Analysis and Modeling in GIS. 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.
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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 descriptiveinput 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
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 suboceanic earthquakes occur closer to the Pacific coast of South America than of North America?
Are gas stations or fast food joints closer to freeways?
Provided through extra cost Extensions or professional versions of desktop packages
Write your own or download from ESRI Web site
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).
Vector
spatial measurement
Centrographic statistics
buffer analysis
spatial aggregation
redistricting
regionalization
classification
Spatial overlays and joins
Raster
neighborhood analysis/spatial filtering
Raster modeling
Attribute Operations
record selection
tabular via SQL
‘information clicking’ with cursor
variable recoding
record aggregation
general statistical analysis
table relates and joins
Description and Basic Analysis(Table of Contents)distance measures
between points
from point or raster to polygon or zone boundary
between polygon centroids
polygon area
polygon perimeter
polygon shape
volume calculation
e.g. for earth moving, reservoirs
direction determination
e.g. for smoke plumes
Comments:
Cartesian distance via Pythagorus
Used for projected data by ArcMap measure tools
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
possible distance metrics:
straight line/airline
city block/manhattan metric
distance thru network
time/friction thru network
shape often measured by:
Projection affects values!!!
perimeter
= 1.0 for circle
= 1.13 for square
Large for complex shape
area x 3.54
Spatial operations: Spatial MeasurementArcGIS 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)
Distances depend on projection.
Perimeter to area ratio differs
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)
Area=(2 x 4)/2=4
Area=(3 x 4)=12
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Area=(5 x 1)/2=2.5
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Spatial Measurement: Calculating the Area of a Polygon
A
B
C
=

=
10
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:
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
Its implementation in Excel is shown below.
0
Measures of Centrality (equivalent to mean)
Measures of Dispersion (equivalent to standard deviation or variance)
polygon
Centroid and Mean CenterNote: many ArcView applications calculate only a “psuedo” centroid: the coordinates of the bounding box (the extent) of the polygon
Can be implemented via:
ArcToolbox>Spatial Statistics Tools>Measuring Geographic Distributions>Mean Center
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Calculating the centroid of a polygon or the mean center of a set of points.
(same example data as for area of polygon)
Calculating the weighted mean center. Note how it is pulled toward the high weight point.
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
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. 6569
Source: US Statistical Abstract 2003
which by Pythagorasreduces to:
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.)
The major axis defines the direction of maximum spreadof the distribution
The minor axis is perpendicular to itand defines the minimum spread
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. 4849 (1st ed.), pp 203205 (2nd ed.)
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
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
Spatial Operations: buffer zonespolygon buffer
point
buffers
line
buffer
Note: only one layer is involved, but the buffer can be output as a new layer
formal (based on in situ characteristics)e.g. city neighborhoods
functional (based on flows or links): e.g. commuting zones
Groupings may be:
contiguous
noncontiguous
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 segmentsyuppies, nerds, etc (class.)
creating soils or zoning map (class)
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
Grouping/combining polygons—is applied to one polygon layer only.
Spatial Operations: spatial aggregationImplement in ArcView 9 thru ArcToolbox>Generalization>Dissolve
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
combine two (or more) layers to:
select features in one layer, &/or
create a new layer
used to integrate data having different spatial properties (point v. polygon), or different boundaries (e.g. zip codes and census tracts)
can overlay polygons on:
points (point in polygon)
lines (line on polygon)
other polygons (polygon on polygon)
many different Boolean logic combinations possible
Union (A or B)
Intersection (A and B)
A and not B ; not (A and B)
can overlay points on:
Points, which finds & calculates distance to nearest point in other theme
Lines, which calculates distance to nearest line
Examples
assign environmental samples (points) to census tracts to estimate exposure per capita (point in polygon)
identify tracts traversed by freeway for study of neighborhood blight (polygon on lines)
integrate census data by block with sales data by zip code (polygon on polygon)
Clip US roads coverage to just cover Texas (polygon on line)
Join capital city layer to all city layer to calculate distance to nearest state capital(point on point)
Spatial Operations:Spatial Matching:Spatial Joins and OverlaysExample: Spatial Matching: Clipping and Erasing
(sometimes referred to as spatial extraction)
ERASE  erases the input coverage features that overlap with the erase coverage polygons.Land Use
a.
b.
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.
Drainage
Basins
Atlantic
A.
G.
cA
Gulf
bG
cG
bA
aA
aG
GIS Union
Set Theory Union
Example: Spatial Matching via PolygononPolygon Overlay: UnionCombined layer
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 explicitly retained.
In set theory terms, the outcome
of the above would simply be:
Another example
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Available in three places
lines in polygon
points on lines (to calculate distance to nearest line)
points on points (to calculate distance to “nearest neighbor” point)
ArcToolbox Examples
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 (8connected)
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
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)
smoothsthe data
use larger window for greater smoothing
median filter
use median (middle value) instead of mean
smoothing, especially if data has extreme value outliers
Spatial Operations:neighborhood analysis/spatial filteringweights must
sum to 1.0
high frequency (high pass) filter
negative weight filter
exagerates rather than smooths local detail
used for edge detection
standard deviation filter (texture transform)
calculate standard deviation of neighborhood raster values
high SD=high texture/variability
low SD=low texture/variability
again used for edge detection
neighorhoods spanning border have large SD ‘cos of variability
Spatial Operations:spatial filtering  high pass filtercell values (vi ) on
each side of edge
filtered values for
highlighted pixel
2
5
1(5)(9)+5(5)(1)+3(2)(1) = 14
1(2)(9)+5(2)(1)+3(5)(1) = 7
1(2)(9)+8(2)(1) = 2
1(5)(9)+8(5)(1) = 5
fi.vi.wi
Processes may be:
Local: one cell only
Neighborhood: cells relating to each other in a defined manner
Zonal: cells in a given section
Global: all cells
ArcGIS implementation:
All raster analyses require either the Spatial Analyst or 3D Analyst extensions
Base ArcView can do no more than display an image (raster) data set
Suitability modeling
Diffusion Modeling
Connectivity Modeling
Spatial Operations:raster–based modelling0
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Site
options
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for
sale
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soil
slope
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System at
time t+1
Incidence
matrix
Probability
mask
Initial
State
Connectivity
matrix
Resultant
State
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
useSelection/Select by Attribute
use table Relates /Joins to select specific data
Select by Graphic
Manually, one point at a time
use Select Features tool
within a rectangle or an irregular polygon
use Selection/Select by Graphic
within a radius (circle) around a point or points
use Selection/Select by Location (are wthin distance)
Select by Location
By using another layer
Use Selection/Select by Location
(same as Spatial Matching discussed previously)
Hot Link
Click on map to ‘hot link’ to pictures, graphs, or other maps
Outputs may be:
Simultaneously highlighted records in table, and features on map
New tables and/or map layers
Examples
Use SQL query to select all zip codes with median incomes above $50,000 (tabular)
identify zip codes within 5 mile radius of several potential store sites and sum household income (graphic)
show houses for sale on map, and click to obtain picture and additional data on a selected house (hot link)
Attribute Operations: record selection or extractionfeatures selected on the map are identified in the table (and visa versa)(assumes a Normal distribution)
25%
25%
23%
23%
14%
34%
34%
14%
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1
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.68
.68
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Attribute Operations: variable recoding(equal width classes on variable)
(equal width classes on variable)
(categories based on 1,2, etc, SDs
above/below mean)
No change in number of records (observations).
Implement in ArcGIS via:
Right click in T of C, select Properties, then Symbology tab
Equal area %
Equal interval %
Standard Deviation
Equal interval score
Equal area score
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)
Attribute Operations:record aggregationrecalc.
sum
sum
count
average
of
medians!
Type of processing:
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)
Associate country layer with type of government: one gov. type assigned to many countriesbut each country has only one gov. type (one to many)
Single most common error in GIS Analysis values on a key variable
intending a one to one join of attribute to spatial table
getting a one to many join of attributes to spatial table
Spatial
After joining attribute to spatial data
Relate: many to one relationship, attributes not appended
Associate country layer with its multiple cities (many to one)
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:
If joined Paris to France, for example, we lose Lyon and Marseille, therefore use relate
Advanced values on a key variable
Proximity/point pattern analysis
nearest neighbor layer
distance matrix layer
surface analysis
cross section creation
visibility/viewshed
network analysis
routing
shortest path (2 points)
travelling salesman (n points)
time districting
allocation
Convex Hull
Thiessen Polygon creation
Specialized
Remote Sensing image processing and classification
raster modeling
3D surface modeling
spatial statistics/statistical modeling
functionally specialized
transportation modeling
land use modeling
hydrological modeling
etc.
Analysis Options: Advanced & Specialized(Table of Contents)Nearest Neighbor values on a key variable
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)
Requires only one output column
altho generalizable to kth nearest neighbor
RandomClusteredDispersed
Advanced Applications: Proximity AnalysisRouting values on a key variable
shortest path between two points
direction instructions (locating hotel from airport)
travelling salesman: shortest path connecting n points
bus routing, delivery drivers
Networkbased Districting
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 networkbased buffering
Networkbased 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
Networkbased market area delimitation
Essentially, networkbased polygon tesselation
Advanced Applications:Network AnalysisIn 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 oneway
streets, no left turn) may also be
critical.
Slope Transform values on a key variable
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: (EW 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
Crosssection Drawings and Volumes
elevation (or slope) values along a line
Volume & cutandfill calculation
Crosssection 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, massedpoints or breakline data
Advanced applications:Surface AnalysisNo! values on a key variable
Advanced Applications: Convex Hullpolygons 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
A
A
Advanced Applications:Thiessen (Dirichlet, Voronoi) Polgonsand Delaunay TrianglesThiessen Polygons
(or proximal regions
or proximity polygons)
Delaunay Triangles
Thiessen neighbors of point A share a common boundary. Delauney triangles are formed by joining point to its Thiessen neighbors.
Remote Sensing/Digital Image Processing within a polygon is closer to the enclosed point than to a point within any other polygon
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
Raster Modeling: 2D
use of direction and friction surfaces to develop models for:
spread of pollution
dispersion of forest fires
Surface Modeling: 3D
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
Specialized ApplicationsWe offer one or more courses on each!
Extensions support many of the Advanced and some Specialized Applications
ArcScripts support other Advanced Applications and Specialized Applications
Specialized Software Packages
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
Available in two places (plus additional user extensions such as districting)
Options in Geoprocessing Wizard (use View/Geoprocessing Wizard to activate)
lines in polygon
points on lines (to calculate distance to nearest line)
points on points (to calculate distance to “nearest neighbor” point)
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
For more scripts, go to: http://arcsripts.esri.com/ Select Avenue language