ENVIRONMENTAL MODELLING PROBABILISTIC MODELS (2)

1
ENVIRONMENTAL MODELLINGPROBABILISTIC MODELS (2)

• Dr Claire H. Jarvis, chj2_at_le.ac.uk

2
Review Major elements of cellular automata
Cell space The space is composed of individual
cells. Theoretically, these cells may be in any
geometric shape. Cell states The states of
each cell may represent any spatial variable,
e.g. the various types of land use. Time steps
A CA will evolve at a sequence of discrete time
steps. At each step, the cells will be updated
simultaneously based on transition rules.
Transition rules A transition rule normally
specifies the states of cell before and after
updating based on its neighbourhood conditions.
White, R., and G. Engelen, 2000,
High-resolution integrated modeling of the
spatial dynamics of urban and regional systems,
Computer, Environment and Urban Systems
24383-400.
3
GEOGRAPHICAL APPLICATIONS OF CAS

• Land use change
• Animal/vegetation movement
• Wild fires

4
Modelling land use transition using CAs

• Modelling urbanization and land use transition as
  formal cellular automaton models began with the
  work of White and Engelen, who examined the
  fractal nature of urban areas and developed a CA
  model of land use transition which they ran on
  data from four U.S. cities (1993)
• Batty and Longley have also used a somewhat
  similar approach, called diffusion-limited
  aggregation, to model urban expansion (1994).
• More recently, the Clarke Urban Growth Model
  builds upon this previous work to create a unique
  and very complex CA model of urban growth and
  land use transition.

5
Simulating the growth of Cincinnati from 1840
till 1960
6
Simulation (left) vs. Reality (right)
7
Much more work by many others

• Batty and Xie (1994) Amherst, New York.
  Survival and Birth of cells to meet overall
  growth. CA with non-local interactions in
  addition to the neighbourhood (radius 10 cells)
  there is the Field (radius 100 cells, enabling
  directional growth preference) and the Region
  (irregular area, with overall constraints).
• Wu (1997), Wu (1998), Wu and Webster (2001)
  Guangzhou, China. Elaborate DSS system with a
  probabilistic CA model fed with GIS data layers
  processed through an AHP MCE procedure
• Introduction of Fuzzy rules rather than Crisp
  transition rules to capture process of land
  encroachment
• Attempt to define transition rules based on
  economic theory
• Li and Yeh (2000), Yeh and Li (2001, 2002) urban
  sprawl and density of urban development in
  Dongguan, P.R. of China
• Takeyama (1996) Geo-algebra, extension to Map
  algebra enabling definition of CA models but also
  other spatial modelling paradigms.

(From http// www.geo.ucl.ac.be/LUCC/MODLUC_Course
/Presentations/ Guy_engelen/Cellular_automata_regi
onal.ppt, Accessed October 2003)
8
Animal/pest movement

• Couclelis CA model of rodent populations (1986)
• Forecasting the spatial dynamics of gypsy moth
  outbreaks (Zhou Liebhold, 1992)
• Dispersal of vegetation (Carey1996)

9
Couclelis CA model of rodent populations (1986)

2-dimensional implementation R.M. Itami, 1994
D.M. Theobald and M.D. Gross, 1994
(From http// www.geo.ucl.ac.be/LUCC/MODLUC_Course
/Presentations/ Guy_engelen/Cellular_automata_regi
onal.ppt, Accessed October 2003)
10

• STUDENT CONTRIBUTIONS
• (VEGETATION)

11
Forest fire

• Spread of forest fire according to forest type,
  weather conditions land topography
  (Karafyllidis Thanailakis 1997)
• Spread of fire as determined by wind direction
  (Theobald Gross 1994)

12
CA model for diffusion processes Forest fire

(From http// www.geo.ucl.ac.be/LUCC/MODLUC_Course
/Presentations/ Guy_engelen/Cellular_automata_regi
onal.ppt, Accessed October 2003)
13

• STUDENT CONTRIBUTIONS
• (WILD FIRE)

14
HOW DO I BUILD MY OWN GEOGRAPHICAL CA MODEL?
(Structure after http// www.geo.ucl.ac.be/LUCC/MO
DLUC_Course/Presentations/ Guy_engelen/Cellular_au
tomata_regional.ppt, Accessed October 2003)
15
Prepare data for building CA

• Determine resolution of the model and acquire a
  minimum of two raster maps for historic
  calibration, an appropriate time apart
• Prepare the land use data in a GIS-system before
  entering it in the model
• aggregate categories, e.g. land use
• consistency checking
• Resample in different areas

16
Building a CA (1)

• Decide on the cell space, cell states, time steps
  and transition rules for your model
• Decide whether to apply the same rule across the
  local neighbourhood, or whether you wish the
  impact of the rule to decay across space
• If introducing decay, then define the distance
  decay functions. Take them from similar model or
  design new distance weight functions. Enter
  and/or change them one at the time only

17
The creation of transition rules is but a
fundamental step, yet the most challenging one,
in building a comprehensive model of land use
change (Lay 2000)
18
Building a CA (2)

• Run the model over and over to check the
  effect(s) of any changed rule(s)
• Run the model from the known initial state till
  the known final state, and investigate any
  systematic differences using the calibration
  methods suggested overleaf

19
Calibrating a CA (1)

• Calibrate visually
• Compare the model results with the know final
  state. Are similar patterns generated? Is their
  size similar and composition similar. Do the
  classes appear in the right locations at the
  right time?
• Change and add distance functions till
  satisfactory result is obtained
• Calibrate qualitatively
• Check qualitative similarities. Compare the
  sizes and frequency of clusters within the model
  results with the know final state.

20
Calibrating a CA (2)

• Calibrate quantitatively
• Check the goodness of fit of the maps generated
  using measures from remote sensing such as the
  kappa coefficient
• Sensitivity analysis
• Consolidate the weight functions. Carry out
  sensitivity on distance functions. Remove
  redundant functions
• Extend
• Having reviewed your model, are there any
  extensions that might improve the accuracy of the
  simulations?

21
From deterministic to stochastic CAs
The single run is not what counts (Engelen
2003)
22
Critique of CAs
23

• Cellular automata provide a class of
  spatio-temporal models with a simple basic
  structure but offer a nearly unlimited range of
  possibilities.
• (Balzer et al 1996)

Do you agree?
24
Advantages of CAs for geographical modelling (1)

• Simplicity
• Complex adaptive systems are difficult to model
  using traditional techniques. Complexity without
  complication (Couclelis 1986)
• Experience does endorse the concepts of bottom-up
  modelling, where complex macro-morphology can
  result from simple principles
• This simplicity is practical as well as
  theoretical since CAs may be readily
  implementation on current digital computing
  hardware. (OSullivan 2001)
• Rule based efficiency lends itself to modelling
  dynamics at high spatial resolutions (White
  Engelen, 1997).

25
Advantages of CAs for geographical modelling (2)

• Inherent spatial nature
• Geographically, CA models are also interesting
  because they are inherently spatial,
  incorporating the intrinsically spatial concept
  of the neighbourhood.
• Clear relationship between CAs and earlier work
  such as Tobler's (1979) cellular geography and
  Hagerstrand's (1968) diffusion models.
  (OSullivan 2001).
• Allow focus on time and space
• Temporally dynamic transitions allow time series
  and Markov processes to be incorporated (Wagner
  1997)
• Equal weight given to the importance of space,
  time and system attributes (Batty, 1997
  editorial)
• Good for building stochasticity into models
• Good for modelling small populations or unusual
  events

26
Disadvantages of CAs for geographical modelling

• Difficult to set appropriate rules
• Defining adequate decision rules problematic (Lay
  2000 OSullivan 2001)
• Reality is a complex state structure, and simple
  rules cannot necessarily capture these
  interactions between multiple phenomena states.
• High simulation times
• Rule based operations known to be computationally
  time-consuming (Webster 1990)
• Local detail comes at the cost of high simulation
  times (Phipps and Langlois 1996)
• Not that easy to implement!
• Interfacing with spatial databases messy
  (Takeyama Couclelis, 1997)
• GIS approaches are inherently flat map with no
  easy way of dealing with dynamic local allocation
  across different time steps i.e. more complex
  versions are difficult to implement
• Discrete models do not cope well with
  missing/irregular temporal data

27
Disadvantages of CAs for geographical modelling

• Assumptions of strict CA formalisms often ignored
  in geographical modelling
• The available theorems on CA's are pretty
  limited, dealing as they do mainly with
  stationary (long-term asymptotic) behaviour in
  situations with small state spaces
• Theoretically underdeveloped in more their
  complex forms such as irregular cells,
  incorporation of distant actions and irregular
  neighbourhoods, non-stationary rules in time and
  space (Balzter et al 1996)
• How much scientific integrity remains when the
  elements of the original framework are amended?
  (Couclelis, 1997)
• Couclelis (1985, page 588) comments that "all the
  simple assumptions of the basic cell-space model
  could be relaxed in principle in practice, of
  course, the result would be forbiddingly
  confusing."
• Many so-called CA models make such significant
  departures from the rather limited assumptions of
  the strict CA formalism that some have questioned
  whether these are really CA models at all
  (Macmillan 1999).

28
Disadvantages of CAs for geographical modelling

• Too simple to be useful?
• Tobler has suggested that traditional Cellular
  Automata are too simple to be useful to model
  socio-economic systems
• This has led some practitioners to regard CA as
  primarily useful for pedagogic purposes (Batty
  and Xie 1997 Couclelis 1988) since they
  demonstrate that the complexity of real world
  phenomena does not necessarily imply that they
  are not amenable to modelling, nor that they are
  necessarily beyond scientific understanding
  (OSullivan 2001)
• It appears to have led others (Clarke, Hoppen,
  and Gaydos 1997 White and Engelen 1997) to
  believe that accurate models of complex urban
  systems and regions can be constructed that will
  provide a sound basis for policy testing and
  formulation. This is certainly implicit in the
  modelling of future scenarios described in such
  model (OSullivan 2001).

29
Alternative related models Constrained cellular
automata
(Slides on constrained celular automata after
http// www.geo.ucl.ac.be/LUCC/MODLUC_Course/Prese
ntations/ Guy_engelen/Cellular_automata_regional.p
pt, Accessed October 2003)
30
Constrained Cellular Automata

• The Cellular Automata dynamics evolve in a
  non-homogeneous geographical space defined by GIS
  attributes and layers (see also most of the
  others)
• Their overall dynamics are not determined by the
  micro Cellular Automata transition rules, but
  by processes at a larger macro scale (see also
  most of the others)
• Cellular Automata models have been integrated
  with more traditional dynamic models, which in
  the most general case are regionalised (spatial
  interaction based) (Engelen et al., 1993).

31
Alternative bottom-up models Agents
32
What are agent technologies?

• Adaptive autonomous agents are systems that
  inhabit a dynamic, unpredictable environment in
  which they try to satisfy a set of time-dependent
  goals or motivations
• (Maes 1996)

33
Why consider multiple agent technologies?

• Improve spatial degrees of freedom (Hiebeler
  1994) land units are not all the same size
• Allow the development of simulations involving a
  number of agents which exist within some
  (possibly dynamic) environment (Minar et al
  1996)
• Simple agents such as cellular automata in
  addition to more complex possibilities are
  facilitated (Hiebeler, 1994)
• Agents may themselves be adaptive, allowing the
  possibility of considering genetic drift (Maes,
  1995)
• As with cellular automata, agent behavior is
  determined by local, not global rules so
  maintaining simplicity
• The state of a cell may be multidimensional,
  qualitative and quantitative (Bura et al 1996)
• Arguably, better suited to multi-disciplinary
  applications (Dibble, 1996). Individual, modular
  components may be developed and then brought
  together.

34
Final questions
What do you think the role of CA models should be
within geography?Can you think of some other
applications, for example in geomorphology, where
a CA modelling approach might be interesting?