Transcript Slide 1

Representing the Earth
RG 620
Week 4
My 03, 2013
Institute of Space Technology, Karachi
Geodesy
Science of measuring the shape of Earth
Modeling the Earth
• The best model of the Earth is 3D globe
• For measuring the Earth, Globes have
certain drawbacks
Modeling the Earth
• At any point on Earth there are three
important surfaces, the Ellipsoid, the Geoid,
and the Earth surface
Geoid
Definition:
“Three-dimensional surface along which
the pull of gravity is constant”
OR
“A continuous surface which is perpendicular
at every point to the direction of gravity”
Geoid
• True shape of the Earth varies slightly from
the mathematically smooth surface of an
ellipsoid
• Differences in the density of the Earth cause
variation in the strength of the gravitational
pull, in turn causing regions to dip or bulge
above or below a reference ellipsoid
• This undulating shape is called a Geoid
Ellipsoid
Mathematical surface obtained by revolving an
ellipse around earth’s polar axis
Ellipsoid Model of the Earth’s
Shape
Ellipsoid
• Different ellipsoid were adopted in various
parts of the world
Why difference in Ellipsoidal Estimates?
• Because there were different sets of
measurements used in each region or
continent
• These measurements often could not be tied
together or combined in a unified analysis
• Due to differences in survey methods and
data analyses.
Local or Regional Ellipsoid
• Origin, R1, and R2of ellipsoid specified such that
separation between ellipsoid and Geoid is small
• Examples: Clarke 1880
Global Ellipsoid
• Global ellipsoid selected so that these have the
best fit “globally”, to sets of measurements taken
across the globe
• Example:
– Geodetic Reference System of 1980 (GRS 1980)
– World Geodetic System 1984 (WGS84)
Globally Applicable Ellipsoids
• Extremely precise measurements across
continents and oceans were possible using
data derived from satellites, lasers, and
broadcast timing signals
• This has led to the calculation of globally
applicable ellipsoids such as GRS80, or WGS84
Set of official
Ellipsoids
Measuring Heights
Measuring Heights
• Orthometric Height/Elevation: Vertical distance
above a geoid
• Ellipsoidal Height: Heights above the ellipsoid
• Geoidal Height/Geoidal Separation: The difference
between the ellipsoidal height and orthometric
height at any location
– Geoidal heights vary across the globe
– The absolute value of the geoidal height is less than 100
meters at most of the Earth locations
– The geoid is not a mathematically defined surface rather it
is a measured and interpolated surface
Datum
• A fixed 3D surface
• Provides a frame of reference for measuring
locations on the surface of the earth
• It defines the origin and orientation of latitude and
longitude lines
• Examples:
– North American Datum of 1983 (NAD 1983 or NAD83),
– North American Datum of 1927 (NAD 1927 or NAD27),
– World Geodetic System of 1984 (WGS 1984)
Datum
• A spheroid model of the Earth is fixed to a
base point
• Example: For NAD27
– Ellipsoid: Clarke 1866
– Fixed at Meade's Ranch, Kansas
Datum
• Horizontal Datum
– Specify the ellipsoid
– Specify the coordinate locations of features on this
ellipsoidal surface
• Vertical Datum
– Specify the ellipsoid
– Specify the Geoid –which set of measurements will you
use, or which model
Datum
• Many datums have been developed to
describe the ellipsoid
• Differences between the datums reflect
differences in the
– control points,
– survey methods, and mathematical models and
– assumptions used in the datum adjustment
Local Datum
• A local datum aligns its spheroid to closely fit the earth's surface
in a particular area
• A point on the surface of the spheroid known as the origin point
of the datum is matched to a particular position on the surface of
the earth
• The coordinates of the origin point are fixed, and all other points
are calculated from it
• The center of the spheroid of a local datum is offset from the
earth's center
• Not suitable for use outside the area for which it was designed
• Examples:
– NAD 1927 (designed to fit North America reasonably well)
– European Datum of 1950 (ED 1950) (created for use in Europe)
Commonly Used Datums
• North American Datum 1927 (NAD27)
– Uses Clarke 1866 spheroid
– Fixed at Meade's Ranch, Kansas
– Yields adjusted latitudes and longitudes for approximately 26,000
survey stations in the United States and Canada
• North American Datum 1983 (NAD83)
– Include the large number of geodetic survey points (250,000 stations)
– GRS80 ellipsoid was used as reference
– NAD83(1986) uses an Earth-centered reference
• World Geodetic System of 1984 (WGS84):
– Earth-centered datum
– Essentially identical to the North American Datum of 1983 (NAD83)
– Uses WGS84 ellipsoid
Other Datums
• Bermuda 1957
• South American Datum 1969
• International Terrestrial Reference Frames,
(ITRF)
Source: http://maic.jmu.edu/sic/standards/datum.htm
Pre-Satellite Datum
• Large errors (10s to 100s of meters),
• Local to continental
• Examples: Clarke, Bessel, NAD27, NAD83(1986)
Post-Satellite Datum
• Small relative errors (cm to 1 m)
• Global
• Examples: NAD83(HARN), NAD83(CORS96),
WGS84(1132), ITRF99
Changing the Datum
• The lat/long value of a place on the Earth's surface
depends upon the datum
• Datum transformation is done to correctly convert
data among datums
• Changing the datum will change the latitude and
longitude of a point on the surface of Earth
• Example:
– Point: middle of the intersection of Baseline Road and
County Line Road near Boulder, Colorado
– Location: Latitude and Longitude
• NAD27: 40o N, 105o W
• NAD83: 39o 59’ 59.97” N, 105o 0’ 01.93” W
• Difference between two is 4ft south and 50 ft west
Datum Shift
Positions on Globe
Global Coordinate System
Positions on Globe: Lines of
Reference
graticules
Figure: 1
Figure: 3
Figure: 2
Positions on Globe
• Measured by Geographical Coordinates (angles) rather than
Cartesian Coordinates
• Locations are represented by Latitudes and Longitudes
• Latitudes (Y) and Longitudes (X) are angles
• Equator is the reference plane used to define latitude
• Prime Meridian is used to define longitude
Geographic Coordinate System (GCS)
• GCS uses a three-dimensional spherical surface to define locations on the
earth.
• Latitude and Longitude are angles denoted by ( °, ', " )
Latitude and Longitude
• The Latitude is measured as the number of degrees
from the Equator
• The Longitude is measured as the number of degrees
from the Prime Meridian
• The lines of constant latitude and longitude form a
pattern called the Graticule
Example: Measuring Lat and Long
Example: In figure
60° E (longitude), 55° N (latitude)
Latitude
“Latitude is the angular distance of any point
on Earth measured north or south of the
Equator in degrees, minutes and seconds”
• At poles (North and South Poles)
latitudes are 90o North and 90o South
• At equator latitude is 0°
• The equator divides the globe into
Northern and Southern Hemispheres
0°
• Each degree of latitude is approximately
69 miles (111 km) (variation because
Earth is not a perfect sphere)
90° N
90° S
Lines of Equal Latitudes
• Lines of constant latitude are called parallels of latitude
(horizontal lines)
• Parallel lines at an equal distance
• On Globe lines of latitude are circles of different radii
• Equator is the longest circle with
zero latitude also called ‘Great
Circle’ (24,901.55 miles)
• Other lines of latitudes are called
‘Small Circles’
• At poles the circles shrink to a
point
• Circle of Equator is divided into
360 degrees
In figure, lines of Latitude or Parallels
Some Important Small Circles
• Tropic of Cancer
– At 23.5°N of Equator and runs through Mexico,
Egypt, Saudi Arabia, India and southern China.
• Tropic of Capricorn
– At 23.5°S of Equator and runs through Chile,
Southern Brazil, South Africa and Australia.
• Arctic and Antarctic Circles
– At 66° 33′ 39″ N and 66° 33′ 39″ S respectively
Map of the World
Tropical Zone
Longitude
“Longitude is the angular distance of any point
on Earth measured east or west of the prime
meridian in degrees, minutes and seconds”
• Measured from 0° to 180° east and 180° west (or
-180°)
• The meridian at 0° is called Prime Meridian
located at Greenwich, UK
• Both 180-degree longitudes (east and west) share
the same line, in the middle of the Pacific Ocean
where they form the International Date Line
• 1 degree of Longitude=
– 69.17 mi at Equator
– 48.99 mi at 45N/S
– 0.0 mi at 90N/S
W 180°
Prime
Meridian
180° E
Lines of Equal Longitude
• Lines of Longitude (vertical lines/meridians)
• They are also called Meridians
• Meridians converge at the poles and are widest at the equator
about 69 miles or 111 km apart
• On Globe lines of longitude are circles of
constant radius which extend from pole
to pole
In figure, lines of longitude or meridian
Prime Meridian
• Royal Astronomical Observatory
in Greenwich, England
S
E
W
Latitude/Longitude Formats
•
Lat/long coordinates can be specified in different
formats:
1. DD.MM.SSXX (degree, minute, decimal second)
2. DD.MMXX (degree, decimal minute)
3. DDXX (decimal degree)
How to convert degree, minute, decimal second format
into decimal degree?
–
•
Decimal degree = (Seconds/3600) + (Minutes/60) + Degrees
In class exercise: DD conversion of24° 48' 58” N 66°
59' E
References
•
•
Bolstad Text Book
http://courses.washington.edu/gis250/lessons/projection/
Solution- Quiz 2 (a)
1.
2.
DD conversion of 38° 20' 20” N 70° 56' 04” E is 38.33889 ° N
and 70.93444 ° E
The DMS version of 5.23456° is 5 ° 14’ 4.416’’