The use of cellular automata-Markov Chain Analysis to predict land use change around a village in Mali

1. The use of cellular automata-Markov Chain Analysis to predict land use change around a village in Mali Some preliminary results Dr. Roy ColeDepartment of Geography and Planning Grand Valley State University Allendale, Michigan, USA

2. The problem: Can GIS be used to reliably predict change? • Purpose. • The application of a stochastic modeling technique in GIS, Markov Chain Analysis, and cellular automata with categorized land use data derived from aerial photographs taken over a 33-year period of an area in Mali. • GIS and land use change. • A relatively new tool to be used in understanding land use change (Briassoulis 2000). • GIS based modeling approaches are said to be under development (Eastman 2003). • Compared to more established land use change modeling techniques their performance is still being evaluated (O’Sullivan and Unwin 2003).

3. Why Markov simulation and celullar automata • I became interested in Markov simulation in 2002 as a temporary alternative to fieldwork after it became apparent to me that I would be unable to get to my study area in the immediate future. • At about the same time Clark Labs developed some new spatial statistical modules for Idrisi GIS. • It was also out of the spirit of curiousity that the current study was undertaken -- I wanted to see what these new modeling modules in Idrisi GIS could do.

4. The study area • Located in central Mali along the southern bank of the Niger River. • 500 km2 in area. • Contains 48 villages. • One village was picked to test the simulation. • About 1/3rd of the study area is floodplain that is has been annually irrigated through a gravity-irrigation scheme since the late 1950s. • The area is almost uniformly flat. • Soils are relatively uniform. • Clays in bottom lands. • Silty loam elsewhere. • Low sand dunes are found in the study area but not in or around the study village.

5. The study area and study village

6. Landsat Thematic Mapper image of study area Year is 2000. Month was not specified on the image but the flood stage looks like September-October.

7. Precipitation

8. Data and analysis • Aerial photographs of study area. • 1952 and 1974 sets. • 1985 set flown while I was doing fieldwork. • Georeferencing with the Geographic Transformer software. • Land cover classification with Cartalinx. • Land use classes were reclassed to 5 categories for each image for the MCA: • Open cultivation. • Specialty crops. • Uncultivated. • Village. • Cemetery. • Summary statistics, Markov probabilites, cellular automata simulation done with Idrisi Kilimanjaro GIS.

9. Markov Chain Analysis • An aggregate, macroscopic, stochastic, modeling process. • A technique for predictive change modeling. • Predictions of future change are based on changes that have occurred in the past. • According to the literature, Markov analysis can be used in three different ways: • For ex-post impact assessment of land use (and associated environmental) changes of projects or policies. • For projecting the equilibrium land use vector as well as for approximating the time horizon at which it may be obtained. • Projecting land use changes at any time in the future given an initial transition probability matrix.

10. ... continued Markov Chain Analysis • Imagine an area subdivided into a number of cells each of which can be occupied by a given type of land use at a given time. • On the basis of observed data between time periods MCA computes the probability that a cell will change from one land use type (state) to another within a specified period of time. • The probability of moving from one state to another state is called a transition probability.

11. ... continued Markov Chain Analysis in Idrisi Kilimenjaro • MARKOV takes two qualitative land cover images from different dates and generates the following files. • A transition matrix. Contains the probability that each land cover category will change to every other category • A transition areas matrix. Contains the number of pixels that are expected to change from each land cover type to each other land cover type over the specified number of time units. • A set of conditional probability images. Reports the probability that each land cover type would be found at each pixel after the specified number of time units.

12. Typical Markov chain analysis layout in Idrisi Kilimanjaro Specify the first (earlier) coverage Specify the second (later) coverage Specify the years between the two coverages Specify the years to run the simulation Results consist of 2 transition tables and one image for each land use type

13. Two limitations to Markov • Markov analysis does not account the causes of land use change. • It ignores the forces and processes that produced the observed patterns. • It assumes that the forces that produced the changes will continue to do so in the future. • An even more serious problem of Markov analysis is that it is insensitive to space: it provides no sense of geography. • Although the transition probabilities may be accurate for a particular class as a whole, there is no spatial element to the modeling process. • Using cellular automata adds a spatial dimension to the model.

14. Cellular automata A simple example • The lattice is 1-dimensional row of 20 cells. • Each row represents a single time step of the automaton’s evolution. • Each cell’s evolution is affected by its own state and the state of its immediate neighbors to the left and right. • THE RULE: • Cells with an odd number of black neighbors (counting themselves) will be black at the next time step. • Otherwise, they are white.

15. A more complicated example: John Conway’s Game of Life Rules: Two cell states: black and white. Each cell is affected by the state of its 8 neighbors in the grid. A white cell becomes black if it has 3 black neighbors. A black cell stays black if it has 2 or 3 black neighbors. ... continued Cellular automata

16. ... continued Cellular automata-MCA in Idrisi • Combines cellular automata and the Markov change land cover prediction. • Adds spatial contiguity as well as knowledge of the likely spatial distribution of transitions to Markov change analysis. • The CA process creates a “spatially-explicit weighting factor which is applied to each of the suitabilities, weighing more heavily areas that are in proximity to existing land uses and ensuring that landuse change occurs in proximity to existing like landuse classes, and not in a wholly random manner” (Eastman 2003). • In each iteration of the simulation each class will normally gain land from one or more of the other classes or it may lose some to one or more of the other classes. • Claimant classes take land from the host based on the suitability map for the claimant class.

17. ... continued Cellular automata • CA_MARKOV uses the transitions area file from MCA and a land use suitability file and a 5 X 5 cell contiguity filter to “grow” land use from time two to some specified later time period. • Filtering. • By filtering a Boolean mask of the class being considered, the mean filter = 1 when it is entirely within the existing class and 0 when it is entirely outside it. • When it crosses a boundary, the filter produces values that quickly transition from 1 to 0. This result is multiplied by the suitability image for that class, progressively downweighting the suitabilities with distance from existing instances of that class. • At each iteration, new class masks are created that reflect the changing geography of each class.

18. The land use changes, 1952, 1974, 1985

22. Five-class land use maps (1952, 1974, 1985) used in the actual simulations • 1952 and 1974 to simulate 1985. • 1952 and 1985 to simulate 2005. • 1974 and 1985 to simulate 2005.

23. Using 1952 and 1974 to predict 1985 Uncultivated: 24.3% predicted compared to 15.5% observed. Open cultivation: 63.2% predicted to 73.2% observed. Specialty crops: 9.3% predicted to 8.9% observed. Village: 3.0% predicted to 2.3% observed. Results

24. Markovian spacelessness

25. Projected land use/cover and the reality

26. Conclusion • In the aggregate Markov Chain Analysis predictions were not too bad – but... • The cellular automata “geography” was virtually meaningless – a failure. WHY? • The cellular automata side of CA-MARKOV requires suitability maps to help the GIS make decisions regarding the allocation of cells between land uses. • To create the suitability maps one specifies the number of objectives to be incorporated into the analysis. Examples of objectives might be distance from water, proximity to roads, water table, etc. • For each objective one must specify four things: • A descriptive caption for constructing a legend for the output map. • A weight to use for each objective to determine the relative weight that each objective will have in resolving conflicting claims for land. • A rank map of the competing land uses. • Areal requirements for each land use (in cells).

27. A broader conclusion • Ultimately one can question the utility of such simulations because the fundamental problem of any model is that there is no way to determine statistically if it is valid or not by examining how well it predicted past history. • A model that predicts the past well says nothing about how well it will predict the future. • There is no guarantee that a totally different model could not have produced the exact result but yet produce a completely different prediction of the future.

28. The way forward • Agent-based models should be used to simulate local land use change in the study area. • Agent-based simulation will permit the use of spatially-explicit models of adaptive behavior in a geographically rich environment over time (Parker, Berger, and Manson 2001)

29. Questions?

30. Bibliography • Briassoulis, H. 2000. Analysis of Land Use Change: Theoretical and Modeling Approaches. The Web Book of Regional Science, http://www.rri.wvu.edu/WebBook/Briassoulis/contents.htm. The Regional Research Institute, West Virginia University. • Eastman, J. R. 2003. IDRISI Kilimanjaro. Guide to GIS and Image Processing. Worcester, MA Clark Labs, Clark University. • O’Sullivan, D. and D. J. Unwin. 2003. Geographic Information Analysis. New York: Wiley. • Parker, D. C., T. Berger, and S. M. Manson. 2001. Agent-Based Models of Land-Use and Land-Cover Change. Report and Review of an International Workshop. October 4–7, 2001, Irvine, California, USA.