1. A single map can be analyzed using summary statistics, measurements of feature aspects, and buffers. 2. There are several ways to calculate summary statistics in ArcGIS including selection statistics, attribute table statistics, and summarization. 3. Measurements that can be made on geographic features include number, area, length, shape, fragmentation, and distance calculations.

1. Single Map Analysis
8 March 2011

2. Things to do with a single map
Summary statistics
Measure aspects of features (area,
length, shape, etc.)
Buffers

3. Summary statistics
There are three ways to compute
summary stats in ArcGIS
1.) Selection Statistics
• Selection  Statistics
2.) Statistics from the attribute table
3.) Summarize

4. Selection statistics example

5. Attribute Table Statistics
Example

6. Summary Statistics example

7. Summarize
You can summarize attribute data
based on unique occurrences of a value
within a field containing any type of
data
Numerical field can be selected to
summarize using a statistical method
(e.g. min, max, mean, StDev, sum,
variance, etc.)

8. Summarize example

9. Measurement
Several different ways to measure
aspects about geographic features
1.) Number 6.) Distance
2.) Area 7.) Pattern
3.) Length
4.) Shape
5.) Fragmentation

10. Shape
Compactness Index
Zonal Geometry
Sinuosity

11. Compactness
Although the perimeter to area ratio
can be used (see pg. 182-183 in
Theobald for formulas), it is more
common to measure shape by
comparing a polygon to a circle

12. Computing Compactness

13. Zonal Geometry
Zonal Geometry can be calculated for
rasters using the raster calculator
ZonalGeometery (<GRID>, [Geometry-
Type], {MaxThickness})
Calculates an aspect of the geometry of
zones, based on the GeometryType
keyword: AREA, PERIMETER,
THICKNESS, ELLIPSE, and ALL
See pg. 251 of Theobald

14. Can also use Hawth’s Tools

15. Sinuosity
The sinuosity of a linear features
represented as a polyline is measured
as the ratio of the straight-line distance
from the start to the end of a line,
divided by the full (meandering) length
of a line
Measures “wiggliness”

16. Calculating Sinuosity

17. Fragmentation
Very useful in landscape ecology!
Classic program is FRAGSTATS
Go to
http://www.umass.edu/landeco/research/fragstats
/fragstats.html to download
Can also calculate some basic things in
ArcGIS

18. FragStats home page

19. ArcGIS Fragmentation
Fragmentation Index
Relative Size of the Largest Patch
Landscape Signature

20. Fragmentation Index
Fragmentation (p) of a map can be
calculated as the ratio of of the number
of contiguous map regions (m), or the
# of polygons that would result after
classifying and dissolving the
boundaries between same-valued
neighboring polygons, to the number of
original polygons (n)

21. Fragmentation Index2
So… p = (m-1) / (n – 1)
This index ranges from 1 (complete
fragmentation) to 0 (completely
connected)
For raster data, m = # of regions
(need to use the RegionGroup
function), and n = the number of cells
in the GRID

22. Relative size of the largest patch
The ratio of the area of the largest patch (a)
to the area of all the patches of the same
class as the largest patch (A). Represented as
RS
So… RS = a / (p * A)
The area of a can be found using the
Statistics tool (features) or the count field
(GRIDs)
RS for a connected landscape approaches
1.0, while in a fragmented landscape it
approaches 0.0

23. Landscape Signature
Both the shape and configuration of
patches can be examined by measuring
how the proportion of a landscape that is
occupied by patches changes when patches
are enlarged and shrunk across a range of
scales
This is then normalized to the total study
area and expressed as a cumulative
distribution function

24. Example

25. Distance calculations
Typically, the distances from the centroids
are calculated
However, you can calculate distance from
the nearest part of the feature or the
average distance from all parts of a feature
(However, note that calculating distance
surfaces involves the closest edge-to-edge
distance)

26. Types of Distance Calculations
1.) Spherical
2.) Euclidean
3.) Constrained distance
4.) Weighted Distance

27. Spherical Distance
Calculating distance using geographic
coordinates requires the use of
spherical geometry
D = Rcos – 1[sin(lat1)sin(lat2)
+cos(lat1)cos(lat2)cos(long1-long2)
Where R = the radius of a spheroid
(6,370,997 m)
Don’t use it for distances < 2 km

28. Other Distance Calculations
Euclidean Distance - Uses the
Pythagorean theorem (just use the
measure tool!)
Constrained Distance assumes
movement is limited to orthogonal
D = |x2 – x1|+|y2-y1|
Weighted Distance depends upon the
weights given to each cell

29. Patterns
Geographic features can be
characterized by their degree of
dispersion
Regular
Random
Clustered

30. Nearest Neighbor
The nearest neighbor index measures
the degree of spatial dispersion of
features based on the minimum
distanced between individual (point &
line) features
It can be computed using ArcToolbox

31. Buffering
Go to ArcToolbox Analysis Tools 
Proximity  Buffer
Can set the buffer as a specified distance,
as multiple buffer rings or based on a
distance from an attribute