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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
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