GEOG 181 Week 4

Projections

Generating globe

The three-dimensional (conceptual) scaled-down model of the Earth

What shape can we use as a generating globe for small scale maps?

Sphere

What shape can we use as a generating globe for large scale maps?

An ellipsoid that provides a good fit for the region

Map distortion at the standard point or line(s)

Features at the standard point or line(s) are undistorted

How should we select a projection for a map of a region?

The standard point or line(s) should be at the region of interest, reducing distortion

Developable surface

Shapes that can be flattened onto a plane without stretching or compressing any part of the surface

Four geometric relationships in projections

1. Equal area

2. Equidistant

3. Conformal

4. Azimuthal

Equal area relationship

Also called equivalent. Areas on the map are proportional to their area on Earth

Equidistant relationship

Distances from a standard point, or perpendicular to a standard line, are true to scale. Certain distances on the map are accurate

Conformal relationship

Scale is constant in all directions at any given point in a map. Shapes of small areas are accurate

Azimuthal relationship

Angles about the standard point are accurately represented

The three commonly used projection classes

1. Plane

2. Cylinder

3. Cone

The three projection aspect

1. Normal

2. Transverse

3. Oblique

Normal aspect

Axis of the projection surface is lined up with the axis of the generating globe

Tangent aspect

Axis of the projection surface is perpendicular to the axis of the generating globe

The two projection cases

1. Tangent

2. Secant

Tangent case

The projection surface lies tangent to the generating globe. There is only one standard point or line

Secant case

The projection surface intersects the generating globe. There is either one or two standard line(s)

Azimuthal projections

Created by projecting onto a flat plane. Correctly represent directional relationships about the standard point or line

Why is the Mercator projection still so heavily used?

1. Loxodromes appear as straight lines, allowing for sailors to plot courses easily

2. Angles and shapes are preserved locally, meaning that intersections intersect perpendicularly on the map

3. Lines of longitude and latitude create perfect rectangles

We consider two things when selecting an appropriate projection

1. The purpose of the map

2. The area of interest that we wish to map

Best projection for dot density maps

An equivalent projection that preserves area

Best projection for navigation maps

A conformal projection:

• Gnomic projection for polar regions

• Mercator projection

Best projection for polar regions

Azimuthal projections

Best projection for mid-latitude regions

Conic projections

Best projection for equatorial regions

Cylindrical projections

Best projection for global maps

Compromise projections

Best projection for showing areas of deforestation globally across 10 years

Sinusoidal projection, since it preserves area

Best projection for a dot map showing zebra populations in Africa

Sinusoidal or Lambert Equal-Area, since they preserve area and equatorial regions are relatively undistorted

Best projection for showing areas of deforestation in South America

Albers Equal Area, since it preserves area and reduces distortion in mid-latitude regions

Best projection for showing state-by-state Coronavirus rates in the U.S.

Albers Equal Area, since it preserves area and reduces distortion in mid-latitude regions

Best projection for displaying navigational routes in Antarctica

Gnomonic projection, since it is azimuthal (good for polar regions), and straight lines on a map create a great circle route

The Universal Transverse Mercator (UTM) projection

A composite projection composed of 120 individual projections

Width of a UTM zone

6 degrees of longitude

Length of a UTM zone

From 80° S to 84° N

Projection class of UTM

Secant, creating two standard lines that run north/south through the zone

False origin point for UTM zone

For each hemisphere of each UTM zone, there is a Cartesian grid based on a false origin point for that half of the zone

Gnomonic projection

• Azimuthal

• Can only show less than half the globe

• Every great circle is a straight line

• Light source is at the centre of the sphere

Creation of gnomic projection

Created by Thales of Miletus in 6th century BC

Stereographic projection

• Azimuthal

• Conformal

• Light source is a point on the generating globe, opposite to the point of tangency

Uses for stereographic projection

• Radiating phenomena around the Earth - shockwaves or earthquakes

• Straight line distances from a point

Orthographic projection

• Azimuthal

• A view of Earth as it would appear from space

Azimuthal equidistant projection

• Azimuthal

• Preserves distances measured from a standard point

• Shows angular relationships about a standard point

Lamber Azimuthal Equal-Area projection

• Azimuthal

• Equal-area

• Preserves angles from the standard point

Lambert Cylindrical Equal-Area projection

• Cylindrical

• Equal-area

• Cylinder is tangent to the generating globe at the equator

Equidistant cylindrical projection

• Cylindrical

• Meridians of longitude are mapped as equally-spaced lines

• Preserves distances in north/south direction

Who is the cylindrical equidistant projection credited to?

Marinus of Tyre at around 100 AD

Sinusoidal projection

• Cylindrical

• Equal-area

• Preserves distances in east/west direction

Mercator projection

• Cylindrical

• Loxodromes appear as straight lines

• Conformal

Van der Grinten projection

• Compromise projection

• Patented in 1904

Robinson projection

• Compromise projection

• Made in 1963

Winkel Tripel projection

• Compromise projection

• Most widely used compromised projection today

Equidistant conic projection

• Conic projection

• Parallels of latitude are concentric arcs

Lambert Conformal Conic projection

• Conic projection

• Conformal

• Straight lines approximate great circle routesAlbers Equal Area

Albers Equal Area projection

• Conic projection

• Equal area

• Commonly used for mapping U.S. and Canada

Map distortion

It is impossible to have a projection that preserves all four geometric relationships