ENVIRONMENTAL MODELLING PROBABILISTIC MODELS (2)

1. ENVIRONMENTAL MODELLINGPROBABILISTIC MODELS (2) Dr Claire H. Jarvis, chj2@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 Systems24:383-400.

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_regional.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_regional.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_regional.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/MODLUC_Course/Presentations/ Guy_engelen/Cellular_automata_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. (O’Sullivan 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. (O’Sullivan 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; O’Sullivan 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 (O’Sullivan 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 (O’Sullivan 2001).

29. Alternative related models Constrained cellular automata (Slides on constrained celular automata after http:// www.geo.ucl.ac.be/LUCC/MODLUC_Course/Presentations/ Guy_engelen/Cellular_automata_regional.ppt, 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?