------Using GIS-Fundamentals of GIS
Lecture 6:
Introduction to Projections and
Coordinate Systems
By Austin Troy and Brian Voigt, University of Vermont,
with sections adapted from ESRI’s online course on projections
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Earth’s Size and Shape
•It is only relatively recently that we’ve been able to
say what both are
•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 the Earth was a
sphere
•By the fifth century BCE, this was firmly established.
•But how big was it?
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Earth’s Size
•It was Posidonius who used the stars to determine the
earth's circumference. “He observed that a given star
could be seen just on the horizon at Rhodes. He then
measured the star's elevation at Alexandria, Egypt, and
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
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Earth’s Shape
•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
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Earth’s Shape
•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%.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Spheroids
• Two common spheroids use slightly
different major and minor axis lengths
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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 “spheroid-like,” 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)
• 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
above or below the ellipsoid
• Overall these differences are small ~ 100 meters
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Geoid
www.esri.com/news/arcuser/0703/geoid1of3.html
•The geoid is actually measured and interpolated, using
gravitational measurements.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Spheroids and Geoids
• We have several different estimates of spheroids
because of irregularities in the earth surface: there are
slight deviations and irregularities in different regions
• Before remote satellite observation, had to use a
different spheroid for different regions to account for
irregularities (see Geoid, ahead) to avoid positional
errors
• 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
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Geographic 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), you have
enough information to create a coordinate
grid or “graticule” for referencing the
position of features on the spheroid.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Geographic 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 0º
longitude (Greenwich,
England)
• Equator is at 0º latitude
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Geographic 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
• Each degree of latitude represents about 110
km, although, that varies slightly because the
earth is not a perfect sphere
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Geographic Grid
• Latitude and longitude can be measured
either in degrees, minutes, seconds (e.g. 56°
34’ 30”), where minutes and seconds are
base-60 (like on a clock)
• Can also use decimal degrees (more common
in GIS), where minutes and seconds are
converted to a decimal
• Example: 45° 52’ 30” = 45.875 °
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
The Geographic Grid
• 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
180 º E or W of meridian; the 180 º line is the date line
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Datums
• 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, not actual locations
• Frame of reference for placing specific locations at
specific points on the spheroid
• Defines the origin and orientation of latitude and
longitude lines.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Datums
• A datum is essentially the model that is used to
translate a spheroid into locations on the earth
• 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
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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
sub-refence points came to be known as the datum.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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
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 required
• Problem: errors compound with distance
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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,
determine a’s location through
solving for B and C by the law
of sines
B=A(sin(b))/(sin(a))
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Satellite-Based Datums
• 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
• Yields a spheroid that when used as a datum
correctly maps the earth such that all lat / lon
measurements from all maps created with that
datum agree.
• Rather than linking points through surface measures
to initial surface point, are measurements are linked
to reference point in outer space
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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 newer
spheroid / datum, created by the US DOD; it is more or
less identical to Geodetic Reference System 1980
(GRS80).
– GPS uses WGS84
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Lat / Long and Datums
• Pre-satellite datums are surface-based.
• A given datum has the spheroid meet the
earth in a specified location.
• Datum is most accurate near the contact
point, less accurate as move away
(remember, this is different from a
projection surface because the ellipsoid is
3D).
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of 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”, 34 º 01’ 43.77884” in NAD83 and
-117º 12’ 54.61539” 34 º 01’ 43.72995” in NAD27
• Click here for a chart of the different coordinates for the
Capital Dome center under different datums (Peter
Dana)
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Datum 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 continental US, 400
m in Hawaii, 35 m in
Vermont
Source: http://www.ngs.noaa.gov/TOOLS/Nadcon/Nadcon.html
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection
• This is the method by which we transform the earth’s
spheroid (real world) to a flat surface (abstraction), either
on paper or digitally
• Because we can’t take our globe everywhere with us!
• Remember: most GIS layers are 2-D
3D
Think about
projecting a globe
onto a wall
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
2D
Fundamentals of GIS
Map Projection
•The earliest and simplest map projection is the plane
chart, or plate carrée, invented around the first century;
it treated the graticule as a grid of equal squares,
forcing meridians and parallels to meet at right angles
•If applied to
the world as
mapped now,
it would look
like:
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Distortion
• By definition, projections distorts:
• Shape
• Area
• Distance
• Direction
• Some projections specialize in preserving one or
several of these features, but none preserve all
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Shape Distortion
• Shape: projection can distort the shape of a
feature. Conformal maps preserve the shape
of smaller, local geographic features, while
general shapes of larger features are
distorted. That is, they preserve local
angles; angle on map will be same as angle
on globe. Conformal maps also preserve
constant scale locally.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Shape Distortion
•Mercator (left)
•World Cylindrical Equal Area
(above)
•The distortion in shape above is
necessary to get Greenland to have the
correct area;
•The Mercator map looks good but
Greenland is many times too big
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Area Distortion
• Area: projection can distort the property of equal
area (or equivalent), meaning that features have the
correct area relative to one another.
• Map projections that maintain this property are
often called equal area map projections.
• For instance, if S America is 8x larger than
Greenland on the globe, it will be 8x larger on map
• No map projection can have conformality and equal
area >>> sacrifice shape to preserve area and vice
versa.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Area Distortion
Mercator Projection
• 827,000 square miles
• 6.8 million square
miles
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Distance Distortion
• Distance: projection can distort measures of
true distance. Accurate distance is
maintained for only certain parallels or
meridians unless the map is localized. Maps
are said to be equidistant if distance from
the map projection's center to all points is
accurate.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Distance Distortion
•4,300 km: Robinson
•5,400 km: Mercator
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Direction Distortion
• Direction: projection can distort true
directions between geographic locations; that
is, it can mess up the angle, or azimuth
between two features. Some azimuthal map
projections maintain the correct azimuth
between any two points. In a map of this kind,
the angle of a line drawn between any two
locations on the projection gives the correct
direction with respect to true north.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Distortion
• When choosing a projection, one must take into
account what it is that matters in your analysis and
what properties you need to preserve.
• Conformal and equal area properties are mutually
exclusive but some map projections can have more
than one preserved property. For instance a map can
be conformal and azimuthal.
• Conformal and equal area properties are global
(apply to whole map) while equidistant and
azimuthal properties are local and may be true only
from or to the center of map.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Projection Specific Distortion
• Mercator maintains shape and direction, but
sacrifices area accuracy.
• The Sinusoidal and Equal-Area Cylindrical
projections both maintain area, but look quite
different from each other. The latter distorts
shape.
• The Robinson projection does not enforce any
specific properties but is widely used because
it makes the earth’s surface and its features
look somewhat accurate.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Projection Specific Distortion
Robinson
Mercator—goes on forever
Sinusoidal
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Quantifying Distortion
• Tissot’s indicatrix, made up of ellipses, is a
method for measuring distortion of a map;
here is Robinson
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Quantifying Distortion
•Sinusoidal
Area of these ellipses
should be same as
those at equator, but
shape is different
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Cylindrical
•Created by wrapping a cylinder
around a globe
•The meridians (longitude) in
cylindrical projections are equally
spaced, while the spacing between
parallel lines (latitude) increases
toward the poles
•Meridians never converge so
poles can’t be shown
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Cylindrical Map Types
1. Tangent to great circle: in the simplest case, the
cylinder is North-South, so it is tangent (touching) at
the equator; this is called the standard parallel and
represents where the projection is most accurate
2. If the cylinder is smaller than the circumference of
the earth, then it intersects as a secant in two places
Source: http://nationalatlas.gov/articles/mapping/a_projections.html
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Cylindrical Map Types
• Secant projections are more accurate because projection
is more accurate the closer the projection surface is to
the globe and a when the projection surface touches
twice, that means it is on average closer to the globe
• The distance from map surface to projection surface is
described by a scale factor, which is 1 where they touch
Standard
meridians
Earth surface
0.9996
Central meridian
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Projection
surface
Fundamentals of GIS
Cylindrical Map Types
3. Transverse cyclindrical projections: in this type
the cylinder is turned on its side so it touches a
line of longitude; these can also be tangent
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Cylindrical Map Distortion
• A north-south cylindrical Projections cause major
distortions in higher latitudes because those points on
the cylinder are further away from from the
corresponding point on the globe
• Scale is constant in north-south direction and in east
west direction along the equator for an equatorial
projection but non constant in east-west direction as
move up in latitude
• Requires alternating Scale Bar based on latitude
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Cylindrical Map Distortion
•If such a map has a scale bar, know that it is only good for
those places and directions in which scale is constant—the
equator and the meridians
•Hence, the measured distance between Nairobi and the
mouth of the Amazon might be correct, but the measured
distance between Toronto and Vancouver would be off; the
measured distance between Alaska and Iceland would be
even further off
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Cylindrical Map Distortion
◦ latitude
25 ◦ latitude
0 ◦ atitude
50
X miles
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Cylindrical Map Distortion
•Why is this? Because meridians are all the same length, but
parallels are not.
•This sort of projection forces parallels to be same length so it
distorts them
•As move to higher latitudes, east-west scale increases (2 x
equatorial scale at 60° N or S latitude) until reaches infinity at the
poles; N-S scale is constant
Fundamentals of GIS
Map Projection: Conic
•Projects a globe onto a cone
•In simplest case, globe touches cone along a single
latitude line, or tangent, called standard parallel
•Other latitude lines are projected onto cone
•To flatten the cone, it must be cut along a
line of longitude (see image)
•The opposite line of longitude
is called the central meridian
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Conic
•Is most accurate where globe and cone meet—at
the standard parallel
•Distortion generally increases north or south of it,
so poles are often not included
•Conic projections are typically used for midlatitude zones with east-to-west orientation. They
are normally applied only to portions of a
hemisphere (e.g. North America)
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Conic
•Can be tangent or secant
•Secants are more accurate for reasons given earlier
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Planar /Azimuthal
• Project a globe onto a
flat plane
• The simplest form is
only tangent at one point
• Any point of contact
may be used but the
poles are most
commonly used
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Planar /Azimuthal
• When another location is
used, it is generally to make a
small map of a specific area
• When the poles are used,
longitude lines look like hub
and spokes
• Because the area of distortion
is circular around the point of
contact, they are best for
mapping roughly circular
regions, and hence the poles
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection: Mercator
•Specific type of cylindrical projection
•Invented by Gerardus Mercator during the 16th
Century
•It was invented for navigation because it
preserves azimuthal accuracy—that is, if you
draw a straight line between two points on a map
created with Mercator projection, the angle of
that line represents the actual bearing you need to
sail to travel between the two points
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Source: ESRI
Fundamentals of GIS
Map Projection: Mercator
• Not so good for
preserving area
• Enlarges high latitude
features like
Greenland &
Antarctica and shrinks
mid latitude features.
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection:
Transverse Mercator
•Invented by Johann Lambert in 1772, this projection is
cylindrical, but the axis of the cylinder is rotated 90°,
so the tangent line is longitudinal, rather than the
equator
•In this case, only the central longitudinal meridian and
the equator are straight lines
All other lines are
represented by complex
curves: that is they can’t
be represented by single
section of a circle
Source: ESRI
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection:
Transverse Mercator
• Transverse Mercator projection is not used on a
global scale but is applied to regions that have a
general north-south orientation, while Mercator
tends to be used more for geographic features with
east-west axis.
• Commonly used in the US with the State Plane
Coordinate system, with north-south features
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection:
Lambert Conformal Conic
•Invented in 1772, this is a form of a conic projection
•Latitude lines are unequally spaced arcs that are portions
of concentric circles. Longitude lines are actually radii of
the same circles that define the latitude lines.
Source: ESRI
Lecture materials by Austin Troy © 2008, except where noted
Fundamentals of GIS
Map Projection:
Lambert Conformal Conic
• Very good for middle latitudes with eastwest orientation.
• It portrays the pole as a point
• It portrays shape more accurately than area
and is commonly used for North America.
• The State Plane coordinate system uses it
for east-west oriented features
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection:
Lambert Conformal Conic
•A slightly more complex form of conic projection
because it intersects the globe along two lines, called
secants, rather than along one, which would be called a
tangent
•There is no distortion along those two lines
•Distortion increases with distance
from secants
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Source: ESRI
Fundamentals of GIS
Map Projection:
Albers Equal Area Conic
•Developed by Heinrich Christian Albers in the early nineteenth century
for European maps
•Conic projection, using secants as standard parallels
•Differences between Albers and Lambert
• Lambert preserves shape Albers preserves area
• Poles are not represented as points, but as arcs, meaning that
meridians don’t converge
•Latitude lines are unequally spaced concentric circles, whose spacing
decreases toward the poles.
•Useful for portraying large land units, like Alaska or all 48 states
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Map Projection:
Albers Equal Area Conic
•Preserves area by making the scale factor of a meridian
at any given point the reciprocal of that along the parallel.
•Scale factor is the ratio of local scale of a point on the
projection to the reference scale of the globe; 1 means the
two are touching and greater than 1 means the projection
surface is at a distance
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Other Selected Projections
• More Cylindrical equal area: (have straight meridians
and parallels, the meridians are equally spaced, the
parallels unequally spaced)
• Behrmann cyclindrical equal-area: single standard
parallel at 30 ° north
•Gall’s stereographic: secant intersecting at 45°
north and 45 ° south
•Peter’s: de-emphasizes area exaggerations in high
latitudes; standard parallels at 45 or 47 °
Thanks to Peter Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at
Boulder for links
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Other Selected Projections
• Azimuthal projections:
•Azimuthal equidistant: preserves distance
property; used to show air route distances
•Lambert Azimuthal equal area: Often used for
polar regions; central meridian is straight, others
are curved
•Oblique Aspect Orthographic
•North Polar Stereographic
Thanks to Peter Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at
Boulder for links
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Other Selected Projections
• More conic projections
•Equidistant Conic: used for showing areas near to,
but on one side of the equator, preserves only
distance property
•Polyconic: used for most of the early USGS quads;
based on an infinite number of cones tangent to an
infinite number of parallels; central meridian
straight but other lines are complex curves
Thanks to Peter Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at
Boulder for links
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Other Selected Projections
• Pseudo-cylindrical projections: resemble cylindrical
projections, with straight, parallel parallels and equally
spaced meridians, but all meridians but the reference
meridian are curves
•Mollweide: used for world maps; is equal-area; 90th
meridians are semi-circles
• Robinson:based on tables of coordinates, not
mathematical formulas; distorts shape, area, scale,
and distance in an attempt to make a balanced map
Thanks to Peter Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at
Boulder for links
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Coordinate Systems
•Map projections provide the means for viewing smallscale maps, such as maps of the world or a continent or
country (1:1,000,000 or smaller)
•Plane coordinate systems are typically used for much
larger-scale mapping (1:100,000 or bigger)
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Coordinate Systems
•Projections are designed to minimize distortions of the
four properties we talked about, because as scale
decreases, error increases
•Coordinate systems are more about accurate
positioning (relative and absolute positioning)
•To maintain their accuracy, coordinate systems are
generally divided into zones where each zone is based
on a separate map projection
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Reason for PCSs
•Remember from before that projections are
most accurate where the projection surface is
close to the earth surface. The further away it
gets, the more distorted it gets
•Hence a global or even
continental projection is bad for
accuracy because it’s only
touching along one (tangent) or
two (secant) lines and gets
increasingly distorted
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Reason for PCSs
•Plane coordinate systems get around this by
breaking the earth up into zones where each zone
has its own projection center and projection.
•The more zones there are and the smaller each
zone, the more accurate the resulting projections
•This serves to minimize the scale factor, or
distance between projection surface and earth
surface to an acceptable level
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
Coordinate Systems
•The four most commonly used coordinate systems in
the US:
•Universal Transverse Mercator (UTM) grid
system
•State Plane Coordinate System (SPC)
•Others:
•The Universal Polar Stereographic (UPS) grid system
•The Public Land Survey System (PLSS)
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
UTM
•Universal Transverse Mercator
•UTM is based on the Transverse Mercator projection
(remember, that’s using a cylinder turned on its side)
•It generally uses either the NAD27 or NAD83 datums,
so you will often see a layer as projected in “UTM83”
or “UTM27”
•UTM is used for large scale mapping applications the
world over, when the unit of analysis is fairly small,
like a state
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
UTM
•UTM divides the earth between 84°N and 80°S into
60 zones, each of which covers 6 degrees of longitude
•Zone 1 begins at 180 ° W longitude.
•Each UTM zone is projected separately
•There is a false origin (zero point) in each zone
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
United States UTM Zones
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
UTM
•Scale factors are 0.9996 in the middle and 1 at the secants
•In the Transverse Mercator projection, the “cylinder” touches at
two secants, so there is a slight bulge in the middle, at the
central meridian. This bulge is very very slight, so the scale
factor is only 0.9996
Standard
meridians
Earth
surface
0.9996
Central meridian
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Projection
surface
Fundamentals of GIS
UTM
•In the northern hemisphere, coordinates are measured
from a false origin at the equator and 500,000 meters
west of the central meridian
•In the southern hemisphere, coordinates are measured
from a false origin 10,000,000 meters south of the
equator and 500,000 meters west of the central
meridian
•Accuracy: 1 in 2,500
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
UTM
•Because each
zone is big, UTM
can result in
significant errors
as get further
away from the
center of a zone,
corresponding to
the central line
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
SPC System
•State Plane Coordinate System is one of the most
common coordinate systems in use in the US
•It was developed in the 1930s to record original land
survey monument locations in the US
•More accurate than UTM, with required accuracy of 1
part in 10,000
•Zones are much smaller—many states have two or
more zones
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
SPC System
•Transverse Mercator projection is used for zones that
have a north south access.
•Lambert conformal conic is used for zones that are
elongated in the east-west direction. Why?
•Units of measurement are feet, which are measured
from a false origin.
•SPC maps are found based on both NAD27 and
NAD83, like with UTM, but SPC83 is in meters, while
SPC27 is in feet
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
SPC System
•Many States have their own version of SPC
•Vermont has the Vermont State Plane Coordinate
System, which is in meters and based on NAD83
•In 1997, VCGI converted all their data from SPC27 to
SPC83
•Vermont uses Transverse Mercator because of its
north-south orientation
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
State Plane Zone Map
of New England
http://www.ems-i.com/smshelp/General_Tools/Coordinates/new_england_state_plane.htm
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
State Plane Zone Map
of the Northwest
http://www.ems-i.com/smshelp/General_Tools/Coordinates/northwest_state_plane.htm
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted
Fundamentals of GIS
SPC System
•Note how a
conic projection
is used here,
since the errors
indicate an eastwest central line
Polygon errors-state plane
Lecture materials by Austin Troy and Brian Voigt © 2011, except where noted