Geographic Framework
Map Projections
Strike flat the thick rotundity o’ th’ world!
Projected maps are flat, compact, portable, useful, and always distorted. Any curved surface gets distorted when you flatten it.
The surface of the earth tears when you
peel and flatten it. Peel a globe and you’ll
get globe gores (below).
Thinking about Map Projections
Distorting Circles
Distorting Data
What Map Projections Preserve
Map Scale
Preserving Shape (Angles)
There are many ways to think about map projections, beyond flattened bodies, oranges, and
toads.
In the 19th century, Nicolas Auguste Tissot
developed his “indicatrix,” which is used
to evaluate map projection distortion.
Mappable data are always associated with a location on the earth’s surface. That is, mappable data are always tied to the grid.
Numerical
Verbal
Preserving Distance, Direction
Preserving Area
Saying that certain map projections preserve shape is not technically correct, but makes sense to normal people.
As long as you are away from areas of high distortion, the shapes of continents look OK in comparison to shapes on the globe.
Mercator projection
Preserving Interruptions
Most map projections stretch and distort
the earth to “fill in” the tears. The Mercator
projection (bottom) preserves angles, and
so shapes in limited areas, but it greatly
distorts sizes. Note the size of Greenland
on the globe as compared to the Mercator.
Our earth’s surface is curved. Most maps are flat. Transforming the curved surface to a flat surface is called map projection.
Escuela Politécnica Nacional
Francis Soria
Referencia: [1] PhD, K. J., & PhD, W. D. (2011). Making Maps, Second Edition: A Visual Guide to Map Design for GIS (2nd ed.). Guilford Publications.
Imagine perfect circles of the same size placed at regular intervals on the curved surface of the earth. These circles are then projected along with the earth’s surface.
Tissot’s circles change area as you move north and south of the equator on the Mercator map projection (left). The more distorted the circles, the more distorted the areas of the land masses. Circle shapes are not distorted.
Tissot’s circles change shape over the surface of this area-preserving map (below). The more distorted the circles, the more distorted the shapes of the land masses. Circle areas are not distorted
Projections matter because of what they do to our data! It’s important that what map projections do to our data clarifies, not muddies, it.
Mollweide projection
Peters (Gall-Peters) projection
Albers equal-area projection
Oval shape, preserves area. Rounded map shape suggests the round earth.
To some map experts, what garlic is to vampires. This area-preserving projection’s straight grid makes north-south relationships straight forward.
A common area-preserving map projection. Poor for world scale maps because of shape distortion and peculiar form.
Transverse Mercator
One of the few conformal world projections. Its distortions of sizes are nasty, and it is a poor choice for a world map.
On the Mercator projection, scale is true along the equator. When that projection is recentered sideways along a meridian (or line of longitude), scale is true along that meridian.
Preserving Everything, Almost
The Geographic Coordinate System, aka the Geographic or Equirectangular projection, is similar to the Plate Carrée projection.
Gnomonic projection:
A straight line anywhere on a Gnomonic projection is a great circle route, the shortest distance between two points.
Azimuthal equidistant projection
Planar (azimuthal) map projections preserve directions (azimuths) from their center to all other points. The azimuthal equidistant projection also preserves distance.
This unpleasant item preserves nothing but distance, principally for north-south measurements.
Interrupted map projections minimize distortions on the uninterrupted part of the map and are typically used on maps of the entire earth.
Map projection is most visible at a global scale, where distortions of areas and shape are most evident.
Interrupted map projections are commonly used for maps of global statistical data.
Globe gores, peeled from a globe and flattened, are akin to interrupted map projections.
Goode’s homolosine projection
Goode’s is a common interrupted map projection used for world maps of statistical data.
The projection does not distort areas, and shape distortions in the uninterrupted areas of the map are minimized.
The Van der Grinten projection
Robinson projection
Does not preserve shape or area, but minimizes their distortions in all but polar regions.
Usually the polar regions are lopped off and the map presented as a rectangle.
Arthur Robinson’s map projection preserves neither area nor shape, but reduces the distortion of both.
Mapping area data on it is OK. The Robinson has rounded sides, suggesting the spherical earth, and avoids excessive distortion near the poles.
Area-preserving projections often badly distort shapes; and shape-preserving projections, area. But there is an alternative – a map projection that does not distort anything!
1 : 22,000,000
1 inch = 1.6 miles
1 cm = 220 kilometers
1 cm = 1 kilometer
1 inch = 350 miles
1 inch = .4 mile
1 cm = 1584 kilometers
1 centimeter = .25 kilometer
1 inch = 2500 miles
1 : 100,000
1 : 155,000,000
1 : 24,000
Earth’s Shape and Georeferencing
Latitude and Longitude
Universal Transverse Mercator (UTM)
Map Coordinates
State Plane Coordinate System (SPCS)
Ellipsoids and Datums
There are a diversity of ellipsoids that can serve as an approximation of our earth.
A datum is based on a single common point shared by the geoid (our imperfect earth) and a particular ellipsoid.
Ellipsoids, datums, projections, and georeferencing systems combine in strange ways with great diversity.
Map coordinates – also known as georeferences – typically consist of a pair of numbers or letters that locate data, tying them to the grid.
Geographic data are distinguished from other data by the fact that they can be located.
There are many different map coordinate systems and means of georeferencing.
The equator is the origin for latitude. Lines of latitude are called parallels. Parallels run east-west, measuring 90° north and 90° south of the equator.
Greenwich, England, is the origin (prime meridian) for longitude. Lines of longitude are called meridians. Meridians run northsouth, measuring 180° east and 180° west of the prime meridian.
Latitude and longitude can operate in a 3D or 2D world. Map projections flatten and distort the grid of latitude and longitude.
UTM, based on the “transverse” (sideways) Mercator projection, covers most of the earth, which is divided into 60 zones, each 6° wide, running from 84° north to 80° south.
UTM is measured in meters. A point is located in terms of how many meters east and north it is from the origin.
UTM is used by environmental scientists, the military, and any other professionals who work at a regional or local scale but need their maps to coordinate with maps of other areas on the earth.
The most recent version of SPCS is based on the NAD83 datum, but not all states have converted.
SPCS is measured in feet, meters, or both.
SPCS is used by planners, urban utilities, and environmental engineers. Similar coordinate systems are used in other parts of the world.