INTRODUCTION

Urbanisation is a dynamic process involving the horizontal and vertical expansion of urban pockets in response to the population growth, industrialization, political, cultural and other socio-economic factors [1,2,3]. Unplanned urbanisation leads tothelarge scale land cover changes [4] affecting the ecological diversity with degradation of the environment, enormous consumption of resources, creation of urban heat islands, changes in local climate [5,6], soil erosion, changes in hydrological cycle impairing surface water and ground water regime [7]. This process often leads to unstable development with increasing economic, social and environmental problems [8] such as radical changes of vegetation, water bodies, etc., with the irretrievable loss of ground prospects due to drastic change in the landscape [9]. These are often driven by the uncontrolled and dispersed growth along the periphery, which is referred as urban sprawl. The process of urban sprawl is common in rapidly urbanizing metropolitan cities. Rapid rise in urban populationhas caused serious environmental damageswith problems such as increasing slums, decrease in standard of living, etc. [10]. The urban sprawl process has been studied in many developing regions [11,12,13,14,15,16] as it leads to drastic change in the landscape. Therefore spatio-temporal changesin urbanisation pattern would help in assessing land use changes, which would provide insights to the extent and rate of urban sprawl. Land use refers to use of the land surface through modifications due to anthropogenic activities or natural phenomena [1,12,17]. Quantification of impervious manmade surfaces in and around the city through mapping would help in estimating the dispersed growth of urban pockets. .The traditional surveying and mapping techniquesto monitor landscape changes over different time frames entails high expenses due totime as well asrequirement of resources for mapping and inventorying exercises. Recent advancements in mapping and modeling [18] through spatial data acquired remotely through space-borne sensors (remote sensing data) and the analysis of spatial data through Geographic Information System [GIS] have enhanced the abilities of spatial data analysis. Remote sensing technique[1,12,15,16,17,18] has advantages such as widersynoptic coverage of the earth surface with varied temporal, spatial and spectral resolutions. Classifications of these data through already proven classification algorithms [1,17,18] provide land use information. These temporal information helps to measure, monitor and visualise changes, which are necessary to model and simulate the likely changes in spatial patterns. Modelling enables the prediction of likely future land cover changes, required for evolving strategies for appropriate decisions and policies, interventions [19] to mitigate the drastic land cover changes. Prediction of changes based on the current trend will help in understanding the role of influencing factors and constraints.Research in this direction have focused on modelling and predicting changes in forest and hydrology, effect of urbanisation on runoff, soil erosion, urban sprawl,etc. [19,20,21,22,23,24]. Models such as Cellular Automata (CA), CA-Markov, Geomod, Land Change Modeler (LCM), Sleuth, Agent Based Modeling (ABM), Multi Criteria Evaluation (MCE), Regression, Neural Networks, etc., have been used for simulating urban sprawl [20,25,26,27,28,29,30]. Studies have demonstrated the use of Markov chains combined with cellular automata as one of the effective technique in modeling urban sprawl pattern [20,26,28,29].

Markov chain and cellular automata: Cellular Automata (CA)are algorithms which define the state of the cell based on the previous state of the cells within a neighborhood, using a set of transition rules. CA have a potential for modelling complex spatio-temporal processes such as urban process. CA is made up of elements represented by an array of cells, each residing in a state at any one time, discrete number of class (states), the neighborhood effect and the transition functions, which define what the state of any given cell is going to be in the future time period.The cell space digitally in the CA consists of a rectangular grid of square cells each representing an area 30mx30m and matches the size as the minimum area mapped in urban areas in the land use datasets. Basic assumption that was used is cells are not homogeneous and arecharacterized by a vector of suitabilities, deciding the future land use. The suitabilities are defined as a weighted linear sum of a series various affecting factors characterizing each cell. They are normalized to values in the range of 0–1, and represent the inherent capacity of a cell to support a particular activity or land use which can be generated by Markovian random process, which is a stochastic process. In this urban cellular automaton, the neighborhood space is defined as a square region around the central cell with a radius of five cells. The neighborhood thus contains 24. The neighborhood influence area and the interactive area for urban land uses and its neighbors.The model uses 4 cell states. The active functions is urban land uses which are forced by demands for land generated exogenously to the cellular automaton in response to the growth of the urban area. Passive is represented by other land use classes. The effect on the neighborhood is thus calculated as summed effect of each transitional potential and its interaction with its neighbors and the transition rules: were determined by various demands of the land use classes, population growth etc.

Finally, spatial metrics have been useful to quantify the land use based on patch, shape, edge etc. This quantification provide insights to the historical and current spatial patterns, which is useful in evaluating the landscape heterogeneity in relation with urban growth [30,31,32]. The objective of the current research is to simulate urbanisation process of Bangalore city for 2020 through CA and CA-Markov model considering transition probabilities (based on Markov chain analysis). Spatial patterns of urbanisation is quantified using landscape metrics.