Transcript Grid-based Map Analysis (Spatial Analysis/Statistics) Traditional GIS Spatial Analysis Erosion Potential (Surface) Forest Inventory Map • Points, Lines, Polygons • Cells, Surfaces • Discrete Objects • Continuous Geographic Space • Mapping and.

Grid-based Map Analysis (Spatial Analysis/Statistics)
Traditional GIS
Spatial Analysis
Erosion
Potential
(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 the Variance (gradient)
• Central Tendency
• Spatial Distribution
• Typical Response (scalar)
• Numerical Spatial Relationships
Grid-Based Map Analysis
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)
Spatial Statistics
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)
(Berry)
Classes of Spatial Analysis Operators
…all spatial analysis involves generating new map values (numbers) as a
mathematical or statistical function of the values
on another map layer(s)
(See |MapCalc\CrossReference for a cross reference of MapCalc operations and ESRI Grid/Spatial Analysis and EDAS)
(Berry)
Reclassifying Maps
(Berry)
Overlaying Maps
(Berry)
Evaluating Habitat Suitability
The Hugag is a curious beast with strong
preferences for terrain configuration:
 Prefers low elevations (severe nose
bleeds at higher altitudes)
 Prefers gentle slopes (fear of falling over
and unable to get up)
 Prefers southerly aspects (a place in the
sun)
Generating maps of animal habitat…
Manual Map Overlay
(Binary)
(digital slide show Hugag2)
Ranking Overlay
(Binary Sum)
Rating Overlay
(Rating Average)
(Berry)
Conveying Suitability Model Logic (Short Exercise #3)
gentle slopes
Elevation
Slope
Slope
Reclassify Preference
Bad 1 to 9 Good
(Times 1)
southerly aspects
Elevation
Aspect
Aspect
Reclassify Preference
Habitat
Rating
(1)
Overlay
Bad 1 to 9 Good
Bad 1 to 9 Good
lower elevations
Elevation
Reclassify Preference
Elevation
(1)
Bad 1 to 9 Good
Overlay
Algorithm
Base Maps
Calibrate
Derived Maps
Interpreted
Maps
Fact
Covertype
0= No, 1 to 9 Good
Weight
Combined
Map
Judgment
Reclassify
Habitat
Rating
Water
Mask
…while
Reclassify and
Overlay
operations aren’t
very exciting, they
are frequently
used
0= No, 1= Yes
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)
Reclassify & Overlay Operations (MapCalc)
Reclassifying Maps
Overlaying Maps
(Berry)
Reclassify & Overlay Techniques (Full Exercise #3)

Spatial analysis …
use MapCalc to implement the following
– SIZE Covertype FOR Covertype_size
– CLUMP Covertype AT 1 Diagonally FOR Covertype_clumps
– SIZE Covertype_clumps FOR Covertype_clump_size
– CONFIGURE Covertype_clumps Edges FOR Covertype_clumps_edges
– CONFIGURE Covertype_clumps Convexity FOR Covertype_clumps_shape
“RENUMBER Slope / Aspect / Elevation FOR S_Pref / A_pref / E_pref” from Hugag_Habitat.scr script
– COMPUTE S_Pref Times A_Pref Times E_Pref FOR Binary_model
– COMPUTE S_Pref Plus A_Pref Plus E_Pref FOR Ranking_model
– CROSSTAB Covertype WITH Water Simply
– CALCULATE (Covertype * 10) + Water FOR CW_codes
– COMPOSITE Covertype WITH Slope Average FOR Covertype_avgSlope
– RENUMBER Covertype ASSIGNING 0 TO 2 THRU 3 FOR OpenWater_binary
– COMPUTE OpenWater_binary Times Slope FOR OpenWater_slope
(Berry)
Establishing Distance and Connectivity
(Berry)
Establishing Distance and Connectivity
(digital slide show DIST2)
(Berry)
Spatial Analysis (Short Exercise #4a)
Distance Operators — simple/and effective proximity
SPREAD Roads TO 100 Simply
FOR Road_prox
Simple Proximity to Roads
Impedance to Movement
Relative Barrier— terrain steepness
Absolute Barrier— water
Friction
wFriction
Difficulty
…far from
Roads
Impassable
sFriction
Effective Proximity to Roads
SPREAD Roads TO 100 Simply THRU Friction
FOR Road_hikingprox
(Berry)
Distance/Connectivity Techniques

(Full Exercise #4a)
Spatial analysis …
use
MapCalc to implement the following
– SPREAD Housing TO 20 FOR Housing_simpleprox
– SPREAD Roads TO 20 FOR Roads_simpleprox
– RENUMBER Covertype ASSIGNING 0 TO 1
ASSIGNING 3 TO 2 ASSIGNING 7 TO 3
FOR C_friction
– SPREAD Roads TO 75 THRU C_friction FOR Road_hikingprox
– RENUMBER Locations ASSIGNING 0 TO 2 THRU 5 FOR Ranch
– SPREAD Ranch TO 35 Simply FOR Ranch_simpleprox
– RENUMBER Roads ASSIGNING 1 TO 1 THRU 43 FOR R_friction
– COVER C_friction WITH R_friction FOR CR_friction
– SPREAD Ranch TO 75 THRU CR_friction FOR Ranch_hikingprox
– RENUMBER Locations ASSIGNING 0 TO 1 ASSIGNING 0 TO 3 THRU 5 FOR Cabin
– STREAM Cabin OVER Ranch_hikingprox FOR Path
– COMPUTE Ranch_hikingprox times path FOR Path_hikingprox
(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
(Store and Streets)
(Berry)
Travel-Time Waves
(digital slide show TTime2)
Travel-time is computed as a series of
increasing waves moving away from a starting
location that are constrained by the streets…
…creates an Accumulation Surface identifying
travel-time to every location considering
absolute (streets) and relative (speed) barriers
to movement
(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;
constant slope
Absolute barrier – abrupt pillars;
constant slope
Relative barrier – gradual humps
with changing slope depending on
relative impedance friction)
…subtracting two
accumulation surfaces
identifies relative advantage
Zero – equidistant
Sign – which store has advantage
Magnitude – strength of advantage
…what would get if you added the
two surfaces?
(Berry)
Analysis Frame as Primary Key (Column, Row)
Raster (cell)
Analysis Frame
…V to R Conversion
plots customers
location in the
analysis frame (grid)
Latitude, Longitude, C, R
Vector (point)
…GeoCoding plots customers
address on the streets map
…can append any GIS
derived information (Col,Row)
…Append
Col, Row, Lat, Lon
of cell location to
customer records
Customer
Database
Customer
Database
(non-spatial)
(spatial)
(Berry)
Variable-Width Buffers (Simple/uphill proximity)
Simple Buffer– “as-the-crow-flies” proximity to
the road; no absolute or relative barriers are
considered
Clipped Buffer–
simple proximity for
just the land areas
Uphill Buffer– simple proximity to the road
for just the areas that are uphill from the
road; absolute barrier (uphill only–
absolutely no downhill steps)
(Berry)
Establishing Visual Connectivity (Viewshed)
Radiate – analogous to
a searchlight casting its
beam light onto the
landscape
Simply – viewshed
Completely – number of
“viewers” that see each location
Weighted – viewer cell value is
added
Seen if new tangent exceeds all
previous tangents along the line
of sight—
At <Viewer_heightValue>
Thru <Screens_heightMap>)
Onto <Target_heightMap>
…like SPREAD, RADIATE starts somewhere (starter cell) and moves
through geographic space by steps (wave front) assigning a 1 (seen)
to locations with tangents larger than the previous ones
(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)
Simply – viewshed
Completely – number of
“viewers” that see each location
Weighted – viewer cell value is
added
(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
Simply – viewshed
Completely – number of
“viewers” that see each location
Weighted – viewer cell value is
added
(Berry)
Spatial Analysis (Short Exercise #4b)
Visual Exposure Operators — viewshed and visual exposure
RADIATE Roads OVER
Elevation AT 1 TO 100 Simply
FOR Road_viewshed
Roads
…not seen
Viewshed from Roads
Elevation
…seen a lot
RADIATE Roads OVER Elevation TO 100
AT 1 Completely FOR Road_VExposure
Visual Exposure from Roads
# Cars
RADIATE Road_classes OVER Elevation TO
100 AT 1 Weighted FOR Road_wVExposure
Road_classes
(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)
Variable-Width Buffers (Line-of-sight)
Line-of-Sight Buffer– identifies all
land locations (clipped) within 250m
that can be seen from the road…
250m “viewshed” of the road
Line-of-Sight
Exposure– notes
the number of time
each location in
the buffer is seen
Line-of-Sight Noise– locations hidden
behind a ridge or farther away from a
source (road) greatly decrease noise
levels.
(Berry)
Visual Analysis Techniques (Full Exercise #4b)

Spatial analysis …
use MapCalc to implement the following
– RADIATE Ranch OVER ELEVATION TO 35
AT 5 SIMPLY FOR Ranch_viewshed
– RADIATE Roads OVER ELEVATION TO 35
AT 5 SIMPLY FOR Roads_viewshed
– RADIATE Roads OVER ELEVATION TO 35
AT 5 COMPLETELY FOR Roads_VExposure
– RADIATE Housing OVER ELEVATION TO 35
WEIGHTED FOR housing_WeightedVE
– SLICE Housing_WeightedVE INTO 4
FOR Housing_VE_Index
– SLICE Roads_VExposure INTO 4
FOR Roads_VE_Index
– ANALYZE Housing_VE_Index
WITH Roads_VE_Index Mean
FOR RH_VE_Index_avg
(Berry)
Characterizing Neighborhoods
(Berry)
Characterizing Terrain Steepness (Slope)
Slope is can be calculated several ways–
by calculating the best fitting plane to all nine elevation values, or
by selecting the maximum, minimum or average of the eight individual slopes
Min= 0.00
Max= 65.00
Avg= 24.38
Min= 0.00
Max= 64.63
Avg= 26.45
Min= 0.00
Max= 17.25
Avg= 3.56
Min= 0.00
Max= 40.24
Avg= 15.13
(Berry)
Creating a Housing Density Map (Scan Total)
The TOTAL number of houses within 500 meters is calculated
for each map location
(Berry)
Creating a Cover Type Diversity Map (Scan Diversity)
…a DIVERSITY map indicates the number of different map values
that occur within a window… e.g., cover types.
As the window is enlarged, the diversity increases.
(Berry)
Spatial Analysis (Short Exercise #5)
Neighbor Operators — summarizing nearby values
SCAN Houses Total 0.0 WITHIN 6 CIRCLE
FOR Housing_density
Houses
Highest
density
Housing_density
Most
diverse
SCAN Covertype Diversity WITHIN 4 CIRCLE
FOR Covertype_diversity
Covertype
Covertype_diversity
Most
rough
SCAN Slopemap CoffVar WITHIN 2 CIRCLE
FOR Roughness
Slopemap
Terrain_roughness
(Berry)
Characterizing “Edginess”
A simple EDGINESS model for the meadow involves assigning 1
to the meadow (Renumber) and then calculating the total values
within a 3x3 window for just the meadow area (Around)
2 Very Edgy
8 Not Edgy
(Berry)
Landscape Analysis
(Berry)
Neighbor Techniques (Full Exercise #5)

Spatial analysis …
use MapCalc to implement the following
– SCAN Covertype DIVERSITY WITHIN 2
FOR Covertype_diversity2
– SCAN Covertype DIVERSITY WITHIN 4
FOR Covertype_diversity4
– SCAN COVERTYPE DIVERSITY WITHIN 4
AROUND ROADS FOR Covertype_diversity4_roads
– SCAN ELEVATION AVERAGE WITHIN 4 FOR Elevation_smooth4
– COMPUTE ELEVATION MINUS Elevation_smooth4 FOR Convex_concave_terrain
– SCAN SLOPE COFFVAR WITHIN 1 FOR Slope_roughness
– SLOPE SLOPE FOR What?
– RENUMBER Ranch_hikingprox ASSIGNING PMAP_NULL TO 100
FOR Ranch_hikingprox_mask
– SLOPE Ranch_hikingprox_masked FOR What_else?
– ORIENT Ranch_hikingprox_masked FOR You_have_to_be_kiding!
(Berry)
…but before we leave Spatial Analysis (operations for reclassify,
overlay, distance and neighbors) to tackle Spatial Statistics, any…
Questions?
Questions?
(Berry)