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Map Locational or Coordinate Systems

Modern maps (except informal sketch maps and mental maps) are based on systematic location encompassing the entire earth (or parts of it).

• Delaware, Ohio is at 40 degrees, 18 min North Latitude, 83 degrees 4 min West Longitude

But in the past...lack of an all encompassing system of locations:

• Native American (Iowa) map of Upper Mississippi River Region

• Rhumb lines (path of a path of constant compass bearing) on Italian Navigation Map: ca 1500

• how does how we think about the world relate to an all encompassing system of locations?

  
  

• Post 1500: view of the world shifting from pieces to a contained framework, into which everything fits
  

Map Locational or Coordinate Systems

• provide a way to locate features on the earth and in GIS and computer mapping

• they often result in coordinates: a pair of numbers specifying location

• basis of these coordinate systems >>> the idea of the graph
  

Four main characteristics that differentiate these coordinate systems:

1. What feature forms are the coordinate system generally used to specify?

• points or areas

2. What kind of geometry does the coordinate system use?

• planar: assume a flat earth
  • advantage: easy mathematics

  • disadvantage: increase in distortion as area covered increases

• spherical: assume a spherical earth
  • advantage: minimal distortion; takes into account spherical shape of earth

  • disadvantage: more difficult mathematics

3. How much area does a coordinate system cover?

• local, state/province/region, part of globe, entire globe

4. What are the units of measurement used?

• metric, english, degrees

Discuss these four characteristics in the context of five different map coordinate systems

Coordinate systems primarily used to locate POINTS

1. State Plane Coordinate System (SPCS)

• geometry: planar (in title)
  
• coverage: U.S. states, or parts of states (in title)
  
• units: english (U.S. system)

2. Universal Transverse Mercator System (UTM)

• geometry: planar
  
• coverage: narrow strips from pole to pole around the globe
  
• units: metric

3. Latitude/Longitude

• geometry: spherical
  
• coverage: global
  
• units: degrees/minutes/seconds

Coordinate systems primarily used to locate AREAS

4. U.S. Public Land Survey System (USPLS)

• geometry: planar
  
• coverage: state-sized areas in middle and western U.S.
  
• units: english

5. Arbitrary Reference Grids

• geometry: planar
  
• coverage: local to global
  
• units: various

Review each of these and detail...

1. How the coordinate system is defined

2. Who uses the coordinate system and what they use it for

3. How the coordinate system is represented on maps

Example Maps:

• Delaware Ohio 1:24,000 topo quad
• Carter Montana 1:24,000 topo quad
• Donaldsonville Louisiana 1:24,000 topo quad
• Scott City, Kansas 1:62,500 topo quad

Coordinate Systems primarily used to locate POINTS

1. State Plane Coordinate System (SPCS)

History:

Defining SPCS: US map with zones

Ohio map with zones / graph

Geometry: Planar

• each zone has a grid/graph imposed over it

  
  

• false origin located outside of the zone to the south and west (0,0)
  • 2,000,000 feet west of central meridian

  • only positive values used in SPCS

• locations are measured in FEET from this origin - read like a graph
  • feet east called "eastings" then feet north called "northings"

Who uses SPCS and for what?

How is SPCS shown on a USGS Topo Sheet

PROP) Delaware OH 1:24,000 quad: lower left, near township name "Concord"

• Black tic outside of map neatline

This point is located as such:

• 1,830,000 feet E, 220,000 feet N, OH, N

2. Universal Transverse Mercator System (UTM)

History:

Defining UTM

UTM Zone on Globe (left) and Rectangular Map (below)







Source




WWW) USGS Information on UTM

Coverage: 60 strips (zones) around entire globe oriented north/south and numbered west to east from the international date line

Each strip...

is 6 degrees wide (i.e., 6 degrees of longitude)
has 2 false origins (one for the north half; one for the south half) located as with the State Plane Coordinate System to the S and W of the zone at (0,0).
only positive values used in SPCS
500,000 meters west in North; 500,000 m west / 10,000,000 meters south in South
locations are measured in METERS from this origin - read like a graph
• meters east then meters north

Geometry: Planar

UTM Zones in US




Ohio in zones 16 (90 degrees to 84 degrees) and 17 (84 degrees to 78 degrees)

Who uses UTM and for what?

How is UTM shown on a USGS Topo Sheet?

PROP) Delaware OH 1:24,000 quad: lower left, near township name "Concord"

• blue tic outside of map neatline

• have to add "000" to numbers on map

This point is located as such:

• 320,000 mE, 4,458,000 mN, Zone 17, N

3. Latitude/Longitude

History:

• Eratosthenes: Greek, 3rd century BC: proposed a system of latitude and longitude for the Earth.

• Hipparchus: Greek, 2nd century BC: using Lat/Long to specify locations on the Earth; determining longitude by comparing the local time of a place with an absolute time.

• Al-Biruni (Persian, 11th century) proposed that the earth rotated on its axis, forming our modern notion of how time and longitude are related.

• Latitude: from the altitude of the sun at noon with the aid of a table giving the sun's declination for the day.

• Longitude: Earth rotates at a rate of 360 degrees per day, or 15 degrees per hour, there is a direct relationship between time and longitude. If the navigator knew the time at a fixed reference point when some event occurred at the ship's location, the difference between the reference time and the apparent local time would give the ship's position relative to the fixed location. Finding apparent local time is relatively easy. The problem, ultimately, was how to determine the time at a distant reference point while on a ship.

Defining Longitude

Also called meridians
Meridians run N and S
• and measure 180 degrees E and 180 degrees W around the globe

• 60 minutes = 1 degree

• 60 seconds = 1 minute

• 10 degrees, 20 minutes, and 30 seconds E Longitude (10o 20' 30" E. Longitude)

• meridians always pass through both poles

Four important characteristics of longitude and meridians

1. All meridians are great circles which pass through both poles: slice the sphere in half; shortest distance between two points on the globe

WWW) Great Circle Generator

2. Prime meridian arbitrary 0 degree base line meridian (Greenwich England)

• longitude measured (from 0 degrees to 180 degrees) E or W of Greenwich

3. Meridians converge at the poles

• one degree of longitude at the equator = 69 miles

• one degree of longitude at the poles = 0 miles (a point)

USGS Topo Quads are defined (in area covered) by longitude (width) and latitude (highth)

PROP) Delaware OH 1:24,000 Quad: At all corners of sheet

4. Longitude is measured by the time difference between greenwich and the point of interest.

Defining Latitude

Also called parallels (parallel to each other)
Parallels run East and West and measure 90 degrees N and 90 degrees S of the equator

Four points about latitude and parallels:

1. Only the equator is a great circle; all other parallels are not

2. Equator is the base line (0 degrees) for latitude

• latitude measured (from 0 degrees to 90 degrees) N or S of equator

3. Parallels never converge

• one degree of latitude always = 69 miles

• USGS Topo Quads are defined by longitude (width) and latitude (highth)
  • PROP) Carter MT 1:24,000 Topo vs Donaldsonville LA 1:24,000

• since parallels never converge and parallels define the highth of a topo sheet the highth of a USGS topo sheet is always the same

• since meridians do converge and meridians define the width of a topo sheet the width of a USGS topo sheet varies (wider in south, narrow in N)

4. Latitude is measured

• by the angle between the horizon and the north star in the northern hemisphere

• by the angle between the horizon and the southern cross in the southern hemisphere

  
  
  

  

...In general, lat/long

• coverage: entire globe

• geometry: spherical

• the latitude/longitude coordinate system

• has an origin of (0 degrees, 0 degrees) and all other locations are specified in degrees, minutes (60 minutes = 1 degree) and seconds (60 seconds = 1 minute)

Who uses Lat/Long and for what?

How is Lat/Long shown on a USGS Topo Sheet

PROP) Delaware OH 1:24,000 Topo: Lat/Long crosshair: S of Radio Tower, near "W" in Delaware

• black crosshair on map

PROP) Delaware OH 1:24,000 quad: lower left corner

• corners; black tics on inside of neatline

This point is located as such:

• 83 degrees 7 minutes 30 seconds W, 40 degrees 15 minutes N

Coordinate Systems primarily used to locate AREAS

4. U.S. Public Land Survey System (USPLS)

History: Metes and Bounds

PROP) French Long Lots: Donaldsonville LA 1:24,000 topo
Land Ordinance of 1785: origin of U.S. Public Land Survey System

Defining USPLS

Eastern US map with USPLS Survey Zones


Coverage: chunks of land primarily defined as they became available for settlement; thus the patchwork pattern
Each area has
• an arbitrary base-line running E/W

• an arbitrary prime meridian running N/S

Township and Range System

Township lines are placed every 6 miles north and south of the base line
Range lines are placed every 6 miles east and west of the prime meridian
The system creates 6 mile by 6 mile squares called townships
Within each township are 36 sections numbered from 1 to 36
• boustrophedonic: "as the ox plows"
each section can be further divided into smaller and smaller parcels

Geometry: Planar

Who uses USPLS and for what?

How is USPLS shown on a USGS Topo Sheet

PROP) order on the land: Scott City, Kansas 1:62360 Topo Quad




Hines School: area is located as such:

NW1/4, Section 15, Township 20 South, Range 32 W, 6th PM

5. Arbitrary Reference Grids

Can be just about any kind of reference system that is set up for a specific map and is not connected in any way with any other map

Campus map with Arbitrary Grid System

Summary: Map Coordinate Systems

Four important aspects of map coordinate systems

1. What feature forms are the coordinate system generally used to specify?

2. What kind of geometry does the coordinate system use?
   • Planar vs. Spherical

3. How much area does a coordinate system cover?

4. What are the units of measurement used?

...and five important systems...

1. State Plane Coordinate System (SPCS)

2. Universal Transverse Mercator System (UTM)

3. Latitude/Longitude

4. U.S. Public Land Survey System (USPLS)

5. Arbitrary Reference Grids

E-mail: jbkrygier@owu.edu

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