GISs beginnings in Cartography

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GISs beginnings in Cartography
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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.

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Scaling
Coordinate transformation
Projection
EARTH
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Models of the Earth

• The earth can be modeled as a
• sphere,
• an oblate ellipsoid, or a
• geoid.

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Earth Shape Sphere and Ellipsoid
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Measuring the Ellipsoid

• Oblate ellipsoid predicted by Newton
• French Academy of sciences sent expeditions to
  Lapland and Peru (now in Ecuador) to measure the
  length of a degree along a meridian
• La Condamine sent to Mitad del Mundo
• Moreau de Maupertius sent to Tornio River Valley

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Measuring the Ellipsoid (ctd)

• Maupertius reported a meridian degree as 57,437.9
  toises (1 toise 1.949 m)
• Meridian degree at Paris was 57,060 toises
• Concluded Earth was flatter at poles
• Measures were erroneous but conclusions were
  correct
• Published as La Figure de la Terre (1738)

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Earth as Oblate Ellipsoid
Flatter, longer
Curved, shorter
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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 WGS83 and GRS80.

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Earth as Ellipsoid
Polar Radius b (WGS-84 value 6356752.3142
meters
b
Equatorial Radius a (WGS-84 value 6378137.0
meters)
a
Flattening f (a-b) / a (WGS-84 value
1/298.257223563)
First Eccentricity Squared e2 2f - f2 (WGS-84
value 0.00669437999013)
Ellipsoidal Parameters
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Earth Models and Datums
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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.

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NAD27 or NAD83

• Geodetic datums based on ellipsoids that touch
  the surface of the earth at a defined point.
• North American Datum 1927 (NAD27) uses the
  spheroid of Clarke 1866 to represent the shape of
  the Earth. The origin of this datum is a point on
  the Earth referred to as Meades Ranch in Kansas.
  Control points were calculated from observations
  taken in 1800s. These calculations were done
  manually and in sections many years. Therefore,
  errors vary from station to station.
• North American Datum 1983 (NAD83) is based upon
  both Earth and satellite observations, using
  GRS80 spheroid. The origin for this datum is the
  Earths center of mass. This affects the surface
  location of all latitude-longitude values enough
  to cause location of previous control points to
  shift, sometimes as such as 500 feet. A ten-year
  multinational effort tied together a network of
  control points for the US, Canada, Mexico,
  Greenland, Central America, and the Caribbean.
  NAD83 is used for US marine, aviation, and
  topographic maps.

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Geoid

• Geoid models attempt to represent the surface
  of the entire earth over
• both land and ocean as though the surface
  resulted from gravity alone.
• Bomford described this surface as the surface
  that would exist if
• the sea was admitted under the land portion
  of the earth by small
• frictionless channels.
• The WGS-84 Geoid defines geoid heights for the
  entire earth.
• The global positioning system (GPS) is based
  on WGS-84.
• Parameters for simple XYZ conversion between
  many datums and
• WGR-84 are published by NIMA (former DMA)
  and are available at
• http//www.mmac.jccbi.gov/avn/iapa/enduser/ne
  wium/TOC.htmlTools.3.1
• section 3.3 Datum Conversion.

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From NIMA (former DMA) 10 by 10 Degree Geoid
Height Grid
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Map Scale

• Map scale is based on the representative
  fraction, the ratio of a distance on the map to
  the same distance on the ground.
• Most maps in GIS fall between 11 million and
  11000.
• A GIS is scaleless because maps can be enlarged
  and reduced and plotted at many scales other than
  that of the original data.
• To compare or edge-match maps in a GIS, both maps
  MUST be at the same scale and have the same
  extent.
• The metric system is far easier to use for GIS
  work.

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Length of the Equator at Scale
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Geographic Coordinates
Prime Meridian
Equator
Prime Meridian
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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.
• A grid of parallels and meridians shown as lines
  on a map is called a graticule.

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Geographic Coordinates as Data
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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.
• If the globe, after scaling, cuts the surface,
  the projection is called secant. Lines where the
  cuts take place or where the surface touches the
  globe have no projection distortion.

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Map Projections (ctd)

• 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.

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Map Projections (ctd)

• Inevitably introduces distortions to distance,
  area, shape, or direction
• Types of projections according to what properties
  are reserved
• equidistant projections
• equal-area projections
• conformal projections
• others

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no flat map can be both equivalent and
conformal.
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Map Projections (ctd)

• Equidistant projections A map is equidistant
  when it portrays distances from the center of the
  projection to any other place on the map.
• Equal-Area projections 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.
• Conformal projections 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.
• Others A map preserves direction when azimuths
  (angles from a point on a line to another point)
  are portrayed correctly in all directions. Or
  miscellaneous projections to accommodate
  distortions among distance, area, and shape.

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Map Projections (ctd)

• Types of projections according to projection
  methods

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Secant azimuthal projection
Azimuthal projection
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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.

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Commonly used projections
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The peters projection a cylindrical equal-area
projection. It uses standards parallels of 45 or
47 degrees to de-emphasize area exaggerations in
high latitudes.
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The Mercator projection has straight meridians
and parallels that meet at right angles.
Straight lines are of constant azimuth. Often
used for marine navigation.
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The Mollweide projection, used for world maps, is
pseudocylindrical and equal-area. The central
meridian is straight. The 90th meridians are
circular arcs. Parallels are straight, but
unequally spaced. Scale is true only along the
standard parallels of 4044 N and 4044 S.
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The Robinson projection is based on tables of
coordinates, not mathematical formulas. The
projection distorts shape, area, scale, and
distance in an attempt to balance the errors of
projection properties.
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Albers Equal Area Conic projection distorts scale
and distance except along standard parallels.
Areas are proportional and directions are true
in limited areas. Used in the United States and
other large countries with a larger east-west
than north-south extent.
North America Albers Equal-Area Conic Origin
23N, 96W Standard Parallels 20N, 60N
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Equidistant Conic Projection direction, area,
and shape are distorted away from standard
parallels. Used for portrayals of areas near to,
but on one side of, the equator.
North America Equidistant Conic Origin 23N,
96W Standard Parallel 20N, 60N
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Lambert Conformal Conic projection Area, and
shape are distorted away from standard
parallels. Directions are true in limited areas.
Used for maps of North America and Australia
North America Lambert Conformal Conic
Projection Origin 23N, 96W Standard Parallels
20N, 60N
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Azimuthal equidistant projections are sometimes
used to show air-route distances. Distances
measured from the center are true. Distortion of
other properties increases away from the center
point.
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The Lambert azimuthal equal-area projection is
sometimes used to map large ocean areas. The
central meridian is a straight line, others are
curved. A straight line drawn through the center
point is on a great circle.
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The Space Oblique Mercator is a projection
designed to show the curved ground-track of
Landsat images. There is little distortion along
the ground-track but only within the narrow band
(about 15 degrees) of the Landsat image.