Projections and Coordinate Systems Overview Projections Examples of different projections Coordinate systems Datums
Projections
Overview Projections and Coordinate Systems GIS must accurately represent locations of features from the earth s surface on a map This requires a reference system, or coordinate system
The earth is a spheroid The best model of the earth is a globe Drawbacks: not easy to carry not good for making planimetric measurement (distance, area, angle)
Maps are flat easy to carry good for measurement scaleable
A map projection is a method for mapping spatial patterns on a curved surface (the Earth s surface) to a flat surface.
Definitions I Coordinate System (CS) provides a frame of reference to define locations Geographic CS Used for 3D (sphere or globe), locations defined by latitude and longitude, usually in decimal degrees Projected CS Used for 2D (maps), locations defined by x,y measured from some origin (0,0), usually in meters, sometimes in feet
Definitions II Spheroid A simplified model of the shape of the earth Spheroid is used interchangeably with ellipsoid Datum Defines the spheroid being used and aligns the spheroid, optimizing fit either for a specific area, or overall globally. This also defines the origin point of the coordinate system. Introductio
Definitions III Projection A mathematical equation to convert from spherical (3-D) to planar (2-D) coordinates Every projection will cause some form of spatial distortion in shape, area, distance, and/or direction Common projections used in the US: Albers Equal Area for national scale State Plane and UTM for state and local scales
North American Datums Common North American datums are: NAD27, Clarke 1866 spheroid and Meade s Ranch, KS as the origin point NAD83, GRS80 (GRS = Geodetic Reference System) spheroid and the earth s center of mass as it s origin WGS84, WGS84 spheroid and the earth s center of mass as it s origin. This datum is used globally In North America, WGS84 is virtually identical to NAD83 Other datum changes will change coordinates of spatial features (e.g. NAD83 to NAD27)
Types of Projections Imagine a globe with a light source inside that projects features on the earth s surface onto a flat surface That flat surface can be configured a number of ways as a cylinder, a cone, or a plane
an imaginary light is projected onto a developable surface a variety of different projection models exist
cone as developable surface secant cone tangent cone
cylinder as developable surface tangent cylinders
plane as developable surface
Map projections always introduce error and distortion
Map projections always introduce error and distortion
Map projections always introduce error and distortion
Map projections always introduce error and distortion Distortion may be minimized in one or more of the following properties: o Shape conformal o Distance equidistant o Direction true direction o Area equal area
Exactly what are map projections? Sets of mathematical equations that convert coordinates from one system to another (x, y) f f (x, y) input unprojected angles (lat/long) output projected Cartesian coordinates
How do projections work on a programmatic level? o o o each set of "coordinates" is transformed using a specific projection equation from one system to another angular measurements can be converted to Cartesian coordinates one set of Cartesian coordinates can be converted to a different measurement framework Projection, zone, datum (units) X Y geographic, NAD27 (decimal degrees) -122.35 47.62 UTM, Zone 10, NAD27 (meters) 548843.5049 5274052.0957 State Plane, WA-N, NAD83 (feet) 1266092.5471 229783.3093
Geographic projection
Examples of different projections Albers (Conic) Shape Area Direction Distance Shape along the standard parallels is accurate and minimally distorted in the region between the standard parallels and those regions just beyond. The 90-degree angles between meridians and parallels are preserved, but because the scale along the lines of longitude does not match the scale along lines of latitude, the final projection is not conformal. All areas are proportional to the same areas on the Earth. Locally true along the standard parallels. Distances are best in the middle latitudes. Along parallels, scale is reduced between the standard parallels and increased beyond them. Along meridians, scale follows an opposite pattern.
Examples of different projections Lambert Azimuthal Equal Area (Planar) Shape Area Direction Distance Shape is true along the standard parallels of the normal aspect (Type 1), or the standard lines of the transverse and oblique aspects (Types 2 and 3). Distortion is severe near the poles of the normal aspect or 90 from the central line in the transverse and oblique aspects. There is no area distortion on any of the projections. Local angles are correct along standard parallels or standard lines. Direction is distorted elsewhere. Scale is true along the Equator (Type 1), or the standard lines of the transverse and oblique aspects (Types 2 and 3). Scale distortion is severe near the poles of the normal aspect or 90 from the central line in the transverse and oblique aspects.
Examples of different projections Mercator (Cylindrical) Shape Area Direction Distance Conformal. Small shapes are well represented because this projection maintains the local angular relationships. Increasingly distorted toward the polar regions. For example, in the Mercator projection, although Greenland is only one-eighth the size of South America, Greenland appears to be larger. Any straight line drawn on this projection represents an actual compass bearing. These true direction lines are rhumblines, and generally do not describe the shortest distance between points. Scale is true along the Equator, or along the secant latitudes.
Examples of different projections Miller (Cylindrical) Shape Area Direction Distance Minimally distorted between 45th parallels, increasingly toward the poles. Land masses are stretched more east to west than they are north to south. Distortion increases from the Equator toward the poles. Local angles are correct only along the Equator. Correct distance is measured along the Equator.
Examples of different projections Mollweide (Pseudocylindrical) Shape Shape is not distorted at the intersection of the central meridian and latitudes 40 44' N and S. Distortion increases outward from these points and becomes severe at the edges of the projection. Area Equal-area. Direction Local angles are true only at the intersection of the central meridian and latitudes 40 44' N and S. Direction is distorted elsewhere. Distance Scale is true along latitudes 40 44' N and S. Distortion increases with distance from these lines and becomes severe at the edges of the projection.
Examples of different projections Orthographic Shape Area Direction Distance Minimal distortion near the center; maximal distortion near the edge. The areal scale decreases with distance from the center. Areal scale is zero at the edge of the hemisphere. True direction from the central point. The radial scale decreases with distance from the center and becomes zero on the edges. The scale perpendicular to the radii, along the parallels of the polar aspect, is accurate.
Coordinate Systems
Coordinates Features on spherical surfaces are not easy to measure Features on planes are easy to measure and calculate distance angle area Coordinate systems provide a measurement framework
Coordinates Lat/long system measures angles on spherical surfaces 60º east of PM 55º north of equator
Lat/long values are NOT Cartesian (X, Y) coordinates constant angular deviations do not have constant distance deviations 1 of longitude at the equator 1 of longitude near the poles
Coordinate systems Examples of different coordinate/projection systems State Plane Universal Transverse Mercator (UTM)
State Plane Coordinate systems Codified in 1930s Use of numeric zones for shorthand SPCS (State Plane Coordinate System) FIPS (Federal Information Processing System) Uses one or more of 3 different projections: Lambert Conformal Conic (east-west orientation ) Transverse Mercator (north-south orientation) Oblique Mercator (nw-se or ne-sw orientation)
Coordinate systems
Pennsylvania State Plane zone definitions Zone SPCS Zone # FIPS Zone # Projection 1st Std. Parallel 2nd Std. Parallel Central Meridian Origin False Easting (m) False Northing (m) PA_N 5126 3701 Lambert Conformal Conic 40 10 00 40 53 00-77 45 00 47 00 00 600000 0 PA_S 5151 3702 Lambert Conformal Conic 39 56 00 40 58 00-120 30 00 39 20 00 600000 0 projection.ppt 42
Coordinate systems Universal Transverse Mercator (UTM) Based on the Transverse Mercator projection 60 zones (each 6 wide) false eastings Y-0 set at south pole or equator
Coordinate systems Every place on earth falls in a particular zone
Universal Transverse Mercator (UTM) Pennsylvania is has 2 UTM Zones (18 and 19)
Datum's
Datum's A system that allows us to place a coordinate system on the earth s surface Initial point Secondary point Model of the earth Known geoidal separation at the initial point
Datum's Commonly used datum's in North America North American Datum of 1927 (NAD27) NAD83 World Geodetic System of 1984 (WGS84)
Scale
Scale Map measurement and true ground measurement ( 24,000" )*( 1' ) = 50' 0.025" * 1" 12" A 1/40th in line on a 1:24,000 scale map is 50 ft on the ground ( 2,000,000) *( 1cm )*( 1" )*( 1' ) = 1,969' 0.30mm* 1 10mm 2.54cm 12" A.30 mm line on a 1:200,000 scale map is almost 2,000 ft on the ground
Map Scale Scale refers to the relationship or ratio between a distance on a map and the distance on the earth it represents. Maps should display accurate distances and locations, and should be in a convenient and usable size. Map scales can be expressed as representative fraction or ratio: 1:100,000 or 1/100,000 graphical scale: verbal-style scale: 1 inch in map equal to 2000 feet on the ground or 1 inch = 2000 feet
GIS is Scale less In GIS, the scale can be easily enlarged and reduced to any size that is appropriate. However, if we get farther and farther from the original scale of the layer, problems appear: details no appear in an enlarged map too dense in a reduced map
Scale in attention The scale of the original map determines the largest map scale at which the data can be used. Road map 1:50,000 scale can NOT be used accurately at the 1:24,000 scale. Water coverage at 1:250,000 scale can NOT be used accurately at the 1:50,000 scale
Scale in attention Data from different sources and scales can vary widely 1:100,000 scale data from USGS DLG
Scale in attention Data from different sources and scales can vary widely 1:1,000,000 scale data from DCW (DMA)
Scale in attention Data from different sources and scales can vary widely 1:2,000,000 scale data from USGS DLG
Beware of scale statements one to two-hundred : does this mean one inch on the map equals 200 inches on the ground? or one inch on the map equals 200 feet on the ground?
Projections in ArcGIS
Projections in ArcGIS All geographic datasets have a GCS Many also have a PCS Unprojected (GCS) data is generally inappropriate for GIS analyses The first layer added to ArcMap defines the projection and datum for the data frame. This can be changed in the data frame properties. All subsequent layers are projected on-the-fly (if necessary) to match the data frame projection. The GCS of the layer must match the data frame or a transformation is required.
How does ArcGIS handle map projections in data frames? o Project data frames to see or measure features under different projection parameters o Applying a projection on a data frame projects data on the fly. o ArcGIS s data frame projection equations can handle any input projection. o However, sometimes on-the-fly projected data do not properly overlap.
Applying a projection to a data frame is like putting on a pair of glasses You see the map differently, but the data have not changed
How does ArcGIS handle map projections for data? Projecting data creates a new data set on the file system Data can be projected so that incompatibly projected data sets can be made to match. ArcGIS s projection engine can go in and out of a large number of different projections, coordinate systems, and datums.
Stored in: Projection Metadata A.prj file for shapefiles A table in geodatabases A prj.adf in coverages and grids A header for other raster formats. This can be either a separate file (.hdr,.tifw) or embedded in the raster file itself Data have a GCS and may have a PCS even if the metadata is missing. These data have an unknown coordinate system.
Projection Metadata CS information can be viewed in ArcMap (layer properties>source tab) and ArcCatalog (Description tab)
Data with Unknown Coordinate Systems Cannot be projected on-the-fly Will generate a warning when added to ArcMap Layer will be added, but may not align with other data Can be fixed with Define Projection tool if you know the CS If you don t, you can try: contacting the source adding the layer to a map with a known CS. If the new layer is registered with existing layers, it is the same CS.
Projecting Raster Data Because projections cause distortions in size and shape, and raster data must have square cells, cells in projected rasters represent different areas on the surface of the earth Resampling is used to assign values to projected cells. Nearest neighbor is fastest and must be used for categorical data like land cover Bilinear interpolation uses a weighted distance average of surrounding cells. Smooths values moderately, useful for continuous data like elevation Cubic convolution fits a curve through surrounding points. Can smooth data significantly and is slower
Map Units vs. Display Units Coordinates of the dataset are stored in map units. Geographic generally uses decimal degrees, while a PCS will usually use meters or feet. Map units can only be changed by changing the CS of the data (Project tool). Display units are independent of map units and are set in the data frame properties. ArcMap reports coordinate values and measurements in display units.
Points to Remember Choose a PCS for each project. When new data is acquired, be sure it is in that PCS or convert it using the Project tool. It is best not to rely on projection on-the-fly in ArcMap. It is especially important to have all data in the same PCS when doing analyses. Try and avoid changing the CS of raster data Use the Project tool to change the CS of data, but use the Define Projection tool to add metadata about the CS CS should be defined for all spatial data