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 (OSullivan 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
Markov Chain Analysis
... continued

• 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
Markov Chain Analysis in Idrisi Kilimenjaro
... continued

• 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
  automatons evolution.
• Each cells 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
Cellular automata
... continued

• A more complicated example John Conways 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.

16
Cellular automata-MCA in Idrisi
... continued

• 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
Cellular automata
... continued
0 0 1 0 0
0 1 1 1 0
1 1 1 1 1
0 1 1 1 0
0 0 1 0 0

• 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
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
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
Results
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.
Category 74-85 dif Sim-74 dif Sim-85 dif Sim-85 dif as of observed 85 class
Village of Ngara 0.6 1.4 0.8 35 more area predicted than observed
Open cultivation 10.4 0.4 -10.0 14 less area predicted than observed
Specialty crops 2.2 2.6 0.4 5 more area predicted than observed
Uncultivated -13.2 -4.5 8.8 56 more area predicted than observed
Cemetery 0.0 0.0 0.0 16 less area predicted than observed
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.e
  du/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.
• OSullivan, 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 47, 2001, Irvine, California,
  USA.