existing urban conditions in many developing countries, the implementation of sustainable urban development plans has struck a bottleneck due to the manifold physical and functional complexities.A viable alternate approach would be "Differential Urbanization" to tackle the existing urban problems effectively while sustaining a balanced growth of the urban centre while it promotes the development activities in the surrounding towns where the plans can be implemented effectively, which alleviates pressure on the existing urban (Ourednicek 2007).
Hierarchical image classification is a promising technique applied in clustering similar image pixels based on spectral signatures (Lee and Crawford 2004;Tanguay et al. 2009).Multiple studies have shown increased efficiency in identifying and grouping the pixels based on hierarchical segmentation like road network extraction, wetland mapping and building extraction (Alshehhi and Prashanth 2017;Mao et al. 2020;Du et al. 2016).However, a general land use and land cover change analysis reveals the per cent of change in the land use/cover, nevertheless, it may not reveal any pattern of the built-up spread or the characteristic of sprawl (Parvaiz et al. 2017;Kriti et al. 2018;Fan et al. 2018).
The need to quantify the growth of the city is firstly, to assess the improper and uncontrolled development of urban both within the city and on the outskirts.Secondly, driving necessary planning and management policies for sustainable growth requires analysis of spatial and temporal data to assess the trend over a period of time (Jegankumar et al. 2018;Mukesh et al. 2015), to understand the adaptive behaviour of the functional activities and local administrative planning for development (Solon 2009;Nickayin et al. 2022).
There are a plethora of metrics and statistical methods to quantify urban sprawl; Bhatta et al. (2010) compiled several measurements and techniques to quantify urban sprawl and urban growth; modelling the urban sprawl quantifies the land area that is changed with concerning temporal scale.Entropy model offers insightful results (Purvis et al. 2019) based on the entire urban into micro-regions of rings on the diversity of the urban sprawl (Das and Angadi 2020;Horo and Punia 2019;Cho et al. 2021).
Urbanization can be studied in multiple dimensions of the context considered.Urban form and morphology are among the widely studied subjects.The varying urban growth is a complex phenomenon which can be better understood with the use of the entropy method (Bitner et al. 2021), which is an appropriate technique for monitoring rapid urban sprawl and quantifying the related impacts on a quick temporal scale (Madhavi et al. 2016).In recent past decades, studies on urban spatial growth have revealed multiple quantitative spatial characteristics like density, 34 Page 4 of 24 growth forms, shape, direction etc. (Dahal et al. 2016).Entropy and landscape metrics are indispensable techniques (Chen et al. 2018) in recent years to assess the spatial patterns, correlation, growth rate and trends, and the underlying impacts, which would provide insights to draw sustainable urban development plans (Ramachandra et al. 2012a(Ramachandra et al. , 2012b(Ramachandra et al. , 2013;;Bharath et al. 2015Bharath et al. , 2017)).
The Shannon Entropy method can be used to quantify the growth pattern (Jat et al. 2007;Parvinnezhad et al. 2021).Urban sprawl has a close association with multitudinous urban-related problems (Mohamed and Worku 2018;Abdul et al. 2017).To effectively manage the problems, a sophisticated approach must be developed incorporating (1) Quantification of the sprawl (2) Location metrics of the sprawl and (3) Sprawl characteristics.Combining these factors to decompose the urban sprawl areas could reduce the complexities of studying them for sustainable urban management (Antoni 2020).Along with entropy methods Weighted Urban Proliferation (WUP) and Urban Permeation (UP) methods can be used in monitoring the urban development and various other spatial entities to associate with decision-making (Nazarnia et al. 2019).
For a sustainable urban transformation, governments must ensure the proper implementation of the Sustainable Developments Goals (SDGs) by the United Nations (Panda et al. 2016).Sustainable urban development depends on knowledge about the underlying problems and the driving factors.To quantify them, remotely sensed satellite imageries provide crucial data on the spatiotemporal dynamics of the urban area (Aguilera et al. 2010).Certainly, these data play an important role in urban planning and resources management to make informed decisions (Phama et al. 2011;Jensen and Cowen 1999;Ahern 1991).Similarly, Fragile ecological regions demand sophisticated sustainable plans for their continued growth (Jayakumar et al. 2008;Fincher et al. 2014).Long-term sustainable urban development goals must include (1) Continuous monitoring (2) Micro to regional level understanding and (3) Integration with socio-economic aspects (Artmann et al. 2019).

Study area
The most dominant urban centres in India during the twentieth century are Mumbai, Delhi, Calcutta, and Chennai.Despite the unabated domination of these urban centres, there are many other urban centres draws importance beginning in the past two decades (Shaw 1999).
Tiruchirappalli district is the geographical centre point of Tamil Nadu, a state of India (Fig. 1).Tiruchirappalli, a historically important pilgrim centre throughout the history of Tamil Nadu, has been the geographical nodal point of the state.Tiruchirappalli is the fifth largest city in Tamil Nadu after Chennai, Coimbatore, Madurai, and Salem (Census of India 2011).Though a historic city, Tiruchirappalli has been overtaken by many other cities, in terms of population and economic activities, that are established in later periods.The city is surrounded by numerous physical and cultural bounds like agriculture-dominant river banks, plentiful lakes, high-valued rock mines and large patches of barren land.Owing to these setbacks, Tiruchirappalli has recorded a low urban growth rate compared to other competing cities.At the same time, the city is growing at a rate with the shortage of land for industrial and residential purposes.The shortage of land has impacted large track of agricultural lands converted into residential plots.To tackle these issues, the study aims to assess the next-level urban centres to promote differential urbanization as an efficient method to boost the economy and ensure equal urban growth.The study has identified six urban centres around Tiruchirappalli corporation within 40 kms of radius viz, Manachanallur, Manapparai, Musiri, Thuraiyur, Thiruverumbur and Viralimalai.These urban centres are selected as their population is more than 25 thousand according to the 2011 census of India.

Method and materials
The present study used Survey of India (SOI) Toposheets for locating the settlements and waterbodies and satellite images for LU/LC classification.The details of the data used are given in Table 1.Land use/cover classes are selected concerning the National Remote Sensing Centre (NRSC 2006) classification framework suitable for use across the states of India.The framework has three levels of classification according to the scale of the map.The satellite images are medium spatial resolution (30 m), which is optimum for classifying the images at Level II of the NRSC classification system (Fig. 2).
For medium-resolution images, hierarchical unsupervised classification techniques could be efficient in classifying land use and land cover (Dhanaraj et al. 2020;Roy and Kasemi 2022).The present study has been carried out by a multi-stage

Image pre-processing
As a general procedure for boundary enhancement, firstly all the images are processed for haze reduction to enhance the image spectral values and to reduce the hazy appearance; secondly the images are radiometrically corrected to balance the contrast between different images of the selected years.

Level-I classification
The present study used a hierarchical unsupervised classification technique with the ISODATA algorithm to classify the image.Medium spatial resolution images have a high probability of spectral mixing, which leads to uncertainty in the expected clusters when the classification is run at NRSC level II instantly.Although the spectral mixing could be avoided by producing NRSC level-I classified image after the first step.

Masking and level-II classification
For each class in the Level-I classified image, the satellite image is masked and the masked image is then classified to produce the sub-categories of the Level-I classification i.e., level-II classes.This procedure is repeated for all the level-I classes which encounter spectral mixing.

Post-processing
Cleaning by grouping the stranded/isolated pixels with the adjacent clusters makes the final LULC classified image.With the land use/land cover maps prepared, urban areas are separated for the assessment of urban diversity using the spatial entropy method.

Built-up density
Built-up density is a direct indicator of urban compactness.It also indicates various other characteristics of the urban morphology and associated urban ecosystem.On a temporal scale, urban development undergoes varying phases of change which can be understood by studying the morphology.Built-up density has been calculated as follows, where, B d = Built-up density; T a is the Total area of the particular ring; B a is the total built-up area of the respective ring.The formula has been applied to the ring segments of all the zones.The approach is unique in revealing the distribution of the built-up radiating from the core of the urban centre.

Spatial entropy/diversity
Like many other scholars, Batty (1974a) cited Shannon's entropy method cannot be used as it is used in the information theory; the discrete nature of the method is not well suited for the analytical purposes in the geographical domains.He also proposed a suitable method, "Spatial Entropy" for use in geographical studies.Entropy methods were derived and applied to the problems associated with geographical decomposition, aggregation, and configuration (Batty 1974b;Cabral et al. 2013 (Batty andLongley 1994)).
In the present study, for a deeper understanding of urban spatial growth, the urban centres are delineated into zones and rings.There are 8 zones based on the direction and the number of rings in each of these zones and ring width is determined concerning the areal extent of the urban centre.Batty's Spatial Entropy is obtained by, where p i is the probability of the event 'i' occurring,l n natural logarithm of a variable, x i spatial interval size.

Results and discussion
Population accretion in an urban area is largely influenced by government policies.The Indian reformations during the 1990s' have enormous effects on urban India in many ways.It became the centre for service providers, employment opportunities, health, and education.lifestyle etc. Tiruchirappalli has also seen a surge in population growth post the implementation of the reformations.The long and vast socio-cultural identity of the city has blended with modern services and industrial functions.

Urban spatial growth-1996, 2008 and 2020
The initial acceleration of population growth in the Tiruchirappalli urban and tier towns has been set up during the period between 1996 and 2006; it reached its peak during the period from 2006 to 2011.After 2011, the growth continued to decelerate due to the changes in the policies and regulations.Although urban spatial growth is decelerating, it cannot be concluded that there is no growth.Urban spatial growth has taken on all directions, at varying degrees.Figure 3 and Table 2 display the spatial growth from the period 1996-2008 and 2008-2020.The six urban centres surrounding Tiruchirappalli urban are the arteries for the sustenance of the Tiruchirappalli urban in numerous ways.All of these urban centres have their unique functions to support spatial growth at varying degrees.Unlike megacities, in a medium-class city, the selection of residential area by an individual is highly determined by the availability of land at a cheaper cost, irrespective of the distance to travel for daily work.This is found in the urban spatial growth analysis for the years 1996, 2008 and 2020.
In the Tiruchirappalli urban, NNW has the highest areal coverage of built-ups throughout the study period, while the WNW zone has witnessed a huge spatial growth rate among other zones; in the zone, the area has doubled during the study period from 1996 to 2008 and 2008 to 2020.SSW and WSW are the other noticeable zones for high spatial growth rates over the study period.These zones are run over by the National Highways (NH) connecting Madurai (NH38) and Dindigul (NH83) districts.During the year 1996, SSW was the second largest zone in terms of builtup area, however, it was overtaken by the WNW zone in the years 2008 and 2020.Tiruchirappalli urban centre has numerous impedes on its fringes like quarries, waterbodies, rivers, vast agricultural fields, and barren wastelands.Owing to this, Tiruchirappalli's urban growth has been polarized towards a few zones.Three of the four southern zones, ESE, SSE, and SSW are promoted by the Directorate of Town and Country Planning (DTCP) of the Tamil Nadu government for the development   1996 2008 2020 1996 2008 2020 1996 2008 2020 1996 2008 2020 1996 2008 2020 1996 2008 2020 1996  of residential or industrial units to further expand the urban on the southern part, while the northern zones are expected to grow at a normal expansion rate.Thiruverumbur has the second largest urban area considering only the built-ups.It is located in the vicinity of the Tiruchirappalli urban.It is well known for Bharat Heavy Electricals Limited (BHEL) and countless other allied industries.The town is on the National Highway-83 en route to Thanjavur District.The built-ups are primarily developed on this highway which covers the WNW and ESE zones.Viralimalai had remarkable spatial growth over the past decade.All of the zones have undergone major growth on the fringe areas as a result of the numerous industrial start-ups.Due to this, the town is expected to continue to attract more investments and people in the future.
All the other towns have recorded uniform spatial growth in all directions during the period from 1996 to 2008; however, during the period from 2008 to 2020, the spatial growth has been recorded as very high.Also, during this period many zones have witnessed zonal shifts and surges in spatial growth, especially in Manachanallur, Musiri, Tiruchirappalli, and Viralimalai.In addition to the spatial growth on the fringe areas, the built-ups were developed at a larger scale in the interior rings as well.This phenomenon was found to be more common in all the urban centres during the period from 1996 to 2008 (Fig. 4).These developments are called infill developments.

Built-up density-1996, 2008 and 2020
Built-up density is an indicator of urban development.Built-up density is a measure of compactness.Density increases in two aspects (1) spatial development is the increase in the area covered horizontally and (2) the increase in the number of floors.Built-up density metrics are another fundamental derivative to understand urban growth characteristics.In contrast to studying a particular urban centre, the present study has taken account of some of the prominent surrounding urban centres to study comparative urban growth.The proliferation of uncontrolled built-up development can deplete land and ecological diversity.A balanced use and controlled growth of built-ups ensures sustainable development.The built-up density implies many aspects of the urban environment in association with the built-up type, average size of the built-ups, average number of floors, open land ratio and many others.In the present study, surface built-up density only has been assessed as part of the spatial entropy model.In an existing urban centre, only two kinds of spatial growth can happen; (1) Infill development: which takes place inside the existing urban boundaries (2) Fringe development: which takes place on the outer boundaries/fringe areas.In the lifetime of the urban development both these characters are observed to be cyclic in nature and occur at certain time intervals.
Tiruchirappalli Urban has both infill development and fringe developments in the study period.From 1996 to 2008 most of the built-ups were developed in the interior boundaries of the urban area, and in contrast to this during the period from 2008 to 2020, the developments were largely recorded on the fringe / outer boundaries.These fringe developments are promoted in two cases, (1) Urban boundaries were expanded for administrative purposes (2) In case the threshold infill developments are made inside the existing urban area.
In a general framework, considering the whole urban area, urban density is higher in the Central Business Districts (CBD) and radiating outward from the CBD, the density tends to decrease.However, in segmenting the urban area into circles and rings for micro-level study, the results do not always comply with the general framework, which implies that some of the rings would have a higher density than the rings closer to the CBD.In the study, the built-up density was assessed in-depth at zonal and ring levels.As discussed earlier, urban centres have eight zones and varying numbers of rings in each zone.For each of the rings (Fig. 5), and at the zonal level (Fig. 6 and Table 3) built-up density has been calculated and plotted on graphs.
In the present study, Tiruchirappalli is the prime urban centre and all the others were the next-tier towns.Tiruchirappalli resembles a gentle declining built-up density from the CBD except the ENE and NNW zones have lesser density around the centre than the following ring.However, some of the other towns have a peculiar wave kind of trend which denotes the town have alternating built-up density among the rings.ESE, ENE, and WNW zones of Musiri, and WNW and WSW zones of Thiruverumbur, are having this phenomenon.Thuraiyur is a sentry post during the historical periods, and the development of the town was completely based on agricultural activities.The town was developed only along the road due to the presence of natural barriers, hence the morphology is very linear which displays strange builtup characteristics.Figure 7 shows the zonal-wise composite density graphs for the seven urban centres.Viralimalai displays a uniform development across the eight zones inferring the circular shape.All the other urban centres have varying density patterns between the zones.

Spatial entropy
The fundamental equation of the entropy method is developed by Claude Shannon (1948) for application in information theories, which cannot be used as is in geographical studies.Spatial entropy is a sophisticated statistical method to study diversity in the urban context (Batty 1974b, a).Spatial entropy is usually calculated at the zonal level.The present study has eight zones for each of the seven urban centres.An ideal urban centre would have equidistant uniform circles of spatial   1996 2008 2020 1996 2008 2020 1996 2008 2020 1996 2008 2020 1996 2008 2020 1996 2008 2020 1996 2008  entropies from the centre of the graph; however, in a real-world scenario to achieve this phenomenon, meticulous planning must be drawn.Figure 7 and Table 4 show the spatial diversity of the urban centres.Manachanallur, Manapparai, Musiri, Thiruverumbur, and Tiruchirappalli are urban centres with almost a uniform rate of change in diversity.In these urban centres, some of the zones have disassociated with the other zones.Viralimalai and Thuraiyur have undergone a rapid change in land use that resulted in many zones with varying diversity values during the study period.An exponential growth of built-up in a zone can result in an abrupt decrease in the diversity index that has been identified in the NNE and SSE zones of Viralimalai town.Similarly, Thuraiyur also has witnessed such a growth of built-up land that resulted in a near '0' diversity index.On the other side, Thiruverumbur and Tiruchirappalli have a gentle decrease in the diversity index throughout the study period.
Another important aspect revealed from the graph is that the new built-up developments in a particular zone can influence the diversity index significantly, like the ESE zone of Thuraiyur and Viralimalai, SSE zone of Viralimalai, WSW zone of Musiri and Manachanallur; which are having higher diversity value than the previous years (Fig. 8).This phenomenon is usually observed in the early stages of urban spatial growth.On the whole, the plotted graph reveals the nature and intensity of the growth with directional information and provides insights to the urban administrators and planners to take decisions for the better management of the urban environment.
Table 4 shows the diversity index for the urban centres across the zones for the selected years.Between the values 0 and 1, an optimum diversity value would be greater than 0.5 which is highlighted in the table that represents the zones with high diversity.From the table, it is very clear that in most of the urban centres, the number of zones having a diversity value higher than 0.5 has been decreasing since 2008, indicating the loss of open area in any form.

Correlation of spatial diversity
The correlation study reveals the relationships between the urban centres in terms of zonal-wise spatial diversity calculated from the spatial entropy method for the respective years (Table 5).The matrix table infers that the relationships are not very static throughout the study period, however, in the period 1996 and 2008, the pattern is almost similar with 10 negative relations out of 21 total relations.During 2020, the pattern changed with two more additional negative relations.Apart from the number of negative relations, the average correlation value has also decreased from 0.21 to 0.17 from the year 1996 to 2020, which indicates that urban spatial diversity is increasingly varying; this infers each of these urban centres has its factors to influence spatial growth.

Conclusion
The World Commission on Environment and Development (WCED, 1987) states, ''Sustainable development is the development that meets the needs of the present without compromising the ability of future generations to meet their own needs".Sustainable urbanization refers to the well-balanced relationship between the social, economic, and environmental agents in society, to accomplish sustainable urban development.Sustainability components have emerged as one of the fundamental planning concepts in many disciplines.A wide range of methods, techniques, and instruments are applied to study urban sustainability assessments to help determine how cities can become more sustainable and resilient.To be sustainable, urban areas must maintain an internal balance between economic activity, population growth, infrastructure and services, pollution, waste, noise, etc. in such a way that the urban system and its dynamics evolve in harmony, internally limiting, as much as is possible, negative impacts on the natural environment (Poyil and Misra 2015).In exercising urban development plans, encroachment and construction of unapproved sites are being one of the crucial elements which deplete the natural environments like water bodies and vegetative covers.On the other hand, it also leads to inadequate housing and promotes slums; such conditions are highly prevailing in urban environments that obstruct sustainable urban development.
The hierarchical unsupervised classification method produced a highly accurate land use land cover image with a high-reliability score (kappa) for the years 1996, 2008 and 2020 (Table 6).The report has been generated for automatically generated control points in the ERDAS software, which are validated concerning google earth images.Vegetation and urban pixels have been classified with less accuracy compared to other classes due to their similarity in the reflectance value with cropland and salty barren land respectively.However, the overall accuracy is promising in continuing the study for built-up density and spatial entropy.
Population accretion in a particular area has many socio-economic benefits; however, it also, sometimes, causes many other associated issues like depletion of natural resources due to over-exploitation and disparities in socioeconomic developments due to biased conditions.With the growing population, many administrative units need to be set up to govern the area.These administrative units further pull a greater number of populations into the urban, and it continues like a cyclic effect.The study area has seven prominent urban centres located surrounding the Tiruchirappalli Municipality Corporation.Except for Viralimalai, all the urban centres have a long history of discharging administrative services at various levels.These urban centres had pulled the rural people to move to these urban centres and controlled a mass transition of population from the surrounding rural areas to the Tiruchirappalli Corporation.This has resulted in comparatively fair population growth in the Tiruchirappalli Corporation.
In addition to the population pulling factor of the urban centres, the location of the tier towns is another factor in controlling the population accretion of an urban centre.Referring to the distance between urban centres, Manachanallur and Thiruverumbur are the closest urban centres with the highest potential in functioning as satellite towns.Musiri, Viralimalai and Manapparai are the next closest towns with prominent connectivity.
Built-up density is one of the crucial indicators to assess the quality of living and morphological characteristics of the urban environment.The temporal changes in the built-up density among the urban centres can be correlated with the other urban centres to assess the relative growth and pattern during the study period.All of the urban centres have recorded remarkable growth in the built-up density; especially, Viralimalai has recorded the greatest change in the built-up density.
Spatial entropy is a technique to assess the diversity of urban spatial growth.Similar to the built-up density, spatial diversity is also an important indicator to assess various associated qualitative and quantitative factors.Tiruchirappalli, at the pivot of the tier urban centres, boosts the developmental activities in these urban centres.
Although, the decreasing trend in the spatial entropy is to be addressed properly to manage the natural environment.The analysis reveals varying degrees of urbanization concerning built-up density and spatial diversity.Manachanallur is emerging as the prominent urban centre next to Tiruchirappalli on the north and Viralimalai on the south.Though Thiruverumbur is located very close to Tiruchirappalli, the study reveals the relative growth is not higher than Manachanallur and Viralimalai.

Fig. 1
Fig. 1 Study area and the location of the urban centres.(Prepared using ESRI's ArcMap application)

Fig. 3
Fig. 3 Urban spatial growth of the Tiruchirappalli and tier towns for the period 1996 to 2020.(Prepared using ESRI's ArcMap application.)

Fig. 4
Fig. 4 Distribution of overall built-up area (in Hectares) of Tiruchirappalli urban and tier towns for the period 1996-2020.(Prepared using MS Office 2019 application) (color figure online)

Fig. 5
Fig. 5 Distribution of built-up density of Tiruchirappalli urban and tier towns across the zones for the period 1996-2020.The blue line represents the year 1996; the orange line represents the year 2008; Grey line represents the year 2020.(Source: Author generated table; Prepared using MS Office 2019 application.)(color figure online)

Fig. 7
Fig. 7 Spatial diversity across the eight zones of the urban centres (Fig a to g).The years 1996, 2008 and 2020 are represented in blue, green and red colour lines respectively.The values are scaled between 0 and 1 displayed in the polar graphs for eight cardinal directions.(Prepared using ESRI's ArcMap application.)(color figure online)

Fig. 8
Fig. 8 The composite diversity graph displays the urban centres with the diversity index.(Prepared in ESRI ArcMap application.)(color figure online)

Table 1
Details of the data used in the study

Table 2
Zonal-wise spatial growth (area in hectares) of the Tiruchirappalli and tier urban centres.The highlighted cells represent the built-up area coverage in order.Bold represents the first order and italic represents the second order.(Source: Author generated table; Prepared using MS Office 2019 application.)Manachanallur

Table 3
Zonal-wise Built-up density of Tiruchirappalli and tier urban centres.Bold represents the zones that have a density higher than 0.4 and Italic represents the zones that have a density lesser than 0.2.(Source: Author generated table; Prepared using MS Office 2019 application.)Manachanallur

Table 4
Zone level spatial diversity of the urban centres for the periods 1996, 2008, and 2020.Italic have a diversity index of more than 0.5.(Source: Author generated table; Prepared using MS Office 2019 application.)