NRPI 377

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NRPI 377
Tues 9/11/2006
Week 4 Lecture 7
Today's Topic
Projected Coordinate Systems (UTM State Plane)
Instructor Mike Gough E-mail GIS_at_mikegough.net

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What's the relationship again between a GCS and
a Datum?
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Review

• A GCS gives us a framework for defining locations
  on the surface of the earth.
• Latitude and Longitude values are established
  based on an associated datum.
• The size and shape of the ellipsoid (i.e., the
  ellipsoid that is used)
• The position of the ellipsoid relative to the
  center of the earth.
• The precise locations of a set of points
  (benchmarks) which are used to determine the
  location of all other points on the surface of
  the earth.

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1 layer in NAD83 1 in NAD27
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Review

• The size and shape of the ellipsoid (i.e., the
  ellipsoid that is used)
• IS DIFFERENT.

NAD27
NAD83
2) The position of the ellipsoid relative to the
center of the earth. IS DIFFERENT.
NAD27 A Local Datum Positions the ellipsoid to
best fit with Meades Ranch.
NAD83 A Geocentric Datum Aligns the ellipsoid
center with the center of the earth.
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Review

• Hence,
• 3) The coordinates for benchmark datum points
  will likely be different.
• 4) The coordinates that define the location of
  features in a GIS layer in GCS_NAD27 WILL LIKELY
  BE DIFFERNT than the coordinates that define the
  location of the same features in GCS_NAD83.

Datum Shifts (NAD83 NAD27)
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Coordinate Systems
The Graticule
Two Types of Coordinate Systems

• Geographic Coordinate systems
• Location on an ellipsoid is defined by latitude
  and longitude that specifies the angle between
  any point and the equator, and the angle between
  any point and the prime meridian.
• Projected Coordinate Systems
• Location on a flat surface is defined by
  Cartesian coordinates (i.e., x and y) that
  specify horizontal and vertical position.

x
y
Arcata
UTM 408,397 E 4,524,944 N
All projected coordinate systems are based on a
GCS
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In Theory...
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In Reality...

• Projecting Latitude and Longitude to UTM
• y northing K1 K2p2 K3p4, where
• K1 Sk0,
• K2 k0sin21" nu sin(lat)cos(lat)/2
• K3 k0sin41" nu sin(lat)cos3(lat)/24(5 -
  tan2(lat) 9e'2cos2(lat) 4e'4cos4(lat)
• x easting K4p K5p3, where
• K4 k0sin1" nu cos(lat)
• K5 (k0sin31" nu cos3(lat)/6)1 - tan2(lat)
  e'2cos2(lat)

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GCS_NAD27
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Use the project tool to project an unprojected
data set (i.e., something That is in lat, long)
to a projected coordinate system (e.g., UTM),
thus defining the location of your features on a
planar surface. Or to change the coordinate
system of your data set including its datum.
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Coordinate Systems

• From one projected coordinate system to another
  (same datums)

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Coordinate Systems

• From one projected coordinate system to another
  (different datums)

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Projected Coordinate Systems

• Many different projected coordinate systems
• UTM (Universal Transverse Mercator)
• Datum Must specify
• Units Meters
• Projections Transverse Mercator
• State Plane
• Datum Must specify
• Units Feet (sometimes meters)
• Projections Lambert Conformal Conic, or
  Transverse Mercator

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Projected Coordinate Systems

• Universal Transverse Mercator
• A Global Coordinate System
• Zones (1-60)
• 6 in longitude
• Extend from 80 south lat. to
• 84 north lat.
• Split North South of Equator
• Each specifies a unique
• Transverse Mercator
• Projection (the central
• meridians are different).
• Locations are defined on a Cartesian grid
• X distances Eastings
• Y distances Northings
• Units are meters

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Projected Coordinate Systems
Our neighbor Zone 11
N. California Zone 10 Central meridian -123 long
Central meridian -117 long
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UTM Zone 11N
Central Meridian -117 longitude
Northing Origin 0 at the equator Easting Origin
0 at 500,000 meters west of Central Meridian.
Location is specified in Eastings
Northings 397,800 meters E 4,922,900 meters N
11,N
Why did they put the Easting origin At 500,000
meters west of the Central meridian?
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Projected Coordinate Systems
Southern UTM Zones

• For Southern Zones the Northing Origin (false
  Northing) is 10,000,000 meters south of the
  equator.
• 10,000,000 meters south of the equator Northings
  0
• At the equator Northings 10,000,000.
• This ensures that only non-negative coordinate
  values are observed for southern UTM zones.

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Projected Coordinate Systems
Zone 14 (southern northern)
N
Easting Origin 500,000 meters west of CM
N
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Projected Coordinate Systems

• State Plane Coordinate System
• Only applicable in the U.S.
• Zones
• Defined by county, parish or other municipal
  boundaries.
• Different number of zones for each state.
• Sometimes identified by the Federal Information
  Processing System (FIPS) Codes.
• Two basic types of map projections
• The Lambert conformal Conic (for e w oriented
  states)
• Two standard parallels.
• Transverse Mercator (for n s oriented states).
• (Alaska also uses oblique Mercator).
• Units Feet (sometimes meters)
• Projection distortions are kept below 1 part in
  10,000

Minnesota
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Projected Coordinate Systems
Projections used for State Plane
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Projected Coordinate Systems
State Plane Zones By State
(Counties)
d
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Projected Coordinate Systems
State Plane Colorado North FIPS 0501
Establish a Zone Origin is usually established
2,000,000 ft to the west of the central meridian,
And at some distance to the south of the zone.
0,0
Distances from the origin are usually measured in
feet
2,164,606 feet E 392,285 feet N Col North
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Projected Coordinate Systems
State Plane California I FIPS 0401
Origin
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Eastings, Northings
,
,
,