1. Definition of Spatial Analysis
Spatial analysis - The process of modeling, examining, and interpreting model results.
Spatial analysis is useful for
evaluating suitability and capability
estimating and predicting
interpreting and understanding
Add new hyperlinks for the yellow words

2. Spatial Analysis - cont.
There are four traditional types of spatial analysis:
Topological overlay and contiguity analysis
Surface analysis
Linear analysis
Raster analysis
Retrieval/classification/measurement
Overlay (arithmetic, various conversions)
Neighborhood
Connectivity
Add new hyperlinks for the yellow words
Read more abt contiguity and other analyses

3. Definition of Spatial Analysis
Spatial data analysis involves the application of operations to coordinate and relate attribute data.
Spatial analyses are applied to solve problems related to geographic decisions
Identify high crime area
Selection of a best location for a new business
Extent of sage brush infestation in Idaho.
Spread of a disease
Etc…

4. Definition of Spatial Analysis - cont.
Spatial operations could be applied sequentially
An output could serve as input
Sequence of spatial operations is important
Bolstad, 2005

5. Definition of Spatial Analysis - cont.
Bolstad, 2005
one input can have many outputs
many inputs can have one output

6. Spatial Operations Local operations Neighborhood operations
Global operations
Use only data at one input location to determine value at corresponding output location
: Use data from both an input location and nearby location to have output value
: Use data value from entire input layer to have each output value
Bolstad, 2005

7. GIS Analysis Functions
Four broad categories

8. 1. Retrieval, Classification, & Measurement Functions
Selective Search
Classification/Reclassification (Overlays, combine)
Identifying a set of features as belonging to a group
Defines patterns
Measurement
Distances, lengths, perimeters, areas
Search/Retrieval Examples: "Locate parcel by address“
In View mode, from Theme Pulldown menu, Select by Theme:
Select features of active themes that
a) completely contain
b) Intersect
c) area within distance of
the selected features of
a) here you scroll through & select from the available themes in your project
Selection distance
a) type in the desired distance criteria
Use Query Builder
Find (one at a time)

9. Selection Selection operations Examples
Involve identifying features based on several conditions or criteria
The attributes or geometry of features are checked against the conditions or criteria
You can write the selected features into new output data layer
You can use the selection for other analysis
Examples

10. Select: State = Arkansas States = entirely north of Arkansas
States_area>84,000 sq. mi.
States both entirely north of Arkansas and larger than 84,000 sq. mi.
Bolstad, 2005

11. Functions of Spatial Analysis
Conditional selection
Set Algebra
Less than (<)
Greater than (>)
Equal to (=)
Not equal to (<>)
Boolean Algebra
Conditions OR, AND, and NOT
Bolstad, 2005

12. Examples of Expression in Boolean Algebra
Bolstad, 2005

13. Select by Location - cont.
Selecting options
That Meet
That Overlap
That Contains
That are Contained by
That are Entirely Contained By
That are Spatially Equal
That Touch
Click on the white text box to show a list of themes and select the theme that contains the layer you want to query. You can change this later if the layer is not in the theme you select. For the example select Gazetteer
Click on the white text box to show a list of layers within the theme and select the layer you want to query. For the example select Addresses
If you want to display all records of your chosen layer within your chosen boundary accept the default, Display all layer records and if you want to filter the records of your chosen layer within your chosen boundary then click next to Query layer records
This defines how the records you are looking for, the first record set, should interact with the second record set
That Meet: Includes only features referenced by the first record set that meet features referenced in the second record set.
That Overlap: Includes only features referenced by the first record set that overlap features referenced in the second record set.
That Contains: Includes only features referenced by the first record set contain features referenced in the second record set.
That are Contained by: Includes only features referenced by the first record set that are contained in the second record set.
That Entirely Contains: Includes only features referenced by the first record set that completely contain the features referenced in the second record set. The boundaries of the features cannot touch in any way; everything must be interior.
That are Entirely Contained By: Includes only features referenced by the first record set that are completely contained in the second record set. The boundaries of the features cannot touch in any way; everything must be interior.
That are Spatially Equal: Includes only features referenced by the first record set that are spatially equal to features referenced in the second record set.
That Touch: Includes only features referenced by the first record set that intersect features referenced in the second record set.

14. Examples of Selection by Location
States adjacent to Missouri
Bolstad, 2005

15. Examples of Selection by Location - cont.
States containing a portion of Mississippi River or its tributaries are selected
Bolstad, 2005

16. Classification
Categorization of geographic objects based on a set of conditions
Also known as reclassification or recoding
Spatial data operation can be used along with selection operation
Example: classify polygons based on size
Bolstad, 2005

17. Classification - cont.
Classification is an operation to create a new group of classes from an existing set of classes
Classification is governed by a a table or array (decided by user before hand)
Bolstad, 2005

18. Classification - example
Classification of land use for obtaining your required information

19. Classification - cont. Binary classification
You need to have two classes
0 and 1
True or false
A and B
Some other two level classifications
Bolstad, 2005

20. Automatic Classification
Good for many classes in one feature file (when it is practically not possible to manually classify into groups)
Requires classification schemes (algorithms or mathematical formula) which will combine various classes into a single group
Equal interval
Defined interval
Natural breaks (Jenks)
Standard deviation

21. Classification Examples
Quantile classification
Bolstad, 2005

22. Retrieval: Selective Search
addresses selected because they fall within circle
The simplest spatial query can be performed on screen using the selection tools that are provided with the GIS software. For instance, you can draw a circle on screen and select all objects falling inside it. This example shows addresses that have been selected because they fall within the circle.

23. Reclassification (Vector)
Dissolving to aggregate polygons
Figure 4.4: Dissolving to aggregate polygons
Another option occurs where a user wants to create aggregate polygons from a more detailed layer. An example of this might be where a user has a polygon layer where each polygon represents a farmer's field with attribute data that includes crop type. If the user is only interested in where particular crops are grown then many field boundaries represent redundant information that can be removed. This is done by what is called a dissolve operation whereby the boundaries of adjacent polygons with the same crop type are removed to form aggregate polygons. This is shown in Figure 4.4.

24. Reclassify by Area Size
Source: (Institute of Water Research, Michigan State University)
Size reclassification allows polygons to be selected based on their area. For linear features, overall length may be used as the selection criterion.
Work with areas > 80 acres

25. Reclassify by Contiguity
Source: (Institute of Water Research, Michigan State University)
The contiguity function allows raster GISs to analyze all examples of a particular class (eg., all forest patches) or to operate on the individual examples of that class of data (eg., any particular forest stand).
Contiguity reclassification identifies 'clumps' of raster cells having the same thematic value. Each new clump is assigned a unique value.
Work with individual forest stands, rather than the class forest as a whole.

26. Work with elevations between 20 and 40 feet
Reclassify values
Work with elevations between 20 and 40 feet
Change feet to meters

27. Buffer one of the most common spatial analysis tools
specific distance representation around a feature 
The distances can either be constant or can vary depending upon attribute values. 
When features are close together, their buffers may overlap. The user can choose to preserve the overlaps or remove them.
The buffer operation creates a new polygon data set

28. Examples of Buffer
Bolstad, 2005

29. Examples of Buffer
So, we really have the same data in both Arc/Info and Idrisi. The Arc/Info coverages are vector, while the Idrisi layers or images are raster.
This slide shows the result of a buffer. In Arc/Info I buffered the roads by 200 units (meters).
I used 200 meters as the buffer distance in Idrisi as well.
[DISCUSS Z-values with Idrisi]

30. Vector Distance Operation: Buffers & Setbacks
Buffer: A zone constructed outward from an isolated object (point or line) to a specific distance.
Setback: A zone inside a POLYGON constructed by a fixed distance from the edge of the polygon; typically used to restrict building or activities too close to the edge of a property parcel.
Diagram of simple buffers and a setback.
NOTE: buffers go outward from lines or areas; setbacks run inside of areas (not lines).
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p fig. 6-1.

31. Buffer Creation: Illustrated
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p 60. fig. 6-3.

32. 2. Overlay Functions Arithmetic Logical Raster & Vector methods differ
addition, subtraction, division, multiplication
Logical
find where specified conditions occur (and, or, >, <, etc.)
Raster & Vector methods differ
Vector good for sparse data sets
Raster grid calculations easier
Overlay (demo – addition)

33. Overlay Another common spatial analysis tool
Allows the user to identify areas where features in two layers overlap. 
A new data set is often created from these overlaps. 
In a Union Overlay, all features are included in the new data set but the features that overlap represent a new feature. 
In an Intersect Overlay, only the areas that overlap are contained in the new data set.

34. Overlay Example Analysis Tools select Overlay Intersect tool
Union tool

35. Examples
Bolstad, 2005

36. Overlay Example - cont.
Vector overlay
Bolstad, 2005

37. Overlay: Combining Attributes
Select attributes of interest for a given location
(Raster & vector methods do this differently, but the results are similar)

38. Vector based Overlay 3 main types of vector overlay point-in-polygon
line-in-polygon
polygon-on-polygon
Vector based GIS Overlay In a vector-based system, overlay operations are much more complex than in a raster-based system. This is because the topological data is stored as points, lines and/or polygons. This requires relatively complex geometrical operations to derive the intersected polygons, and the necessary creation of new nodes (points) and arcs (lines), with their combined attribute values.
In a vector-based system, topological map overlay operations allow the polygon features of one layer to be overlaid on the polygon, point, or line features of another layer. Depending on the objectives of the Overlay operation, different output features can result.
Classification of Vector Overlay Operations Topological vector overlay operations can be classified via two methods:
1. Through the elements contained in the layers to be overlaid (i.e.. whether the layers contain point, line or polygon elements), or
2. By operation type (for example; the user wants to generate a layer comprising of the Union, Intersection, or some other Boolean operation of the two input layers).
When classifying the vector overlay operation via method one, the element types each layer contains are considered. The following table identifies which overlay options exist for each possible combination of element types contained in the two input layers.
Input layer element typesPointsLinesPolygonsPointsPoints CoincidePoint int LinePoint in PolygonLinesPoint in LineLine IntersectionLine in PolygonPolygonsPoint in PolygonLine in PolygonPolygon Overlay
Complex databases such as GIS classify vector overlay operations via method two, where the particular overlay operation a user wishes to perform defines which element types may be contained in the two input layers.

39. point-in-polygon example
Vector based overlay
New Meteorological Station Attribute Table
Point ID Land Use
1 Forest
2 Forest
3 Non-Forest
point-in-polygon example

40. line-in-polygon example
Vector based overlay
line-in-polygon example

41. polygon-in-polygon example
Vector based overlay
polygon-in-polygon example

42. Raster Based Overlay: Simple Addition
Ratings assigned to categories for a county Solid Waste Plan. Ratings for grid cells were added to obtain a composite ranking.
It is possible to make direct calculation on the raster data layers.
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p fig

43. Raster Overlay: Boolean Combine
Sources in this image have been processed using a centroid-to-cell rule. The output shows two queries, each using two of the input sources.
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p 125. fig. 5-3.

44. Raster Overlay: Composite Combine
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p 126. fig. 5-4.

45. Overlay Example - cont.
Raster overlay

46. Vector Overlay: Composite Structure
A composite topological structure is constructed by finding all intersections, then polygons are labeled with a unique identifier & linked to the source attribute tables.
Process creates a single coverage with links to all the attributes.
Attribute-based operations can produce results from the table and apply to the coverage.
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p 127. fig. 5-5.

47. 3. Neighborhood Functions
Basic Functions
Average, diversity, majority, minimum/maximum, and total
Parameters to define:
Target location(s)
Specification of neighborhood
Function to perform on neighborhood elements
3 parameters
Target location(s)
Specification of neighborhood
Function to be performed on elements in neighborhood
Basic Neighborhood Functions
Average
Diversity
Majority
Maximum, minimum
Total

48. 3. Neighborhood Function (cont)
Search Operation
most common neighborhood operation
Example
count the number of customers within 2 miles of the grocery store

49. 3. Neighborhood Functions (cont)
Point or Line in Polygon Operation
Vector Model
specialized search function
Raster Model
polygons one data layer
points or lines in separate data layer
Buffers (demo - point, line, polygon)

50. Neighborhood Functions: 4 x 4 Window Processing

51. Neighborhood Functions: 4X4/Annulus/Circular/Wage Neighborhood Processing

52. Neighborhood Functions: Wedge Neighborhood Processing

53. 4. Connectivity Functions
Used to accumulate values over an area being navigated
Parameters to define:
specification of way spatial elements are connected
rules that specify allowed movement along interconnections
a unit of measurement

54. 4. Connectivity Functions (cont).
Proximity Operation
measure of the distance between features
not restricted to distance; can be noise, time, pollution, etc.
Parameters to define:
target location
unit of measure
function to calculate proximity (distance/time/noise)
area to be analyzed
Proximity
Measure of the distance between features
Not always distance, can be time, noise, etc.
Need:
target locations
unit of measure
function to calculate proximity (time/distance)
area to be analyzed

55. Example: Connectivity (Raster)
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p161. fig. 6-4.
Proximity Operation: Distance From Neighbor

56. Example: Connectivity (Vector)
Proximity Operation: Road Buffer

57. 4. Connectivity Functions (cont).
Contiguity Operation
spatial units are connected - defines “unbroken area”
Contiguity measures:
size of neighboring area(s)
shortest/longest straight line distance across adjacent area(s)
specific shape of neighboring area(s)

58. Combines adjacent units together when they share a common attribute
Contiguity Functions
Combines adjacent units together when they share a common attribute
May allow areas to be broken by certain features (such as roads)
Accomplished in raster by collecting pixels until value changes
In vector, one simply removes arcs separating matching polygons (dissolve)
Combines adjacent units together when they share a common attribute

59. 4. Connectivity Functions (cont).
Network Operations
set of interconnected lines that represent a set of features through which resources flow
Common network functions
shortest path problem (route optimization)
location-allocation modeling (resource allocation)
traveling salesperson problem (route optimization)
route tracing (prediction of network loading)
3 GIS Network Functions
prediction of network loading - flood control
route optimization - emergency routing
resource allocation - metropolitan service zones - fire, police

60. Spread Function: Calculation of Distance
Fig 7.32 The Calculation of Distance Using a Spread Function

61. Spread Function: Equidistant Travel Zones from Target (A)
Fig 7.33 Travel Zones Defined Using a Spread Function. Equidistant travel zones in 1 km increments from the target (A) are indicated by the concentric rings. The shortest travel distance from A to B is shown by the dashed line.

62. Real time tracking, route-finding, best to respond
Emergency Services
Real time tracking, route-finding, best to respond
Emergency services
By using the GIS as a computerised map, controllers of police vehicles and ambulances can instantly call up a detailed map of the area around an incident. By tracking the vehicles in real time and using route-finding GIS functions, the controller can identify the best vehicle to attend and give directions for the fastest way to the incident. They can even store historical information and look for incident patterns and black spots.

63. 4. Connectivity Functions (cont).
Visibility Analysis Operations
identification of areas of terrain that can be seen from a particular point on the surface
Viewshed Operation
uses digital elevation model data (DEMs) or.....
digital terrain model data (DTMs) or......
triangulated irregular network data (TINs)
DEM: A digital model of height (elevation or altitude) represented as regularly or irregularly spaced point height values.
DTM: A digital model of a topographic surface using information on height, slope, aspect, breaks in slope and other topographic features.
TIN: An irregular set of height observations in a vector data model. Lines connect these to produce an irregular mesh of triangles. The faces represent the terrain surface and the vertices represent the terrain features (elev points).
Intervisability
Viewshed Data Sets
TIN
TIN Tables

64. Connectivity Function Example: Viewshed Analysis
predicting what sites can see each other
uses: providers of cellular phones service can determine areas served by transmission facilities and then locate new sites to serve blind spots.
fig 8-1: Cross sectional view of a line of sight as it intersects the surface. Near objects block objects that fall below the previous angle. Obstructions on the surface can be modeled by increasing the height of the surface.
Intervisibility Functions
This GIS function is typified by the phrase LINE OF SIGHT. It is a graphic depiction of the area that can be seen from the specified target areas. Areas visible from a scenic lookout, or the required overlap of microwave transmission towers can be mapped using this procedure. Intervisibility functions rely on digital elevation data to define the surrounding topography. Applications such as landscape layouts, military planning, and the obvious communication utilization are best serviced.
The output of this function is somewhat unique in that it is often displayed in a SIDE VIEW format. The vertical field of view and maximum viable distance are the component parameters.
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p fig

65. Viewshed aka Intervisibility

66. Environmental Impact Analysis
3-D environmental impact analysis
By building a 3-D model of a landscape it is possible to simulate the construction of a new feature which may have an impact on the natural beauty of an area. For example, planning a wind farm. By using accurate map data for the area, a realistic model can be created and viewed from all angles. This will help identify the location that the new wind farm will have the least impact upon.
3D landscape model impact on natural beauty

67. The 3rd Dimension: Height Analysis
Contours
Hill shading
Spot height symbols
Cliff & slope symbols
Viewpoint symbols
Source: ©Crown copyright 2003

68. With Spatial Analysis Tools Use What You Can Do?
Find suitable locations.
Find the best path between locations.
Perform distance and cost-of-travel analyses.
Perform statistical analysis based on the local environment, small neighborhoods, or predetermined zones.
Generate new data using simple image processing tools.
Interpolate data values for a study area based on samples.
Clean up a variety of data for further analysis or display.

69. 3D height data changing water levels-danger areas
Flood Risk
Flood risk
Using 3-D height data and map data for river features it is possible to build a computer model of changing water levels; this can be used for predicting flood patterns and identifying areas in danger. By combining this model with address data, the likelihood of individual properties being flooded can be assessed. This is not just of environmental concern but of great value to insurance companies.
3D height data changing water levels-danger areas

70. Derived Mapping: Data from images
Source: ©Crown copyright 2003
Imagery – usually from aerial or satellite sensors – is widely used on GIS platforms as a backdrop to vector mapping. An image may contain an abundance of visual information that is not conveyed by the points, lines and polygons of a vector map. As far as GIS software is concerned, however, an image is a dumb background. A key research challenge is to derive vector objects from imagery. An image is a raster dataset: it is a grid of squares or pixels. Each pixel has a numerical value that may relate to colour, height or indeed virtually anything measurable.
Numerical Values
Color Representation

71. Derived Mapping: Data from images
Source: ©Crown copyright 2003
Human interpretation is often used to derive data from imagery. An operator traces lines over the on-screen image in a technique known as heads-up digitising. This process remains very labour intensive, however, and significant efforts are being made to find ways to automate it.
Aerial Imagery
Digitized Buildings

72. Derived Mapping: Data from images
Source: ©Crown copyright 2003
One approach is to look for abrupt changes or discontinuities in the image that will equate to a line feature in a map. This can be achieved using an edge detection algorithm that applies a mathematical function to each pixel and its immediate neighbours in turn. The result is an image of lines that can simply be converted into vectors. These lines are often very messy, however, and this method is best used where the discontinuity itself is distinct and separate. An alternative approach is to use software to look for similar clusters of pixels and thereby classify the image into distinct areas. Where successful, this will identify real objects such as buildings, fields and bodies of water within a classified image, which may then be converted into a vector map. Accurately and appropriately deriving vector data in this way is a complex activity at the forefront of research. The ability to automatically generate a map from an aerial photograph or satellite image is a holy grail of GIS because it would help make data far more inexpensive and up to date.
Satellite Imagery
Derived Area Map
This is a goal: Not there yet!

73. Airport Noise Pollution
noise complaints mapped by address location
Airport-noise pollution
Restrictions on the permissible levels of aircraft noise affect all busy airports. GIS can help monitor not only the noise itself but also complaints from nearby residents. The spread of sound from the airport can be mapped against the nearby built-up areas to identify how many houses are going to be affected by high noise levels. By logging the addresses of people who complain about noise, the airport can monitor the effectiveness of their noise control measures and whether or not the airlines are obeying guidelines.