Peri-urban dynamics: assessing expansion patterns and influencing factors

Background Peri-urbanization, the expansion of large metropolitan centers into adjacent peri-urban regions, is a growing concern due to land scarcity and escalating housing costs. These zones, a blend of rural and urban features, blur the line between urban and rural areas, creating new landscapes. This study examines historical, present, and potential growth trends in the peri-urban area surrounding Durgapur Municipal Corporation (DMC). Analytical techniques and spatial metrics are used to track development intensity changes over time, including built-up density, Shannon’s entropy, Landscape expansion index, Average Weighted Mean Expansion Index, Annual Built-Up Expansion Rate, Built-Up Expansion Intensity Index, and Built-Up Expansion Difference Index. Landscape indices like Patch Density, Edge Density, Landscape Shape Index, Largest Patch Index, Ratio of Open Space, and Area Weighted Mean Patch Fractal are used to understand fragmentation, connectivity, and spatial relationships. The Logistic Regression Model (LRM) is used to identify influencing factors and CA-Markov modeling for future built-up areas. Results Between 1991 and 2001, built-up area in the region increased significantly, primarily due to urban development near industrial zones, roadways, and mining areas. The growth was primarily concentrated in the western sector and near National Highway-2 (NH-2). Urban sprawl was a continuous trend, with the highest built-up density in the South-South-East (SSE) direction from 1991 to 2011. Additionally, a key determinant of built-up development was the distance to the city core. By 2031, the built-up area is expected to concentrate in the western and southeast regions, reaching 177.90 km 2 . Conclusions This expansion is attributed to urban development near industrial zones, roadways, mining areas, and other infrastructure. The study identifies distance to the city center as a significant influencing factor for built-up development. The results emphasize the need for inclusive urban planning methods prioritizing sustainable development principles and prudent resource management for future growth and efficient management in the DMC’s peri-urban area.


Introduction
Urbanization, driven by modern infrastructure and job opportunities, is a global phenomenon influenced by economic and demographic factors (Jat et al 2008;Abdo 2018).In developing nations, the demand for urban land is intensified by burgeoning population densities and socioeconomic drivers (Dutta et al. 2020;Nasir et al 2022;Hussain et al 2024).The liberalization of India's economy in 1991 led to rapid urban expansion, a concern increasingly echoed by urban planners (Ahluwalia 2002), especially in Indian cities (Ghosh and Das 2019).The United Nations projects that by 2050, 66% of the world's population will reside in urban areas (United Nations 2015).The allure of cities lies in their superior infrastructure, employment opportunities, and educational facilities (Aijaz 2019).However, urban areas are witnessing population growth beyond their core boundaries due to land scarcity and escalating housing expenses, with rural migrants often passing major cities (Paul 2012).Periurbanization, the expansion of large metropolitan centers into adjacent peri-urban regions, raises global concerns (Kuusaana and Eledi 2015).The intricate interplay of factors driving urbanization highlights the challenges faced by policymakers and urban planners amidst rapid urban sprawl (Mortoja and Yigitcanlar 2020;Mondal and Sen 2020).Peri-urban areas, situated at the nexus of rural and urban landscapes, serve as buffer zones around urban and regional hubs (Woltjer 2014;Mondal and Banerjee 2021).
Peri-urban zones are developed regions outside the city's formal boundaries, where rural and urban features merge due to rapid population growth and migration (Varkey and Manasi 2019;Rajput 2021).These zones blur the line between urban and rural areas, creating new landscapes as they encroach upon urban limits (Budiyantini and Pratiwi 2016).Key attributes of peri-urban zones include transitional status between agricultural and urban land uses, integration of urban characteristics into rural settings, and uncontrolled expansion near urban centers, often driven by infrastructure development and economic opportunities (UNESCO 2014; Hudalah et al 2007).Yunus (2006) identified four primary zones within peri-urban areas: townscape, rural-urban scape, urbanrural scape, and rural scape.In India, the close proximity between census towns and statutory towns is referred to as "peri-urban expansion." Peri-urbanization has become a significant phenomenon, leading to the emergence of transitional zones between rural and urban ecosystems (Paul and Dasgupta 2012).These regions not only bridge the gap between rural and urban areas but also pose unique challenges and offer opportunities.
Academic studies have used various methodologies to analyze and evaluate the expansion of peri-urban areas (Banzhaf et al. 2009;Ramachandra et al. 2012).Shaw and Das (2018) used remote sensing and Geographic Information System (GIS) techniques to illustrate the dynamics of peri-urban expansion in small and medium-sized cities.They used measures such as Shannon's entropy, built-up density analysis, zonal analysis, and the Urbanisation Intensity Index (UII).Dutta et al. (2020) used indicators like the Built-up Density Index (BUDI), Annual Built-Up Change Index (ABUCI), and Annual Urban Spatial Expansion Index (AUSEI) to quantify peri-urban growth.Rajput (2021) used spatial metrics like Growth Density, Urban Expansion Speed Index (UESI), Urban Expansion Intensity Index (LUII), and Landscape Expansion Index (LEI) to monitor spatial expansion dynamics in peri-urban areas.Lakshmipathi et al. (2021) investigated population growth changes in peri-urban areas using the Land Use/Land Cover Classification System (LULC).Dutta (2012) integrated multi-temporal satellite imagery to study peri-urban expansion characteristics.
This study uses advanced analytical techniques and models to analyze historical, present, and potential growth trends in the peri-urban area surrounding Durgapur Municipal Corporation (DMC).It uses built-up density, Shannon's entropy, built-up development analysis, Landscape Expansion Index, Average Weighted Mean Expansion Index, Annual Built-Up Expansion Rate, Built-Up Expansion Intensity Index, and Built-Up Expansion Difference Index to track development intensity changes over time.Landscape indices like Patch Density, Edge Density, Landscape Shape Index, Largest Patch Index, Ratio of Open Space, and Area Weighted Mean Patch Fractal are used to understand fragmentation, connectivity, and spatial relationships.The Logistic Regression Model (LRM) is used to identify influencing factors in peri-urban growth.CA-Markov modeling is used for projecting future built-up areas, providing insights into potential landscape changes for urban planning and decision-making.These methodologies provide a comprehensive understanding of peri-urban dynamics in the DMC area.From the above discussion, several research gaps have been identified like-the lack of an integrated, holistic approach to studying peri-urbanization dynamics in Indian cities, specifically focusing on comprehensive models that combine historical, present, and future growth trends while addressing both the spatial and socioeconomic drivers of peri-urban expansion.This research explores peri-urban growth dynamics in the DMC area using advanced analytical techniques and models.It tracks changes in development intensity over time, uses Shannon's Entropy to evaluate spatial dispersion, and uses landscape indices to understand fragmentation and spatial relationships.The study also employs the LRM to identify growth drivers and uses CA-Markov modeling to project future built-up areas.This comprehensive approach offers a holistic understanding of periurban dynamics, providing insights for urban planning and decision-making in the rapidly urbanizing region of DMC.

Study area
The Durgapur Municipal Corporation (DMC) is situated within the Paschim Bardhaman district of West Bengal.The renowned Bardhaman district, spanning from 23°53′N to 22°56′N and 88°25′E to 86°48′E, underwent a division on April 7, 2017.This division resulted in the creation of Purba Bardhaman district covering an area of 5421 km 2 and Paschim Bardhaman district covering 1603 km 2 (Government of West Bengal 2017).Paschim Bardhaman district is further segmented into two subdivisions, eight Community Development Blocks (CD Blocks), two Municipal Corporations, two Municipalities, 65 census towns, and 611 villages (District Survey Report 2021).Within the Durgapur Subdivision, there exists one municipal corporation, four CD Blocks, 41 census towns, and 161 villages (Fig. 1).The population has experienced a notable increase from 519,695 in 1991 to 642,855 in 2011, indicating a growth rate of 23.7% (Census of India 1991, 2001, 2011).Urban expansion in the southern region faces a natural barrier in the form of the Damodar River, consequently leading to a linear pattern of urban growth along the National Highway and Railway line.The Asansol Durgapur Development Authority (ADDA) oversees the planning and development of the sub-division, making it the second largest urban area in West Bengal after Kolkata (ADDA 1980;Choudhury et al. 2019).The Durgapur Municipal Corporation transitioned from a notified area to a municipal corporation between October 1, 1962and October 7, 1996(Census of India 2001).Surrounding the Durgapur Municipal Corporation are four community development blocks: Kanksa to the east, Faridpur Durgapur to the north, Ondal to the west, and Pandabeswar to the northwest.The area is bordered by the Damodar and Ajoy rivers to the south and north, and it represents a transition zone between the Jharkhand plateau and the Ganga-Brahmaputra mature delta plain (Ghosh et al. 2015;Haldar et al. 2023a, b).The region is notable for its agricultural practices and industrial complexes, fueled by abundant coal and mineral resources, which support human habitation and foster urban growth.The Durgapur region is well-connected to the rest of India via NH-2 and the eastern railway (Choudhury et al. 2019).This study focuses on the Durgapur subdivision, a boundary area between rural and urban zones, witnessing significant expansion since the establishment of Durgapur as a municipal corporation.The study specifically targets the peri-urban area in the periphery of the DMC to understand its dynamic growth.The study is divided into six sections.The first section provides an overview of urban areas, discusses periurban challenges, describes the study's location, objectives, and reviews relevant literature.The second section details data sources and methodology.Results obtained through various models are presented in the third section, with causes explored in the fourth section.The growth, dynamics, and validation of results are discussed in the fifth section, while the final section summarizes findings and outlines future research directions.

Image pre-processing and classification
To achieve the specified goals, Landsat TM data from 1991, 2001, and 2011, along with OLI TIRS data from 2021, were acquired via the USGS Global Visualization Viewers (GLOVIS).Detailed information regarding these data sources is provided in Table 1.The obtained satellite data underwent processing using ERDAS Imagine software.The layer stacking function within the Spectral toolbox was utilized to create false-color composite images.Radiometric tools were employed to carry out necessary corrections, thereby enhancing the overall quality of the satellite imagery.In preparation for image classification, all images were cropped to extract the research area defined by the Area of Interest (AOI).Image classification, as described by Lillesand and Keifer (1994), involves assigning specific labels or land cover categories to each pixel value based on its inherent properties.
This study utilized supervised classification with the maximum likelihood algorithm (MLC) technique.Over 2000 signatures were collected from four images and merged to distinguish distinct features for each land-use class.Ground truth points were used to classify satellite data into specific classes based on unique Digital Number (DN) values.To validate the classification, cross-referencing with disputed locations was conducted using Google Earth images.The satellite imagery of the research area facilitated the identification of various land types, such as fallow land, vegetation, settlements, water bodies, etc., based on their characteristics.Given the inherent limitations of satellite images, including limited spatial resolution and mixed pixels, visual interpretation was necessary for certain pixel values.This interpretation followed the approach outlined by Jensen et al. (2004) and was guided by changes in tone, texture, shape, size, and pattern of the features (Singh et al. 1997).

Accuracy assessment of LULC maps
Accurate evaluation of Land Use/Land Cover (LULC) data reliability and the precision of derived information are crucial (Butt et al. 2015).In order to uphold the credibility of our data, we meticulously conducted an accuracy assessment of LULC analysis spanning the years 1991, 2001, 2011, and 2021.Carefully selecting 100 ground truth points through the Google Earth platform, we applied both overall accuracy and the kappa coefficient to each categorized image.This comprehensive approach enabled a thorough examination of the alignment between the extracted values and the actual ground truth.To quantify the level of agreement between the extracted data and factual information, we employed four key metrics: overall accuracy, user accuracy, producer accuracy, and the kappa coefficient.
These metrics were calculated using established formulas (Gwet 2002;Viera and Garrett 2005).Additionally, the kappa coefficient was utilized to validate the CA Markov model.For validation, we collected over 100 random points from the actual 2021 LULC data and compared them to the predicted 2021 LULC data, following a set of defined steps: The result of kappa lies within 0 to 1.The value 1 implies the prefect or strong agreement and less than 1 reflects the less perfect agreement.Monserud and Leemans (1992) were classified the kappa coefficient into five categories on the basis of actual and expected result of images (Table 2).

Zonal analysis utilizing concentric rings
To initiate a detailed analysis of the built-up growth concerning direction, distance from the city center, and the peri-urban boundary of the DMC, the first step involved extracting built-up data from the Land Use/Land Cover (LULC) dataset.The study area was then divided into (1) Overall Accuracy = Total number of correctly classified pixels (diagonal) Total number of reference pixels × 100 (2) Users Accuracy = Number of correctly classified pixel in each category Total number of classified pixel in that category (the row total) × 100 (3) Producer Accuracy = Number of correctly classified pixel in each category Total number of reference pixel in that category (the colum total) × 100 six zones, following a clockwise pattern with 45-degree intervals.Simultaneously, concentric rings at 500-m intervals emanated from the city center, as established by Shaw and Das (2018).These directional zones were designated as SSW (South-South West), NNW (North-North West), N (North), ENE (East-North East), ESE (East-South East), and SSE (South-South East).The orientation of administrative units was determined based on the geographical center of these units.Buffer rings were seamlessly integrated with the directionally categorized administrative units to facilitate a comprehensive analysis of built-up growth across various dimensions (Fig. 1).

Built-up density index (BUDI)
The built-up density index serves as a valuable metric for assessing the ratio of the total built-up area to the overall area (Dutta et al. 2020).This index proves instrumental in gauging the extent of built-up intensity per unit area and evaluating the degree of urbanization in a specific area.In this study, the Built-Up Density Index (BUDI) was computed for the years 1991, 2001, and 2011.This calculation aimed to discern the spatio-temporal changes in built-up intensity per unit area, employing the following equation:

Shannon's entropy
Shannon's entropy, one of the most important metrics for assessing the urban sprawl problem, can be computed using the following formula (Sudhira et al. 2003): where the proportion of the variables in the ith zone is P i , and the total number of zones in the area is n.The Shannon entropy varies between 0 and lgn.Here, lgn represents the upper limit.A resulting value of 0 indicates a highly concentrated distribution, suggestive of sprawl.Conversely, a distribution extending towards lgn suggests urban sprawl (Sudhira et al. 2003;Shaw and Das 2018).

Landscape expansion index
The method for categorizing urban growth into infilling, edge expansion, and spontaneous growth originally proposed by Wilson et al. (2003) was later refined by Xu et al. (2007) and Pham and Yamaguchi (2011).In this study, the growth of the built-up area is quantified using the Landscape Expansion Index (LEI), which assesses the proportion between the length of the newly formed urban body and the old urban body (Nong et al. 2018;Sun et al. 2013;Mandal et al. 2020).The calculation of LEI is based on the formula introduced by Xu et al. (2007).
where P is the newly expanded urban body's perimeter and Lc is the length of the shared boundary between the old and new urban bodies.The value falls between 0 and 1.When the resulting value is 0 < LEI ≤ 0.5, edge expansion is taken into consideration, when the LEI value is > 0.5, the infilling growth type is taken into consideration, and when the LEI value is 0 it is considered spontaneous growth (Nong et al. 2018).

Area-weighted mean expansion index (AWMEI)
Liu et al. ( 2010) introduced the Area-Weighted Mean Expansion Index (AWMEI) as a method for discerning the relative prevalence of different forms of urban growth across terrain or over time (Nong et al. 2018).The calculation of AWMEI is as follows: (5) Builtup Density = Total builtup area Total area × 100 (6) where LEIi is the Landscape Expansion Index of ith zone, a i is the area of new built-up and A is the total area of new built-up patches.Higher density is indicated by a higher AWMEI value, while spontaneous expansion or leapfrog developments are implied by lower values.

Annual built-up expansion rate (ABER)
The ABER (Average Built-up Expansion Rate) computes the mean yearly expansion rate of developed land across the entire study area during two specified periods (Akubia and Bruns 2019).This index provides an assessment of the area-specific quantum rate of change in developed land (Acheampong et al. 2016).The formula for ABER is outlined below: where t1 is the base year, t2 is the final year, and BUA i is the built-up area of the ith year.

Built-up expansion intensity index (BEII)
The BEII (Built-up Expansion Intensity Index) quantifies the average annual proportion of newly added builtup urban area relative to all changed areas, serving as a representation of urban expansion potential.This index assesses the rate or intensity of urban land-use change over time (Abdullahi and Pradhan 2017).The formula for BEII, as provided by Akubia and Bruns (2019), is presented below: where BUA i is built-up area of ith year, t1 is the base year and t2 is the final year.The study region's total area is denoted by the TLA i and t is the interval of two time periods.

Built-up expansion difference index (BEDI)
The BEDI serves as an indicator of the pace of urban growth relative to the broader research domain (Lu et al. 2014).Utilizing this index facilitates the analysis of urban built-up land expansion patterns across diverse geographical units, enabling the identification of urbanization hotspots (Li et al. 2015).Essentially, the measure compares the urban growth of a specific unit with that of the entire study area (Acheampong et al. 2016).The formula for calculating the BEDI is provided below (Akubia and Bruns 2019): (9 where BUA t1 i and BUA t2 i are the built-up area for the time period of base year and the final year of the ith unit.

Built-up landscape metrics
Landscape metrics play a crucial role in analyzing the urban growth pattern through built-up patch.In this context, a "patch" refers to a reasonably homogeneous region that distinguishes itself from neighboring areas, representing a fundamental unit in any landscape (Sun et al. 2013).The study employs patch analysis to assess changes in the built-up landscape pattern.Various indicators, each with specific implications for the performance of urban patches, are utilized in this research.The selection of these metrics is based on prior studies, as there is no standardized definition of a pattern metric or a systematic process for their application in specific contexts.Detailed descriptions of the selected indicators are provided in Table 3.

Factors associated in urban growth
This study focuses on the urban expansion that occurred from 1991 to 2011, using it as the dependent variable for a logistic regression analysis to establish a causal relationship.The urban expansion is represented through a map incorporating two land use categories: Urban Expansion (y = 1), identifying regions with significant growth during 2001-2011, assigned a value of 1; and No Urban Expansion (y = 0), covering areas without noticeable growth in that time frame, assigned a value of 0 (Salem et al. 2019).The study utilizes this map-based classification to conduct a logistic regression analysis (Shu et al. 2014), exploring the relationship between predictor variables and the likelihood of urban expansion.The selection of independent variables, crucial in logistic regression, involved identifying eight factors (Table 4) based on insights from literature reviews and expert discussions.These factors were chosen with the aim of incorporating them into the model (Salem et al. 2019;Ju et al. 2016;Osman et al. 2016).

Variance inflation factor test
To run the Logistic regression, in this study the Variance Inflation (VIF) Factor and Tolerance have been measured to validation of explanatory variable.The VIF value was calculated by following equation: where a i indicate the coefficient of determination of the regression equation of vectors.
When the VIF value is > 5 and Tolerance value < 0.1 also indicate the multicollinearity problem of dataset.In this study, the VIF and tolerance value were obtained < 5 and > 0.1 respectively, which indicates no multicollinearity among the explanatory variables (Bera et al. 2020).

Logistic regression model (LRM)
A logistic regression analysis was employed to examine the driving factors behind the expansion of built-up areas in the peri-urban region of DMC.The model was applied to estimate the probability of built-up expansion based on independent variables, as outlined by Sefidi and Ghalehnoee (2016).In this study, the model was fitted to identify areas undergoing built-up expansion.The dependent variables in the model had binary values of 0 and 1, where 0 indicated non-built-up expansion areas, and 1 represented built-up expansion areas during the period 2001-2011, as previously mentioned.The random point selection technique was utilized to gather data points for both built-up and non-built-up areas, with over 1000 sites selected randomly (Bera et al. 2020).Given the binary nature of the dependent variable, the logistic regression model was deemed suitable for application.All mathematical assumptions were based on the probability of the dependent variable taking the value of 1, following a logistic curve, and its calculation was expressed by the following equation: where b 1 , b 2 , b 3 are the coefficients, and x 1 , x 2 , x 3 are the causative variable, a stands for constant values.
where function y represents the logit(P), y is associated function of causative factors and P represents the probability.

Accuracy assessment and LR model validation
Any study must include validation as a critical component that ensures the validity of the results (Butt 2015).Our main focus in this study was to assess how well the (13  Logistic Regression Model (LRM) predicted the most important variables driving the growth of DMC's periurban area.We used a graphical depiction known as the Receiver Operating Characteristic (ROC) curve to illustrate this goal.It shows the true positive rate (y-axis) and the false positive rate (x-axis) across a range of threshold levels (Zou et al. 2007).We applied 1,000 stratified random sampling sites as part of our thorough validation process.For the ROC calculation, we used a tried-andtrue technique (Steen 2021).
where TPR is true positive rate, FPR is false positive rate, TP is true positive, FP is false positive, TN is a true negative, and FN is false negative respectively.

Forecasting of built-up area
The Land Change Modeler (LCM) module within TerrSet software has successfully integrated Markov chain modeling using the Multi-Layer Perceptron Classifier (MLP) to assess and forecast land cover changes as outlined by Clark Labs (2020).The LCM module offers tools for Change Analysis, Transition Potentials, Change Prediction, and Planning Interventions (Ngoy et al. 2021).In this research, MLP was used to identify trends, assess urbanization expansion, model transition potentials, and forecast changes.The study focused on understanding land conversion from different classes to urbanized regions and detailed spatial changes over three distinct time periods (Singh et al. 2022).Spatial trend plots were generated using a ninth-order polynomial function to capture evolving patterns over time.Higher values on trend plots indicate more significant modifications, (17 while lower values suggest stable or less variable conditions (Clark Labs 2020).Smaller orders reveal more generalized trends, while larger orders reveal more detailed trends.These analyses were conducted within the LCM software's integrated spatial analysis module, providing valuable insights into the dynamic nature of land use and land cover transformations.
The Land Change Modeler (LCM) was used to generate transition potential maps in this study, which employs a supervised backpropagation algorithm and consists of three layers: the input layer, the hidden layer, and the output layer.The hidden layer plays a crucial role in identifying patterns and relationships between inputs and outputs (Bhanage et al. 2021).Each neuron calculates values based on the product of values within nodes and network weights connecting them.The backpropagation algorithm is used to iteratively train neurons by adjusting network weights to minimize errors (Ngoy et al. 2021).The Multi-Layer Perceptron Neural Network (MLPNN) was used to estimate transition potentials.A randomized set of sample cells was generated within each land transition sub-model, representing areas that had either undergone or not undergone the Land Use and Land Cover (LULC) transition from one class to another (Singh et al. 2022).Almost 50% of these sample cells were allocated for training and the remaining 50% for testing (Clark Labs 2020; Sang et al. 2011).The weights of each connection were adjusted through iterative steps to minimize errors.After 10,000 iterations, the MLPNN achieved an accuracy rate exceeding 70%, considered satisfactory (Sang et al. 2011).These generated transition potentials played a pivotal role in predicting future LULC changes.Methodological workflow of the study assessing built-up growth and its spatial zoning in the peri-urban region of DMC is addressed in Fig. 2.

Built-up growth and spatial zoning Spatiality of built-up growth in the peri-urban region of DMC
The study used satellite imagery to analyze Land Use/ Land Cover (LULC) types in the peri-urban and rural areas of DMC between 1991DMC between , 2001DMC between , 2011DMC between , and 2021.Results showed remarkable precision, with producer and user accuracies consistently exceeding 90% for all four years.The Kappa coefficient showed high values.Vegetated land initially dominated peri-urban and rural areas around DMC, covering 47.76% of total land use and land cover in 1991.However, its coverage decreased to 34.59% in 2001 and 23.86% in 2011.Agricultural land expanded to become the primary LULC type in 2001, 2011, and 2021.Built-up land and mining areas also grew from 1991 to 2021, while fallow land increased but declined (Table 5).Water bodies covered decreased in 2011 but

Typology of built-up growth in the peri-urban region of DMC
Using the Land Expansion Index (LEI), the study looked at peri-urban region of DMC, urban growth patterns from 1991 to 2001 (Fig. 4a), 2001 to 2011 (Fig. 4b), and 2011 to 2021 (Fig. 4c).The main growth mode was mostly edge expansion, which covered 46.73 km 2 .Outgrowth occurred between 2001 and 2011 and between 2011 and 2021.On the other hand, infilling growth was negligible, making up a mere 0.02 km 2 .The results of the investigation showed that edge expansion dominated in all directions.Additionally, the developed growth showed continuity, with outgrowth units growing in the second and decreasing in the third periods (Varkey and Manasi 2019).The spatial and temporal profile of AWMEI (Area Weighted Mean Expansion Index) was assessed utilizing LEI (Land Expansion Index) values in conjunction with the multiplication of LEI values by the ratio of new built-up to total builtup area, as previously elucidated (Singh et al. 2022).
During the initial time frame (depicted in Fig. 4d), the predominant characteristic was dispersal, encompassing the largest area, while certain segments within buffer zones ranging from 15,000 m to 19,500 m in the SSW, NNW, and ESE directions displayed compact features.Between 2001 and 2011, a more compact region was discerned in the same directions, albeit with an expanded area (Woltjer 2014;Xu et al. 2007).Particularly noteworthy was the compactness observed in the SSW direction within a radius spanning from 14,000 m to 18,500 m, and in the NNW direction from a buffer zone of 12,500 m to 20,000 m (Fig. 4e).Conversely, in the ESE and SSE directions, a compact zone was identified between buffer zones of 7500 m and 11,000 m, contrasting the trends observed previously.In the third temporal period (Fig. 4f ), dispersal characteristics retained dominance over compact regions.The relatively compact area sustained its expansion and spatial location, mirroring the patterns observed in the preceding two time periods.

Typology of urban sprawling in the peri-urban region of DMC
The assessment of urban expansion in the periphery of the Durgapur municipal corporation employed Shannon's entropy method.The analysis encompassed 202 administrative units and six directional sectors with 41 buffer zones based on built-up surfaces.In 1991, the collective entropy value for all zones stood at 6.34, which rose to 6.41 by 2001, indicating a more dispersed distribution of built-up areas compared to the previous decade.The logarithmic value (lgn) for the entire peripheral region in 2001 reached 7.01 (Shu et al. 2014;Siddiqui et al. 2018).Subsequently, by 2011, the entropy value further escalated to 6.48, and by 2021, it peaked at 6.51, suggesting a consistent trend of urban sprawl dispersion from 1991 to 2021.The analysis also examined the directional aspects of sprawl over the years.In 1991, the entropy value for the entire area was 4.39 (Fig. 5a), marginally increasing to 4.54 by 2001 (Fig. 5b).In 2011 and 2021, the entropy values for sprawl direction were 4.51 and 4.54, respectively (Fig. 6c and d).Notably, the logarithmic value (lgn) for the ENE direction in 2021 was 5.41.In the ESE direction, entropy values were 4. 45, 4.56, 4.51, and 4.54 for 1991, 2001, 2011, and 2021, respectively, with a corresponding lgn value of 5.23.The N direction exhibited increasingly dispersed sprawl, with entropy values of 4. 64 and 4.70 in 1991 and 2001, rising to 4.76 and 4.77 in 2011 and 2021, respectively (Fig. 5c and d).The lgn value for this direction in 2021 was 5.43.Conversely, in the NNW direction, entropy values were 4. 95, 4.85, 4.91, and 4.99 for 1991, 2001, 2011, and 2021, respectively, accompanied by a lgn value of 5.64.For the SSE direction, the lgn value stood at 3.58, with entropy values of 3. 14, 3.19, 3.17, and 3.11 for 1991, 2001, 2011, and 2021, respectively.Finally, in the SSW direction, entropy values were 4. 55, 4.59, 4.57, and 4.57 for 1991, 2001, 2011, and 2021, respectively, alongside a lgn value of 5.03 (Rajput 2021;Li et al. 2015).

Typology and spatiality of built-up expansion and intensity in the peri-urban region of DMC
The section investigates the Average Annual Rate of Built-up Land Expansion (ABER) in various directional zones within the peri-urban area.ABER measures the yearly growth of built-up areas.From 1991 to 2001, the average ABER was 4.48 km 2 per year (Fig. 6a), with the ENE direction expanding at 1.88 km 2 per year.From 2001 to 2011, the mean ABER increased to 4.62 km 2 per year, with ENE seeing a significant rise to 7.22 km 2 per year (Fig. 6b).However, from 2011 to 2021, the overall ABER decreased to 1.55 km 2 per year (Fig. 6c).Notably, areas with very low expansion increased while those with low and moderate expansion decreased.In the ESE direction, ABER declined from 8.10 km 2 per year (1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001) to 1.32 km 2 per year (2011-2021), indicating active urban growth.In the N direction, ABER fluctuated, showing a dynamic growth pattern.These findings highlight the changing urban expansion rates, offering insights into the evolving peri-urban landscape.
With a noticeably low (2.00) Built-up Expanding Intensity Index (BEII), the BEII values were divided into five groups.While places with extremely low intensity fell by 19.09% between 2001 and 2011, areas with intermediate intensity increased by 0.37%.BEII stood at 0.70% in the ESE direction between 1991 and 2001 (Fig. 6d), increased to 0.72% between 2001 and 2011 (Fig. 6e), and then decreased to 0.23% between 2011 and 2021 (Fig. 6f ).There were regions classified as high and very high intensity between 1991 and 2001 (1.57% and 1.01%), which rose between 2001 and 2011 (2.19% and 1.50%), but fell by 0.65% between 2011 and 2021.Between 2011 and 2021, the region with extremely low intensity increased steadily, reaching 15.98%.BEII increased from 0.08% in the N direction in 1991-2001 to 0.11% in 2001-2011.Low-and very-low-intensity regions showed patterns of dynamic expansion that peaked between 2001 and 2011 and then declined.Between 2011 and 2021, the extremely low intensity zone grew significantly, reaching 22.94%.Between 2001 and 2021, there was a significant rise in very low intensity areas (1.67%) and high intensity areas (0.33%) and very high intensity areas (0.21%) compared to the previous year (Sang et al. 2011).BEII stood at 1.11% in the west-northwest direction from 1991 to 2001, dropped to 0.64% from 2001 to 2011, and then rose once more to 1.11% from 2011 to 2021.While low and extremely low intensity regions showed variations, regions of very high, high, and moderate intensity peaked from 2011 to 2021 and fell from 2001 to 2011.
The Built-up Expansion Density Index (BEDI) is crucial in understanding urbanization trends in peri-urban areas under Durgapur Municipal Corporation's jurisdiction across three periods : 1991-2001, 2001-2011, and 2011-2021.BEDI values are categorized into five classes.With an average BEDI of 3.11 (Fig. 6g) in the peri-urban area, there was a notable increase between 1991 and 2001.By 2001-2011, the figure abruptly increased to 6.34 (Fig. 6h), showing rapid expansion, and by 2011-2021, it had dropped to 2.81 (Fig. 6i), demonstrating monitored growth.In various directions, BEDI dynamics varied, with intense urbanization in the ENE sector and controlled expansion in the ESE region.Shifts in urbanization dynamics were observed in the Nand NNW zones.Continuous urban expansion was noted in the SSE sector, while strategic planning drove growth in the SSW direction (Sarkar and Chouhan 2020).The spatial distribution indicated an increase in very low BEDI regions by 2011-2021, alongside a decrease in areas with high BEDI scores, highlighting controlled urbanization strategies.These shifts reflect the complex interaction of socioeconomic factors, policies, and geographical constraints, guiding future developmental policies (Pham and Yamaguchi 2011;Paul and Dasgupta 2012).

Assessing built-up fragmentation using landscape metrics
Patch density (PD) serves as a crucial metric for assessing landscape fragmentation, offering insights into the varied urban growth patterns.It is influenced by both the quantity of patches and the size of the study area.In 1991, the analysis revealed the highest PD values in the SSW, NNW, and SSW directions, while the lowest values were observed in the ENE direction (Fig. 7a.i).By 2001, a similar trend persisted, albeit with an overall increase in PD values (Fig. 7a.ii).In 2011, maximum PD values continued to be prominent in the same directions observed in 1991 and 2001, with additional increments in the N and ESE directions (Fig. 7a.iii).Remarkably, by 2021, there was a substantial escalation in PD across all directions (Fig. 7a.iv).The highest PD values were identified in the SSW, NNW, ESE, and SSE directions, while the lowest values were noted in the N and ENE directions.This indicates a more diversified and fragmented urban growth pattern, characterized by a proliferation of minor patches (Osman et al. 2016).
The Largest Patch Index (LPI) is a vital measure in assessing spatial fragmentation within built-up landscapes.This study focuses on analyzing the growth pattern of built-up areas in DMC.In 1991 (Fig. 7b.i), the highest LPI values were observed in the SSW and SSE directions, with most areas characterized by very low LPI values.By 2001 (Fig. 7b.ii), regions with high and very high LPI expanded in the SSW, NNW, ESE, and SSE directions.In 2011 (Fig. 7b.iii), the trend continued, with high LPI regions increasing in the same directions.In 2021, a notable rise in very high LPI values was noted in the SSW direction, while high LPI regions decreased in the NNW and ESE directions (Fig. 7b.iv).This suggests an ongoing trend towards increased clustering and contiguity of built-up areas, particularly in the SSW direction, in the DMC.
Edge density (ED) measures landscape fragmentation, with higher values indicating increased fragmentation.This affects habitat quality, connectivity, and water, nutrient, and energy flow.It's crucial for evaluating urbanization's impact on landscapes and guiding land use and conservation planning.As shown in Table 6, the edge densities in 1991 were largest in the SSW, NNW, ESE, and SSE directions and significantly lower in the N and ESE directions, indicating a potential vulnerability to fragmentation brought on by urbanization.Changes in edge density over time varied according to direction.N, ENE, and SSE had a decrease in density in 2001, but SSW, NNW, and ESE saw an increase (Nong et al. 2018).This difference in density may have resulted from changes in land use, such as the conversion of agricultural land (Mortoja and Yigitcanlar 2020;Ngoy et al. 2021).By 2011, the denser area decreased relative to the previous  , 1991(Fig. 7c.i), 2001(Fig. 7c.ii), 2011 (Fig. 7c.iii), and 2021 (Fig. 7c.iv) reveals significant shifts in all six directions.Notably, the highly elevated region has diminished in extent in the ENE direction since 1991, with a slight increase in 2001 but a substantial decrease in 2021.Conversely, the low region has expanded in this direction since 2001.In the ESE direction, the maximum area occupied by the highly elevated region has steadily decreased since 1991, reaching a minimum in 2021, while the low region has consistently expanded.Similarly, in the NNW direction, the maximal area covered by the highly elevated region has decreased since 1991, with a continued trend evident in 2021, while the low region has steadily increased over the years.In the SSE direction, the area of the highly elevated region has fluctuated, rising from 2001 to 2011 but decreasing in 2021, with the very low region witnessing progressive expansion over the years.In the N and SSW directions, LSI values have continuously decreased, indicating diminishing complexity over time, with relatively modest areas allocated to low, moderate, and high regions.In summary, the data highlights significant alterations in LSI across all six directions in the vicinity of the Durgapur municipal corporation area, showcasing varying trends in the sizes of different regions (Mondal and Banerjee 2021;Mandal et al. 2020).
Urban openness is measured by the Open Space Porosity Ratio (OSPR), which is calculated by dividing the entire area covered by built-up elements by the total area of voids.More openness is indicated by a higher OSPR score, while more built-up space is indicated by a lower value.It takes into account both built-up and open spaces, and its range is 0 to infinity.More open space and less built-up areas are indicated by a higher OSPR, which helps researchers, politicians, and urban planners make future development decisions (Maimaiti et al. 2021;Lakshmipathi et al. 2021).The expansion of urban areas in those sectors during that time may be responsible for the trend of increased OSPR observed from 1991 to 2011 (Fig. 7d.i-7d.iv) in the SSW, NNW, ESE, and SSE directions.The consumption of non-built-up regions like woods, agricultural fields, and water bodies as a result of urban expansion causes the summization area of all "holes" to increase and the summization area of all "patches" to decrease.An increased OSPR could result from this expansion's creation of additional open spaces inside the built-up region.But in 2021, the pattern clearly changes, with a decline in OSPR seen in both N and ENE directions in addition to the same directions (SSW, NNW, ESE, and SSE).
Area-weighted mean fractal dimension (AWMPFD) is a metric in landscape ecology that gauges spatial complexity by combining fractional dimension and patch size distribution.It evaluates variability and fragmentation in the environment, with higher values indicating intricate shapes and lower values indicating smoother patterns with smaller sections.The study unveils a landscape characterized by complex and irregular shapes, with a consistent decrease in shape complexity from 1991 to 2021 (Fig. 7e.i-e.iv).Additionally, AWMPFD values consistently diminish in all directions throughout the three-decade period, suggesting a gradual reduction in the complexity of landscape patches or objects.The lowest AWMPFD value observed in 2021 indicates a shift towards simpler shapes, likely influenced by urbanization, land use alterations, and human activities.This data holds significance for informing sustainable development policies and management strategies.
The Class Area (CA) metric serves as a quantitative measure of land cover or land use type, spanning from 0 to infinity.Higher CA values signify greater development, whereas lower values suggest conservation efforts.Analyzing CA values across various land cover types can unveil areas undergoing rapid land use transformations, thereby facilitating project planning, zoning initiatives, and development regulations.In 1991 (Fig. 7f.i), significant changes were observed in the SSW, SSE, and ESE directions, with high CA values.By 2001 (Fig. 7f.ii), the SSE direction declined, indicating completion or shift.However, development continued in the SSW, NNW, and ESE directions, with expansions in 2011 (Fig. 7f.iii) respectively.The 2021 study found high CA regions in SSW, NNW, ESE, and SSE directions (Fig. 7f.iv), indicating sustained development over the past decade, while N and ENE directions showed low CA values, highlighting the disparate development distribution in peri-urban region of DMC.

Relation between built-up growth and fragmentation metrics
Over the years 1991-2021, there have been notable changes in the patterns of urban development in the peri-urban region of DMC.The share of developed regions has increased in the years that followed, especially on an upward trend in 2011 and 2021.This expansion is predominantly concentrated in the Ondal and Pandabeswar blocks, as well as along NH-2, owing to various factors such as the presence of railway stations (including Pandabeswar, Ukhra, Siduli, Ondal Junction, Kajoragram, Baktarnagar, Pinjrapol, Waria, Durgapur, Rajbandh, and Panagarh stations), major roads (such as NH-2, NH-60, and the Raniganj-Suri Road), and mining zones, all of which foster the city's growth.Concurrently, there has been a steady rise in population density, driven by significant growth in DMC cities (Gupta and Chatterjee 2015;Buchori et al. 2020;Banzhaf et al. 2009;Shaw and Das 2018).A well-established transportation network plays a pivotal role in regional development, offering ample opportunities to bolster economic progress, enhance access to resources and markets, and elevate overall living standards.A robust transportation system not only enhances travel efficiency but also stimulates commerce (Haldar et al. 2023a, b), investment, and connectivity in surrounding areas, thus serving as a catalyst for societal advancement and urban development (Sarkar et al. 2020).The situation is similar in peri-urban region of DMC, due to factors such as established road connectivity, presence of railway stations, proximity to mining areas, and presence of industrial areas (Haldar et al. 2023a, b).These factors explain the patterns of urban development and growth seen in major cities.
Access and connectivity to the main road network will make the surrounding area more attractive for urban expansion.In addition, railway stations can act as catalysts for development by increasing accessibility and stimulating economic activity.Proximity to mining sites makes it easier for residents to build infrastructure to support mining operations.Industrial areas attract workers and industry, encouraging the development of urban areas.The interaction of these factors creates a dynamic environment that encourages the expansion of certain areas around the city, driven by the main purposes of development in those areas (Salem et al. 2019).Shannon entropy is used in this study to analyze the characteristics of growth.A trend towards a more dispersed pattern of urban expansion and the rapid expansion of built-up regions in the research area are shown by the obtained Shannon entropy values, which exhibit a significant increase over time.It is critical to comprehend this data in order to focus on new spatial patterns, opportunities, and difficulties as well as how urbanization is evolving in the area (Shaw and Das 2018;Sudhira et al. 2003).
The analysis carried out using the LEI model showed a significant increase in lateral expansion, especially in the areas of the Ondal and Pandabeswar Blocks and on the NH-2 road.In the following decades (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011), the maximum ABER shifted slightly to the N and NE, indicating a change in the distribution of urban sprawl.From 2011 to 2021, the expansion of the city along NH-2 shows the continuous growth of the city in this well-connected region (Nong et al. 2018;Lakshmipathi et al. 2021).Analyzing the BEII from 1991 to 2021, low BEII values were found in the areas surrounding the DMC, with growth rates initially observed alongside NH-2 and NH-60.Looking at the BEDI by region, it can be seen that most regions have low or very low Expanded Difference Index values from 1991 to 2021.This indicates slower cumulative growth for other regions.Recently, areas west of the DMC, especially along NH-2, have shown high BEDI values, indicating a rapidly expanding urban area (Akubia and Bruns 2019;Kuusaana and Eledi 2015;Ghosh and Das 2019).
It came to light that all of the measures showed an increased trajectory when more indices were examined, including Patch Density (PD), Edge Density (ED), Landscape Shape Index (LSI), Landscape Pattern Index (LPI), and Clumsiness Index (CA).Trends in the SSW, NNW, ESE, and SSW orientations were especially noteworthy and revealed a unique urban layout (Mandal et al. 2020).The Landscape Shape Index (LSI) consistently decreased from 1991 to 2021, suggesting a trend toward increased compactness in urban areas.Despite the expansion of built-up areas leading to a growth in the total class area, this continuous decrease was observed (Sun et al. 2013).These findings are consistent with the diffusion-coalescence theory, emphasizing the urban expansion trend in the study region (Nong et al. 2018).The Ratio of Open Space (ROS) exhibited growth from 1991 to 2011, indicating infilling between built-up areas during that period.However, a recent slight decrease in ROS suggests that new construction areas in 2021 have filled these spaces (Dutta and Das 2019).Regarding the Average Weighted Mean Patch Fractal Dimension (AWMPFD), built-up areas underwent a transition from a less complex structure to a more compact form from 1991 to 2021 (Dasgupta et al. 2010).
Important new insights into the dynamic transformation in the peri-urban region and the changing patterns of growth within the research domain are provided in this study.These observations give politicians and planners the strategic information they need to get ready for future urban development.An analysis of urban development patterns and trends in the peri-urban area of DMC spanning from 1991 to 2021 reveals significant transformations.Particularly noteworthy is the substantial increase in built-up areas observed in the years 2011 and 2021, notably in high-growth zones such as Ondal and Pandabeswar blocks, as well as along NH-2, serving as pivotal centers of growth.This expansion was facilitated by well-established transportation networks, encompassing roads, railways, and access to mining and industrial zones.To elucidate the drivers of urban growth and anticipate future city expansion, this study employed the Logistic Regression Model (LRM).The LRM analysis identified key drivers such as distance to infrastructure and water sources, proximity to the city center, and population density (Salem et al. 2019).Furthermore, the Cellular Automata (CA) Markov Analysis was utilized to model potential future urban growth based on historical data, providing insights into the probable locations and trajectories of expansion (Singh et al. 2022).Together, these methodologies constitute a robust framework for examining urban growth dynamics, offering invaluable insights for urban planning and strategic decision-making.

Model fit evaluation and multicollinearity analysis
Two common indicators, the variance inflation factor (VIF) and tolerance values, were examined to evaluate multicollinearity (Salem et al. 2019;Bera et al. 2020) among the independent variables.The investigation revealed that all variables had a VIF of less than 5 and tolerance values exceeding 0.1 (Table 7), indicating the absence of significant multicollinearity among the variables.
This indicates that the model effectively captured the relationship between independent variables and the percentage change in urban area (Dai et al. 2018).To assess how well the model explained the variation in urban expansion, two pseudo-R-square values, Cox and Snell R-squared, and Nagelkerke R-squared, were used.The Cox and Snell R-squared, indicating the proportion of variance left unexplained, was approximately 0.262, while the Nagelkerke R-squared was 0.388 (Table 8).Overall, these values indicate that the model provides a moderate level of explanatory power and makes a significant contribution to the understanding of factors influencing urban expansion (Salem et al. 2019).

Impact of independent variable on expansion of built-up areas
The study examines the relationship between urban expansion and the factors influencing development in a region, focusing on the coefficients of independent variables, which indicate the magnitude and direction of the relationship.These coefficients, derived from linear regressions, indicate both the magnitude and direction of the relationship between each independent variable and the response variable, urban expansion (Siddiqui et al. 2018).Positive coefficients are observed for variables such as "distance to industry" (Fig. 8b), "population density" (Fig. 8d), and "distance from railway station" (Fig. 8e).
Consequently, an increase in these variables correlates with a higher probability of urban growth.On the contrary, variables like "distance to city center" (Fig. 8a), "distance to mining area" (Fig. 8c), "distance to regional center" (Fig. 8f ), "distance to nearest main road" (Fig. 8g), and "distance to water stream" (Fig. 8h) exhibit negative coefficients.This implies that as these variables increase (indicating greater distance from these features), urban sprawl is more likely to decrease.Areas situated farther from the city center, mines, regional cities, major roads, and water streams are less prone to expansion.For instance, the negative coefficient associated with "distance to city center" (in Table 9) suggests that as the distance from the city center increases, urbanization tends to decrease.This aligns with the typical pattern of urbanization spreading outward from city centers, with areas further away being less likely to undergo urban development (Salem et al. 2019).
The study reveals that urban expansion is influenced by eight factors, with odds ratios indicating their impact on urban growth.The probability of urban expansion in areas near the city center is approximately 5.52 times higher than that 1 unit further away.The odds ratios for areas near mining sites, regional centers, nearest main roads, and water streams are 0.592, 0.670, 0.989, and 0.673, respectively.These ratios suggest that the expected urban expansion in these areas is 1.69, 1.49, 1.01, and 1.49 times the urban expansion rate.For industrial areas, the odds ratio is 1.356, indicating that a 1 unit increase  in distance to industrial areas corresponds to an approximately 0.74 times increase in urban expansion.For population density, the odds ratio is 1.521, indicating that a 1 unit increase in distance to densely populated areas results in 0.65 times increase in the tendency for urban expansion.For railway stations, the odds ratio is 1.336,  suggesting that a 1 unit increase in distance to a railway station corresponds to an approximately 0.75 times increase in the odds of urban expansion (see Table 10).In essence, areas closer to railway stations are more likely to undergo urban development (Ghosh et al. 2015).
There are interesting patterns among the dependent variables when the estimated means are analyzed.The likelihood of urban expansion experiences a notable decline at a distance of 1.81 units from the city; reaching 0.966 (see Fig. 9a).Subsequently, a discernible correlation emerges, illustrating that as the distance from the city expands, and the probability of urban sprawl continues to diminish.This trend suggests that areas proximate to the city within the Durgapur Municipal Corporation exhibit higher levels of urbanization, whereas those farther away demonstrate lower degrees of urban development.Regarding the variable "distance to industry, " it was observed that the likelihood of urban expansion rises with increasing distance from industrial zones (Fig. 9b).Similarly, analyzing the distance to mining sites reveals a decline in the probability of urban sprawl as the distance from mining areas increases (Fig. 9c).
The greatest probabilities were identified in close proximity to mining regions, indicating a tendency towards urban development in those locales.A consistent pattern emerges concerning the population density index, indicating a heightened risk of urban sprawl from regions with higher population density to those with lower densities (Fig. 9d).The examination of the "distance to train station" demonstrates that the risk of urban sprawl escalates with distance from the station (see Fig. 9e).Similarly, the likelihood of urban expansion in relation to the "distance to regional center" (Fig. 9f ) significantly diminishes with increasing distance from said center.For instance, in the vicinity of the DMC, the calculated probabilities at mean distances of 1.62, 2.58, and 3.54 units are 0.898, 0.856, and 0.802, respectively, indicating a greater urban growth propensity in closer proximity to regional centers.Furthermore, an analysis of the "distance from the nearest main road" reveals that closer proximity to main roads correlates with a higher potential for urban sprawl (Fig. 9g).Lastly, the assessment of "distance to water flow" indicates that the potential for urban sprawl decreases as the distance from water sources increases (Fig. 9h).Regions adjacent to water bodies often exhibit a higher likelihood of urbanization, underscoring the influence of water bodies on urban development patterns.

Model validation
In this study, we used ROC (relative operating characteristics) curves to evaluate the effectiveness of a model for predicting the probability of development expansion in the peri-urban areas of Durgapur Municipal Corporation.The ROC curve serves as a clear visual representation of the balance between true and false positive predictions, providing insight into the accuracy of the model (Zou et al. 2007).The curve is plotted with the true positive rate on the Y axis and the false positive rate on the X axis.AUC value of 0.843 indicates (Fig. 10) a high level of validity and reliability in predicting settlement expansion in peri-urban areas of DMC (Table 10).It is important to emphasize this point when it comes to model validation.AUC examines the relationship between true positive rate and false positive rate over different probability thresholds.This method provides a robust assessment of a model's predictive ability and is distinguished from accuracy metrics, which measure the ratio of correctly predicted samples to the total number of samples (Zvornicanin 2021).

Analysis of spatial trends and transition models in built-up growth
This sub-section tries to investigate the transformation of land from non-built-up to built-up areas between 2001 and 2011 (Fig. 11a), focusing on the western sector of study region.Despite the presence of extensive built-up lands along NH-2 and in the western region, including industrial zones, mining areas, major road networks, and close proximity to Raniganj Municipality and Durgapur Municipal Corporation, the western area demonstrates a higher inclination for land transformation.The analysis delves into spatial trends within various land categories, including shifts from agriculture to built-up land (Fig. 11b), fallow land to built-up land (Fig. 11c), conversion of mining areas into built-up lands (Fig. 11d), transformation from vegetation to built-up land (Fig. 11e), and alterations from water bodies to built-up land (Fig. 11f ).The most significant trend values are identified in the western and southern segments of the peri-urban region under the jurisdiction of DMC.

Prediction and validation of 2021 LULC and built-up area for 2031
The peripheral region of DMC has experienced significant expansion since 1991, with a built-up area of 32.57km 2 .A projection for 2021's built-up area was 135.43 km 2 , based on MLP Markov analysis.The projection was compared with the actual built-up area through LULC analysis and assessed using the Kappa coefficient.
A rigorous cross-validation process involved randomly generating 100 sampling points for analysis.The model demonstrated an impressive 93% overall accuracy, with a Kappa coefficient of agreement of 0.82, indicating a substantial agreement between the predicted and actual data.
A validation map was generated to identify 'hits' and 'mis' regions, with 'hits' indicating where the predicted 2021 built-up data matched the actual data, and 'mis' regions indicating disparities between the anticipated and observed data.This comprehensive validation process confirms the accuracy and reliability of the model's calculations for the built-up area in 2021 (Fig. 12a).The projected built-up area in the DMC peri-urban zone for 2031 is expected to be 177.90km 2 (Fig. 12b), primarily concentrated in the western and southeast regions.This increase is primarily due to the extension of urban development towards the boundaries of the current builtup region, particularly in close proximity to industrial zones, roadways, and mining areas.This indicates a significant increase in the peri-urban area of DMC, which is expected to be a significant increase from the estimated 2021 built-up area.

Underlying process of urban growth in surroundings of DMC
The study reveals that built-up areas in the peri-urban region of Durgapur (DMC) have shifted from vegetation cover to agriculture and fallow land between 1991 and 2001, and from 2001 to 2011.This shift is particularly evident in the western and southern parts of the study area.The spatial analysis shows major trends in land classification change, with agriculture, fallow, mining, and vegetation shifting to impervious surfaces.Periurban growth has been observed in the direction of SSW, NNW, ESE, and SSE, with Shannon's entropy indicating sprawling.Most peri-urban areas experience edge expansion, while N and ENE experience outgrowth due to low built-up growth (Sarkar and Chouhan 2020).The study reveals a significant urban sprawling nature and compact urban growth in the direction of SSW, NNW, ESE, and SSE.The analysis of PD values shows a consistent increase in landscape fragmentation from 1991 to 2021, indicating a diverse urban growth pattern.The LPI shows spatial fragmentation of built-up areas, particularly in the SSW direction, indicating urban clustering.Fluctuating ED values suggest dynamic changes in urbanization impact (Shaw and Das 2018).LSI indicates increasing complexity over time, while the ROS shows a decrease in open spaces within built-up areas by 2021.The CA analysis shows uneven development distribution around the DMC, with built-up landscape metrics indicating dynamic, unplanned growth (Ramachandra et al. 2012).Negative coefficient for distance to city centers, mining areas, regional centers, and water streams negatively influences built-up expansion (Maimaiti et al. 2021).
The study reveals that mining areas in the western part of the peri-urban region face regulatory restrictions and environmental considerations that limit urban expansion.The proximity to water streams has a negative influence on the expansion of impervious areas due to the prevalence of fertile agriculture land near the Ajoy and Damodar Rivers.The smallest drainage patterns are nonperennial rivers primarily used for agricultural purposes during the rainy season.Population density near industry, railway stations, and main roads has a positive influence on urban growth (Diao et al. 2017).The total population has increased from 519,695 in 1991 to 642,855 persons in 2011.The western part of the study area has the highest population concentration, with railway stations such as Waria, Pinjrapol, Andal, Baktarnagar, Kajora Gram, Siduli, Ukhra, and Pandabeswar attracting the highest density of industries and mining activities.Major highways NH-2 and NH-60 are also situated in the area, fueling built-up growth.Railway stations and road transportation play a crucial role in urban development, offering greater accessibility and facilitating the transfer and movement of goods (Bubelíny et al. 2021).Infrastructure acts as drivers of economic activity and population growth, shaping the spatial distribution and trend of urban growth (Banister and Lichfield 2010).

Limitations of the study
The study on urban growth using multi-temporal remote sensing data has several limitations.These include data resolution and quality, temporal gaps and data availability, modeling and prediction limitations, ground truth verification, environmental and climatic factors, socio-economic and policy influences, and limitations in addressing informal settlements.Lower resolution images may not capture fine details, and variations in image quality over time due to different sensors, atmospheric conditions, and seasonal changes can affect data consistency.Temporal gaps and data availability may also affect the continuity and comprehensiveness of the study.The study's focus on accessibility and infrastructure may overlook other critical factors such as migration patterns, housing policies, and economic shifts.The model might not capture emergent phenomena or feedback loops inherent in urban systems, leading to an oversimplification of urban growth dynamics.By recognizing these limitations, the study's findings can be contextualized and further research directed towards addressing these gaps to enhance understanding and management of urban growth processes.

Conclusion
Using multi-temporal remote sensing data, this study sought to extensively investigate the growth patterns and important factors impacting the evolution of urbanized zones surrounding the Durgapur Municipal Corporation (DMC) in India.The data analysis revealed that there was a 15.20% increase in built-up land, an 8.09% increase in agricultural land, and a 3.94% increase in mining operations as a result of the growth of urban areas and increasing economic activity.On the other hand, decreases of 20.35%, 6.83%, and 0.21% were seen in vegetated land, uncultivated land, and aquatic bodies, respectively.These results illustrate the transformative effects of urbanization and economic development in the examined region, providing insightful information about the shifting landscape.
The study explores how patterns and trends in urban development have changed over almost three decades, from 1991 to 2021, in the peri-urban area of the DMC.Between 2011 and 2021, a notable and noteworthy expansion was noted in built-up areas, especially in strategic locations like Ondal, Pandabeswar blocks, and NH-2.Access to mining and industrial zones, together with well-established transportation infrastructure such as roads and railways, were cited as contributing factors to this rise.The study used a logistic regression model (LRM) to pinpoint the main factors-such as accessibility to the city center, water bodies, and infrastructure-that contribute to urban growth in emerging nations.These patterns offer insights into historical trends and aid in forecasting future urban evolution, providing valuable guidance for urban planners and policymakers grappling with the challenges of rapid urbanization and shifting socio-economic dynamics.Forecasts for 2031 show a considerable rise in the amount of built-up land in the peri-urban areas of the DMC, especially in the areas to the west and southeast.It is projected that the mining, transportation, and industrial sectors will account for the majority of this projected growth, which will encompass 49.77 km 2 and add to the overall area of 177.90 km 2 .The process of urbanization is bringing about a dynamic shift in the physical environment of the city, mainly due to the expansion of infrastructure and industry.These projections highlight the need for inclusive urban planning methods that give priority to sustainable development principles and prudent resource management in order to allow for future growth and guarantee efficient management in the DMC's peri-urban area.

Fig. 1
Fig. 1 Peri-urban region of Durgapur Municipal Corporation (DMC) for zonal analysis utilizing concentric rings no limit A is the total area of the landscape, and n i is the number of patches in the landscape of each patch type Patch density per 100 hectares Higher values indicate a more fragno limit Landscape boundary segments that represent the true edge only involving patch type i, included in the overall length of edge between patch types i and k Sum of all edge segment lengths (measured in metres) for each hectare of the landscape Higher values indicate a more fragno limit Length of all edges in the landscape; includes all landscape boundary and background edge segments, regardless of whether they actually represent edges A landscape's overall shape complexity can be determined by a normalised edge-to-area ratio Higher value indicates the highly complex or irregular shape Porosity ratio of open space (ROS) (S′/S)×100% ROS ≥ 0, no limit In the extracted urban area, s' is the summarization area of all "holes, " and s is the summarization area of all "patches." In respect to the estimated urban area, it calculates the total area of the open spaces Higher values indicate a less developed landscape Area weighted mean patch fractal dimension (AWMPFD) no limit a ij is the total area of patch ij Total class area (CA) is equal to the sum of all patch areas (

Fig. 8
Fig. 8 Independent variables on expansion of built-up areas to (a) Distance to City center, (b) Distance to Industry, (c) Distance to Mining Area, (d) Population Density, (e) Distance to Railway Station, (f) Distance to Regional Center, (g) Distance to Major Road, (h) Distance to Water Stream in the peri-urban region of DMC The research incorporates eight explanatory variables and utilizes LULC maps from 2001 and 2011 to train the MLP neural network model within the LCM transition sub-model framework.The model achieved an accuracy of 82.22% with a skill measure of 0.45, highlighting the

Fig. 9
Fig. 9 Intriguing patterns using estimated marginal means to (a) Distance to City Center, (b) Distance to Industry, (c) Distance to Mining Area, (d) Population Density, (e) Distance to Railway Station, (f) Distance to Regional Center, (g) Distance to Major Road, (h) Distance to Water Stream in the peri-urban region of DMC

Fig. 11
Fig. 11 Spatial trends of land transformation for (a) Non-built-up to built-up land, (b) Agriculture to built-up land, (c) Fallow to built-up land, (d) Mining area to built-up land, (e) Vegetation to built-up land, (f) Water bodies to built-up land in the peri-urban region of DMC

Table 1
Information about satellite imageries used in the study

Table 2
Description of results from kappa coefficient

Table 3
Landscape metrics used for assessing urban growth in this study

Table 4
Nature of variable for LRM Dhandadihi, among others, displayed the highest proportion of built-up areas relative to the periurban zones of the DMC in 1991.By 2011, Parashkol, Gopalpur, Bamunara, Kajora, and Chhora had the largest share of built-up area in the SSW, ESE, and NNW 40%, by 2011, and by 2021, they accounted for 16.89%.On the other hand, the N and SSE directions showed very little development, with notable rises starting after 2001.The density of built-up areas is a crucial measure for evaluating the concentration of urban development within

Table 5
Areal coverage of LULC types in the peri-urban region of DMC

Table 6
Direction wise mean value of built-up landscape metrics in the peri-urban region of DMC

Table 7
Collinearity statistics of independent variables

Table 8
Model Fit Measures