Lecture 4
Understanding Coordinate Systems
Geographic Coordinate systems
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Spherical
Ellipsoidal
Curved
GCS
Projected coordinate systems
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(PCS)
2D
Flat
Planar
Cartesian
GCS
PCS
GCS has angular units of measure
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Degrees
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Radians
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2 pi per circle
~6.3 per circle (~57 degrees each)
Gradian
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360 per circle
Decimal degrees
Degree, minute, second
400 per circle
Gon
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Same as gradians
To some grad = degree
PCS has linear units of measure
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Linear units
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Meters
Feet
X and Y coordinates
Length, angles, and areas are constant
Y
Data
XY+
X+
Y+
usually here
X
XY-
X+
Y-
Map projection
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Math to transform GCS
Map projection
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Math to transform GCS to PCS
Flattening the earth – round to flat
Distortions make geographers SADD
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Shape, Area, Distance, and Direction
Plate Carrée projection
PCS properties example
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Name – NAD 1983 UTM Zone 11N
GCS – NAD 1983
Map Projection – Mercator
Projection parameters
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Central meridian, latitude of origin, scale factor,
false easting
Linear unit of measure (i.e., meters)
Geographic coordinate systems
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Mathematical model of a planetary body - spheroid
Parameters describe the spheroid shape
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Smooth, without imperfections
GCS for earth, planets, and more
GCS properties
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Spheroid
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Major and minor axis
Units (lat/long, radians, grads)
GCS properties
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Spheroid
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Major and minor axis
Units (lat/long, radians, grads)
Datum
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Spheroid’s position in relation to actual earth
Local datum: spheroid touches edge of earth, good fit there
Great
fit here
Bad fit
here
Local datum
GCS properties
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Spheroid
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Major and minor axis
Units (lat/long, radians, grads)
Datum
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Spheroid’s position in relation to actual earth
Local datum: spheroid touches edge of earth, good fit there
Earth-centered: spheroid and earth center match
All around
best fit for
the entire
planet
Great
fit here
Bad fit
here
Local datum
Earth-centered datum
GCS properties example
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Name
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European Datum 1950
Datum
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European Datum 1950
Spheroid
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Prime Meridian
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International 1924
Greenwich
Angular unit of measure
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Degrees
GCS with a local datum
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Spheroid
GCS with a local datum
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Datum
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Spheroid’s position in relation to actual earth
GCS with a local datum
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Datum
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Spheroid’s position in relation to actual earth
GCS with a local datum
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Datum
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Spheroid’s position in relation to actual earth
GCS with a local datum
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Datum
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Spheroid’s position in relation to actual earth
GCS with a local datum
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Datum
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Spheroid’s position in relation to actual earth
GCS with a local datum
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Datum
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Spheroid’s position in
relation to actual earth
Local datum: spheroid
touches edge of earth,
good fit there
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Bad fit on the other side
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GCS with an Earth Centered datum
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Spheroid
GCS with an Earth Centered datum
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Datum
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Spheroid’s center matched to earth center
GCS with an Earth Centered datum
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Datum
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Spheroid’s center matched to earth center
GCS with an Earth Centered datum
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Datum
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Spheroid’s center matched to earth center
GCS with an Earth Centered datum
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Datum
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Spheroid’s center matched to earth center
GCS with an Earth Centered datum
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Datum
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Spheroid’s center matched to earth center
GCS with an Earth Centered datum
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Datum
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Spheroid’s center
matched to earth center
Best fit all around the
earth
Common GCS parameters in use today (US)
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As measurement gets better, new GCS are defined
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NAD27 – parameters defined in 1866 (log tables)
NAD83 – parameters defined in 1979 (pre-GPS)
WGS84 – parameters defined in 1984 (GPS)
North American
Datum 1927
North American
Datum 1983
World Geodetic
Survey 1984
Warning: different geographic
coordinate system…
Geographic transformation
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Math to transform from one GCS to another
ESRI-Redlands
117 Degrees
34 Degrees
11 Minutes
3 Minutes
39.2 Seconds
23.1 Seconds
West
North
NAD 27
Geographic transformation
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Math to transform from one GCS to another
Changing GCS changes the lat/long for same point
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The same spot on earth has differing coordinates
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ESRI-Redlands
ESRI-Redlands
117 Degrees
34 Degrees
117 Degrees
34 Degrees
11 Minutes
3 Minutes
11 Minutes
3 Minutes
42.36 Seconds
23.14 Seconds
39.2 Seconds
23.1 Seconds
West
North
West
North
NAD 83
NAD 27
ArcMap’s GCS and PCS behavior
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Data frame - has both
Spatial data - has GCS, may have PCS
Metadata - prj, XML, mdb, or none
Tools that help
On-the-fly projection
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ArcMap data frames have a GCS and a PCS
 You should set them
 If not set, data frames take first layer’s GCS/PCS
Data frame: Bonne PCS
On-the-fly projection
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ArcMap data frames have a GCS and a PCS
 You should set them
 If not set, data frames take first layer’s GCS/PCS
If needed, new layers are projected on-the-fly (to match)
 If no CS metadata, new layer cannot be projected onthe-fly
Input layer: Robinson PCS
Data frame: Bonne PCS
ArcMap projects
data on-the-fly into
a data frame
GCS and PCS metadata for spatial
data
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Stored in internal geodatabase tables
Stored in projection files
 Shapefiles can have a .prj text file (e.g., streets.prj)
 Coverages can have a prj.adf text file (e.g.,
/rivers/prj.adf)
Stored optionally in XML files created by ArcCatalog
Non-native ESRI datasets use various other formats
Warning!
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GCS and PCS metadata is NOT required
You might get data that is missing its
coordinate system metadata
If researched and discovered, you can add it
If not, use Spatial Adjustment to move the
data into place
Spatial reference problems and solutions
Problem
Solution
 You know the coordinate system
information, but it is missing
 Define Projection tool
 The PCS is defined correctly,
 Project tool or data frame
project on-the-fly
but is not the one you need
 The GCS is defined,
but it is not NAD27 or NAD83
 Project tool or set a geographic
transformation in the data frame
properties