Geodesy, Coordinate Systems, and Map Projections

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Geodesy, Coordinate Systems, and Map Projections
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Objectives

• Introduce you to the main concepts of geodesy
  coordinate systems, datums, ellipsoids, and
  geoids
• Describe map projections and coordinate systems
  we use in GIS

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Geodesy (science of measuring the size and shape
of the earth)
Main Entry geodesy Pronunciation
jE-'ä-d-sEFunction nounEtymology Greek
geOdaisia, from geO- ge- daiesthai to divide
Date 1570 a branch of applied mathematics
concerned with the determination of the size and
shape of the earth and the exact positions of
points on its surface and with the description of
variations of its gravity field- geodesist
/-d-sist/ noun
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Geoid Even if the earth was completely covered
with water and there were no wind or waves, the
surface of the earth would not so nice as to
conform to an ellipsoid
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Why? Because there are variations in the
gravitational pull of the earth, which causes
dimples and moles
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Neither Ellipsoid nor Geoid are the Same as
the Earth Surface
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The Geoid shape is determined empirically, that
is, it is measured (from boats, planes, and
autos) Over most of the Earth this undulating
geoid varies by less than 100 meters from the
ellipsoid. It is this geoidal variation that is
the caused different ellipsoids to be used)

• So now we have three surfaces to keep track of at
  each point on terra firma
• the ellipsoid
• the geoid, and
• the actual physical surface

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Earths is Flattened - an Ellipsoid Two radii
semi-major (through Equator) semi-minor
(through poles)
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There are different ellipsoids used by different
countries because the Earth shows local
departures from an ideal ellipsoidal shape.
  The Earth geoid exhibits many surface
undulations, not easily defined mathematically.
Thus, different mathematical equations for the
ellipsoid fit these undulations well on one part
of the planet, while sacrificing accuracy in
another. geoid The equipotential surface of
the Earth's gravity field which best fits, in a
least squares sense, global mean sea level
http//www.ngs.noaa.gov/GEOID/geoid_def.html
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Ellipsoids adopted by various countries have been
"named", i.e., Clarke 1866, Bessel, Clarke
1880   Some ellipsoids seemed to "fit" local
conditions (geodesy and political) better than
others.
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The Clarke Spheroid of 1866 fit the globe surface
in North America well and was the official
surface adopted by the U.S., Mexico, and Canada
from 1879 until 1983. Recently these governments
have shifted to a geoid known as GRS80, for the
geodetic reference system of 1980. The
equatorial and polar radii for GRS80 are 6,378.1
km. and 6,356.7 km., respectively.
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Why all three? Because how we define horizontal
and vertical coordinates depends on the ellipsoid
and geoid We use Our north-south and east-west
(X-Y) coordinate system is defined in terms of
the ellipsoid Our vertical height (Z) is defined
relative to the geoidal height
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• Geographic Coordinates
• So far, we've discussed the shape of the earth,
  without worrying about specifying locations.
• Distances between points, and hence locations,
  depend on the earth's shape.
• Generally, location is defined in three
  dimensions, the X, Y, and Z
• X often, but not always, approximately east-west
• Y often, but not always, north-south
• Z usually vertical ray relative to earth's
  center, or local geoidal surface

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Coordinate Systems

• Cartesian (right angle)
• 2-Dimensional X approx. East
• Y, approx. South
• 3-Dimensional Z vertical from Earth Surface
• Geographic (angular coordinates)
• Angular coordinates can specify a location on
  Earth, often degrees of Latitude and Longitude.

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Geographic Coordinates Origin at Greenwich Observ
atory and Equator
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As latitude changes, surface distance changes
little at equator, 1 degree 110.5 km (68.7
mi) at poles, 1 degree 111.7 km (69.4
mi) Distance changes considerably with
longitude, at equator, 1 degree 111.3 km
(69.2 mi) at poles, 1 degree 0 km Geographic
coordinates are uniquely defined for each point
on the earth
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In practice, we know the exact longitude of only
one point on earth. The Greenwich observatory,
which is defined to have a longitude of
zero.   We don't know the exact latitude of
anyplace on earth.
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Not to say we don't have precise measurements of
latitudes.   Latitudes can be measured to nearest
millimeter using proper techniques
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Astronomical Observations
Optical observation of celestial bodies.
Precise timing signal, plus correction for
atmospheric distortion
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Local horizontal and vertical location surveys
use this network of control points as a starting
point. The set of precisely surveyed points is
known as a Geodetic Control (NGS) Network, also
called a Datum NGS is the National Geodetic
Survey Datum a set of constants use to define
a coordinate system (i.e. equatorial polar
radii of the ellipsoid and starting point for
locations of latitude and longitude). Main
Entry datum Pronunciation 'dA-tm, 'da-,
'dä-Function nounEtymology Latin, from neuter
of datusDate 16461 plural data /-/
something given or admitted especially as a basis
for reasoning or inference2 plural datums
something used as a basis for calculating or
measuring Source (http//www.m-w.com/cgi-bin/di
ctionary)
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How do you know where to look for these NGS
control points? NGS has a "bluebook", a registry
of control. Most state, county, and local
surveyors know where local control is, can access
bluebook. What do survey points look
like? Usually bronze disks, about 3" diameter,
NAD or NAVD stamped on top, but may be chiseled
squares or circles, iron posts, other long-term
marks This network then used as starting point
for precise local surveys, e.g., property line
surveys
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Benchmarks Brass disk Chisel marks Rock
piles Buried monuments Must be
recoverable by field surveyor
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Defining a Datum
Horizontal Datum
Specify the ellipsoid Specify the coordinate
locations of features on this ellipsoidal surface
Vertical Datum
Specify the ellipsoid Specify the Geoid which
set of measurements will you use, or which model
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Specifying a Horizontal Datum

• Measure positions (celestial observations,
  surveys, satellite tracking)
• Adjust measurements to account for geoid,
  determine position on adopted ellipsoid

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Specifying a Horizontal Datum
A horizontal datum is a reference ellipsoid, plus
a precisely-measured set of points that establish
locations on the ellipsoid. These points define
the reference surface against which all
horizontal positions are measured
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Defining the Horizontal Datum

• Horizontal datums are determined from the
  measurement an analysis of large survey networks
• Define the shape of the Earth (the ellipsoid)
• Define the location of a set of known points
  control points for which the position on the
  ellipsoid is precisely known
• This is the reference surface and network against
  which all other points will be measured

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Datum, Survey Network

• Historically
• Triangulation Network
• Astronomical observation
• Initial, intermittent, and ending baselines
• Multiple, redundant angle measurements
• Why these technologies?
• Easy to measure angles
• Difficult to measure distance accurately
• Time consuming to measure point position
  accurately

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There are two horizontal control networks
commonly referred to North American Datum of
1927 (also NAD27) North American Datum of 1983
(also NAD83), to replace NAD27
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Survey Network, 1900
(from Schwartz, 1989)
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North American Datum of 1927, NAD27 based on
approximately 26,000 measured points, used the
Clarke 1866 spheroid, held the latitude/longitude
fixed for a starting point in Kansas
NAD27 survey network
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Survey Network, 1981
(from Schwartz, 1989)
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NAD83 successor to NAD27, involving approximately
250,000 measurement points in network, involving
over 2 million distance measurements   NAD83
referenced to GRS80 ellipsoid, held no fixed
stations    
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There is a separate surveys for vertical control
points   Like horizontal, but referenced to
standard elevation (something like mean sea
level), and established using vertical
leveling Like horizontal, but referenced to
standard elevation (something like mean sea
level), and established using vertical
leveling  Again, two major vertical
datums,  North American Vertical Datum of 1927
(NAVD29), and an update,  North American Vertical
Datum of 1988 (NAVD88)
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Horizontal Survey Benchmarks
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Welcome to the Planet Earth CreditApollo17Crew,NA
SA
http//antwrp.gsfc.nasa.gov/apod/ap990131.html
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The earth's surface is curved - how to make a
flat map?
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The earth's surface is curved - how to make a
flat map?
MAP PROJECTION
A systematic rendering of points from the earth
to points on a flat sheet  
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The earth's surface is curved - how to make a
flat map?
MAP PROJECTION
A systematic rendering of points from the earth
to points on a flat sheet   (Think of it as
passing rays of light from some point through the
globe and onto the map surface)
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Categorized by the location of projection
source Gnomonic - center of globe   Stereographic
- at the antipode   Orthographic - at infinity
Sourcehttp//www.fes.uwaterloo.ca/crs/geog165/map
proj.htm
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Note in figure, points A and B are projected
inward, and are relatively closer together on map
than on earth surface
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Points C and D are projected outward, and are
relatively farther apart than on earth surface
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Two Most Common Projection Types 1) Transverse
Mercator 2) Lambert Conformal Conic
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1) Transverse Mercator Projections,   2) Lambert
Conformal Conic   Both are used to define a
standard coordinate set for each state, known as
the State Plane Coordinate System  

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For each state, the chosen map projection and
zones are tailored to the state.   For the
Lambert CC, the cone intercepts the globe at two
lines of latitude (parallels) running
east-west   The two lines chosen, along with a
couple of other parameters, determine the
particular Lambert CC for that zone. An origin
is defined, usually south and west of any point
in the zone, and assigned a X (northing) and Y
(easting) values of 0.   In this way, all
coordinates are kept positive.
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For the transverse mercator, the meridians where
the cylinder is centered and where the cylinder
intersects the globe are used to define the
state/zone projection Zone boundaries,
meridans, and other parameters are chosen to
maintain distortion in distance measurement to
less than 1 part in 10,000   This means zones are
less than about 160 miles (266 km) wide. Error
between measuring distance on ground and distance
on projected surface will be approximately 1 foot
every two miles.
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• UTM
• Universal Transverse Mercator
• 60 zones
• 6 degrees wide
• Extends from 80 degrees S latitude to 84
  degree N
• Numbered easterly from 180
• Considerable data from US Federal government is
  in UTM
• Central Meridian set at 500,000 E
• Equator is 0 N

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UTM Universal Transverse Mercator Measured in
meters To avoid using negative numbers as
coordinates, the east/west origin is placed
500,000 meters west of the Central Meridian of
the zone. Often the is called a false
easting False northing established for the
Southern Hemisphere zones the Equator (the
origin) is set at 10,000,000m coordinates
increment northward from the South Pole.
(avoiding negative values)
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UTM Measurements of distance, shape area with
.04 or less distortion. Grid allows a slight
tilt from True North. UTM grid declination
Source http//www.okono.com/coordinates.html
Declination east compass least Declination west
compass best
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Coordinate Systems Notation Latitude/Longitude D
egrees Minutes Seconds 45 3' 38" N Degrees
Minutes (decimal) 45 3.6363' N Degrees
(decimal) 45.0606 N State Plane
(feet) 2,951,384.24 N UTM
(meters) 4,996,473.72 N
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UTM Coordinates (meters) Common DRG
format 530421m E Easting (East of the zone
meridian remember false easting
concept) 5176641m N Northing (North of the
Equator) Standard UTM 15N 530421E 5176641N
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Start ArcMap Open P\ENR3031-5031\images\Iverson_C
.tif
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Lecture Question Using in the map Estimate the
coordinates of the SW corner of Section 11 (T
49N, R 18W, 4th PM) Where is it using UTM
coordinates? If you can also try
Latitude/Longitude (DMS)?
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Lecture Question Using in the map Estimate the
coordinates of the SW corner of Section 11 (T
49N, R 18W, 4th PM) 15N 530816.63E
5175698.97N Where is it using UTM
coordinates? If you can also try
Latitude/Longitude (DMS)? 92 35' 48'' W 46
44' 10'' N