Land use change modelling using a Markov model and remote sensing

Abstract

Land-use/land-cover (LU/LC) change is an important component of global environmental change. The need to understand LU/LC change is essential for regional development and land use management towards sustainable development. To understand LU/LC change, the different LU/LC categories and their spatial as well as temporal variability in Tiruchirappalli city has been studied over a period of eight years (1998–2006), using the analysis of Indian Remote Sensing Satellite (IRS) images. In this, an attempt was made to adopt Markov model for obtaining and understanding LU/LC dynamics. Model performance was evaluated between the empirical LU/LC map extracted from CARTOSAT-1 PAN image and the simulated LU/LC map obtained from the Markov model. The future landscape distribution in the year 2014 and 2022 was derived using a Markov model. This result shows that Markov model and geospatial technology together are able to effectively capture the spatio-temporal trend in the landscape pattern associated with urbanization in this region.

1. Introduction

In recent years, global change research has been one of the most active areas of research internationally. Human activities are continually changing the environment on an unprecedented scale and speed. Among the several issues of global environmental change, land-use/land-cover (LU/LC) change can be said to be closely cross-questioned related to natural and human processes. In order to reveal the interaction between the global environment for human survival along with the evolving production systems (agriculture, industrialization/urbanization, etc.), the International Geosphere-Biosphere Programme (IGBP) and the International Human Dimensions Programme on Global Environmental Change (IHDP) jointly proposed LU/LC change research programme in 1995, making it the forefront and hot spot of global change research (Vitousek 1994; Turner et al. 1995). Anthropogenic changes in LU/LC are being increasingly recognized as critical factors influencing global change.

Viewing the earth from space is now becoming crucial to study and understand the influence of man's activities on the natural resource base over time. In situations of rapid and often unrecorded LU/LC change, observations of the earth from space provide objective information of human utilization of the landscape. Over the past years, data from earth sensing satellites have become vital in mapping the earth's features and infrastructures, managing natural resources and studying environmental change (Opeyemi 2006).

In the recent years, with the enhancement of more advanced remote sensing technology and geo-analysis models, monitoring the status and dynamic change of LU/LC thoroughly using high resolution remotely sensed data have become one of the most rapid, credible and effectual methods (Yin et al. 2007; Sylla et al. 2012).

The models of LU/LC change process fall into two groups: regression-based and spatial transition-based models (Baker 1989; Lambin 1997; Theobald and Hobbs 1998). A majority of researches utilizes regression-based approach, which relates the locations of LU/LC change to a set of spatially explicit variables, and uses models such as logistic (Landis 1994; Turner 1987; Wear et al. 1998) and hedonic price models (Geohegan et al. 1997). Spatial transition-based models often refer to cellular automaton simulation models, which allow for predicting future land development based on probabilistic estimates with Monte Carlo or other methods ( Clarke et al. 1997; Clarke & Gaydos 1998). One crucial limit to the development of the process models is, however, the deficiency of explicit modelling tools for change processes in the current generation of remote sensing and GIS systems. Equally important is the issue of data availability (Baker 1989). Moreover, few studies have attempted to link satellite remote sensing and GIS to stochastic modelling methods in LU/LC change studies, in spite of the fact that the techniques for such linkages have become mature in recent years due to advances in the technology of GIS and its integration with remote sensing (Weng 2002).

For all the models available, Markov model has been widely used to model LU/LC changes including both urban and non-urban areas at large spatial scales. It studies the initial occupation and transition probabilities of different states, accordingly to determine the trend of development and predict the state of the future. It is widely used in the analysis of different LU/LC types and dynamic changes. Its applicability and feasibility had been testified in many research papers and its results approximately conform to observed results (Dongjie et al. 2008; Huang et al. 2008; Dadhich & Hanaoka 2010; Zhang et al. 2011).

The aim of the study is to explore the changes that have taken place in the LU/LC over Tiruchirappalli city of Tamil Nadu. A time series of Indian Remote Sensing Satellite (IRS) images, covering eight years were used to obtain and analyse LU/LC change dynamics by the combined use of satellite remote sensing, geographic information systems (GIS) and stochastic modelling technologies. An attempt was also made to obtain simulated LU/LC for the year 2022 using a Markov model. The model is the spatial transition based whereby transition areas and probabilities are generated from two time series LU/LC maps in order to predict changes at a specified time in the future (Logsdon et al. 1996).

2. Study area and data

2.1. Study area

The study area is Tiruchirappalli town, Tamil Nadu (figure 1), one of the famous historical and cultural cities in India. The spatial extend of the study area is between 10˚44’ 46” to 10˚ 52’ 46” N latitude and 78˚ 39’ 11” to 78˚ 44’ 13” E longitude. The study covers an area of approximately 13,262 ha. The average annual rainfall is 821.4 mm. The mean maximum and minimum temperature range from 41.1°C and 18.6°C, respectively (National Informatics Centre 2010). The area has been experiencing remarkable LU/LC changes due to urban expansion and population pressure (figure 2). Its landscapes are abundant with economic and social activity facilitated by rapid developments in residential, educational, commercial, industrial, recreational and traffic and transportation sectors (Tiruchirappalli Local Planning Authority 2012). So, it is necessary to monitor the LU/LC change for understanding the current scenario and to plan the future development of the city. In this, the latest geospatial technology is required to simulate current and future changes for the study area.

Figure 1. Location of study area.

Figure 2. Population growth in Tiruchirappalli city during 1871–2011 [National Informatics Centre].

2.2. Data

To study the dynamic changes in LU/LC in Tiruchirappalli city, IRS images were used (table 1). A base map of the Tiruchirappalli city of 2005 was provided by the Local Planning Authority of Tiruchirappalli for preparing the study area boundary. Remote sensing image processing was performed using ERDAS Imagine 9.1 software. IRS data of years 1998, 2006 and 2009, and Survey of India (SOI) Toposheet 58 J/9 (1:50,000) were used to find the spatial and temporal changes in the study area, during the period of study.

Table 1. List of the satellite data used in the study.

Sl. no.	Data product	Imagery date	Resolution (m)	Path/row
1	IRS-1D PAN	19/10/1998	5.8	(101–066)
2	IRS-P6 LISS IV	22/02/2006	5.8	(101–112)
3	CARTOSAT-1 PAN	02/05/2009	2.5	(553–345)

3. Method

3.1. Image classification

In this study, six LU/LC classes were considered, namely waste land, vegetation, water bodies, grass, built-up land and agricultural land (table 2). The classes in the images were decided based on the LU/LC classification system devised by National Remote Sensing Agency (NRSA) for Indian conditions (Reddy 2002). A supervised approach for classification of the image was adopted with the maximum likelihood rule used as a parametric rule (Lillesand & Kiefer 2003; Coskun et al. 2008). The classified LU/LC maps for years 1998 and 2006 were produced from IRS images and are given in figure 3 and figure 4, respectively. The area statistics for Tiruchirappalli city is given in table 2.

Table 2. The area statistics from 1998 to 2006.

	Area (ha)
LU/LC classes	1998	2006
Waste	4501	3470
Vegetation	565	537
Water	797	778
Grass land	3153	2491
Built-up land	2531	5048
Agricultural	1716	938

Figure 3. Classified 1998 IRS image of LU/LC in Tiruchirappalli city.

Figure 4. Classified 2006 IRS image of LU/LC in Tiruchirappalli city.

3.2. Markov model in LU/LC change

Markov model is a convenient tool for simulating LU/LC change when changes and processes in the landscape are difficult to describe. A Markov process is one in which the future state of a system can be simulated purely on the basis of the immediately preceding state. Markov model will describe LU/LC change from one period to another and use this as the basis to project future changes. This is achieved by developing a transition probability matrix of LU/LC change from time one to time two, which shows the nature of change while still serving as the basis for projecting to a later time period (Logsdon 1996). Markov model provided a simple methodology and by which a dynamic system could be dissected and examined (Muller & Middleton 1994; Dongjie et al. 2008; Huang et al. 2008; Dadhich & Hanaoka 2010; Zhang et al. 2011). Numerous researches have testified the accuracy of the Markov model (Jianping et al. 2005; Zhang et al. 2011). The methodology required for Markov model is explained below.

Converting one state into another state of a system is called state transition. If P is transition probability, namely the probability of converting current state to another state in next time, the expression is as follows: (1) where P stands for probability from state i to state j (Jianping et al. 2005; Dongjie et al. 2008). Equation (1) must satisfy the next two conditions: (2) (3) The key step of the Markov model lies in getting a primary matrix and matrix of transition probability (P_ij). Then the Markov forecast model is as follows: (4) where P_n stands for state probability of any time and P₍₀₎ stands for primary matrix.

3.3. Primary matrix for Tiruchirappalli city

The LU/LC types in the study area are divided into six classes. So, on the basis of the information on waste land, vegetation, water bodies, grass, built-up land and agricultural land area that was extracted from IRS image of the year 1998, the calculated area of the above six land use types accounts for 74500.64, 564.66, 796.83, 3153.16, 2531.11 and 1715.67 hectares (table 2) and which becomes the primary matrix P₍₀₎ = [74500.64, 564.66, 796.83, 3153.16, 2531.11 and 1715.67], for further analysis.

3.4. Matrix of transition probability for Tiruchirappalli

Transition speed from one state to another state is named transition probability, and it may be calculated through annual average transition rate of a certain LU/LC type. Table 3 shows the transition probability of six LU/LC types area in square kilometres (waste land, vegetation, water bodies, grass, built-up land and agricultural land). According to the definition, transition matrix gives the probability that an LU/LC class will change to another class in the future, given the present state of the class. Using equation (1), i.e. , the transition probability of a certain LU/LC type in 1998 converted into the same LU/LC type in 2006 was calculated. Table 4 shows the primary transition probability of six LU/LC types during 1998–2006.

Table 3. LU/LC transitional matrix between 1998 and 2006 (ha).

1998	2006
	Waste	Vegetation	Water	Grass land	Built-up land	Agricultural
Waste	20.18	2.26	2.03	7.81	10.79	1.94
Vegetation	1.63	0.37	0.39	1.44	1.15	0.66
Water	1.39	0.30	2.96	1.75	0.98	0.59
Grass land	7.99	2.24	1.37	8.55	8.04	3.34
Built-up land	6.84	1.31	1.15	4.71	10.14	1.15
Agricultural	3.50	1.21	1.03	5.36	3.21	2.85

Table 4. Matrix of primary transition probability of LU/LC types in Tiruchirappalli city during 1998–2006.

LU/LC classes	Waste	Vegetation	Water	Grass land	Built-up land	Agricultural
Waste	0.448	0.050	0.045	0.174	0.240	0.043
Vegetation	0.289	0.066	0.069	0.254	0.204	0.116
Water	0.174	0.037	0.372	0.219	0.123	0.075
Grass land	0.254	0.071	0.043	0.271	0.255	0.106
Built-up land	0.000	0.000	0.000	0.000	1.000	0.000
Agricultural	0.204	0.071	0.060	0.313	0.187	0.166

Note: In practice, the built-up area seldom transfers to other land uses. Thus, the transition probabilities of the built-up state to other states are given as ‘zeros’.

4. Results and discussion

4.1. LU/LC change analysis

The LU/LC classification results are summarized for the years from 1998 to 2006 in table 2. From 1998 to 2006, built-up area increased by 18.97%. On the other hand, waste land, agricultural land and grass land decreased by 10.68, 8.06 and 6.87%, respectively. All these LU/LC change are closely related with the development of regional economy and the population growth in the city. The trend of LU/LC change in the city is shown in figure 5.

Figure 5. Comparison of LU/LC change in Tiruchirappalli from 1998 to 2006.

4.2 Accuracy assessment of classification

Each of the LU/LC map was compared with reference data to assess the accuracy of the classification. A GPS field survey was employed as ground truth data to verify the classification accuracy using ERDAS Imagine 9.1 software. The accuracy assessment procedure is a very effective way to represent accuracy in that the accuracies of each category are plainly described along with both the errors of inclusion (commission errors) and errors of exclusion (omission errors) present in the classification (Congalton 1991). The overall accuracy of the images of 1998 and 2006 were observed to be 85.47% and 88.27%, respectively and the corresponding kappa coefficients were 0.85 and 0.89. Both producer's and user's accuracy (Congalton 1991; Verbyla 2005) were over 85%. The minimum level of interpretation accuracy in the identification of LU/LC categories from remote sensing data should be at least 85% (Anderson et al. 1976).

4.3. Modelling results and validation

Markov model is a model about the trends forecast, and if current artificial factors continued, the results would gradually change along a certain trend, and tend to stabilize in a long time and reach a balance state at last. Equation (4) was used to find the change in trend of LU/LC types in the successive years. The Excel MMULT function calculates the matrix product of two arrays. The format of the function is: MMULT (array1, array2). Where array1 and array2 are arrays of numerical values, representing matrices, where the number of columns in array1 is equal to the number of rows in array2. Using the function MMULT in EXCEL, through multi-step operation, the transition probability matrix P_ij was obtained and was thus used to simulate the changes for the future. Table 5 shows the simulated change trends of LU/LC types in Tiruchirappalli city for the next 16 years.

Table 5. Change trend of LU/LC types simulated by Markov model.

Year	LU/LC classes
	Waste	Vegetation	Water	Grass land	Built-up land	Agricultural
1998	4501	565	797	3153	2531	4501
2006	3470	537	778	2491	5048	3470
2014	2699	488	654	1904	6816	2699
2022	2091	376	523	1472	8260	2091

The simulated results based on a Markov model indicate that the area percentage of built-up land in Tiruchirappalli city had sharply increased from 19.08% in 1998 to 38.06% in 2006 and after 16 years, i.e. in the year 2022, the percentage would have increased to 62.28%. The main reasons of built-up land increase could be because of the gradual population increase, infrastructural, industrial and transportation network development in Tiruchirappalli city. The LU/LC change from 1998 to 2022 in the city is shown in figure 6.

Figure 6. Simulated LU/LC change from 1998 to 2022 in ha.

The LU/LC modelling is incomplete without validating the model with actual data. So, the results of LU/LC simulated areas need to be compared with actual area. Therefore, the simulated LU/LC areas of 2009 is compared with the actual areas interpreted from 2009 satellite image (CARTOSAT - 1) and result tested with actual values using χ² test in order to ensure suitability of the model. The test results were as follows: These findings show that, there is no significant difference between simulated value and actual value. Therefore, Markov model can be used in LU/LC forecast in Tiruchirappalli city. The validation of LU/LC change forecast of Tiruchirappalli city can be seen in table 6.

Table 6. Validation of LU/LC change forecast based on Markov model.

LU/LC classes	Chi-square test
	Simulated value (O)	Actual value (E)	(O−E)	(O−E)^.2	(O−E)^2/E
Waste	30.25	30.83	0.58	0.34	0.01
Vegetation	5.57	5.27	−0.30	0.09	0.02
Water	8.01	7.70	−0.31	0.10	0.01
Grass land	22.91	22.43	−0.49	0.24	0.01
Built-up land	58.88	59.92	1.04	1.07	0.02
Agricultural	6.98	6.47	−0.52	0.27	0.04

Note: χ² = ∑(O−E)²/E = 0.106; degree of freedom = 5 and χ² _0.05 (5) = 11.07.

5. Conclusions

This paper aims to show a remote sensing approach in analysing and simulating LU/LC changes of Tiruchirappalli city using multi-dated RS images of years 1998 and 2006. The approach involved remote sensing, geographical information systems and Markov model techniques. The result showed that the areas of the urban settlements in Tiruchirappalli city increased by 19.08% to 38.06% from 1998 to 2006. During this period, waste land (−10.68%) area decreased. The LU/LC trends were simulated for the year 2022 through the use of Markov model. Results indicated that built-up land would have increased by 62.28% in the year 2022. This result shows that the natural equilibrium of the Tiruchirappalli city is threatened by the population pressure of the last 30 years. This work shows that it is feasible to simulate LU/LC change based on remote sensing images and Markov model.

The Markov model, coupled with the geospatial technology has indicated the descriptive capability of trend projection. This spatio-temporal model provides not only a quantitative description of change in the past but also the direction and magnitude of change in the future. However, based on the experimental results and exploratory analysis, limitations are present in the current study.

In this study, only two images were used for analyse the LU/LC change and the images were captured in different date. The transition probability in the Markov chain model is assumed to be uniform. Therefore, it is still difficult to accommodate the unpredictable influence of variables, such as the climate, governmental policy or human disturbance. However, it can be concluded that by incorporating more temporal, high accuracy and same dated images into the prediction of LU/LC change, more accurate long-term forecasts can be made in the future.

Acknowledgements

The authors thank National Remote Sensing Centre (NRSC), India for proving the IRS satellite data. We are also thankful to the Tiruchirappalli City Municipal Corporation and Tiruchirappalli Local Planning Authority for providing the necessary data for the work. We thank two anonymous reviewers and the editor for their valuable comments on the draft of this paper.