Lecture 1-30-17 - Geodesy, Datums, and Coordinate Systems -...

Geodesy, Datums, and
Coordinate Systems
Dr. Stephen Crabtree
January 30, 2017

Geodesy :
•
The science of measuring the size
and shape of the Earth
Datum : a reference surface
•
Example: a site datum - a
reference height against which
elevations are measured
– Site plan for a subdivision
– Establish datum as a fixed
elevation at the lowest point
on the property.
– All heights are measured
relative to this site datum

Defining Coordinate Systems
•
Display of Earth’s curvature necessarily
complicated for three reasons
–
Most people see geography as a Cartesian set of
planar, 90° x , y , and z coordinates
–
Earth is not truly spherical, but is a more
distorted form
–
Measurements are rarely perfect, and add error
margins
•
Result: Multiple coordinate sets and
standards to report identical locations

Different Ellipsoids
in Different Countries
There are locally “best fit” ellipsoids
Ellipsoid
A
Ellipsoid
B

The Earth has irregularities
in it - deviations from a
perfectly ellipsoidal shape
These deviations are due
to differences in the Earth’s
density and gravitational pull
Deviations are NOT the
surface topography
The Earth is NOT an Ellipsoid
(only very close in shape)

The Earth’s True Shape is Best
Described as a GEOID

Definition of the Geoid
A Geoid is the surface perpendicular to a
plumb line, and for which the pull of gravity
is a given constant – essentially, sea level

Separation between the Geoid and best-
fitting
global ellipsoid averages about 30 meters –
this “undulation” is always below 100 meters

Geoid takes into account
measurements for local ellipsoids
There are locally “best fit” ellipsoids
geoid
Ellipsoid
A
Ellipsoid
B

Local or Regional
Ellipsoids:
Origin, R
1
, and R
2
of
ellipsoid specified such
that separation between
ellipsoid and Geoid is
small
Global Ellipsoid:
Selected so that is has
the best fit to sets of
geoid measurements
taken across the globe.

Three surfaces to keep track of at each
point on Earth
•
The Ellipsoid
•
The Geoid
•
The Physical Surface
surface
ellipsoid
geoid

Conversions
Can transform
positions from one
ellipsoid to another
via mathematical
operations
e.g., an origin shift,
and mapping from one
surface to the next

Geocentric Ellipsoid and
Coordinate System
•
3-D Cartesian system
•
Origin (0,0,0) at the
Earth center of mass
•
Best globally fit
spheroid, e.g.,
WGS84, used for
global coordinate
systems
Y
Z
X

Geocentric Ellipsoid and
Coordinate System
•
Lines of Latitude
–
Run East-to-West
parallel to the
equator
–
Values range ± 90°
•
Line of Longitude
–
Run North-to-South
perpendicular to
equator
–
Values range ± 180°
45
67.5 22.5
90
-67.5
-45
-22.5
0
-45
-67.5
22.5
45
67.5
longitude
meridians
parallels
equator
Greenwich
meridian
90
-
north pole
south pole

Datum : a reference surface
A Geodetic Datum consists of two
major components:
•
An ellipsoid with a spherical or