Project 1: Plotting Coordinates and Projections
The map projection that I used for the above map was the Albers Equal-Area Conic projection. This projection shows the continental 48 states and portions of North America, including Beaverton, Oregon’s location within them. The bounding coordinates for this area of interest are 50° North, 25° South, -65° East, and -125°West. The standard parallels are set at 30° and 45° with a central meridian of -95°. The standard parallels were used to minimize the distortion within the above projection and the map was centered along the central meridian.
As mentioned above, distortion was reduced by using the two standard parallels. Distortion, however, can never be removed from a map projection. DiBiase notes that:
As you can imagine, you can't flatten a globe without breaking or tearing it somehow. Similarly, the act of mathematically transforming geographic coordinates to plane coordinates necessarily displaces most (but not all) of the transformed coordinates to some extent. Because of this, map scale varies within projected (plane) UTM coordinate system grids (DiBiase 2007).
Map projections are used to reduce or manage the distortions within a specified area of a map. The Albers-Equal Area Conic projection is free of scale distortion along the two standard parallels at 30° and 45°. According to Kennedy (2000), the distortion is “minimized in the region between the standard parallels.” Distortion is also constant along any given parallel within the projection (Snyder and Voxland, 1994). I used this projection because it is well-suited for showing landmasses extending east-to-west, such as the United States, (Kennedy 2000) and because I wanted to preserve the size of the conterminous 48 states to show the location of Beaverton.
I decided to create an additional map to show the location of Beaverton, Oregon within a more detailed projection of the Pacific Northwest. This map shows the location of Beaverton in relationship with the states of Oregon and Washington as well as the Pacific Ocean. The projection used for the above map is a Transverse Mercator with a central meridian of -122.4813, which is the longitude of Beaverton. The map extent is (in decimal degrees) 48° North, 43° South, -125° West, and -120° East. A Transverse Mercator map is “best suited for areas that stretch north to south” (Kennedy 2000:101). This is because it is a cylindrical map that is projected around a meridian, reducing the amount of distortion in the region of the central meridian of the map. By using the longitude of Beaverton as the central meridian, the distortion in the region of my hometown was minimized, allowing a better reference for the location of Beaverton within the Pacific Northwest.
As described above, a Transverse Mercator projection is a cylindrical map centered on a meridian. This cylindrical projection is conformal, preserving the shapes and angles within the projection. The area, distance and direction are distorted within the above map, but by preserving the shape, the map viewer can determine Beaverton’s location in relationship with the correct shape of Oregon and Washington as well as the shape of the coastline.
Both maps were created using the Interactive Album of Map Projections, by Ryan Baxter, found at http://projections.mgis.psu.edu.
Geographic Coordinates
The place name shown on the above maps represents the location of my current hometown. The geographic coordinates of Beaverton, OR are:
Latitude: 45° 17' 29" N, Longitude: 122° 28' 53" W
The geographic coordinate system is a measurement scale that, according to DiBiase (2007) “… is used to specify positions on the Earth's roughly spherical surface.” A geographic coordinate system is similar to a grid with a horizontal (x) axis and a vertical (y) axis, with latitude replacing the x axis and longitude replacing the y axis. Every position on the Earth has a latitude and longitude and these positions are measured in degrees. Latitudes range from -90° at the South pole to 90° at the North pole while longitudes range from -180° to 180°. The latitude associated with 0° is the equator, while the longitude associated with 0° is the prime meridian. The prime meridian runs through the Royal Greenwich Observatory in London, England and was adopted in 1884 as the international standard (Paul 2007). The International Date Line generally follows the longitude at 180°.
The prime meridian at the Royal Greenwich Observatory is the horizontal datum from which all other longitudes are measured (Paul 2007). A horizontal datum “defines the geometric relationship between a coordinate system grid and the Earth’s surface” (DiBiase 2007).
Latitudes and longitudes are expressed as degrees, minutes, and seconds or as decimal degrees. Because the Earth is spherical in shape, latitude and longitude are curved measurement lines that are measured in degrees by necessity. The geographic coordinates in degrees, minutes, and seconds for Beaverton, Oregon is 45° 17' 29" N, 122° 28' 53" W. In decimal degrees, Beaverton, OR is at 45.2913° and -122.4813°. The negative sign signals that the longitude is west of the prime meridian. Latitude and longitude are not projected measurements.
UTM Coordinates
The UTM coordinates (NAD83) of Beaverton, Oregon:
Easting: 515346.781 meters, Northing: 5037064.827 meters, Zone: 10
The Universal Transverse Mercator (UTM) is a grid system that divides the majority of the Earth’s surface into 60 different zones that each span 6° of longitude. The zones extend from a latitude of 80° 30' 00" South to 84° 30' 00" North (Different polar coordinate systems are used beyond these limits). The zones are numbered 1 through 60, starting at 180° west (roughly the position of the International Date Line). The zones are uniformly shaped, at 660,000 meters wide along the equator and tapering to 70,000 meters at the northern edge of the zone and 116,000 meters along the southern edge (DiBiase 2007).
The UTM grid uses the Transverse Mercator projection to reduce north-south distortion. The standard meridians are 180,000 meters east and west of the central meridian of a UTM zone. No distortion occurs along the standard meridians, with minimal distortion within the zone between the meridians. Northings and eastings are used by UTM to map and find locations. All northings and eastings are positive numbers to aid in reducing calculation errors and stem from the origin of that zone, to the south and west of the zone.
As mentioned previously, a horizontal datum defines the relationship between a coordinate system and the Earth’s surface. More specifically, a horizontal datum is the relationship between the ellipsoid (a model of the Earth’s shape) and the coordinate system. The North America Datum of 1927 (NAD27) was based upon the Clarke 1866 ellipsoid (DiBiase 2007). Its point of origin coincides with the geodetic center of the U.S., at Meade's Ranch, Kansas. The North America Datum of 1983 (NAD83) is based upon GRS 80, which is a global ellipsoid whose point of origin is the Earth’s center of mass (DiBiase 2007). Based on NAD27, fixed control points were created and located along the Earth’s surface and given coordinate values. NAD83 was created after the creation of the more accurate GRS 80 ellipsoid. While the control points' position on the Earth’s surface did not change, their position within the UTM coordinate system changed due to a different horizontal datum. This shift was different at every control point, and no formula can be created to show how much all the points shifted.
State Plane Coordinates
The State Plane coordinates (NAD83) of Beaverton, OR are:
Easting: 2319953.220 meters, Northing: 204840.477 meters, Zone: 3601
The State Plane Coordinate (SPC) system is a system of over 120 zones that cover all 50 states. The zones are small enough that they minimize distortion within the projection. States are typically divided into multiple zones, and each zone uses a unique map projection in order to minimize distortion (a distortion ratio of no more then 1 part in 10,000) (DiBiase 2007). SPC are mapped in meters using eastings and northings. They are expressed in meters because plane coordinates are easier to use than latitude and longitude in measuring distance (DiBiase 2007). State Plane coordinates are similar to UTM in that they were based upon NAD27 and later on NAD83. As such, the control points established within the State Plane Coordinate system shifted with the adoption of NAD83. The shifts were different at every control point within the coordinate system, just like with the UTM coordinate system.
Comparison
The three coordinate systems (geographic coordinates, Universal Transverse Mercator [UTM] coordinates, and State Plane Coordinates [SPC]) have many different uses. Geographic coordinates are measured in decimal degrees or degrees, minutes, and seconds. UTM coordinates and SPC are measured in meters using the NAD83 datum. Mathematical equations are used to change geographic coordinates into UTM coordinates and SPC. This is called map projection. Before the development of the GRS 80 ellipsoid and the adoption of the NAD83 datum, NAD27 was used as the primary datum for North America and was measured in feet. NAD27 was based on the Clark 1866 ellipsoid with its origin in Meade Ranch, Kansas. With better technology came a new ellipsoid, GRS 80, which has its origin at the Earth’s center. Because of its better accuracy, NAD83 was adopted as the horizontal datum, shifting the location of all the control points based upon NAD27.
The main difference between the systems is the scale in which they are used. Geographic coordinates are curved measurements and are based upon the spherical nature of the globe. While these are best for measuring the entire surface of the globe, portions of the globe are greatly distorted. UTM coordinates cover most of the globe (omitting the poles) and break the earth up into 60 zones. Distortion is minimized by the UTM coordinates to an extant of 1 part in 2,500 at any part of the zone (DiBiase 2007). SPC cover the United States, breaking up the states into over 120 different zones. Because the SPC system has so many different zones, each with its own unique projection, the SPC minimizes distortion to 1 part in 10,000. Together, the three different coordinate systems allow the map user three different ways to establish locations within maps of different scales.
Sources
DiBiase, David (1999-2006) The Nature of Geographic Data, Lesson 2. The Pennsylvania State University World Campus Certificate Program in GIS. Accessed 4 November 2007.
Kennedy, Melita (2000) Understanding Map Projections. http://kartoweb.itc.nl/geometrics/Map%20projections/Understanding%20Map%20Projections.pdf Accessed 4 November 2007.
National Geodetic Survey (2002) NADCON - North American Datum Conversion Utility. http://www.ngs.noaa.gov/TOOLS/Nadcon/Nadcon.html Accessed 4 November 2007.
National Geodetic Survey (2002) SPC Utilities. http://www.ngs.noaa.gov/TOOLS/spc.html Accessed 4 November 2007.
National Geodetic Survey (2002) UTM Utilities. http://www.ngs.noaa.gov/TOOLS/utm.html Accessed 4 November 2007.
Paul, Jeremy (1999) History of the Prime Meridian – Past and Present http://gpsinformation.net/main/greenwich.htm Accessed 4 November 2007.
Penn State Online GIS Education (2005) Interactive Album of Map Projections http://projections.mgis.psu.edu/ Accessed 4 November 2007.
United States Geological Survey (2002) Geographic Names Information System. http://geonames.usgs.gov/ Accessed 4 November 2007.
This document is published in fulfillment of an assignment by a student enrolled in an educational offering of The Pennsylvania State University. The student, named above, retains all rights to the document and responsibility for its accuracy and originality.