Transcript Document

Modeling
• A model is an abstraction of reality
– No model can include all the complexity of the
real world. Hopefully a model includes enough
complexity from the real world to adequately
represent the system.
– As model complexity increases so does the
resources needed to use the model ($$) and the
chances for uncertainty (more variables that can be
wrong).
– All GIS is a modeling exercise.
Types of Models
• Types of Models
– Physical: tangible representation
• Models of dams, airplanes, etc.
– Theological: logical or mathematical representation
• GIS models are theological
• Level of Theory
– Empirical: based solely on data (e.g. regression).
– Biophysical (social-economic): based solely on basic
principles. Also called theologically-based.
– Conceptual (or Hybrid) – usually has theological
framework with empirical derived parameters. The
empirical parameter provides for natural variability.
• Most cartographic models are conceptual
USCAE San Francisco Bay Model
http://www.spn.usace.army.mil/bmvc/
Models based on logic
• Logic is used in the conceptualization and
formulation of the model.
• Inductive logic: build models based on individual
data or instances. This is done by employing
empirical tests. Requires data!
• Deductive logic: based on known premise of the
important factors and interactions. Moves from
general knowledge to specific outcomes through
conceptualization, formulation, flow-charting, and
implementation of the model.
Types of Models
• Methodology
– Stochastic: based on statistical probabilities
• Potential for many outcomes with the same input.
– Deterministic: based on known functional linkages
and interactions
• Only one potential outcome with a given input
– They can be linked.
• A deterministic hydrologic model can be linked to a
stochastic weather generator to provide stochastic
results (i.e. a potential range of flows from a give
landscape configuration)
Y=a+b*X
Y
Y = a + b *X + έ
X
Time
• Static modeling utilizes a single realization or slice of time of a
physical process or description of the landscape given the
existing conditions (for example, a suitability model). The
static approach can be either deterministic or stochastic.
• Dynamic modeling is an approach in which pieces of a model,
or the entire model, are rerun with the output of the model
becomes the input for the next iteration of the model. Usually,
in dynamic GIS models, time and space are explicitly
modeled. The dynamic approach can be either deterministic or
stochastic.
Management Applications of GIS
• Graphics and Visualization
• Spatial Database Management System
• Spatial Analysis (including statistics)
• Modeling
- Cartographic Modeling (within GIS)
- Interface and DBMS for standalone models
*
Map Products for Decision-Making
Raw Data
Analysis
Modeling - “Synthesis”
Interpretation
Information
1. Current Conditions
Representing current conditions for important thematic
variables maybe the most common application. All planning
efforts require a description of the “starting point”, what
resources are available and what problems exist. Raw data can
be represented different ways (normalization, indices) to help
in interpretation.
2. Change Analysis
Comparison between past vs. current conditions. Isolating
areas of concern due to changes.
Example: Delineate areas that have developed over the past
decade to identify areas with potential water quality problems.
Land cover change on the Upper San Pedro
- NALC classification data
1973
1986
1992
1997
Grassland Fragmentation Index
1997
1973

FI  1   SizeofBigg estPatch
TotalArea 

Courtesy Bill Kepner, US-EPA
Human Use Index
1973
1997
Area near Sierra Vista, AZ
Fast-growing city
Courtesy Bill Kepner, US-EPA
3. Future Scenario Simulation
Develop models to forecast future conditions that may be used
to predict potential impacts.
Examples:
Projection of future growth rates to assess if the current
infrastructure is adequate. One way this can be accomplished
by taking the current zoning and then evaluate that would
happen if the land was developed (full build-out) at its
potential density (# houses/area) or economic use (residential
vs. commercial). What would happen if zoning were changed
(e.g. higher densities)? How would this affect flooding and
floodplains?
Predict potential deforestation with potential new roads.
Urban Growth Modeling
The SLEUTH Model
SLEUTH belongs to the cellular automata class of models, so the study area
is represented as a regular grid of cells and each cell has only two states:
urbanized or non-urbanized.
The current version of SLEUTH is not capable of modeling density of
development within a pixel.
Whether or not a cell will become urbanized is determined by four growth
rules, each of which attempts to simulate a particular aspect of the
development process.
Urban Growth Modeling
SLEUTH simulates four types of growth, which areapplied
sequentially during each growth cycle :
•
•
•
•
Spontaneous new growth, which simulates the random
urbanization of land,
New spreading centers, which simulates the development of
new urban areas,
Edge growth, which stems from existing urban centers,
Road influenced growth, which simulates the influence of
the transportation network on development patterns.
Campbell et al.
http://gis.esri.com/library/userconf/proc01/professional/papers/pap324/p324.htm
4. Assessment of Hazards – delineating areas with high
vs. low risk.
Erosion Hazard
Landslide Hazard
Flooding
Water Quality Impairment
Potential for groundwater contamination (Drastic Mapping)
Health risks due to pollution
Hazards usually represent constraints to other land uses or
activities.
Used to delineate/define areas for Best Management Practices
(BMPs).
Regional Ground Water Vulnerability –
Detail (1500m x 1500m) Scale
Potential Risk for Nitrates – Use of Logistic Regression
Watershed Classification: Selenium Example
One common source of elevated selenium in the western United States is flood
irrigation drainage from seleniferous soils. The fuzzy logic classification for
selenium in each subwatershed of this Upper Gila Watershed example was
created based on ADEQ water quality assessment data and the percentage of
agricultural land in each subwatershed.
5. Assessment of Potential – delineating areas have a
high or low promise of a potential outcome. Similar
to hazard.
Examples:
Archeological sites – probability of occurrence.
Deforestation – probability of occurrence
Potential crop yield (kg/ha) under different condition
Deforestation Probability Surface
• Cell by Cell Logistic Regression for Each Analysis Year (1986 to
1999) using 5 % Stratified Random Samples (> 1,100,000 cells):
– Dependent Variable: Deforested (1) / Forested (0)
– Independent Variables: LN distance to Roads, LN Distance to
Settlements, Well (1) / Poorly (0) Draining Soils
Variables:
Dependent
Deforestation
1997
Independent
LN site
distance 1997
Logistic
regression
coefficients:
-> 10.006 ->
Corrected yintercept
Sum of
weighted
grids
Weighted Grids:
x -1.087 =
LN road
distance 1997
x -0.430 =
Soil drains
well/poorly
x 0.955 =
logistically
transformed
Deforestation
probability
surface 1997
Results
1986
Observed
Deforestation
1986 Deforestation
Probability Surface
1986 – Logistic Regression
%
Prediction Results
Correct
(0.5 Cut Value)
Observed vs. Forested
99.7
Predicted
Deforested
7.1
Cells
Overall
96.4
Results
1995
Observed
Deforestation
1995 Deforestation
Probability Surface
1995 – Logistic Regression
%
Prediction Results
Correct
(0.5 Cut Value)
Observed vs. Forested
98.7
Predicted
Deforested
20.0
Cells
Overall
92.5
6. Suitability Analysis – delineating areas based on their
appropriateness to support for an activity. This is also
referred to as Site or Location analysis.
Examples:
Wildlife habitat suitability (usually species specific)
Locating the sites for a business
Locating the path for a road/trail/power line
Suitability for use as irrigated cropland
Ability to support riparian restoration activities
http://aap.cornell.edu/crp/outreach/scpw-2007.cfm
http://www.innovativegis.com/basis/MapAnalysis/MA_Intro/MA_Intro.htm
7. Capability Analysis – delineating areas based on their
suitability to support difference sets of activities.
Examples:
Land Use Zoning - usually presented as a hierarchy of activities
with increasing constraints
If an area is zoned to medium density residential (<= 2 houses/ac)
it can be used for low density residential (<= 1 house /ac) or rural
residential (<= 0.25 house / ac). However, if something is zoned
“open space” it cannot be developed.
But note that: To some people a zoning map represents the
“potential” since it is assumed you would want to develop the land
for the maximum profit.
If you are dealing with only one activity suitability and capability
are the same.
Methods
1. Gestalt (user defined)
2. Logic/Rule Approach (Qualitative)
Exclusion – remove areas based on policy/conditions
3. Model – based on a theoretical or empirical model of the
system (e.g. Universal Soil Loss Equation)
4. Statistical Approaches
- Bayesian statistics
- Classification methods (clustering or PCI)
- Classification Regression Trees (CART)
- Regression (e.g logistic – probability of occurrence)
5. Map Overlay Approaches – the combination of different
factors to create an ordinal (rank) map.
- Boolean
- Ordinal Combination
- Linear Combination (with weights)
6. Optimization Approaches
- Shortest Path – Network Analysis
- Multi-criteria
- Fuzzy Logic
- AHP
- Neural Networks/ Genetic Algorithms