Introduction to GIS
©2008 Austin Troy
Introduction to GIS
Find the Treasure?
©2008 Austin Troy
Introduction to GIS
The Earth’s Shape and Size
• Only recently have we known both
• Estimates of shape by the ancients
have ranged from a flat disk, to a
cube to a cylinder to an oyster.
• Pythagoras was the first to postulate it was a sphere
• By the 5th century BCE, this was firmly established.
• But how big was it?
©2008 Austin Troy
Introduction to GIS
The Earth’s Size
Posidonius used the stars to
determine the earth's
circumference. He observed that
the star Canopus could be seen
just on the horizon at Rhodes
(Greece) but appeared above the
horizon when viewed from
Alexandria, Egypt (1st century
BCE).
-source: ESRI
©2008 Austin Troy
Introduction to GIS
The Earth’s Size
He calculated the angle of
difference to be 7.5 degrees or
1/48th of a circle. Multiplying 48
by what he believed to be the
correct distance from Rhodes to
Alexandria (805 kilometers or
500 miles), Posidonius calculated
the earth's circumference to be
38,647 kilometers (24,000 miles)
– an error of only three percent.”
-source: ESRI
©2008 Austin Troy
Introduction to GIS
So, what shape IS the earth?
• Earth is not a sphere, but an ellipsoid, because the
centrifugal force of the earth’s rotation “flattens it
out”.
Source: ESRI
• This was finally proven by the French in 1753
• The earth rotates about its shortest axis, or minor axis,
and is therefore described as an oblate ellipsoid
©2008 Austin Troy
Introduction to GIS
And it’s also a….
• Because it’s so close to a sphere, the earth is often
referred to as a spheroid: that is a type of ellipsoid
that is really, really close to being a sphere
Source: ESRI
• These are two common spheroids used today: the
difference between its major axis and its minor axis is
less than 0.34%....
©2008 Austin Troy
Introduction to GIS
Spheroids
• The International 1924 and the Bessel 1841 spheroids
are used in Europe while in North America the
GRS80, and decreasingly, the Clarke 1866 Spheroid,
are used
• In Russia and China the Krasovsky spheroid is used
and in India the Everest spheroid
©2008 Austin Troy
Introduction to GIS
Spheroids
• Note how two different spheroids have slightly
different major and minor axis lengths
Source: ESRI
©2008 Austin Troy
Introduction to GIS
Scale… revisited
1:2,000,000
©2008 Austin Troy
vs.
1:20,000
Introduction to GIS
Spheroids
• One more thing about spheroids: If your mapping scales
are smaller than 1:5,000,000 (small scale maps), you can
use an authalic sphere to define the earth's shape to make
things more simple
• For maps at larger scale (most of the maps we work with
in GIS), you generally need to employ a spheroid to
ensure accuracy and avoid positional errors
©2008 Austin Troy
Introduction to GIS
Geoid
While the spheroid represents
an idealized model of the
earth’s shape, the geoid
represents the “true,” highly
complex shape of the earth,
which, although “spheroidlike,” is actually very
irregular at a fine scale of
detail, and can’t be modeled
with a formula (the DOD
tried and gave up after
building a model of 32,000
coefficients)
©2008 Austin Troy
Introduction to GIS
Geoid
• It is the 3 dimensional surface of the earth along
which the pull of gravity is a given constant; ie. a
standard mass weighs an identical amount at all
points on its surface
• The gravitational pull varies from place to place
because of differences in density, which causes the
geoid to bulge or dip below or above the ellipsoid
• Overall these differences are small (~100 meters)
©2008 Austin Troy
Introduction to GIS
Geoid
www.esri.com/news/arcuser/0703/geoid1of3.html
• The geoid is actually measured and interpolated,
using gravitational measurements.
©2008 Austin Troy
Introduction to GIS
Spheroids and Geoids
• We have several different estimates of spheroids
because of irregularities and slight deviations that are
quite variable across the Earth’s surface
• Before remote satellite observation, we had to use a
different spheroid for different regions to account for
irregularities (see Geoid) to avoid positional errors
©2008 Austin Troy
Introduction to GIS
Spheroids and Geoids
That is, continental surveys were isolated from each
other, so ellipsoidal parameters were fit on each
continent to create a spheroid that minimized error in
that region, and many stuck with those for years
©2008 Austin Troy
Introduction to GIS
The Geographic Graticule/Grid
Once you have a spheroid, you also define the location
of poles (axis points of revolution) and equator
(midway circle between poles, spanning the widest
dimension of the spheroid), and you then have enough
information to create a coordinate grid or “graticule” for
referencing the position of features on the spheroid.
©2008 Austin Troy
Introduction to GIS
The Geographic Graticule/Grid
• This is a location reference system for the earth’s
surface, consisting of:
• Meridians: lines of longitude and
• Parallels: lines of latitude
• Prime meridian is at
Greenwich, England (that
is 0º longitude)
• Equator is at 0º latitude
Source: ESRI
©2008 Austin Troy
Introduction to GIS
The Geographic Graticule/Grid
• This is like a planar coordinate system, with an origin
at the point where the equator meets the prime
meridian
• The difference is that it is not a Grid because grid lines
must meet at right angles; this is why it’s called a
graticule instead
©2008 Austin Troy
Introduction to GIS
The Geographic Graticule/Grid
Each degree of latitude represents about 110 km,
although that varies slightly because the earth is not a
perfect sphere
©2008 Austin Troy
Introduction to GIS
The Geographic Grid/Graticule
• Latitude and longitude can be measured in degrees,
minutes, seconds (e.g. 56° 34’ 30”); minutes and
seconds are base-60, like on a clock
• Can also use decimal degrees (more common in GIS
– Why?), where minutes and seconds are converted to
a decimal
• Example: 45° 52’ 30” = 45.875°
©2008 Austin Troy
Introduction to GIS
The Geographic Grid/Graticule
• Latitude lines form parallel circles of different sizes,
while longitude lines are half-circles that meet at the poles
• Latitude goes from 0 to 90º N or S and longitude to 180º
E or W of meridian; the 180º line is the date line
Source: ESRI
©2008 Austin Troy
Introduction to GIS
Horizontal Datums
• Definition: a three dimensional surface from which
latitude, longitude and elevation are calculated
• Allows us to figure out where things actually are on the
graticule since the graticule only gives us a framework
for measuring, and not the actual locations
Where is the origin?
©2008 Austin Troy
Introduction to GIS
Horizontal Datums
• Hence, a datum provides a frame of reference for
placing specific locations at specific points on the
spheroid
• Defines the origin and
orientation of latitude and
longitude lines.
• A datum is essentially the
model that is used to
translate a spheroid into
locations on the earth
©2008 Austin Troy
Introduction to GIS
Horizontal Datums
• A spheroid only gives you a shape—a datum gives
you locations of specific places on that shape.
• Hence, a different datum is generally used for each
spheroid
• Two things are needed for datum: spheroid and set of
surveyed and measured points
©2008 Austin Troy
Introduction to GIS
Geoid and the vertical datum
• There is also a vertical datum, based on the geoid
• The geoid serves as the earth’s reference elevation
when “sea level” is inadequate, which it is in many
cases because the sea is not everywhere and because
the sea can be affected by wind or weather
• The geoid provides the reference elevation from
which vertical measurements can be taken.
©2008 Austin Troy
Introduction to GIS
Surface-Based Datums
• Prior to satellites, datums were realized by connected series of
ground-measured survey monuments
• A central location was chosen where the spheroid meets the
earth: this point was intensively measured using pendulums,
magnetometers, sextants, etc. to try to determine its precise
location.
• Originally, the “datum” referred to that “ultimate reference
point.”
• Eventually the whole system of linked reference and
subrefence points came to be known as the datum.
©2008 Austin Troy
Introduction to GIS
Surface Based Datums
• Starting points need to be very central relative to
landmass being measured
• In NAD27 center point was Mead’s Ranch, KS
©2008 Austin Troy
Introduction to GIS
Surface Based Datums
• NAD27 resulted in lat/long coordinates for about
26,000 survey points in the US and Canada.
• Limitation: requires line of sight,
so many survey points were
required
• Problem: errors compound with
distance from the initial reference.
This is why central location
needed for first point
©2008 Austin Troy
Introduction to GIS
Surface Based Datums
• These were largely done without having to measure
distances. How?
• Using high-quality celestial observations and distance
measurements for the first two observations, could
then use trigonometry to determine distances.
Mead’s Ranch
D
c
B
A
Secondary
Measured
point
E
b
a
C
With b and c and A known,
we can determine a’s
location through solving for
B and C by the law of sines
B=A(sin(b))/(sin(a))
©2008 Austin Troy
Introduction to GIS
©2008 Austin Troy
Introduction to GIS
Satellite Based Datums
• With satellite measurements the center of the spheroid can be
matched with the center of the earth.
• Satellites started collecting geodetic information in 1962 as
part of National Geodetic Survey
• This gives a spheroid that when used as a datum correctly
maps the earth such that all Latitude/Longitude measurements
from all maps created with that datum agree.
• Rather than linking points through surface measures to initial
surface point, measurements are linked to reference point in
outer space
©2008 Austin Troy
Introduction to GIS
Common Datums
• Previously, the most common spheroid was Clarke 1866; the
North American Datum of 1927 (NAD27) is based on that
spheroid, and has its center in Kansas.
• NAD83 is the new North American datum (for Canada/Mexico
too) based on the GRS80 geocentric spheroid. It is the official
datum of the USA, Canada and Central America
• World Geodetic System 1984 (WGS84) is a newer
spheroid/datum, created by the US DOD; it is more or less
identical to Geodetic Reference System 1980 (GRS80). The
GPS system uses WGS84.
©2008 Austin Troy
Introduction to GIS
Lat/Long and Datums
• These pre-satellite datums are surface based.
• A given datum has the spheroid meet the earth in a
specified location somewhere.
• Datum is most accurate near the touching point, less
accurate as move away (remember, this is different
from a projection surface because the ellipsoid is 3D)
• Different surface datums can result in different
lat/long values for the same location on the earth.
• So, just giving lat and long is not enough!!!
©2008 Austin Troy
Introduction to GIS
Lat/Long and Datums
• Lat/long coordinates calculated with one datum are
valid only with reference to that datum.
• This means those coordinates calculated with NAD27
are in reference to a NAD27 earth surface, not a
NAD83 earth surface.
• Example: the DMS control point in Redlands, CA is
-117º 12’ 57.75961”, 34º 01’ 43.77884” in NAD83
and
-117º 12’ 54.61539”, 34º 01’ 43.72995” in NAD27
©2008 Austin Troy
Introduction to GIS
Datum Shift
• NAD83 is superior to NAD27 because:
• NAD83 is more accurate and NAD27 can result in a
significant horizontal shift
• When we go from a surface-oriented datum to a
spheroid-based datum, the estimated position of
survey benchmarks improves; this is called datum
shift
• That shift varies with location: 10 to 100 m in the
cont. US, 400 m in Hawaii, 35 m in Vermont
• Click here for
an example from Peter Dana
©2008 Austin Troy
Introduction to GIS
Datum Shift Example
©2008 Austin Troy
source;: http://gallery.geocaching.com.au/Maps/DatumShift
Introduction to GIS
Datum Shift Example
©2008 Austin Troy