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Geographical Data Presentation

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Geographical Data Presentation Powered By Docstoc
					Geographical Data Presentation


         Map Projections
                by
         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)
Latitude


           30oN Parallel


            Equator
Longitude
95 degrees
west
             Greenwich
meridian
             Meridian
             (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)
(meridian)

                                   Great circle
                                   (Equator)
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
    map
   Developable (intermediate)
           surfaces
 1.   Azimuthal projections
  – scale preserved at one point (point of zero
    distortion)
  – 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
    hemispheres
 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
    distortion
  – 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
 Cylindrical   projections (cont.)
  – world map rectangular
  – scale changes outwards from line of zero
    distortion
  – isograms are also straight lines parallel to line
    of zero distortion
Mercator
 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
  – cone tangential to spherical surface
  – circular arc forms line of zero distortion
Conical
 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
Sinusoidal
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
    distortion
    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
    used.
    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
         Projection
 1.   Conformality (e.g. Mercator)
  – deformation increases regularly in all
    directions
  – small circle on spherical surface represented by
    small circle on map
  – no angular deformation
  – map can be used to measure angles
Mercator
 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
    mapping
  – 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
Mollweide
 Equivalence   (cont.)
  – useful for statistical maps (number of symbols
    per unit area)
  – dot densities, choropleth mapping
  – visual impression of density must not be
    contradicted
  – cannot be conformal (shapes distorted/angles
    deformed)
 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
    azimuthal:
        scalepreserved along the meridians (parallels equally
         spaced)
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
Robinson
Azimuthal Equal Area

				
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