Transcript (Spatial Distribution) The

Introduction to GIS Modeling
Week 7 — GIS Modeling Examples
GEOG 3110 –University of Denver
Presented by
Joseph K. Berry
W. M. Keck Scholar, Department of Geography, University of Denver
Example Real-World Projects; Introduction to Spatial
Statistics (revisited); mini-Project Working Session
Class Logistics and Schedule
Midterm Study Questions
(hopefully you are participating in a study group)
Midterm Exam …you will download and take the 2-hour exam online (honor system) sometime between
8:00 am Friday February 10 and must be completed by 5:00 pm Wednesday February 15
Blue Light Special …20 minutes of Instructor “Help” on midterm study question “toughies “
Exercise #6 (mini-project) — you will form your own teams (1 to 4 members) and tackle one of the
eight projects; we will discuss the project “opportunities” in great detail later in class
…assigned tonight Thursday, February 11 and final report due Monday, February 20 by 5:00pm
Submit via two emails, one with report Body attached and the other with Appendix attached
No Exercise Week 7 —
a moment for “a dance of celebration”
Exercises #8 and #9 — you can tailor to your interests by choosing to not complete either or both of these
standard exercises; in lieu of an exercise, however, you must submit a short paper (4-8 pages) on a GIS modeling
topic of your own choosing. I need to know your choices by next Wednesday as I will form new teams for exercises
#8 and #9.
Berry
Map Analysis Evolution (Revolution)
Traditional GIS
Spatial Analysis
…past six weeks
Store
Travel-Time
(Surface)
Forest Inventory
Map
• Points, Lines, Polygons
• Cells, Surfaces
• Discrete Objects
• Continuous Geographic Space
• Mapping and Geo-query
• Contextual Spatial Relationships
Traditional Statistics
Spatial Statistics
Spatial
Distribution
(Surface)
Minimum= 5.4 ppm
Maximum= 103.0 ppm
Mean= 22.4 ppm
StDev= 15.5
• Mean, StDev (Normal Curve)
• Map of Variance (gradient)
• Central Tendency
• Spatial Distribution
• Typical Response (scalar)
• Numerical Spatial Relationships
(Berry)
BP Pipeline Routing (Global Model)
The simulation is queued for processing then displayed as the Optimal
Route (blue line) and 1% Optimal Corridor (cross-hatched)
FC
Fort Collins
4% Corridor
SD
1% Corridor
San Diego
(digital slide show BP_Pipeline_routing)
Optimal
Path
(Berry)
Modeling Wildfire Risk
Increased population growth into the
wildland/urban interface raises the
threat of disaster…
…a practical method is
needed to identify areas
most likely to be impacted
by wildfire so effective
pre-treatment,
suppression and recovery
plans can be developed
(digital slide show Wildfire Risk Modeling)
(Berry)
Modeling Retail Competition
(digital slide show Combat Zone)
(Berry)
Is Technology Ahead of Science?
“Maps as Data”
• Is the "scientific method" relevant in the
data-rich age of knowledge engineering?
• Is the "random thing" pertinent in deriving
mapped data?
• Are geographic distributions a natural extension
of numerical distributions?
• Can spatial dependencies be modeled?
• How can commercial “on-site studies"
augment traditional research?
(Berry)
Map Analysis Evolution (Revolution)
Traditional GIS
Spatial Analysis
Store
Travel-Time
(Surface)
Forest Inventory
Map
• Points, Lines, Polygons
• Cells, Surfaces
• Discrete Objects
• Continuous Geographic Space
• Mapping and Geo-query
• Contextual Spatial Relationships
Traditional Statistics
Spatial Statistics
…next week
Spatial
Distribution
(Surface)
Minimum= 5.4 ppm
Maximum= 103.0 ppm
Mean= 22.4 ppm
StDev= 15.5
• Mean, StDev (Normal Curve)
• Map of Variance (gradient)
• Central Tendency
• Spatial Distribution
• Typical Response (scalar)
• Numerical Spatial Relationships
(Berry)
GIS and Map-ematical Perspectives (SA)
Spatial Statistics Operations – Numerical Context
GIS Perspective:
Map Analysis Toolbox
Surface Modeling (Density Analysis, Spatial Interpolation, Map Generalization)
Spatial Data Mining (Descriptive, Predictive, Prescriptive)
Map-ematical Perspective:
Grid Map Layers
Basic Descriptive Statistics (Min, Max, Median, Mean, StDev, etc.)
Basic Classification (Reclassify, Binary/Ranking/Rating Suitability)
Unique Map Descriptive Statistics (Roving Window Summaries)
Map Comparison (Joint Coincidence, Statistical Tests)
Surface Modeling (Density Analysis, Spatial Interpolation)
Advanced Classification (Map Similarity, Maximum Likelihood, Clustering)
Predictive Statistics (Map Correlation/Regression, Data Mining Engines)
Berry
Map-ematical Perspective (Examples)
Keystone concept is…
Geographic Distribution
“Spatial Autocorrelation”
Inverse Distance
Weighted (IDW)
spatial interpolation
assigned distanceweighted average of
sample points
Standard Normal Curve
Continuous Map Surface
Discrete Point Map
Average = 22.9
Geographic
Space
StDev = 18.7
…lots of NE locations
exceed +1Stdev
X= 22.9
Data Space
+ 1StDev
(41.6)
22.9
-1StDev
(4.2)
Numeric Distribution
…click anywhere on the histogram
and all map locations in that range
are highlighted
…click anywhere on the map
surface and the corresponding
histogram pillar is highlighted
Surface Modeling techniques
are used to derive a continuous
map surface from discrete point
data– fits a Surface to the data.
In Data Space, a standard
normal curve can be fitted to the
histogram of the map surface
data to identify the “typical value”
(Average)– fits a Curve.
In Geographic Space, this
typical value forms a horizontal
plane implying the average is
everywhere.
Berry
Spatial Interpolation (Spatial Distribution)
The “iterative smoothing” process is similar to slapping a big chunk of
modeler’s clay over the “data spikes,” then taking a knife and cutting away
the excess to leave a continuous surface that encapsulates the peaks and
valleys implied in the original field samples …mapping the Variance
…repeated
smoothing
slowly “erodes”
the data surface
to a flat plane
= AVERAGE
(digital slide show SSTAT)
(Berry)
Visualizing Spatial Relationships
Phosphorous (P)
Geographic Distribution
What spatial relationships
do you SEE?
…do relatively high levels
of P often occur with high
levels of K and N?
…how often?
…where?
“Maps are numbers first, pictures later”
Multivariate Analysis— each map layer is a
continuous map variable with all of the math/stat
“rights, privileges and responsibilities” therewith …simply “spatially organized “ sets of numbers (matrix)
(Berry)
Calculating Data Distance
…an n-dimensional plot depicts the multivariate distribution—
the distance between points determines the relative similarity in data patterns
Actual data in JMP
Pythagorean
Theorem
2D Data Space:
Dist = SQRT (a2 + b2)
3D Data Space:
Dist = SQRT (a2 + b2 + c2)
…expandable to N-space
…this response
pattern (high, high,
medium) is the least
similar point as it
has the largest data
distance from the
comparison point
(low, low, medium)
(See Beyond Mapping III, “Topic 16”, Characterizing Spatial Patterns and Relationships, www.innovativegis.com/basis)
(Berry)
Clustering Maps
…groups of “floating balls” in data space identify locations in the field
with similar data patterns– data zones
Spatial Data Mining
Map surfaces are clustered to identify
data pattern groups
Relatively low
responses in P, K and N
Relatively high responses in P, K and N
Geographic Space
Data Space
Clustered Data
Zones
…other techniques, such as Level Slicing, Similarity and Map Regression,
can be used to discover relationships among map layers
…map-ematics/statistics
(Berry)
The Precision Ag Process (Fertility example)
As a combine moves through a field it 1) uses GPS to check its location then
2) checks the yield at that location to 3) create a continuous map of the
yield variation every few feet. This map is
Steps 1) – 3)
4) combined with soil, terrain and other maps to
derive 5) a “Prescription Map” that is used to
6) adjust fertilization levels every few feet
in the field (variable rate application).
On-the-Fly
Yield Map
Step 4)
Map Analysis
Farm dB
Zone 3
Cyber-Farmer, Circa 1992
Zone 2
Zone 1
Prescription Map
Variable Rate Application
Step 5)
Step 6)
(Berry)
…mini-projects working session
Who is doing what…
Alicia and Michael are working on the Landslide Susceptibility Project
Paulina and Graham are working on the Visual Exposure to Timber Harvesting Project
Rob and Courtney are working on the Hugag Habitat Project
Sharon and Mingming are working on the Wildfire Risk Analysis Project
…deleted Spatial Analysis
“enrichment” slide sets
(Optional)
(digital slide show ForestAccess)
(digital slide show TerrainFeatures )
Topic 29 – Spatial Modeling in Natural Resources
Topic 11 – Characterizing Micro Terrain Features
(Berry)