Page 1 of 1 Assessing Application of Markov Chain Analysis in Predicting Land Cover Change: A Case Study of Nakuru Municipality
Kenneth W. Mubea Email: kpwmubea@yahoo.com Dr. Thomas G. Ngigi Email: tomngigi@hotmail.com Dr. Charles N. Mundia Email: charlesndegwam@yahoo.com Department of Geomatic and Geospatial Information Systems, Jomo Kenyatta University of Agriculture and Technology, Po. Box. 62000 - 00200, Nairobi, Kenya. ABSTRACT Land cover change is a major issue of global environment change. The modelling and projecting of land cover change is essential to the assessment of consequent environmental impacts. Rapid land cover change has taken place in Nakuru Municipality over the past three decades due to accelerated industrialization and urbanization. Landsat images of 1973, 1986 and 2000 were used. Land cover change dynamics were investigated by the combined use of satellite remote sensing, geographic information systems (GIS), and stochastic modelling technologies. The results indicated that there was a notable and uneven urban growth and a tremendous loss in forest land between 1973 and 2000. The study demonstrates that the integration of satellite remote sensing and GIS was an effective approach for analyzing the rate, and spatial pattern of land cover change. The further integration of these two technologies with Markov modelling was found to be beneficial in describing and analysing land cover change process. Subsequently, an attempt was made at projecting the observed land cover change in the next 15 years. Results indicated an increase in urban land cover by 14.28 km2 in year 2015 from 19.04 km2, 23.53 km2 and 37.31 km2 respectively in the years 1973, 1986 and 2000. 1. INTRODUCTION Urban studies are becoming important tools for planners knowing that in 2015 more than half world’s population will be living in cities, (UNECE, 2003). Models are, perhaps, the best way of understanding the land change phenomenon and anticipate correct planning activities for sustainable cities. This is an important topic in current research agenda and a significant number of scientists are dedicating efforts in the study of this phenomenon (Batty et al., 1999, Cheng, 2003, Herold et al, 2003). Satellite remote sensing, in conjunction with geographic information systems (GIS), has been widely applied and been recognized as a powerful and effective tool in detecting land cover change (Ehlers et al., 1990; Meaille and Wald, 1990; Treitz et al., 1992; Westmoreland and Stow, 1992; Harris and Ventura, 1995; Yeh and Li, 1996, 1997, 1999; Weng, 2001). Satellite remote sensing provides cost-effective multi-spectral and multi-temporal data, and turns them into information valuable for understanding and monitoring land development patterns and processes and for building land cover data sets. GIS technology provides a flexible environment for storing, analyzing, and displaying digital data necessary for change detection and database development. Satellite imagery has been used to monitor discrete land cover types by spectral classification or to estimate biophysical characteristics of land surfaces via linear relationships with spectral reflectance or indices (Steininger, 1996). Post-classification comparison and multi-date composite image change detection are the two most commonly used methods in the change detection (Jensen, 1996). Remote sensing and GIS based change detection studies have predominantly focused on providing the knowledge of how much, where, what type of land cover change has occurred. Only a few models have been developed to address how and why the changes occurred. The models of land cover change process fall into two groups: regression-based and spatial transition-based models. In this research, Markov chain model was used to model land covers in the years 2000 and 2015. The model is spatial transition based whereby transition areas and probabilities are generated from two time series land cover maps in order to predict change at a specified time in the future. The aim of this study was to explore Markov Chain based urban growth model and predict land cover in year 2015. To achieve these objectives Landsat images of 1973, 1986 and 2000 were used. Land cover change dynamics were investigated by the combined use of satellite remote sensing, geographic information systems (GIS), and stochastic modelling technologies. It was deduced that rapid industrialization and urbanization has resulted in the loss of a significant amount of rangeland and forest. This has been due to lack of appropriate land use planning and the measures for sustainable development. All these changes have the potential to undermine the long-term harmonious people environment relationship. There is an urgent need for evaluating the magnitude, pattern, and type of land cover changes and for projecting future land development. 2. The study area Nakuru municipality lies approximately between 0° 15' and 0° 31' South, and 36° 00' and 36° 12' East, with an average altitude of 1,859 meters above sea level, covering an area of 290 km˛. Within Nakuru municipality lays Nakuru town, Lake Nakuru National Park, and Lanet town. Nakuru town is located 160 km North West of Nairobi and is the fourth largest urban centre in Kenya after Nairobi, Mombasa and Kisumu. (Figure 1) Nakuru population has been growing at the rate of 5.6% per annum. From a population of 38,181 in 1962, the population reached 163,927 in 1989, and 289,385 in 1999 (GOK, 2000). By the year 2015, the population is projected to rise to 760,000, which is approximately 50% above the present levels. (Mwangi, 2007)  Figure 1: Map of Study Area 3. METHODOLOGY Three Landsat imageries acquired on 31st January 1976 covering scene p181060, 28th January 1986 covering scene p169r060, and 27th January 2000 covering scene p169r060 were selected for this study. Hence, the study period covered about 27 years. Ground control points were used as reference data and for accuracy assessment.  The image processing and data manipulation were conducted using algorithms supplied with the Idrisi Kilimanjaro image processing software, which also incorporates GIS functions. ArcGIS 9.2 was used for GIS overlay analyses. A modified version of the Anderson Scheme (Anderson et al., 1976) was adopted for this study. In total, six land cover classes were established namely water, forest, agriculture, rangeland, urban and barren land as show in table 2.  Some of the factors considered during the design of classification scheme included; the major land cover categories found within the study area, differences in spatial resolutions of the three sensors which varied from 30 meters for TM (Thematic Mapper) and ETM+ (Enhanced Thematic Mapper) to 80 meters for MSS (Multi-Spectral Scanner) and the need to consistently discriminate land cover classes irrespective of the seasonal differences. All the images were re-sampled to 3 metres using nearest neighbour. This would enable times series analysis on the images. Supervised classification was used in which maximum likelihood classifiers was run on the Landsat scenes (MSS, TM & ETM). This approach is totally dependent on the spectral pattern recognition (Lillesand, 1994). Two methods of accuracy assessment used were the Kappa statistic and overall accuracy. The Kappa statistic is a statistical method of assessing the accuracy that takes into account the chance of random agreement. This statistic has been used by many researchers in their studies Selamat, et al., (2002). The produced results in this study are shown in table 3 and the accuracy assessment results are shown in table 4. Calculation of the area in square kilometres of the resulting land cover types for each study year was done and subsequently comparing the results as show in table 3. Results obtained from land cover maps of 1973, 1986 and 2000 were used to predict land cover in year 2000 and 2015. Land cover classification and Markov chain analysis in year 2000 results were compared. 4. RESULTS AND DISCUSSION Land cover maps for the years 1973, 1986 and 2000 were generated using maximum likelihood classifier. The maps produced were of certain levels of accuracy with an overall accuracy of 88%, 97% and 86% respectively for the years 1973, 1986 and 2000. The Kappa indices for the 1973, 1986 and 2000 maps were 0.88, 0.96 and 0.82 respectively. Clearly, this data met the minimum standards of 85% as stipulated by the USGS classification scheme (Anderson et al., 1976).      Figure 2: Land Cover Map of Nakuru in 1973 Land Cover Changes The figures presented in table 3 represents the statistics of each land cover category for each study year. It can be noted that the urban land cover has been increasing from 19.04 km2 in 1973, 23.53 km2 in 1986 and 37.31 km2 in 2000. Forest cover has been decreasing from 21.11 km2, 20.35 km2, and 19.02 km2 respectively for years 1973, 1986 and 2000 as people encroach on forest land for cultivation and settlement. Agricultural activity has increased towards the year 2000 from 61.13 km2 in 1986 to 83.27 km2 in 2000. Water decreased from 39.73 km2 in 1973 to 35.00 km2 in 1986 because of the drought experienced globally in 1982 but resumed later on then it decreased slowly to 39.32 km2 in 2000. Such phenomenon was an impetus for this research in view of projecting land cover into the future, year 2015. This was achieved using Markovian model where urban land cover was of major concern.  Figure 3: Trends in Land Covers between 1973 and 2000 Markov Chain Analysis The transition probability matrix records the probability that each land cover category will change to the other category. This matrix is produced by the multiplication of each column in the transition probability matrix be the number of cells of corresponding land cover in the later image. For the 6 by 6 matrix table presented in tables 5 and 6, the rows represent the older land cover categories and the column represents the newer categories. Although this matrix can be used as a direct input for specification of the prior probabilities in maximum likelihood classification of the remotely sensed imagery, it was however used in predicting land cover of 2000 and 2015.  Row categories represent land cover classes in 1986 whilst column categories represent 2000 classes. As seen from the table, water has a 0.6844 probability of remaining water and a 0.0013 of changing to forest in 2000. Forest land has a 0.2687 probability of remaining forest land in 2000 and a 0.4304 probability of changing to rangeland. Barren land also has a probability of 0.006 to remain as barren land in 2000 which signifies that it’s likely to change to other classes with a 0.603 probability of changing into rangeland. Urban land has a 0.071 probability of remaining as urban land and a 0.6541 probability of changing to rangeland. Agriculture has a 0.2506 probability of remaining as agricultural land and a 0.6307 of changing to rangeland indicating close interaction of these two land covers. Rangeland has a 0.5265 probability of remaining of remaining rangeland and a 0.2871 probability of changing to agricultural land.  Row categories represent land cover classes in 2000 whilst column categories represent 2015 classes. As seen from the table, water has a 0.8456 probability of remaining water and a 0.0863 of changing to agricultural land in 2015. Forest land will change to other classes with a 0.5872 probability of remaining forest land in 2015 and 0.0792 of changing to urban land. Barren land also has a probability of 0.0818 to remain as barren land in 2015 which signifies that it’s likely to change to other classes with a 0.5292 probability of changing into water signifying close interaction between these classes. Urban land has a 0.3208 probability of remaining as urban land and a 0.2886 probability of changing to agriculture. Agriculture has a 0.369 probability of remaining as agricultural land and a 0.4288 of changing to rangeland indicating close interaction of these two land covers. Rangeland has a 0.4195 probability of remaining of remaining rangeland and a 0.4053 probability of changing to agricultural land.  Figure 4: Markov Chain Analysis for the year 2000 Figure 4 is derived from land cover maps of 1973 and 1986. From figure 4 and 5, it can be noted that clustering of urban land cover is along the road network. Concentration of houses is prominent along the various streets.  Figure 5: Markov Chain Analysis for the year 2015 Figure 5 is derived from land cover maps of 1986 and 2000. From figure 5, urban land cover will be densely concentrated compared to year 2000 in figure 4.  From table 7, Markov Chain Analysis is able to predict land cover as it can be seen in the case of urban land cover with a difference of 1.83 km2 in area.  From table 8, it can be noted that urban land, agriculture, barren land and water will increase respectively by 16.10 km2, 21.00 km2, 5.79 km2 and 19.94 km2 between years 2000 and 2015 whereas forest and rangeland will decrease respectively by 0.88 km2 and 62.03 km2.  Figure 6: Trends in Land Cover between 1973 and 2015 From figure 6, it can be noted that urban land cover and agriculture has been increasing from 1973 to 2015 whereas water, forest and barren land have been decreasing. 5. DISCUSSION AND CONCLUSION Increasing land cover changes due to rapid urban growth and concentration of people were observed in Nakuru municipality during the study period. To investigate the changes, image processing algorithms were used to generate change information from multi-temporal data sets for years 1973, 1986 and 2000. Additionally the land cover trends were simulated into the year 2015 through the use of Markov model. Results indicated that urban land cover will have increased to 51.58 km2 raising questions as to what needs to be done in terms of planning and policy to cater for this urban sprawl. The Markov chain models have shown the capabilities of descriptive power and simple trend projection for land cover change, regardless of whether or not the trend actually persists. The analysis can serve as an indicator of the direction and magnitude of change in the future, as well as a quantitative description of change in the past. Simulated pattern of urban sprawl will have significant implications in policy making and urban planning. Further research need to be conducted with recent images for example Landsat ETM+ 2008 and project further to 2030 when Kenya envisages achieving Vision 2030. Agent based models should also be used to simulate local land cover change in the study area. ACKNOWLEDGEMENTS The authors want to sincerely thank the anonymous reviewers for their valuable comments and suggestions. REFERENCES
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