1. Spatial Data What is special about Spatial Data?
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2. What is needed for spatial analysis?
Location information—a map
An attribute dataset: e.g population, rainfall
Links between the locations and the attributes
Spatial proximity information
Knowledge about relative spatial location
Topological information
Topology --knowledge about relative spatial positioning
Topography --the form of the land surface, in particular, its elevation
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3. Berry’s geographic matrix
Berry, B.J.L Approaches to regional analysis: A synthesis . Annals of the Association of American Geographers, 54, pp. 2-11
1990
location
Attributes or variables
Variable 1
Variable 2 …
Variable P
areal unit 1
areal unit 2 .
areal unit n
time
2000
location
Attributes or variables
Population
Income …
Variable P
areal unit 1
areal unit 2 .
areal unit n
2010
location
Attributes or Variables
Population
Income …
Variable P
Henan
Shanxi .
areal unit n
geographic
associations
geographic
distribution
geographic
fact
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4. Briggs Henan University 2012

5. Briggs Henan University 2012
Types of Spatial Data
Continuous (surface) data
Polygon (lattice) data
Point data
Network data
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6. Spatial data type 1: Continuous (Surface Data)
Spatially continuous data
attributes exist everywhere
There are an infinite number locations
But, attributes are usually only measured at a few locations
There is a sample of point measurements
e.g. precipitation, elevation
A surface is used to represent continuous data
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7. Spatial data type 2: Polygon Data
polygons completely covering the area*
Attributes exist and are measured at each location
Area can be:
irregular (e.g. US state or China province boundaries)
regular (e.g. remote sensing images in raster format)
*Polygons completely covering an area are called a lattice
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8. Spatial data type 3: Point data
Point pattern
The locations are the focus
In many cases, there is no attribute involved
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9. Spatial data type 4: Network data
Attributes may measure
the network itself (the roads)
Objects on the network (cars)
We often treat network objects as point data, which can cause serious errors
Crimes occur at addresses on networks, but we often treat them as points
See: Yamada and Thill Local Indicators of network-constrained clusters in spatial point patterns. Geographical Analysis 39 (3) 2007 p
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10. Which will we study? Point data Polygon data* Continuous data*
1: Analyzing Point Patserns (clusterirg and dispersion) 2: Analyzing Polygons  (Spatial Autocorrelation and Spatial Regression models) 3Surface analysis: nterpolation, trend surface analysis and kriging)
Which will we study?
Point data
(point pattern analysis: clustering and dispersion)
Polygon data*
(polygon analysis: spatial autocorrelation and spatial regression)
Continuous data*
(Surface analysis: interpolation, trend surface analysis and kriging)
*in the fall semester
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11. Briggs Henan University 2012
Converting from one type of data to another. --very common in spatial analysis
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12. Converting point to continuous data: interpolation
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13. Briggs Henan University 2012
Interpolation
Finding attribute values at locations where there is no data, using locations with known data values
Usually based on
Value at known location
Distance from known location
Methods used
Inverse distance weighting
Kriging
Simple linear interpolation
Unknown
Known
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14. Converting point data to polygons using Thiessen polygons
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15. Thiessen or Proximity Polgons (also called Dirichlet or Voronoi Polygons)
Polygons created from a point layer
Each point has a polygon (and each polygon has one point)
any location within the polygon is closer to the enclosed point than to any other point
space is divided as ‘evenly’ as possible between the polygons
Thiessen or Proximity Polygons A
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16. How to create Thiessen Polygons
1. Connect point to its nearest (closest) neighbor
2. Draw perpendicular line at midpoint
3. Repeat for other points
4. Thiessen polygons
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17. Converting polygon to point data using Centroids
Centroid—the balancing point for a polygon
used to apply point pattern analysis to polygon data
More about this later
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18. Using a polygon to represent a set of points: Convex Hull
No!
the smallest convex polygon able to contain a set of points
no concave angles pointing inward
A rubber band wrapped around a set of points
“reverse” of the centroid
Convex hull often used to create the boundary of a study area
a “buffer” zone often added
Used in point pattern analysis to solve the boundary problem.
Called a “guard zone”
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19. Models for Spatial Data: Raster and Vector
two alternative methods for representing spatial data
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20. Briggs Henan University 2012
Concept of Vector and Raster
house
river
trees
Real World
Raster Representation
Vector Representation
point
line
polygon
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21. Comparing Raster and Vector Models
Raster Model
area is covered by grid with (usually) equal-size, square cells
attributes are recorded by giving each cell a single value based on the majority feature (attribute) in the cell, such as land use type or soil type
Image data is a special case of raster data in which the “attribute” is a reflectance value from the geomagnetic spectrum
cells in image data often called pixels (picture elements)
Vector Model
The fundamental concept of vector GIS is that all geographic features in the real work can be represented either as:
points or dots (nodes): trees, poles, fire plugs, airports, cities
lines (arcs): streams, streets, sewers,
areas (polygons): land parcels, cities, counties, forest, rock type
Because representation depends on shape, ArcGIS refers to files containing vector data as shapefiles
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22. Briggs Henan University 2012
Raster model
Image
Land use (or soil type)
corn
wheat
fruit
clover
186 21
Each cell (pixel) has a value between 0 and 255 (8 bits) 1 2 3 4 5 6 7 8 9
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23. Briggs Henan University 2012
Vector Model
point (node): 0-dimensions
single x,y coordinate pair
zero area
tree, oil well, location for label
line (arc): dimension
two connected x,y coordinates
road, stream
A network is simply 2 or more connected lines
polygon : dimensions
four or more ordered and connected x,y coordinates
first and last x,y pairs are the same
encloses an area
county, lake 1 2 7 8 .
x=7
Point: 7,2
y=2
Line: 7,2 8,1
Polygon: 7,2 8,1 7,1 7,2
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24. Using raster and vector models to represent surfaces
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25. Representing Surfaces with raster and vector models –3 ways
Contour lines
Lines of equal surface value
Good for maps but not computers!
Digital elevation model (raster)
raster cells record surface value
TIN (vector)
Triangulated Irregular Network (TIN)
triangle vertices (corners) record surface value
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26. Contour (isolines) Lines for surface representation
Contour lines of constant elevation
--also called isolines (iso = equal)
Advantages
Easy to understand (for most people!)
Circle = hill top (or basin)
Downhill > = ridge
Uphill < = valley
Closer lines = steeper slope
Disadvantages
Not good for computer representation
Lines difficult to store in computer

27. Raster for surface representation
Each cell in the raster records the height (elevation) of the surface
105
110
115
120
Raster cells with elevation value
Surface
Contour lines
Raster cells
(Contain elevation values)
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28. Triangulated Irregular Network (TIN):
Vector surface representation
a set of non-overlapping triangles formed from irregularly spaced points
preferably, points are located at “significant” locations,
bottom of valleys, tops of ridges
Each corner of the triangle (vertex) has:
x, y horizontal coordinates
z vertical coordinate measuring elevation.
valley
ridge
vertex 1 2 4 3 5

29. Draft: How to Create a TIN surface: from points to surfaces
Thiessen3.jpg
Thiessen4.jpg
Links together all spatial concepts: point, line, polygon, surface
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30. Briggs Henan University 2012
Using raster and vector models to represent polygons (and points and lines)
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31. Briggs Henan University 2012
Representing Polygons (and points and lines) with raster and vector models X 1 2 3 4 5 6 7 8 9
Raster model not good
not accurate
Also a big challenge for the vector model
but much more accurate
the solution to this challenge resulted in the modern GIS system
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32. Using Raster model for points, lines and polygons --not good!
For lines and polygons
Line not accurate
Point “lost” if two points in one cell
Polygon boundary not accurate
Point located at cell center
--even if its not
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33. Briggs Henan University 2012
Using vector model to represent points, lines and polygons: Node/Arc/Polygon Topology
The relationships between all spatial elements (points, lines, and polygons) defined by four concepts:
Node-ARC relationship:
specifies which points (nodes) are connected to form arcs (lines)
Arc-Arc relationship
specifies which arcs are connected to form networks
Polygon-Arc relationship
defines polygons (areas) by specifying which arcs form their boundary
From-To relationship on all arcs
Every arc has a direction from a node to a node
This allows
This establishes left side and right side of an arc (e.g. street)
Also polygon on the left and polygon on the right for
every side of the polygon
from to
Left
Right
from to
New!
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34. Node/Arc/ Polygon and Attribute Data1 II 2
Birch
Node/Arc/ Polygon and Attribute Data
Example of computer implementation
Smith
Estate I
A34
III
A35 4 IV 3
Cherry
Attribute Data
Spatial Data
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35. Briggs Henan University 2012
This is how a vector GIS system works! This data structure was invented by Scott Morehouse at the Harvard Laboratory for Computer Graphics in the 1960s. Another graduate student named Jack Dangermond hired Scott Morehouse, moved to Redlands, CA, started a new company called ESRI Inc., and created the first commercial GIS system, ArcInfo, in Modern GIS was born!
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36. Other ways to represent polygons with vector model
2. Whole polygon structure
3. Points and Polygons structure
Used in earlier GIS systems before node/arc/polygon system invented
Still used today for some, more simple, spatial data (e.g. shapefiles)
Discuss these if we have time!
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37. Vector Data Structures: Whole Polygon
Whole Polygon (boundary structure): list coordinates of points in order as you ‘walk around’ the outside boundary of the polygon.
all data stored in one file
coordinates/borders for adjacent polygons stored twice;
may not be same, resulting in slivers (gaps), or overlap
all lines are ‘double’ (except for those on the outside periphery)
no topological information about polygons
which are adjacent and have a common boundary?
used by the first computer mapping program, SYMAP, in late 1960s
used by SAS/GRAPH and many later business mapping programs
Still used by shapefiles.
Topology --knowledge about relative spatial positioning
-- knowledge about shared geometry
Topography --the form of the land surface, in particular, its elevation
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38. Whole Polygon: illustration
Data File
A 3 4
A 4 4
A 4 2
A 3 2
B 4 4
B 5 4
B 5 2
B 4 2
C 3 2
C 4 2
C 4 0
C 3 0
C 3 2
D 4 2
D 5 2
D 5 0
D 4 0
E 1 5
E 5 5
E 5 4
E 3 4
E 3 0
E 1 0 5 E A B C D 4 3 2 1
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39. Vector Data Structures: Points & Polygons
Points and Polygons: list ID numbers of points in order as you ‘walk around’ the outside boundary
a second file lists all points and their coordinates.
solves the duplicate coordinate/double border problem
still no topological information
Do not know which polygons have a common border
first used by CALFORM, the second generation mapping package, from the Laboratory for Computer Graphics and Spatial Analysis at Harvard in early ‘70s
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40. Points and Polygons: Illustration
Points File
Polygons File 12
A 1, 2, 3, 4, 1
B 2, 5, 6, 3, 2
C 4, 3, 8, 9, 4
D 3, 6, 7, 8, 3
E 11, 12, 5, 1, 9, 10, 11 5 11 2 5 1 4 3 A B E 3 4 2 6 C D 1 10 9 8 7
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41. Monday, we will begin talking about Spatial Statistics
Hopefully, you now have a better understanding of what is special about spatial data!
Monday, we will begin talking about Spatial Statistics
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42. Briggs Henan University 2012