NATIONAL SPATIAL REFERENCE SYSTEM

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Basic Geodesy
Merriam-Webster  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
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Basic Geodesy
Basically it is what we use to geo-reference or
position our civil works projects with respect to
other related projects such as SLOSH models,
historical high water marks, ADCIRC models,
DFIRMS, Bridges, etc.
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Sun not directly overhead
7 º 12 or 1/50th of a circle
Eratosthenes had observed that on the day of the
summer solstice, the midday sun shone to the
bottom of a well in the Ancient Egyptian city of
Swenet (known in Greek as Syene).
He also knew that Alexandria and Syene were 500
miles apart
The accepted value along the equator is 24,902
miles, but, if you measure the earth through the
poles the value is 24,860 miles He was within 1
of todays accepted value Eratosthenes'
conclusions were highly regarded at the time, and
his estimate of the Earths size was accepted for
hundreds of years afterwards.
To these observations, Eratosthenes concluded
that the circumference of the earth was 50 x 500
miles, or 25000 miles.
He knew that at the same time, the sun was not
directly overhead at Alexandria instead, it cast
a shadow with the vertical equal to 1/50th of a
circle (7 12').
Eratosthenes Egypt about 240 BC
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Vertical Datums
The Geoid

• Gravity Local Attraction
• Unfortunately, the density of the earths crust
  is not uniformly the same. Heavy rock, such as
  an iron ore deposit, will have a stronger
  attraction than lighter materials. Therefore, the
  geoid (or any equipotential surface) will not be
  a simple mathematical surface.

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What is the GEOID?
Vertical Datums
The Geoid

• The equipotential surface of the Earths gravity
  field which best fits, in the least squares
  sense, global mean sea level.
• Cant see the surface or measure it directly.
• Modeled from gravity data.

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Vertical Datums
The Geoid
Equipotential Surfaces
Topography
Reference Surface (Geoid)
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Earth
An ellipsoid of revolution is the figure which
would be obtained by rotating an ellipse about
its shorter axis. The GRS80 ellipsoid is used for
the NAD83.
So we squash the sphere to fit better at the
poles. This creates a spheroid
Close Fit At The Equator But The Poles Are Out
b 6,356,752.31414 m
a 6,378,137.00000 m
GRS80 fits geoid to about /- 300
a 6378137.00000 meters b 6356752.31414
meters f 1/(a-b)/a 298.2572220972
NAD83 uses the GRS80 Ellipsoid
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Latitude - Longitude
GRS80 Ellipsoid
h
Earths Surface
Equator
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Datum
A point, line, or surface used as a reference, as
in surveying, mapping, or geology.
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Local vs. Global Reference Ellipsoid
Basic Geodesy
CLARKE 1866
GRS80-WGS84
Earth Mass Center
Approximately 236 meters
GEOID
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UNITED STATESELLIPSOID DEFINITIONS
Basic Geodesy
BESSEL 1841 a 6,377,397.155 m 1/f
299.1528128
CLARKE 1866 a 6,378,206.4 m 1/f
294.97869821
GEODETIC REFERENCE SYSTEM 1980 - (GRS 80) a
6,378,137 m 1/f 298.257222101
WORLD GEODETIC SYSTEM 1984 - (WGS 84) a
6,378,137 m 1/f 298.257223563
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Ellipsoid vs. Geoid
Vertical Datums

• Ellipsoid
• Simple Mathematical Definition
• Described by Two Parameters
• Cannot Be 'Sensed' by Instruments
• Geoid
• Complicated Physical Definition
• Described by Infinite Number of Parameters
• Can Be 'Sensed' by Instruments

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Ellipsoid vs. Geoid
Vertical Datums
High Density
ellipsoid
Low Density
geoid
Earths surface
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H elevation relative to geoid (orthometric or
NAVD88)
They are instead referenced to the GRS80
ellipsoid, that squashed sphere that best fits
the earth and is used for NAD83
The geoid is the equipotential surface of the
earths attraction and rotation which, on the
average, coincides with mean sea level in the
open ocean.
h elevation relative to ellipsoid (GRS80)
N separation between geoid and
ellipsoid (Geoid03)
This is what we reference our project elevations
to. These are the elevations you get from the NGS
datasheets and traditionally were obtained from
geodetic leveling
To convert GPS derived heights to NAVD88 you must
use the latest geoid model (currently Geoid03)
GPS heights are not related to either orthometric
or hydraulic/tidal elevations.
Lets take a look at the difference between
NAVD88 elevations (orthometric heights) and the
ellipsoid heights from GPS
h
h H N
H
Ellipsoid (GRS80)
N
Earth's Surface
Geoid
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Geoid Model
GRS80
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Geoid Model
GRS80
Geoid Surface
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Vertical Datums
h H N

H is measured traditionally h is measured with
GPS ObservationsN is modeled using Gravity Models
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GRS80 (NAD83/GPS)
-59.56'
14.00'
13.51'
13.01'
LMSL
NAVD88
NGVD29
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NSRS Coordinate Systems

• Latitude Longitude
• State Plane Coordinates
• UTM Coordinates
• NAD 83
• NAD 27

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Surfaces Used In State Plane Coordinate Systems
Basic Geodesy
Lambert Projection
Transverse Mercator Projection
IMAGINARY CONE
IMAGINARY CYLINDER
EARTH
A
B
EARTH
A
B
D
C
158 miles wide
C
D
North-South
East-West

• Conformal (preserve distances and directions
  within defined limits)
• 158 miles for 110,000

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Conic Projections(Lambert)
The lines where the cone is tangent or secant are
the places with the least distortion.
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Cylindrical Projections(Mercator)
The lines where the cylinder is tangent or secant
are the places with the least distortion.
Panhandle of Alaska
Transverse
Oblique
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Basic Geodesy
UTM Zones
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UTM Zone 14
Basic Geodesy
-99
-102
-96
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Origin
Equator
-120
-90
-60
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Basic Geodesy
NAD83 State Plane Coordinate Zones
State Plane Coordinate System - 1983
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Basic Geodesy
NAD83 State Plane Units of Measure
2007
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Questions?
Additional Information Available
at http//crunch.tec.army.mil/information/SM_CoP/
ndsp mark.w.huber_at_usace.army.mil