Source: Baxter, R., Sloan, J.L., Gutowski, M., Wherley, M., Pfeiffer, C., and DiBiase, D. (n.d.). Interactive Album of Map Projections. Retrieved September 12, 2014, from http://projections.mgis.psu.edu
The map above is known as a Robinson map projection. It was introduced in 1963 by Arthur H. Robinson (Egsc.usgs.gov, n.d.). Robinson projections are Pseudocylindrical. Distortions ellipses in the map are noted by the by the red circles. “Distortion is very low along the Equator and the 45°of center. Greatest near the poles.” (Egsc.usgs.gov, n.d.). This map is a “compromise” between known map distortion properties, as it seeks to minimize distortion as much as possible (DiBiase,Ch.2, p29). Since the Earth isn’t a perfect sphere, one can more associate the Earth to an ellipsoid. Most maps are subject to these distortion properties under four main spatial properties.
These properties are: Area, Distance, Shape, and Direction. The Robinson map used above preserves Distance well along the Equator and other parallels. Direction is true along all parallels and the central meridian. Scale is true along 38° North and South. It is constant along any given parallel and the same along North and South parallels from the equator (Egsc.usgs.gov. (n.d.).
The map has been drawn with an extent of 40° North, 30° South, -120° West, and -100° East.
Geographic Coordinates
The place name shown on the map above represents the location of my hometown, Los Alamos, New Mexico. The geographic coordinates of my home town are:
The place name shown on the map above represents the location of my hometown, Los Alamos, New Mexico. The geographic coordinates of my home town are:
Latitude: 35° 53' 17" N, Longitude: -106° 18' 25" W
The Geographic Coordinate System is a three-dimensional spherical system used to navigate along earth’s surface utilizing a degree system based of measurement. Longitude is a function of moving between positions East and West on the globe from 0° to 180°and -90° and -180°. Latitude is a function of moving North and South along the globe between ranges of 90° at the North Pole and -90° at the South Pole. Coordinates are usually represented in degrees, minutes, and seconds based on the 360° dimensions of a sphere. “A line of latitude is known as a parallel.” (DiBiase, Ch.2, p.11). Imagine a grid of intersecting lines running north and south. The lines running north and south are meridians. The lines running east and west are known as parallels. The coordinate system utilizes control points known as datums. The horizontal datums on earth’s surface are define the geometric relationship between a coordinate system grid and the Earth surface (DiBiase, Ch2, p13).
UTM Coordinates
The UTM coordinates (NAD83 or NAD27) of my hometown (Los Alamos, NM) are:
Easting: 376,075.305 meters, Northing: 3,957,906.025 meters, Zone&Hemisphere: 13N
Source: DiBiase, D. and others 2014, Ch. 2, p.23, Figure 2.23.2. Retrieved September 27, 2014, from https://www.e-education.psu.edu/natureofgeoinfo/c2_p23.html
The Universal Transverse Mercator (UTM) coordinate system is based off the Transverse Mercator Projection. It is comprised of a system of 60 zones divided along the earth’s surface, with 6°of longitude. The zones are numbered from West to East with a starting point from 1 to 60. They begin at 180° West longitude (DiBiase, D. and others 2014). In the polar zones, latitudes of greater than 84° in the north and 80° in the South are excluded. Each zone labels coordinates as Eastings and Northings, typically they are measured in units of meters measured from a horizontal datum. Easting headings are distances east of the origin. Northing headings are distances north of the origin. The best way to describe these headings would be to assign an “x-coordinate” value to all Eastings measurements and a “y-coordinate” to all Northing measurements (Easting and Northing. n.d.). The measurements are expressed in meters instead of degrees as each grid cell in a UTM projection represents 500,000 meters on each side of the origin. The widest part (666,000 meters wide) is located at the equator. Because earth surface is not perfect, relative sizes and shapes needed to be created as guide. To get precise coordinates, transformations need to be calculated between different ellipsoids in the past and present (DiBiase, D. and others 2014).
National or Regional Coordinates
The State Plane coordinates (NAD83 or NAD27) of my hometown (Los Alamos, NM) are:
Easting: 494,858.946 meters, Northing: 542,094.502 meters, NAD83 Zone: 3002
The State Plane Coordinate System (SPC) consists of 124 zones which cover the United States. It utilizes “Eastings” and “Northings” the in same manner as the UTM systems does. SPC zones have been designed with three main objectives. The first objective sets out to use plane coordinates for ease of use on flat grids. The second objective seeks to have all known values positive. “SPC Zone origins are defined so as to ensure that every easting and northing in every zone are positive numbers.” (DiBiase, Ch2_p27). The third objective seeks to keep the maximum error in each zone to “1 part in 10,000 or better.”(DiBiase, Ch2_p26). SPC zone are plotted via a Transverse Mercator or Lambert Conformal Conic map projections (DiBiase, Ch2, p26). SPC zones cover smaller areas, which leads to fewer distortions errors over the map than the UTM system. These distortions are reduced by using two standard parallel lines.
The horizontal datum relates to the SPC coordinates though the NAD27 to NAD 83 datum. The NAD27 datum was created in 1927 and was eventually replaced by a more geocentric ellipsoid called the GRS80. When converting from old datums to new ones, some error or “datums shift” is observed in the new data transformations (DaBaise, Ch2, p19). When converting from NAD27 to NAD83 in the NADCON conversion utility, a shift of 52.942 meters was recorded in my hometown of Los Alamos, NM (National Geodetic Survey, 2004).
Comparison
The coordinate systems Geographic, Universal Transverse Mercator (UTM), and State Plane Coordinate (SPC) all have unique properties and characteristics. The Geographic system is based off a system in a spherical 360°degrees. The Geographic Coordinate System uses a Degrees, Minutes, Seconds system to navigate between areas on a map (DiBiase, D. and others 2014). Geographic Coordinate Systems are best used when viewing large areas. The UTM and SPC projections utilize measurements of meters. SPC zones tend to be projected on a Lambert Conic Conformal or Transverse Mercator map, which have parameters like standard lines and central meridians which are optimized for each zone (DiBiase, Ch2_p26). Geographical coordinates are not projected due to the earth almost spherical like shape. The UTM system is projected via a Transverse Mercator containing 60 zones; whereas, SPC has 124 zones. The SPC system tends to be more accurate as it covers a smaller area (DaBaise, D. and others 2014). UTM has a much better representation of measuring distance and area than the Geographical Coordinate System does; however, UTM measurements can become cumbersome when trying to measure outside of each zone. The NAD (North American Datum) 27 and NAD83 datums are both horizontal datums. The NAD27 is based off the Clarke 1866 ellipsoid. The NAD83 datum was founded off the GRS80 ellipsoid. NAD27 and NAD83 differ only in that are based off different ellipsoids (DiBiase, D. and others 2014).
In Summary, the three different coordinate systems vary in shapes and sizes depending on the type of map projection desired. Depending on the scale and detail of the map, some projections work better than others. Some maps preserve fewer distortions near standard lines and some exaggerate distortions near the poles. One can choose from many datums available to utilize the best ellipsoid required for the map desired or needed to show data correctly.
References:
Baxter, R., Sloan, J.L., Gutowski, M., Wherley, M., Pfeiffer, C., and DiBiase, D. (n.d.). Interactive Album of Map Projections. Retrieved September 12, 2014, from http://projections.mgis.psu.edu
DiBiase, D. and others (2014). Nature of Geographic Information. The Pennsylvania State University. Retrieved September 12, 2014 from https://www.e-education.psu.edu/natureofgeoinfo/.
Easting and Northing. (n.d.). In Wikipedia. Retrieved September 30, 2014, from http://en.wikipedia.org/wiki/Easting_and_northing
Egsc.usgs.gov. (n.d.). Map Projections Poster. Retrieved September 28, 2014 from http://egsc.usgs.gov/isb//pubs/MapProjections/projections.html#robinson
National Geodetic Survey (2004) NADCON – North American Datum Conversion Utility. Retrieved September 12, 2014 from http://www.ngs.noaa.gov/cgi-bin/nadcon.prl
National Geodetic Survey (2004a). SPC Utilities. Retrieved September 12, 2014, from http://www.ngs.noaa.gov/TOOLS/spc.html
National Geodetic Survey (2004b). UTM Utilities. Retrieved September 14, 2014, from http://www.ngs.noaa.gov/TOOLS/utm.html
United States Geological Survey (2006a). Geographic Names Information System. Retrieved September 12, 2014, from http://geonames.usgs.gov
United States Geological Survey (2006b). Map Projections Poster. Retrieved September 12, 2014, from http://www.scribd.com/doc/92268542/Map-Projections-Poster-USGS 
