What is Geodesy?
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Geodesy is the study of:
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The size, shape and motion of the earth
The measurement of the position and motion of
points on the earth's surface, and
The study of the earth's gravity field and its
temporal variations
Types of Geodesy
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terrestrial or classical geodesy
space geodesy
theoretical geodesy
Basic Geodesy Facts
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Geographic/true directions determined by the
orientation of the graticule on the earths' surface
Magnetic directions must take into account the
compass variation (magnetic declination)
Great circle – arc formed by the intersection of the
earth with a plane passing through any two surface
points and the center of the earth (equator)
Rhumb line, loxodrome or constant azimuth – line
which makes a fixed angle with all meridians; spirals
to pole
Horizontal Geodetic Control
For North America:
¾ Horizontal – 200,000+ points marked by bronze survey
monument – measured on the geoid, adjusted for height to
lie on ellipsoid
¾ 1833 – U.S. Coast & Geodetic Survey established the first
baseline; networks of lines triangulated from this baseline
¾ 1927 – all U.S., Canadian, Mexican networks adjusted and
integrated into single network – NAD27
¾ 1983 – adjustment of 1927 datum to reflect higher accuracy,
2 million + control points, tie to WGS84 ellipsoid - NAD83
Vertical Geodetic Control
For North America:
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Vertical – beginning in 1856, vertical control point marked
by bronze benchmark; level lines created between two
endpoints, measured on geoid relative to mean sea level
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1929 – 67,000 + miles of level lines in U.S. And Canada
(500,000+ control points) adjusted and combined to
National Geodetic Vertical Datum of 1929 (NGVD29)
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1983 – National Vertical Datum of 1983, adjustment of all
(now) 388,000+ miles of level lines (NVD83)
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GPS elevations made relative to GRS80 or WGS84 ellipsoid
General Concepts
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Earth is three- dimensional
Map (screen) is 2- D
Geographic coordinate system (Datum)
locates in 3- D
Map Projection converts 3- D to 2- D
3- D to 2- D causes distortions
Coordinate Systems
Geographical coordinate system:
6 Older of two systems now in general use
6 Uses latitude and longitude to locate positions on the
uniformly curved surface of the earth
6 Primary system – used for navigation and surveying
Rectangular/plane coordinate systems:
6 Used for locating positions on a flat map
6 Evolved from cartesian coordinates
Geographic Coordinate System
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The Equator and Prime
Meridian are the reference
points
Latitude/ longitude measure
angles
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Latitude (parallels) 0º - 90º
Longitude (meridians) 0º - 180º
Defines locations on 3- D
surface
Units are degrees (or grads)
Not a map projection!
Prime Meridians
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Origin of Longitude lines
Usually Greenwich, England
Others include Paris, Bogota, Ferro
City
Athens, Greece
Bern, Switzerland
Bogota, Colombia
Brussels, Belgium
Ferro (El Hierro)
Jakarta, Indonesia
Lisbon, Portugal
Madrid, Spain
Paris, France
Rome, Italy
Stockholm, Sweden
Meridian
23° 42' 58.815"
7° 26' 22".5
74° 04' 51".3
4° 22' 04".71
17° 40' 00"
106° 48' 27".79
9° 07' 54".862
3° 41' 16".58
2° 20' 14".025
12° 27' 08".4
18° 03' 29".8
E
E
W
E
W
E
W
W
E
E
E
Latitude/ Longitude
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Not uniform units of measure
Meridians converge near Poles
1° longitude at Equator = 111 km
at 60° lat. = 55.8 km
at 90° lat. = 0 km
Decimal Degrees (DD)
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Decimal degrees are similar to
degrees/minutes/seconds (DMS) except
that minutes and seconds are
expressed as decimal values.
Decimal degrees make digital storage of
coordinates easier and computations
faster.
Conversion from DMS to DD:
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Example coordinate is 37° 36' 30"
(DMS)
Divide each value by the number of
minutes or seconds in a degree:
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36 minutes = .60 degrees (36/60)
30 seconds = .00833 degrees (30/3600)
Add up the degrees to get the answer:
37° + .60° + .00833° = 37.60833 DD
Cartesian Coordinate System
ƒ Used for locating positions on a flat
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map
Coordinates tell you how far away
from the origin of the axes you are
ƒ Referenced as (X,Y) pairs
In cartography and surveying, the X
axis coordinates are known as
Eastings, and the Y axis coordinates
as Northings.
ƒ False easting and northings are typically
added to coordinate values to keep
coordinates in the upper right hand
quadrant of the ‘graph’ – positive values
3D Cartesian Coordinates
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Cartesian Coordinates
can define a point in
space, that is, in three
dimensions.
To do this, the Z axis
must be introduced.
This axis will represent a
height above above or
below the surface
defined by the x and y
axes.
Local 3D Cartesian Coordinates
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This diagram shows the
earth with two local
coordinate systems
defined on either side of
the earth.
The Z axis points
directly up into the sky.
Instead of (X,Y) it is
(X,Y,Z)
GCS is defined by:
The Earth is Not Round
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First the earth was flat
500 BC Pythagoras declared it was a sphere
In the late 1600’s Sir Issac Newton
hypothesized that the true shape of the earth
was really closer to an ellipse
More precisely an Oblate Ellipsoid (squashed
at the poles and fat around the equator)
And he was right!
Shape of the Earth
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Earth as sphere
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simplifies math
small- scale maps (less than 1:
5,000,000)
Earth as spheroid
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maintains accuracy for larger- scale
maps (greater than 1: 1,000,000)
Geoid, Ellipsoid & Sphere
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Geoid - estimates the earth's surface using mean sea level of the
ocean with all continents are removed
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It is an equipotential surface - potential gravity is the same at every
point on its surface
Ellipsoid - It is a mathematical approximation of the Geoid
Authalic Sphere - a sphere that has the same surface area as a
particular oblate ellipsoid of revolution representing the figure of
the Earth
Spheroid or Ellipsoid?
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What is a Spheroid anyway?
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An ellipsoid that approximates the shape of a sphere
Although the earth is an ellipsoid, its major and
minor axes do not vary greatly.
In fact, its shape is so close to a sphere that it is
often called a spheroid rather than an ellipsoid.
ESRI calls it a spheroid but the two can be used
interchangeably
For most spheroids, the difference between its
semi-major axis and its semi-minor axis is less
than 0.34 percent.
How About a Few Ellipsoids
Why Do We Need More Than
One Spheroid (Ellipsoid)?
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The earth's surface is not perfectly
symmetrical
the semi-major and semi-minor axes
that fit one geographical region do not
necessarily fit another one.
What is the best Ellipsoid for you?
After James R. Smith, page 98
Shape of the Earth
Relation of Geoid to Ellipsoid
From James R. Smith, page 34
Vertical Deflection
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Important to
surveyors
Deflection of the
Vertical =
difference between
the vertical and the
ellipsoidal normal
Described by the
component tilts in
the northerly and
easterly directions.
Measuring Height
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Traditionally measured as
height above sea level
(Geoid) but is changing
due to GPS
The distance between the
geoid and the spheroid is
referred to as the geoidspheroid separation or
geoidal undulation
Can convert but it is
mathematically complex
Datums (simplified)
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Reference frame for locating points
on Earth’s surface
Defines origin & orientation of
latitude/ longitude lines
Defined by spheroid and spheroid’s
position relative to Earth’s center
Geodetic Datums (complex)
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consists of an initial origin; the azimuth for one line; the parameters of
the reference ellipsoid and the geoid separation at the origin. The
deflection of the vertical and geoid-spheroid separation are set to zero
at an origin point eg Johnson in Australia
geodetic latitudes and longitudes depend on both the reference
spheroid and coordinate datum
often the spheroid is implicitly linked to the datum, so it has become
common to use the datum name to imply the spheroid and vice versa
eg WGS84
the orientation and scale of the spheroid is defined using further
geodetic observations
horizontal and vertical
(θ, φ, ρ) = (theta , phi, roe) roe describes the distance from the origin,
theta is the angle from the XY plane and phi is the angle from the Z
axis
Creating a Datum
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Pick a spheroid
Pick a point on the Earth’s surface
All other control points are located
relative to the origin point
The datum’s center may not coincide
with the Earth’s center
Datums, cont.
2 types of datums
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Earth- centered
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(WGS84, NAD83)
Local
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(NAD27, ED50)
Relationship between 2
datums
Why so many datums?
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Many estimates of Earth’s size and
shape
Improved accuracy
Designed for local regions
North American Datums
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NAD27
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Clarke 1866 spheroid
Meades Ranch, KS
1880’s
NAD83
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GRS80 spheroid
Earth- centered datum
GPS- compatible
North American Datums
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HPGN / HARN
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NAD27 (1976) & CGQ77
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GPS readjustment of NAD83 in the US
Also known as ‘NAD91’ or ‘NAD93’
27 states & 2 territories (42 states in PE)
Redefinitions for Ontario and Quebec
NAD83 (CSRS98) – GPS
readjustment
International datums
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Defined for countries, regions, or the
world
World: WGS84, WGS72
Regional:
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ED50 (European Datum 1950)
Arc 1950 (Africa)
Countries:
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GDA 1994 (Australia)
Tokyo
Datum transformations
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Grid- based
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NADCON / HARN (US),
NT v1 / NT v2 (Canada, Australia, NZ)
Equation- based
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Molodensky, Bursa- Wolf,
Coordinate Frame, Three Parameter,
Seven Parameter
Method accuracies
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NADCON
HARN/ HPGN
CNT (NTv1)
Seven parameter
Three parameter
15 cm
5 cm
10 cm
1- 2 m
4- 5 m
GPS
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Uses WGS84 datum
Other datums are transformed and
not as accurate
Know what transformation method is
being used