Statistical techniques in geographical analysis

Statistical Techniques in Geographical
Analysis
By Damon Verial, eHow Contributor
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Geographical analysis is the application of analytical techniques to geographical data.
Much of the results in this field would not be possible without the strong statistical
techniques that support the analysis of data. Geographical analysts rely on many
statistical techniques, including probabilistic methods, hypothesis testing, sample
selection and statistical inference, to perform analyses that allow for the results in this
field.
Other People Are Reading
· How to Select a Data Analysis Technique
· Techniques of Statistical Analysis
1. Probability
o Probability is a useful tool in geographical analysis, especially in
situations where hard data does not exist. The application of probability
can allow a geographical analyst to make reasonable predictions in these
situations. Consider the lack of data regarding how people in the United
States migrate and change residences. A geographical analyst can use the
probabilities of moving certain distances along with the probabilities of
moving certain directions to predict the average migration patterns of
citizens of the United States.
Hypotheses Tests
o In geographical analysis, analysts often want to make meaningful
comparisons. However, whether the data be air pollution levels in big
cities or state population growth, simply looking at the data to determine if
there are differences present is poor method to make this determination.

Statistics offers geographical analysts the ability to use hypotheses tests to
conclude with high probability whether differences are present and in what
ways the things being compared differ.
o
Data Selection
o Geographical analysis relies heavily on finding data sets with which to
perform analyses; yet the choice of data is a complicated procedure. To
avoid collecting a biased data set, geographical analysts must employ a
suitable sampling method for the situation. How to appropriately select a
sample is a well-researched topic of statistics, and geographical analysts
make heavy use of the well-founded statistical practice of selecting
unbiased, representative samples.
Inference
o Often, geographical analysts perform analysis on a small geographical
area because of restrictions in funding, time or other resources. In spite of
this, analysts execute their analyses with the overall goal of making
inferences about larger geographical areas. The problem is that without the
appropriate statistical techniques these inferences will not hold. Statistics
inference allows analysts to move away from simply describing their
sample and move toward using their results to make larger, more general
conclusions.
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http://education.nationalgeographic.com/education/geographic-skills/?ar_a=1
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· Written By: S.E. Smith
· Edited By: Bronwyn Harris
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Cartography is the art and science of map making, practiced by cartographers. Humans
have been drawing maps for thousands of years, as part of an effort to understand their
environment. The quest for an accurate map drove explorers to adventure to far-flung
areas well into the 1700s, and cartographers in the modern day find frequent employment
still, thanks to constant political and geological changes around the world. To train in
cartography, a student should be prepared to take years of courses in multiple disciplines.
The term comes from two Greek words, chartis, meaning map, and graphos, meaning to
draw or write. In historic times, an individual cartographer hand drew a map in entirety,
often with limited information. Modern practitioners of cartography have the advantage
of computers and other equipment to assist them, making their maps more precise. The
science of cartography has also evolved, as many maps have become multimedia data
explosions, chock full of information for the reader.

Basic cartography covers two data components. The first is location data, indicating
where the area being depicted is located. In ancient maps, location data often showed
where something was in relation to something else, but modern maps usually use
geographical coordinates such as latitude and longitude to orient their features. The
second type of data is attributional data, showing bodies of water, mountains, valleys,
hills, and other geographical features of interest and of note.
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A map of the world reflects an immense mathematical and aesthetic challenge, that of
translating the globe to a two dimensional surface. Many cartographers have struggled
with this issue over the centuries, striving to project the features of the globe accurately
and effectively. Numerous approaches have been taken to solve this problem, including
the Mercator Projection, a map which distorts geological features north and south of the
Equator in order to fit the globe into a neat rectangle. Other maps portray the globe in
sections, reducing the amount of distortion necessary.
The skills needed for cartography are immense. Cartography relies heavily on math to
represent the Earth, along with science to help describe and understand geological
features. Specialized maps may include things like ocean soundings, which requires a
knowledge of oceanography, or unique rock formations, which implies geological study
of the region. Knowledge of ongoing political events is also important, as nations divide,
change names, or disappear more frequently than many people realize.
The products of cartography can be divided into two rough types of map, although they
may frequently overlap. A topographical map is one which is designed to be true to the
landscape that it is depicting. Topographical maps usually include elevations, major
geographical features, and other information which someone who use to orient him or
herself. These maps can often be used for decades, unless a major geological event such
as a volcanic eruption or earthquake occurs.
A topological map, on the other hand, is used for conveying information such as highway
routes, dangerous regions of a country, or population density. Topological maps can

sometimes be quite complex, showing multiple important features to readers to highlight
and educate, and they change frequently as the lives of the people and places depicted on
them change.
http://www.wisegeek.com/what-is-cartography.htm
Home Resources Careers
Digital Pamphlet
Careers in Cartography
What Are the Cartographic Sciences ?

The cartographic sciences are geodesy, surveying, photogrammetry, remote sensing,
geographic information systems (GIS), global positioning systems (GPS) and, of course,
mathematics and statistics. In recent years, multimedia and virtual reality became part of
the cartographic experience. These are all separate, though somewhat overlapping,
disciplines, and they share an intimate relationship with cartography; indeed some have
their own cartographic components. A working acquaintance with these fields is an
essential part of the education of the modern cartographer.
Geodesy
Geodesy is a very specialized science concerned with determining the shape and size (the
'figure') of the earth--not the solid earth, but the geoid, the surface defined by mean sea
level--and establishing a framework of points whose locations are known very precisely
in terms of latitude and longitude. This is achieved in two ways, by studying the earth's
gravitational field and by conducting very high-accuracy surveying operations. At one
time, such work was entirely ground-based, but satellite observations are now routine.
Geodesy plays a fundamental role in cartography, for in order to map the earth, it is
obviously necessary to know how big and what shape it is and to have reference points of
known locations on its surface.
Surveying
If geodesy is unfamiliar to most people, surveying is quite the opposite, for almost
everyone has seen the surveyor at work on city streets with transit, level or distance
meter. There are many branches of surveying, including engineering surveys (carried out
in connection with construction projects), cadastral surveys (concerned with property
boundaries), hydrographic surveys (depicting water bodies) and mine surveys (outlining
what is underground). The relation between surveying and cartography is very close
indeed, and the end-product of the surveyor's work is often a map of some sort. One
branch of surveying--topographic surveying-- has the production of maps as its express
aim. Surveying, like cartography, has undergone major changes in recent years, but none
so dramatic as those being brought about by Global Positioning Systems (GPS).
Global Positioning Systems (GPS)
A constellation of twenty-four satellites operated by the U.S. Department of Defense
comprises GPS. It enables surveyors to determine ground locations very precisely at the
click of a button on a hand-held receiver under any weather condition. GPS is
revolutionizing the practice of surveying at a very fast pace. Today, a position on the
earth's surface can be determined within fractions of a centimeter. The standard piece of
information provided by a GPS receiver is a readout of the calculated latitude and
longitude of a given position. These latitude and longitude positions obtained from a GPS
can be plotted on a chart or on a map.
Photogrammetry

Photogrammetry means literally measurement with light and has as its principal aim the
production of topographic maps from aerial photographs. An earlier technological change
that revolutionized topographic surveying, photogrammetry emerged in the 1930s.
Previously topographic maps (large-scale maps in sheet form showing natural and
cultural features in the landscape) were produced by traditional ground surveying
methods, and while ground surveys are still needed, most of the detail on these maps--the
rivers, coastlines, roads, buildings, contours, and so on--is now derived from airphotos.
The work is done by the operator of a photogrammetric plotter, a complex piece of
machinery that enables one to trace landscape features from a three-dimensional 'model'
of the earth's surface created by viewing airphotos stereoscopically. In modern
photogrammetry, the movements of the tracing device, or 'floating mark,' are translated
directly into digital form and the map is plotted automatically.
Remote Sensing
A more recent discipline, dating from the 1960s, is remote sensing, the process of
obtaining information about the earth's surface using sensors carried in aircraft and
satellites. Though the discipline is new, the original form of remote sensing--aerial
photography--dates from the nineteenth century, and techniques of airphoto interpretation
have long been highly developed. All types of remote sensing involve the measurement
of electromagnetic energy reflected from or radiated by the earth's surface, and
photographic cameras (based on visible light) are now accompanied by other sensing
devices operating at longer wavelengths. Examples are thermal scanners in the infrared
waveband and radar systems in the microwaves. The information obtained may be in
image form (like a photograph) or in digital form, and one of the most intriguing
applications of remote sensing is the computer processing of digital multispectral data
(data obtained simultaneously in more than one waveband) to produce land cover maps
of the earth's surface. Another application of increasing importance is image mapping,
the incorporation of a remote sensing image, enhanced by computer processing, into the
map itself. Remote sensing, especially sensing from space, is a major source of mappable
data, and as such plays a key role in modern cartography.
Geographical Information Systems (GIS)
Another new discipline, perhaps the most exciting of all, GIS is a computer-based system
for handling geographical data, that is, data relating to the earth's surface. The word
'handling' conceals a wealth of different operations, however. Some, like data storage and
retrieval, are fairly mundane, but others, especially analytical operations like buffering,
overlay, network analysis and viewshed modelling, are truly staggering in their potential
for solving real-world problems. Maps are integral to a GIS. Data are stored in the
computer in the form of 'layers,' each in effect a digital map of some component of the
landscape (e.g. a streams layer, a roads layer, a soils layer) and analyses are achieved by
performing operations on these layers, sometimes one at a time, sometimes on several
layers simultaneously. Each stage in an analysis is displayed in map form on a high-resolution
computer monitor, and the end-product is very commonly itself a map. GIS
has become a billion-dollar business since the early eighties, which is not surprising
given the range of proven applications. These include forest management, urban

planning, emergency vehicle dispatch, mineral prospecting, retail outlet location,
maintenance of public utilities, and waging war, as well as a host of applications with
purely scientific ends.
Mathematics and Statistics
Mathematics and statistics are heavily involved in the mapping process, not only because
of the geometric aspects of describing locations in space, but also because of clear needs
to describe and summarize the characteristics of spatial data. Through creative
mathematical approaches, cartographers may find new solutions to solve spatial
problems.
Multimedia (MM)
Computer systems allow for integrated access to a range of data through the means of
stimulation of human senses using digital technology. This includes the integration of
images, video and graphics, maps and photographs, text and sound and perhaps in the
future smell and taste. This technology has a wide range of applications including
education, scientific research, military activities and, of course, entertainment.
Virtual Reality (VR)
A computer system that is able to combine a mixture of real world experiences and
computer generated material to allow for simulated real world representation produces a
"virtual reality." VR addresses the construction of artificial worlds with clear spatial
dimensions. The movie "Twister" is an excellent example how VR works. These same
kind of images can be very useful for the scientist to model or demonstrate an event such
as a natural hazard. Cartographers have a major role to play in the identification of VR as
a potential research tool.
Cartography and the cartographic sciences are all concerned in some way with data
relating to the earth's surface, whether it be data acquisition, management, analysis or
display, and there is a growing trend, driven by a common dependence on computer
technology, for the disciplines described here to move even closer together. Reflecting
this trend, the term geomatics is used in Canada to denote an integrated multi-disciplinary
approach to dealing with earth-related data. In a sense, geomatics is an umbrella term for
cartography and the cartographic sciences.
http://www.cca-acc.org/careers-2.asp
Types of Maps:
Projections Geography Glossary Geography Label Me Printouts

A map is a representation of a place. There are many different types of maps
that have different uses.
Projections: Maps are called projections because map-makers have to project a
3-D surface onto a 2-D map. A projection is a representation of one thing onto
another, such as a curved 3-Dimensional surface (like the Earth) onto a flat 2-
Dimensional map. There are 3 major types of projections: cylindrical, conic,
and planar.
Since a map is 2-dimensional representation of a 3-dimensional world,
compromises must be made in accuracy (some information must be lost when
one dimension is ignored). Different maps differ in the relative accuracy of the
depiction of the area, the shapes of objects, actual distances, and compass
direction. Maps that focus on maintaining one feature (like preserving distance)
must distort other features (like area, shape and compass directions).
Maps that accurately reflect area are often called equal-area maps (an example
is the Albers equal-area conic map). Maps that maintain the shape of objects
are called conformal. Maps that correctly show the distance between points are
often called equi-distant maps (note that the shortest distance between two
points on a map is generally not a straight line. but a curve). Navigational maps
need accurate compass directions maintained on the map (like the Mercator
map).
Related Terms:
central
meridian
A central meridian
is a meridian that
passes through the
center of a
projection. The
central meridian is
often a straight line
that is an axis of
symmetry of the
projection.
conic projection
A conic projection is a
type of map in which a
cone is wrapped
around a sphere (the
globe), and the details
of the globe are
projected onto the
cylindrical surface.
Then, the cylinder is
unwrapped into a flat
cylindrical projection
A cylindrical projection is a
type of map in which a
cylinder is wrapped around a
sphere (the globe), and the
details of the globe are
projected onto the cylindrical
surface. Then, the cylinder is
unwrapped into a flat
surface, yielding a
rectangular-shaped map.
Cylindrical maps have a lot
equator
The equator is
an imaginary
circle around
the earth,
halfway
between the
north and
south poles.

surface.
of distortion in the polar
regions (that is, the size of
the polar regions is greatly
exaggerated on these maps).
geographical
coordinate
system
A geographical
coordinate system
is a system that
uses latitude and
longitude to
describe points on
the spherical
surface of the
globe.
latitude
Latitude is the
angular distance
north or south
from the
equator to a
particular
location. The
equator has a
latitude of zero
degrees. The
North Pole has a
latitude of 90
degrees North;
the South Pole
has a latitude of
90 degrees
South.
longitude
Longitude is the
angular distance east
or west from the
north-south line that
passes through
Greenwich, England,
to a particular
location. Greenwich,
England has a
longitude of zero
degrees. The farther
east or west of
Greenwich you are,
the greater your
longitude. Midway
Islands (in the Pacific
Ocean) have a
longitude of 180
degrees (they are on
the opposite side of
the globe from
Greenwich).
Mercator projection
A Mercator projection is a
type of rectangular map in
which the true compass
direction are kept intact (lines
of latitude and longitude
intersect at right angles), but
areas are distorted (for
example, polar areas look
much larger than they really
are). Mercator projections are
useful for nautical
navigation. Geradus
Mercator devised this
cylindrical projection for use
in navigation in 1569.
meridian
A meridian a circular
arc of longitude that
meets at the north and
south poles and
connects all places of
the same longitude.
The prime meridian
(0 degrees longitude)
passes through
Greenwich, England.
Mollweide projection
A Mollweide projection is a type of
sinusoidal projection map in which
the entire surface of the Earth is
shown within an ellipse. Lines of
latitude are parallel to the equator, but
lines of longitude are curved in such a
Orthographic
projection
An Orthographic projection
is a type of map in which is
essentially a drawing of
(one side of) a globe. There
is a lot of distortion of area
in this type of map, but one
gets the idea that the globe
is being represented.

way that area distortion is minimal.
The distortion is greatest at the edges
of the ellipse. This type of projection
was created by Carl B. Mollweide in
1805.
Orthophanic projection
The Orthophanic (meaning 'right
appearing') projection, also called the
Robinson projection, is a widely-used
type of map in which the Earth is shown
in a flattened ellipse. In this
pseudocylindrical. projection, lines of
latitude are parallel to the equator, but
lines of latitude are elliptical arcs. In a
Robinson projection, area is represented
accurately, but the distances and
compass directions are distorted (for
example, compass lines are curved).
This type of projection was first made in
1963 by Arthur H. Robinson.
parallel
A parallel (of
latitude) is a line on
a map that represents
an imaginary east-west
circle drawn on
the Earth in a plane
parallel to the plane
that contains the
equator.
planar projection
A planar projection is a
type of map in which the
details of the globe are
projected onto a plane (a
flat surface) yielding a
rectangular-shaped map.
Cylindrical maps have a
lot of distortion towards
the edges.
Robinson projection
The Robinson projection is a
widely-used type of map in
which the Earth is shown within
an ellipse with a flat top and
bottom. In this
pseudocylindrical. projection,
lines of latitude are parallel to
the equator, but lines of latitude
are elliptical arcs. In a Robinson
projection, area is represented
accurately, but the distances and
compass directions are distorted
(for example, compass lines are
curved). This type of projection
was first made in 1963 by
Arthur H. Robinson; it is also
called the Orthophanic
projection (meaning 'right
sinusoidal projection
A sinusoidal projection is
a type of map projection in
which lines of latitude are
parallel to the equator, and
lines of longitude are
curved around the prime
meridian.
Winkel Tripel
projection
A Winkel Tripel projection
is a type of preudocylindrical
projection map in which both
the lines of latitude and
longitude are curved. The
Winkel Tripel projection was
adopted by the National
Geographic Society in the
late 1990s (replacing the
Robinson projection).

appearing').
http://www.enchantedlearning.com/geography/glossary/projections.shtml
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The Three Main Families of Map Projections
On this page…
Unwrapping the Sphere to a Plane
Cylindrical Projections
Conic Projections
Azimuthal Projections
Unwrapping the Sphere to a Plane
Mapmakers have developed hundreds of map projections, over several thousand years.
Three large families of map projection, plus several smaller ones, are generally
acknowledged. These are based on the types of geometric shapes that are used to transfer
features from a sphere or spheroid to a plane. As described above, map projections are
based on developable surfaces, and the three traditional families consist of cylinders,
cones, and planes. They are used to classify the majority of projections, including some
that are not analytically (geometrically) constructed. In addition, a number of map
projections are based on polyhedra. While polyhedral projections have interesting and
useful properties, they are not described in this guide.
Which developable surface to use for a projection depends on what region is to be
mapped, its geographical extent, and the geometric properties that areas, boundaries, and
routes need to have, given the purpose of the map. The following sections describe and
illustrate how the cylindrical, conic, and azimuthal families of map projections are
constructed and provides some examples of projections that are based on them.
Cylindrical Projections

A cylindrical projection is produced by wrapping a cylinder around a globe representing
the Earth. The map projection is the image of the globe projected onto the cylindrical
surface, which is then unwrapped into a flat surface. When the cylinder aligns with the
polar axis, parallels appear as horizontal lines and meridians as vertical lines. Cylindrical
projections can be either equal-area, conformal, or equidistant. The following figure
shows a regular cylindrical or normal aspect orientation in which the cylinder is tangent
to the Earth along the Equator and the projection radiates horizontally from the axis of
rotation. The projection method is diagrammed on the left, and an example is given on
the right (equal-area cylindrical projection, normal/equatorial aspect).
For a description of projection aspect, see Projection Aspect.
Some widely used cylindrical map projections are
· Equal-area cylindrical projection
· Equidistant cylindrical projection
· Mercator projection
· Miller projection
· Plate Carrée projection
· Universal transverse Mercator projection
Pseudocylindrical Map Projections
All cylindrical projections fill a rectangular plane. Pseudocylindrical projection outlines
tend to be barrel-shaped rather than rectangular. However, they do resemble cylindrical
projections, with straight and parallel latitude lines, and can have equally spaced

meridians, but meridians are curves, not straight lines. Pseudocylindrical projections can
be equal-area, but are not conformal or equidistant.
Some widely-used pseudocylindrical map projections are
· Eckert projections (I-VI)
· Goode homolosine projection
· Mollweide projection
· Quartic authalic projection
· Robinson projection
· Sinusoidal projection
Conic Projections
A conic projection is derived from the projection of the globe onto a cone placed over it.
For the normal aspect, the apex of the cone lies on the polar axis of the Earth. If the cone
touches the Earth at just one particular parallel of latitude, it is called tangent. If made
smaller, the cone will intersect the Earth twice, in which case it is called secant. Conic
projections often achieve less distortion at mid- and high latitudes than cylindrical
projections. A further elaboration is the polyconic projection, which deploys a family of
tangent or secant cones to bracket a succession of bands of parallels to yield even less
scale distortion. The following figure illustrates conic projection, diagramming its
construction on the left, with an example on the right (Albers equal-area projection, polar
aspect).
Some widely-used conic projections are
· Albers Equal-area projection

· Equidistant projection
· Lambert conformal projection
· Polyconic projection
Azimuthal Projections
An azimuthal projection is a projection of the globe onto a plane. In polar aspect, an
azimuthal projection maps to a plane tangent to the Earth at one of the poles, with
meridians projected as straight lines radiating from the pole, and parallels shown as
complete circles centered at the pole. Azimuthal projections (especially the orthographic)
can have equatorial or oblique aspects. The projection is centered on a point, that is either
on the surface, at the center of the Earth, at the antipode, some distance beyond the Earth,
or at infinity. Most azimuthal projections are not suitable for displaying the entire Earth
in one view, but give a sense of the globe. The following figure illustrates azimuthal
projection, diagramming it on the left, with an example on the right (orthographic
projection, polar aspect).
Some widely used azimuthal projections are
· Equidistant azimuthal projection
· Gnomonic projection
· Lambert equal-area azimuthal projection
· Orthographic projection
· Stereographic projection

· Universal polar stereographic projection
For additional information on families of map projections and specific map projections,
see Supported Map Projections.
http://www.mathworks.com/help/map/the-three-main-families-of-map-projections.html
Cylindrical Projection
A cylindrical projection map is the most common type of map that we see. Imagine
placing the movie screen around the globe in a cylinder shape. The projection that results
is depicted in this image. Notice that areas close to the equator have very little distortion.
However, the closer to the poles that one travels, the more distorted the map becomes. In
this example, Greenland appears to be many times larger than it really is.
Conic Projection
A conic projection map is created by placing a cone shaped screen on a globe. The
resulting projection is more accurate than the cylindrical projection map discussed above.
However, the further we travel down the map, the more distorted and less accurate the
map becomes.

Plane Projection
A plane projection is created by placing an imaginary screen directly above or below a
globe. The image that would result is called a plane projection. This type of map
projection is not commonly used.

Interrupted Projection
There are many different types of interrupted projection maps. These types of maps try to
depict the continents as accurately as possible by leaving blank space in the less
important areas of the map, such as in the oceans.

Map Projections - types and distortion
patterns
The shape of the Earth is represented as a sphere. It is also modeled more accurately as an
oblate spheroid or an ellipsoid. A globe is a scaled down model of the Earth. Although
they can represent size, shape, distance and directions of the Earth features with
reasonable accuracy, globes are not practical or suitable for many applications. They are
hard to transport and store; for example you can not stuff a globe in your backpack while
hiking or store it in your car’s glove compartment. Globes are not suitable for use at large
scales, such as finding directions in a city or following a hiking route, where a more
detailed image is essential. They are expensive to produce, especially in varying sizes
(scales). On a curved surface, measuring terrain properties is difficult, and it is not
possible to see large portions of the Earth at once.
Maps do not suffer from the above shortcomings and are more practical than globes in
most applications. Historically cartographers have tried to address the challenge of

representing the curved surface of the Earth on a map plane, and to this end have devised
map projections. A map projection is the transformation of Earth’s curved surface (or a
portion of) onto a two-dimensional flat surface by means of mathematical equations.
During such transformation, the angular geographic coordinates (latitude, longitude)
referencing positions on the surface of the Earth are converted to Cartesian coordinates
(x, y) representing position of points on a flat map.
Types of map projections based on developable surface
One way of classifying map projections is by the type of the developable surface onto
which the reference sphere is projected. A developable surface is a geometric shape that
can be laid out into a flat surface without stretching or tearing. The three types of
developable surfaces are cylinder, cone and plane, and their corresponding projections
are called cylindrical, conical and planar. Projections can be further categorized based on
their point(s) of contact (tangent or secant) with the reference surface of the Earth and
their orientation (aspect).
Keep in mind that while some projections use a geometric process, in reality most
projections use mathematical equations to transform the coordinates from a globe to a flat
surface. The resulting map plane in most instances can be rolled around the globe in the
form of cylinder, cone or placed to the side of the globe in the case of the plane. The
developable surface serves as a good illustrative analogy of the process of flattening out a
spherical object onto a plane.
Cylindrical projection
In cylindrical projections, the reference spherical surface is projected onto a cylinder
wrapped around the globe. The cylinder is then cut lengthwise and unwrapped to form a
flat map.

Tangent vs. secant cylindrical projection
Cylindrical projection - tangent and secant equatorial aspect © USGS
The cylinder may be either tangent or secant to the reference surface of the Earth. In the
tangent case, the cylinder’s circumference touches the reference globe’s surface along a
great circle (any circle having the same diameter as the sphere and thus dividing it into
two equal halves). The diameter of the cylinder is equal to the diameter of the globe. The
tangent line is the equator for the equatorial or normal aspect; while in the transverse
aspect, the cylinder is tangent along a chosen meridian (i.e. central meridian).
In the secant case, the cylinder intersects the globe; that is the diameter of the cylinder is
smaller than the globe’s. At the place where the cylinder cuts through the globe two
secant lines are formed.
The tangent and secant lines are important since scale is constant along these lines
(equals that of the globe), and therefore there is no distortion (scale factor = 1). Such
lines of true scale are called standard lines. These are lines of equidistance. Distortion
increases by moving away from standard lines.
In normal aspect of cylindrical projection, the secant or standard lines are along two
parallels of latitude equally spaced from equator, and are called standard parallels. In
transverse aspect, the two standard lines run north-south parallel to meridians. Secant
case provides a more even distribution of distortion throughout the map. Features appear
smaller between secant lines (scale < 1) and appear larger outside these lines (scale > 1).

Cylindrical aspect – equatorial (normal), transverse, oblique
Cylindrical projection - transverse and oblique aspect © USGS
The aspect of the map projection refers to the orientation of the developable surface
relative to the reference globe. The graticule layout is affected by the choice of the
aspect.
In normal or equatorial aspect, the cylinder is oriented (lengthwise) parallel to the
Earth’s polar axis with its center located along the equator (tangent or secant). The
meridians are vertical and equally spaced; the parallels of latitude are horizontal straight
lines parallel to the equator with their spacing increasing toward the poles. Therefore the
distortion increases towards the poles. Meridians and parallels are perpendicular to each
other. The meridian that lies along the projection center is called the central meridian.
In transverse aspect, the cylinder is oriented perpendicular to the Earth’s axis with its
center located on a chosen meridian (a line going through the poles). And the oblique
aspect refers to the cylinder being centered along a great circle between the equator and
the meridians with its orientation at an angle greater than 0 and less than 90 degrees
relative to the Earth’s axis.
Examples of cylindrical projections include Mercator, Transverse Mercator, Oblique
Mercator, Plate Carré, Miller Cylindrical, Cylindrical equal-area, Gall–Peters, Hobo–
Dyer, Behrmann, and Lambert Cylindrical Equal-Area projections.
Conical (conic) projection
In conical or conic projections, the reference spherical surface is projected onto a cone
placed over the globe. The cone is cut lengthwise and unwrapped to form a flat map.

Tangent vs. secant conical projection
Conic projection - tangent and secant © USGS
The cone may be either tangent to the reference surface along a small circle (any circle on
the globe with a diameter less than the sphere’s diameter) or it may cut through the globe
and be secant (intersect) at two small circles.
For the polar or normal aspect, the cone is tangent along a parallel of latitude or is secant
at two parallels. These parallels are called standard parallels. This aspect produces a map
with meridians radiating out as straight lines from the cone’s apex, and parallels drawn as
concentric arcs perpendicular to meridians.
Scale is true (scale factor = 1) and there is no distortion along standard parallels.
Distortion increases by moving away from standard parallels. Features appear smaller
between secant parallels and appear larger outside these parallels. Secant projections lead
to less overall map distortion.
Conical aspect – equatorial (normal), transverse, oblique
The polar aspect is the normal aspect of the conic projection. In this aspect the cone’s
apex is situated along the polar axis of the Earth, and the cone is tangent along a single
parallel of latitude or secant at two parallels. The cone can be situated over the North or
South Pole. The polar conic projections are most suitable for maps of mid-latitude
(temperate zones) regions with an east-west orientation such as the United States.
In transverse aspect of conical projections, the axis of the cone is along a line through the
equatorial plane (perpendicular to Earth’s polar axis). Oblique aspect has an orientation
between transverse and polar aspects. Transverse and oblique aspects are seldom used.
Examples of conic projections include Lambert Conformal Conic, Albers Equal Area
Conic, and Equidistant Conic projections.
Planar projection – Azimuthal or Zenithal

In planar (also known as azimuthal or zenithal) projections, the reference spherical
surface is projected onto a plane.
Tangent vs. secant planar projection
Planar (azimuthal) projection - tangent and secant © USGS
The plane in planar projections may be tangent to the globe at a single point or may be
secant. In the secant case the plane intersects the globe along a small circle forming a
standard parallel which has true scale. The normal polar aspect yields parallels as
concentric circles, and meridians projecting as straight lines from the center of the map.
The distortion is minimal around the point of tangency in the tangent case, and close to
the standard parallel in the secant case.
Planar aspect – polar (normal), transverse (equatorial), oblique
The polar aspect is the normal aspect of the planar projection. The plane is tangent to
North or South Pole at a single point or is secant along a parallel of latitude (standard
parallel). The polar aspect yields parallels of latitude as concentric circles around the
center of the map, and meridians projecting as straight lines from this center. Azimuthal
projections are used often for mapping Polar Regions, the polar aspect of these
projections are also referred to as polar azimuthal projections.
In transverse aspect of planar projections, the plane is oriented perpendicular to the
equatorial plane. And for the oblique aspect, the plane surface has an orientation between
polar and transverse aspects.
These projections are named azimuthal due to the fact that they preserve direction
property from the center point of the projection. Great circles passing through the center
point are drawn as straight lines.

Examples of azimuthal projections include: Azimuthal Equidistant, Lambert Azimuthal
Equal-Area, Gnomonic, Stereographic, and Orthographic projections.
Azimuthal Perspective Projections
Some classic azimuthal projections are perspective projections and can be produced
geometrically. They can be visualized as projection of points on the sphere to the plane
by shining rays of light from a light source (or point of perspective). Three projections,
namely gnomonic, stereographic and orthographic can be defined based on the location
of the perspective point or the light source.
Gnomonic Projection (also known as Central or Gnomic Projection)
Gnomonic Projection © USGS
The point of perspective or the light source is located at the center of the globe in
gnomonic projections. Great circles are the shortest distance between two points on the
surface of the sphere (known as great circle route). Gnomonic projections map all great
circles as straight lines, and such property makes these projections suitable for use in
navigation charts. Distance and shape distortion increase sharply by moving away from
the center of the projection.

Stereographic Projection
Stereographic projection © USGS
In stereographic projections, the perspective point is located on the surface of globe
directly opposite from the point of tangency of the plane. Points close to center point
show great distortion on the map. Stereographic projection is a conformal projection, that
is over small areas angles and therefore shapes are preserved. It is often used for mapping
Polar Regions (with the source located at the opposite pole).
Orthographic Projection
Orthographic projection © USGS
In orthographic projections, the point of perspective is at infinite distance on the opposite
direction from the point of tangency. The light rays travel as parallel lines. The resulting
map from this projection looks like a globe (similar to seeing Earth from deep space).
There is great distortion towards the borders of the map.
Map projection types based on distortion characteristics
As stated above spherical bodies such as globes can represent size, shape, distance and
directions of the Earth features with reasonable accuracy. It is impossible to flatten any
spherical surface (e.g. an orange peel) onto a flat surface without some stretching,

tearing, or shearing. Similarly, when trying to project a spherical surface of the Earth
onto a map plane, the curved surface will get deformed, causing distortions in shape
(angle), area, direction or distance of features. All projections cause distortions in varying
degrees; there is no one perfect projection preserving all of the above properties, rather
each projection is a compromise best suited for a particular purpose.
Different projections are developed for different purposes. Some projections minimize
distortion or preserve some properties at the expense of increasing distortion of others.
The choice of a projection for a map depends on such factors as the purpose for which the
map will be used, the area being mapped, and the map’s scale (distortion is more
pronounced in small-scale mapping).
Measuring map scale distortion – scale factor &
principal (nominal) scale
As mentioned above, a reference globe (reference surface of the Earth) is a scaled down
model of the Earth. This scale can be measured as the ratio of distance on the globe to the
corresponding distance on the Earth. Throughout the globe this scale is constant. For
example, a 1:250000 representative fraction scale indicates that 1 unit (e.g. km) on the
globe represents 250000 units on Earth. The principal scale or nominal scale of a flat
map (the stated map scale) refers to this scale of its generating globe.
However the projection of the curved surface on the plane and the resulting distortions
from the deformation of the surface will result in variation of scale throughout a flat map.
In other words the actual map scale is different for different locations on the map plane
and it is impossible to have a constant scale throughout the map. This variation of scale
can be visualized by Tissot's indicatrix explained in detail below. Measure of scale
distortion on map plane can also be quantified by the use of scale factor.
Scale factor is the ratio of actual scale at a location on map to the principal (nominal)
map scale (SF = actual scale / nominal scale). This can be alternatively stated as ratio of
distance on the map to the corresponding distance on the reference globe. A scale factor
of 1 indicates actual scale is equal to nominal scale, or no scale distortion at that point on
the map. Scale factors of less than or greater than one are indicative of scale distortion.
The actual scale at a point on map can be obtained by multiplying the nominal map scale
by the scale factor.
As an example, the actual scale at a given point on map with scale factor of 0.99860 at
the point and nominal map scale of 1:50000 is equal to (1:50000 x 0.99860) = (0.99860 /
50000) = 1:50070 (which is a smaller scale than the nominal map scale). Scale factor of 2
indicates that the actual map scale is twice the nominal scale; if the nominal scale is
1:4million, then the map scale at the point would be (1:4million x 2) = 1:2million. A
scale factor of 0.99950 at a given location on the map indicates that 999.5 meters on the
map represents 1000 meters on the reference globe.

As mentioned above, there is no distortion along standard lines as evident in following
figures. On a tangent surface to the reference globe, there is no scale distortion at the
point (or along the line) of tangency and therefore scale factor is 1. Distortion increases
with distance from the point (or line) of tangency.
Map scale distortion of a tangent cylindrical projection - SF = 1 along line of tangency
Scale distortion on a tangent surface to the globe
On a secant surface to the reference globe, there is no distortion along the standard lines
(lines of intersection) where SF = 1. Between the secant lines where the surface is inside
the globe, features appear smaller than in reality and scale factor is less than 1. At places
on map where the surface is outside the globe, features appear larger than in reality and
scale factor is greater than 1. A map derived from a secant projection surface has less
overall distortion than a map from a tangent surface.
Map scale distortion of a secant cylindrical projection - SF = 1 along secant lines

Scale distortion on a secant surface to the globe
Tissot's indicatrix – visualizing map distortion pattern
A common method of classification of map projections is according to distortion
characteristics - identifying properties that are preserved or distorted by a projection. The
distortion pattern of a projection can be visualized by distortion ellipses, which are
known as Tissot's indicatrices. Each indicatrix (ellipse) represents the distortion at the
point it is centered on. The two axes of the ellipse indicate the directions along which the
scale is maximal and minimal at that point on the map. Since scale distortion varies
across the map, distortion ellipses are drawn on the projected map in an array of regular
intervals to show the spatial distortion pattern across the map. The ellipses are usually
centered at the intersection of meridians and parallels. Their shape represents the
distortion of an imaginary circle on the spherical surface after being projected on the map
plane. The size, shape and orientation of the ellipses are changed as the result of
projection. Circular shapes of the same size indicate preservation of properties with no
distortion occurring.
Equal Area Projection – Equivalent or Authalic
Gall-Peters cylindrical equal-area projection Tissot's indicatrix
© Eric Gaba – Wikimedia Commons user: Sting
Equal area map projections (also known as equivalent or authalic projection) represent
areas correctly on the map. The areas of features on the map are proportional to their

areas on the reference surface of Earth. Maintaining relative areas of features causes
distortion in their shapes, which is more pronounced in small-scale maps.
The shapes of the Tissot’s ellipses in this world map Gall-Peters cylindrical equal-area
projection are distorted; however each of them occupies the same amount of area. Along
the standard parallel lines in this map (45° N and 45°S), there is no scale distortion and
therefore the ellipses would be circular.
Equal area projections are useful where relative size and area accuracy of map features is
important (such as displaying countries / continents in world maps), as well as for
showing spatial distributions and general thematic mapping such as population, soil and
geological maps. Some examples are Albers Equal-Area Conic, Cylindrical Equal Area,
Sinusoidal Equal Area, and Lambert Azimuthal Equal Area projections.
Conformal Projection – Orthomorphic or Autogonal

Mercator - conformal projection Tissot's indicatrix
In conformal map projections (also known as orthomorphic or autogonal projection)
local angles are preserved; that is angles about every point on the projected map are the
same as the angles around the point on the curved reference surface. Similarly constant
local scale is maintained in every direction around a point. Therefore shapes are
represented accurately and without distortion for small areas. However shapes of large
areas do get distorted. Meridians and parallels intersect at right angles. As a result of
preserving angles and shapes, area or size of features are distorted in these maps. No map
can be both conformal and equal area.
Tissot’s indicatrices are all circular (shape preserved) in this world map Mercator
projection, however they vary in size (area distorted). Here the area distortion is more
pronounced as we move towards the poles. A classic example of area exaggeration is the
comparison of land masses on the map, where for example Greenland appears bigger than
South America and comparable in size to Africa, while in reality it is about one-eight the
size of S. America and one-fourteenth the size of Africa. A feature that has made

Mercator projection especially suited for nautical maps and navigation is the
representation of rhumb line or loxodrome (line that crosses meridians at the same angle)
as a straight line on the map. A straight line drawn on the Mercator map represents an
accurate compass bearing.
Preservation of angles makes conformal map projections suitable for navigation charts,
weather maps, topographic mapping, and large scale surveying. Examples of common
conformal projections include Lambert Conformal Conic, Mercator, Transverse
Mercator, and Stereographic projection.
Equidistant Projection
Equirectangular (equidistant cylindrical) projection Tissot's indicatrix
In equidistant map projections, accurate distances (constant scale) are maintained only
between one or two points to every other point on the map. Also in most projections there
are one or more standard lines along which scale remains constant (true scale). Distances
measured along these lines are proportional to the same distance measurement on the
curved reference surface. Similarly if a projection is centered on a point, distances to
every other point from the center point remain accurate. Equidistant projections are
neither conformal nor equal-area, but rather a compromise between them.
In this world map equidistant cylindrical projection (also known as plate carrée),
Tissot’s ellipses are distorted in size and shape. However while there are changes in the
ellipses, their north-south axis has remained equal in length. This indicates that any line
joining north and south poles (meridian) is true to scale and therefore distances are
accurate along these lines. Plate carrée is a case of equirectangular projection with
Equator being a standard parallel.
Equidistant projections are used in air and sea navigation charts, as well as radio and
seismic mapping. They are also used in atlases and thematic mapping. Examples of
equidistant projections are azimuthal equidistant, equidistant conic, and equirectangular
projections.

True-Direction Projection – Azimuthal or Zenithal
Gnomonic projection © Wikimedia Commons
Directions from a central point to all other points are maintained accurately in azimuthal
projections (also known as zenithal or true-direction projections). These projections can
also be equal area, conformal or equidistant.
The gnomonic map projection in the image is centered on the North Pole with meridians
radiating out as straight lines. In gnomonic maps great circles are displayed as straight
lines. Directions are true from the center point (North Pole).
True-direction projections are used in applications where maintaining directional
relationships are important, such as aeronautical and sea navigation charts. Examples
include Lambert Azimuthal Equal-Area, Gnomonic, and azimuthal equidistant
projections.
Compromise Projections
Robinson projection © Eric Gaba – Wikimedia Commons user: Sting
Some projections do not preserve any of the properties of the reference surface of the
Earth; however they try to balance out distortions in area, shape, distant, and direction

(thus the name compromise), so that no property is grossly distorted throughout the map
and the overall view is improved. They are used in thematic mapping. Examples include
Robinson projection and Winkel Tripel projection.
http://geokov.com/education/map-projection.aspx
Listing and description of various map projections
http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html
http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?
TopicName=List_of_supported_map_projections
http://www.radicalcartography.net/index.html?projectionref
http://en.wikipedia.org/wiki/List_of_map_projections
http://www.quadibloc.com/maps/mapint.htm
http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html
http://mathworld.wolfram.com/topics/MapProjections.html
http://www.csiss.org/map-projections/
Map projection visualization applications / software
USGS Decision Support System: http://mcmcweb.er.usgs.gov/DSS/
http://www.giss.nasa.gov/tools/gprojector/
http://www.flexprojector.com/
http://www.uff.br/mapprojections/mp_en.html
http://slvg.soe.ucsc.edu/map.html
http://demonstrations.wolfram.com/WorldMapProjections/
http://demonstrations.wolfram.com/DistortionsInMapProjections/
http://www.geometrie.tuwien.ac.at/karto/
http://www.btinternet.com/~se16/js/mapproj.htm
Educational videos
"Many ways to see the world": http://www.earthdaytv.net/ Go to "In The Classroom"
channel, 4th page
http://www.youtube.com/watch?v=2LcyMemJ3dE&feature=related
http://www.youtube.com/watch?v=e2jHvu1sKiI&feature=rec-LGOUT-exp_fresh+div-
1r-3-HM
http://www.youtube.com/watch?v=_XQfRYfxPig&feature=related
http://www.youtube.com/watch?NR=1&v=EPbQQNrBIgo
http://www.youtube.com/watch?v=AI36MWAH54s&feature=related
http://www.youtube.com/watch?v=b1xXTi1nFCo
http://www.youtube.com/watch?v=qgErv6M19yY

Other Useful Links
http://kartoweb.itc.nl/geometrics/Map%20projections/mappro.html
http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html
Map Projections - A Working Manual (USGS PP 1395, John P. Snyder, 1987)
http://www.ec-gis.org/sdi/publist/pdfs/annoni-etal2003eur.pdf
https://courseware.e-education.psu.edu/projection/index.html

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Statistical techniques in geographical analysis