1. Spatial Analysis What is spatial analysis?
It is the means by which we turn raw geographic data into useful information
It does so by adding greater informative content and value
Spatial analysis reveals patterns, trends, and anomalies that might otherwise be missed
It provides a check on human intuition
It allows for analysis of data that could never be done by humans

2. Spatial Analysis
Analysis is considered spatial if the results depend on the locations of the objects being analyzed.
Thus if you move the objects, the results of spatial analyses will change.
To conduct a spatial analysis generally requires both attributes and locations of objects.

3. Steps in Spatial Analysis
Frame the question we wish to ask.
Find appropriate data to answer the question.
Choose analytical method appropriate to answer question.
Process the data using the chosen method.
Review and question the results (often refining the approach by collecting more data and improving the analysis)

4. Spatial Relationships are at the Core of Spatial Analysis
Most spatial analyses are based on topological questions:
How near is Feature A to Feature B
What features contain other features?
What features are adjacent to other features?
What features are connected to other features?
From these topological building blocks, we can develop all sorts of spatial analysis approaches to answer many complex questions

5. Types of Spatial Analysis
We will consider six categories of spatial analyses:
Queries
Measurements
Transformations
Descriptive summaries
Optimization
Hypothesis testing

6. 1. Queries
Queries
Attribute based
Example: show me all pixels in a raster image with BV > 80.
Location based
List all the block groups that fall within Orange County
A GIS can respond to queries by selecting the appropriate data in
A map view
A table
Both

7. The Map View (~ a View)
Queries can be performed through interaction with a GIS on-screen map.
Identify objects
Query data objects based on specific criteria of attributes
Find coordinates of objects

8. The Table View (~ a Table)
Queries can be performed through interaction with a table.
Attribute based queries can be performed in the table.
When objects are selected in a table, a GIS can automatically highlight the selected data objects in the map view, and vice versa.

9. Queries
Queries can be performed through command windows/programs, “Old School” style.

10. 2. Measurements Measure: Distance between two points Area of a polygon
Distances can be summed
Example: a truck makes multiple stops on a route. What is the total distance traveled on the route?
Other mathematical operations can be applied to distances:
We can square a set of distances, add them up, divide by the amount of distances calculated in the set, and take the square root. What is an example of when this operation is used?
Area of a polygon
Example: What is the area of a preserved forest tract?

11. Measurement of Length Types of length measurements
Euclidean distance: straight-line distance between two points on a flat plane (as the crow flies)
Manhattan Distance limits movement to orthogonal directions
Great Circle distance: the shortest distance between two points on the globe
Network Distance:
Along roads
Along pipe network
Along electric grid
Along phone grid
By river channels

12. Euclidean Distance P2 (x2,y2) (x1 – x2)2 + (y1 – y2)2 C= C P1 (x1,y1)
Distances can be calculated between points, along lines, or in a variety of fashions with areas
Euclidean Distance – calculated in a Cartesian frame of reference:
P2 (x2,y2)
(x1 – x2)2 + (y1 – y2)2 C= C
P1 (x1,y1)
On what scales is this valid?
Can we use this with latitude and longitude?

13. Manhattan Distance P2 (x2,y2) dm = | x1 – x2 | + | y1 – y2 |
Manhattan Distance is useful in some urban environments with orthogonal road networks.
Movement is limited to city streets:
P2 (x2,y2)
dm = | x1 – x2 | + | y1 – y2 |
a reminder – the | symbols denote absolute value
P1 (x1,y1)

14. Great Circle Distance
Everyone here knows what and where the equator is.
The equator is a natural origin, or about as natural as you can get on a big floating rock in space. It is effectively the midpoint between the two poles.
But, the Prime Meridian is arbitrary. Who can tell me the city that the PM passes through?
Greenwich, England.
The Great Circle distance is the shortest distance between two points on the globe.
The two points must be specified using latitude & longitude positions.

15. Network Distance Yahoo maps:
Starting from: Carrboro, NC Save Address Arriving at: Washington, DC Save Address
istance:272.5 miles Approximate Travel Time:5 hours 23 mins

16. Issues with Length Measurement
The length of a true curve is longer than the length of its polyline or polygon representation:

17. Issues with Length Measurement
Length measurements in GIS are usually calculated in 2 dimensions. But changes in elevation increase distances. X Z

18. 3. Transformations
Spatial transformations includes many analytical approaches, applicable to:
Vector data
Raster data
Both
Transformations can create new:
Attributes
Data objects

19. Buffering (Proximity Analysis)
Buffering operations create new objects consisting of areas within a user-defined distance of existing objects.
Examples of uses:
to determine areas impacted by a proposed highway
to determine the service area of a proposed hospital
Buffering can be performed in both the vector and raster spatial data models

20. Buffering (Proximity Analysis)
Buffering: The delineation of a zone around the feature of interest within a given distance. For a point feature, it is simply a circle with its radius equal to the buffer distance:

21. Variable Distance Buffering
The buffer zone constructed around each feature can be based on a variable distance according to some feature attribute(s)
Suppose we have a point pollution source, such as a power plant. We want to zone residential areas some distance away from each plant, based on the amount of pollution that power plant produces
For smaller power plants, the distance might be shorter.
For larger power plants that generate a lot of pollutant, we choose longer distances

22. Buffering Points, Lines, and Polygons
Buffering higher order objects involves moving a circle of specified radius along the line (or the lines forming polygon)

23. Line and Polygon Buffer Examples
Buffer lines
Buffer polygons

24. Raster Buffering
Buffering operations also can be performed using the raster data model
In the raster model, we can perform a simple distance buffer, or in this case, a distance buffered according to values in a friction layer (e.g. travel time for a bear through different landcover):
lake
Areas reachable in 5 minutes
Areas reachable in 10 minutes
Other areas

25. Feature in Feature Transformations
These transformations determine whether a feature lies inside or outside another feature
The most basic of these transformations is point in polygon analysis, which can be applied in various situations:

26. The Point in Polygon Algorithm
How do GIS programs calculate this?
Draw a line from the point to infinity in any direction, and then count the number of intersections between this line and each polygon’s boundary
The polygon with an odd number of intersections is the containing polygon; all other polygons have an even number of intersections

27. Point in Polygon Algorithm
For the point to be inside the polygon, there must be an odd number of intersections on either side of the point .

28. Point Frequency/Density Analysis
We can use point in polygon results to calculate frequencies or densities of points per area
For example, given a point layer of bird’s nests and polygon layer of habitats, we can calculate densities:
Bird’s Nests A B D C
Habitat Types A B D C
Analysis Results
Habitat Area(km2) Frequency Density
A nests/km2
B nests/km2
C nests/km2
D nests/km2

29. Line in Polygon Analysis
Overlay line layer (A) with polygon layer (B)
In which B polygons are A lines located?
» Assign polygon attributes from B to lines in A
Example: Assign land use attributes (polygons) to streams (lines): A B
David Tenenbaum – GEOG 070 – UNC-CH Spring 2005

30. Polygon Overlay, Discrete Object Case
In this example, two polygons are intersected to form nine new polygons.
One is formed from both input polygons (1);
four are formed by Polygon A and not Polygon B (2-5);
four are formed by Polygon B and not Polygon A (6-9) B A 5 9 2 8 1 4 7 6 3

31. Polygon Combination B A 5 9 2 8 1 4 7 6 3
Common ways to combine polygons:
Show all new polygons as in diagram.
UNION (Boolean OR)
INTERSECTION (Boolean AND) B A 5 9 2 8 1 4 7 6 3

32. What level of accuracy is ‘good’? (from lecture 20)
The Overall accuracy (and row and column accuracies) are generally considered good/acceptable if they are above 85%. The USGS uses this as a guideline.
The Kappa statistic describes agreement between the classified data and the reference data (it represents the increased accuracy of the performed classification over that of a random classification). A Kappa statistic of:
Above 80% is considered to have strong agreement.
Between 40% and 80% is considered to have moderate agreement.
Below 40% is considered to have poor agreement.

33. Some non-error data quality issues
Compatibility: can two or more geographic data sets be used together properly?
e.g. is it meaningful to overlay roads data digitized at 1:10,000 scale with road hazard sites digitized at 1:250,000?
Completeness: does a given data set adequately cover a study area? Are there gaps in space or time?
Example: a city’s municipal cadastral database -- do all parcel polygons have attribute information? Are any parcels missing?
Consistency: are geographic data sets consistent in terms of content, format, etc?
Example landcover data layer for a study area -- different sub-areas produced from two satellite scenes...
one Landsat TM & classified into 10 classes -vs.-
one Landsat MSS & classified into 5 classes