Spatial Modeling with GIS
Longley et al., Chapter 16
Spatial Modeling with GIS
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Introduction
Types of Model
Modeling Technology
Multicriteria Methods
Accuracy and Validity
Spatial modeling
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Modeling: An overworked term
data model a template for data
relational, object-oriented, coverage,
shapefile
Model concerned with how the world
looks
Model also a representation of some
real-world process
Concerned with how the world works
Spatial modeling
• Manipulation of geographic information in
multiple steps
• Steps may represent stages in some complex
analysis
• Calculation of indicators over space (potentials)
• Steps may represent time
• Dynamic model
• Iterative analysis
• Geocomputation (see www.geocomputation.org)
Analog or Digital Modeling?
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Analog use of a scale model
Analogous process
Varignon frame
Need a digital process represented in 0s
and 1s
• program in C
• GIS script in VBA
• Python
Scaled Real Models
Army Corps of Engineers:WES
Varignon Frame
“Live” table: Pollution demo
Scale in a digital model?
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Spatial resolution/extent
Temporal resolution/extent
Define what is left out of the model
Leave out uncertainty about model data,
predictions
• Model must run faster than the real world
• Ecological fallacy
Why model?
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Support some design process
Allow the user to experiment with a replica
Investigate what-if scenarios
To understand change and dynamics
Test sensitivity and confidence
Analysis vs. Modeling
• To analyze or model?
• Evacuation scenarios
– Tom Cova's analysis
– Church's simulations
– LANL
Analysis
Modeling
LANL TRANSIMS
Individual vehicle-based
traffic simulation
of entire cities
Limits of Analysis
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Static, one point in time
Search for patterns, anomalies
Generating hypotheses
Revealing what would otherwise be
invisible
• Form vs. process
Modeling multiple stages
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Perhaps different points in time
Implementing ideas and hypotheses
Experimenting with policy options
Scenario based planning
Types of Model
• Static models and indicators
• Combining GIS layers through overlay
e.g., using ModelBuilder
• Universal Soil Loss Equation
• A = R x K x LS x C x P
• DRASTIC model of groundwater
vulnerability
• Karst groundwater protection model
• DRASTIC
Santa Barbara Regional Impacts of
Growth Study: 2040 forecasts
Karst groundwater protection model in
Model Builder
Model result
Modeling Approach
• Individual vs. Aggregate models
• Is it possible to model every individual
element in the system?
• Every molecule of groundwater?
Every person in a crowd?
• Autonomous agent models
Mass Behavior: Problems
Twenty-one Hajj pilgrims trampled
Wednesday, February 12, 2003 Posted: 2:33 PM
EST (1933 GMT)
MINA, Saudi Arabia -- Another 21 people were trampled to death Wednesday on
their way to one of the rituals of the Hajj, the annual Muslim pilgrimage to
Mecca, Saudi officials said. Wednesday's deaths happened on a bridge as the
throngs of pilgrims were heading to throw stones at one of three pillars representing
Satan's temptation of Abraham, the officials said. The stoning represents a rejection
of evil deeds. On Tuesday, a similar incident killed 14 pilgrims.
Notting Hill Carnival
Cellular Models
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Work on a raster: Good match to GIS
Initial conditions
Each cell in one of a number of states
Rules of state transition at each timestep
based on states of cell and neighbors
• Conway’s Game of Life
• SLEUTH land use change model
(Universal) Turing machine
Cellular automata
• Framework for systems experiments
• Simplest way to demonstrate complex
systems behavior
• Wolfram: Formal framework
• {Cells, States, Initial conditions,
Neighborhood, Rules, Time}
• Conway’s LIFE
The game of life
• Grid of square cells extending infinitely in every direction.
• A cell can be live or dead.
• Each cell in the grid has a neighborhood consisting of the eight
cells in every direction including diagonals.
• To apply one step of the rules, we count the number of live
neighbors for each cell.
– A dead cell with exactly three live neighbors becomes a live cell
(birth).
– A live cell with two or three live neighbors stays alive (survival).
– In all other cases, a cell dies or remains dead (overcrowding or
loneliness).
Some examples
More examples
Urban Growth as a CA
B e h a v io r R u le s
T0
T1
sp o n ta ne ou s
sp re a d in g
ce n te r
o rg a n ic
ro a d
in flu en ced
f (slo p e
resistan ce,
d iffu sio n
co efficien t)
f (slo p e
resistan ce,
b reed
co efficien t)
f (slo p e
resistan ce,
sp read
co efficien t)
f (slo p e resistan ce,
d iffu sio n co efficien t,
b reed co efficien t,
ro ad grav ity)
d e lta tron
F or i tim e periods (years)
SLEUTH applied to Santa Barbara
U rb a n g ro w th to 2 0 4 0
N o n ew road s
U p grad e all local road s
Technology for Modeling in GIS
• Graphic user interface e.g. GISMO in ERDAS
• ModelBuilder
– access to all ArcGIS functions
– no looping at present
• Scripts ARC/INFO AML
• ArcView 3.x Avenue
• ArcGIS
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Visual Basic for Applications
Perl
Python
JScript
ArcScripts
Model Coupling
• linking model software to GIS
• Loose coupling
– Exchanging files
– Entering results
• Tight coupling
– Common files
– Common interface
– Common code
• Modeling languages
Multcriteria Methods
• Multiple factors affect decisions
• Weighted by difference levels of importance
• Karst case
– slope > 5%
– land use = cropping
– distance from stream < 300m
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Simple binary decision
How to assign weights to each factor?
Stakeholders may disagree on weights
MCDM = multicriteria decision making
Analytical Hierarchy Process
• Devised by Thomas
Saaty
• Each stakeholder
compares each pair of
factors
• Assigns comparative
weights
– e.g., slope 7 times as
important as land use
– e.g., distance from stream
1/2 as important as slope
• forming a complete matrix
• Weights must sum to one
Slope
Land use
Slope
Distance from
Stream
7
Land use
1/7
Distance from
Stream
1/2
2
1/3
3
AHP example:Idrisi
Model accuracy and validity
• How do we know if the model is correct?
• How do we know that forecasts are accurate?
• Results from a computer are often trusted
implicitly
• How to calibrate the model?
– Hindcasting
– Boostrapping
• A model is never more than an approximation to
reality but how good/bad is the approximation?
• Important to provide measures of confidence in
results
Sensitivity testing
• Varying the inputs to observe effects on outputs
• Some inputs affect outputs more than others
• These are the inputs that most need to be
correct
• Error propagation
• Examining the impacts of input errors on outputs
• Mostly by simulation
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