FNR 65 Fall 2014
Lecture 7 9/16/14
•
•
•
•
Lab 2: Map Critique
Geographic Coordinate Systems
Projections
Lab 3: Projections
http://www.wunderground.com/wundermap/
Lab 2: Map Critique
http://egsc.usgs.gov/isb//pubs/MapProjection
s/projections.html
Geographic Coordinate
Systems (GCS)
• LATITUDE
• the equator is the origin for
latitude
• 1 degree of latitude is
ALWAYS 69 miles (111km)
• LONGITUDE
• Greenwich, England, is the
origin for longitude.
• 1 degree of longitude is 69
miles (111km) at the equator
• 1 degree of longitude is 0
miles at the poles
• ORIGIN
• single origin is off the coast
of Africa
• Latitude and longitude are angles expressed in
degrees, minutes, and seconds
• 1 degree = 60 minutes
• 1 minute = 60 seconds
• 125°30’ 45’’
•
•
= 125 + 30/60 + 45/60/60
= 125.5125
Public Lands Survey System
• The mapping of the U.S. and where U.S.
coordinates originated from
• Thomas Jefferson proposed the Land Ordinance of
1785
• Begin surveying and selling (disposing) of lands to
address national debt
• Surveying begins in Oregon in 1850
• U.S. not linked by the PLS until 1903!
• Provided first quantitative measurement from coast-tocoast
Figure 2.10. Origin, township, and
section components of the Public Land
Survey System.
T2N
R3E
Principal Meridian
First Guide Meridian West
Baseline
First Guide Meridian East
First Standard Parallel North
T2N R3E
6
5
4
3
2
1
7
8
9
10
11
12
18
17
16
15
14
13
19
20
21
22
23
24
30
29
28
27
26
25
31
32
33
34
35
36
NW 1/4, NE 1/4, Section 17
NW
1/4
Initial Point
N1/2
SW
1/4
First Standard Parallel South
S1/2
SW
1/4
NW
¼ NE
1/4
SW
¼ NE
1/4
NE ¼
NE
1/4
SE ¼
NE
1/4
W1/2
SE 1/4
E1/2
SE 1/4
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
http://en.wikipedia.org/wiki/Sphere
https://www.youtube.com/watch?v=jp1kyWm7T9g
http://principles.ou.edu/earth_figure_gravity/geoid/
http://en.wikipedia.org/wiki/Figure_of_the_Earth
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.
• A datum is a
mathematical
representation (model,
a set of reference
points) of the shape of
the Earth’s surface
• It serves as the
reference or base for
calculating the
Geographic
Coordinate of a
location.
• Two kinds of datum:
• A global/geocentric datum: is centered on the
earth's center of mass.
• World Geodetic System of 1984 (WGS 84).
• A local datum: is slightly offset to a convenient
location in order to accommodate a particular
region of study.
• The North American Datum of 1927 (NAD27)
• The North American Datum of 1983 (NAD83)
North American Datums
• North American Datum of 1927 (NAD27) is a datum based on
the Clarke ellipsoid of 1866. The reference or base station is
located at Meades Ranch in Kansas. There are over 50,000
surveying monuments throughout the US and these have
served as starting points for more local surveying and
mapping efforts. Use of this datum is gradually being
replaced by the North American Datum of 1983.
• North American Datum of 1983 (NAD83) is an earthcentered datum based on the Geodetic Reference System of
1980. The size and shape of the earth was determined
through measurements made by satellites and other
sophisticated electronic equipment; the measurements
accurately represent the earth to within two meters.
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.
Projections: Why?
• Projection is the process that transforms threedimensional space onto a two-dimensional map.
• a Map Projection
• this is what gets
us flat
• Scale change
• zoom into the
area of interest
• Map Coordinates
• this helps us
locate things on
the map
• ANY projected flat map distorts reality by compromising
on one of the following:
•
•
•
•
Shape
Area
Distance
Direction
[S]
[A]
[D]
[D]
• There are names for the different classes of projections
that minimize distortion. Those that minimize distortion:
•
•
•
•
in shape:
in distance:
in area:
in direction:
conformal.
equidistant.
equal-area.
true-direction.
Also realize that using the
“appropriate” projection depends on
your objectives for displaying and
analyzing the map data
Conical
(e.g., Lambert
conformal
conic projection)
Types of Map Projections
Cylindrical
(e.g., Mercator
projection)
Planar
projection
Interrupted projection
Distance Units: Decimal Degrees
Projection: None
No projection
Undistorted distance measurement is 2451 miles
Shapes are distorted, but ArcGIS 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
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
Mercator 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
Transverse Mercator
projection
Regular Mercator
projection
Western part of CA (W of
120˚W—NV/CA border) is
in Zone 10 S
Basic components
of a UTM zone
Northing
metric distance
north of the equator
Easting
metric distance
east of a false origin. Origin set
so that central meridian of the
zone is 500,000 m E
Determining coodinatates on maps
1. Lat/Long
2. UTM (northings, eastings)