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Earth Coordinate Systems
Earth Coordinate Systems
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  2. 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. 2
  3. 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. 3
  4. 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. 4
  5. 5. GEOID 5
  6. 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. 6
  7. 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. 7 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. 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. 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. 9
  10. 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. 10
  11. 11. NATURE OF PROJECTION SURFACE 11 Cylindrical Conical Planar
  12. 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. 12
  13. 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 13
  14. 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. 14
  16. 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. 16
  17. 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. 17
  18. 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. 18
  19. 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. 19
  20. 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. 20
  22. 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. 22
  23. 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. 23
  24. 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. 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. 25
  26. 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. 26
  29. 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. 29
  30. 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. 30
  31. 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. 31
  32. 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. 32
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  34. 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. 34
  35. 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. 35
  36. 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. 36
  37. 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 37
  38. 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. 38
  39. 39. 39 Thank You