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
0/27
Basically it is what we use to georeference 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.
1/27
Sun not directly overhead
7 º 12’
or
1/50th
of a circle
Alexandria
Syene
Eratosthenes
that
on
He also knewhad
thatobserved
Alexandria
and
accepted
value solstice,
along thethe
theThe
day
of the
summer
Syene
were
500 miles
apart
equator
is
24,902
miles,
but,
if you
midday sun shone to the bottom
of
measure
earth through
a well
in thethe
Ancient
Egyptianthe
city
poles
the value
is 24,860
miles
of Swenet
(known
in Greek
as
To these observations,
Syene).
He was within
1% of today’s
Eratosthenes
concluded
that
accepted
the circumference
of time,
the the
He knew
that
at the value
same
earth
x 500 overhead
miles, were
or at
sun
waswas
not 50
directly
Eratosthenes'
conclusions
25000
miles.
Alexandria;
instead,
castand
a
highly
regarded
at the ittime,
Eratosthenes
shadow
with the
vertical
equal
his estimate
of the
Earth’s
sizeto
1/50th
a circle
was
accepted
for
Egyptof
about
240hundreds
BC(7° 12'). of
years afterwards.
2/27
Vertical Datums
The Geoid
Gravity: Local Attraction
Unfortunately, the density of the earth’s 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.
3/27
Vertical Datums
The Geoid
What is the GEOID?
• “The equipotential surface of the
Earth’s gravity field which best fits, in
the least squares sense, global mean
sea level.”
• Can’t see the surface or measure it
directly.
• Modeled from gravity data.
4/27
Vertical Datums
The Geoid
Equipotential Surfaces
Topography
5/27
But The Poles Are Out
b = 6,356,752.31414 m
An ellipsoid of So
revolution
is the
would be
we squash
the figure
spherewhich
to
obtained by rotating
an ellipse
fit better
at the about
poles. its shorter axis.
The GRS80 ellipsoid is used for the NAD83.
This creates a spheroid
Close Fit At The Equator
a = 6,378,137.00000 m
GRS80 fits geoid to
about +/- 300’
NAD83 uses the
GRS80 Ellipsoid
a= 6378137.00000 meters
b= 6356752.31414 meters
f= 1/(a-b)/a =
298.2572220972 6/27
7/27
P
8/27
A point, line, or
surface used as a
reference, as in
surveying, mapping,
or geology.
9/27
Basic Geodesy
Local vs. Global
Reference Ellipsoid
CLARKE 1866
GRS80-WGS84
Earth Mass
Center
Approximately
236 meters
GEOID
10/27
Basic Geodesy
UNITED STATES
ELLIPSOID DEFINITIONS
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
11/27
Vertical Datums
Ellipsoid vs. Geoid
• 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
12/27
Vertical Datums
Ellipsoid vs. Geoid
High Density
ellipsoid
geoid
Earth’s surface
Low Density
13/27
H = elevation relative to geoid
(orthometric or NAVD88)
They are instead referenced
The
geoid
is the
equipotential
to the
GRS80
ellipsoid,
that
h = elevation relative
surface
of sphere
the earth’s
squashed
that best
to ellipsoid (GRS80)
attraction
andand
rotation
which,
fits the earth
is used
for
on
the average, coincides
N = separation between
NAD83
with mean sea level in the
geoid and ellipsoid
open ocean.
This is what we reference
our
(Geoid03)
To convert GPS derived heights to
project elevations to. These are the
NAVD88 you must use the latest
GPS
heights
are
not
related
to
either
Let’s take ayou
look
atfrom
the difference
elevations
get
the NGS between
geoid model (currently Geoid03)
orthometric
or
hydraulic/tidal
NAVD88 elevations
(orthometric
datasheets
and traditionally
wereheights) and
elevations.
the
ellipsoid
heights
from
GPS
obtained
from
geodetic
leveling
h=H+N
14/27
15/27
Geoid Model
16/27
Vertical Datums
h =H+N
H is measured traditionally
h is measured with GPS Observations
N is modeled using Gravity Models
17/27
18/27
NSRS Coordinate Systems
Latitude & Longitude
State Plane Coordinates
UTM Coordinates
NAD 83
NAD 27
19/27
Basic Geodesy
Surfaces Used In State Plane Coordinate Systems
Lambert Projection
Transverse Mercator Projection
IMAGINARY CONE
IMAGINARY CYLINDER
EARTH
EARTH
A
A
B
C
D
B
D
C
East-West
158 miles
wide
North-South
•Conformal (preserve distances and directions within defined limits)
158 miles for 1:10,000
20/27
Conic Projections
(Lambert)
The lines where the
cone is tangent or
secant are the
places with the
least distortion.
21/27
Cylindrical Projections
(Mercator)
The lines where the
cylinder is tangent or
secant are the places
with the least
distortion.
Panhandle of
Alaska
Transverse
Oblique
22/27
Basic Geodesy
UTM Zones
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
168W 162 156 150 144 138 132 126 120 114 108 102 96 90 84 78
72 66 60 54W
23/27
Basic Geodesy
UTM Zone 14
-99°
-102° -96°
6°
Origin
-120°
-90 °
Equator
-60 °
24/27
Basic Geodesy
NAD83 State Plane Coordinate Zones
State Plane Coordinate System - 1983
25/27
Basic Geodesy
NAD83 State Plane Units of Measure
2007
26/27
Additional Information Available at:
http://crunch.tec.army.mil/information/SM_CoP/ndsp
mark.w.huber@usace.army.mil
27/27