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Modeling in GIS


									Modeling in GIS

7 April 2011
Types of models
   A model may be a representation of
   data (e.g. a DEM)
   A conceptual model is an idea of how
   something functions (often described with a
   flow chart)
   Rule-based modeling uses rules and
   numerical thresholds to interpret
   information represented in multiple data
More types of models
   Mathematical modeling involves use of
   equations that may be implemented within
   GIS or linked to GIS
     Statistical mathematical models are based
     on empirical observations and contain one or
     more random variables
     Deterministic mathematical models do not
     contain any random variables
     Environmental simulation models are
     mathematical models that represent
     environmental processes
Even more models
   Cartographic modeling involves GIS analysis of
   spatial data with Boolean or mathematical
   Statistical GIS modeling involves developing
   relationships between GIS-derived environmental
   characteristics (independent variables) and
   measures of ecological function (dependent
   In coupled GIS/simulation modeling, GIS are
   used to derive input variables required by a
   simulation model
Cartographic modeling example
Cartographic modeling
   Cartographic modeling is often used to
   identify suitable habitats for organisms from
   environmental variables
     E.g. maps of vegetation, food, roads, etc. can be
     combined to predict a species distribution
     Has been used on Wild Turkeys, Golden-cheeked
     Warblers, Wood Storks, White-tailed Deer, Gopher
     Tortoise, California Condor, etc.
Cartographic modeling
   It is also possible to combine the variables in a
   mathematical model where each data layer
   represents a separate variable
     For example, it is possible to compute soil loss bass on
     six variables:
      • 1.) Rainfall erosion index (R)      4.) Slope length (S)
      • 2.) Inherent soil erodibility (K)   5.) Cover & management factor (C)
      • 3.) Slope percentage (L)            6.) Conservation practice factor (P)
     A = RKLSCP
     A similar approach has been used to model non-point
     source pollution
California Gnatcatcher
   Listed as threatened
   in 1993 under ESA
   Fewer than 5,000
   pairs are present in
   southern CA
   Has lost 60-65% of
   habitat in San Diego
•From Exercise 4 in
Geoprocessing in ArcGIS
Rule-based modeling
   Expert systems are computer systems
   that help solve problems that would
   normally require a human expert’s
   Expert systems can be linked with a GIS
   and thus made spatially explicit
   Expert systems utilize three types of
Three types of rules for rule-
based modeling
   1.) Database rule to evaluate numerical
   2.) Map rules to evaluate mapped
   categorical variables
   3.) Heuristic rules to evaluate the
   knowledge of experts
     Heuristic: pertaining to a trial-and-error
     method of problem solving used when an
     algorithmic approach is impractical
Inductive-spatial modeling
In inductive-spatial modeling, a GIS
“learns” relationships between datasets in
the geographic database, developing rules
based on the analysis of the input data
  This is a form of rule-based
  This approach has been
  used to model habitat
  suitability for Red Deer in
Spatial Decision Support System
   SDSS is a type of rule-based modeling
   A SDSS adds the ability to recommend
   management solutions to environmental
   It can also help evaluate the
   consequences of various management
   scenarios, aiding in decision-making
SDSS example
Statistical modeling
   If the relationships needed for
   development of a model are not known,
   GIS can be used to:
     Assemble spatial data on landscape
     Derive new data that are syntheses of the
     Statistically analyze the new data to
     determine the strength of the interactions
Statistical modeling example
Avoiding spatial bias in
statistical modeling
   How do you minimize autocorrelation?
     Autocorrelation: A correlation between
     all the elements of a series and those
     separated from them by a given interval
   Random sample selection
   Choosing sample points that are
   regularly spaced (at a distance that
   meets an acceptable level of spatial
Statistical models for continuous
   In GIS-univariate statistical modeling
   what are dependent variables and what
   are independent variables?
     Dependent variables are typically field
     measurements (e.g. biomass, diversity,
     richness, etc.)
     Independent variables are derived from a
     digital database containing continuous data
     (e.g. elevation)
Example of a univariate model
Examples of statistical models
   Regression analysis to relate vegetation
   alteration by beaver dams to beaver colony
   ANCOVA to compare expansion rates of oak
   wilt fungus in urban vs. rural areas in TX
   Stepwise multiple regression to relate the %
   of trees / cell damaged by spruce budworm
   to physical and vegetative site characteristics
   represented by a number of GIS data layers
Statistical models for categorical
   Categorical data requires a different
   analysis than continuous data

   Expected vs. observed outcomes
   Bayesian statistics
Expected vs. observed outcomes
   Most rely on a chi-square (χ2) analysis
   For example:
     Young et al. (1987) used χ2 analysis to
     demonstrate that Northern Spotted Owls used old-
     growth more often than would be expected based
     on its percentage of the landscape
     Agee et al. (1989) used χ2 analysis to examine
     habitat preferences of grizzly bears
Expected vs. observed outcomes2
   In addition to χ2 analysis, it is also possible
   to utilize logistic regression
     Logistic regression compares the attributes of
     the locations where the phenomenon is present
     with those of the location where the
     phenomenon is absent
   Pereira and Itami (1991) used logistic
   multiple regression to model the potential
   effects of a proposed observatory on the
   Mount Graham Red Squirrel
Mt Graham Red Squirrel

Squirrel numbers
Bayesian Statistics
   Bayesian statistics provide a framework
   for combining relative values of being right
   or wrong (subjective probabilities) with the
   probabilities of being right of wrong
   (conditional probabilities)
   Relies upon state-conditional probability
   density functions, the a priori probability of
   a state, and the a posteri probability of
   each state, given certain conditions
GIS coupled with mathematical
   GIS is most successful when coupled
   with models that predict outcomes of
   processes (e.g. succession, NDVI,
   nutrient cycling, etc.)
   Often used as an iterative process to
   simulate responses to new
   environmental conditions or to produce
   new maps of predicted ecosystem
   properties along spatial gradients
   1.) Hypotheses are formulated on how behavior
   of organisms or ecosystems depends on their
   spatial relation with systems & environment
   2.) Combinations of environmental variables are
   3.) Spatial distribution, coincidence, or proximity
   of variables identified with the GIS can be input
   into the computer models to examine the
   hypothesized consequences of spatial relations
Population simulation models
   Population growth depends upon both
   intrinsic and extrinsic factors
     Intrinsic factors: birth rate, death rate,
     immigration, emigration
     Extrinsic factors: Physical environment,
     interaction/competition with other species, etc.
   Including spatial data (as an extrinsic factor)
   often produces more useful models
Ecosystem and landscape
simulation models
   Ecosystem and landscape simulation models
   attempt to duplicate ecological function via
   coupled differential equations that describe
   key ecosystem and landscape processes
   For example, JABOWA and FORET forest
   models simulate the birth, growth, and death
   of individual trees based on deterministic,
   intrinsic stand variables (e.g. shading,
   crowding) and stochastic environmental
   variables (e.g. heat sums, temperature
   extremes, soil moisture)
Ecosystem and landscape
simulation models continued
   These models can be linked to a GIS in
   two ways
     1.) Data from a GIS can be extracted and
     used to run a model
     2.) The results of the model can be
     displayed in GIS
Spatially dynamic ecosystem
   Although many of the models described
   previously work fairly well, they all have
   difficulty incorporating stochastic elements
   (e.g. fire and weather events)
   In order to account for these things, you
   need a Monte Carlo simulation
   To date, few spatially dynamic models have
   been linked to a GIS, primarily due to the
   computational requirements

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