Geographic Cellular Automata

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Geographic Cellular Automata

• Maa 123.3570 Geospatial Simulation
• 2nd Session (March 31st)
• Sini Ooperi

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Classical Cellular Automata

• homogeneous environment all cells are equal
• discrete states each cell takes one of a finite
  number of possible discrete states
• local interactions each cell interacts only with
  cells that are in its local neighborhood
• discrete dynamics each cell updates its current
  state according to a transition rule taking into
  account the state of the cells in its
  neighborhood.

• self-organizing systems with emergent properties
  locally defined rules result in macroscopic
  ordered structures

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Geographic Cellular Automata

• operate
• in geographical 2D space
• in spatially heterogeneous environment, cell are
  not equal, they have different attribute values
• with transition rules that consider the
  cell-specific attribute values, a set of source
  layers as input variables in transition rules
• with transition rules that may also consider
  location of the neighboring cell (northern cell,
  eastern cell, southern cell, and western cell)
• also with continuous states, for example
  probability values between zero and one
• in vast number of domains
• urbanization models (urban geography)
• diffusion of ideas, new technology (social
  geography)
• fire models (wildfire dynamics),
• hydrological models (fluid dynamics),
• weather models (heat and humidity dynamics),
• spread models of animals and plants (dispersal
  and invasion dynamics)
• forest suggestion models (forest ecology)

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Comparison of CA and GCA
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Comparison of CA and GCA
output layer/lattice
ouput layer
Initial configuration
initial configuration
heterogenous space
homogeneous space, all cells are equal
Intermediate layer(s), new input variable(s) to
be used in transfer rules
Input variables (source layers)
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Categorizing Automata

• Geographic cellular automata (GCA)
• cellular automata operating in a geographic space
  (georeferenced media)
• Geographic automata (GA)
• geographic cellular automata (GCA)
• fixed objects and moving agents
• houses, residents
• buildings, pedestrians
• habitat patches, animals

Will be the subject of MAS (multi-agent systems)
lecture
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Geographic Cellular Automata

• Loose coupling
• cellular automata model is coupled with GIS
  software
• GIS contains raster layers with attribute values
  of the cells
• for example, urban spread model SLEUTH has 6
  source layers
• Slope
• Land cover
• Exclusion
• Urban
• Transportation network
• Hill shade

SLEUTH project website http//www.ncgia.ucsb.edu/
projects/gig/
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Spread of Urban Areas SLEUTH model

• spread of urban spatial pattern as a function of
• Slope
• Land cover
• Exclusion layer (water, swamps etc.)
• Urban
• Transportation network
• Hill shade
• changes in urban pattern are implemented in four
  sub steps
• Spontaneous growth (F1)
• Generation of new diffusing centers (F2)
• Diffusion at the edges of urbanized areas (F3)
• Road-influenced diffusion (F4)

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Five Growth Coefficients

• values affect how the growth rules are applied.
• calibrated by comparing simulated land cover
  change to a study area's historical data.
• dispersion_coefficient controls the number of
  times a pixel will be randomly selected for
  possible urbanization
• breed_coefficient determines the probability of a
  spontaneous growth pixel becoming a new spreading
  center
• spread_coefficient determines the probability
  that any pixel that is part of a spreading center
  will generate an additional urban pixel in its
  neighborhood
• slope_coefficient, if high, increasingly steeper
  slopes are less likely to urbanize. As the slope
  coefficient gets closer to zero, an increase in
  local slope has less affect on the likelihood of
  urbanization
• road_gravity_coefficient is the maximum search
  distance for a road from a pixel

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Suitability to Urbanization

• Two measures of suitability affect the likelihood
  of urbanization throughout the growth process.
• The suitability is defined by
• exclusion layer (for example, water, swamps,
  etc.)
• slope, slope above 21 cannot be urbanized. Given
  that the local slope (slope (i,j)) is below 22,
  the slope_coefficient determines the weight of
  the probability that the location (i,j) may be
  built upon

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1.Spontaneous Growth

• defines the occurrence of random urbanization of
  land. Any non-urbanized cell on the lattice has a
  certain (small) probability of becoming urbanized
  in any time step.
• whether a given cell U(i,j,t) at coordinate (i,j)
  at time t will be urbanized at time t1 can be
  expressed by
• U(i,j,t1) f1 dispersion_coefficient ,
  slope_coefficient , U(i,j,t), random ,
• parameters
• dispersion coefficient determines the (small)
  spontaneous, global urbanization probability
• slope coefficient determines the weighted
  probability of the local slope.
• stochasticity of the process is indicated by
  random. If the cell is already urbanized or
  excluded from urbanization, it will not change

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Spontaneous Growth

• F(dispersion_coefficient, slope_coefficient)
  for (p lt dispersion_value) select pixel
  location (i,j) at random if ((i,j) is
  available for urbanization) (i,j)
  urban New Spreading Center Growth
  end spontaneous growth

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2.Generation of New Diffusion Centers

• determines whether any of the new, spontaneously
  urbanized cells will become new urban spreading
  centers.
• global parameter, breed coefficient, defines the
  probability for each new urbanized cell
  U(i,j,t1) to become a new spreading center
  U'(i,j,t1), given two neighboring cells also are
  available for urbanization
• U'(i,j,t1) f2 breed-coefficient,
  U(i,j,t1), random ,
• where (k,l) are nearest neighbors to (i,j).
• If the cell is allowed to become a spreading
  center, two additional cells adjacent to the new
  spreading center cell also have to be urbanized.
  Thus an urban spreading center is defined as a
  location with three or more adjacent urbanized
  cells.
• actualization of this step is dependent upon the
  slope coefficient-weighted topography and the
  availability of neighborhood cells to make the
  transition.

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New Diffusion Centers

• F(breed_coefficient,slope_coefficient) if
  (random_integer lt breed_coefficient) if (two
  neighborhood pixels are available for
  urbanization) (i,j) neighbors urban end
  new spreading center growth

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3.Diffusion at the Edges of Urbanized Areas

• Edge-growth dynamics define the part of the
  growth that stems from existing spreading
  centers.
• growth propagates both the new centers generated
  in step 2 in this time step, time (t1), and the
  more established centers from earlier times
• if a non-urban cell has at least three urbanized
  neighboring cells, it has a certain global
  probability to become urbanized defined by the
  spread coefficient, given it is possible to build
  on the cell (slope coefficient).
• edge growth can be expressed by
• U(i,j,t1) F3 spread_coefficient,
  slope_coefficient, U(i,j,t), U(k,l), random
  ,
• where (k,l) belongs to the nearest neighborhood
  of (i,j)

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Edge Growth

• F(spread_coefficient,slope_coefficient) for
  (all non-edge pixels (i,j)) if ((i,j) is
  urban) and (random_integer lt
  spread_coefficient) if (at least two urban
  neighbors exist) if (a randomly chosen,
  non-urban neighbor is available for
  urbanization) (i,j) neighbor urban end
  edge growth

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4.Road-influenced Diffusion

• determined by the existing transportation
  infrastructure as well as the most recent
  urbanization done under steps i, ii and iii.
• with a probability defined by breed_coefficient,
  newly urbanized cells (at time t1) are selected,
  and the existence of a road is sought in their
  neighborhoods. If a road is found within a given
  maximal radius (determined by road_gravity
  coefficient) of the selected cell, a temporary
  urban cell is placed at the point on the road
  that is closest to the selected cell.
• Next, this temporary urban cell conducts a random
  walk along the road (or roads connected to the
  original road) where the number of steps is
  determined by the parameter dispersion_coefficient
  .
• the final location of this temporary urbanized
  cell is then considered as a new urban spreading
  nucleus. If a neighboring cell to the temporary
  urbanized cell (on the road) is available for
  urbanization, it will happen (randomly picked
  among possible candidates).
• If two adjacent cells to this newly urbanized
  cell are also available for urbanization it will
  happen (randomly picked among candidates).

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Road-influenced Diffusion

• Thus the creation of the temporary urbanized cell
  on the road is defined by
• 1. U'(k,l,t1) f4.1 U(i,j,t1),
  road_gravity_coefficient, R(m,n), random
• where i,j,k,l,m, and n are cell coordinates, and
  R(m,n) defines a road cell. The random walk on
  the road may be expressed by
• 2. U''(i,j,t1) f4.2 U'(k,l,t1),
  dispersion_coefficient, R(m,n), random .
• where (i,j) are road cells neighboring (k,l). If
  we define the location of the temporary urbanized
  cell at the end of the random walk by (p,q), the
  new adjacent urban spreading center will be
  defined by
• 3. U'''(i,j,t1) f4.3 U''(p,q,t1), R(m,n),
  slope_coefficient, random ,
• and two additional adjacent urbanized cells may
  be added using
• 4. U''''(i,j,t1) f4.4 U'''(p,q,t1),
  slope_coefficient, random ,
• where (i,j) and (k,l) belong to the nearest
  neighborhood of (p,q).
• The four steps above are collectively referred to
  as a road trip. Each attempt to select a newly
  urbanized pixel to move to a road is a new road
  trip. The number of attempted road trips in any
  given growth cycle is determined by the
  breed_coefficient.

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Road-influenced Diffusion

• F(breed_coefficient, road_gravity_coefficient,
  dispersion_coefficient, slope_coefficient)
  for (p lt breed_coefficient) road_gravity
  value which is a function of image size
  and road_gravity_coefficient max_search
  maximum distance, determined by
  road_gravity, for which a road pixel is searched
  (i,j) randomly selected pixel, urbanized
  within the current growth cycle road_found
  search outward from (i,j), up to
  max_search, for a road pixel if (road_found)
  walk along the road, in randomly selected
  directions, for a number of steps
  determined by the road_value and the
  dispersion_coefficient if (a neighboring
  pixel is available for urbanization) (i,j)
  neighbor urban if (two neighbors of the
  newly urban pixel are available for
  urbanization) two urban pixel neighbors
  urban end road-influenced growth

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Predictions for Urban Growth of Santa Barbara,
California
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Urban forecast 2020
Urban forecast 2030
Urban forecast 2050
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Urban automata links

• Environmental Explorer
• http//lov.riks.nl/
• OBEUS http//eslab.tau.ac.il/Research/OBEUS/defaul
  t.aspx
• SLEUTH model http//www.ncgia.ucsb.edu/projects/gi
  g/

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Spread of Forest Fire

• Seven source layers input variables
• Fuel load layer
• Slope layer
• Aspect layer
• Fire status layer, initial weights based on wind
  direction terrain
• Air temperature
• Relative humidity
• Fuel moisture content
• DLA, diffusion limited aggregation growth takes
  place only onto existing structure, not random
  jumps to further away
• stochastic GCA, a random number between zero and
  seven is drawn to choose the direction, and then
  a random number between zero and 100 is drawn. If
  the number is less than the weighted probability
  level, then the fire moves in this direction
  (Monte Carlo risk probabilities)
• algorithm is iterated and then the result is
  averaged

intermediate layer weights modified by fuel and
terrain
Clarke K.C., Brass J.A., P.J. Riggan.(1994) A
cellular automata model for wildfire propagation
and extinction. Photogrammetric Engineering
Remote Sensing, vol.60(11) 1355-1367.
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Fire motion decisions are made using weights from
the data layers
Aspect Layer
Fuel Load Layer
Slope Layer
weights modified by fuel and terrain
Fire Status Layer
movement decision made by random number
assignment by weights
W7
W0
W1
W6
W2
W5
W3
W4
Initial weights based on wind direction and
magnitude
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Basic fire behavior
Time 1
Time 2
Time 3
Burning at Time 2
Fire source
Burning at Time 1
Burning at Time 3
Fire movement
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Next Time More Diffusion Modeled with
Geographic Cellular Automata

• probabilistic transition rules
• stochastic input variables in transition rules
  (random component)
• neural network-based probabilities
• fuzzy input variables in transition rules
  (uncertainty in parameters)
• memory-based transition rules (current--,
  current-, current, next)
• constrained automata
• rules with constrains road network usually grows
  from current nodes onwards, not from single
  fractions
• landscape with constrains obstacles and
  barriers (deep slopes, rivers and lakes)
• domain specific limiting constrains

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and also

• Modeling example from spatial ecology
• A geographic automata model of Colorado Beetle in
  a novel environment
• Hands-on-geographic cellular automata
• and
• Presentation of Assignment 1
• Two web links to applications
• probability based forest fire http//schuelaw.whit
  man.edu/JavaApplets/ForestFireApplet/
• general diffusion limited aggregation
• http//apricot.polyu.edu.hk/lam/dla/dla.html