Analysis and Modeling in GIS pps

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals Spatial operations: Spatial Measurement SHAPE AREA PERIMETER CNTY_ CNTY_ID NAME FIPS Shape Index The shape index can be calculate

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

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.

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

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

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?

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)

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

Description and Basic Analysis

– variable recoding – record aggregation – general statistical analysis

– table relates and joins

Spatial measurements:

• distance measures

– between points

– from point or raster

to polygon or zone boundary

– between polygon centroids

– e.g for smoke plumes

Spatial operations: Spatial Measurement

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)

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!!!

perimeterarea x 3.54

= 1.0 for circle

= 1.13 for squareLarge for complex shape

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)

Distances depend on projection

Perimeter to area ratio differs

2

2 ( ) )

d = − + −

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

Spatial operations: Spatial Measurement

SHAPE AREA PERIMETER CNTY_ CNTY_ID NAME FIPS Shape Index

The shape index can be calculated from the area and perimeter

measurements (Note: shapefile and shape index are unrelated)

Spatial Measurement: Calculating the Area of a Polygon

)/2 Y Y

( ) X -

1 i

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

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

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)

Centroid and Mean Center

• balancing point for a spatial distribution

– analogous to the mean

– single point representation for a polygon (centroid)

– 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

centroid outside polygon

n

Y Y

n

X X

n

i i n

Note: 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

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

n

Y Y

n

X X

n

i i n

i

n

i i i

w

Y w Y

w

X w

4,7

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

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

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:

which by Pythagoras

reduces 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.)

N

Y Y X

X

n i

n

c i

Standard Distance Deviation Example

N

Y Y X

X sdd

n i

n

i i c c

4,7

Circle with radii=SDD=2.9

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

For formulae for its calculation, see

Lee and Wong Statistical Analysis with ArcView GIS pp 48-49 (1st ed.), pp 203-205 (2nd ed.)

There appears to be

no major difference between the location

of the software and telecommunications industry in North Texas

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

• 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

polygon buffer

line buffer

point

buffers

Note: only one layer is involved, but the buffer can be output as a new layer

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:

Implement in ArcView 9 thru

– original polygons preserved

• Regionalization (or dissolving)

– grouping polygons into

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

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

Spatial Operations:

Spatial Matching: Spatial Joins and Overlays

• 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)

07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

•ERASE - erases the input

coverage features that overlap with the erase coverage

polygons.

•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.

Example: Spatial Matching:

Clipping and Erasing (sometimes referred to as spatial extraction)

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:

Example: Spatial Matching via

Polygon-on-Polygon Overlay: Union

Drainage

Basins

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

Combined layer

Another example

Available in three places

• via Selection/Select by Location

– 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

• 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)

– 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

Implementing Spatial Matching in ArcGIS 9

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

• low frequency ( low pass) filter:

– smooths the data – use larger window for greater smoothing

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

1(5)(9)+5(5)(-1)+3(2)(-1) = 14 1(2)(9)+5(2)(-1)+3(5)(-1) = -7

1(5)(9)+8(5)(-1) = 5 1(2)(9)+8(2)(-1) = 2

cell values (vi ) on

each side of edge

–kernel for example ( wi)

-1 -1 -1 -1 9 -1 -1 -1 -1

filtered values forhighlighted pixel

fi. v

i. w

i