Description of commonly used map projections, their advantages, drawbacks and specific applications.

1. PROJECTIONS AND ITS TYPES
DEPARTMENT OF AGRICULTURE
METEOROLOGY
Asmita
2021A02PGDC
CCS-HAU 24 February, 2022

2. INTRODUCTION TO PROJECTIONS
• Projections are a systematic conversion of spherical coordinates (latitude
and longitude) and transform them to an XY (planar) coordinate system.
• These mathematical equations enables us to create a map that shows
distances, areas, or directions. Either one or more or all features are
compromised based on the type of projection used.
• These are not true portrayals of the globe because a two-dimensional
plane cannot accurately represent large portions of the rounded,
curvilinear surface of the Earth.
• The first step is to select a model that approximates the shape and size of
the earth.
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3. SHAPE OF THE EARTH
• Earth is a complex three-dimensional object with physical dimensions.
• With a non-straight, curvilinear surface.
• To effectively represent the shape and size of the Earth for scientific and
real-life applications, a calculable, formula-driven model of the Earth is
required.
• The closer a model comes to the actual surface of the Earth, the better it
is for geographic positioning.
• Earth’s rugged, irregular surface and the positions of Earth features are
not significant compared to the diameter of earth.
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4. GEOID
• Geoid is an approximated figure of the Earth.
• It is not a smooth surface, but rather rugged and undulating one.
• The gravitational pull is not uniform throughout the Earth surface. This is
mainly because of density variation inside the Earth.
• The geoid is considered as a reference from which elevations or heights
can be measured. It is the reference surface for ground survey. The
horizontal and vertical positions are mapped with reference to the geoid
surface.
• Horizontal positions are later adjusted to the ellipsoid surface, because
the irregularities on the geoid surface would make projection and other
mathematical computations extremely complex.
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5. GEOID
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6. ELLIPSOID
• The Earth is an ellipsoid rotating upon its minor
axis, which is functionally called the axis of rotation
or axis of revolution.
• The ellipsoid’s flattening causes two axes:
i) a longer axis
ii) a shorter axis.
• The north-to-south axis through the Earth’s core is
the shorter axis and, as such, is called the minor
axis or polar axis. The east-to-west axis through the
Earth’s core is longer and is called the major axis or
equatorial axis.
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7. ELLIPSOID
• The flattening of the ellipse is directly related to the differences in both the
semi-major axis(a) and semi-minor axis(b).
• It is represented by the formula
• Flattening (f) = (a – b) / a
• Newton in the seventeenth century had predicted the flattening to be about
1/300th of the equatorial axis. And present day measurements show, it as
1/298th of the equatorial axis.
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Name Year Semi-major
axis
Semi-minor
axis
Polar
Flattening
WGS 84 1984 6,378,137.00 6,356,752.30 1/298.257

8. DATUM
• Datum is a reference on the Earth’s surface against which positions are
measured.
• Datum defines the origin of coordinate system from where the
measurements are made.
• There are hundreds of locally developed reference datums around the
world, usually referenced to some convenient local reference point.
• A specific point on the Earth can have substantially different coordinates
depending on the datum used to make the measurement.
• There are following two types of datums:
• Horizontal Datum and
• Vertical Datum. 8

9. CO-ORDINATE SYSTEMS
• We require a coordinate system in order to locate points precisely as well
as measure distance and direction correctly. A coordinate is a number set
that denotes a specific location within a reference system. In general,
there are following two types of coordinate systems:
• Geographic coordinate system, and
• Planar coordinate system
• Planar Coordinate System Planar coordinate system is used to locate
positions on a flat map representing Earth’s curved surface. It is the most
popularly used reference system in mathematics, science, and GIS.
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10. CLASSIFICATION OF PROJECTIONS
• CLASS
Nature of the projection surface or otherwise developable surface.
• ANGLE
Coincidence or contact of the projection surface with the globe
• FIT
Position or alignment of the projection surface in relation to the globe.
• DISTORTION of properties of map projection.
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11. NATURE OF PROJECTION SURFACE
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Cylindrical
Conical
Planar

12. CYLINDERICAL PROJECTION
• A cylinder is assumed to circumscribe a transparent globe so that the
cylinder touches the equator through its circumference.
• Assuming as if a light bulb is placed at the centre of the globe, the
graticule of globe is projected onto the cylinder.
• By cutting open the cylinder along a meridian and unfolding it, a rectangle-
shaped cylindrical projection can be visualised.
• The globe’s longitudes and latitudes are represented by equidistant,
parallel straight lines that intersect one another at right angles.
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13. CYLINDERICAL PROJECTION
• The cylindrical projection is a clear grid representation of the curvilinear
surface that is true at the equator and more distorted towards the poles
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14. CONICAL PROJECTION
• Assume that a cone is placed on the globe in such a way that the apex of
the cone is exactly over the polar axis.
• The cone must touch the globe along a parallel of the latitude, known as
the standard parallel, selected by the user. Along this standard parallel,
scale is correct and there is least distortion. When the cone is cut open
along a meridian and laid flat, it appears fan shaped.
• The meridians appear as straight lines radiating from the vertex at equal
angles, while the parallels appear as arcs of concentric circles.
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15. CONICAL PROJECTION
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16. PLANAR PROJECTION
• A plane surface is placed so that it touches the globe at the North or South
Pole. It is circular in shape with meridians projected as straight lines
radiating from center of the circle, the pole.
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17. POSITION OF THE PROJECTION SURFACE
• The developable surface may be placed in three different ways relative to
the globe: normal, transverse or oblique
• Different aspects of map projections are selected to preserve certain
desired properties for particular applications.
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18. COINCIDENCE OF PROJECTION SURFACE
• The coincidence can be of 2 types: tangent & secant.
• Mathematically, it is possible to make the developable surface cut through
the globe as a secant cylinder, cone, or plane. The secant case is
introduced to increase the contact between the globe and the
developable surface and thus increase the area of minimum distortion.
• Two standard parallels are produced, where the scale will be in better
control than in other parts of the map.
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19. PROPERTIES OF PROJECTION
• Area, Distance, Shape, Direction.
• For spherical Earth, all these four properties are correct.
• However, while transforming the Earth features onto a plane, only some of
the properties can be retained.
• Different map projections are designed to achieve one or two of these
properties for specific applications.
• It is clear that scale requirements for both conformality (shape) and
equivalence(area) are contradictory and cannot be obtained.
• This leads to devising of 4 types of map projections.
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20. PROPERTIES OF PROJECTION
• Conformal or Orthomorphic : Preserves shape by retaining correct angles
between points. In this condition, the parallels and meridians will intersect
at 90 ̊.
• Equal Area : Preserve areas
• Equidistant : Preserves distances between certain points by maintaining
the consistency of scale along the standard lines or meridians.
• Azimuthal : Preserves direction of all points on the map correctly with
respect to the center.
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21. COMMONLY USED MAP
PROJECTIONS
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22. MERCATOR’S PROJECTION
• A normal cylindrical
projection.
• Conformal. Parallels and
meridians are straight
lines intersecting at right
angles.
• Meridians are equally
spaced. The parallel
spacing increases with
distance from the equator.
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23. MERCATOR’S PROJECTION
• The projection was originally designed to display accurate compass
bearings for sea travel. Any straight line drawn on this projection
represents a true direction line
• Sailing the shortest distance course means that the direction changes
every moment.
• The Mercator projection is sometimes inappropriately used in atlases for
maps of the world, and for wall-maps as area distortions are significant
towards the polar regions. This exaggeration of area as latitude increases
makes Greenland appear to be as large as South America when, in fact, it
is only one eight of the size.
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24. TRANVERSE MERCATOR PROJECTION
• A transverse cylindrical
projection.
• Angles and shapes are
shown correctly.
• The developable cylinder is
longitudinal along a
meridian instead of the
equator.
• The distortion increases
with the increase in
distance from the standard
parallels. 24

25. UNIVERSAL TRANSVERSE MERCATOR
(UTM) PROJECTION
• The Universal Transverse Mercator (UTM) projection uses a transverse
cylinder, secant to the reference surface.
• It is recommended for topographic mapping by the United Nations
Cartography Committee in 1952. The UTM divides the world into 60
narrow longitudinal zones of 6 degrees, numbered from 1 to 60. The
narrow zones of 6 degrees make the distortions so small that they can be
ignored when constructing a map for a scale of 1:10,000 or smaller.
• The UTM coordinates extend around the world from 84° N to 80° S.
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26. PSEUDO-CYLINDRICAL PROJECTIONS
• Projections in which the parallels are represented by parallel straight lines,
and the meridians by curves. The central meridian is the only meridian
that is straight.
• Equal-area, certainly not conformal because the parallels and meridians
do not always cross at right angles.
• Examples are Mollweide, Sinusoidal, Robinson’s projection.
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27. ROBINSON PROJECTION
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28. MOLLWEIDE'S PROJECTION
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29. LAMBERT CONFORMAL CONIC PROJECTION
• A conformal conical
projection.
• The parallels and
meridians intersect at
right angles
• Areas are inaccurate
• Widely used for
topographic maps.
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30. SIMPLE CONIC PROJECTION
• A normal conical projection
with one standard parallel. All
circular parallels are spaced
evenly along the meridians,
which creates a true scale
along all meridians. The map is
therefore equidistant along
the meridians.
• Both shape and area are well
preserved.
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31. PSEUDO-CONICAL PROJECTIONS
• Not conformal
• The meridians are represented by
curves, and the parallels are equally
spaced concentric circular arcs. The
central meridian is the only meridian
that is straight. Examples are Bonne
and Werner projection.
• Bonne's projection is a pseudo-conical
equal-area projection, with every
parallel true to scale.
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32. AZIMUTHAL PROJECTIONS
• Azimuthal projections are made upon a plane tangent (or secant) to the
reference surface. 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.
• All azimuthal projections possess the property of maintaining true directions
from the centre of the map. In the polar cases, the meridians all radiate out
from the pole at their correct angular distance apart.
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34. AZIMUTHAL PROJECTIONS
• A subdivision may be made
based upon the imaginary source
of light rays.
• In gnomonic projection, the
perspective point, is the centre
of the Earth. For
the stereographic this point is
the opposite pole to the point of
tangency, and for
the orthographic the perspective
point is at infinite distance.
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35. STEREOGRAPHIC PROJECTION
• A conformal projection, parallels &
meridians meet at right angles.
• In the polar aspect the meridians are
equally spaced straight lines, the
parallels are unequally spaced circles
centered at the pole.
• The scale is constant along the
projection centre, but increases
moderately with distance from the
centre.
• Areas increase with distance from the
projection center.
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36. ORTHOGRAPHIC PROJECTION
• Distortion in size and area near the
projection limit appears more
realistic than almost any other
projection.
• In the polar aspect, meridians are
straight lines radiating from the
center, and the lines of latitude are
projected as concentric circles that
become closer toward the edge of
the globe. Only one hemisphere can
be shown.
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37. GNOMONIC PROJECTION
• Neither conformal nor equal-area.
• The scale increases rapidly with the distance from the center. Area, shape,
distance and direction distortions are extreme.
• It's wise to orient the centre of the map at the point of interest, since scale
distortions increase rapidly away from the center.
• The projection is useful for defining routes of navigation for sea and air
travel, because the shortest route between any two locations is a always a
straight line.
• It should however not be used for regular geographic maps or for distance
measurements
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38. LAMBERT AZIMUTHAL
EQUAL-AREA PROJECTION
• Preserves areas while
simultaneously maintaining a true
direction from the center. The
general pattern of distortion is
radial. Scale distorts with distance
from the center.
• It is best suited for maps of
continents or regions that are
equally extended in all directions
from the centre, such as Asia and
the Pacific ocean.
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