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Grid-based Map Analysis Techniques and
Modeling Workshop
Part 1 – Maps as Data
Part 2– Surface Modeling
Part 3 – Spatial Data Mining
Part 4 – Spatial Analysis
Suitability mapping
Measuring effective distance/connectivity
Visual exposure analysis
Analyzing landscape structure
Characterizing terrain features
Part 5 – GIS Modeling
Grid-Based Map Analysis
Surface Modeling maps the spatial distribution and pattern of point data…
 Map Generalization— characterizes spatial trends (e.g., titled plane)
 Spatial Interpolation— deriving spatial distributions (e.g., IDW, Krig)
 Other— roving window/facets (e.g., density surface; tessellation)
Data Mining investigates the “numerical” relationships in mapped data…
 Descriptive— aggregate statistics (e.g., average/stdev, similarity, clustering)
 Predictive— relationships among maps (e.g., regression)
 Prescriptive— appropriate actions (e.g., optimization)
Spatial Analysis investigates the “contextual” relationships in mapped data…
 Reclassify— reassigning map values (position; value; size, shape; contiguity)
 Overlay— map overlay (point-by-point; region-wide; map-wide)
 Distance— proximity and connectivity (movement; optimal paths; visibility)
 Neighbors— ”roving windows” (slope/aspect; diversity; anomaly)
(Berry)
Evaluating Habitat Suitability
Assumptions – Hugags like gentle slopes,
southerly aspects and lower elevations
Generating maps of animal habitat…
Manual Map Overlay
Ranking Overlay
Rating Overlay
(Berry)
Conveying Suitability Model Logic
Calibrate
Algorithm
Elevation
gentle slopes
Slope
Slope
Preference
Weight
Bad 1 to 9 Good
southerly aspects
Elevation
Aspect
Aspect
Preference
Habitat
Rating
Bad 1 to 9 Good
Bad 1 to 9 Good
lower elevations
Elevation
Base Maps
Derived Maps
Fact
Covertype
Elevation
Preference
Habitat
Rating
Bad 1 to 9 Good
0= No, 1 to 9 Good
Interpreted
Maps
Solution
Map
Judgment
Water
Mask
0= No, 1= Yes
(See map Analysis, “Topic 22” for more information)
Constraint Map
(Berry)
Extending Model Criteria
gentle slopes
Elevation
Slope
Slope
Preference
Bad 1 to 9 Good
(Times 10)
southerly aspects
Elevation
Aspect
Aspect
Preference
(1)
Bad 1 to 9 Good
Habitat
Rating
Bad 1 to 9 Good
lower elevations
Elevation
Preference
Elevation
(1)
Bad 1 to 9 Good
forests
Forests
Forest
Proximity
Forest
Preference
(10)
Bad 1 to 9 Good
water
Water
Water
Proximity
Water
Preference
Bad 1 to 9 Good
(10)
Additional criteria can be
added…
—Hugags would prefer to
be in/near forested areas
—Hugags would prefer to
be near water
—Hugags are 10 times
more concerned with slope,
forest and water criteria
than aspect and elevation
(Berry)
Establishing Distance and Connectivity
(digital slide show DIST)
(Berry)
Grid-based Simple Proximity Surfaces
Point
Orthogonal distances are the same as calculated by
the Pythagorean Theorem and align with a circle
of a given radius…
…other distances contain slight “rounding” errors
Proximity Ripples for a large steps away
from a starting location align fairly well
with an exact circle…
…but poorly align for
small steps
Points
Lines
Polygons
…an excellent technique for
generating simple and effective
proximity surfaces respecting
absolute and relative barriers to
movement from sets of points,
lines and polygons
(impossible to do with the
Pythagorean Theorem )
(Berry)
Calculating Effective Distance (Demo)
Simple Proximity
…as the crow flies
…the Splash Algorithm is like tossing a rock into a
still pond with increasing distance rings that abut
and bend around absolute and relative barriers
0= not able to cross
2= two min. to cross
7 = seven min. to cross
Effective Proximity
…as the crow walks
(Berry)
Generating an Effective Travel-time Buffer
(a) superimposition
of an analysis
grid over the
area of interest
(b) “burns” the
store location
into its
corresponding
grid cell
(c) “burns”
primary and
residential
streets are
identified
(d) travel-time
buffer derived
from the two
grid layers
(Berry)
Travel-Time Connectivity
…increasing distance from a
point forms bowl-shaped
accumulation surface
…steepest downhill path identifies
the optimal path– wave front that
got there first.
…SPREADing from multiple
locations identifies catchment
areas– locations closest to
starting locations
…what do you think the ridges
represent?
(Berry)
Accumulation Surface Analysis
…increasing distance from a point forms bowl-shaped accumulation surface
Simple distance – symmetrical bowl
Absolute barrier – abrupt pillars
Relative barrier – gradual humps
…subtracting two proximity
surfaces identifies relative
advantage
Zero – equidistant
Sign – which has the advantage
Magnitude – strength of advantage
…what would get if you added the
two surfaces?
(See Map Analysis, “Topic 5” and “Topic 17” for more information)
(Berry)
Establishing Visual Connectivity
Seen if new tangent exceeds all
previous tangents along the line
of sight—
At <Viewer_heightValue>
Thru <Screens_heightMap>)
Onto <Target_heightMap>
…like measuring proximity, it starts somewhere (starter cell) and moves through geographic space
by steps (wave front) evaluating whether the moving tangent is beat—
…if so, the location is marked as “seen” and its tangent is assigned as the one to beat
Radiate – visual
exposure is calculated
bay a series of “waves”
that carry the tangent to
beat.
Simply – viewshed
Completely – number of
“viewers” that see each location
Weighted – viewer cell value is
added
(Berry)
Calculating Visual Exposure (# Times Seen)
Visual exposure identifies how many times each map location is
seen from a set of viewer locations
(Berry)
Visual Exposure from Extended Features
A visual exposure map identifies how many times each location is seen from an
“extended eyeball” composed of numerous viewer locations (road network)
(Berry)
Weighted Visual Exposure (Sum of Viewer Weights)
Different road types are weighted by the relative number of cars per unit of time …the total
“number of cars” replaces the “number of times seen” for each grid location
(See Map Analysis, Topic 15, “Deriving and Using Visual Exposure Maps” for more information)
(Berry)
Calculating Visual Exposure (Demo)
Viewshed
…as the crow sees
(seen or not seen)
Visual Exposure
…as the flock sees
(# times seen)
Weighted
Visual Exposure
…as the flock sees
(not all in the flock are the same)
(Berry)
Real-World Visual Analysis
(Senior Honors Thesis by University of Denver Geography student Chris Martin, 2003)
Weighted visual
exposure map for an
ongoing visual
assessment in a
national recreation
area— the project
developed visual
vulnerability maps
from the reservoir in
the center of the park
and a major highway
running through the
park. In addition,
aesthetic maps were
generated based on
visual exposure to
pretty and ugly
places in the park
(Berry)
Neighborhood Techniques (Covertype Diversity Map)
…a DIVERSITY map indicates the number of different map values
(categories) that occur within a window… e.g., cover types
As the window is enlarged, the diversity generally increases
(Berry)
Neighbor Techniques (Demo)
–SCAN Covertype diversity within 3 for Cover_diversity3
–SCAN Slope coffvar with 2 for Roughness
–SCAN Housing total with 5 for Housing_density
–RENUMBER Housing_density for High_hdensity
assign 0 to 0 thru 15 assign 1 to 15 thru 50
–COMPOSITE Districts with Housing_density average
for Districts_HDavg
Housing Density
by Districts
Average housing density
for each district
(Berry)
Neighborhood Variability
(See MapCalc Applications, “Assessing Cover Type Diversity and Delineating Core Area” and “Assessing Covertype Diversity” for more information)
(Berry)
Spatial Analysis of Landscape Structure
Area Metrics (6), Patch Density, Size and Variability Metrics (5), Edge Metrics (8),
Shape Metrics (8), Core Area Metrics (15), Nearest Neighbor Metrics (6),
Diversity Metrics (9), Contagion and Interspersion Metrics (2)
…59 individual indices
For example,
Area Metrics
…Area per patch

(US Forest Service 1995 Report PNW-GTR-351)
Size of individual patches is an
important first-order assessment of
landscape structure
Shape Metrics
…Shape Index per patch

Edge Metrics
…Edge Contrast per patch

(digital slide show FRAG)
(digital slide show NN_statistics)
See http://www.innovativegis.com/products/fragstatsarc/index.html for more information
P/A ratio
tracks patch
shape…
boundary
irregularity
The amount and
type of edge tracks
the nature of the
patch interface
(Berry)
Grid-Based Map Analysis
Surface Modeling maps the spatial distribution and pattern of point data…
 Map Generalization— characterizes spatial trends (e.g., titled plane)
 Spatial Interpolation— deriving spatial distributions (e.g., IDW, Krig)
 Other— roving window/facets (e.g., density surface; tessellation)
Data Mining investigates the “numerical” relationships in mapped data…
 Descriptive— aggregate statistics (e.g., average/stdev, similarity, clustering)
 Predictive— relationships among maps (e.g., regression)
 Prescriptive— appropriate actions (e.g., optimization)
Spatial Analysis investigates the “contextual” relationships in mapped data…
 Reclassify— reassigning map values (position; value; size, shape; contiguity)
 Overlay— map overlay (point-by-point; region-wide; map-wide)
 Distance— proximity and connectivity (movement; optimal paths; visibility)
 Neighbors— ”roving windows” (slope/aspect; diversity; anomaly)
(Berry)