Analysis and Modeling in GIS
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
1
GIS and the Levels of Science
Description:
Using GIS to create descriptive models of the world
--representations of reality as it exists.
Analysis:
Using GIS to answer a question or test an hypothesis.
Often involves creating a new conceptual output layer, (or table or chart),
the values of which are some transformation of the values in the
descriptive input layer.
--e.g. buffer or slope or aspect layers
Prediction:
Using GIS capabilities to create a predictive model of a real world
process, that is, a model capable of reproducing processes and/or
making predictions or projections as to how the world might appear.
--e.g. flood models, fire spread models, urban growth models
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
2
The Analysis Challenge
• Recognizing which generic GIS analytic capability (or
combination) can be used to solve your problem:
– meet an operational need
– answer a question posed by your boss or your board
– address a scientific issue and/or test a hypothesis
Send mailings to property owners potentially affected by a proposed change
in zoning
Determine if a crime occurred within a school’s “drug free zone”
Determine the acreage of agricultural, residential, commercial and industrial
land which will be lost by construction of new highway corridor
Determine the proportion of a region covered by igneous extrusions
Do Magnitude 4 or greater sub-oceanic earthquakes occur closer to the
Pacific coast of South America than of North America?
Are gas stations or fast food joints closer to freeways?
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
3
Availability of Capabilities in GIS Software
• Descriptive Focus: Basic Desktop GIS packages
–
–
–
–
Data editing, description and basic analysis
ArcView
Mapinfo
Geomedia
• Analytic Focus: Advanced Professional GIS systems
– More sophisticated data editing plus more advanced
analysis
– ARC/INFO, MapInfo Pro, etc.
Provided through extra cost Extensions
or professional versions of desktop packages
• Prediction: Specialized modeling and simulation
– via scripting/programming within GIS
» VB and ArcObjects in ArcGIS
» Avenue scripts in ArcView 3.2
» AMLs in Workstation ARC/INFO (v. 7)
Write your own or download from ESRI Web site
– via specialized packages and/or GISs
» 3-D Scientific Visualization packages
» transportation planning packages e.g TransCAD
» ERDAS, ER Mapper or similar package for raster
Capabilities move
‘down the chain’
over time.
In earlier generation
GIS systems, use of
advanced applications
often required learning
another package with
a different user
interface and
operating system
(usually UNIX).
Description and Basic Analysis
(Table of Contents)
• Spatial Operations
Vector
– spatial measurement
– Centrographic statistics
– buffer analysis
– spatial aggregation
» redistricting
» regionalization
» classification
– Spatial overlays and
joins
Raster
– neighborhood
analysis/spatial filtering
– Raster modeling
7/12/2016 Ron Briggs, UTDallas
• Attribute Operations
– record selection
» tabular via SQL
» ‘information clicking’
with cursor
– variable recoding
– record aggregation
– general statistical
analysis
– table relates and joins
GISC 6381 GIS Fundamentals
5
Spatial operations: Spatial Measurement
Spatial measurements:
• distance measures
–
–
–
•
•
•
•
Comments:
•
between points
from point or raster
to polygon or zone boundary
between polygon centroids
dij  ( Xi  Xj ) 2  (Yi  Yj ) 2
Used for projected data by ArcMap measure tools
•
polygon area
polygon perimeter
polygon shape
volume calculation
Spherical distance via spherical coordinates
Cos d = (sin a sin b) + (cos a cos b cos P)
where:
d = arc distance
a = Latitude of A
b = Latitude of B
P = degrees of long. A to B
Used for unprojected data by ArcMap measure tools
– e.g. for earth moving, reservoirs
•
• direction determination
– e.g. for smoke plumes
ArcGIS geodatabases contain automatic
variables:
shape.length: line length or
polygon perimeter
shape.area: polygon area
Automatically updated after editing.
For shapefiles, these must be calculated
e.g. by opening attribute table and applying
Calculate Geometry to a column (AV 9.2)
7/12/2016 Ron Briggs, UTDallas
Cartesian distance via Pythagorus
possible distance metrics:
–
–
–
–
•
straight line/airline
city block/manhattan metric
distance thru network
time/friction thru network
shape often measured by:
perimeter
area x 3.54
•
= 1.0 for circle
= 1.13 for square
Large for complex shape
Projection affects values!!!
GISC 6381 GIS Fundamentals
Distances depend on
projection.
Perimeter to area ratio
differs
6
Spatial operations: Spatial Measurement
SHAPE
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
AREA PERIMETER CNTY_ CNTY_ID NAME
0.265
2.729
2605
2605 Anderson
0.368
2.564
2545
2545 Andrews
0.209
2.171
2680
2680 Angelina
0.072
2.642
2899
2899 Aransas
0.233
1.941
2335
2335 Archer
0.233
1.941
2103
2103 Armstrong
0.299
2.278
2870
2870 Atascosa
0.224
0.222
0.368
0.072
1.900
1.889
2.580
1.421
2471
2481
2106
2386
2471
2481
2106
2386
Dallas
Dawson
Deaf Smith
Delta
FIPS
48001
48003
48005
48007
48009
48011
48013
Shape Index
1.50
1.19
1.34
2.78
1.14
1.14
1.18
48113
48115
48117
48119
1.13
1.13
1.20
1.50
Area and Perimeter measures are automatically maintained in the
attributes table for a Geodatabase or coverage. For a shapefile, you
need to apply Calculate Geometry to an appropriate column in the
attribute table (or convert to a geodatabase) .
The shape index can be calculated from the area and perimeter
measurements. (Note: shapefile and shape index are unrelated)
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
7
10
Spatial Measurement: Calculating the Area of a Polygon
A
Area=(2 x 4)/2=4
C
10
Area=(3 x 4)=12
-
B
=
4,7
7,3
2,3
0
5
5
-
10 0
5
5
10
0
10
5
6,2
0
Area=(5 x 1)/2=2.5
0
=
0
5
5
7,7
5
10
The area of the above
polygon is 18.5, based on
dividing it into rectangles
and triangles. However,
this is not practical for a
complex polygon.
Area of triangle =
(base x height)/2
7/12/2016 Ron Briggs, UTDallas
The actual algorithm used obtains the area of A by
calculating the areas of B and C, and then subtracting.
The actual formulae used is as follows:

i 1
n
(X2 - X1) ( Y1  Y2)/2
Its implementation in Excel is shown below.
i
X
Y
X2-X1
(Y1+Y2)/2
product
sum
1
2
3
4
5
2
4
7
7
6
2
3
7
7
3
2
3
2
3
0
-1
-4
5
7
5
2.5
2.5
10
21
0
-2.5
-10
10
31
31
28.5
18.5
GISC 6381 GIS Fundamentals
8
Spatial Operations:
Centrographic Statistics
• Basic descriptors for spatial point distributions
• Two dimensional (spatial) equivalents of standard descriptive
statistics (mean, standard deviation) for a single-variable
distribution
Measures of Centrality (equivalent to mean)
– Mean Center and Centroid
Measures of Dispersion (equivalent to standard deviation or variance)
– Standard Distance
– Standard Deviational Ellipse
• Can be applied to polygons by first obtaining the centroid of
each polygon
• Best used in a comparative context to compare one
distribution (say in 1990, or for males) with another (say in
2000, or for females)
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
9
Centroid and Mean Center
• balancing point for a spatial distribution
n
n
analogous to the mean
Xi
Yi


single point representation for a polygon (centroid)
X  i 1 , Y  i 1
n
n
single point summary for a point distribution (mean center)
can be weighted by ‘magnitude’ at each point (analogous to weighted mean)
minimizes squared distances to other points, thus ‘distant’ points have bigger
influence than close points ( Oregon births more impact than Kansas births!)
– is not the point of “minimum aggregate travel”--this would minimize distances (not
their square) and can only be identified by approximation.
–
–
–
–
–
• useful for
– summarizing change over time in a distribution (e.g US pop. centroid every 10 years)
– placing labels for polygons
• for weird-shaped polygons,
centroid may not lie within polygon
Note: many ArcView applications calculate
only a “psuedo” centroid: the coordinates of the
bounding box (the extent) of the polygon
7/12/2016 Ron Briggs, UTDallas
centroid outside
polygon
Can be implemented via:
ArcToolbox>Spatial Statistics Tools>Measuring
Geographic Distributions>Mean Center
10
GISC 6381 GIS Fundamentals
10
Calculating the centroid of a
polygon or the mean center of
a set of points.
4,7
7,7
5
1
2
3
4
5
7,3
2,3
2
4
7
7
6
sum
Centroid/MC
26
5.2
n
X
22
4.4
 Xi
i 1
n
n
Y
i
,Y 
i 1
n
0
6,2
(same example data as
for area of polygon)
3
7
7
3
2
0
10
10
5
Calculating the weighted mean
center. Note how it is pulled
toward the high weight point.
4,7
5
7,7
7,3
2,3
0
6,2
0
5
7/12/2016 Ron Briggs, UTDallas
i
X
Y
weight
1
2
3
4
5
2
4
7
7
6
3
7
7
3
2
3,000
500
400
100
300
sum
w MC
26
22
4,300
wX
6,000
2,000
2,800
700
1,800
13,300
3.09
wY
9,000
3,500
2,800
300
600
n
n
wX
wY
X
,Y 
w
w
i
i
i 1
i i
i 1
i
i
16,200
3.77
10
GISC 6381 GIS Fundamentals
11
Median Center:
Intersection of a north/south and an east/west
line drawn so half of population lives above
and half below the e/w line, and half lives to
the left and half to the right of the n/s line.
Same as “point of minimum aggregate
travel” the location that would minimize
travel distance if we brought all US residents
straight to one location.
Mean Center:
Balancing point of a weightless map, if equal
weights placed on it at the residence of every
person on census day.
Note: minimizes squared distances. The point
is considerable west of the median center
because of the impact of “squared distance” to
“distant” populations on west coast
Source: US Statistical Abstract 2003
For a fascinating discussion of the effect of
population projection see: E. Aboufadel & D.
Austin, A new method for calculating the
mean center of population center of the US
Professional Geographer, February 2006, pp.
65-69
Standard Distance Deviation
single unit measure of the spread or dispersion of a distribution.
• Is the spatial equivalent of standard deviation for a single variable
• Equivalent to the standard deviation of the distance of each point from the mean
center
• Given by:
2
2
(
X
i

X
c
)

(
Y
i

Y
c
)
i 1
i 1
n
n
N
which by Pythagoras
reduces to:
2
d
iC
i 1
n
N
---the square root of the average squared distance
---essentially the average distance of points from the center
We can also weight each point and calculate weighted standard distance (analogous
to weighted mean center.)
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
13
10
Standard Distance Deviation Example
Circle with radii=SDD=2.9
4,7
5
7,7
X
Y
(X - Xc)2
(Y - Yc)2
1
2
3
4
5
2
4
7
7
6
3
7
7
3
2
10.2
1.4
3.2
3.2
0.6
2.0
6.8
6.8
2.0
5.8
sum
Centroid
26
5.2
22
4.4
18.8
23.2
sum
divide N
sq rt
42.00
8.40
2.90
6,2
0
i
7,3
2,3
0
10
5
i
X
Y
(X - Xc)2
(Y - Yc)2
1
2
3
4
5
2
4
7
7
6
3
7
7
3
2
10.2
1.4
3.2
3.2
0.6
2.0
6.8
6.8
2.0
5.8
sum
Centroid
26
5.2
22
4.4
18.8
23.2
sum of sums
divide N
sq rt
sdd 
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals

n
i 1
42
8.4
2.90
( Xi  Xc ) 2  i 1 (Yi  Yc ) 2
n
N
14
Standard Deviational Ellipse: concept
• Standard distance deviation is a good single
measure of the dispersion of the incidents around
the mean center, but it does not capture any
directional bias
– doesn’t capture the shape of the distribution.
• The standard deviation ellipse gives dispersion in
two dimensions
• Defined by 3 parameters
– Angle of rotation
– Dispersion along major axis
– Dispersion along minor axis
The major axis defines the
direction of maximum spread
of the distribution
The minor axis is perpendicular to it
and defines the minimum spread
Standard Deviational Ellipse: example
There appears to be
no major difference
between the location
of the software and
telecommunications
industry in North
Texas.
For formulae for its calculation, see
Lee and Wong Statistical Analysis with ArcView GIS pp. 48-49 (1st ed.), pp 203-205 (2nd ed.)
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
16
Spatial Operations: buffer zones
• region within ‘x’ distance units
• buffer any object: point, line or
polygon
• use multiple buffers at progressively
greater distances to show gradation
• may define a ‘friction’ or ‘cost’ layer
so that spread is not linear with
distance
• Implement in Arcview 3.2 with
Theme/Create buffers
in ArcGIS 8 with
ArcToolbox>Analysis Tools>Buffer
point
buffers
line
buffer
polygon buffer
Examples
• 200 foot buffer around property
where zoning change requested
• 100 ft buffer from stream center
line limiting development
• 3 mile zone beyond city
boundary showing ETJ (extra
territorial jurisdiction)
• use to define (or exclude) areas
as options (e.g for retail site) or
for further analysis
• in conjunction with ‘friction
layer’, simulate spread of fire
Note: only one layer is involved, but the
buffer can be output as a new layer
Spatial Operations:
spatial aggregation
• districting/redistricting
•
– grouping contiguous polygons
into districts
– original polygons preserved
Regionalization (or dissolving)
– grouping polygons into
contiguous regions
– original polygon boundaries
dissolved
• classification
– grouping polygons into noncontiguous regions
– original boundaries usually
dissolved
– usually ‘formal’ groupings
Implement in ArcView 9 thru
ArcToolbox>Generalization>Dissolve
Grouping/combining polygons—is
applied to one polygon layer only.
Criteria may be:
–
–
formal (based on in situ characteristics)
e.g. city neighborhoods
functional (based on flows or links):
e.g. commuting zones
Groupings may be:
–
–
contiguous
non-contiguous
Boundaries for original polygons:
–
–
may be preserved
may be removed (called dissolving)
Examples:
•
•
•
•
•
•
elementary school zones to high school
attendance zones (functional districting)
election precincts (or city blocks) into
legislative districts (formal districting)
creating police precincts (funct. reg.)
creating city neighborhood map (form. reg.)
grouping census tracts into market
segments--yuppies, nerds, etc (class.)
creating soils or zoning map (class)
Districting: elementary school attendance zones grouped to form
junior high zones.
Regionalization: census tracts grouped into neighborhoods
Classification: cities categorized as central city or suburbs
soils classified as igneous, sedimentary, metamorphic
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
19
Spatial Operations:
Spatial Matching: Spatial Joins and Overlays
•
•
•
•
Examples
• assign environmental samples
– select features in one layer, &/or
(points) to census tracts to estimate
– create a new layer
exposure per capita (point in
used to integrate data having different
polygon)
spatial properties (point v. polygon), or
different boundaries (e.g. zip codes
• identify tracts traversed by freeway
and census tracts)
for study of neighborhood blight
can overlay polygons on:
(polygon on lines)
– points (point in polygon)
• integrate census data by block with
– lines (line on polygon)
sales data by zip code (polygon on
– other polygons (polygon on polygon)
polygon)
– many different Boolean logic
• Clip US roads coverage to just
combinations possible
cover Texas (polygon on line)
» Union (A or B)
» Intersection (A and B)
• Join capital city layer to all city
» A and not B ; not (A and B)
layer to calculate distance to
can overlay points on:
nearest state capital
– Points, which finds & calculates distance
(point on point)
to nearest point in other theme
combine two (or more) layers to:
– Lines, which calculates distance to
nearest line
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
20
Example: Spatial Matching:
Clipping and Erasing
(sometimes referred to as spatial extraction)
•CLIP - extracts those features from an input
coverage that overlap with a clip coverage.
This is the most frequently used polygon
overlay command to extract a portion of a
coverage to create a new coverage.
7/12/2016 Ron Briggs, UTDallas
•ERASE - erases the input
coverage features that overlap
with the erase coverage
polygons.
GISC 6381 GIS Fundamentals
21
Example: Spatial Matching via
Polygon-on-Polygon Overlay: Union
Land Use
Drainage
Basins
a.
Atlantic
Gulf
Combined layer
c.
b.
A.
G.
aA bA
bG
aG
cA
cG
The two layers (land use
& drainage basins) do not
have common
boundaries. GIS creates
combined layer with all
possible combinations,
permitting calculation of
land use by drainage
basin.
Note: the definition of Union in GIS is a little different from that in mathematical set
theory. In set theory, the union contains everything that belongs to any input set, but
original set membership is lost. In a GIS union, all original set memberships are
Another example
explicitly retained.
In set theory terms, the outcome
1 2
3
of the above would simply be:
GIS Union
Set Theory Union
Implementing Spatial Matching in ArcGIS 9
Available in three places
• via Selection/Select by Location
–
•
–
–
via Spatial Join (right click layer in T of C, select Join/Joins and Relates, then click down arrow in
first line of Join Data window---see Joining Data in Help for details)
–
–
•
this selects features of one layer(s) which relate in some specified spatial manner to the features in another
layer
if desired, selected features may be saved later to a new theme via Data/Export Data
Individual features are not themselves modified
Use for:
points in polygon
lines in polygon
points on lines (to calculate distance to nearest line)
points on points (to calculate distance to “nearest neighbor” point)
operate on tables and normally creates a new table with additional variables, but again does not modify
spatial features themselves
via ArcToolbox
–
–
Generally these tools modify geographic feature, thus they create a new layer (e.g. shape file)
Tools are organized into multiple categories
ArcToolbox Examples
• Dissolve features based on an attribute
–
•
•
•
–
Combine contiguous polygons and remove common border
ArcToolbox>Generalization>Dissolve
Clip one layer based on another
–
–
ArcToolbox>Analysis Tools>Extract>Clip
Use one theme to limit features in another theme
(e.g. limit a Texas road theme to Dallas county only)
Intersect two layers (extent limited to common area)
–
–
ArcToolbox>Analysis Tools>Overlay>Intersect
Use for polygon on polygon overlay
Union two layers (covers full extent of both layers)
–
–
ArcToolbox>Analysis Tools>Overlay>Intersect
Use for polygon on polygon overlay
Spatial Operations:
neighborhood analysis/spatial filtering
• spatial convolution or filter
– applied to one raster layer
– value of each cell replaced by
some function of the values of
itself and the cells (or
polygons) surrounding it
– can use ‘neighborhood’ or
‘window’ of any size
» 3x3 cells (8-connected)
» 5x5, 7x7, etc.
– differentially weight the cells
to produce different effects
– kernel for 3x3 mean filter:
1/9 1/9 1/9
1/9 1/9 1/9
1/9 1/9 1/9
7/12/2016 Ron Briggs, UTDallas
weights must
sum to 1.0
• low frequency ( low pass) filter:
mean filter
– cell replaced by the mean for
neighborhood
– equivalent to weighting
(mutiplying) each cell by
1/9 = .11 (in 3x3 case)
– smooths the data
– use larger window for greater
smoothing
median filter
– use median (middle value)
instead of mean
– smoothing, especially if data
has extreme value outliers
GISC 6381 GIS Fundamentals
24
Spatial Operations:
spatial filtering -- high pass filter
high frequency (high pass) filter
negative weight filter
– exagerates rather than smooths
local detail
– used for edge detection
standard deviation filter
(texture transform)
cell values (vi ) on
each side of edge
– again used for edge detection
– neighorhoods spanning border
have large SD ‘cos of
variability
2
filtered values for
highlighted pixel
5
1(5)(9)+5(5)(-1)+3(2)(-1) = 14
– calculate standard deviation of
neighborhood raster values
– high SD=high texture/variability
– low SD=low texture/variability
1(2)(9)+5(2)(-1)+3(5)(-1) = -7
–kernel for example (wi)
1(2)(9)+8(2)(-1) = 2
-1 -1 -1
-1 9 -1
1(5)(9)+8(5)(-1) = 5
-1 -1 -1
f .v .w
i
7/12/2016 Ron Briggs, UTDallas
i
i
GISC 6381 GIS Fundamentals
25
Spatial Operations:
raster–based modelling
• Relating multiple rasters
• Processes may be:
• Suitability modeling
0
0
1
0
1
0
soil
slope
– Local: one cell only
1
0
1
1
1
1
– Neighborhood: cells relating
to each other in a defined
• Diffusion Modeling
manner
– Zonal: cells in a given section
Incidence
Probability
– Global: all cells
matrix
mask
• ArcGIS implementation:
– All raster analyses require
either the Spatial Analyst or
3-D Analyst extensions
– Base ArcView can do no
more than display an image
(raster) data set
7/12/2016 Ron Briggs, UTDallas
2
0
3
2
Site
options
for
sale
System at
time t+1
• Connectivity Modeling
Initial
State
Connectivity
matrix
GISC 6381 GIS Fundamentals
Resultant
State
26
Attribute Operations: record selection or extraction
--features selected on the map are identified in the table (and visa versa)
Select by Attribute (tabular)
•
Independent selection by clicking table rows:
– Open Attribute Table & click on grey selection box at
start of row (hold ctrl for multiple rows)
•
Create SQL query
–
•
use Selection/Select by Attribute
Outputs may be:
• Simultaneously highlighted
records in table, and features
on map
• New tables and/or map layers
use table Relates /Joins to select specific data
Select by Graphic
Examples
• Manually, one point at a time
• Use SQL query to select all
– use Select Features tool
zip codes with median
• within a rectangle or an irregular polygon
incomes above $50,000
– use Selection/Select by Graphic
(tabular)
• within a radius (circle) around a point or points
• identify zip codes within 5
– use Selection/Select by Location (are wthin distance)
mile radius of several
Select by Location
potential store sites and sum
household income (graphic)
• By using another layer
– Use Selection/Select by Location
• show houses for sale on map,
(same as Spatial Matching discussed previously)
and click to obtain picture and
additional data on a selected
Hot Link
house (hot link)
• Click on map to ‘hot link’ to pictures, graphs, or
other maps
27
7/12/2016 Ron Briggs, UTDallas
GISC 6381 GIS Fundamentals
Attribute Operations:
statistical analysis on one or more columns in table
• univariate (one variable or column)
– central tendency: mean, median, mode
– dispersion: standard deviation, min, max
– To obtain these statistics in ArcGIS:
» Right click in T of C and select Open attribute table
» Right click on column heading and select Statistics
• bivariate (relating two variables or columns)
– interval and nominal scale variables: sum or mean by category
» average crop yield by silt-sand-clay soil types
» To implement in ArcGIS, proceed as above but use Summarize
– two interval scale variables: correlation coefficients
» income by education
» ArcScripts are available for this on ESRI web site (or use Excel!)
• multivariate (more than two variables)
– usually requires external statistical package such as SAS, SPSS, STATA or S-PLUS
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Attribute Operations: variable recoding
• establishing/modifying number of classes and/or their boundaries for
continuous variable. Options for ArcGIS
– natural breaks (default)
(finds inherent inherent groups via Jenks optimization which minimizes the variances
within each of the classes).
– quantile (classes contain equal number of records-- Implement in ArcGIS via:
or equal area under the frequency distribution)
Right click in T of C, select
– equal interval (user selects # of classes)
Properties, then Symbology tab
(equal width classes on variable)
– Defined interval (user selects width of classes)
(assumes a Normal distribution)
(equal width classes on variable)
25% 25%
Equal area %
– standard deviation
23%
23%
(categories based on 1,2, etc, SDs
Equal interval %
14%
34%
34%
14%
above/below mean)
Standard Deviation
-2
-1
0
1
2
– Manual (user defined)
Equal interval score
0
-.68
.68
Equal area score
» whole numbers (e.g. 2,000)
» meaningful to phenomena (e.g zero, 32o)
• aggregating categories on a nominal (or ordinal) variable
– pine and fir into evergreen
No change in number of records (observations).
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Attribute Operations:
record aggregation
•
•
•
•
•
•
combining two or more records
into one, based on common
values on a key variable
the attribute equivalent of
regionalization or classification
equivalent of PROC
SUMMARY in SAS
interval scale variables can be
aggregated using mean, sum,
max, min, standard deviation,
etc. as appropriate
ordinal and nominal require
special consideration
example: aggregate county data
to states, or county to CMSA
Record count decreases (e.g. from 12
to 2)
Fips PMSA_90 PMSA_93 Pop90 Pop95_est Pop90-95% MedInc89 Suburb Name
48085 1920
1920
264036
346232
5.93
46020
1
Collin
48113 1920
1920 1852810
1959281
1.09
31605
0
Dallas
48121 1920
1920
273525
334070
4.22
36914
1
Denton
48139 1920
1920
85167
94223
2.03
30553
1
Ellis
48213
1920
58543
64293
1.87
20747
1
Henderson
48231
1920
64343
66972
0.78
25317
1
Hunt
48257 1920
1920
52220
60114
2.88
27280
1
Kaufman
48397 1920
1920
25604
32725
5.30
42417
1
Rockwall
48221
2800
28981
33384
2.89
31627
1
Hood
48251 2800
2800
97165
106181
1.77
30612
1
Johnson
48367 2800
2800
64785
73794
2.65
30592
1
Parker
48439 2800
2800 1170103
1278606
1.77
32335
0
Tarrant
Source: US Bureau of the Census
MedInc=Median Household Income. Pop90 as of April 1. Pop95 as of July 1.
Fips
PMSA_90 PMSA_93 Pop90 Pop95_est Pop90-95% MedInc89 Suburb Name
1920 2676248
2957910
2.00
32607
7
Dallas
2800 1361034
1491965
1.83
31292
3
Fort Worth
sum
sum
re-calc.
Type of processing:
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GISC 6381 GIS Fundamentals
count
average
of
medians!
30
Attribute Operations: Joining and Relating Tables
associating spatial layer to non-spatial table
Join: one to one, or one to many, relationship appends attributes
Associate table of country capitals with country layer: only one capital for
each country (one to one)
Country Code
Country
29
France
68
Saudi Arabia
106
Chad
248
Spain
199
Venezuela
9
UK
96
Philippines
Layer Attribute Table
Country Code
Capital
199
Caracas
96
Manila
68
Riyadh
29
Paris
106
N'Djamena
9
London
248
Madrid
NonSpatial Table
Country Code Country
Capital
9
UK
London
29
France
Paris
68
Saudi Arabia
Riyadh
96
Philippines
Manila
106
Chad
N'Djamena
199
Venezuela
Caracas
248
Spain
Madrid
Layer Attribute Table after Join
Associate country layer with type of government: one gov. type assigned to
many countries--but each country has only one gov. type (one to many)
Gov. Code
Country
20
France
30
Vietnam
15
UK
20
Argentina
10
Saidi Arabia
15
Sweden
45
Portugal
Layer Attribute Table
7/12/2016 Ron Briggs, UTDallas
Gov. Code
10
15
20
30
45
Type
Absolute Monarchy
Const. Monarchy
Republic
Communist State
Parliamentary Democracy
NonSpatial Table
Gov. Code
Country
Type
20
France
Republic
30
Vietnam
Communist State
15
UK
Const. Monarchy
20
Argentina
Republic
10
Saudi Arabia
Absolute Monarchy
15
Sweden
Const. Monarchy
45
Portugal
Parliamentary Democracy
Layer Attribute Table after Join
GISC 6381 GIS Fundamentals
31
Single most common error in GIS Analysis
--intending a one to one join of attribute to spatial table
--getting a one to many join of attributes to spatial table
NAME
Alabama
Alaska
…..
Georgia
Hawaii
Idaho
…..
Wisconsin
Wyoming
Spatial
FID
0
1
SHAPE
Polygon
Polygon
11
12
13
14
15
16
Polygon
Polygon
Polygon
Polygon
Polygon
Polygon
53
54
Polygon
Polygon
NAME
FIPS
Alabama
01
Alaska
02
…..
Georgia
13
Hawaii-Hawaii 15
Hawaii-Maui
15
Hawaii-Oahu
15
Hawaii-Kauai 15
Idaho
16
…..
Wisconsin
55
Wyoming
56
7/12/2016 Ron Briggs, UTDallas
FIPS
01
02
CODE
AL
AK
13
15
16
GA
HI
ID
8,186,453
1,211,537
1,293,953
55
56
WI
WY
5,363,675
493,782
Total
282,421,906
51 states
CODE
AL
AK
POP2000
4,447,100
626,932
POP2000
4,447,100
626,932
GA
HI
HI
HI
HI
ID
8,186,453
1,211,537
1,211,537
1,211,537
1,211,537
1,293,953
WI
WY
5,363,675
493,782
Total
286,056,517
GISC 6381 GIS Fundamentals
After joining
attribute to
spatial data
32
Attribute Operations: Joining and Relating Tables
associating spatial layer to non-spatial table
(contd.)
Relate: many to one relationship, attributes not appended
Associate country layer with its multiple cities (many to one)
Country Code
Country
29 France
68 Saudi Arabia
106 Chad
248 Spain
199 Venezuela
9 UK
96 Philippines
Layer Attribute Table
Country Code
City
129
Mombasa
129
Nairobi
29
Paris
29
Lyon
29
Marseille
60
Katmandu
248
Madrid
248
Barcelona
248
Valencia
NonSpatial Table
If joined Paris to France, for
example, we lose Lyon and
Marseille, therefore use relate
Note: if we flip these tables we can do a join since there is only one country for
each city (one to many)
For both Joins and Relates:
•
•
Association exists only in the map document
Underlying files not changed unless export data
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Analysis Options: Advanced & Specialized
(Table of Contents)
Advanced
Specialized
• Proximity/point pattern analysis
– nearest neighbor layer
– distance matrix layer
• surface analysis
– cross section creation
– visibility/viewshed
• network analysis
– routing
• raster modeling
• 3-D surface modeling
• spatial statistics/statistical
modeling
• functionally specialized
» shortest path (2 points)
» travelling salesman (n points)
– time districting
– allocation
• Convex Hull
• Thiessen Polygon creation
7/12/2016 Ron Briggs, UTDallas
• Remote Sensing image
processing and classification
–
–
–
–
transportation modeling
land use modeling
hydrological modeling
etc.
GISC 6381 GIS Fundamentals
34
Advanced Applications: Proximity Analysis
Nearest Neighbor
•
•
location (distance) relative to nearest
neighbor ( points or polygon centroids)
location (distance) relative to nearest objects
of selected other types (e.g. to line, or
point in another layer, or polygon boundary)
Point Pattern Analysis
is pattern?
Random Clustered Dispersed
Requires only one output column
– altho generalizable to kth nearest neighbor
Full matrix
•
measure location of each object relative
to every other object
– requires output matrix with as many
columns as rows in input table
Requires the application of
Spatial Statistics such as
•Nearest neighbor statistic
•Moran’s I
which are based on proximity
of points to each other
ArcToolbox>Spatial Statistics Tools
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Advanced Applications:
Network Analysis
Routing
• shortest path between two
points
Network-based Districting
•
– direction instructions (locating
hotel from airport)
• travelling salesman: shortest
path connecting n points
– bus routing, delivery drivers
In all cases, ‘distance’ may be
measured in miles, time, cost or
other ‘friction’ (e.g pipe diameter
for water, sewage, etc.).
Arc or node attributes (e.g one-way
streets, no left turn) may also be
critical.
7/12/2016 Ron Briggs, UTDallas
expand from site along network until
criteria (time, distance, cost, object
count) is reached; then assign area to
district
– creating market areas, attendance
zones, etc
– essentially network-based buffering
Network-based Allocation
•
assign locations to the nearest center
based upon travel thru network
– assign customers to pizza delivery
outlets
•
draw boundaries (lines of
equidistance between 2 centers)
based on the above
– Network-based market area
delimitation
– Essentially, network-based
polygon tesselation
GISC 6381 GIS Fundamentals
36
Advanced applications:
Drawings and Volumes
Surface Analysis Cross-section
• elevation (or slope) values along a
Slope Transform
• fit a plane to the 3 by 3
neighborhood around every cell, or
use a TIN
• output layer is the slope (first
derivative) of the plane for each
cell
Aspect Transform
• direction slope faces: (E-W
oriented ridge has slopes with
northern and southern aspects)
• aspect normally classified into
eight 45 degree categories
• calculate as horizontal component
of the vector perpendicular to the
surface
7/12/2016 Ron Briggs, UTDallas
line
• Volume & cut-and-fill calculation
• Cross-section easy to produce for
raster, more difficult for vector
especially if uses contours lines
Viewshed/Visibility
• terrain visible from a specific point
• applications
– visual impact of new construction
– select scenic overlooks
– Military
• Contouring
– Lines joining points of equal
(vertical) value
– From raster, massed-points or
breakline data
GISC 6381 GIS Fundamentals
37
Advanced Applications: Convex Hull
• Formally: the smallest convex polygon (no
concave angles) able to contain a set of
points
• Informally: a rubber band wrapped around
a set of points
No!
• Just as a centroid is a point representation
for a polygon, the convex hull is the
polygon representation for a set of points
• Go to the following web site for a neat
application showing how convex hull
changes as you move points around
–http://www.cs.princeton.edu/~ah/alg_anim/version1/ConvexHull.html
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Advanced Applications:
Thiessen (Dirichlet, Voronoi) Polgons
and Delaunay Triangles
•
•
•
•
•
polygons generated from a point layer such
that any location within a polygon is closer to
the enclosed point than to a point within any
other polygon
they divide the space between the points as
‘evenly’ as possible
used for market area delimitation, rain gauge
area assignment, contouring via Delaunay
triangles (DTs), etc.
elevation, slope and aspect of triangle
calculated from heights of its three corners
DTs are as near equiangular as possible and
longest side is as short as possible, thus
minimizes distances for interpolation
Thiessen Polygons
(or proximal regions
or proximity polygons)
A
Delaunay Triangles
A
Thiessen neighbors of point A share a common
boundary. Delauney triangles are formed by
joining point to its Thiessen neighbors.
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Specialized Applications
Remote Sensing/Digital Image
Processing
• reflectance value (usually 8 bit; 256
values) collected for each bands
(wavelength area) in the electromagnetic spectrum
–
–
–
–
•
1 band for grey scale (Black & white)
3 for color
up to 200 or so for ‘hyperspectral’
permits creation of image
‘spectral signature’: set of reflectance
values/ranges over available bands
typifying a specific phenomena
– provides basis for identification of
phenomena
Location Science/Network Modeling
• Network based models for optimum
location decisions for (e.g.)
–
–
–
–
–
police beats
School attendance zones
Bus routes
Hazardous material routing
Fire station location
7/12/2016 Ron Briggs, UTDallas
Raster Modeling: 2-D
• use of direction and friction surfaces to
develop models for:
– spread of pollution
– dispersion of forest fires
Surface Modeling: 3-D
– flood potential
– ground water/reservoir studies
– Viewshed/visibility analysis
Spatial Statistics/Econometrics
• analyses on spatial data which explicitly
incorporates relative location or
proximity property of observations
Global (applies to entire study area)
– spatial autocorrelation
– Regressions adjusted for spatial
autocorrelation
Local (separately calculated for local areas)
– LISA (local indicators of spatial
autocorrelation)
– Geographically weighted regression
We offer one or more courses on each!
GISC 6381 GIS Fundamentals
40
Implementation of Advanced and Specialized Applications
in ArcGIS 8/9
Extensions support many of the Advanced and some Specialized Applications
• Spatial Analyst extension provides 2-D modeling of GRID (raster) data (AV 3.2 and 8/9)
• 3-D Analyst extension provides 3-D modeling (AV 3.2 and 8/9)
• Geostatistical Analyst extension provides interpolation (ArcGis 8/9 only)
• Network Analyst extension (3.2 only) and ArcLogistics Route (standalone) for routing
and network analysis
• Image Analyst extension for remote sensing applications in AV 3.2
– Leica Image Analysis and Stereo Analyst for ArcGIS 8 (9 version not yet released-Fall ’04)
• Spatial Statistics Tools in ArcToolbox provide spatial statistics (centroid, etc..)
ArcScripts support other Advanced Applications and Specialized Applications
• ArcScripts (in Visual Basic, C++, etc.) are used to customize ArcGIS 8
– A variety of scripts available at http://support.esri.com/ >downloads
– Note: ArcScripts written in Avenue work only in ArcView 3 and will not work in ArcGIS 8/9
– Many functions previously requiring Avenue scripts for AV 3.2 are built into ArcGIS 8/9
Specialized Software Packages
• Remote Sensing packages such as Leica GeoSystems Imagine (formerly ERDAS
Imagine)
• For links to some of these packages go to:
http://www.utdallas.edu/~briggs/other_gis.html
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41
Appendix
Implementing Spatial Analysis in
ArcView 3.2/3.3
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Implementing Spatial Measurement in ArcView 3.2
•
Unlike in ArcGIS 8.1 where spatial measurements are provided automatically, in
AV 3.2 spatial measurement often has to be implemented using Avenue code:
– in functional expressions
– in scripts
•
Using functional expression for areas and lengths:
– Use Edit/Add field to add a new variable to atttributes of…table called area (or similar)
– Use Field/calculate and make this variable equal to: [Shape].ReturnArea
–
Calculation is based on map units irrespective of defined distance units.
–
If map units are feet, to obtain square miles use: [Shape].ReturnArea/5280/5280
– If file is a polyline file (arcs), for length of arcs use: [Shape].ReturnLength
•
Using a Script for areas, perimeters and lengths
In Project window, select Script and click new button to open script window
Use Script/load text file to load code from an existing text file
e.g. arcview\samples\scripts\calcapl.ave will calculate areas, perimeters, lengths
Click the “check mark” icon to compile the code.
Open a View and be sure the theme you want processed is active.
Click on script window then click the Runner icon to run script.
variables measuring area and perimeter will be added to theme table
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Implementing Spatial Matching in ArcView 3.2
Available in two places (plus additional user extensions such as districting)
• via Theme/select by theme
•
– this selects features of the active theme which relate in some specified spatial manner to
another theme
– if desired, selected features may be saved later to a new theme via Theme/convert to shape file
via Geoprocessing Wizard Extension (use File/Extensions to load)
– this creates a new theme (shape file) & combines attribute tables from 2 or more input themes
– Six options available for different types of matching
Options in Geoprocessing Wizard (use View/Geoprocessing Wizard to activate)
• Dissolve features based on an attribute
– Use for spatial aggregation/dissolving
•
Merge themes together
•
Clip one theme based on another
•
Intersect two themes
•
Union two themes
•
Assign data by location (Spatial Join)
– Use for edge matching
– Use one theme to limit features in another theme
(e.g. limit a Texas road theme to Dallas county only)
– Use for polygon on polygon overlay
– Use for polygon on polygon overlay
– Use for:
•Scripts and extensions can provide
additional capabilities
•Download from ArcScripts at ESRI
http://gis.esri.com/arcscripts/
scripts.cfm
•Place extensions (.avx) in your
folder Arcview/ext32
•The extension district.avx is good
for doing spatial aggregation or
“districting”
points in polygon
lines in polygon
points on lines (to calculate distance to nearest line)
points on points (to calculate distance to “nearest neighbor” point)
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Using Extensions and Scripts in ArcView 3.2
• Obtain copy of script or extension
– Write yourself with Avenue language
– Supplied with ArcView in folder: arcview/samples/scripts or
arcview/samples/ext
» Go to ArcView Help/Contents/Sample Scripts and Extensions for documentation
– Buy from ESRI and other companies
– Supplied free by ESRI or users and available on ESRI web site at:
http://arcsripts.esri.com/ Select Avenue language
» or go to www.esri.com and click Support
» Be sure to print or download documentation/description
• To load and use an extension
– Place .avx file in arcview/ext32 folder
– Open ArcView, choose File/extensions, place tick next to name, click OK
• To load and use a script
In Project window, select Script and click new button to open script window
Use Script/load text file to load code from existing text file containing avenue code (.ave)
e.g. \av_gis30\arcview\samples\scripts\calcapl.ave
will calculate areas, perimeters, lengths
Click the “check mark” icon to compile the code.
Take steps within ArcView as appropriate for specific script
e.g. Open a View and be sure the theme you want processed is active.
Click on script window then click the “Runner" icon to run script.
e.g. variables measuring area and perimeter will be added to theme table
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Some Example Avenue Scripts
for ArcView 3
• Avenue scripts and extensions for AV 3.2 can be downloaded from
ESRI Web site to do many basic, advanced and specialized
applications not available in standard products. Some examples are:
– Addxycoo.ave: adds X,Y coordinates of points (e.g of geocoded
addresses), or of centroid for polygons, to attributes of … file
– Polycen.ave: creates point theme containing polygon centroids
– Dwizard.zip: various districting applications
» Use avdist31b which is an update
– Line.zip: enhanced buffering of lines
– Nearestneighbor.zip: nearest neighbor analysis
For more scripts, go to: http://arcsripts.esri.com/ Select Avenue
language
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