Introduction to Geographic Information Systems

Map Projections and Datums

• maps are the main source of data for GIS
• the traditions of both cartography geodesy are fundamentally important to GIS
• GIS has roots in the analysis of information on maps, and overcomes many of the limitations of manual analysis

• How does GIS differ from cartography, particularly automated cartography, which uses computers to make maps?
• How is GIS more functional or versatile than traditional cartography?

• Understanding the way maps are encoded to be used in GIS requires knowledge of cartography.
• Cartography is the science that deals with the construction, use, and principles behind maps.

• according to the International Cartographic Association, a map is:
  • a representation, normally to scale and on a flat medium, of a selection of material or abstract features on, or in relation to, the surface of the Earth
• in a broader sense, a map is:
  • a 2-dimensional graphical representation of the surface of the Earth
• even more loosely, a map may be:
  • any visual display of information that is abstract, generalized, or schematic

• Before we can model reality through our generalized view, we must agree on the locations of the features on the map
• We may think of locations strictly in terms of some coordinate system, but we must also consider the irregular shape of the earth, which makes our assigning these locations difficult . . . or at least complicated
• Projections and datums result from our efforts at defining the earth's shape and how it will be shown in two dimensions

• To locate coordinates accurately, we must account for the earth’s irregular geometry
• This is geodesy--geodesists construct geodetic datums based on spheroids
  • define the size and shape of the earth
• There are hundreds of datums
  • using the wrong one can result in position errors of hundreds of feet

• The earth is not a true sphere
  • it bulges at the equator and flattens at the poles
  • the resulting shape is an ellipsoid
  • for maps to be accurate, they must account for this shape

• Two things must happen when a mapmaker constructs a map
  • features in the real world must be "georeferenced" to a spheroid
  • the spheroid must be projected onto the paper (or some virtual "surface" in a computer)

    

• The spheroid models the shape of the earth's surface
  • it is an idealization that does not account for local changes in topography
• The datum adds georeferencing to the spheroid
  • it specifies where a clearly identifiable point on earth (the base point) should appear on the spheroid
  • it shows where a base direction, such as north, points on the spheroid at the base point
• This results in several different "earth surfaces"

  

• Projecting is an operation that mathematically distorts and shrinks a portion of the spheroid onto flat paper
  • projecting can be undone ("inverted")
  • "unprojection" expands a feature on a map and plasters it back onto the spheroid
• All of these operations are mathematical exercises

• Two maps may use two different datums and two different projections
  • this happens frequently in GIS projects
  • the process of relating features on one map to features on another--especially for accurate overlays--is involved, but straightforward

• Unproject the source map
• Determine the real-world location of the feature to be mapped
• Reference the real feature to the destination datum
• Project the newly referenced feature

  

• Often the middle steps are combined into one operation--a datum shift
  • you can use ArcView’s Projection Utility, but only if you know the datums of your maps
• The datum shift guarantees that the features on the destination map correctly represent the same real-world objects depicted by the features on the source map

• Don’t be tempted simply to reproject a map when you also need to shift datums
  • software will often let you do this, and the features on your source map will shift to new locations on the destination map
  • but they will be the wrong locations
• Depending on scale and the projections involved, the distance error could be hundreds of feet

  

  

  

• There are a few datums you will use more often than others
  • for U.S. maps, these are NAD27 and NAD83
  • for the most recent world maps, it is WGS84
    • the World Geodetic System of 1984
    • based on satellite measures of the earth’s shape/size
    • an earth-centered datum
    • the datum used for GPS measurements

• The North American Datum of 1927
• Based on the Clarke spheroid of 1866
  • an origin point at Meades Ranch, Kansas
  • lots of control points calculated from observations in the 1800s--also, lots of errors
  • Many USGS maps--and thus lots of spatial data--use this datum
  • The datum used with UTM in the U.S.

• The North American Datum of 1983
• Based on the GRS80 spheroid
  • used revised earth and satellite observations
  • origin is the earth’s center of mass
• Much more accurate than NAD27
  • some control points shifted as much as 500 ft
• Newer USGS data use this datum

• Transferring the spherical surface of the Earth to a flat map requires the cartographer to use one of a number of map projections
• These are simply systematic methods for transferring 3-D Earth features to the 2-D map surface

• In the projection process, distortion is inevitably introduced
• 4 Earth/map properties are distorted
  • area
  • shape
  • direction (angles)
  • distance
• Prompted an old saying:
  • "all maps lie flat, and all flat maps lie"
• Distortion, then, is unavoidable
• However, different map projections can minimize distortion of one or another Earth/map properties

• Equal-area - correctly represents areas, but distorts angles and shapes on map margins
• Equidistant - distance/scale shown accurately along selected lines
• Azimuthal - accurately shows direction or angles from one central point to all others
• Conformal - generally preserves shape by showing relative local angles accurately

• Cylindrical--result from projecting a spherical surface onto a cylinder
• Conic--result from projecting a spherical surface onto a cone
• Azimuthal--result from projecting a spherical surface onto a plane
• Other--unprojected maps, compromise projections, and other examples

• Mercator
  • a classic, conformal projection, but areas are grossly distorted poleward
• Gall-Peters
  • an equal-area projection, with distinct shape distortions
• Robinson
  • a compromise projection--neither conformal nor equal area
  • an ideal choice for world maps

• Conic projections work best for large areas
  • Lambert Conformal Conic
    • 2 standard parallels limits distortion to the edges
    • ideal choice for the contiguous 48 states
    • used by the State Plane Coordinate System
  • Albers Equal Area Conic
    • also 2 standard parallels
    • also a good choice for the lower 48 states

    

• To map smaller areas, other projections are prominent, especially in government work
• UTM
  • conformal projection used in some USGS maps
  • also a coordinate system
• State Plane
  • actually a coordinate system that uses either the UTM or Lambert Conformal Conic projection

• A coordinate system is a standardized method for assigning codes to locations so that locations can be found using the codes alone.
• Standardized coordinate systems use absolute locations.
• A map captured in the units of the paper sheet on which it is printed is based on relative locations or map millimeters.
• In a coordinate system, the x-direction value is the easting and the y-direction value is the northing. Most systems make both values positive.

• Geographic coordinates are the earth's latitude and longitude system, ranging from 90 degrees south to 90 degrees north in latitude and 180 degrees west to 180 degrees east in longitude.
• A line with a constant latitude running east to west is called a parallel.
• A line with constant longitude running from the north pole to the south pole is called a meridian.
• The zero-longitude meridian is called the prime meridian and passes through Greenwich, England.
• A grid of parallels and meridians shown as lines on a map is called a graticule.

• Some standard coordinate systems used in the United States are
  • geographic coordinates
  • universal transverse Mercator system (UTM)
  • military grid
  • state plane
• To compare or edge-match maps in a GIS, both maps MUST be in the same coordinate system.

• grid system adopted for topographic maps, satellite imagery, natural resources databases
• a metric system--the meter is the basic unit
• actually derived from a map projection
  • wrapping the cylinder around the poles
• provides highly precise georeferencing for nearly the entire globe
• established in 1936, and adopted by the US Army in 1947

• UTM covers the earth between 84 degrees North to 80 degrees South latitude
  • divided into north-south columns (zones)
  • 6 degrees wide
• zones are numbered (1-60 eastward) beginning at the 180th meridian
  • Indiana is in zone 16
• each column is divided into quadrilaterals of 8 degrees of latitude
• a coordinate system exists for each zone
  • a central meridian splits the zone
  • northings measure distance north in meters from zero (to 10 million)
    • the South Pole in the Southern Hemisphere
    • the equator in the Northern Hemisphere
  • eastings measure distance east in meters from a false origin lying about half a degree west of the zone boundary
    • central meridian has an easting of 500,000 meters
    • allows overlap of zones during mapping
  • example: Schnabel Hall, Valparaiso University
    • 496,810 meters east; 4,590,040 meters north
    • Zone 16 T (90-84 degrees West)
    • Northern Hemisphere

• Map Projection Overview, by Peter Dana
• Coordinate System Overview, by Peter Dana
• Reprojecting Geographic Features, by Bill Huber