Finding Our Way: Coordinate Systems In GIS

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Finding Our WayCoordinate Systems In GIS

• Talbot Brooks
• Delta State University

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Modern Coordinate SystemsThey all started
here
Royal Observatory, Greenwich, UK Photos by T.
Brooks
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The National Geodetic Survey- a brief overview -

• Formed in 1807 by President Jefferson
• Survey of the Coast (1807 - 1878)
• US Coast Geodetic Survey (1878 - 1970)
• Geodesy is the applied science that deals with
  the size and shape of the earth.
• Responsible for the establishment and maintenance
  of the National Spatial Reference System (NSRS)
• Geodetic Advisor program puts an NGS geodesist in
  cooperating States

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Overview

• There are many basic coordinate systems familiar
  to students of geometry and trigonometry.
• These systems can represent points in
  two-dimensional or three-dimensional space.
• René Descartes (1596-1650) introduced systems of
  coordinates based on orthogonal (right angle)
  coordinates.
• These two and three-dimensional systems used in
  analytic geometry are often referred to as
  Cartesian systems.
• Similar systems based on angles from baselines
  are often referred to as polar systems.

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Geometric Earth Models

• Early ideas of the figure of the earth resulted
  in descriptions of the earth as an oyster (The
  Babylonians before 3000 B.C.), a rectangular box,
  a circular disk, a cylindrical column, a
  spherical ball, and a very round pear (Columbus
  in the last years of his life).
• Flat earth models are still used for plane
  surveying, over distances short enough so that
  earth curvature is insignificant (less than 10
  kms).

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Geometric Earth Models, Contd

• Spherical earth models represent the shape of the
  earth with a sphere of a specified radius.
  Spherical earth models are often used for short
  range navigation (VOR-DME) and for global
  distance approximations. Spherical models fail to
  model the actual shape of the earth. The slight
  flattening of the earth at the poles results in
  about a twenty kilometer difference at the poles
  between an average spherical radius and the
  measured polar radius of the earth.
• Ellipsoidal earth models are required for
  accurate range and bearing calculations over long
  distances. Loran-C, and GPS navigation receivers
  use ellipsoidal earth models to compute position
  and waypoint information. Ellipsoidal models
  define an ellipsoid with an equatorial radius and
  a polar radius. The best of these models can
  represent the shape of the earth over the
  smoothed, averaged sea-surface to within about
  one-hundred meters.

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ACRONYMS US
R
NAD 27
ITRF 97
GRS 80
WGS 84
NAVD 88
EGM 96
GEOID 99
NGVD 29
NAD 83
GEOID 96
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DATUMS

• A set of constants specifying the coordinate
  system used for geodetic control, i.e., for
  calculating coordinates of points on the Earth.
• Specific geodetic datums are usually given
  distinctive names. (e.g., North American Datum of
  1983, European Datum of 1950, National Geodetic
  Vertical Datum of 1929)

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Geodetic Datums

• Geodetic datums define the reference systems that
  describe the size and shape of the earth.
  Hundreds of different datums have been used to
  frame position descriptions since the first
  estimates of the earth's size were made by
  Aristotle. Datums have evolved from those
  describing a spherical earth to ellipsoidal
  models derived from years of satellite
  measurements.

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Geodetic Datums, Contd

• Modern geodetic datums range from flat-earth
  models used for plane surveying to complex models
  used for international applications which
  completely describe the size, shape, orientation,
  gravity field, and angular velocity of the earth.
  While cartography, surveying, navigation, and
  astronomy all make use of geodetic datums, the
  science of geodesy is the central discipline for
  the topic.

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Geodetic Datums, Contd

• Referencing geodetic coordinates to the wrong
  datum can result in position errors of hundreds
  of meters. Different nations and agencies use
  different datums as the basis for coordinate
  systems used to identify positions in geographic
  information systems, precise positioning systems,
  and navigation systems. The diversity of datums
  in use today and the technological advancements
  that have made possible global positioning
  measurements with sub-meter accuracies requires
  careful datum selection and careful conversion
  between coordinates in different datums.

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HORIZONTAL DATUMS

• 8 Constants
• 3 specify the location of the origin of the
  coordinate system.
• 3 specify the orientation of the coordinate
  system.
• 2 specify the dimensions of the reference
  ellipsoid

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VERTICAL DATUMS

• A set of fundamental elevations to which other
  elevations are referred.

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Ellipsoid of RevolutionMathematical Model of the
Earth
N
b
a
S
a Semi major axis b Semi minor axis f
a-b Flattening a
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UNITED STATESELLIPSOID DEFINITIONS
BESSEL 1841 a 6,377,397.155 m 1/f
299.1528128
CLARKE 1866 a 6,378,206.4 m 1/f
294.97869821
GEODETIC REFERENCE SYSTEM 1980 - (GRS 80) a
6,378,137 m 1/f 298.257222101
WORLD GEODETIC SYSTEM 1984 - (WGS 84) a
6,378,137 m 1/f 298.257223563
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HORIZONTAL DATUMS

• BESSEL 1841 -------------- LOCAL ASTRO DATUMS
  (1816-1879)
• 
  NEW ENGLAND DATUM (1879-1901)
• 
  U.S. STANDARD DATUM (1901-1913)
• 
  NORTH AMERICAN DATUM (1913-1927)
• 
  NORTH AMERICAN DATUM OF 1927
• OLD
  HAWAIIAN DATUM
• CLARKE 1866 PUERTO RICO DATUM
• 
  ST. GEORGE ISLAND - ALASKA
• 
  ST. LAWRENCE ISLAND - ALASKA
• 
  ST. PAUL ISLAND - ALASKA
• 
  AMERICAN SAMOA 1962
• 
  GUAM 1963
• GRS80 ----------- NORTH AMERICAN DATUM OF
  1983
• 
  (As of June 14, 1989)

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COMPARISON OF DATUM ELEMENTS

• 
  NAD 27 NAD 83
• ELLIPSOID CLARKE 1866 GRS80
• a 6,378,206.4 m
  a 6,378,137. M
• 1/f 294.9786982
  1/f 298.257222101
• DATUM POINT Triangulation
  Station
  NONE
• MEADES RANCH, KANSAS EARTH MASS
  CENTER
• ADJUSTMENT 25k
  STATIONS 250k STATIONS
• Several Hundred Base Lines
  Appox. 30k EDMI Base Lines
• Several Hundred Astro Azimuths
  5k Astro Azimuths
• 
  Doppler Point Positions
• 
  VLBI Vectors
• BEST FITTING North
  America
  World-Wide

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NAD 27 and NAD 83
Can you say Metadata?
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Datums Currently In Use

• http//www.colorado.edu/geography/gcraft/notes/coo
  rdsys/coordsys_f.html

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Ellipsoids

• Ellipsoidal earth models are required for
  accurate range and bearing calculations over long
  distances. Loran-C, and GPS navigation receivers
  use ellipsoidal earth models to compute position
  and waypoint information. Ellipsoidal models
  define an ellipsoid with an equatorial radius and
  a polar radius. The best of these models can
  represent the shape of the earth over the
  smoothed, averaged sea-surface to within about
  one-hundred meters.
• Reference ellipsoids are defined by semi-major
  (equatorial radius) and semi-minor (polar radius)
  axes.
• Other reference ellipsoid parameters such as
  flattening, and eccentricity are computed from
  these two terms.

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Geoid Models

• The topographical surface of the earth is the
  actual surface of the land and sea at some moment
  in time. Aircraft navigators have a special
  interest in maintaining a positive height vector
  above this surface.
• Sea level is the average (methods and temporal
  spans vary) surface of the oceans. Tidal forces
  and gravity differences from location to location
  cause even this smoothed surface to vary over the
  globe by hundreds of meters.
• Gravity models attempt to describe in detail the
  variations in the gravity field. The importance
  of this effort is related to the idea of
  leveling. Plane and geodetic surveying uses the
  idea of a plane perpendicular to the gravity
  surface of the earth, the direction perpendicular
  to a plumb bob pointing toward the center of mass
  of the earth. Local variations in gravity, caused
  by variations in the earth's core and surface
  materials, cause this gravity surface to be
  irregular.

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Geoid Models, Contd

• Geoid models attempt to represent the surface of
  the entire earth over both land and ocean as
  though the surface resulted from gravity alone.
  Bomford described this surface as the surface
  that would exist if the sea was admitted under
  the land portion of the earth by small
  frictionless channels.
• The WGS-84 Geoid defines geoid heights for the
  entire earth.
• The U. S. National Imagery and Mapping Agency
  (formerly the Defense Mapping Agency) publishes a
  ten by ten degree grid of geoid heights for the
  WGS-84 geoid.
• By using a four point linear interpolation
  algorithm at the four closest grid points, the
  geoid height for any location can be determined.

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Global Coordinate Systems

• Coordinate systems to specify locations on the
  surface of the earth have been used for
  centuries. In western geodesy the equator, the
  tropics of Cancer and Capricorn, and then lines
  of latitude and longitude were used to locate
  positions on the earth. Eastern cartographers
  like Phei Hsiu used other rectangular grid
  systems as early as 270 A. D.
• Various units of length and angular distance have
  been used over history. The meter is related to
  both linear and angular distance, having been
  defined in the late 18th century as one
  ten-millionth of the distance from the pole to
  the equator.

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Latitude, Longitude, and Height

• The most commonly used coordinate system today is
  the latitude, longitude, and height system.
• The Prime Meridian and the Equator are the
  reference planes used to define latitude and
  longitude.
• The geodetic latitude (there are many other
  defined latitudes) of a point is the angle from
  the equatorial plane to the vertical direction of
  a line normal to the reference ellipsoid.
• The geodetic longitude of a point is the angle
  between a reference plane and a plane passing
  through the point, both planes being
  perpendicular to the equatorial plane.
• The geodetic height at a point is the distance
  from the reference ellipsoid to the point in a
  direction normal to the ellipsoid.

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Review and relevance Map Accuracy(National Map
Accuracy Standards)

• NMAS gt120,000 90 of well defined features
  will be within 1/50 inch on map of true position.
• USGS 124,000 series topo maps NMAS
• _at_ 124,000, 90 of well defined mapped features
  will be within 12.19-m of true position on the
  ground.
• _at_ 124,000, 12-m 0.5-mm...
  ...or dot from 0.5-mm
  pencil lead
• Knowing what coordinate system, datum,
  projection, etc directly effect the accuracy of
  position measurement!!!

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Review and relevance GPS Accuracy
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The lessons 1) Do not point at position with
your finger. 2) Attention to detail when
working.
Attention to detail when working.
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Commonly Used Coordinate Systems in the USA

• Geographic
• Universal Transverse Mercator
• Military/US National Grid
• State Plane
• Public Land Rectangular Surveys

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Geographic Coordinate System

• Is an X-Y angular coordinate system
• Based on Prime Meridian and Equator

Prime Meridian
Equator
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Universal Transverse Mercator coordinate system

• Abbreviated UTM
• Most commonly used system in GIS
• Divides earth into zones based on geographic
  coordinate system
• Each zone is 6 degrees wide and 8 degrees tall
• 60 zones total
• CONUS lies between zones 10-19
• MS Split between zones 15 and 16
• Each zone projected in Transverse Mercator
  projection

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UTM continued

• Each zone is subdivided based on hemisphere
• N-S coordinate called Northings
• Measured in meters
• Southpole is 0, Equator is 10 million
• Process is repeated for E-W split
• Called Eastings

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State Plane Coordinate Systems

• State plane systems were developed in order to
  provide local reference systems that were tied to
  a national datum.
• Some smaller states use a single state plane
  zone.
• Larger states are divided into several zones.
• State plane zone boundaries often follow county
  boundaries.
• Lambert Conformal Conic projections are used for
  rectangular zones with a larger east-west than
  north- south extent.
• Transverse Mercator projections are used to
  define zones with a larger north-south extent.

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State Plane, Contd

• Abbreviated SPCS
• In the United States, the State Plane System was
  developed in the 1930s and was based on the North
  American Datum 1927 (NAD27).
• NAD 27 coordinates are based on the foot.
• While the NAD-27 State Plane System has been
  superseded by the NAD-83 System, maps in NAD-27
  coordinates (in feet) are still in use.

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State Plane, Contd

• Most USGS 7.5 Minute Quadrangles use several
  coordinate system grids including latitude and
  longitude, UTM kilometer tic marks, and
  applicable State Plane coordinates.
• The State Plane System 1983 is based on the North
  American Datum 1983 (NAD83).
• NAD 83 coordinates are based on the meter.

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Public Land Rectangular Surveys

• Public Land Rectangular Surveys have been used
  since the 1790s to identify public lands in the
  United States.
• The system is based on principal meridians and
  baselines.
• Townships, approximately six miles square, are
  numbered with reference to baseline and principal
  meridian.
• Ranges are the distances and directions from
  baseline and meridian expressed in numbers of
  townships.

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Public Land, Contd

• Every four townships a new baseline is
  established so that orthogonal meridians can
  remain north oriented.
• Sections, approximately one mile square, are
  numbered from 1 to 36 within a township.
• Sections are divided into quarter sections.
• Quarter sections are divided into 40-acre,
  quarter-quarter sections.

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• Quarter-quarter sections are sometimes divided
  into 10-acre areas.
• Fractional units of section quarters, designated
  as numbered lots, often result from irregular
  claim boundaries, rivers, lakes, etc.
• Abbreviations are used for Township (T or Tps),
  Ranges (R or Rs), Sections(sec or secs), and
  directions (N, E, S, W, NE, etc.).

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Military/US National Grid

• Based on UTM
• Sub-divides each zone into subsequently smaller
  zones
• UTM divided into 6 x 8 degree grids
• Each 6 x 8 degree grid broken down into 100,000-m
  squares that are lettered
• Subdivision continues until 1000 x 1000 m grids
  defined
• Uses letter-number identification system
• VERY ACCURATE must be to accurately fire on an
  enemy without wiping out own troops
• Uses WGS 84 Datum. When NAD 83 datum used, MGRS
  becomes the US National Grid.

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Part III Making the Right Map

• Where Software and Reality Diverge

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Fundamentals of Mapping Support

• Two audiences
• Decision Makers
• Provide a picture (aka a map) that describes
  the situation in a way that supports informed
  decision making
• The picture should be framed in a common,
  spatially-based operational framework
• Field Personnel
• Navigation tools
• Local decisions (where is)

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GIS Professionals Gone Bad (aka Oh, how we
forget!)
ARGH!!! BAD MAP MAKER!!!
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The Need For Standardized and Paper Map Products

• Users Need Maps With
• Standard Scale
• Standard Symbology
• USNG or similar coordinate system
  overlay/graticule
• The four fundamentals
• North arrow(s)
• Scale bar
• Legend
• Title

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Size Does Matter

• While we, as geospatial professionals, often have
  plotters available, most responders do not. They
  get stuck with
• Printing to fit
• Printing cut-out areas
• A map thats not to scale (also a problem with
  Internet mapping services)
• Simple strategies that consider the users will
  help far more than elaborate spatial data
  clearinghouses, large format plots, etc..
• Consder exporting 8.5 x 11 maps into pdf or
  GeoPDF format and pre-position on the Web and
  promote a Know Before You Go attitude.

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Common USNG Mistakes With ESRI Products

• Grid zone junctions will not display correctly if
  creating the grid as a graphic in layout view.
• Graticule coordinates will be incorrect if the
  correct UTM zone is not set as the base
  coordinate system.
• Easy to confuse MGRS/USNG N and S portions of
  zone designations
• Tick marks are at odd intervals
• Scale bar done in feet and/or in odd intervals

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Significance of projections and coordinate systems

• GIS integrates multiple data types/sets, each of
  which may have its own projection or coordinate
  system
• Without an explanation of a given projection or
  coordinate system, a map may be very misleading

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Contributors
Elizabeth Wentz, Professor Department of
Geography Arizona State University Tempe, AZ
85287 wentz_at_asu.edu Tom Terry Geospatial Plans
and Policy Branch United States Marine
Corps Washington, DC Neri.terry_at_usmc.mil Kurt
Shultz Coordinate Systems Analysis Team Natl
Geospatial Intelligence Agency St. Louis,
MO kshultz_at_nga.gov
Talbot Brooks, Director Center for
Interdisciplinary GIT Delta State
University Cleveland, MS 38733 tbrooks_at_deltastate.
edu Dick Kotapish, Director Lake County GIS
Department 105 Main Street Painesville, Ohio
44077 Dick.Kotapish_at_lakecountyohio.gov Dave
Minkel, AZ Advisor National Geodetic
Survey Phoenix, AZ minkel_at_ngs.gov