Chapter2 is344(gis db map-projections,structures, and scale))(amended)

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Abdisalam Issa-Salwe, Taibah University
Michael G. Wing and Pete Bettinger (2008): Geographic Information Systems: Applications in Natural Resource Management,
2nd Editon. Oxford University Press.
GIS Databases:
Map Projections, Structures,
and Scale
(IS344)
Chapter 2
Abdisalam Issa-Salwe
Information Systems Department
College of Computer Science & Engineering
Taibah University
Chapter 2 Objectives
 Definition of a map projection, and the components that
comprise a projection
 Components and characteristics of a raster data
structure
 Components and characteristics of a vector data
structure
 The purpose and structure of metadata
 Types of information available on a typical topographic
map and
 Definition of scale and resolution as they relate to GIS
databases
Abdisalam Issa-Salwe, College of Computer Science & Engineering, Taibah University
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Big questions…
 What is the size and shape of the earth?
 Geodesy: the science of measurements
that account for the curvature of the earth
and gravitational forces
 We are still refining our approximation of
the earth’s shape but are relying on GPS
measurements for much of this work
3
Syene
Alexandria
Vertical
712’
Earth
Rays parallel
to the sun
712’
Figure 2.1. Eratosthenes’ (276-194 BC) approach to determining the Earth’s
circumference.
360 / 712’ = 1/50
500 miles * 50 = 25,000
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a
b
Ellipsoid
Equator
North Pole
Figure 2.2. The ellipsoidal shape of the Earth deviates from a perfect
circle by flattening at the poles and bulging at the equator.
Isaac Newton (end of the 17th century) theorized this shape.
Field measurements, beginning in 1735, confirmed it.
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Earth measurements & models
 Datums
Horizontal and vertical control measurements
 Ellipsoids (spheroids)
The big picture
 Geoids
Gravity and elevation
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Horizontal Datums
 Geodetic datums define orientation of the
coordinate systems used to map the earth
 Hundreds of different datums exist
 Referencing geodetic coordinates to the wrong
datum can result in position errors of hundreds
of meters.
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Spheroids
 Newton defined the earth as an ellipse rather
than a perfect circle (1687)
 Spheroids are all called ellipsoids
 Represents the elliptical shape of the earth
 Flattening of the earth at the poles results in
about a twenty kilometer difference at the poles
between an average spherical radius and the
measured polar radius of the earth
 Clarke Spheroid of 1866 and Geodetic
Reference System (GRS) of 1980 are common
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Geoids
 Attempts to reconcile the non-spherical shape
of the earth
 Earth has different densities depending on
where you are and gravity varies
 A geoid describes earth’s mean sea-level
perpendicular at all points to gravity
 Coincides with mean sea level in oceans
 Geoid is below ellipsoid in the conterminous US
 Important for determining elevations and for
measuring features across large study areas
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Figure 2.3. Earth, geoid, and spheroid surfaces
Spheroid
Geoid
Earth
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Coordinate Systems
 Used to describe the location of an object
 Many basic coordinate systems exist
 Instrument (digitizer) Coordinates
 State Plane coordinates
 UTM (Universal Transverse Mercator) coordinate
system
 Geographic
 Rene Descartes (1596-1650) introduced
systems of coordinates
 Two and three-dimensional systems used in
analytical geometry are referred to as
Cartesian coordinate systems
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1 2 3 4 5 6 7 8 9
9
8
7
6
5
4
3
2
1
0
2,6
6,1
x
y
Figure 2.4. Example of point locations as identified by Cartesian coordinate geometry.
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Equator
Prime
meridian
W E
N
S
30°N, 30°W
30°S, 60°E
Figure 2.5. Geographic coordinates as determined from
angular distance from the center of the Earth and
referenced to the equator and prime meridian.
0° latitude
90° South latitude
90° North latitude
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Geographic coordinates
 Longitude, latitude (degrees, minutes,
seconds)
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Map Projections
 Map projections are attempts to portray the
surface of the earth or a portion of the earth
on a flat surface
 Earth features displayed on a computer monitor or
on a map
 Earth is not round, has a liquid core, is not static,
and has differing gravitational forces
 Distortions of conformality, distance,
direction, scale, and area always result
 Many different projection types exist:
 Lambert, Albers, Mercator
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Map projection process: 2 steps
 Measurements from the earth are placed
on a globe or curved surface that reflects
the reduced scale in which measurements
are to be viewed or mapped
This is the reference globe
 Measurements placed on the three-
dimensional reference globe are then
transformed to a two-dimensional surface
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Envisioning map projections
 Transforming three-dimensional earth
measurements to a two-dimensional map sheet
 Visualize projecting a light from the middle of the
earth and shining the earth’s features onto a
map
 The map sheet may be:
 Planar
 Cylindrical
 Conic
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Figure 2.6. The Earth’s graticule projected onto azimuthal, cylindrical, and
conic surfaces.
Azimuthal Cylindrical Conic
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Figure 2.7. Examples of secant azimuthal, cylindrical, and conic map
projections.
Azimuthal Cylindrical Conic
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Map projections within GIS
 There are several components that make up
a projection:
 Projection classification (the strategy that drives
projection parameters)
 Coordinates
 Datum
 Spheroid or Ellipsoid
 Geoid
 Most full-featured GIS can project coordinate
systems to represent earth measurements on
a flat surface (map)
 GIS software handles most projections
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Map projection importance
 GIS analysis relies strongly on covers being in
the same coordinate system or projection
 Do not trust “projections on the fly”
 This is the visual referencing of databases in different
projections to what appears to be a common
projection
 Failure to ensure this condition will lead to bad
analysis results
 You should always try to get information about
the projection of any spatial themes that you
work with
 Metadata- Data about data
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The classification of map projections
according to how they address distortion
 Conformal
 Useful when the determination of distances or angles
is important
 Navigation and topographic maps
 Equal area
 Will maintain the relative size and shape of landscape
features
 Azimuthal
 Maintains direction on a mapped surface
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Figure 2.8. The orientation of the Mercator and transverse Mercator to the
projection cylinder.
Mercator
transverse Mercator
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Common Map Projections
 Lambert (Conformal Conic)- Area and shape are
distorted away from standard parallels
 Used for most west-east State Plane zones
 There is also a Lambert Azimuthal projection that is
planar-based
 Albers Equal Area (Secant Conic)-
 Maintains the size and shape of landscape features
 Sacrifices linear and distance relationships
 Mercator (Conformal Cylindrical)- straight lines on
the map are lines of constant azimuth, useful for
navigation since local shapes are not distorted
 Transverse Mercator is used for north-south State Plane
zones
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126°W 120°W 114°W 108°W 102°W 96°W 90°W 84°W 78°W 72°W 66°W
10 11 12 13 14 15 16 17 18 19
Figure 2.9. UTM zones and longitude lines for
the U.S.
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Where do coordinates come from?
 Many measurements
 Initially these are manual measurements
The Public Land Survey System (PLSS)
within the U.S.
The Dominion Land Survey within Canada
 GPS is now used to refine measurements
and support coordinate systems
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GIS software has Projection Capabilities
 GIS software Projection Abilities
GIS software will allow you to project
shapefiles
Example, ArcEditor and ArcInfo will allow you
to project shapefiles and coverages
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GIS software Response to Projection
Mismatch
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Projection information
 Within GIS software, you can examine
projection information (if it exists) by
examining a layer’s properties
 Without the projection information, you’ll
need to do detective work
Probability for success: low
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Two primary GIS data structures: Raster
& Vector
 Two different approaches to capturing and
storing geographic data
 “Yes raster is faster, but raster is vaster,
and vector just seems more corrector.” C.
Dana Tomlin 1990
 Decision to use one or both structures will
be based on project objectives, existing
data, available data, and monetary
resources
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Raster or grid cell
Columns
Rows
Figure 2.10. Generic
raster data structure.
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Raster data
 Many different types of raster data
Satellite imagery
 Landsat TM, IKONOS, AVHRR, SPOT
Aerial imagery
 LIDAR, color and infrared digital photographery
Digital raster graphics (DRGs)
Digital orthophoto quadrangles (DOQS)
32

17
Figure 2.11. Landsat 7 satellite image captured using the
Enhanced Thematic Mapper Plus Sensor that shows the Los
Alamos/Cerro Grande fire in May 2000. This simulated natural
color composite image was created through a combination of
three sensor bandwidths (3, 2, 1) operating in the visible
spectrum. Image courtesy of Wayne A. Miller, USGS/EROS Data
Center.
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Figure 2.11 Digital elevation model (DEM).
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Figure 2.12. Digital orthophoto quadrangle (DOQ).
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Figure 2.13. Digital raster graphics (DRG) image.
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Figure 2.14. Corvallis Quadrangle with neatlines around map areas to be
described in detail.
Figure 2.17 Figure 2.19
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Figure 2.15. Lower right-hand corner of the Corvallis Quadrangle.
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Scale Standard
1:1,200 ± 3.33 feet
1:2,400 ± 6.67 feet
1:4,800 ± 13.33 feet
1:10,000 ± 27.78 feet
1:12,000 ± 33.33 feet
1:24,000 ± 40.00 feet
1:63,360 ± 105.60 feet
1:100,000 ± 166.67 feet
Table 2.16. Map scales and associated National Map Accuracy Standards
for horizontal accuracy.
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Vector data structure
 In contrast to raster, not necessarily
organized in a pattern
 Vector data are usually irregular in shape
and represent precise locations
 The vector world is organized using three
basic shapes
points, lines, and polygons
referred to as the GIS feature model
40

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Figure 2.17. Point, line, and polygon vector shapes.
Point Line
Polygon
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Topology
 The spatial relationships between points,
lines, and polygons
 Determines
Distance between points
Whether lines intersect
Whether points, lines, or polygons are within
the extent of a polygon
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Figure 2.18. Examples of adjacency, connectivity, and
containment.
Adjacent polygons
Connected stream
network
One polygon contained inside
another polygon
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Topological building blocks
 Topology needs to be coded and
described mathematically
 Most GIS programs will have database
tables that describe topology
 All vector shapes must be isolated and
located using a coordinate system
44

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Figure 2.19. Examples of nodes, links, and vertices.
Node
Vertex
Link
45
Link Begin
node
End node Left
polygon
Right
polygon
1 1 5 A C
2 5 6 A E
3 1 2 C B
4 2 4 C D
5 4 3 E D
6 3 2 B D
7 3 6 E B
Node X Y
1 1.1 4.2
2 3.4 5.2
3 4.4 2.5
4 8.1 5.7
5 8.9 9.9
6 4.7 1.1
1
2
4
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3 2
4
5
AB
C
D
Y
X
6
7
3
6
E
Figure 2.20. Vector topological data. Network of nodes, links, and
polygons (a), node coordinate file (b), and topological relationship file.
a. Network
of nodes,
links, and
polygons
b. node coordinate file
c. topological relationship file
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Figure 2.21. Examples of topological errors. In the
first (a), an undershoot has occurred and instead of a
closed figure creating a polygon, a line has been
created. In the second (b), a small loop has been
formed extraneously adjacent to a polygon. This
might represent a digitizing error or the result of a
flawed overlay process.
a. An un-closed polygon
b. An extraneous polygon
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Raster & vector: must I choose one?
 These are complimentary data structures and
you will use both if you conduct GIS analysis
 More commonly, GIS software will allow you to
read both data types
 Some software (GIS software) will allow you to
analyze both types simultaneously
 Demonstrated in chapters 13 and 14
 Not uncommon for some analysts to convert
from one structure to another
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.
.
.
.
.
Figure 2.22. Point, line,
and polygon features in a
raster or grid
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(a)
(b)
(c)
A forest stand boundary in vector
format (a) scanned or converted
to a raster format using 25 m grid
cells (b), then converted back to
vector format (c) by connecting
lines to the center of each grid
cell.
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Characteristic Raster Vector
Structure complexity simple complex
Location specificity limited not limited
Computational efficiency high low
Data volume high low
Spatial resolution limited not limited
Representation of topology difficult not difficult
among features
Summary of Raster and Vector Characteristics
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Other types of data structures/models
 Other hybrid forms of data structures exist
 May help you solve spatial analysis
challenges
 TINs
 Landforms
 Regions
 Area
 Routes
 Linear features
Abdisalam Issa-Salwe, College of Computer
Science & Engineering, Taibah University 52

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Triangular Irregular Network
 Triangles to represent earth surfaces
 A generic (not dominated by a specific software
manufacturer ) reference to a data structure that
is similar to vector yet possesses
 An alternative to raster in representing
continuous surfaces
 May help reduce some of the ambiguities
presented by a raster structure
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Figure 2.23. McDonald Forest (perspective view from SW corner)
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Regions
 Not all GIS software can accommodate
regions
 GIS software can
 Allows for overlapping polygons
 May reduce database complexity
 Large woody debris study
55
Figure 2.24. Large Woody Debris
 One record for
each log
possible
 Reduces data
storage needs
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Routes
 Dynamic Segmentation
Traditionally linked to ESRI products
 For linear networks but can also handle
points
 Stream habitat
 Delivery / emergency routing
 Recreation use patterns
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Routes Example: Aquatic Habitat Database
 One record to
represent the many
links that make up
a primary channel
 Simplify structures
 Reduce data
storage redundancy
Abdisalam Issa-Salwe, College of Computer
Science & Engineering, Taibah University 58

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Map scale and resolution
 GIS databases are often described in
terms of their scale or resolution
 These terms make reference to the source
data that was used to create the GIS
database
 Scale and resolution will often provide
guidance in the application of a GIS
database for specific purposes
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Map Scale
 Scale is the relationship between a linear
feature on a map or photograph and the
actual distance on the ground
 Scale is usually expressed as a
representative fraction
 1:24,000
 One inch on the map or photograph represents 24,000
inches (or 2000 feet) of on the ground distance
 1:200,000
 One cm on the map or photograph represents 200,000
cm (or 2000 m) of on the ground distance
 Scale plays a strong role in determining the
proper use of a spatial database
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Map Scale
 Do not confuse the scale of a spatial data layer
with how closely you are zoomed in on it
 Scale is tied to on the ground measurements
 Most scale measurements of vector data usually
come to us from the scale derived from aerial
photograph measurements
 A relationship between the focal length of the camera
lens and the height of the lens above terrain
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Resolution
 With raster data, scale is often expressed
in terms of resolution or the amount of
ground that each side of a pixel, or cell,
covers
Measurements typically are the same on all
sides of a pixel or cell
1 meter, 10 meter, 30 meter
 These measurements are squared to represent
area
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Map Scale
 Relative size of scales is dependent on the
representative fraction
1:24,000 is considered a large-scale map
1:100,000 is usually considered a small scale
map, at least in comparison to 1:24,000
 You may also use the terms fine and
coarse-scale resolution to avoid confusion
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1:100,000 map 1:24,000 map
Figure 2.25. Map of stream network displayed at scales of 1:100,000 and
1:24,000.
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Map Scale and Resolution
 Be wary of mixing data themes that are
drawn from widely different scales or
resolutions
Mixing 1:24,000 scale data with 1:250,000 is
probably not a good idea
Sometimes, there may be no alternatives and
you’ll have to take “your best shot”
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