The Nature of Geographic
Data
Based in part on Longley et al.
Ch. 3 and Ch. 4 up to 4.4
(Ch. 4 up to 4.6 to be covered in Lab 8)
Library Reserve #VR 100
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
Bears are easily conceived as discrete
objects, maintaining their identity as
objects through time and surrounded by
empty space.
(Hal Gage/Alaskastock/Photolibrary Group Limited)
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.
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
A
B
b
c
3
C
A
b
a
4
0
C
d
a
5
C
B
d
b
6
B
D
e
e
7
B
0
d
c
Poly No. of
ID
arcs
0
A
2
a
3
C
List of
arcs
A
3
-1, -2, 3
B
4
2,2,-7,
-7,5,5,6 -6
C
3
-3, -5, 4
D
1
6
c
1
4
6
D
e
b
5
B
d
7
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)
Why Topology Matters
Topological data structures very important in
GIS software.
Allows automated error detection and
elimination.
“Tolerances” important - features can move or
disappear
“snapping”, elimination, merging, etc.
Makes map overlay feasible.
Makes other kinds of spatial analysis possible.
Nodes that are close together are snapped.
An area (solid line) and its approximation by a polygon
(dashed line)
Raster representation:
Bathymetry
Raster representation
Each color represents a
different value of an integer
variable denoting land cover
class
Object/Vector Feature Types
Example of a BOUNDARY
PROBLEM:
Lakes are difficult to
conceptualize as
discrete objects
because it is often
difficult to tell where a
lake begins and ends,
or to distinguish a
wide river from a lake.
(Oliviero Olivieri/Getty Images, Inc.)
“Boundary Problem” Handled by Mixed Pixels
Effect of a raster
representation using:
(B) the central
point rule
(A) the largest
share rule
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!
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.
Spatial Autocorrelation and Scale
A Sierpinski carpet at two levels of resolution
(A) coarse scale
(B) finer scale In general, measures of
spatial and temporal autocorrelation are
scale dependent
Individual rocks may
resemble the forms of
larger structures, such
as rock outcrops or
eroded coastlines
(© PauloFerreira/iStockphoto)
The coastline of Maine,
at three levels of
recursion…
(A) the base curve of
the coastline
(B) approximation using
100-km steps
(C) 50-km step
approximation
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.
Tobler’s law - nearer things are key, in a
smooth, continuous fashion
Pollution from an oil spill
Noise from an airport, etc
Effect of distance between sample observations
(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?”
IDW - nearer points given more importance
Sampling still important!!!
Many other interpolation methods and
functions
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