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Dynamic Processes, Model Complexity, and Dynamic Modeling Techniques

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Title: Dynamic Processes, Model Complexity, and Dynamic Modeling Techniques


1
Dynamic Processes, Model Complexity, and Dynamic
Modeling Techniques
  • Dr. Dawn Cassandra Parker
  • Dept. of Geography and Env. Science and Policy
  • Center for Social Complexity
  • George Mason University

2
Where we areWhat real-world spatial, temporal,
and behavioral processes do you strive to
represent?andWhat is the minimum level of
complexity for the model?
3
Main questions to consider
  • What spatial, temporal, and behavioral processes
    do we believe are important in the system we want
    to model?
  • How much complexity do we need to build into our
    model to capture those processes?
  • How little complexity can we get away with?

4
Complexity
  • Many uses of this word in modeling
  • Here, complex means
  • not simple
  • having many system elements change within the
    model
  • operating at multiple scales
  • We will look at sources of spatial, temporal, and
    behavioral complexity
  • We will also look at degree of endogeneity and
    cross-scale feedbacks

5
Spatial Complexity Spatial autocorrelation
  • Example one land use is more likely when it has
    another land use type as a neighbor, due to
  • Technology adoption and other imitative behavior
  • Scale economies
  • Spatial competition
  • Negative spatial spillovers/externalities
  • Ecological spillovers (edge effects)

6
More spatial complexity Spatial dependence
  • Example two land uses share a similar spatial
    characteristics, such as
  • Soil type
  • Accessibility
  • Climate
  • Topography
  • Political zone
  • Note this type of spatial dependence may motivate
    combining data at different spatial scales

7
More spatial complexity Networks
  • Physical
  • Transportation infrastructure
  • hydrology
  • Social
  • communication,
  • social ties,
  • trade and commerce

8
Temporal complexity Growth and decay
  • Population growth and decline (animal and human)
  • Soil degradation
  • Carbon sequestration
  • Erosion
  • Social trends
  • Financial investments

9
Temporal complexity Temporal lags
  • Growth and decay functions lead to temporal
    autocorrelation
  • Modeling current state may require information on
    states in previous time periods
  • For processes that also diffuse over space, it
    may require both spatial and temporal lags
    (example species colonization)

10
Temporal complexity Path dependence
  • Different conditions at one time period can lead
    to very different outcomes over space and time
  • This is an important source of uncertainty in
    modeling
  • Dan Brown will elaborate .

11
Temporal complexity forward-looking behavior
  • Humans and other animals are forward-looking.
    Examples
  • Food and seed storage
  • Crop rotation
  • Strategic behavior, such as pre-emptive land
    clearing
  • Successful models must take this into account
  • Therefore, models must build in expectations of
    the future and possible responses

12
Behavioral Complexity
  • Different types of actors
  • Multiple goals
  • Heterogeneity within
  • Expectations
  • Strategies
  • Motivations
  • Interconnectivity of agents in social, economic,
    and ecological networks

13
How many model elements are determined within the
model?
  • Issue here is the degree of endogeneity, or
    connectedness, of the components of the dynamic
    system
  • The more endogeneity is present, the broader the
    scope of the model, and the larger the number of
    questions that can be asked and answered with the
    model
  • The more endogeneity is present in a model, the
    more difficult it is to analyze and understand
    the working of the model

14
Cross-scale dynamics
  • Higher-level processes often constrain
    lower-level processes
  • Lower-level processes may feed back to influence
    higher-level processes

15
Example roads, colonization, and deforestation
  • National level policies (subsidized timber prices
    and/or roads) encourage road construction and
    deforestation
  • National level policies (distribution of land for
    frontier settlement) encourage settlement along
    roads
  • Rural ag. producers become more integrated with
    the market (new people, new techniques, new
    opportunities)
  • Results may be greater sensitivity to financial
    factors such as ag prices, off-farm wages,
    credit, timber prices) (Angelsen and Kaimowitz)

16
Example Residential location and employment
  • Spatial structure at one level determined as
    residents locate within commuting distance of
    place of employment
  • Spatial structure at another level determined as
    firm locates around other complementary firms
    (result is polycentric node)
  • Spatial structure at higher level determined by
    relationship between polycentric nodes
  • At a still higher level, spatial structure
    between cities is determined through migration
    (Anas et al.)

17
Example Ag production and price feedbacks
  • Spike in demand may cause ag extensification
    (production on previously marginal lands).
    Example organic rice for Japanese consumption
  • Increased supply at a local level feeds back to
    depress globally determined price (classic cobweb
    model)
  • Note that integration of new markets may have the
    same effects (example coffee production)

18
Where we areWhat modeling methodologies are
most appropriate??
19
Classifications of Dynamic Models by Technique
  • Dynamic Optimization models (mathematical
    programming)
  • Cellular Automaton models
  • Statistical/Regression models
  • Agent based/Multi-agent system models
  • Integrated/Hybrid models (not covered today)

20
Dynamic Optimization Models
  • Optimization models derive an ideal or optimal
    solution for a given system, based on a
    quantitative objective
  • Dynamic optimization models incorporate temporal
    lags and/or forward looking behavior
  • Models can be positive, under the assumption that
    system agents (generally animals or humans)
    behave as if they optimize
  • Models are most often normative and used for
    policy
  • Spatial dynamic optimization models are often
    difficult to solve

21
Example Carpentier et al. Amazon model
  • Purpose of model--Investigate
  • Will settlement farmers in the Brazilian Amazon
    adopt more intensive production systems?
  • If they do, will this adoption slow
    deforestation?
  • What will be the effect will adoption have on
    incomes?

22
Modeling framework
  • Dynamic linear programming model chooses optimal
    path of land use over time
  • Farmers optimize subject to constraints on
    available resources (land, labor, capital)
  • In addition, dynamic relationships between
    land-use activities and productivity, as well as
    savings and investments, are accounted for
    through constraints and equations of motion

23
Land-use systems
24
Spatial complexity
  • Only spatial aspect of this model are
    location-specific biophysical conditions and
    socio-economic conditions

25
Temporal complexity
  • Agents can anticipate future effects of current
    decisions
  • Temporal interactions between cropping decisions
    and soil fertility are included
  • Like other applications, likely land-use life
    cycles are built in

26
Behavioral Complexity
  • A wide variety of parameters (prices,
    productivity, resource endowments) affect agent
    decisions
  • Agents are forward-looking
  • By changing model parameters, a variety of agent
    types could be analyzed, in principle.
  • However, no agent-agent interactions are present

27
Is this model spatial?
  • No
  • Object have no explicit location
  • Location is not explicitly represented
  • Location/distance does not enter into model
    calculations
  • The model modifies the landscape only through
    changes in composition
  • But
  • Travel cost to market could easily be added
  • Results could be used to simulate landscape
    change
  • See Berger and Deadman et al. for more space

28
Some strengths and weaknesses of dynamic
optimization models
  • Strengths
  • Great for representing temporal dynamics
  • Good models of behavior in certain contexts
  • Useful for creating benchmarks/goals for policy
  • Weaknesses
  • Spatial aspects are incorporated with difficulty
  • Can easily become difficult or impossible to
    solve
  • For normative models sometimes knowing the
    optimal outcomes doesnt help if we dont know
    how to get there

29
Cellular Automaton Models
  • CA models are dynamic simulation models, where
    cell transitions are based on the state of the
    current cell and the states of neighboring cells.
  • Neighbors can be very broadly defined, and may
    include multi-scale influences
  • Cellular structures are generally grids, but can
    be any cellular structure, in principle

30
Example DUEM model (Batty, Xie, and Sun)
  • Purpose of the model
  • Demonstrate how urban sprawl can occur without
    population growth

31
Model Mechanisms
  • Model inputs real-world raster layers to define
    initial land uses
  • Possible land-use classes include housing,
    commercial, industrial, vacant, and roads
  • Transition rules are influenced by spatial
    influences and temporal constraints

32
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33
Spatial Complexity
  • The urban system is represented by three nested
    scales Neighborhood, Field, and Region
  • Transitions are influenced by
  • the other land uses in the local neighborhood
  • the density of land uses in the district
  • constraints on development in the region
  • The radial extent of the neighborhood is
    determined parametrically by the user

34
Temporal Complexity
  • Land-use generation sequences are restricted (for
    example, streets generate only streets)
  • Land uses have life cycles, and can revert to
    vacant land
  • Only new land uses generate other new land uses

35
Behavioral Complexity
  • No explicit behavioral complexity in this model,
    as there are no explicit decision-making agents
  • Effects of agent decisions are implicitly
    represented through transition probabilities

36
Is the DUEM model spatial?
  • Yes
  • Spatial outcomes will change as we change
    starting landscapes
  • Representations of land uses and road networks
    are a part of the model
  • Distance from other land uses influences cell
    transitions and growth of new roads
  • The model grows a new urban landscape

37
Some strengths and weaknesses of cellular
automaton models
  • Strengths
  • Models are very strong at representing local
    spatial processes
  • Models tend to do well at replicating real-world
    spatial patterns, especially fractal structures
  • Weaknesses
  • Models may place too much emphasis on local
    interactions
  • Models are not strong at representing behavior
  • Often, models require projections of rates and
    quantities of change to run

38
Statistical/Regression Models
  • These models find a set of best-fit model
    coefficients that express a statistical
    relationship between a dependent variable (often
    land use or cover) and a series of independent
    variables (representing drivers of LUCC)
  • Models produce a transition probability,
    conditional on states of independent variables
  • Models are only dynamic when some set of rules is
    used to generate transitioned landscapes using
    those estimated probabilities

39
Example CLUE-S model (Verburg et al.)
  • Purpose of the model
  • Projections of land-use change under status quo
  • Scenario analysis
  • Hypothetical impacts of new protected area
  • Identify possible hot-spots of land-use change

40
Model structure
  • Non-spatial model determines aggregate demand for
    land
  • Spatial statistical model determines transition
    probabilities for particular land uses
  • User-determined conversion rules limit possible
    transitions, in order to correctly reflect
    temporal dynamics
  • Dynamic allocation protocol allocates change
    based on estimated transition probabilities and
    conversion elasticities

41
Model structure
Structure
42
Spatial Complexity
Characteristics
Characteristics complexity
  • Interaction through accessibility
  • The suitability of a location is (partly)
    determined by its access to facilities and/or
    other land uses
  • Direct interaction
  • Influence of neighboring land uses
  • Centripetal forces economies of scale, labor
    markets etc.
  • Centrifugal forces congestion, environmental
    pollution etc.

43
Temporal Complexity
  • Not all land use conversions are reversible
  • Urban area and residential area
  • Deforestation of primary rain forest
  • Other conversions are very costly
  • Fruit tree plantations
  • Some locations are converted after a short time
    period
  • Abandonment after shifting cultivation (nutrient
    depletion)

44
Characteristics
Characteristics complexity
Example of the translation of a land use change
sequence into a land use conversion matrix
45
Behavioral Complexity
  • Location and community specific information such
    as population density, literacy and income enter
    the statistical model
  • There is no explicit decision-making function
  • There are no explicit agent-agent-interactions

46
Sibuyan island, Philippines
Applications
47
Applications
forest
grassland
oil palm
rice
48
Is the CLUE-S model spatial?
  • Yes
  • Because of neighborhood effects and
    transportation cost, estimated transition
    probabilities would change if land uses were
    rearranged in space
  • CLUE-S inputs and output spatial data
  • Neighborhood effects and transport cost enter
    into the model
  • When used for dynamic simulation, CLUE-S produces
    a map of projected land uses over time

49
Some strengths and weaknesses of spatial
statistical/regression models
  • Strengths
  • Models provide information on key drivers of
    change
  • Spatial and temporal lags can be incorporated
  • Data can be entered at multiple scales
  • Weaknesses
  • Models themselves dont produce projections of
    spatial change
  • Arbitrary transition rules may lead to different
    change projections for the same data
  • Simulations of change require projections of
    rates and quantities of change
  • Models may have little out-of-sample power

50
Multi-agent/Agent-Based Models
  • Spatial agent-based models are simulation models
    consisting of
  • A collection of autonomous decision-making agents
  • An interaction environment (landscape model)
  • Interdependencies among agents, their
    environment, or both
  • Rules governing sequencing of actions and
    information flows
  • More from Dan Brown and Kevin Johnston

51
Example SLUDGE (Simulated land use dependent on
edge-effect externalities) (Parker et al.)
  • Purpose of the model--Investigate
  • Can spatial externalities lead to economically
    inefficient levels of landscape fragmentation?
  • How do initial land-use patterns influence future
    land-use fragmentation?
  • Are spatial externalities sufficient to produce
    urban sprawl?
  • How to interactions between spatial externalities
    and transportation costs influence sprawl?

52
What is a spatial externality?
  • Costs or benefit to a neighbor of a surrounding
    land use, which are not taken into account when
    the generating neighbor makes a decision about
    land use

53
Model Mechanisms
  • Model operates as a hybrid CA/ABM model, with a
    single agent in each cell
  • Agents form expectations regarding land-use
    profitability, based on neighboring land uses and
    current land use pattern and composition
  • Agents choose the highest-valued land use in each
    time period
  • A landscape evolves where no agent can do better
    by changing land uses
  • The model reports land rents, economic welfare
    measures, and measures of landscape fragmentation

54
Spatial Complexity
  • Neighborhood effects payoffs to a given land
    use depend on the actions of four neighbors
  • Induced landscape heterogeneity payoffs now vary
    spatially
  • Spatial pattern effects Landscape productivity
    depends on the spatial arrangement of land uses,
    as well as amount of land in each use
  • Transportation costs affect payoffs to each land
    use

55
Temporal Complexity
  • Agents form expectations about the future
    productivity of the urban land use
  • Little other temporal complexity
  • No constraints on land-use transitions
  • No land-use life cycles

56
Behavioral Complexity
  • Prices, landscape pattern, and actions of
    neighbors influence agent decisions
  • Agents have fairly mathematically sophisticated
    decision rules
  • However
  • Agents are homogeneous
  • Agents are not forward-looking
  • Agents interact with other agents indirectly

57
NIMBY plus Ag/Urban setback
Demand Function pu 140.8/q Transportation
Costs 0.01 Externality Damage on A by U
0.125 Us Aversion Distance to U
0.125 Urban/Ag Setback 0
58
Outcome Summary
Economic Outcomes
Market-Clearing Rent for U 1.05 Proportion
Urban Parcels 0.189 Average Urban
Production 0.788 Average Urban Transport
Cost 0.056 Proportion Agricultural
Parcels 0.811 Average Agricultural
Production 0.932 Change in Total Surplus -0.0267
59
Is the SLUDGE model spatial?
  • Yes
  • Because of neighborhood effects and
    transportation cost, land-use transitions, land
    rents, and welfare measures would change if land
    uses were rearranged in space
  • SLUDGE operates on a spatial landscape model
  • Neighborhood effects and transport cost enter
    into the model
  • The SLUDGE landscape changes as the model runs

60
Some strengths and weaknesses of agent-based
models
  • Strengths
  • Models can incorporate important sources of
    spatial, temporal, and behavioral complexity
  • Very strong format for integrated models
    (human-environment interactions
  • Potentially strong for cross-scale feedbacks
  • Weaknesses
  • Can be difficult to map and communicate model
    mechanisms and outcomes
  • Error propagation is potentially very high
  • Can be very data hungry

61
Summing Up
62
Acknowledgements
  • Project and overview article authors authors
    (references follow)
  • Students from Land-use modeling class for
    discussions and article summaries (esp. Maction
    Komwa and Rich DeBell)
  • Thanks to you for your interest and ESRI for
    sponsorship

63
Additional Resources
  • MODLUC international graduate workshop
    http//www.geo.ucl.ac.be/LUCC/MODLUC_Course/MODLUC
    .html
  • CSISS sponsored MaSpace resources
    http//www.csiss.org/resources/maslucc/
  • Class resources, Land-use Modeling Techniques
    and Applications http//mason.gmu.edu/dparker3/
    lumta_04/lumta.html
  • Class resources, Spatial Agent-based Models of
    Human-Environment Interactions
    http//mason.gmu.edu/dparker3/spat_abm/spat_abm.h
    tml
  • This talk available at http//mason.gmu.edu/dpar
    ker3/talks/dcp_esri2005.ppt

64
References
  • Agarwal, C., G. M. Green, J. M. Grove, T. Evans,
    and C. Schweik. 2002. A review and assessment of
    land-use change models Dynamics of space, time,
    and human choice. Burlington, VT USDA Forest
    Service Northeastern Forest Research Station
    Publication NE-297. http//www.fs.fed.us/ne/newtow
    n_square/publications/technical_reports/pdfs/2002/
    gtrne297.pdf.
  • Anas, A., R. Arnott, and K. A. Small. 1998. Urban
    Spatial Structure. Journal of Economic Literature
    36 (3) 1426-1464
  • Angelsen, A., and D. Kaimowitz. 1999. Rethinking
    the causes of tropical deforestation Lessons
    from economics models. The World Bank Research
    Observer 14 (1) 73-98. http//www.worldbank.org/r
    esearch/journals/wbro/obsfeb99/pdf/article4.pdf.

65
References, Cont.
  • Batty, M. Forthcoming. Urban Growth Models in D.
    J. Maguire, M. F. Goodchild, and M. Batty, eds.
    GIS, Spatial Analysis and Modeling. ESRI Press,
    Redlands, CA
  • Berger, T. 2001. Agent-based spatial models
    applied to agriculture A simulation tool for
    technology diffusion, resource use changes, and
    policy analysis. Agricultural Economics 25 (2-3)
    245-260
  • Briassoulis, H. 1999. Analysis of Land Use
    Change Theoretical and Modeling Approaches.
    Regional Research Institute, West Virginia
    University. http//www.rri.wvu.edu/WebBook/Briasso
    ulis/contents.htm.

66
References, Cont.
  • Carpentier, C. L., S. A. Vosti, and J. Witcover.
    2000. Intensified production systems on western
    Brazilian Amazon settlement farms could they
    save the forest? Agriculture, Ecosystems and
    Environment 82 (1-3) 73-88.
  • Deadman, P., D. Robinson, E. Moran, and E.
    Brondizio. In Press. Effects of Colonist
    Household Structure on Land-Use Change in the
    Amazon Rainforest An Agent-Based Simulation
    Approach. Environment and Planning B

67
References, cont.
  • Geist, H., and E. F. Lambin. 2002. Proximate
    causes and underlying driving forces of tropical
    deforestation. Bioscience 52 (2) 143-150.
    http//www.geo.ucl.ac.be/LUCC/pdf/02_February_Arti
    cle_Geist_.pdf.
  • Lambin, E. F., H. Geist, and E. Lepers. 2003.
    Dynamics of land-use and land-cover change in
    tropical regions. Annual Review of Environmental
    Resources 28 205-241
  • Parker, D. C. Forthcoming. Integration of
    Geographic Information Systems and Agent-Based
    Models of Land Use Prospects and Challenges in
    D. J. Maguire, M. F. Goodchild, and M. Batty,
    eds. GIS, Spatial Analysis and Modeling. ESRI
    Press, Redlands

68
References, cont.
  • Parker, D. C., S. M. Manson, M. A. Janssen, M.
    Hoffmann, and P. Deadman. 2003. Multi-Agent
    Systems for the Simulation of Land-Use and
    Land-Cover Change A Review. Annals of the
    Association of American Geographers 93 (2).
    http//www.csiss.org/events/other/agent-based/pape
    rs/maslucc_overview.pdf.
  • Parker, D. C., and V. Meretsky. 2004. Measuring
    pattern outcomes in an agent-based model of
    edge-effect externalities using spatial metrics.
    Agriculture, Ecosystems and Environment 101
    (2-3) 233-250

69
References, cont.
  • Verburg, P. H., P. Schot, M. Dijst, and A.
    Velkamp. Forthcoming. Land-Use Change Modeling
    Current Practice and Research Priorities.
    GeoJournal. http//www.geo.ucl.ac.be/LUCC/MODLUC_C
    ourse/PDF/T.20Veldkamp20(intro).pdf.
  • Verburg, P. H., W. Soepboer, A. Veldkamp, R.
    Limpiada, V. Espaldon, and S. S. A. Mastura.
    2002. Modelling the spatial dynamics of regional
    land use The Clue-S model. Environmental
    Management 30 (3) 391-405. http//www.geo.ucl.ac.
    be/LUCC/MODLUC_Course/PDF/P.20Verbrug20b.pdf.
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