Coordinate Systems, Datums and
Map Projections
Geodesy
The study of the size and shape of the
Earth.
The Earth is…
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3000 BP Bablonians
An oyster
600 BP Greeks
Flat
500 BP a perfect shape A sphere
300 BP Circumference ~ 25,000 miles,
Dark ages
Flat again
1492 Columbus
A pear
1753 French
Oblate ellipsoid
Spheriod
Geoid to describe the deviations from a
spheriod
The Earth as a Geoid
Geographic Coordinate System
•Parallels
•Meridians
•Great and Small Circles
Geographic Coordinate System
GCS uses a 3-D spherical
surface to define locations
on Earth.
GCS includes an angular unit
of measure, a prime meridian
and a datum.
Geographic Coordinate System
• Longitude and Latitude
– Degrees, minutes, seconds
– 1o latitude = ~110.5 km (equator)
– 1o longitude = cosine of the
latitude
– 1 minute of latitude = ~1852
meters
How to convert form DMS to DD
• Example: 37°36’30”
• Divide each value by the number of
minutes or seconds in a degree
• 36 minutes = .60 degrees (36/60)
• 30 seconds = .00833 degree (30/3600)
• Add it all up
• 37° + .60 + .00833 = 37.60833 DD
Sphere vs. Speroid
A sphere is okay for small scale maps (<1:5,000,000).
For larger scale maps a spheroid is necessary, the spheroid used
will depend upon the purpose, location, and accuracy of the data.
Datums
• Reference frame for locating points on
Earth’s surface
• Defines origin & orientation of
latitude/longitude lines
• Defined by spheroid and spheroid’s
position relative to Earth’s center.
Position of the Capital of Texas
N. American Datums
• NAD27
– Clarke 1866 spheroid
– Meades Ranch, KS
– Local datum
• NAD83
– GRS80 spheroid
– Earth-centered datum
– GPS-compatible
• NAD27
NAD83 up to 500’ shift
Datums and Elevation
• Horizontal and Vertical Datums
• Sea - level?
– Panama Canal
• Height Above Ellipsoid (HAE)
• Height Above Geoid (HAG)
A spherical planet in plane terms
Projected coordinate systems are any coordinate system designed for
a flat surface.
Map Projection
• Distortions are inherent in maps
– Earth is round, map is flat
• Projection is the term used to describe
the process of mapping a round surface to
flat paper
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Projection & Datum Overview
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Earth is three-dimensional
Map (screen) is 2-D
Projections convert 3-D to 2-D
3-D to 2-D causes distortions
Datums locate in 3-D
Map Projections
• Map projections always introduce
distortion of some kind
• Distance
• Direction
• Shape
• Area
Map Projections, cont.
• There are many kinds of projections
for different parts of the world
• Different projections produce
different distortions
• Key is choosing appropriate
projection for a particular situation
Map Projections Types
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Map Projections and GIS, cont.
• Should be considered before starting to
automate GIS data or starting a GIS
project
• Must also be considered if you obtain
data from other sources (who doesn’t?)
• Map projections are central to insuring
different GIS databases properly register
to one another (really important in GIS!)
• Important for valid spatial analysis
The State Plane Coordinate System (SPCS)
• Not a true map projection but rather a set
of coordinate systems for every state.
• Designed in the 1930s to provide a local
reference system tied to a national datum.
• Most USGS 7.5 minute maps indicate state
plane coordinates (as well as UTM, and
lat-long grid)
• Some states (depending on size and
latitudinal extent) have multiple zones
State Plane Zones for NAD 1983
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The State Plane Coordinate System (SPCS), cont.
• East-West oriented States use the Lambert
Conformal Conic projection (ex. Tennesse)
• North-South oriented States use the
Transverse Mercator projection (ex.
Illinois)
• One zone in Alaska uses Oblique Mercator
• Based on the North American Datums:
NAD27 and NAD83
• Reference Eastings and Northings
UTM
Universal Transverse Mercator
• Transverse Cylindrical (Mercator) Projection
• 60 zones
– 6o wide
– Central meridian is 500,000 m
• Eastings
– 0 is 500,000m west of central meridian
• Northing
– depends on hemisphere and is measured in meters from the
equator
• We are in Zone 10 N
UTM Zones
A Generic UTM Zone
Central Meridian
Easting = 500,000
meters
Equator:
Northern Hemisphere:
Northing = 0 meters
Northern
Hemisphere
Origin
Southern Hemisphere:
Northing = 10,000,000
meter
Southern
Hemisphere
Origin
X
We are in UTM zone 10 north
Basic Feature of Maps
• Scale can never be totally accurate all over the
map, unless the map covers a very small area.
• Features: Title, Date, Legend (key), North
Arrow (magnetic vs. true north)
Map Characteristics
• Scale
– Ratio between distance on map to distance on Earth
– Small scale - cover large area
• e.g. 1 : 1,000,000
– Large scale - shows more detail
• e.g. the 1 : 2,400
– Types: Representative fraction, linear, verbal
• Resolution
– accuracy that location and shape can be depicted
– Diminishes with scale
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Topographical vs. Thematic Maps
• Topographical
– Maps whose primary purpose is to indicate the
general lay of the land
– outline natural features
– topographical maps often show other features
such as roads, boundaries, rail links
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Topographical vs Thematic Maps
• Thematic Maps
– displays geographic concepts
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population density
climate
land use
etc.
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Types of Thematic Maps
• Chloropleth Maps
– maps that display information using man-made
reporting areas. Areas shaped according to
their value.
• census tracts, ZIP codes, counties, etc.
• Area Class Maps
– maps that display information by constant
attribute
• e.g. coniferous Vs deciduous forest
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Types of Thematic Maps
• Isopleth (Isoline) Maps
– maps showing imaginary surfaces -connects all
points with equal value.
• contours
• pressure
• temperature
• pollution levels
• Isolines are:
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drawn at regular intervals
never cross
they are closed lines
values inside are higher than outside
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