Application of a Hybrid Cellular Automaton – Markov (CA-Markov) Model in Land-Use Change Prediction: A Case Study of Saddle Creek Drainage Basin, Florida

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2.2. Data Sources and Processing

Three land-use land cover vector data sets for Polk County prepared by Southwest Florida Water Management District (SWFWMD) dated 1995, 1999 and 2006 were used for this project. Because we intended to demonstrate the applicability of the CA-Markov model in land use change prediction, the choice of the dates were entirely based on the availability of datasets. These land-use land cover shape files were prepared by South West Florida Water Management District ^{[8, 9, 10, 11]}. The land-use land cover classes were categorized using Florida Land Use and Cover Classification System (FLUCCS) ^[12]. For this study, relevant land-use classes were aggregated into eight major land-use classes; urban and builtup, agricultural areas, rangeland, upland forests, water bodies, wetlands, barren land, and transportation and utilities. ArcGIS 9.2 Desktop ^[13] was utilized to reclassify land-use land cover shape files into raster images with major land-use classes and a cell resolution of 30m*30m. These land-use maps were then exported into TIFF files for further analysis in IDRISI Andes (v 15.0) ^[14] for land-use change prediction. In IDRISI Andes, modules like MARKOV, CA-MARKOV, and VALIDATE were used for modeling and projecting the land-use change for the Saddle Creek drainage basin for the year 2015 by using 2006 land-use map as the base map. In order to see how rapidly land-use changes, we set the forecast year to 2015 for this study.

2.3. Markov Model

Markov model has been widely used in ecological modeling ^{[Landscape Ecology, 9, 151-157. 1994.">15, Journal of Environmental Management, 59, 247-263. 2000.">16]}. Markov model takes into account past states to predict how a particular variable changes over time. The applicability of Markov model in land-use change modeling is promising because of its ability to quantify not only the states of conversion between land-use types but also the rate of conversion among the land-use types ^[17]. A homogenous Markov model for predicting land-use change can be represented mathematically as;

and

where, L_(t+1) and L_(t) are the land-use status at time t+1 and t respectively. ( and , ) is the transition probability matrix in a state.

2.4. CA-Markov Model

CA-Markov model combines cellular automata, Markov chain, multi-criteria, and multi-objective land allocation to predict land cover change over time ^[17]. It adds into Markov model not only spatial contiguity but also the probable spatial transitions occurring in a particular area over a time. MARKOV and CA_MARKOV modules in IDRISI Andes were used to create transition probability and transition area matrix. A transition probability matrix is obtained by cross tabulation of two images of different time and it determines the probability of a pixel in a land-use class to change into another class during that time.

A transition area matrix, on the other hand, contains the number of pixels that are expected to change to a land-use class from another class during a time period. Land-use map dated 1995 and 2006 were used to create transition probability matrix in order to project land use for the year 2015 (Table 1). For creation of transition probability matrix, MARKOV module in IDRISI Andes was used and the proportional error was set to be 15% ^[18].

Table 1. Transition probability matrix calculated using land-use maps 1995 and 2006

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Tables index

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2.5. Suitability Maps for Land-Use Change Projection:

Suitability maps were prepared by setting transition rules from a land-use state to another state. While socio-economic factors are prime drivers of land-use change, only physical factors were considered in this project. The physical proximity to an existing land-use class is thought to be a driver of change into a particular land-use class in the future. Also some restrictions such as developing an urban area into agricultural area were also taken into consideration for preparation of land-use suitability maps. Transition rules were prepared for each land-use class and suitability maps were prepared. The pixel values in suitability maps ranged from 0 to 255, 0 representing unsuitable and 255 representing highly suitable. Figure 2 represents the suitability maps for each land-use classes.

Generally areas near an existing land-use class are likely to change into that class compared to areas that are far from that class. So, inverse J-shaped monotonic decrease function was used to determine the relative suitability of an existing land-use to change into that same land-use. Also, restrictions for agricultural area, barren land, rangeland, upland forests were the urban and built up areas, water bodies, and transportation and utilities.

The CA_MARKOV module in IDRISI uses a hybrid Markov- CA model that iterates the land-use allocation until the areas that are predicted by Markov model are identified. Also the number of iteration is dependent upon the number of years a projection is made. In this project, the number of iterations performed was 9 because the land-use map of 2006 was taken as a base map for projecting the land-use in 2015. A contiguity filter of a kernel size of 5*5 pixels that accounts the neighborhood pixels was used to create spatially explicit contiguous weighing factors so that the pixels that are far from the existing land-use class have lower suitability than the pixels that are near. In this project, the filter used for analysis was;

The weighted suitability maps are then run through a multi-objective land allocation process to allocate the predicted land-use change and resolve the conflicts on allocation by allocating a cell to a particular land-use class for which its weighted suitability is highest ^[19].

Figure 2. Suitability maps for a. urban and built up b. agricultural area c. rangeland d. upland forest e. water bodies f. wetland g. barren land h. transport and utilities. The values represent the likelihood of a pixel being changed into a land-use class.

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Table 2. Projected land-use in 2015 in Saddle Creek drainage basin and percentage total area in 2006

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3. Results and Discussion

The projected land-use map for the year 2015 is provided in Figure 3. Land-use classes like urban and built up and transportation and utilities will have a notable increase in area in 2015 compared to 2006 land-use. Agricultural areas, upland forest and wetland areas will have a notable decrease in area in 2015 (Table 2). In 2015, urban areas are projected to cover 49.3% of the total area of Saddle Creek drainage basin followed by water bodies (17.2 %), wetlands (10.8%), transportation and utilities (5%), upland forest (4.4%), rangeland (0.6%), and barren land (0.08%).

Figure 3. Projected land-use map of Saddle Creek drainage basin, Florida for 2015

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Decline in the natural vegetation of Florida has been observed over the past few decades. For instance, Kautz et al. (2007) ^[20] documented a decline rate as high as 94 thousand hectares per year from mid 1980s to early 2000. In addition, reduction in agricultural land have been observed in florida with an annual reduction rate as high as almost 25 thousand hectares ^[20]. With urban sprawling, coverstion of forest areas and agricultural land to urban areas was expected in this drainage basin.

While estimates of the rate of land-use conversions via remote sensing techniques are influenced by spatio-temporal resolution, the unforseeable nature of land-use change dynamics obscure the accuracy of change prediction. Nevertheless, population growth and migration into urban areas will lead to relatively higher land-use conversion to urban and residential areas. Other factors such as family size ^[21] and income ^[22] also have predictable influence the dynamics of land-use change. For example, families with low income will likely reside in the outskirts of urban area or near urban-agricultural fringe and thereby facilitate land conversion. Because CA-Markov model allows to include the effects of these factors on land-use change, past studies have used successfully predicted land-use change using hybrid models like in this study ^{[Mathematical and Computer Modelling, 54, 938-943. 2011.">17, Journal of environmental management, 64(3), 273-284. 2002.">23]}.

Table 3.Validation of projected 1999 land-use map with actual 1999 land-use map

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Figure 4. Actual and Projected land-use in Saddle Creek drainage basin for 1999

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