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Map Projections - GIS and Mapping - Lecture Slides, Slides of Geochemistry

Aligarh Muslim UniversityGeochemistry

In these Lecture Slides, the primary aim of the Lecturer is to illustrate the following key points : Map Projections, Geographic Coordinates, Reference Globe, Developable, Surface, Graticules and Grids, (Parallels, Meridians, Graticule, Distortions

Typology: Slides

2012/2013

Uploaded on 07/23/2013

ramanuja
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Map Projections
•Geographic coordinates can be translated into planar
coordinates using formulae taking the general form:
x = f (φ,λ)
y = g (φ,λ)
•For example, the formulae for the Mercator projection are:
x = λ
y = ln tan (φ/2 + π/4)
•A projection may be thought of as analogous to shining a
light through a reference globe onto a developable
surface which can be rolled out as a flat plane.
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Map Projections

  • Geographic coordinates can be translated into planar coordinates using formulae taking the general form: x = f (φ,λ) y = g (φ,λ)
  • For example, the formulae for the Mercator projection are:

x = λ y = ln tan (φ/2 + π/4)

  • A projection may be thought of as analogous to shining a light through a reference globe onto a developable surface which can be rolled out as a flat plane.

Distortions

  • All projections involve disotrtions.
  • There are four properties one might wish to preserve:
    • Shape
    • Area
    • Distance
    • Direction
  • Whilst a projection may be able to preserve some of these properties, this will be at the expense of other properties.

Map Scale

  • The scale of a projected map may be thought of as having two components: - Principal scale. The ratio of the size of the reference globe to the Earth. - Scale factor. The ratio of the size of a feature on the projected map to its size on the reference globe.
  • The scale factor is often different in the x and y directions, and often varies throughout the map. It can be thought of as a measure of local distortion (1.0 = no distortion).

Shape

  • A conformal (or orthomorphic ) map preserves the shape of features at local level (e.g. Lambert Conformal Conic, Mercator).
  • To do this the projected map must preserve the angle between parallels and meridians (i.e.90 degrees).
  • The Mercator projection uses straight parallel lines for both parallels and meridians. However, in the real world the meridians converge at the poles.
  • The space between the meridians must therefore be stretched in the projected map to remain parallel.

Shape (2)

  • To retain the correct shape, the space between the parallels must also be stretched by the same amount (i.e. the parallels or lines of latitude become further apart as you move toward the poles).
  • In other words, s (^) x must be equal to at s (^) y at all points on the map.
  • Other conformal projections use curved lines, but the basic principles are the same.
  • s (^) x and s (^) y obviously change as you move around the map.
  • One implication is that although you can preserve shape at local level, it is impossible to preserve overall shape.

Distance

  • Equidistant projections (e.g. Equidistant Azimuthal, Sinusoidal) attempt to minimise distortions in measures of distance between points.
  • There are two approaches:
    • Accurate distance measures are preserved along one (or sometimes two) lines of latitude ( standard parallels ). Distortions increase as you move away from these lines.
    • Accurate distance measures may be preserved in all directions from one (or possibly two) points.
  • No map can preserved accurate distance measures for every direction from every point on the map.

Direction

  • Azimuthal projections (e.g. Lambert Equal Area Azimuthal, Equidistant Azimuthal) preserve direction (e.g. for navigation purposes).
  • However, they are only accurate for one or two selected points.
  • The Mercator projection preserves the correct compass bearing between any two points, but does not indicate the shortest route.