Geographical Data Presentation

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					Geographical Data Presentation

         Map Projections
         Alastair Pearson
Global Coordinate Systems
 Determining   coordinates:
  – a) Latitude:angle between point and equator
    along the meridian. Range -90o (S. Pole) to +
    90o (N. Pole)
  – b) Longitude: angle on equatorial plane
    between meridian of the point and prime
    meridian (Greenwich)

           30oN Parallel

95 degrees
             (0 degrees)
  Terms to describe Graticule
 meridian  - line of constant longitude
 parallel - line of constant latitude
 great circle - plane passing through the
  centre of the earth
 small circle - plane that does not pass
  through the centre of the earth.
                             Great circle
   Great circle (meridian)   (meridian)
                                  Small circle
Great circle                      (parallel)

                                   Great circle
Fundamental properties of
    map projections
 Indicators
  – shape of outline of projection
  – pattern of distortion in relation to zero
    distortion line or point
  – pattern of distortion in relation to boundary of
   Developable (intermediate)
 1.   Azimuthal projections
  – scale preserved at one point (point of zero
  – plane of map tangential to sphere at a point
  – no angular distortion at point of zero distortion
    (bearings and azimuths are correct)
Azimuthal Equidistant
 Azimuthal   projections (cont.)
  – world or hemisphere is circular
  – scales change radially from point of zero
    distortion (concentric rings)
  – distortion isograms are also concentric circles
  – Group includes gnomonic, orthographic, and
    stereographic projections.
Azimuthal - Gnomonic
Azimuthal - Orthographic
Azimuthal - Stereographic
 Gnomonic
  – rays projected from center of the earth.
  – covers areas of less than a hemisphere
 Orthographic
  – projecting rays from infinity. Covers
 Stereographic
  – projection source is a point diametrically
    opposite the tangent point
  – nearly covers the whole earth
 2.   Cylindrical projections
  – contact line of cylinder forms line of zero
  – typically equator (normal aspect) or meridian
    (transverse aspect)
  – contact line represented at correct scale
  – plane surface of map rolled around sphere
    (great circle forms contact line)
 Cylindrical   projections (cont.)
  – world map rectangular
  – scale changes outwards from line of zero
  – isograms are also straight lines parallel to line
    of zero distortion
 3.   Conical projections
  – small circle forms line of zero distortion
    (parallel of latitude)
  – this line is correct scale
  – equivalent to plane map rolled into shape of
  – cone tangential to spherical surface
  – circular arc forms line of zero distortion
 4.   Other projections
  – many other more complex projections
  – no longer imagine simple geometric models
  – some have two or more intersecting lines of
    zero distortion e.g. Sinusoidal
  – great variation in distortion isograms
Confining distortion
 1.   Selecting suitable aspect
  – deformation to have least effect over mapped area
  – use projection in oblique aspect if necessary
 2.   Introduce more than one line of zero distortion
  – Cylindrical:
           secant cylinder
           two lines of zero distortion (small circles)
           equidistant from centre of map
           still rectangular shape
           reduces range of distortion (spread out)
Secant cylinder
– Conical:
    secant cone
    two small circles (standard parallels) form lines of zero
    redistributes scale error within the map

– Polyconic projection:
    seriesof cones is assumed, each cone touching the globe at
    a different parallel
    only the area in the immediate vicinity of each parallel is
    large area may be mapped with considerable accuracy.

    offer good compromise in the representation of area,
    distance, and direction over small areas.
– Azimuthal:
   tangent plane transformed to secant plane
   forms standard circle

   circle is line of zero distortion (parallel)

   used with stereographic projection

   less frequent than modifications to cylindrical and
   conical projections
Special Properties of a Map
 1.   Conformality (e.g. Mercator)
  – deformation increases regularly in all
  – small circle on spherical surface represented by
    small circle on map
  – no angular deformation
  – map can be used to measure angles
 Conformality   (cont.)
  – shapes of small areas are preserved (orthomorphic)
  –  large areas distorted e.g.Greenland
  –  absence of angular deformation is most valuable:
  –  navigation charts, military mapping, topographic
  – area always distorted
  – larger areas near margins
 2. Equivalence or Equal area (e.g. Mollweide,
  Albers Equal Area)
  – areas are preserved
  – small circle on spherical surface represented by
    ellipse on map
  – all regions have correct relative size
 Equivalence   (cont.)
  – useful for statistical maps (number of symbols
    per unit area)
  – dot densities, choropleth mapping
  – visual impression of density must not be
  – cannot be conformal (shapes distorted/angles
 3.   Equidistance (e.g. Azimuthal Equidistant)
  – no projection can preserve all distances
  – equidistant projections preserve distances from
    one or two points or lines only
  – circles on sphere are ellipses on map
  – Normal aspect of cylindrical, conical and
        scalepreserved along the meridians (parallels equally
Azimuthal Equidistant
 Equidistance   (cont.)
  – not an important property in itself - can be used
    to plot airline routes from a point
  – balances all errors (not excessive area or
    angular distortion
  – compromise when conformality or equivalence
    are not essential
  – used for general reference maps in atlases for
    contries and continents
Azimuthal Equal Area