Representing the earth on maps: projections and coordinate systems

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Representing the earth on maps projections and
coordinate systems

• J426 Class 5
• January 27, 2009

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Overview

• Longitude and latitude
• Map projections
• Projected coordinate systems

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Placing the geographic features on the map

• Geographic locations measured using latitude and
  longitude
• Latitude
• Degrees north or south of equator
• North and south poles 90 degrees
• Longitude
• Degrees east or west or prime meridian running
  through Greenwich, England
• Maximum 180 degrees at (approximately)
  International Date Line in Pacific

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Lines of latitude (horizontal) and longitude
(vertical)
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GIS and decimal degrees

• Degrees of latitude and longitude traditionally
  measured in degrees, minutes, and seconds,
  specifying north or south latitude, east or west
  longitude
• GIS and computers use decimal degrees, specifying
  positive (north and east) or negative (south and
  west)

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Positive and negative decimal degrees
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Location of Business/SPEA Building
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Further complications

• Specifying latitude and longitude dependent upon
  shape of earth, which is an oblate spheroid
• Model used for shape of earth affects
  measurements
• Specification of sea level affects measurements
• Complete specification called datum
• North American Datum 1927 (NAD 27)
• North American Datum 1983 (NAD 83)

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Map projections

• Latitude and longitude are coordinates on surface
  of (approximately) a sphere
• To represent 3-dimensional surface of earth on
  2-dimensional map requires some form of
  projection
• Projections always involve some form of distortion

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World Mercator projection
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World Mollweide projection
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Properties of projections

• Projections can preserve some aspects of
  relationships on map while distorting others
• Conformal projections preserve directions and
  shapes for small areas
• Equal area projections preserve areas
• Equidistant projections preserve distances from
  one or two points

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United States Lambert conformal conic projection
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United States Albers equal area projection
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Choice of projection

• For maps used for navigation, want projection
  that preserves direction, e.g., Mercator
• For other purposes, want projection that
  preserves distance
• For maps focusing on areas of different subareas,
  like thematic maps, want projection that
  preserves area

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Choice of projection (continued)

• Projection used makes greater difference on
  smaller-scale maps
• Maps of world vary drastically with projection
• Maps of United States vary significantly with
  projection
• Errors brought about by projection are greatest
  at smallest scales

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Choice of projection (continued)

• Projection used makes less difference on
  larger-scale maps
• Maps of Central Indiana vary little with
  projection used
• Projection introduces very little error in
  large-scale maps

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Projections in ArcGIS

• In ArcGIS, data in decimal degrees can be
  displayed unprojected, using latitude and
  longitude as x- and y-coordinates
• Leads to vertically-squashed appearance of maps
• Data in decimal degrees can also be projected to
  other projections for display

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Map of Indiana counties in decimal degrees,
unprojected
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Projections in ArcGIS (continued)

• Files in ArcGIS can also be in projected
  coordinates
• These files can likewise be projected to other
  projections for display
• Coordinates of first file added to map determines
  default projection (but can be changed)

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Projected coordinate systems

• For smaller areas, in which errors associated
  with projection are small, sometimes more
  convenient to measure locations on earth in
  rectangular coordinate system rather than in
  degrees latitude and longitude
• Involves establishing projection, determining
  rectangular coordinate system in this projection,
  measuring in feet or meters from origin using
  these coordinates

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Projected coordinate xystems (continued)

• In U.S., State Plane coordinate systems used for
  much local data collection
• Each state has one or more State Plane coordinate
  systems
• Indiana East (most often used for Marion County)
• Indiana West
• State Plane systems can use either NAD27 or NAD83

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State Plane coordinate system areas
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Universal Transverse Mercator (UTM) coordinate
system

• Universal Transverse Mercator system divides
  world into slices having width of 6 degrees
  longitude
• Rectangular coordinate systems for each numbered
  zone
• Indiana is in Zone 16
• Used on USGS topographic maps
• Similar system used by U.S. military
• Smaller countries have national coordinate systems

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Universal Transverse Mercator (UTM) zones in
United States
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U.S. National Grid coordinate system

• Based upon UTM coordinate system
• Further subdivides zones into square grid areas
• Standard system for identifying grids,
  coordinates within grids
• Being advocated by U.S. Department of Homeland
  Security for all emergency operations

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Importance of understanding projections even when
doing large-scale maps for small areas

• Suppose you are displaying map with UCR crime
  data, other layers, using State Plane Indiana
  East NAD 1983 coordinates
• Download census tract boundaries from web to
  include on map
• Convert from decimal degrees to State Plane
  Indiana East but choose NAD 1927

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Result after adding census tract boundaries to map
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Result after zooming out to display all