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INTRODUCTION TO GIS
GIS stands for Geographical Information System. It is defined as an integrated tool, capable of mapping, analyzing, manipulating and storing geographical data in order to provide solutions to real world problems and help in planning for the future. GIS deals with what and where components of occurrences. For example, to regulate rapid transportation, government decides to build fly-over (what component) in those areas of the city where traffic jams are common (where component). GIS means differently to different people and therefore has different definitions. For example, Burrough (1998) defined GIS as “ a powerful set of tools for collecting, storing, retrieving at will, transforming and displaying spatial data from the real world for a particular set of purposes” Objectives of GIS Some of the major objectives of GIS are to Maximizing the efficiency of planning and decision making Integrating information from multiple sources Facilitating complex querying and analysis Eliminating redundant data and minimizing duplication Components of a GIS A GIS has following components: Hardware : It consists of the equipments and support devices that are required to capture, store process and visualize the geographic information. These include computer with hard disk, digitizers, scanners, printers and plottersetc. Software : Software is at the heart of a GIS system. The GIS software must have the basic capabilities of data input, storage, transfosrmation, analysis and providing desired outputs. The interfaces could be different for different softwares. The GIS softwares being used today belong to either of the category –proprietary or open source. ArcGIS by ESRI is the widely used proprietary GIS software. Others in the same category are MapInfo, Microstation, Geomedia etc. The development of open source GIS has provided us with freely available desktop GIS such as Quantum, uDIG, GRASS, MapWindow GIS etc., GIS softwares. Data : The data is captured or collected from various sources (such as maps, field observations, photography, satellite imagery etc) and is processed for analysis and presentation. Procedures : These include the methods or ways by which data has to be input in the system, retrieved, processed, transformed and presented. People : This component of GIS includes all those individuals (such as programmer, database manager, GIS researcher etc.) who are making the GIS work, and also the individuals who are at the user end using the GIS services, applications and tools.

2. MAPS AND MAP SCALES
Introduction A map is a two dimensional representation of earth surface which uses graphics to convey geographical information. It describes the geographical location of features and the relationship between them. Maps are fundamental to society. Cartography refers to the art and science of map preparation. Though, the earliest of the maps were technically not as impressive as they are today but they certainly highlighted their role in communicating information about the location and spatial characteristics of the natural world and of society and culture. The new discoveries in Science and Geography fortified maps with facts and technical details. Improvements in the fields of Geodesy, Surveying and Cartography helped in bringing the maps to their present form. The digital technology has altered the way of creating, presenting and distributing the geographic information. The conventional cartography is now getting replaced by computer aided designs and graphics, and the analog maps (paper maps) by digital maps. The growing field of technology promises to bring more advances to Cartography to render maps and allied services that serve the society in a better manner. Figure 1: Map showing Landuse of Himachal Pradesh
Copyright IIT Delhi © 2009-2011. All rights reserved.

Types of Maps

The maps can be classified on the following criteria:

Scale Purpose

Scale is important for correct representation of geographical features and phenomenon. Different features require different scales for their display. For example preparation of a cadastral map of a village and the soil map of a state would use different scale for representing the information. According to scale, maps can be classified as follows:

a. Cadastral : These maps register the ownership of land property. They are prepared by government to realize tax and revenue. A village map is an example of cadastral map which is drawn on a scale of 16 inches to the mile or 32 inches to the mile.

b. Topographical: Topographical maps are prepared on fairly large scale and are based on precise survey. They don’t reveal land parcels but show topographic forms such as relief, drainage, forest, village, towns etc. The scale of these maps varied conventionally from 1/4 inch to the mile to one inch to the mile. The topographical maps of different countries have varying scales.

Topographical survey map of British Ordnance Survey are one inch maps. The scale of European toposheets varies from 1:25000 to 1:100000. USA toposheets are drawn on the scale 1:62500 and 1:125000. The international map which is a uniform map of the world is produced on the scale of 1:1000000.

c. Chorographical/Atlas: Drawn on a very small scale, atlas maps give a generalized view of physical, climatic and economic conditions of different regions of the world. The scale of atlas map is generally greater than 1:1000, 000. `

On the basis of Purpose or the content, the maps can be classified as follows:

a. Natural Maps:

These maps represent natural features and the processes associated with them. Given below is the list of some such maps:

Astronomical map : It refers to the cartographic representation of the heavenly bodies such as galaxies, stars, planets, moon etc.

Geological map : A map that represents the distribution of different type of rocks and surficial deposits on the Earth.

Relief map : A map that depicts the terrain and indicates the bulges and the depressions present on the surface.

Climate map : A climate map is a depiction of prevailing weather patterns in a given area. These maps can show daily weather conditions, average monthly or seasonal weather conditions of an area.

Vegetation map : It shows the natural flora of an area.

Soil map : A soil map describes the soil cover present in an area.

b.Cultural Maps

These maps tell about the cultural patterns designed over the surface of the earth. They describe the activities of man and related processes. Given below is the list of such maps:

Political map: A map that shows the boundaries of states, boundaries between different political units of the world or of a particular country which mark the areas of respective political jurisdiction

Military map : A military map contains information about routes, points, security and battle plans.

Historical map : A map having historical events symbolized on it.

Social map : A map giving information about the tribes, languages and religions of an area.

Land-utilization map : A map describing the land and the ongoing activities on it.

Communication map : A map showing means of communication such as railways, road, airways etc.

Population map : A map showing distribution of human beings over an area. The word globe comes from the Latin word globus which means round mass or sphere. A terrestrial globe is a three dimensional scaled model of Earth. The fact that earth resembles a sphere was established by Greek astronomy in the third century BC and the earliest globes came from that period. Unlike maps, the globe is a representation which is free from distortions (distortion in shape, area). The modern globes have longitudes and latitudes marked over it so that one is able to tell the approximate coordinates of a specific place. To make the illustration better, people have tried depicting variations of earth surface over the globe. The relief raised globes allow a user to visualize the mountain ranges and plains as the features are modeled using elevations and depressions. But the relief is not scaled rather exaggerated. The raised relief would be virtually invisible if a scale representation were attempted. Figure 5: A Globe depicting relief (Image source: http://www.1worldglobes.com/1WorldGlobes/classroom_relief_globe.htm )  The map and the globe are similar in a manner that both of them represent earth (on particular scales) but there also exist a few differences between them, which are enumerated below: Globe Map Three dimensional representation of earth in the form of a sphere Two dimensional representation of earth in the form of a flat surface Impossible to see all the countries of the world at a glance as only half of the globe can be seen at a time All countries of the world can be seen on a world map at a glance The shape and size of geographical features is correctly represented. Due to projection there are distortions in shape and size of geographical features. Accurate tracing of the maps is not possible due to the curvature of the globe Maps can be accurately traced A part of earth can’t be separately represented on the globe A part of earth can be separately represented on the map Inconvenient to carry Easy to carry References Burrough, P. A & McDonnell, R. A. 1998, Principles of geographical information systems, Oxford University Press, UK. Goodchild, M.F., Longley, P.A., Maguire, D. J. & Rhind, D.W 2001, Geographic information systems and science, John Wiley & Sons Ltd. , England.                      Georeferencing and projection                                           Understanding the earth Earth’s shape The earth is generally viewed as a sphere; however its shape is not as perfect as a sphere in reality. Given below are the models that have attempted to describe the shape of the earth: Spherical model Based on a circle, it treats earth as a sphere to make mathematical calculations easier. Ellipsoid/ Oblate spheroid model Based on an ellipse, rotating an ellipse around the semi-minor axis creates an ellipsoid. Latitude, longitude and planar coordinate systems are determined with respect to the ellipsoid. Earth is flattened at poles with a bulge at equator and this is attributed to the earth’s rotation. Rotation of earth has centrifugal force associated with it, which causes an object to move away from the centre of gravity. The force is greatest at equator causing an outward bulge and thus giving that region a larger circumference Geoid model Describes unique and irregular shape of the earth. The variation in the density of different rock types and irregularities caused by mountain ranges and ocean depths affect the gravity of earth. Geoid can be perceived as a sea level surface (where dynamic effects such as tides and waves are excluded) whose irregular shape is attributed to the earth’s gravity No simple surface such as sphere or spheroid/ellipsoid can model the sea level surface completely so best fit of the spheroid/ellipsoid to the sea level surface is performed. Figure 1: Representation of geoid model The geoid differs from the shape of ellipsoid by upto ± 100 m and this difference is known as geoid separation or geoid undulation  Elevations and contour lines depicted on maps are measured with respect to the geoid Datums A datum is a reference point or surface against which measurements are made using models of the shape of the earth. Vertical Datum : A vertical datum is a reference surface used to measure elevations of the point on earth’s surface. It is tidal, based on sea level, or geodetic, based on ellipsoid The tidal vertical datum takes local mean sea level as reference for height measurement. Mean sea level is the arithmetic mean of the hourly water elevation taken over a specific 19 years cycle which is defined as zero elevation for local area and is close approximation to the geoid (geoid and local mean sea level differ by not more than a couple of meters). As zero elevation defined for one country is not necessarily same for other countries, therefore a number of local vertical datums are defined. Figure 2 : Vertical Datum The mean sea level height is also known as orthometric height or geoid height. The geodetic vertical datum uses ellipsoid as the reference surface. The surface of the ellipsoid is considered to represent zero altitude. Points above the ellipsoid represent positive altitude and points below the surface represent negative altitude. The altitude is also known as ellipsoidal or geodetic height. GPS devices furnish ellipsoidal heights. The relationship between ellipsoidal height H and geoid height h is given as where N refers to the geoid ellipsoid separation. Horizontal datum : A horizontal or geodetic datum is defined as an ellipsoid which is used as a reference surface for the planimetric measurements on the Earth surface usually expressed in latitudes and longitudes. It can be of two types: a. Local geodetic datum: The one which best approximates the size and shape of a particular part of earth’s sea level surface. The centre of this spheroid doesn’t coincide with centre of mass of the earth Figure 3: Local geodetic datum b. Global/Geocentric datum: The one that best approximates the size and shape of the whole earth. The centre of this spheroid coincides with centre of mass of the earth. The US Global Positioning System uses geocentric datum Figure 4: Geocentric datum The use of local datums results in uneven connectivity of longitudinal and latitudinal lines between different countries/regions.  These mismatches were common over hundred meters and created confusion about locating an area correctly. With the advent of Global Positioning System (GPS) technology this disagreement was no longer acceptable.  World-wide datums which are now used in all countries/regions began to be developed. The datum presently used for GPS is called WGS 84 (World Geodetic System 1984). It consists of a three-dimensional Cartesian coordinate system and an associated ellipsoid. The positions can either be described as XYZ Cartesian coordinates or latitude, longitude and ellipsoid height coordinates. The origin of the datum is the centre of mass of the Earth and it is designed for positioning anywhere on Earth.                                    Coordinate System A coordinate system is a reference system used for locating objects in a two or three dimensional space Geographic Coordinate System A geographic coordinate system, also known as global or spherical coordinate system is a reference system that uses a three-dimensional spherical surface to determine locations on the earth. Any location on earth can be referenced by a point with longitude and latitude. We must familiarize ourselves with the geographic terms with respect to the Earth coordinate system in order to use the GIS technologies effectively. Pole: The geographic pole of earth is defined as either of the two points where the axis of rotation of the earth meets its surface. The North Pole lies 90º north of the equator and the South Pole lies 90º south of the equator Latitude : Imaginary lines that run horizontally around the globe and are measured from 90º north to 90º south. Also known as parallels, latitudes are equidistant from each other. Equator : An imaginary line on the earth with zero degree latitude, divides the earth into two halves–Northern and Southern Hemisphere. This parallel has the widest circumference. Figure 5: Division of earth into hemispheres Longitude : Imaginary lines that run vertically around the globe. Also known as meridians, longitudes are measured from 180º east to 180º west. Longitudes meet at the poles and are widest apart at the equator Prime meridian : Zero degree longitude which divides the earth into two halves–Eastern and Western hemisphere. As it runs through the Royal Greenwich Observatory in Greenwich, England it is also known as Greenwich meridian Figure 6: Latitude and longitude measurements Equator (0º) is the reference for the measurement of latitude. Latitude is measured north or south of the equator. For measurement of longitude, prime meridian (0º) is used as a reference. Longitude is measured east or west of prime meridian. The grid of latitude and longitude over the globe is known as graticule. The intersection point of the equator and the prime meridian is the origin (0, 0) of the graticule. Coordinate measurement The geographic coordinates are measured in angles. The angle measurement can be understood as per following: A full circle has 360 degrees 1 circle = 360º A degree is further divided into 60 minutes 1º = 60′ A minute is further divided into 60 seconds 1′ = 60″ An angle is expressed in Degree Minute Second. While writing coordinates of a location, latitude is followed by longitude. For example, coordinates of Delhi is written as 28° 36′ 50″ N, 77° 12′ 32″ E. Decimal Degree is another format of expressing the coordinates of a location. To convert a coordinate pair from degree minute second to decimal degree following method is adopted: We have 28 full degrees, 36 minutes - each 1/60 of a degree, and 50 seconds - each 1/60 of 1/60 of a degree While writing coordinates of a location, latitude is followed by longitude. For example, coordinates of Delhi is written as Similarly 77° 12′ 32″ can be written as 77.2088. So, we can write coordinates of Delhi in decimal degree format as: 28.6138 N, 77.2088 E Local Time and Time Zones With rotation of earth on its axis, at any moment one of the longitudes faces the Sun (noon meridian), and at that moment, it is noon everywhere on it. After 24 hours the earth completes one full rotation with respect to the Sun, and the same meridian again faces the noon. Thus each hour the Earth rotates by 360/24 = 15 degrees. This implies that with every 15º of longitude change a new time zone is created which is marked by a difference of one hour from the neighboring longitudes specified at 15º gap. The earth's time zones are measured from the prime meridian (0º) and the time at Prime meridian is called Greenwich Mean Time. Thus, there are 24 time zones created around the globe. Date The International Date Line is the imaginary line on the Earth that separates two consecutive calendar days. Generally, it is said to be lying exactly opposite to the prime meridian having a measurement of 180º meridian but it is not so. It zigs and zags the 180º meridian following the political jurisdiction of the states but for sake of simplicity it is taken as 180º meridian. Starting at midnight and going east to the International Date Line, the date is one day ahead of the date on the rest of the Earth. Projected Coordinate system A projected coordinate system is defined as two dimensional representation of the Earth. It is based on a spheroid geographic coordinate system, but it uses linear units of measure for coordinates. It is also known as Cartesian coordinate system. In such a coordinate system the location of a point on the grid is identified by (x, y) coordinate pair and the origin lies at the centre of grid. The x coordinate determines the horizontal position and y coordinate determines the vertical position of the point. Figure 7: Cartesian coordinate system In such a coordinate system the location of a point on the grid is identified by (x, y) coordinate pair and the origin lies at the centre of grid. The x coordinate determines the horizontal position and y coordinate determines the vertical position of the point. Map Projection Map projection is a mathematical expression using which the three-dimensional surface of earth is represented in a two dimensional plane. The process of projection results in distortion of one or more map properties such as shape, size, area or direction. A single projection system can never account for the correct representation of all map properties for all the regions of the world. Therefore, hundreds of projection systems have been defined for accurate representation of a particular map element for a particular region of the world. Classification of Map Projections Map projections are classified on the following criteria: Method of construction Development surface used Projection properties Position of light source Method of Construction The term map projection implies projecting the graticule of the earth onto a flat surface with the help of shadow cast. However, not all of the map projections are developed in this manner. Some projections are developed using mathematical calculations only. Given below are the projections that are based on the method of construction: Perspective Projections : These projections are made with the help of shadow cast from an illuminated globe on to a developable surface Non Perspective Projections :These projections do not use shadow cast from an illuminated globe on to a developable surface. A developable surface is only assumed to be covering the globe and the construction of projections is done using mathematical calculations. Development Surface Projection transforms the coordinates of earth on to a surface that can be flattened to a plane without distortion (shearing or stretching). Such a surface is called a developable surface. The three basic projections are based on the types of developable surface and are introduced below: 1. Cylindrical Projection It can be visualized as a cylinder wrapped around the globe. Once the graticule is projected onto the cylinder, the cylinder is opened to get a grid like pattern of latitudes and longitudes. The longitudes (meridians) and latitudes (parallels) appear as straight lines Length of equator on the cylinder is equal to the length of the equator therefore is suitable for showing equatorial regions. Aspects of cylindrical projection: (a) (b) (c) (a) Normal: when cylinder has line of tangency to the equator. It includes Equirectangular Projection, the Mercator projection, Lambert's Cylindrical Equal Area, Gall's Stereographic Cylindrical, and Miller cylindrical projection. (b) Transverse: when cylinder has line of tangency to the meridian. It includes the Cassini Projection, Transverse Mercator, Transverse cylindrical Equal Area Projection, and Modified Transverse Mercator. (c) Oblique: when cylinder has line of tangency to another point on the globe. It only consists of the Oblique Mercator projection. 2. Conic Projection It can be visualized as a cone placed on the globe, tangent to it at some parallel. After projecting the graticule on to the cone, the cone is cut along one of the meridian and unfolded. Parallels appear as arcs with a pole and meridians as straight lines that converge to the same point. It can represent only one hemisphere, at a time, northern or southern. Suitable for representing middle latitudes. Aspects of conic projection: (a) Tangent: when the cone is tangent to only one of the parallel. (b) Secant: when the cone is not big enough to cover the curvature of earth, it intersects the earth twice at two parallels. 3. Azimuthal/Zenithal Projection It can be visualized as a flat sheet of paper tangent to any point on the globe The sheet will have the tangent point as the centre of the circular map, where meridians passing through the centre are straight line and the parallels are seen as concentric circle. Suitable for showing polar areas Aspects of zenithal projection: (a) Equatorial zenithal: When the plane is tangent to a point on the equator. (b) Oblique zenithal: when the plane is tangent to a point between a pole and the equator. (c) Polar zenithal: when the plane is tangent to one of the poles. Projection Properties According to properties map projections can be classified as: Equal area projection: Also known as homolographic projections. The areas of different parts of earth are correctly represented by such projections. True shape projection: Also known as orthomorphic projections. The shapes of different parts of earth are correctly represented on these projections. True scale or equidistant projections: Projections that maintain correct scale are called true scale projections. However, no projection can maintain the correct scale throughout. Correct scale can only be maintained along some parallel or meridian. Position of light source Placing light source illuminating the globe at different positions results in the development of different projections. These projections are: Gnomonic projection: when the source of light is placed at the centre of the globe Stereographic Projection: when the source of light is placed at the periphery of the globe, diametrically opposite to the point at which developable surface touches the globe Orthographic Projection: when the source of light is placed at infinity from the globe opposite to the point at which developable surface touches the globe Figure 8: Projections and position of light source (Imagesource:http://www.geo.hunter.cuny.edu/~jochen/GTECH201/Lectures/Lec6concepts/Map%20coordinate%20systems/Perspective.htm) Constructing Map Projections ( Adapted from Singh, G 2004, Map work and practical geography ) Cylindrical Projection Let us draw a network of Simple cylindrical Projection for the whole globe on the scale of 1: 400,000,000 spacing meridians and parallels at 30º interval Calculations: Figure 9 : Simple cylindrical projection graticule Steps of constrution: Draw a line AB, 9.975 cm long to represent the equator. The equator is a circle on the globe and is subtended by 360º. Since the meridians are to be drawn at an interval of 30º divide AB into 360/30 or 12 equal parts. The length of a meridian is equal to half the length of the equator i.e. 9.975/2 or 4.987 cm. To draw meridians, erect perpendiculars on the points of divisions of AB. Take these perpendiculars equal to the length specified for a meridian and keep half of their length on either side of the equator. A meridian on a globe is subtended by 180º. Since the parallels are to be drawn at an interval of 30º, divide the central meridian into 180/30 i.e. 6 parts. Through these points of divisions draw lines parallel to the equator. These lines will be parallels of latitude. Mark the equator and the central meridian with 0º and the parallels and other meridians. EFGH is the required graticule. Conical Projection Let us draw a graticule on simple conical projection with one standard parallel on the scale of 1: 180,000,000 for the area extending from the equator to 90º N latitude and from 60º W longitude to 100º E longitude with parallels spaced at 15º interval, meridians at 20º, and standard parallel 45º N. Calculations: Steps of construction: Draw a circle with a radius of 3.527 cm that represents the globe. Let NS be the polar diameter and WE be the equatorial diameter which intersect each other at right angles at O. To draw the standard parallel 45º N, draw OP making an angle of 45º with OE. Draw QP tangent to OP and extend ON to meet PQ at point Q. Draw OA making an angle equal to the parallel interval i.e. 15º with OE. Draw line LM, it represents the central meridian With L as the centre and QP as the radius, draw an arc intersecting LM at n. This arc describes the standard parallel 45º N. The distance between the successive parallels is 15º. The length of the arc subtended by 15º is calculated as under: From point n, mark off distances nr, rs, st, nu, uv and vM , each distance being equal to 0.923 cm. With L as centre, draw arcs passing through the points t, s, r, u, v and M. These arcs represent the parallels. Draw OB making an angle of 20° with OW Length of the arc subtended by 20° is calculated as under: With O as centre and radius equal to the arc WB (1.231 cm) draw arc abc. From point b, drop perpendicular bd on line ON. Now db is the distance between the meridians. Keeping in view the number of meridians to be drawn, mark off distances along the standard parallel toward the east and west of the point n, each distance being equal to db. Join point L with the points of divisions marked on the standard parallel and produce them to meet the equator. Figure 10 : Simple conic projection Azimuthal Projection Let us draw Polar zenithal equal area projection for the northern hemisphere on the scale of 1: 200,000,000 spacing parallels at 15° interval and meridians at 30° interval. Calculations: Steps of construction: Draw a circle with radius equal to 3.175 cm representing a globe. Let NS and WE be the polar and equatorial diameter respectively which intersect each other at right angles at O, the centre of the circle. Draw radii Oa, Ob, Oc, Od, and Oe making angles of 15°, 30°, 45°, 60° and 75° respectively with OE. Join Ne, Nd, Nc, Nb, Na and NE by straight lines. With radius equal to Ne, and N’ as centre draw a circle. This circle represents 75° parallel. Similarly with centre N’ and radii equal to Nd, Nc, Nb, Na and NE draw circles to represent the parallels of 60°, 45°, 30°, 15° and 0° respectively. Draw straight lines AB and CD intersecting each other at the centre i.e. point N. Radius N’B represents 0° meridian, N’A 180° meridian, N’D 90° E meridian and N’C 90° W meridian. Using protractor, draw other radii at 30° interval to represent other meridians Figure 11 : Polar zenithal equal area projection Selection of Map Projection Choosing a correct map projection for an area depends on the following: Map Purpose Considering the purpose of the map is important while choosing the map projection. If a map has a specific purpose, one may need to preserve a certain property such as shape, area or direction On the basis of the property preserved, maps can be categorized as following a. Maps that preserve shapes. Used for showing local directions and representing the shapes of the features. Such maps include: Topographic and cadastral maps. Navigation charts (for plotting course bearings and wind direction). Civil engineering maps and military maps. Weather maps (for showing the local direction in which weather systems are moving). b. Maps that preserve area The size of any area on the map is in true proportion to its size on the earth. Such projections can be used to show Density of an attribute e.g. population density with dots Spatial extent of a categorical attribute e.g. land use maps Quantitative attributes by area e.g. Gross Domestic Product by country World political maps to correct popular misconceptions about the relative sizes of countries. c. Maps that preserve scale Preserves true scale from a single point to all other points on the map. The maps that use this property include: Maps of airline distances from a single city to several other cities Seismic maps showing distances from the epicenter of an earthquake Maps used to calculate ranges; for example, the cruising ranges of airplanes or the habitats of animal species d. Maps that preserve direction On any Azimuthal projection, all azimuths, or directions, are true from a single specified point to all other points on the map. On a conformal projection, directions are locally true, but are distorted with distance. General purpose maps There are many projections which show the world with a balanced distortion of shape and area. Few of these are Winkel Tripel, Robinson and Miller Cylindrical.For larger-scale maps, from continents to large countries, equidistant projections are good at balancing shape and area distortion. Depending on the area of interest, one might use Azimuthal Equidistant,Equidistant Conic and Plate Carrée. Study area Geographical location The line of zero distortion for a cylindrical projection is equator. For conical projections it is parallels and for Azimuthal it is one of the poles. If the study area is in tropics use cylindrical projection, for middle latitudes use conical and for Polar Regions use Azimuthal projections. Shape of the area Young in 1920 described a way of selecting the map projection which is known as Young’s rule. According to this rule, if the ratio of maximum extent (z) (measured from the centre of the country to its most distant boundary) and the width (δ) of the country comes out to be less than 1.41, Azimuthal projection is preferable. If the ratio is greater than 1.41 a conical or cylindrical projection should be used. Z/δ < 1.41 Azimuthal Projection Z/δ >1.41 Conical or Cylindrical projections Projection Systems Given below is the description of the projection systems that are mostly used: Cylindrical Projection I. Equirectangular projection This is a Projection on to a cylinder which is tangent to the equator. It is believed to be invented by Marinus of Tyre, about A.D. 100. (Image source: http://en.wikipedia.org/wiki/File:Equirectangular_projection_SW.jpg ) Poles are straight lines equal in length to the equator Meridians are straight parallel lines, equally spaced and are half as long as the equator. All meridians are of same length therefore scale is true along all meridians. Parallels are straight, equally spaced lines which are perpendicular to the meridians and are equal to the length of the equator. Length of the equator on the map is the same as that on the globe but the length of other parallels on map is more than the length of corresponding parallels on the globe. So the scale is true only along the Equator and not along other parallels. Distance between the parallels and meridians remain same throughout the map. Since the projection is neither equal area nor orthomorphic, maps on this projection are used for general purposes only. II. Lambert's cylindrical equal-area projection  It is devised by JH Lambert in 1772. It is a normal perspective projection onto a cylinder tangent at the equator (Image source: http://en.wikipedia.org/wiki/File:Lambert_cylindrical_equal-area_projection_SW.jpg ) Parallels and meridians are straight lines The meridians intersect parallels at right angles The distance between parallels decrease toward the poles but meridians are equally spaced The length of the equator on this projection is same as that on globe but other parallels are longer than corresponding parallels on globe. So, the scale is true along the equator but is exaggerated along other parallels Shape and scale distortions increase near points 90 degrees from the central line resulting in vertical exaggeration of Equatorial regions with compression of regions in middle latitudes Despite the shape distortion in some portions of a world map, this projection is well suited for equal-area mapping of regions which are predominantly north-south in extent, which have an oblique central line, or which lie near the Equator. III. Gall's stereographic cylindrical projection Invented by James Gall in 1855, this projection is a cylindrical projection with two standard parallels at 45ºN and 45ºS. (Image source: http://en.wikipedia.org/wiki/File:Gall%E2%80%93Peters_projection_SW.jpg ) Poles are straight lines. Meridians are straight lines and are equally spaced. Parallels are straight lines but the distance between them increases away from the equator. Shapes are true at the standard parallels. Distortion increases on moving away from these latitudes and is highest at the poles. Scale is true in all directions along 45ºN and 45ºS. Used for world maps in British atlases. IV. Mercator projection  Gerardus Mercator in 1569 invented this projection. (Image source: http://en.wikipedia.org/wiki/File:Mercator_projection_SW.jpg ) Parallels and meridians are straight lines Meridians intersect parallels at right angle Distance between the meridians remains the same but distance between the parallels increases towards the pole The length of equator on the projection is equal to the length of the equator on the globe whereas other parallels are drawn longer than what they are on the globe, therefore the scale along the equator is correct but is incorrect for other parallels As scale varies from parallel to parallel and is exaggerated towards the pole, the shapes of large sized countries are distorted more towards pole and less towards equator. However, shapes of small countries are preserved The image of the poles are at infinity Commonly used for navigational purposes, ocean currents and wind direction are shown on this projection V.Transverse Mercator  This projection results from projecting the sphere onto a cylinder tangent to a central meridian. (Image source: http://en.wikipedia.org/wiki/Transverse_Mercator_projection ) Only centre meridian and equator are projected as straight lines. The other parallels and meridians are projected as curves. The meridians and the parallels intersect at right angles Small shapes are maintained but larger shapes distort away from the central meridian. The area distortion increases with distance from the central meridian Used to portray areas with larger north-south extent. British National Grid is based on this projection only. Pseudo-cylindrical Projections A pseudo cylindrical projection is that projection in which latitudes are parallel straight lines but meridians are curved. I. Mollweide Projection (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=69#Mollweide ) The poles are points and the central meridian is a straight line The meridians 90º away from central meridians are circular arcs and all other meridians are elliptical arcs. The parallels are straight but unequally spaced. Scale is true along 40º 44' North and 40º 44' South. Equal –area projection Used for preparing world maps II. Sinusoidal Projection (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=110#sinusoidal ) The central meridian is a straight line and all other meridians are equally spaced sinusoidal curves. The parallels are straight lines that intersect centre meridian at right angles. Shape and angles are correct along the central meridian and equator The distortion of shape and angles increases away from the central meridian and is high near the edges Equal area projection Used for world maps illustrating area characteristics. Used for continental maps of South America, Africa, and occasionally other land masses, where each has its own central meridian. III. Eckert VI (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=54#Eckert%20VI ) Parallels are unequally spaced straight lines. Meridians are equally spaced sinusoidal curves. The poles and the central meridians are straight lines and half as long as equator. It stretches shapes and scale by 29% in the north-south direction, along the equator. This stretching reduces to zero at 49º 16' N and 49º 16' S. The areas near the poles are compressed in north-south direction. Suitable for thematic mapping of the world. Conical Projection I. Bonne’s Projection (Image source: http://en.wikipedia.org/wiki/File:Bonne_projection_SW.jpg ) Pole is represented as a point and parallels as concentric arcs of circles Scale along all the parallels is correct Central meridian is a straight line along which the scale is correct. Other meridians are curved and longer than corresponding meridians on the globe. Scale along meridians increases away from the central meridian Central meridian intersects all parallels at right angle. Other meridians intersect standard parallel at right angle but other parallels obliquely. Shape is only preserved along central meridian and standard parallel The distance and scale between two parallels are correct. Area between projected parallels is equal to the area between the same parallels on the globe. Therefore, is an equal area projection Maps of European countries are shown in this projection. It is also used for preparing topographical sheets of small countries of middle latitudes. II. Polyonic Projection (Image source: http://en.wikipedia.org/wiki/File:Polyconic_projection_SW.jpg ) The parallels are arcs of circles with different centers Each parallel is a standard parallel i.e. each parallel is developed from a different cone Equator is represented as a straight line and the pole as a point Parallels are equally spaced along central meridian but the distance between them increases away from the central meridian. Scale is correct along every parallel. Central meridian intersects all parallels at right angle so the scale along it, is correct. Other meridians are curved and longer than corresponding meridians on the globe and so scale along meridians increases away from the central meridian. It is used for preparing topographical sheets of small areas. Azimuthal/Zenithal Projection I. Polar Zenithal Equal area projection  This projection is invented by J.H Lambert in the year 1772. It is also known as Lambert’s Equal Area Projection. (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=167#zenithal%20equal-area ) The pole is a point forming the centre of the projection and the parallels are concentric circles. The meridians are straight lines radiating from pole having correct angular distance between them. The meridians intersect the parallels at right angles. The scale along the parallels increases away from the centre of the projection. The decrease in the scale along meridians is in the same proportion in which there is an increase in the scale along the parallels away from the centre of the projection. Thus the projection is an equal area projection. Shapes are distorted away from the centre of the projection. Scale along the meridians is small and along the parallels is large so the shapes are compressed along the meridians but stretched along the parallels. Used for preparing political and distribution maps of polar regions. It can also be used for preparing general purpose maps of large areas in Northern Hemisphere. II. Polar Zenithal Equidistant Projection (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=168#zenithal%20equidistant ) The pole is a point forming the centre of the projection and the parallels are concentric circles. The meridians are straight lines radiating from pole having correct angular distance between them. The meridians intersect the parallels at right angles. The spacing between the parallels represent true distances, therefore the scale along the meridians is correct. The scale along the parallels increases away from the centre of the projection. The exaggeration and distortion of shapes increases away from the centre of the projection. The projection is neither equal area nor orthomorphic. It is used for preparing maps of polar areas for general purposes. III. Gnomonic Projection  It is also known as great-circle sailing chart. (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=156#gnomonic ) The pole is a point forming the centre of the projection and the parallels are concentric circles. The meridians are straight lines radiating from pole having correct angular distance between them. The meridians intersect the parallels at right angles. The parallels are unequally spaced. The distances between the parallels increase rapidly toward the margin of the projection. This causes exaggeration of the scale along the meridians. The scale along the parallels increases away from the centre of the projection. The exaggeration and distortion of shapes increases away from the centre of the projection. The exaggeration in the meridian scale is greater than that in any other zenithal projection. It is neither equal area nor orthomorphic. An arc on the globe which is a part of a great circle is represented as a straight line on this projection. This is because the radii from the centre of the globe are produced to meet the plane placed tangentially at the pole. It is used to show great-circle paths as straight lines and thus to assist navigators and aviators in determining appropriate courses. IV. Sereographic Projection (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=162#stereographic ) The pole is a point forming the centre of the projection and the parallels are concentric circles. The meridians are straight lines radiating from pole having correct angular distance between them. The meridians intersect the parallels at right angles. The parallels are unequally spaced. The distances between the parallels increase toward the margin of the projection. The exaggeration in the meridian scale is less than that in the case of Gnomonic projection. The scale along the parallels also increases away from the meridian and in the same proportion in which it increases along the meridians. At any point scale along the parallel is equal to the scale along the meridian. The areas are exaggerated on this projection and the exaggeration increases away from the centre of the projection. A circle drawn on the globe is represented by a circle on this projection. It is used to show world in hemispheres. Also used for preparing aeronautical charts and daily weather maps of the polar areas. V. Orthographic Projection (Image source: http://www.mapthematics.com/ProjectionsList.php?Projection=159#orthographic ) The pole is a point forming the centre of the projection and the parallels are concentric circles. The meridians are straight lines radiating from pole having correct angular distance between them. The meridians intersect the parallels at right angles. The parallels are not equally spaced. The distances between them decrease rapidly towards the margin of the projection. So, the scale along the meridians decreases away from the centre of the projection. The scale along the parallel is correct. The distortion of the shapes increases away from the centre of the projection. It is neither equal area nor orthomorphic. The projection is used to prepare charts for showing the celestial bodies such as moon and other planets. Universal Transverse Mercator (UTM) UTM projection divides the surface of the Earth into a number of zones, each zone having a 6 degree longitudinal extent, Transverse Mercator projection with a central meridian in the center of the zone. UTM zones extend from 80 degrees South latitude to 84 degrees North latitude. The zones are numbered from west to east. The first zone begins at the International Date Line (180°). (Image source: http://www.resurgentsoftware.com/GeoMag/utm_coordinates.htm ) The particular transverse Mercator map that is used to represent each zone has its central meridian running north-to-south down the center of the zone. This means that no portion of any particular zone is very far from the central meridian of the transverse Mercator map that is used to depict the zone. Since a Universal Transverse Mercator zone is 6° of longitude wide, no portion of a UTM zone is more than 3° of longitude from the zone's central meridian. Since the distortion in a transverse Mercator map is relatively low near the map's central meridian, the result of this close proximity to the map's central meridian is that the transverse Mercator map used to depict each zone within the coordinate system contains relatively little distortion. Adapted from the report Map Projections of Europe (2001), the table gives an account of the commonly used projection systems. Property Developable surface Aspect Projections Extent of use Conformal (True shape) Cylinder Normal Mercator Equatorial regions (east-west extent) Transverse UTM (Universal Transverse Mercator) Whole world except polar areas Oblique Rosenmund Oblique Mercator Small regions, oblique & east - west extent Cone Normal Lambert Conformal Conic Small regions, oblique & east - west extent (1 or 2 standard parallels) Plane Any Stereographic Small regions upto the hemisphere Polar UPS (Universal Polar Stereographic) Polar regions Homolographic (Equal area) Cylinder Normal Lambert Equal Area Equatorial areas (east-west extent) Cone Normal Albers Equal Area Smaller regions & continents with east-west extent Plane Any Lambert Azimuthal Equal Area Smaller regions about same north-south , east-west extent Equatorial Hammer-Aitoff World Equidistant Cylinder Normal Plate Caree World Transverse Cassini Soldner Locally used for large scale mapping Cone Normal Equidistant Conic Smaller regions & continents with (1 or 2 standard parallels) east-west extent Plane Any Azimuthal Equidistant Smaller regions about same north-south , east-west extent Georeferencing It is a process of locating an entity in real world coordinates. It aligns geographic data to a known coordinate system representing earth defined through projection systems so it can be viewed, queried, and analyzed with other geographic data. To georeference a geographic data, the positions of known points, called control points, are determined. The Ground Control Points (GCPs) are defined as the points with known geographical location, whose positions on map correspond to their positions on earth. GCPs are collected from fixed objects and are marked on the data to be georeferenced that define where the data is on earth. The whole data adjusts itself according to these GCPs. At least three control points are required for georeferencing a data.  Additional control points help increasing the accuracy. Once the data is georeferenced, each point has a coordinate associated to it which means the location of any object in the data (map) can now be determined Figure 16 : Georeferencing an image In brief, the process of georeferencing establishes control points; inputs the known geographic coordinates of these control points, chooses the coordinate system and other projection parameters and then minimizes residuals. Residuals are the difference between the actual coordinates of the control points and the coordinates predicted by the geographic model created using the control points. The residuals help in determining the level of accuracy of the process. The quality of the rectification depends on the number, accuracy, and distribution of the control points and the choice of transformation model. Georeferencing Raster Data The raster data occupy a raster space which is defined as a digital image of the arrangement of the pixels in a grid. The computer reads the header of the data file and determines the dimension of the raster space. The position of a cell in the raster space is referenced by row and column (row, column). This system of referencing the raster cells is called raster coordinate system. The origin for this system lies at the upper left corner of the monitor because the computer monitor displays an image from left to right and from top to bottom. The method of referencing positions in raster space is different from that on maps. The origin of the map coordinate system is the lower left corner. To visualize raster data spatially raster data needs to be transformed into a map coordinate system i.e. the raster coordinates (row, column) are transformed into corresponding ground coordinates (East, West). There are two approaches to georeferencing: Image to Map rectification Image to Image registration Image to Map: rectification is the process by which geometry of an image is made planimetric. It involves the measurement of the image coordinates of the reference cells (GCPs) and the corresponding ground coordinates to relate the image with the real world. The two sets of coordinates are used to solve a set of polynomial equations whose order depends upon the amount of geometric distortion in the raster image. Generally affine transformation is used for the purpose: Where X and Y are the ground coordinates, and, x and y are the image coordinates. A minimum of three GCPs are required to solve these equations, though greater the GCPs more accurate is the rectification. On solving the equations we get the values of the six (a, b, c, d, e and f) coefficients. Any image coordinate can then be substituted in the equations to get the corresponding ground position on the used map coordinate system. The positions of the original grid cells will have to be interpolated in the mapping coordinate system. After the coordinate transformation the raster cells may have been oriented differently than the way they were originally in the raster coordinate system. The attribute value is to be interpolated for the cells oriented to the new coordinate system. This is called resampling. There are three common methods of resampling: Nearest neighbor: In this method, the attribute value of the original cell nearest to a cell in the output raster layer is assigned to the corresponding cell. Bilinear interpolation: It assigns the value to a cell in the output raster layer by taking weighted average of the surrounding four cells in the original grid nearest to it. Cubic convolution: It assigns the value to a cell in the output raster layer by taking weighted average of the surrounding sixteen cells in the original grid nearest to it. Among these three the nearest neighbor is preferred because it doesn’t change the values of the original grid cells assigned to the reoriented grid cells but it produces blocky images. The cubic convolution on the other side does change the values but it generates smoother images. The result of an image to map rectification is a geometrically correct grid of raster cells. Image to Image registration is a method of georeferencing a raster layer with the help of another raster, which is already georeferenced by the process of image to map rectification. The already georeferenced raster is used as a reference for the raster which is to be rectified. Control points are selected from the two raster layers, the coordinate transformation and resampling is then done in the similar manner as it is done for image to map rectification. Image to Image registration is used to spatially match several raster layers to a single reference raster layer.