Transcript mapprojections - Auburn University

Cartography and GIS
• Understanding the way maps are encoded
to be used in GIS requires knowledge of
cartography
• Cartography is the science that deals with
the construction, use, and principles
behind maps
• A map is a depiction of all or part of the
earth or other geographic phenomenon as
a set of symbols and at a scale whose
representative fraction is less than one to
one
Earth to Globe to Map
Shape of the Earth
We think of the
earth as a sphere
It is actually a spheroid,
slightly larger in radius at
the equator than at the poles
Models of the Earth
The earth can be modeled as a
– sphere,
– oblate ellipsoid
– geoid
Geographic Coordinates (f, l, z)
• Latitude (f) and Longitude (l) defined
using an ellipsoid, an ellipse rotated about
an axis
• Elevation (z) defined using geoid, a surface
of constant gravitational potential
• Earth datums define standard values of the
ellipsoid and geoid
The Spheroid and Ellipsoid
• The sphere is about 40 million meters in
circumference.
• An ellipsoid is an ellipse rotated in three
dimensions about its shorter axis.
• The earth's ellipsoid is only 1/297 off
from a sphere.
• Many ellipsoids have been measured, and
maps based on each. Examples are
WGS84 and GRS80.
Earth as Ellipsoid
The Datum
• An ellipsoid gives the base elevation for
mapping, called a datum.
• Examples are NAD27 and NAD83.
• The geoid is a figure that adjusts the best
ellipsoid and the variation of gravity
locally.
• It is the most accurate, and is used more
in geodesy than GIS and cartography.
Representations of the Earth
Mean Sea Level is a surface of constant
gravitational potential called the Geoid
Sea surface
Ellipsoid
Earth surface
Geoid
Definition of Elevation
Elevation Z
P
•
z = zp
z = 0 Land Surface
Mean Sea level = Geoid
Elevation is measured from the Geoid
Earth Models and Datums
Height
Terrain
Geoid
Sea Level
Ellipsoid
Sphere
Figure 2.4 Elevations defined with reference to a sphere, ellipsoid, geoid, or local sea level will all
be different. Even location as latitude and longitude will vary somewhat. When linking field data
such as GPS with a GIS, the user must know what base to use.
Geographic Coordinates
• Geographic coordinates are the earth's latitude
and longitude system, ranging from 90 degrees
south to 90 degrees north in latitude and 180
degrees west to 180 degrees east in longitude.
• A line with a constant latitude running east to
west is called a parallel.
• A line with constant longitude running from the
north pole to the south pole is called a meridian.
• The zero-longitude meridian is called the prime
meridian and passes through Greenwich,
England.
The most commonly used coordinate system today is the latitude,
longitude, and height system. The Prime Meridian and the Equator
are the reference planes used to define latitude and longitude.
Figure 10. Equator and Prime Meridian
Map Projections
• A transformation of the spherical or ellipsoidal
earth onto a flat map is called a map projection.
• The map projection can be onto a flat surface or a
surface that can be made flat by cutting, such as a
cylinder or a cone.
Map projections
Map Projections (contd)
• Projections can be based on axes parallel to the
earth's rotation axis (equatorial), at 90 degrees to it
(transverse), or at any other angle (oblique).
• A projection that preserves the shape of features
across the map is called conformal.
• A projection that preserves the area of a feature
across the map is called equal area or equivalent.
• No flat map can be both equivalent and conformal.
Most fall between the two as compromises.
• To compare or edge-match maps in a GIS, both
maps MUST be in the same projection.
No flat map
can be both
equivalent and
conformal.
Coordinate Systems for the US
• Some standard coordinate systems
used in the United States are
– geographic coordinates
– universal transverse Mercator
system
– military grid
– state plane
• To compare or edge-match maps in a
GIS, both maps MUST be in the same
coordinate system.
GIS Capability
• A GIS package should be able to move
between
–
–
–
–
map projections,
coordinate systems,
datums, and
ellipsoids.
Universal Transverse Mercator (UTM)
Universal Transverse Mercator (UTM) coordinates define
two dimensional, horizontal, positions. Each UTM zone is
identified by a number. UTM zone numbers designate
individual 6° wide longitudinal strips extending from
80° South latitude to 84° North latitude.
Alabama is in UTM Zone 16
STATE PLANE COORDINATE SYSTEMS
State plane systems were developed in order to provide local
reference systems that were tied to a national datum. In the
United States, the State Plane System 1927 was developed in
the 1930s and was based on the North American Datum 1927
(NAD_27). NAD_27 coordinates are in English units (feet).
NAD_27 State Plane Coordinate Example
The State Plane System 1983 is based on the North American
Datum 1983 (NAD_83). NAD_83 coordinates are metric.
State Plane Coordinate System Example
________________________________________________________________________
NAD_83 Latitude, Longitude of 30:16:28.82 N 97:44:25.19 W
is
NAD_83 Texas Central Zone
State Plane Coordinates, Easting and Northing
949465.059m, 3070309.475m
______________________________________________________________________
While the NAD_27 State Plane System has been superceded by the
NAD_83 System, maps in NAD_27 coordinates are still in use.
Most USGS 7.5 Minute Quadrangles show several coordinate system
grids including latitude and longitude, UTM kilometer tic marks,
and applicable State Plane coordinates.
Each state has its own State Plane system with specific parameters
and projections. Software is available for easy conversion to and from
latitude and longitude. Some smaller states use a single state plane zone
while larger states are divided into several zones. State plane zone
boundaries often follow county boundaries.
Figure 24. State Plane Zone Example
Two projections are used in all State Plane systems, with one exception.
Lambert Conformal Conic for regions with a larger east_west than north_south extent
Transverse Mercator for regions with a larger north_south extent
The exception is one State Plane zone in Alaska which uses an Oblique Mercator
projection for a thin diagonal area.
Also realize that using the
“appropriate” projection depends
on your objectives for displaying
and analyzing the map data
Distance Units: Decimal Degrees
Projection: None
No projection
Undistorted distance measurement is 2451 miles
Shapes are distorted, but ArcView computes distance
from spherical coordinates of latitude and longitude,
taking the earth’s round surface into account
Mercator projection
Distance = 3,142 miles…691 miles further
Changing to the Mercator projection shows shapes and
direction accurately, but sacrifices distance and area.
Peters Equal-Area Cylindrical projection
Distance = 2,238 … about 213 miles less than actual
Peters Equal-Area Cylindrical projection preserves area
but sacrifices shape, distance, and direction.
Equidistant Conic (Coterminous U.S.)
Distance = 2,452 (almost the same as original)
Projection preserves shape and accurate east-west
distances, but sacrifices direction and area
No projection
Mercator projection
Undistorted distance measurement is 2451 miles
Shapes are distorted, but ArcView computes distance
from spherical coordinates of latitude and longitude,
taking the earth’s round surface into account
Peters Equal-Area Cylindrical projection
Distance = 3,142 miles…691 miles further
Changing to the Mercator projection shows shapes and
direction accurately, but sacrifices distance and area.
Equidistant Conic (Coterminous U.S.)
Distance = 2,452 (almost the same as original)
Distance = 2,238 … about 213 miles less than actual
Peters Equal-Area Cylindrical projection preserves area
but sacrifices shape, distance, and direction.
Projection preserves shape and accurate east-west
distances, but sacrifices direction and area