Transcript The Nature of Geographic Data

The Nature of Geographic
Data
Based in part on Longley et al.
Chapters 3 and 4
What are Geographic Data?
“Location, location, location!”
to map, to link based on the same place,
to measure distances and areas
Attributes
physical or environmental
soci-economic (e.g., population or income)
Time
height above sea level (slow?)
Sea surface temperature (fast)
Problems w/ Representing
Geographic Data
Digital Earth
Entire Earth into single
digital representation
Infinite complexity
What to leave in, what
to leave out
Representations are
partial (data models)
Discrete Objects and Continuous Fields
( Vector and Raster Structures)
DISCRETE
Well-defined boundaries
in empty space
“Desktop littered w/
objects”
World littered w/ cars,
houses, etc.
Counts
49 houses in a
subdivision
Dimensionality of Objects:
A way of identifying them
0-D
1-D
2-D
The discrete object view leads to a
powerful way of representing geographic
information about objects
Example of representation of geographic information as a table. The locations and attributes are for each of
four grizzly bears in the Kenai Peninsula of Alaska. Locations, in degrees of longitude and latitude, have
been obtained from radio collars. Only one location is shown for each bear, at noon on July 31, 2000.
Fields:Not points, lines, areas, but what varies and
how smoothly…. “What occurs everywhere”
care to count every peak, valley, ridge, slope???
Object/Vector Feature Types
Data Models and Data Structures
Data Models: fields and objects are no more than
conceptualizations, or ways in which we think about
geographic phenomena. They are NOT always designed to
deal with the limitations of computers.
Field & Object Data Models
Data Structures: methods of representing the data model in
digital form w/in the computer
Raster and Vector Data Structures
Raster Data Structure
Mixed Pixels
Examples of the largest share rule, where a cell's value is on the value that occupies the largest share of
the cell's area, and the central point rule, where a cell's value is based on the value that occupies the
central point of the cell.
Vector Data Structure:
Lines vs. Polygons
An area (red line) and its approximation by a polygon (blue line).
Slivers due to double digitizing and overlay
can be eliminated.
Sliver
Rasters and Vectors
Vector-based line
Raster-based line
Flat File
4753456 623412
4753436 623424
4753462 623478
4753432 623482
4753405 623429
4753401 623508
4753462 623555
4753398 623634
Flat File
0000000000000000
0001100000100000
1010100001010000
1100100001010000
0000100010001000
0000100010000100
0001000100000010
0010000100000001
0111001000000001
0000111000000000
0000000000000000
Now YOU!
Topology
Science and mathematics of geometric relationships
Simple features + topological rules
Connectivity
Adjacency
Shared nodes / edges
Topology needed by
Data validation
Spatial analysis (e.g. network tracing, polygon adjacency)
An Object Model uses a Vector
(Arc/Node) Data Structure
Object data model evolved into the
arc/node variation in the 1960s.
Points in sequence build lines.
Lines have a direction - nodes or
ordering of the points.
Lines in sequence build polygons.
Vectors (Arcs) and Topology
Vectors without topology are spaghetti
structures.
Points, lines, and areas
stored in their own files, with links between
them.
stored w/ topology (i.e. the connecting
arcs and left and right polygons).
Relationships are computed and stored
Arc Left
ID Poly
Connectedness, Adjacency, Contiguity,
Rt From To
Geo-Relational
Poly node node
1
A
0
c
a
2
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B
b
c
3
C
A
b
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C
d
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B
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Poly No. of
ID
arcs
0
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a
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List of
arcs
A
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-1, -2, 3
B
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2,2,-7,
-7,5,5,6 -6
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-3, -5, 4
D
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7
Topology, GIS, and You
Topological data structures very
important in GIS software.
Must BUILD topology from unconnected
arcs
rarely are maps topologically clean when
digitized, imported, or “GPSed.”
“Tolerances” important - features can
move or disappear
“snapping”, elimination, merging, etc.
Nodes that are close together are snapped.
The bounding rectangle
(xmax, ymax)
(xmin, ymin)
Why Topology Matters
allows automated error detection and
elimination.
allows many GIS operations to be done
without accessing the (x,y) files.
makes map overlay feasible.
makes spatial analysis possible.
Issues w/ Raster & Vector
Issue
Raster
Vector
Volume of Data
Depends on cell size
Depends on density
of vertices
Sources of data
Remote sensing,
imagery
Socio-econom ic,
environ. sampling
Applications
Resources,
envirom ental
Socio-econom ic,
administrative
Software
Raster GIS, image
processing
Vector GIS, autom .
Cartography
Resolution
Fixed
Variable
TIN: Triangulated Irregular Network
Based on the Delaunay
triangulation model of a
set of irregularly
distributed points.
Way to handle raster
data with the vector
data structure.
Common in most GISs.
More efficient than a
grid.
triangulation
TIN surface
Courtesy www.ian-ko.com/resources/triangulated_irregular_network.htm
pseudo 3D
Spatial Autocorrelation
Tobler’s 1st Law of Geography: everything is related to
everything else, but near things are more related than
distant things
S. autocorrelation: formal property that measures the
degree to which near and distant things are related.
Close in space
Dissimilar in attributes
Attributes
independent
of location
Close in space
Similar in attributes
Arrangements of dark and light colored cells exhibiting negative, zero, and positive spatial autocorrelation.
Sampling: The Quest to Represent the Real World
Field - selecting discrete objects from a continuous surface
Object - selecting some discrete objects, discarding others
a spatially
random
sample
a spatially
systematic
(stratified)
sample
a stratified
random
sample
Spatially systematic sampling presumes
that each observation is of equal
importance in building a representation.
a sampling
scheme with
periodic random
changes in the
grid width of a
spatially
systematic
sample
Spatial Interpolation:
“Intelligent Guesswork”
the process of filling in the gaps between
sample observations.
attenuating effect of distance between
sample observations
selection of an appropriate interpolation
function
Tobler’s law - nearer things are key, in a
smooth, continuous fashion
Pollution from an oil spill
Noise from an airport, etc.
(Artificial) Smooth & Continuous Variation:
contours equally spaced, along points of equal
elevation
Is Variation in Nature Always Smooth
and Continuous?
Graduate Student’s Corollary to Tobler’s 1st
Law of Geography
“The real world is infinitely complex, so why
bother?”
For true nature of geographic data, use other
interpolation methods and functions
IDW - nearer points given more importance
Sampling still important!!!
An Example from ArcGIS
Examine Attributes of Points
Choose Interpolation Parameters
IDW Interpolation
Hillshade ( hypothetical illumination )
to Better Visualize
Another set of sample points
Examine Attributes
Same Interpolation Parameters
Same IDW Interpolation
( but higher elevations skewed to right )
Hillshade
Comparison