Map Projections M. SCOTT HARRIS, PH.D., P.G.

FULBRIGHT-GREECE, THE NATIONAL AND KAPODISTRIAN UNIV. OF ATHENS

UNIVERSITY OF CHARLESTON AT THE COLLEGE OF CHARLESTON, SOUTH CAROLINA, USA

Is the Earth flat?

A flat earth would be

great for mapping

purposes, but alas…

The Earth is not flat. But maps are…and thus the

need for Map Projections

FlatEarthSociety.org

What is a map projection?

An attempt, mathematical or otherwise, to

display/portray/project the earth’s surface on a flat

surface (the map!)

Transforming a 3-dimensional surface onto a flat sheet

Imago Mundi

Babylonian Map

c. 600 BCE

Is this map clear and do you

think that all the lines are

properly oriented?

© Trustees of the British Museum

Fra Mauro Map, 1450

Know where you are?

Map Projections lecture outline

What is a Map Projection

Earth’s shape, real and

modeled

Types of Coordinate

Systems

Projection Methods

What map will you be

making?

Issues

Earth’s Shape

Easy math:

Spheroid

Ellipsoid

Complexity:

Geoid

Easy math:

Spheroid

Ellipsoid

Complexity:

Geoid

Earth’s Shape

What is a Coordinate System

A reference system that allows you to locate geographic

features on the surface of the Earth (or other body)

Defined by its:

Measurement framework

Geographic (spherical coordinates from Earth’s center)

Projected or Planimetric (earth coordinates projected on a

flat surface)

Units (meters, degrees, cubits…)

Map projection definition

Reference spheroid, datum, parallels, central meridian, X-Y

shift, etc.

Paraphrased from ArcGIS.com

Types of Coordinate Systems

Geographic

(hundreds in ArcGIS)

Global/spherical

Projected (thousands in ArcGIS)

Globe flat map

How would you project the ‘sphere’

of the earth onto a flat map?

Projection

Types Cylindrical

Conic

Azimuthal

Other…

Conformal

Equidistant

Polyhedral

Carlos Furuti, Progonos

Projection Methods

Braun

Stereographic

Lambert

Equal

Area

Various aspects applied to different

projection methods

Carlos Furuti, Progonos

Various aspects applied to different

projection methods

Carlos Furuti, Progonos

What map will you be making?

Where and for what purpose? Small region? (Athens)

Large region? (Europe)

Low to mid-latitudes? (Greece)

High-latitudes? (Greenland, Antarctica)

What should be preserved?

Equal area (equivalent)

Shape (conformal)

Distance

Direction

https://www.flickr.com/photos/pinguino

https://www2.ucar.edu/atmosnews/news/215

4/ocean-currents-likely-carry-oil-along-

atlantic-coast

Some Examples

WGS_1984_Web_Mercator_Auxiliary_Sphere

WGS_1984_UTM_Zone_34N (transverse Mercator)

Greek_Grid (transverse Mercator)

If you choose the wrong map

projection for Greece or Australia

Good choice for Greece Good Choice for Australia

Europe Map Projection Australia Map Projection

What are the issues?

What should be

preserved?

Area ratios

Shape

Distance

Direction

Carlos Furuti, Progonos

Various projections of S. America

By using a Map Projection, you lose something

Areas (equivalence) (Greenland example)

Mercator map projection Mollweide equal area map projection

Compare Greeland vs. Africa

Blue circles have 200-km diameter

Shape (conformal) (Now which shape is preserved? What changes?)

Mercator map projection Mollweide equal area map projection

Blue circles have 200-km diameter

Distance ( example)

Mercator map projection (usually just

for low to mid-latitude!) North_Pole_Azimuthal_Equidistant

Blue circles have 200-km diameter

Angle and directional

preservation (Great circle example)

Carlos Furuti, Progonos

Mercator map projection (angles preserved)

Polar azimuthal equidistant map projection

where distance is preserved

Red Line is the Great Circle

Blue Line is the loxodrome

Math Simple Azimuthal Orthographic Projection (from Carlos’ site:

http://www.progonos.com/furuti/MapProj/Normal/CartHow/HowOrtho/howOrtho.html)

Final note -- Math Not so simple…I will leave that for you to review online

http://www.progonos.com/furuti/MapProj/Normal/CartHow/HowBraunC/howBraunC.html

Let’s look into ArcGIS a little

View -> Data Frame Properties

Geographic Coordinate Systems

Projected Coordinate Systems

“New Data” (excel, etc.)

Defining the projection

My favorites

No projection

World Geodetic Survey-1984

(WGS)

Universal Transverse Mercator

(UTM)

WGS 1984 Web Mercator (auxiliary

sphere) (for ArcGIS Online and

google)

Summary and Suggestions

Projections are your friend

You need to know what

you want before you start

Many, many projections

exist for different reasons

Know your data VERY well

Metadata

WGS-84 LL Collection

UTM Zone 34 WGS-84

Presentation

Citations, Resources, and good

references

ArcGIS: http://desktop.arcgis.com/en/arcmap/10.3/guide-books/map-

projections/what-are-map-projections.htm

Carlos @ Progonos:

http://www.progonos.com/furuti/MapProj/CartIndex/cartIndex.html

List of Projections and their limitations/capabilities:

http://www.learnnc.org/lp/editions/mapping/6433

World borders: http://thematicmapping.org/downloads/world_borders.php

Amherst:

http://www.ats.amherst.edu/software/gis/mapping_coordinate_data

Math for converting LL to UTM:

http://www.uwgb.edu/dutchs/usefuldata/utmformulas.htm

M. Scott Harris, Ph.D., P.G.

HarrisS@cofc.edu

This presentation is not an official Department of State lecture, and the

views and information presented are their own and do not represent the Fulbright Program, Fulbright-Greece, or the U.S. Department of State