19 Map Projections

Dr. Puneeta Pandey

 

1. Contents

  • What is map projection
  • Primary relationship between coordinate system and map projection Basic of scale factor and its transformation
  • What are the metric properties of map Classification of map projection
  • Aspects of map projection Distortion properties of map
  • How map projection is applicable in GIS What is Datum
  • What is UTM zones and,
  • Which is the wildly use map projection and Datum in GIS platform?

 

2. Aim of the Module

  • Understand the techniques how to represent Earth’s curved surface on a flat surface 
  • Transform geographic coordinates to projected coordinates
  • Explain basic types of map projection and the use of particular projections for mapping purposes Explain its application in Geographic Information System

 

3. Introduction

 

Maps are one of the oldest types of document and have been integral in the scientific expedition since ages. While the objective of map projections is basically deals with transforming the curved surface of the earth in to a flat surface, the greatest challenge one face is the shape of the earth itself. Since the earth is conceptually a spherical surface and while transforming into a flat surface reducing of scale becomes important so as to use it for reference. Thus distortion becomes the biggest hurdle. One of the simplest ways to map the earth surface without any kind of distortion is the globe. But it has its own disadvantages; it is expensive to make, difficult to practice (measure and draw on) and reproduce and difficult to carry. Another is that in globe only half of the globe is visible at one time. Thus all these drawbacks of globes can be solved out if a map is prepared on a flat surface. But constructing a map on a plane surface does require an important operation which requires mathematically converts features between a spherical or ellipsoidal surface to a projected flat surface.

 

Representing the curved earth on a flat paper or on a computer screen requires mapping of earth on the two dimensional (2D) mapping plane. Mapping on a 2D surface means transforming each and every point on the reference surface with geographic coordinates (ϕ, λ) into the set of projected coordinates (x, y) that can be represented on the position of the features on a flat surface. It is a systematic transformation of the latitudes and longitudes of a particular location on surface of the sphere into location on a flat surface. While projecting map on a flat surface distortion of the earth surface to some limited extent is obvious and thus, depending upon the purpose of the map, projections are applied in order to maintain or preserve some particular properties.

Fig 01 Show how the geographic coordinates are projected on the flat 2D surface with the help of map projection. Source: kartowe.itc.nl

 

4.   Metric Properties of Map

The metric properties of maps that need to preserve are;

 

a.       Area

b.      Shape

c.       Distance

d.      Direction

e.       Bearing and

f.       Scale.

 

Every map projection maintains these properties while the purpose of the map generally determines which of the map projection is best suitable. Another consideration in the configuration of a map projection is its compatibility with data sets to be used on the map. Data sets are geographic information, collected depending on the chosen datum (Model) of the Earth.

 

5.   Scale factor and transformation

 

Projections are constructed in two stages; first the reduction of the size of the earth in reference to a hypothetical globe that is scale, second transform each and every point of the globe into a flat surface (x, y), that is transformation of Geographic coordinates into projected coordinates.

 

The scale factor is the transformation of globe scale that is representative fraction (RF), also called the Principal scale into a scale of a flat surface where the principal scale divides the radius of the earth by the radius of the globe. The scale factor (SF) is the actual scale divided by the principal scale.

Fig 02: Distortion of scale due to flatting of a piece of spherical reference surface.

Source: kartowe.itc.nl.

 

6.   Relationship between Coordinates and map projection:

 

The coordinates are the latitude and longitudinal position of an earth’s point that are usually represented as (x, y). X refers to longitudinal position while y refers to latitudinal position of a particular earth’s point. A coordinate system is super imposed on the map surface to provide the referencing framework by which x, y positions are can compute and measured.

 

7.      Types of Map projection:

 

Map projection can be divided in terms of 7.1 Developable surface that are

 

a.       Cylindrical: the developable surface is a cylinder

b.      Conical: the developable surface is a cone

c.       Planar or Azimuthal: the developable surface is a flat.

Fig 03 map projection according to three developable surface.

Source: kartowe.itc.nl.

 

7.2 According to projection point or view point, that is,

 

a. Gnomonic projection, view point at the canter of the globe

b. Orthographic projection, view point at the infinity

c. Stereographic projection, view point on the surface at the far side of the globe

Fig: 05 Stereographic projection

Source: Britannica .

 

Fig 06 map projection according to view point or projection point.

Sourece: hdimagelib.

 

8.   Aspect of the map projection :

 

During the constrution of a projection system the developable surface of the map can be placed in three different ways.

  1. Normal aspect,
  2. Transverse aspect and
  3. Oblique aspect.

 

Fig: 07 three different aspects in Azimuthal projection

9.   Distortion Properties map projection:

 

The selection of a map projection system is determines by the kind of distortion it will preserve and compare in reference to real earth surface.

 

In a conformal (orthomorphic) map projection the angles between lines in the map are very much identical to the angles between the original lines on the curved surface (reference) which means the angles and shapes are projected correctly on the map that is true to scale.

 

In an equal-area (equivalent) map projection the areas in the map are identical to the areas on the curved surface (reference) while taking into account the map scale and thus areas are projected correctly on the map and are true to scale.

 

In an equidistant map projection the length of particular lines in the map are the same as the length of the original lines on the curved surface (reference) while taking into account the map scale and are true to scale.

 

Therefore in projecting a map it become important to have the properties above which means that map projection cannot be both conformal and equal-area and can only be equidistant (true to scale) at certain places or in certain directions. The two major concerns are the compatibility of different data sets and the amount of tolerable metric distortions. While in a small areas (large scale) data compatibility issues are more important since metric distortions are minimal and in very large areas (small scale) distortion is a more important factor to consider.

10. Some of the important map projections and their description are given below:

 

11. Application in GIS

 

GIS (Geographic information system) has evolved out of a long tradition of map making which is a computer based integrated information system for computing, storing, analysing, rectifying and display data that are related to geographical position on the earth surface. Cartographic limitations are also applied to digital maps and thus application of GIS makes the process of map making more effective and so it also can be termed as digital cartography (map making).

 

The application of map projections in GIS is the transformation of spherical or ellipsoid surface in to flat surface represented by many methods that use to represent on a 2D plane in cartography. The process of map making considered by the cartographer is to maintain or preserve the map projection system in reference to other spatial data that is known as Geo-referencing while applying proper projection system considering the other spatial data, distorting properties, metric poverties of map making. Thus Geo-referencing is the process of assigning spatial coordinates to the raster data set well known as rectification. During the process of geo-referencing one has to assign the map projection, datum and the coordinate system.

 

12. What is Datum:

 

A datum is a mathematical model that fits the earth to an ellipsoid as the earth surface is not perfectly sphere or round. The datum is used to maintain or correct this undulation of the earth in the process of map making. Most commonly used ellipsoid in GIS is WGS 84 (world geodetic survey 1984). It is mostly useful as well as suitable if we are going to compute and compare data collected by GPS (global positioning system) on map. Therefore it is widely used in GIS in topographical mapping.

 

13. What is Coordinate system:

 

A coordinate system is a reference system used to represent the locations of geographic features, imagery, and observations, such as Global Positioning System (GPS) locations, within a common geographic framework.

 

14. What is UTM in GIS?

 

The Universal Transverse Mercator (UTM) is the most common and widely used projection system in GIS. It divides the world into 60 narrow longitudinal zones of 6 degrees numbering from 1 to 60, while 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. UTM was recommended for topographic mapping by the United Nations Cartography Committee (UNCC) in 1952.

Fig10: The projection plane of the UTM projection is a secant cylinder in a transverse position.

Source: www.tankonyvtar.hu .

 

The UTM was designed in such a way that it covers the whole world but excluding the Arctic and Antarctic region which are in the northern hemisphere from 84° to 90° north and in the southern hemisphere from80° to 90° south. This particular area can be mapped with help of the Universal Polar Stereographic (UPS) projection. The India comes under between UTM zone 42 of north hemispheres to UTM zone 47 of northern hemisphere.

 

Fig 11: UTM zones.

Source: Art of Directional drilling.

  1. Bibliography:
  • Keates, J.S., (2008): Cartographic Design and production, London, Longman
  • Lillesand, Thomas M. and Kiefer, Ralph, W., (2007): Remote Sensing and Image Interpretation, 4th Edition, John Wiley and Sons, New York
  • Peterson, M.P., (1995): Interactive and Animated Cartography, Upper Sadde River, NJ: Prentice Hall.
  • Robinson A.H. & Morrison J.L, (1995): Elements of Cartography, John Wiley & Sons