Scale Factor - GIS and Mapping - Lecture Slides, Slides of Geochemistry

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Map projections

The world is like an orange …

Watch video (2.5 min)

What is a Map Projection?

Map projection: a mathematical expression representing the 3D surface of the earth on a 2D map.

1. 3D Earth 2.Mercator Projection

This processalways results in distortion to map properties: such as area, shape, or direction.

….hundreds of projections have been developed to best suit a particular type of map.

the distortion, flattening or stretching needs to be done systematically. (Watch video 3.5 min)

Literally projecting the globe onto a map … 3 of the earliest projections (by the ancient Greeks)

[Gnomon = pagan sundial]

Projection Terms a. Scale Factor (SF)

For example, in any projection, where every line of latitude is equal in length (whereas the relative lengths on the globe are 1 at the equator, 0.5 at 60 latitude and 0 at the Poles),

SF along lines of latitude are: at the equator SF = 1; at 60, SF =2; at 90, SF = ∞

The SF in the other direction (along meridians) may not be the same.

b. Developable surface: A two dimensional surface onto which the globe is projected

Conic Cylindrical Azimuthal (planar)

Distortion increases with distance between the ‘globe’ and the surface

c. Standard Line: The standard line is a line along which the scale factor equals 1 (often the point / line of contact)

CONIC projections … are all ‘normal’ (e.g. Albers)

They can be varied by :

A: angle of the cone B: 1 or 2 standard parallels

e. Distortion : compared to the graticule:

Lines of latitude are 'parallel' and evenly spaced.

Meridians converge at the poles, half at 60 degrees.

All grid lines cross at right angles.

Scale factor is 1 in all directions.

‘Great circles’ are straight lines e.g. meridians, equator, 'straight' flight lines

Projection Properties

Projections may preserve shape or area, … but NOT both area and shape.

a. Area

A projection that maintains 'area' is equal area (or equivalent).

This is achieved by sacrificing shape: stretching in one direction to counter for earth curvature must be compensated by compaction in the other.

In other words, the product of the two Scale factors at any point in the two directions (N-S and E-W) is 1.0 (e.g 1 x 1, 2 x 0.5 etc..)

b. Shape

A projection that maintains shape is conformal or orthomorphic.

For example a 2x2 square becomes a 1x1 or 4x4 square. Stretching in one direction is matched by stretching in the other: that is, the scale factors are equal at a point in the two directions (i.e. there is 'equal-stretching').

Lambert Equal-Area projection

SF x SF (N-S, E-W) = 1 …. at any point

e.g. equator 1,1 60N/S 0.5, 2

c. Distance

Distances can be correct in one direction from a line, usually a standard line … or distances can be correct in all directions from a point.

In these cases, the projection is termed equidistant (but only N-S)

Plate Carrée projection Docsity.com

Definitions

• Co-ordinate System - records the

location of any feature on the surface of the

Earth uniquely. (Latitude/longitude)

• Datum - a system which allows the location

of latitudes and longitudes (and heights) to be

identified onto a round surface (Earth)

• Projection: the process of transferring the

information from the surface of a 3

dimensional (3D or spherical), irregularly

shaped sphere (the Earth) to a 2-dimensional

(2D or flat) 'piece of paper'

Conic Cylindrical Planar (azimuthal)

Sub-groups based on projection orientation ( normal , transverse, oblique)

Map projections – 3 major groups/techniques