GeoreferencingGeoreferencingCoordinate SystemsLatitude & LongitudeThe Geographic Coordinate SystemThe Geographic Coordinate SystemThe Geographic Coordinate SystemPlanar Coordinate SystemsPlanar Coordinate SystemsPlanar Coordinate SystemsPlanar Coordinate SystemsPlanar Coordinate SystemsUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorUniversal Transverse MercatorState Plane Coordinate SystemState Plane Coordinate SystemState Plane Coordinate SystemDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Georeferencing• GOAL: To assign a location to all the features represented in our geographic information data• In order to do so, we need to make use of the following elements:– ellipsoid/geoid–datum– projection– coordinate system– scale• The next few lectures will introduce you to these elementsTo determine a position on the Earth, you’ll need to understand how these elements relate to each other in order to specify a positionDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Georeferencing• We have addressed both the issue of how to model the shape of the 3-dimensional Earth as an ellipsoid/geoid, and how to transform spatial information from the Earth’s surface to a 2-dimensional representation using the projectionprocess• Our remaining task is to conceive of some system by which we can precisely specify locations on a projected map that correspond to actual locations on the surface of the Earth Æ For this, we need to use some coordinate systemDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Coordinate SystemsWe are going to discuss two kinds of coordinate systems:•The geographic coordinate system expresses positions in terms of latitude and longitude, and like all spherical coordinate systems, the definitions of these quantities are in terms of angles• Planar coordinate systems place a Cartesiangrid on a 2-dimensional surface (like our projected maps and geodatabases) and express a position in terms of (x,y) coordinate pairsDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Latitude & Longitude• Lines of latitude are called parallels• Lines of longitude are called meridiansDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005• The Equator is the origin for latitude– positive in N. hemisphere– negative in S. hemisphere•The Prime Meridian is the origin for longitude– positive in E. hemisphere– negative in W. hemisphereThe Geographic Coordinate System• Every coordinate system needs to have an origin where the coordinate values are zero, and the geographic coordinate system’s origin is specified using:David Tenenbaum – GEOG 070 – UNC-CH Spring 2005The Geographic Coordinate System• This is a spherical coordinate system that specifies in terms of two angles, latitude and longitude, and is ideal for use with unprojected data• Longitude is the angle formed by a line going from the intersection of the Prime Meridian and the center of the Earth and a second line from the center of Earth to the location in question• Latitude is an angle formed by a line from the Equator to the center of the Earth and a second line from the center of Earth to the location in question (taking into account the shape of the ellipsoid)Earth from aboveEarth from the sideDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005The Geographic Coordinate SystemViewing latitude and longitude angles from a 3D perspective:David Tenenbaum – GEOG 070 – UNC-CH Spring 2005Planar Coordinate Systems• Once we start working with projected spatial information, using latitude and longitude becomes less convenient• We can instead use a planar coordinate system that has xand y axes, an arbitrary origin (a Cartesian plane), and some convenient units (e.g. ft. or m.)• When applied in a geographic context:– Eastings are x values– Northings are y valuesDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Planar Coordinate Systems• So, if we move south or westwe are moving in the negativedirection, and if a location is south or west of the origin, that locations would have a negative ordinate (or two)• It is for this reason that we often define the origin using a false easting and northingthat are well west and south of the area of interest to make sure that nothing we map will have negative coordinatesDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Planar Coordinate Systems• A key reason to use a planar coordinate system is that it is much easier to perform distance or area calculations• Because of the distortioninherent in projections, using latitude and longitude for these purposes on projected data can be very tricky• Distances simply use the Pythagorean theorem, areas use the formulae for finding the areas of various regular shapesDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Planar Coordinate Systems• Planar coordinates used more often with projected data• They are more useful in the context of flat maps• It is mathematically simpler to use them to calculate distances and areasDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Planar Coordinate Systems• Some common examples of planar coordinate systems that are in use:–The Universal Transverse MercatorCoordinate System is used throughout the world– In the United States, the State Plane Coordinate System is used, which provides coordinate grids for each state, using multiple zones and grids in many of the larger states in order to minimize projection distortionsDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Universal Transverse Mercator• Earlier, you were introduced to the Transverse Mercator projection• That projection is used as the basis of the UTM coordinate system, which is widely used for topographical maps, satellite images, and many other uses• The projection is based on a secant transverse cylindrical projection• Recall that this projection uses a transverse cylinder that has standard lines that run north-south, and distortionincreases as we move further east or westDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Universal Transverse Mercator• In order to minimize the distortion associated with the projection, the UTM coordinate system uses