Project 1:
Plotting Coordinates and Projections

James H. Kompanek

Figure 1. Plate Carrée (Geographic) projection showing the location of Lexington, Kentucky.

Penn State Online GIS Education (2006) Interactive Album of Map Projections http://projections.mgis.psu.edu/ Accessed 1 February 2006.

The above map, Figure 1, shows my new home town of Lexington, Kentucky.  The map is a Plate Carrée (Geographic) projection, showing distortion ellipses--It is bounded to the north at Latitude +60.00^° and on the south at +20.00^° (Penn State Online GIS Education 2006).  It is also bounded on the west at Longitude -90.00^° and east at -70.00^° . 

The above projection is classified as both cylindrical and equidistant (DiBiase 2006).  This projection can be visualized by wrapping a rectangular piece of paper around a globe (creating a tube) and transferring the information contained on the surface of the globe onto the outside of the tube.  If this tube was rolled flat, the above map would make up a small, rectangular portion of it.

As can be observed with the distortion ellipses, the north-south diameter of each ellipse is consistent along each meridian (DiBiase 2006).  If the above the map was expanded to show the entire globe, the same scale would be observed for each meridian between the poles.  The property of equidistance (north-south) is maintained regardless of how far away any given point is from the equator. As can also be observed with the distortion ellipses, the property of equidistance is also maintained along each east-west parallel, equidistant from the equator.  The east-west scale also increases the further north or south any point is from the equator but remains consistent along its respective parallel.

All of this results in a degree of distortion in the map.  If one were to measure out a centimeter, its scale would be the same north-south for any point on the map.  It would also be the same for any east-west point (as long as they are equidistant from the equator).  What this means in terms of the above map is that the east-west scale for Quebec is significantly larger than it is for Cuba, although the north-south scale would remain the same for both.

Lexington, Kentucky (NAD83)
- Latitude: 37° 59' 19" N
- Longitude: 84° 28' 40" W (United States Geological Survey 2006)

Figure 2. Geographic Names Information System query under "Lexington".

United States Geological Survey (2006) Geographic Names Information System. http://geonames.usgs.gov/ Accessed 1 February 2006.

The geographic coordinate system is a 3-dimensional coordinate system based on earth being spherical and is expressed in terms of curved measurement scales: Latitude and Longitude (DiBiase 2006).  This system can be used to express the position of any point on the globe.  As can be seen in Figure 2, there are many "populated places" across the United States named Lexington (United States Geological Survey 2006).

Latitude designates the number of degrees from the equator (Figure 3).  Latitude ranges from 0°  latitude at the equator, to +90° (the north pole) or -90° (the south pole) (DiBiase 2006).  It can be visualized with an imaginary line running across the equator, with the latitude being the number of degrees from the equator to any given point on the earth, with either pole being right angles, or 90° (with + designating north and - designating south of the equator).  A line of latitude is also referred to as a parallel, because unlike longitude, each line of latitude is parallel to the next.

Longitude designates the number of degrees from the prime meridian (Figure 3) (DiBiase 2006).  The prime meridian is an imaginary line running along the surface of the earth to either pole.  This line runs through Greenwich, England and since 1884 has been internationally accepted as 0° longitude (Paul 1999).  Longitude is expressed in degrees ranging from 0° at the prime meridian to +/- 180° at the international date line.  East of the prime meridian these degrees are positive and to the west they are negative (DiBiase 2006).

As mentioned above, the geographic coordinate system is expressed in degrees (DiBiase 2006).  There are two formats:  Degrees, minutes, seconds, and decimal degrees.  Both systems express the same information and neither is more accurate than the other.  The first way of expressing coordinates is based on degrees, which can be divided into 60 minute intervals, which can be further divided into 60 second intervals (XX° XX' XX").  Decimal degrees simply converts the minutes and seconds into a decimal number (XX.XXX°).

Figure 3. Diagram showing the basis for the longitude and latitude in the geographic coordinate system.

DiBiase, David (2006) The Nature of Geographic Data, Lesson 2.  The Pennsylvania State University World Campus Certificate Program in GIS. Accessed 2 February 2006.

- Easting: 721496 meters  Northing: 4207553 meters

- Zone: 16 North (National Geodetic Survey 2006c)

UTM, or Universal Transverse Mercator, is a plane coordinate system (DiBiase 2006).  Units are expressed in meters east and north of designated origin lines.  UTM offers an alternative to the geographic coordinate system discussed above.  While the geographic coordinate system are well suited for plotting positions on a 3-dimensional globe, the curved measurement scale is awkward when used on a 2-dimensional map.  Nearly the entire earth, minus the extreme polar regions can be expressed with UTM coordinates (a Polar coordinate system is used for extreme latitudes).  Geographic coordinates can be converted to UTM using a Transverse Mercator map projection.

The UTM system divides the earth into 60 zones spanning 6° each in longitude (60 zones x 6° = 360°) (DiBiase 2006).  The relatively large number of zones allows for the maximum error associated with any point with it to be no more than 1 part in 2,500, with an error of 0 along any of the meridians.  Each zone is divided roughly in half at the equator and runs 84° 30' North and 80° 30' South.  Each zone is also 666,000 meters wide at the equator and 70,000 meters and 116,000 meters wide at its northern and southern limits respectively.  Coordinates are expressed in meters from its origin.  In the north zone, this would be expressed in meters north of the equator, and meters east of 500,000 meters west of the zone's central meridian.  The origin is expressed in the same manner for the southern zones, except that instead of measuring from the equator, the northern coordinate is expressed in meters north of 10,000,000 m south of the equator.  The initially unintuitive manner of expressing coordinates are used to prevent the necessity of negative coordinates in the system.

A datum is the benchmark that links a coordinate system grid to the Earth's actual surface (DiBiase 2006). For example, in my field upon identification of an archaeological site, one of the first things an archaeologist would do is to establish a datum.  This could simply mean identifying a road intersection, prominent standing structure, etc., or in some cases, sinking a long piece of steel rebar encased in concrete well into to the subsoil.  This identified point would be assigned coordinates, which are typically positive (i.e. N1000 E1000) to allow for all positions on the grid to be positive.  All subsequent mapping would be based off the coordinates of this reference point.  As can be seen with Figure 3, a map of excavations at the Painted Stone Farm site in Shelby County, Kentucky, a datum was established at N1000 E1000, which was linked to actual geographic features (the sinkhole and pond to the northeast) and well documented modern points (such as KY 55 or the numerous telephone poles) (Wingfield et al. 1996).  The use of a datum at N1000 and E1000 technically refers to an imaginary origin 1000 meters to the west and south, of which all coordinates at the site are based on.  This is roughly comparable to UTM origins, which always result in positive coordinates.

Figure 4. Schematic plan map of excavations at the Painted Stone Farm site in Shelby County, Kentucky.

Wingfield, Derek M, Michael D. Richmond and Henry S. McKelway, Ph.D (1996) Archaeological Remains of a Mid Nineteenth Century Brick Clamp: A First Look at Brick Clamps in Kentucky.  Cultural Resource Analysts, Inc.  http://www.crai-ky.com/education/reports/brick-clamp.html Accessed 1 February 2006.
 

On a global scale, the same fundamental concept applies (although much more complicated).  As any backpacker, hiker, or anyone who relies on USGS topographic quadrangles knows, there are two widely used datums: NAD83 and NAD27 (DiBiase 2006).  The North American Datum of 1927 (NAD27) was designed specifically for North America.  It is based on The Clarke 1866 ellipsoid, with its origin set at the geographic center of the continental United States, at Meade's Ranch, Kansas.  The North American Datum of 1983 (NAD83) is based on a "global ellipsoid whose initial point is the Earth's center of mass" (DiBiase 2006).  The transition from NAD27 to NAD83 allowed for more accuracy because the NAD83 ellipsoid better depicted the surface of the earth and corrected "distortions that had accrued in the older datum" (DiBiase 2006).  According to the North American Datum Conversion Utility (National Geodetic Survey 2006a), the datum shift between the NAD27 and NAD83 datums for Lexington, Kentucky was 10.256 meters.

This may seem like a relatively small amount of error but it is something that can be significant to anyone who has to deal with a variety of maps.  For example, prior to an archaeological survey, it is standard practice to consult a variety of historical maps to attempt to identify potential structures, mounds, etc. that may no longer be standing.  If an archaeologist were to plot out coordinates for house on a 1935 15 minute or  7.5 minute topographic quadrangle using NAD27 and then plot the same coordinates on a 2001 quadrangle (or programmed into a handheld GPS) using NAD83 (without taking the datum shift into account), this 10 meter distortion could cause problems.  Considering that standard methods for an archaeological survey involve digging 30 cm shovel-tests on a 20 meter grid (Sanders 2001), it's easy to see how being 10 - 20 meters off mark would result in not finding what you were looking for.

Lexington, Kentucky (NAD83)

Easting: 479990 meters  Northing: 54258  meters

Zone: 1601  Area: Kentucky North (National Geodetic Survey 2006b)

The State Place Coordinate (SPC) system is similar to UTM, as it is also a plane coordinate system and coordinates are described in distance east and north from an origin (DiBiase 2006).  The SPC system was designed with zones small enough to minimize distortion but large enough to still be practical.  This system divides the United States into approximately 120 separate zones (compared to UTM's 60 which span the entire globe), with small states comprising a single zone and larges state comprising of two or more.  A result of the quantity of zones is a high degree of precision, with distortion only being 1 part in 10,000 (versus 1 part in 2,500 in UTM).  Like UTM, the origins of SPC are designed to allow for all positive coordinates of any point in a zone, as the origins are always outside of the included counties.  Depending on the size and shape of a state, two map projections were used for developing SPC zones.  For states taller than they are wide, such as Illinois, a Transverse Mercator map projection was used, and in "wide" states, such as Kentucky or Pennsylvania, the Lambert Conic Conformal map project was.  As seen in Figure 4, Lexington (Fayette County) is located in the northern zone of Kentucky.

Figure 4. Map showing the two zones of Kentucky.  Lexington is Located in Kentucky North. 

Kentucky Division of Geographic Information (2006).  Kentucky State Plane Coordinate System.  http://ogi.ky.gov/data/drg/drgzone.htm.  Accessed 1 February 2006.

Conclusion:

Of the three coordinate systems discussed above, each has its own advantages and disadvantages (United States Geological Survey 2000).  If you were given a globe and a variety of positions to plot, geographic coordinates would be the simplest to deal with.  Geographic coordinates are very useful in 3-dimensional representation of the earth.  One can imagine when sailing around the world, geographic coordinates would be very useful when plotting positions onto a globe.  It would also be useful for an Elementary school teacher showing his or her class where the space shuttle was at any time (as I recall from third grade) as updates were given on the news.  Although, if you were just given two geographic coordinates, it would be extremely difficult to calculate their distance from each other, as one degree of longitude does not equal the same physical distance at the equator as it would on the north pole.  Attempting to determine area between three or more geographic coordinates would also be extremely challenging.

For plotting positions on a 2-dimensional map, plane coordinate systems are more practice.  Distance and area can be easily determined with a plane coordinate system.  Both UTM and SPC are derived from map projections, which convert 3-dimensional coordinates onto a 2-dimensional plane.  Both are very useful in a variety of applications.  If the US Department of Transportation was planning a new Interstate from Cleveland, Ohio to Miami, Florida, UTM would be more appropriate than SPC due to the magnitude of the undertaking.  This theoretical Interstate would only cross only one or two UTM zones, versus ten or more SPC zones (Figures 4 & 5).  If this theoretical road crossed the state of Tennessee, it is also reasonable that the Tennessee Department of Transportation would use SPC to instruct construction crews on the ground, because of it's lower distortion of 1 part in 10,000 (versus 1 part in 2,500 with UTM).  The state of Tennessee is also made up of a single SPC zone, versus two UTM zones (16 and 17).

Figures 4 & 5.  The continental United States contrasting UTM (left) and SPC (right) zones.

DiBiase, David (2006) The Nature of Geographic Data, Lesson 2.  The Pennsylvania State University World Campus Certificate Program in GIS. Accessed 2 February 2006.

SPC would be more useful for mapping that involves smaller scales.  If a developer was designing a housing complex in Cincinnati, Ohio, SPC might be used because of its lower distortion.  But if a regional development agency was tracking all development in the Cincinnati metro area, UTM might be used because the Cincinnati metro encompasses Ohio, Kentucky, and Indiana (three SPC zones).  Another advantage of SPC is that its zones run along county lines versus arbitrarily cutting across cities and geographic features like UTM which spans every 6 degrees in longitude (DiBiase 2006).  If a city were to be contained entirely within county lines, such as Lexington, Kentucky, SPC would be more appropriate.  UTM could also be used when the potential distortion is irrelevant.  If the Department of Defense were to roughly show the location of every military installation in the United States, it would be simpler to do so on Figure 4 than Figure 5 and the potential distortion difference between UTM and SPC would be moot, as the actual point marked on the map would be much larger than any potential inaccuracy with UTM.

Each system has its pros and cons.  As in archaeology, and I'm sure many other fields, it is necessary to coordinate between a wide variety of government agencies and developers, each one using a variety of different systems.  For example, an archaeologist might receive a project plan map from a developer using SPC (NAD83).  As a result, it would be necessary to plot points of structures from a historic topographic quadrangle using Latitude and Longitude (NAD27), and submit a report to the Office of State Archaeology using UTM (NAD83).  No coordinate system is universally more useful than the next and often with UTM versus SPC, the pros and cons of each are quite comparable and neither outweighs the other.  Flexibility if a prerequisite for any real world scenario.