Lecture 03 : Projections and Coordinate Systems (link to Powerpoint file)
Lab 3: Map Projections
GIS in Archaeology: Projections and Coordinate Systems
Coordinate Systems and Projections
Geographic coordinate system is a spherical coordinate system; it measures spatial coordinates in latitude and longitude and can measure coordinates in degrees, minutes and seconds (DMS), or in decimal degrees (DD).
Map Projection Transformations
Map projections transform the earth's 3-D surface into a flat 2-D surface; transforming to planar coordinates makes spatial calculations easier. The process of geographic projection always incurs some distortion: slope, area (or size), direction and distance.
Steps of Transformation
Need 3 things to transfrom from geographic to planar coordinates:
1. Sphere or sheroid representation of earth's shape
2. Datum point -- the zero point from which all other point coordinates are measured (you can use an earth centered or local datum)
3. Transformation (or projection) system: cylindrical, conic, planar
Shape of the Earth
We often visualize the earth as a sphere. Actually it is not a true sphere but is wider at the ples. Conceptualizing hte earth as a sphere induces error inlocal measures.
Projection Datum
Datum is the base point from which all other locations have their coordinates measured. The same projection with a different datum will yield different coordinates for a location. WG S84 is the standard datum for GPS systems.
Cylindrical Projection
A globe is projected onto a cylinder that is wrapped around it. The cylinder will touch the globe only along one line. All geographic measures will only be accurate along this line. Distortion increases as you move away from the line.
Conic Projection
A globe is projected onto a cone that is draped over it. The cone can touch the globe at one or two lines. This projection is only suited for a portion of a hemisphere because distortion increases greatly at the bottom of the cone.
Planar (aka Azimuthal) Projection
A globe is projected onto a plane. The plane touches the globe at a single point.
Projection Systems and Distortion
The process of geographic projection always incurs some distortio:
–Shape
–Size (or Area)
–Direction
–Distance
Conformal Projections preserve directions and shapes, but sizes/areas are distorted.
Equivalent (aka Equal Area) projections preserve areas, but shapes are distorted.Equidistant Projections preserve accurate distances.Azimuthal Projections preserve accurate directions.Conformal and Equivalent projections are mutually exclusive, others can be combined. Different projections are better for different mapping purposes.
Common Geographic Projections
Transverse mercator is the best known projection for mapping the world. Lambert Conformal Conic is good for large areas taht are wider east-west than north-south (eg. the US). Albers Equal Area Conic is similar to Lambert but preserves areas rather than angles and shapes. Equidistant Conic preserves distances.
Plane Coordiante Systems
Plane coordinate systems are designed for local mapping where accurate positions is the most important property of the projection. 3 Common US plane coordinate systems:
–Universal Transverse Mercator: divides world up into 6 degree longitudinal areas; maintains distance accuracy of at least 1 meter in 2.5 Km.
–Universal Polar Stereographic: similar to UTM but is used for polar areas.
–State Plane Coordinate: sets up different coordinate systems for each state in such a way that there is an accuracy of at least 1 meter in 10 km. Some states require more than one State Plane Coordinate zone
Map Projections and Coordinate Systems
For spatial data to be associated with a specific geographic location they must be stored in a map projection system. To properly overly different data sets they must have their coordinates transformed to the same coordinate system.