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...
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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
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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
Data Models and Data Structures
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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)
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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.
The discrete object view leads to a powerful way of representing geographic information about objects
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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.
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Vectors (Arcs) and TopologyVectors 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
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A
C B
1
2
3
4
5
0
D6
ab
c
d
e7
Arc
ID
L e f t
Poly
R t
Poly
From
n o d e
T o
n o d e
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
ID
No. of
arcs
List of
arcs
A 3 - 1 , - 2 , 3
B 4 2, -7, 5, -6
C 3 - 3 , - 5 , 4
D 1 6
2, -7, 5, 6
Connectedness, Adjacency, Contiguity, Geo-Relational
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Topology
Science and mathematics of geometric relationships
Simple features + topological rulesConnectivityAdjacencyShared nodes / edges
Topology needed byData validationSpatial analysis (e.g., network tracing, polygon adjacency)
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Why Topology MattersTopological 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.
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Nodes that are close together are snapped.
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An area (solid line) and its approximation by a polygon (dashed line)
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Raster representation:Bathymetry
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Each color represents a different value of an integer variable denoting land cover class
Raster representation
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Object/Vector Feature Types
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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.)
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Effect of a raster representation using:
“Boundary Problem” Handled by Mixed Pixels
(A) the largest share rule
(B) the central point rule
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Rasters and VectorsVector-based line
4753456 6234124753436 6234244753462 6234784753432 6234824753405 6234294753401 6235084753462 6235554753398 623634
Flat File
Raster-based line
00000000000000000001100000100000101010000101000011001000010100000000100010001000000010001000010000010001000000100010000100000001011100100000000100001110000000000000000000000000
Flat File
Now YOU!
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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-economic,
environ. sampling
Applications Resources,
enviromental
Socio-economic,
administrative
Software Raster GIS, image
processing
Vector GIS, autom.
Cartography
Resolution Fixed Variable
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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.
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triangulation
Courtesy www.ian-ko.com/resources/triangulated_irregular_network.htm
TIN surface
pseudo 3D
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Spatial Autocorrelation
Arrangements of dark and light colored cells exhibiting negative, zero, and positive 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
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(A) coarse scale
(B) finer scale In general, measures of spatial and temporal autocorrelation are scale dependent
A Sierpinski carpet at two levels of resolution
Spatial Autocorrelation and Scale
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Individual rocks may resemble the forms of larger structures, such as rock outcrops or eroded coastlines
(© PauloFerreira/iStockphoto)
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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
(D) 25-km step approximation.
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Sampling: The Quest to Represent the Real World
a spatially random sample
a spatially systematic (stratified)
sample
a stratified random sample
a sampling scheme with
periodic random changes in the grid width of a
spatially systematic
sample
Field - selecting discrete objects from a continuous surface
Object - selecting some discrete objects, discarding others
Spatially systematic sampling presumes that each observation is of equal importance in building a representation.
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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 spillNoise from an airport, etc
Effect of distance between sample observations
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(Artificial) Smooth & Continuous Variation:contours equally spaced, along points of equal elevation
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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 importanceSampling still important!!!Many other interpolation methods and functions
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An Example from ArcGIS
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Examine Attributes of Points
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Choose Interpolation Parameters
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IDW Interpolation
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Hillshade ( hypothetical illumination ) to Better Visualize
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Another set of sample points
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Examine Attributes
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Same Interpolation Parameters
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Same IDW Interpolation( but higher elevations skewed to right )
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Hillshade
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Comparison
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