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Chapter 9
A Guide to Selecting Map Projections
for World and Hemisphere Maps
Bernhard Jenny, Bojan Šavrič, Nicholas D. Arnold,
Brooke E. Marston and Charles A. Preppernau
Abstract Selecting the most suitable projection can be challenging, but it is as
essential a part of cartographic design as color and symbol selection and should be
given the same degree of consideration. A poorly chosen projection can result in
misinterpreted information and impact the effectiveness of a map. This chapter
provides guidance in selecting projections for world and hemisphere maps.
9.1 Introduction
Hundreds of different projections for world maps have been developed over the
centuries as cartographers sought a projection that best minimized distortion for
various applications. Each projection distorts space in a different way whether it is
the size of areas, directions, the distances between places, or a combination of these
properties. With so many projections to choose from, it can be challenging to select
one projection that is most appropriate for what is being mapped and the purpose of
the map.
B. Jenny
School of Science, Geospatial Science, RMIT University, Melbourne, Australia
B. Jenny (&)B. ŠavričN.D. Arnold B.E. Marston C.A. Preppernau
College of Earth, Ocean and Atmospheric Sciences, Oregon State University,
Corvallis, OR, USA
e-mail: bernhard.jenny@rmit.edu.au
B. Šavrič
Esri Inc., Redlands, CA, USA
N.D. Arnold
Arnold Geographics, Portland, OR, USA
B.E. Marston
U.S. Department of State, Washington, DC, USA
C.A. Preppernau
National Geographic, Washington, DC, USA
©Springer International Publishing AG 2017
M. Lapaine and E.L. Usery (eds.), Choosing a Map Projection,
Lecture Notes in Geoinformation and Cartography,
DOI 10.1007/978-3-319-51835-0_9
213
Guidelines exist to help the mapmaker select an appropriate projection. The most
commonly recommended and applied guide was published by John P. Snyder
(1926–1997), an American cartographer (Snyder 1987). Snyder created a hierar-
chical tree organized by the extent of the region that was to be mapped and the
desired property of the map (e.g., equal-area, conformal, or equidistant). The first
selection in Snyder’s decision tree is among three different geographic extents:
(1) world maps; (2) maps showing a hemisphere; and (3) maps showing a continent
or smaller areas. This chapter focuses on projections for world and hemisphere
maps. Snyder’s selection guideline is not deterministic. Discretion must still be
exercised when selecting one of the suggested projections.
9.2 Criteria for the Selection of a Map Projection
Distortion is an inevitable consequence of transforming a sphere or an ellipsoid
onto a plane. It is impossible to cut and unfold the surface of the Earth onto a planar
surface, like a map, without distortion (Fig. 9.1). Distortion is easy to spot on
small-scale world maps where landmasses are considerably altered in geometric
appearance.
Because map projections cannot preserve all properties of the original sphere,
cartographers must consider which properties are the most important to retain. This
consideration is based on the purpose of the map and the cartographic technique
used to visualize information. Additional criteria are to be taken into account such
Fig. 9.1 The earth is impossible to unfold onto a planar surface without distortion
214 B. Jenny et al.
as aesthetic appearance of the map, aspect ratio, whether available software applies
the projection, and users’preferences.
9.2.1 Deciding What Property to Preserve
Because the primary objective for most maps is to minimize geometric distortion, it
is important to determine which geometric properties to preserve. This decision is
based on the purpose of the map, that is, what mapping technique is applied and for
what applications the reader will use the map.
Equal-area projections maintain the size of map elements relative to one
another. This is an essential property to preserve when comparing the size of objects
on a map. For example, a choropleth map should be equal-area because the size of
enumeration units is being compared.
Conformal projections preserve local angles about any point on a
map. Generally, this property is only required for large-scale maps when angles are
to be measured from maps, for example when reading an angle from a map using a
protractor for navigation or surveying. All conformal maps showing the entire
world or large portions of it grossly enlarge or reduce some areas.
Equidistant projections preserve distances between points along some directions.
This property is important for comparing distances between locations. For example,
a map showing concentric circles that denote the distance from a point requires the
distance relative to the center of the circles to be true. However, only some dis-
tances can be preserved; it is impossible to correctly display distances between all
points on a flat map.
Compromise projections do not preserve area, local angles, or distance. As the
name suggests, a compromise projection is an attempt at balancing the distortion.
Compromise projections are generally only useful for maps showing the entire
world or large portions of it.
9.2.2 Aesthetics and Aspect Ratio
It is possible for the projection selection process to yield several potential projec-
tions for maps showing the entire world or a hemisphere. A cartographer should
consider making a selection based upon aesthetic preference. This is a subjective
decision made by the cartographer or the client. In this case, personal taste is a
major selection criterion (Šavričet al. 2015a).
There are often constraints on the size and format of the available space for a
map. Choosing a projection that fits the aspect ratio efficiently can greatly improve
the page layout.
9 A Guide to Selecting Map Projections …215
9.2.3 Mapping Software
Another factor in the selection of a map projection is its availability in mapping
software. Many projections are supported across various packages, but some useful
projections are difficult to find. A few of the projections recommended and dis-
cussed in this chapter are currently unavailable in some of the more commonly used
GIS software.
9.2.4 User Preferences
When selecting a world map projection, cartographers can base their selection on
map-reader preferences for world maps. So far, three user studies (Gilmartin 1983;
Werner 1993;Šavričet al. 2015a) have assessed user preferences. Gilmartin (1983)
found a preference for elliptical maps over rectangular maps. Gilmartin also found
that projections with a distinctively longer width than height are preferred. A user
study by Werner (1993) showed that the most preferred projections are uninter-
rupted pseudocylindrical, followed by interrupted projections, and the least favored
were rectangular maps. Šavričet al. (2015a) confirmed that map-readers prefer
uninterrupted projections. They also found that map-readers dislike world map
projections with curved parallels, as well as pseudocylindrical projections with
bulging meridian curves.
9.3 Projections for World Maps
The main distinguishing characteristics of maps showing the entire world are the
distortion properties (equal-area, compromise, or equidistant), the curvature of
parallels and meridians, and the representation of poles as either points or lines. In
this section, recommendable equal-area and compromise projections are discussed
first. Then, projections with other properties are discussed, as well as oblique
aspects and interruptions. This section concludes with a summarizing selection-tree
table for world map projections.
Conformal projections are not discussed here as they are not useful for world
maps. The major disadvantage of conformal projections when applied to world
maps is their gross distortion of areas.
1
1
Despite their gross area distortion, Snyder also includes conformal projections in his guideline.
He suggests the Mercator projection in the normal, transverse, or oblique aspect, for when scale
has to be preserved along the equator, a meridian, or an oblique great circle, respectively. Snyder
also recommends the conformal Lagrange, August, and Eisenlohr projections.
216 B. Jenny et al.
Most projections for world maps recommended here are pseudocylindrical
projections. When centered on the equator, these projections have straight parallels
and curved meridians.
9.3.1 Equal-Area World Map Projections
Equal-area world maps projections are required for area comparisons, such as with
choropleth and dasymetric maps, or when the number of features per area unit is
estimated, as is the case with dot maps.
The cartographer can select between world map projections representing poles as
either points or lines. The criteria for this selection are the cartographer’s aesthetic
preferences and the degree of acceptable deformation. When representing poles as
points, landmasses located close to both a pole and an edge of the map are greatly
deformed. When representing poles as lines, features located at these extreme
locations are also deformed, but to a lesser degree. Features are vertically com-
pressed when using an equal-area projection with a pole line (Fig. 9.2).
Commonly used projections representing the poles as points are the Mollweide,
Hammer, Boggs Eumorphic, and sinusoidal projections (Fig. 9.3). The Mollweide
projection is very popular for atlases (Canters and Decleir 1989) and is more
aesthetically pleasing to many cartographers than other projections due to its
elliptical shape (Snyder 1993, p. 112). The sinusoidal projection has significant
angular distortion near the edges, especially in higher latitudes (Canters and Decleir
1989, p. 81). The Boggs Eumorphic projection is a blend between the sinusoidal
and Mollweide projections that better represents areas near the poles than the
sinusoidal projection (Snyder 1993, p. 200). The Hammer projection represents the
entire world in an ellipse with curved parallels and unequally distributed meridians.
Recommendable equal-area projections showing the poles as lines are the
Eckert IV, Eckert VI, Wagner IV, Wagner VII, and McBryde-Thomas Flat-Polar
Fig. 9.2 With a projection showing poles as points, the shape of Greenland tends to be more
deformed (left) than with a projection showing poles as lines (right). Mollweide (left) and
Eckert IV (right) projections centered on 90°E
9 A Guide to Selecting Map Projections …217
Quartic projections (Fig. 9.4).
2
Eckert IV is an equal-area projection with very low
mean angular distortion (Canters and Decleir 1989). Its rounded corners, where
meridians meet the pole line, suggest that the projection represents a spherical
Earth. However, Max Eckert preferred his sixth projection with sinusoidal merid-
ians, the Eckert VI projection (Canters and Decleir 1989). The Wagner IV pro-
jection is similar in appearance and distortion characteristics to the Eckert IV
projection, but the Wagner IV projection does not have the rounded corners of the
Eckert IV projection. The Wagner VII projection has curved parallels and pole
lines. Unfortunately, only a few software packages include this projection. Snyder
includes all projections by McBryde and Thomas in his selection tree, but out of
their nine projections, only the McBryde-Thomas flat-polar quartic projection
(Fig. 9.4) is commonly used by cartographers (Snyder 1993).
9.3.2 Compromise World Map Projections
Compromise projections with low areal distortion are commonly used for a variety
of thematic world maps. These projections include the Robinson, Winkel Tripel,
Mollweide Hammer
Boggs Eumorphic Sinusoidal
Fig. 9.3 Equal-area world map projections with poles represented as points
2
Snyder states that any pseudocylindrical equal-area projection is suitable. He does not include the
Wagner VII projection, which is not a pseudocylindrical projection.
218 B. Jenny et al.
Natural Earth, and Wagner V projections (Fig. 9.5).
3
The Robinson projection is
perhaps the most used compromise projection for world maps. National Geographic
used the Robinson projection for their world maps for about a decade until the
Winkel Tripel projection replaced it in 1998 (Slocum et al. 2009). The Winkel
Tripel projection has curved parallels and a comparatively large height-to-width
ratio. It also has low area and scale distortion compared to other compromise
projections. The Natural Earth projection has characteristic rounded corners where
parallels meet the pole lines (Jenny et al. 2008;Šavričet al. 2011). The Natural
Earth II projection (not depicted here) is an alternative pseudocylindrical projection
with meridians steeply bending toward short pole lines resulting in a map with
highly rounded corners (Šavričet al. 2015b). The Wagner V projection is similar to
McBryde-Thomas Flat-Polar Quartic
Eckert IV Eckert VI
Wagner IV Wagner VII
Fig. 9.4 Equal-area world map projections with poles represented as lines
3
Snyder’s selection guideline contains only two compromise projections: the Robinson and the
Miller cylindrical projections. Snyder’s list of compromise projections is extended here with
projections with similar distortion characteristic as the two mentioned by Snyder.
9 A Guide to Selecting Map Projections …219
the Robinson projection, but has a smaller height-to-width ratio and has slightly
more curved meridian lines.
Many cartographers do not recommend projections that transform the entire
Earth into a rectangle because they greatly distort space (Canters 2002, p. 263) and
because of the idea that rectangular world maps mislead the map reader’s inter-
pretation of the world’s shape. This selection guideline, therefore, does not rec-
ommend using rectangular projections for most world maps. However, there are
some rare phenomena based on longitude that are best represented by a map with
straight meridians, such as a map showing world time zones. Also, rectangular
projections may be preferred for aesthetic reasons. The Miller cylindrical projection
is a compromise projection that is recommended for these applications (Fig. 9.6).
When using the Miller cylindrical projection, one has to be aware of the fact that
this projection greatly exaggerates the size of Polar areas. The Plate Carrée (also
known as the equidistant cylindrical or geographic) is an alternative cylindrical
projection that takes up less space vertically than the Miller projection and has less
areal distortion in polar areas. The Plate Carrée is a common projection for
exchanging geospatial data, because its equations are trivial. The Patterson cylin-
drical projection is nearly identical in tropical and mid-latitude regions to the Miller
cylindrical projection, but polar regions are less exaggerated (Fig. 9.6, Patterson
et al. 2014).
Robinson Winkel Tripel
Natural Earth Wagner V
Fig. 9.5 Compromise world map projections
220 B. Jenny et al.
9.3.3 Equidistant World Map Projections
On some occasions, such as mapping airport connections where the cartographer
would like to preserve distances from the airport, an equidistant projection is
essential (Fig. 9.7). The azimuthal equidistant projection is the only projection that
preserves all distances relative to its center. Only distances along straight lines
passing through the center are portrayed correctly. When the cartographer selects
one of the poles as the center, parallels are equally spaced concentric circles
(Fig. 9.7).
The only projection that preserves distances relative to two points on a flat map
is the two-point equidistant projection (Fig. 9.7 bottom). The cartographer can
define the two points. Distances measured along lines passing through either point
are mapped without distortion. The two-point equidistant projection is appropriate,
for example, for determining the distance from a ship at a known location to the
start and end of its voyage (Snyder and Voxland 1989).
The Plate Carrée (Fig. 9.6 bottom) and the more general equirectangular pro-
jection preserve distances along all meridians and are useful when differences in
latitude are measured. The sinusoidal projection preserves distances along all par-
allels (Fig. 9.3).
Plate Carrée
Patterson
Miller Cylindrical
Fig. 9.6 Cylindrical world map projections show polar areas with considerable distortion
9 A Guide to Selecting Map Projections …221
Polar azimuthal equidistant Oblique azimuthal equidistant
(Washington)
Two-point equidistant
(Mexico City & London)
Fig. 9.7 Equidistant map projections
9.3.4 Interrupted World Map Projections
Small-scale world maps usually represent the world on a continuous space without
interruptions. An interrupted projection is an alternative (Fig. 9.8), however inter-
rupted projections are not frequently used, and they seem to be disliked by many
map readers (Šavričet al. 2015a). Interruption can be applied to most of the
equal-area and compromise world map projections suggested in the sections above.
Depending on the purpose of the map (i.e., whether showing land or ocean), the
locations of intersections and central meridians are adjusted.
The McBryde S3 projection is sometimes recommended as an interrupted
equal-area projection with a pole line (Fig. 9.8). The Goode homolosine is an
equal-area projection that is often used in interrupted form. A disadvantage of the
Goode homolosine is the discontinuities at approximately ±41°N and S latitudes,
222 B. Jenny et al.
which can be visually disruptive. The interrupted form of the Mollweide projection
is similar in appearance, but does not show the same discontinuities.
9.3.5 World Maps with Shifted Central Meridian
and Oblique Aspect
Many world maps are centered on the Greenwich meridian, but there are often good
reasons to center the map on a different meridian, mainly to better show spatial
relations of the centered area to neighboring areas (Fig. 9.9 left). Shifted meridians
can be applied to any projection.
World maps with an oblique aspect are centered on any point on Earth’s surface
(Fig. 9.9 right). While a shifted meridian only relocates the mapped features in an
Goode’s Homolosine
Mollweide
Boggs Eumorphic
McBryde S3
Fig. 9.8 Examples of interrupted projections for mapping continents (top) and oceans (bottom)
Robinson centered on 90° W Oblique Mollweide
Fig. 9.9 Examples of world maps with shifted central meridian and oblique aspect
9 A Guide to Selecting Map Projections …223
east-west direction, an oblique aspect better represents spatial relations of features
near one of the poles because the pole is moved toward the center of the
map. Oblique aspects can be applied to any world map projection.
9.3.6 Selection Tree for World Maps
Table 9.1 presents a selection tree for world map projections summarizing the
discussion above. The cartographer will reach a list of recommended projections
after considering a projection’s property (first column) and its pole representation
(second column).
Table 9.1 Selection tree for projections for mapping the entire sphere (adapted from Snyder
1987)
Property/characteristic Poles as Named projection
Equal-area Points
†
Mollweide
Hammer (or Hammer-Aitoff)
*Boggs Eumorphic
Sinusoidal
Lines
†
Eckert IV
Wagner IV (or Putnins P2′)
Wagner VII (or Hammer-Wagner)
McBryde-Thomas flat-polar quartic
Eckert VI
Compromise distortion Lines
†
Natural Earth
Natural Earth II
Winkel Tripel
Robinson
Wagner V
Plate Carrée (or geographic)
Miller (or Miller Cylindrical I)
Interrupted (equal-area) Points *Mollweide
*Boggs Eumorphic
Goode homolosine
Lines *McBryde S3
*Any of the equal-area projections with a pole
line listed above
Equidistant Centered on a pole Points Polar azimuthal equidistant
Centered on
arbitrary point
Oblique azimuthal equidistant
Relative to two
points
Two-point equidistant
Along meridians Lines Plate Carrée (or geographic)
An asterisk (*) marks projections that are often not available in GIS and mapping software.
Synonyms are given in parentheses.Anobelisk (†) marks a group of projections ordered by mean
scale distortion, from least to greatest weighted mean error in the overall scale distortion index
(after Canters 2002)
224 B. Jenny et al.
9.4 Projections for Hemisphere Maps
Three recommendable projections exist for creating maps depicting a hemisphere
with a circular boundary. The three projections, which all belong to the azimuthal
class of projections, are the Lambert azimuthal equal-area projection, the azimuthal
equidistant projection, and the orthographic projection (Fig. 9.10).
4
Adjusting the central longitude and latitude of the three recommendable pro-
jections can shift the area of interest to the center of the map. Polar aspect, that is,
maps showing one of the poles in the center of the map, can be created with the
three projections (for an example, see Fig. 9.7 top left).
Of the three recommendable projections, the Lambert azimuthal projection is the
only projection that preserves areas. It is, therefore, a useful projection for hemi-
sphere maps where the size of countries or other features are compared. The
Lambert azimuthal projection is not limited to a single hemisphere, but can show
the entire globe in a circle. However, the projection is rarely used to show the entire
sphere because of the considerable distortion of angles and distances close to the
edge of the circle.
The orthographic projection shows the globe as seen from space at an infinite
distance. The orthographic projection is particularly useful for locator maps in
combination with large- and medium-scale maps to show the location and extent of
a mapped area because it creates pictorial views of the Earth, accentuating its round
shape.
The azimuthal equidistant projection preserves distances relative to the central
point of the map. Consequently, it is a useful projection for reading distances to a
point of interest placed in the center of a map. For example, a map showing the
Lambert Equal-area Equidistant Orthographic
Fig. 9.10 Azimuthal projections for hemisphere maps (centered on 45°N and 45°E)
4
Snyder also includes the conformal azimuthal stereographic projection for hemisphere maps in his
selection schema. The azimuthal stereographic projection is not generally useful for mapping a
hemisphere as it grossly distorts shape and area along the border of the projected hemisphere.
Preserving angles is rarely needed for hemisphere maps and certainly not for locator inset maps, a
typical use case for these projections. The azimuthal stereographic projection is therefore not
recommended for maps showing an entire hemisphere in a circle.
9 A Guide to Selecting Map Projections …225
relative distance of a country to immediate and distant neighboring countries, or the
location of a tsunami wave over time, should use the azimuthal equidistant pro-
jection. Because distances are only correct along straight lines when they pass
through the projection center, it is crucial to define the central point accordingly.
The visual difference between the Lambert azimuthal equal-area projection and
the equidistant projection are small when used for a hemisphere (Fig. 9.10). For
locator inset maps, the selection of a projection is a matter of personal taste. The
authors recommend using the orthographic projection when the spherical shape of
the globe is to be accentuated in inset maps.
9.5 Selecting a Projection with Projection Wizard
Projection Wizard is an online map projection selection tool available at projec-
tionwizard.org that assists cartographers in selecting projections (Fig. 9.11)(Šavrič
et al. 2016). Projection Wizard integrates Snyder’s selection guideline with the
extensions suggested in this book chapter. It includes the projections for world
Fig. 9.11 Selecting a projection with Projection Wizard at projectionwizard.org
226 B. Jenny et al.
maps listed in Table 9.1 and the projections for hemisphere maps discussed above.
The user selects the desired distortion property, and a projection is then suggested
and a preview map generated. Projection Wizard is simple to use and can also
suggest projections for maps at larger scales, showing continents or smaller areas.
For these maps, the user defines the area to be mapped on an interactive web map.
9.6 Conclusion
Although the selection of map projections is one of the most important aspects of
mapping, it is often given little consideration. The map projection is the basis for
the rest of the map and is therefore, an important component of cartographic design.
Map projections must be selected carefully according to criteria such as the map’s
extent, purpose, and cartographic visualization technique. An appropriate projection
can minimize distortion when measuring distances, angles, or areas. Most impor-
tantly, a poorly chosen projection can result in misinterpreted information and
impact the effectiveness of a map.
This chapter only includes a selection of projections for world and hemisphere
maps. Many alternative projections exist with similar distortion properties and
visual appearance that may also be appropriate for small-scale maps.
Snyder’s selection guideline relies on the answers to two main questions: what is
the geographic extent mapped, and, which distortion properties need to be pre-
served? The selection guideline then leads the cartographer to a set of appropriate
projections for world and hemisphere maps.
Snyder published his selection guideline in 1987 at a time when cartographers
were using computer algorithms for creating maps with a variety of projections, but
before Web mapping services, such as Google Maps, existed. Google introduced
their Web mapping service in 2005 and the underlying Mercator projection quickly
became the de facto standard for Web maps (Battersby et al. 2014). While the
Mercator projection is included in Snyder’s selection tree for some maps, it is a
poor choice for world maps because it shows polar areas with enormous areal
distortion. Web mapping services will hopefully include more alternative projec-
tions for world maps in the future. A viable option could be adaptive composite
map projections (Jenny 2012) that automatically adjust the map’s geometry in
accordance with Snyder’s selection guideline.
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