Transcript The use of cellular automata-Markov Chain Analysis to

The use of cellular automataMarkov Chain Analysis to
predict land use change
around a village in Mali
Some preliminary results
Dr. Roy Cole
Department of Geography and Planning
Grand Valley State University
Allendale, Michigan, USA
The problem: Can GIS be used to
reliably predict change?
 Purpose.
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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.
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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).
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.
The study area
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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.
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Clays in bottom lands.
Silty loam elsewhere.
Low sand dunes are found in the study area but not in or around the study
village.
The study area
and study
village
Landsat
Thematic
Mapper
image of
study
area
Year is 2000.
Month was not
specified on the
image but the
flood stage looks
like SeptemberOctober.
Precipitation
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.
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.
... 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.
... 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.
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
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.
Cellular automata
A simple example
1.
The lattice is 1-dimensional row of 20
cells.
2.
Each row represents a single time step of
the automaton’s evolution.
3.
Each cell’s evolution is affected by its own
state and the state of its immediate
neighbors to the left and right.
4.
THE RULE:
• Cells with an odd number of black
neighbors (counting themselves) will
be black at the next time step.
• Otherwise, they are white.
... continued
Cellular automata
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-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.
Cellular automata
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... continued
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.
The land use changes, 1952,
1974, 1985
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.
Using 1952 and 1974 to predict 1985
Results
Category
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.
74-85
dif
Sim74 dif
Sim-85
dif
Sim-85 dif as % of observed 85 class
Village of Ngara
0.6%
1.4%
0.8%
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
-13.2%
-4.5%
8.8%
56% more area predicted than observed
0.0%
0.0%
0.0%
16% less area predicted than observed
Uncultivated
Cemetery
35% more area predicted than observed
Markovian spacelessness
Projected land use/cover and the
reality
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:
1. A descriptive caption for constructing a legend for the output map.
2. A weight to use for each objective to determine the relative weight that
each objective will have in resolving conflicting claims for land.
3. A rank map of the competing land uses.
4. Areal requirements for each land use (in cells).
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.
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)
Questions?
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.