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’s True Shape is Best
Described as a GEOID

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

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
three-dimensional Cartesian