GIS501 Fundamentals of Geographical Information Systems (GIS) Coordinate Systems Working with georeferenced data What is georeferencing? Geographically referenced data which is, in some way, referenced to locations on the earth. Several different coordinate systems are used to locate data on the map plane.?! Coordinate systems Map projections Projection distortion Datum Coordinate conversion Geographic and Projected Coordinate System Geographic (Spherical) Coordinate System Latitude and Longitude values belong to a Geographic Coordinate System. Latitude: Equator, 0-90 degrees (North & South) Longitude: Prime Meridian, 0-180 degrees (East & West) Units: degree, minute, and second The location of any given place can be defined with reference to lines of latitude and longitude, which create an imaginary mesh over the world. Meridians and parallels always intersect at right angles. 38 51' N, 77 2' W P(x,y,z) or P(,, ); X=120, Y=150 Every spatial data set in GIS stores latitude-longitude coordinates for its features. These coordinates make up its Geographic Coordinate System (GCS). A data set that has been projected also stores Cartesian coordinates for its features. These make up its Projected Coordinate System (PCS). Projected (Planer) Coordinate Systems Why do we need to project our data? X = 2,750.05 Meters along X Axis Y = 7,747.44 Meters along Y Axis Just as location on a sphere is defined by Latitude and Longitude, location of a map is defined by Cartesian coordinates (positions on horizontal X-axis and vertical Y-axis). This is called Planer or Rectangular Coordinate System. 38 51' N, 77 2' W P(x,y,z) or P(,, ); X=120, Y=150 Map Projection are systematic transformation of the spheroidal shape of the earth so that the curved, three dimensional shape of a geographic area on the earth can be represented in two dimensions, as X, Y coordinates. It allows us to have map and distance unit in feet/meter or miles/kilometer instead of degree, second, and minute. 1
Coordinate System Components Projection Datum Ellipsoid What is projection? Maps lie. Especially world maps, because they are merely a representation - on a flat sheet of paper - of the globe. Since a globe cannot be peeled off and laid out flat, world maps are always a compromise. Only a projection of the globe. Principle of projection systems Map projections are attempts to portray the surface of the earth or a portion of the earth on a flat surface. Distortions result in changes to the shape, size, area, and direction on a map. Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projection are attempts to only moderately distort all of these properties. Conformality: When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps. Distance: A map is equidistant when it portrays distances from the center of the projection to any other place on the map. Direction: A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions. Scale: Scale is the relationship between a distance portrayed on a map and the same distance on the Earth. Area: When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map. History of Map Projections The beginnings of map projections are approximately 2000 years old, when the Greek scientists first introduced the mathematical principals into the foundations of mapping the earth and the sky, and started to apply the graticule. The works of Anaximander, Eratosthenes, Apolonious and Hipparchus played an important role in the development of cartography. Thales from Milet is considered the creator of the first map in a projection in 600 B.C. It was a map of the celestial sphere in gnomonic projection. The stereographic and ortho-graphic projections are among the oldest projections which were used by famous Greek astronomer and mathematician Hipparchus, also for making maps of the celestial sphere about 150 B.C. Several hundred map projections have been invented up to the present Beginning of the Coordinate Systems City plans in Ancient times Thales of Miletus (624-545 BC) 2
Basic Concept of Map Projections Basic Concept of Map Projections Lambert Equal-Area Cylindrical projection tangent at the Equator Conic Projection Orthographic Projection UTM- Universal Transverse Mercator Divided in several zones Unit: Meter Most of the satellite images and USGS maps are in this system 3
Distortion rates Map projections distort shape, area, distance, and direction. If you are working with a fairly small area and using an appropriate projection, the effects of distortion are insignificant. If you are working with whole world, there is bound to be significant distortion of some spatial property. Horizontal Distance -Distortion Relationship Ellipsoid, Geoid and Topograph What is Datum? A datum is a mathematical representation of the shape of the earth s surface. A datum is defined by a spheroid, which approximates the shape of the earth and the spheroid s position relative to the center of the earth. 4
Original Program Original Program A datum is a set of parameters defining a coordinate system Coordinate Conversion Basic Concept of Coordinate Conversion Coordinate Conversion Formulas 5