Introduction to Coordinate System and Geographic Projections

Welcome to the course on Geospatial Analysis in Urban Planning. This is the NPTEL Online Certification Course and we are I mean in the 2nd lecture of module 1 which is Introduction to Geographic Information Systems and Geographic Distribution. And we would be dealing with geodesy the concepts of geodesy, geographic projection and the coordinate system in thisparticular lecture.
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So, we would be talking about the basic concepts of geodesy; geoid, what is an ellipsoid, what is the datum and then we will see how what are the different types of map projectionsand how can it be used in gis.
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Now, if we see the shape of the earth, we can we generally call it as a geoid. It is basically oblate sphere having depression at the pole. So, it looks more like an orange basically I mean we just depressed at the pole and at the equator it is I mean inflated. I mean this shape resultsbecause of difference in the density of the materials, materials of the earth crust upper crust basically and it would I mean have an impact on the direction and the I mean intensity of the gravity across the different points on earth surface.
We know that earth surface at the equator roughly I mean is about 6387 kilometers whereas,at the poles it is slightly less which is about 6357 kilometers. So, I mean the biggest challengefor us is to represent this particular surface as a geometric surface.
So, I mean mapping or modeling this surface becomes a very complex task and it is reallydifficult to have a equation of a 3D solid which would encapsulate this earth surface in eachof the points. So, what happens is we try to create regional I mean fit is which regionalmodels which would fit the I mean different zones of the earth.
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So, if we look into the concepts of geodesy so, this equipotential surface is basically a geoidand it I mean is a representative surface of the earth’s gravity field and mean sea level whichis the meniscus of the earths I means ocean surface across the earth is taken as I mean datum
or a reference surface and this is taken as a in the global context to measure the elevation ofgiven points.
So, this equipotential surface is generally measure is used to measure the precise surfaceelevations on the earth. Now, there is another term which is known as orthometric heightwhich is height above an imaginary surface which we have just now referred to as geoidwhich is determined by the earth’s gravity and approximated by the mean sea level.
Now this magnitude of earth’s gravity varies as the mass is not uniform and we have already Imean talked about it in our earlier slide. This is because that gravitational strength byelevation data. I mean if we portray it I mean if you refer to the first image, we can see that itlooks like I mean deformed shape 3 dimensional shape which represents which looks like apotato.
So, this is this image was generally termed as Potsdam gravity potato because this gravitydata was analyzed in Potsdam in Germany. Now this gravity anomalies are often due tounusual concentrations of mass in a given region and this presence of ocean trenches ordepression of landmass caused by presence of glaciers millennia ago can cause negativegravity anomaly.
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Now, if we go to the horizontal datums, we have horizontal references or vertical referencesfrom which we measure the horizontal points or the vertical points. So, generally thehorizontal datums are the latitudes and longitudes or other coordinate systems which aremeasured in unit is of distances.
We also have vertical datums basically it is reference to the geoid which measures theelevations or the depths with respect to that particular surface. Now, your we have seen thatthe geoid is an irregular surface. So, to approximate it as a geometric surface what we do is,we create a ellipsoidal surface which is basically a surface resulting when we rotate an ellipseabout it is semi minor axis.
Now there are a variety of ellipsoids which has been I mean formulated for covering theentire earth because I mean it is so deformed that it is difficult for us to have one ellipsoidcovering the entire earth surface.
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Now, ellipsoid is basically a reference surface which from which we can measure differentheights or distances along x or y and heights in the z mention. It is a mathematicalapproximation of the surface of the earth and we said it is a surface of revolution. So,ellipsoid can be defined by three axis and in this case we have termed the radius; in thisequation the radiuses are a, b and c and it is represented by this particular equation.
So, it is a surface of revolution basically created as a result of revolution. This equation is xsquare by a square plus y square by b square plus z square by c square which equals 1. Now ifa and b and c are equal, then the resulting geometry would be that of a sphere.
If a and b are same, but it is greater than b then what happens is if the resulting geometrywould be that of an oblate sphere and it would be depressed at pole. So, we coin a term whichis known as flattening. It is the difference of a and b the two different axis along the x and they divided by a for earth this ratio basically comes to about 1 by 300.
Now, this reference ellipsoid is the mathematically defined surface which approximates thegeoid and this is a quadratic surface as we have seen it in the equation. The GPS uses heightabove the reference ellipsoid that approximates the earth surface.
The traditional orthometric height is the height above an imaginary surface called the geoidwhich is determined by the earth’s gravity and approximated by mean sea level. Now, geoidheight is the ellipsoidal height from an ellipsoidal datum to the geoid.
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Talking about global ellipsoidal systems, we have created different ellipsoidal systems inglobal context or in local context. So, let us see the global ellipsoidal system which is knownas the world geodetic system abbreviated as WGS84 and is generally used for satellitenavigation extensively in the GPS.
So, all the GPS readings that you take from your handheld GPS or I mean dual frequencyGPS or your mobile GPS readings are based on this ellipsoidal system that is WGS 84. Thiswas given by the Department of Defense of US and this is applicable globally there wereearlier versions in 60, 66 and 72.
So, this the earlier version of the that is WGS72 did not I mean provide sufficient data for theaccuracy in terms of resolution of the distances or height. So, the GRS parameters withavailable Doppler, satellite laser ranging and very long baseline interference interferometry
observations constituted a significant new information. The new source of data had becomeavailable from the satellite radar altimetry as well.
So, the advanced least square method called collocation which allowed consistentcombination solution from different types of measurement all related to earth’s gravity fieldthat is geoid, gravity anomalies, deflection, dynamic doppler etcetera were used in thesubsequent correction to formulate the WGS 84 system over the preceding forms I mean theWGS 60, 66 and 72. So, this was corrected to a in the WGS 84 reference system.
So, it is geocentric and globally consistent this particular system within plus minus 1 meters.So, the current geodetic realization of the geocentric reference system family that is theInternational Terrestrial Reference System ITRS is maintained by IERS are consistent even atfew centimeter levels and meter level consistent with WGS 84.
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Now, if we look at some of the local ellipsoids. There are few ellipsoids which are applicablein different parts of the world like we have the Australian ellipsoid of 1965 which is usedextensively in Australia, Krasovsky of 1940 which is used in Soviet Union, we have Clarkewhich is Clarke 1980 and 1980 1860 and 1860 1880 which is used in most of the Africa,France, Northern America and Philippines.
We use the Erie ellipsoid for great Britain, Bessel is used in Central Europe, Chile andIndonesia and the Everest ellipsoid is used in India, Burma, Pakistan, Afghanistan, Thailandand predominantly the Indian subcontinent. So, this Everest or the Indian system has beenused in India for more than 150 years.
This Everest ellipsoid is a mathematical spheroid roughly representing the shape of Indiansubcontinent and has been assumed by the surface of India and all measurements are relatedto this particular spheroid. It was defined in 1830 by Colonel, it is a George Everest and itwas updated in 1956.
The reference datum fixed by the survey of India is located near Kalyanpur in MadhyaPradesh. The Indian spheroid has been marginally modified on a number of occasions so thatthe parameters assumed for this spheroid have been refined slightly from time to time. So, thechanges were made in the year 1930. The first version came in 1830. The revisions were donein 1930 and 1956. The it is important to know that the center of Everest spheroid does notconcede with the center of the earth.
So, the flattening parameter for the Everest ellipsoid is about 300.8017 wherein in the earliercase we have seen for the WGS 84, the flattening parameter was about 298.257 meters.
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Going to the components of the GIS I mean when we are talking about map projections ourearth as we have seen is curved and it is very difficult for us to create a map out of this curvedsurface that is to represent this map, I means this curved surface as a flat surface.
So, basically the projection a map projection is the mathematical process by which we flattenthe earths surface onto a 2 dimensional surface. So, this process is very difficult I mean wecannot always have a proper representation of a 3D surface on a 2D surface. So, there wouldbe errors or distortions involved and the types of this distortions are mostly four types; one isconformality in terms of the nature of the shape of the map whether the dispreserved or not.
Then we have accuracy in terms of measurement of distance I mean if we scale the particularmap whether that is accurate when we corresponded to the measurements on the earth
surface. The next is the area whether the area of the map is proportional or to the actual areathat is measure on the ground or earth and the directions.
So, I mean whether the directions are measured properly along the I mean points on the mapsurface and it basically correlates well with appropriate measurement on the ground.
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Projecting the three 3D surface of earth on a piece of paper can be imagined similar to aproblem of arranging orange peel on a flat surface. Now the map projection is themathematical approach of projecting earths 3D surface on a 2D map surface and we haveseen that it will result in distortions.
So, the first that we had discussed conformality that is the accuracy of the shape is mostcommon and most important projections are conformal or orthomorphic normally. The
relative local angles about every point on the map are preserved. Since local angles arecorrect meridians intersect parallels at right angles and on a conformal projection, a localscale in every direction around any one point is constant. Most large scale maps throughoutthe world are now prepared on a conformal projection.
Now, talking about distance I mean measuring the accuracy of the distances measured on themap to the actual measurements on the earth surface, I mean talking about it no mapprojection actually shows the scale correctly throughout the map. But there are usually one ormore lines on the map along which is scale would remain true.
Some projections show that true scale along meridians are known as equidistant projections.The I mean when we have area specific distortions the map would cover exactly the samearea of the actual earth, I mean the projections which would reduce the amount of distortionsin terms of area.
So, the common terms used for equal area projections are equivalent homolographic orhomalographic and no map can be both equal area as well as conformal. Talking aboutpreserving the direction conformal maps gives the relative location directions correctly at anygiven points. The azimuths of all points on the map are shown correctly with respect to thecenter and are known as azimuthal projection.
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So, I mean talking about the representation of earth as a ellipsoid, we have we define twolines. First is the meridian which is a standard line along the latitude. So, I mean before weget to learn about the map projections it is important for us to know these concepts.
So, this meridians of longitude are formed with the series of imaginary lines, they all intersectboth at the north and the South Pole and crisscross each parallel of latitude at right angles, butstriking the equator at various points. Now we have the standard parallel which is shown inthe image. So, it is when parallels of latitude are formed by circles surrounding the earth andin planes parallel with that of the equator.
So, if we are to represent a surface I mean planar surface representing that of a 3D surface, wecan I mean circumscribe a sheaf of paper in either a cylindrical way as has been shown or inor to make a cone and it would touch the surface of the earth either as a tangent or it could be
in a secant form wherein it would intersect the surface of the earth at two points or we canalso put it in a orthographic mode azimuthal mode wherein we put the sheaf of paper and thelines are projected.
So, let us see the first one that is the cylindrical projection. So, cylindrical projection mosts ofthe cylindrical projections are of two types; it is either vertical, it could be oblique as well orit could be transverse. So, the most popular projection which is used globally is the transversecylindrical projection.
Now, this cylindrical projections they are conformal in nature and they have central meridianand each meridian is 90 degree from the central meridian and equators are straight lines. Theother meridians are parallel and they are complex curves as you can see that when we expandthis we I mean cut this sheaf of paper which is basically super scribing this globe and open itup as a map, you can see the standard parallels and basically the meridians.
So, I mean it has been shown for each of these cases in the particular images. So, the scale inthis particular case is true along the central meridian or along two straight lines equidistantfrom and parallel to the central meridian. It is used for extensively for making quadranglemaps ranging with scales ranging from 1 is to 24000 to 1 is to 2000 2,50,000.
Now, talking about the conic projection, we have seen that the cone could be superimposedon the surface of the earth in two ways either tangentially or I mean having secants. Theparallels in this case are unequally spaced arcs of concentric circles and it is more closelyspaced at the north and south edges of the map. The meridians are equally spaced radii of thesame circles cutting parallels at right angle. There is no distortion in scale or shape along thetwo standard parallels.
So, the scale would be I mean true and the shape is also preserved; normally or along just oneof these standard parallels. The poles are arcs of the circles. These type of projectionsspecially the conic projections I mean an example is the polyconic projection or the Lambert
conformal conic projection. So, these are used for equal area maps of regions havingpredominantly east west expands.
So, I mean talking about the conformal projection, I mean we had earlier talked about theconformal projection these are I mean they have a constant scale along the equator and theyare generally referred to as Mercator projection and the constant scale along the meridian incase of your transverse Mercator projection. For the equal area we have the third type whichis the azimuthal projection or the equal area projection.
So, in this type we have the standard without interruption which is known as Hammerprojection or the Mollweide (Refer Time: 23:41) 4 or the version 6 Macbride Thomasvariations, Boggs Eumorphic or sinusoidal projection. So, these azimuthal equidistantprojection are centered on pole and these types of projections are basically polar azimuthalequidistant projection or centered on a city which is oblique azimuthal equidistant projection.
So, the azimuthal projection can be three types; I mean we can place the paper in aorthographic mode and we can project the standard parallels and the meridians in aorthographic mode. The second the way of projecting the standard meridians and the parallelscould be in a stereographic format or it could also be done in a gnomonic format gnomonicway as shown in the particular image.
So, with this we conclude this particular I mean lecture and in this particular lecture, we havecovered the basic concepts of geodesy. We have defined what is a geoid, what is a ellipsoid,what are ellipsoidal heights, what are geoidal heights. We have also talked about the differenttypes of projections and what are the types of errors that would be introduced due toprojecting a 3 dimensional surface on a 2 dimensional paper plane when we are creatingmaps.
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So, we have a book some reference books which you can read further to I mean learn moreabout this particular topic. So, we have the first book by Maling it is from the PergamonPress. It is titled Coordinate Systems and Map Projections and the second book is byBugayevskiy and John Snyder. It is from CRC Press, book title Map Projection: A ReferenceManual.
Thanks.