Transcript Projections

Representations of the Earth
Maps, GIS and Remote Sensing
1
The first Lines of Parallel and
Meridians
© Vicki Drake
2
LATITUDE AND LONGITUDE
Lines of Parallel equate to Latitude.
Latitude is measured from the equator to the poles (00 –
900)
Lines of Meridians equate to Longitude.
Longitude is measured from the Prime Meridian (00) to
International Date Line (1800 E/W)
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3
Coordinate Systems –Latitude and
Longitude
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4
MEASURING LATITUDE
• The equator is a Great Circle: dividing the
•
•
earth into two equal halves
Lines of latitude are parallel and evenly
spaced: a degree of latitude represents a
constant distance on the ground.
– Approximately 69 miles (111 kilometers)
These lines of parallels are measured in
angular degrees (°).
– There are 90 angular degrees of latitude
from the equator to each of the poles.
– The equator has an assigned value of 0°.
– Measurements of latitude are also defined
as being either north or south of equator
to distinguish the hemisphere of their
location
© Vicki Drake
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MEASURING LONGITUDE
• All lines of longitude can be “Great Circles”
• Lines of longitude or meridians are non-parallel circular
•
•
•
arcs that meet at the poles.
– At the equator, a degree of longitude measures
approximately 69 miles (111 kilometers)
– At 400 N or S, a degree of longitude measures
approximately 53 miles (85 kilometers)
– At the poles, a degree of longitude measures 0 miles or
kilometers – all meridians converge to a single ‘point’ at
the north or south pole
There are 180° of longitude either side of a starting
meridian which is known the Prime Meridian.
– The Prime Meridian has a designated value of 0°.
– The Prime Meridian starts at Royal Observatory,
Greenwich, London, England
Measurements of longitude are also defined as being either
west or east of the Prime Meridian.
The maximum value that a meridian of longitude can have
is 180° which is the distance halfway around a circle.
– This meridian is called the International Date Line.
– Designations of west and east are used to distinguish
where a location is found relative to the Prime Meridian.
• For example, all of the locations in North America
have a longitude that
is designated west.
© Vicki Drake
6
Projections--Going from 3D to
Flat Maps
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Projections—From a Sphere to
Flat Maps
 Projections are created by transferring points on the earth onto a
flat surface. You can think of this as having a light in the middle of
the earth, shining through the earth’s surface, onto the projection
surface. There are three basic methods for doing this:
Cylindrical--projection surface wrapped around the Earth; point of
contact is equator
 Conformal projection (‘preserves’ shape of continents at equator
only)
Planar--projection surface is a ‘flat’ surface against the Earth at a
particular latitude or longitude
 Neither Conformal or Equal Area
 Does not ‘preserve’ shape of continents nor provide measure
for equal area
Conic–- projection surface is a cone is placed on or through the
surface of the Earth
 Where the projection surface touches the Earth is the “Standard
Line.”
 Can be either Conformal or Equal Area
© Vicki Drake
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Trouble with Projections
 Distortion--It is impossible to flatten a round object without
distortion.
 Projections try to preserve one or more of the following
properties:
Area--sometimes referred to as equal area (for small
areas)
Projections that preserve ‘area’ are referred to as “Equal
Area” projections
Shape--usually referred to as “conformality”, again for
small sections
Projections that preserve “shape” are referred to as
“Conformal” projections
Direction--or “azimuthality” - cardinal directions
(N,S,E,W)
Distance – a difference in distance between two points
© Vicki
Drake
on the Earth and same
two
points represented on map
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PROJECTION CHALLENGES
• Conformality
– When the scale of a map at any point on the map is the same in any
direction, the projection is conformal.
• Meridians (lines of longitude) and parallels (lines of latitude) intersect at
right angles.
• Shape is preserved locally on conformal maps.
• Distance
– A map is equidistant when it accurately portrays distances from the
center of the projection to any other place on the map.
• Direction
– A map preserves direction when azimuths (angles from a point on a
line to another point) are portrayed correctly in all directions.
• Area
– When a map portrays areas over the entire map so that all mapped
areas have the same proportional relationship to the areas on the
Earth that they represent, the map is an equal-area map.
• Scale
– Scale is the relationship between a distance portrayed on a map and
the same distance on the Earth.
• CONFORMAL VS EQUAL AREA: Projections can be either conformal
or equal area – but not both!
© Vicki Drake
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Projections--Cylindrical
Projection
Point of contact at
equator
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Projections--”Developing” a
Cylindrical Projection
© Vicki Drake
12
Cylindrical Projection: A Conformal
Projection
Note increasing distance between lines
of latitude….why?
© Vicki Drake
13
Why Mercator? NAVIGATION!!
• In a Mercator projection, the lines of longitude are
•
straight vertical lines equi-distance apart at all latitudes,
and horizontal distances are stretched above and below
the equator.
This stretching is exaggerated near the poles
– The Mercator projection mathematically stretches vertical
distances by the same proportion as the horizontal distances so
that shape and direction are preserved
– Shape is preserved….what happens to the measurement of
area?
• Mercator’s projection preserves exactly what sailors in
•
the 16th century needed -- shapes and directions; they
were very willing to accept the size distortion.
Any straight line drawn between two points on a
Mercator Projection represents a “rhumb line” –
true compass direction
© Vicki Drake
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Rhumb Line – True Compass Heading:
Mercator Projection
Mercator Projection was the navigation map
for sailing ships: good direction but longest
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route
15
MERCATOR PROJECTION
• The normal aspect of the Mercator projection
showing the great circle between Miami and
Tokyo
– Great Circles are the shortest distance between two
points on a globe
Shortest distance, but
not true compass
headings
© Vicki Drake
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Projections--Polar Planar
Projection
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Polar Planar Projection
Projection
centered on
North Pole
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Planar Projection: Gnomonic
Gnomonic projections can be either “Conformal” or “Equal
Area”, but not both
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Gnomonic Projection
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NAVIGATION: GNOMONIC
• Any straight line drawn
on a gnomonic
projection is an Arc of a
Great Circle Route –
shortest distance
between two points on
a globe
– Great circles are
represented by straight
lines, making it very
useful in plotting great
circle routes between
arbitrary destinations
• Gnomonic Maps are the
navigational maps for
“air” age
Straight line between two
points on map is shortest
distance
© Vicki Drake
21
Projections--Conic Projection
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Conic Conformal Projection
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CONIC PROJECTIONS
• A better choice for mapping regions such
as the United States is a conic projection,
which projects shapes from the Earth’s
sphere onto a cone.
• Locations near the line where the cone is
tangent to the Earth will be relatively free
of distortion
© Vicki Drake
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PROBLEMS WITH CONIC PROJECTIONS
Projection Distortion--shown with a conic projection cutting through
the earth’s surface at 2 parallels
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PROJECTION WOES!
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© Vicki Drake
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MAP SCALE
• Map Scale is the ratio of the distance between
•
two points on the Earth’s surface and the
distances between corresponding points on a
map
There are several types of map scales:
– Verbal Scale: 1 inch = 1 mile
– Bar Scale: a graph depicting distances
– Representative Fraction:
• One unit of measured distance on a map equal some units of
measured distance in the real world
© Vicki Drake
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REPRESENTATIVE FRACTION
• Representative Fraction (RF) is the ratio
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•
between measured distances on a map and
measured distances on the Earth’s surface.
RF is a unitless measure – however, both sides
of the ratio must be identical units
A RF scale expressed as a ratio of 1:25,000
means that one unit of distance measured on
the map represents 25,000 identical units of
distance on the ground (‘in the real world’).
– 1 inch measured on a map represents 25,000 inches
on the Earth’s Surface or…
– 1 cm measured on a map represents 25,000
centimeters on the Earth’s surface.
© Vicki Drake
29
LARGE-SCALE VS SMALL-SCALE
• Large-Scale Maps show very small portions
of the real world, but with great detail.
– Large-Scale maps have small denominators i.e.,
1:12,000 or 1:10,000
– Topographic maps are examples of large-scale
maps
• Small-Scale maps show very large portions
of the real world, but with minimal detail
– Small-scale maps have large denominators, i.e.,
1:100,000 or 1:1,000,000
– Wall maps are examples of small-scale maps
© Vicki Drake
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LARGE SCALE VS. SMALL SCALE
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Very Early Maps!
Town Plan from Catal Hyük, Anatolia
(6200 B.C.)
Reconstruction of Drawing
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Early Maps
• Clay tablets from GaSur
2500 B.C.
Interpretation of
drawing
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Early World Maps
• The world according to Herodotus 450 BC
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Early World Map
• Reconstruction of world map according to Dicaearchus (300 B.C.)
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Babylonian Clay Map and
Interpretation – 600AD
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Topographic Maps
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3-D Topographic Maps
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Temperature Maps
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Ethnicity Maps
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Sea Floor Maps
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Precipitation Maps
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Population Maps
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COMPUTER MAPPING: GIS
• GIS, Geographic Information Systems, are
a way to visualize, manipulate, analyze
and display spatial and non-spatial data
– Spatial data is geo-referenced
– Non-spatial data is descriptive
• A spatial database (“geodatabase”) is used
© Vicki Drake
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GIS is an Integrating Technology
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HOW DO GIS USE DATABASES?
• Geodatabases provide geo-referenced and
descriptive data for analysis
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Cities use GIS to locate vulnerable
pipelines
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Parcels in 100-year Flood Zone
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Income Maps – Census tracts
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Earthquake Maps - Locations
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Earthquake Maps – Faults
© Vicki Drake
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Southern California Earthquakes,
2000- Creating Density Maps
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3-Dimensional Symbolization of
Data (using 3-D Analyst)
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Remote Sensing and Maps
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Remote Sensing Platforms
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• Typical Remote
Sensing Platforms
used today
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Remote Sensing uses Energy
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Spectral Signatures
All objects (natural or synthetic) reflect and emit
electromagnetic radiation over a range of wavelengths
characteristic of the object.
Distinctive reflectance and emittance properties are the
spectral signatures of object
Remote sensing depends upon operation in wavelength
regions of spectrum where these spectral signatures
occur for identification purposes.
© Vicki Drake
60
Broadleaf shrubs
Water
Grassland
Needleleaf
Forest
© Vicki Drake
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Space-based Remote Sensing
• When the sun’s energy passes through the atmosphere,
three reactions can occur:
– Transmission
– Reflection
– Scattering
– Absorption
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Spatial Resolution – by pixel
MODIS: 250meters x 250meters
Landsat: 30meters x 30meters
IKONOS: 1meter x 1meter
© Vicki Drake
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Sample Landsat TM image along
Missouri River
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