GEOG 482 Project 1:
Plotting Coordinates and Projections

The map above was generated from the Online Map Creation web site (Weinelt 2005).  I chose a mercator projection of an area that is approximately one-half degree plus or minus (+/-) of the longitude and latitude of my home town, Dillsburg, PA.  This projection minimizes any distortions of scale and yet provides sufficient detail to locate both the name of the town in my postal address and as you will see below, the actual location of my home in South Central PA.  The map also displays the distinguishing features of a horizontal red line toward the lower part of the map that is the Pennsylvania - Maryland border, the cities of York and Harrisburg, and the diagonal blue line in the upper right portion of the map representing the Susquehanna River.

The map used is a transverse mercator projection based upon a mathematical formula used to transform geographic coordinates into plane coordinates.  The distortion inherent with this form of projection (from among an infinite set of projections) is zero along a standard line, in this case along the equator, and increases toward the poles.  As the latitude increase (i.e. the farther north or south from the equator represented by the projection) the level of distortion increases due to the fact that we are projecting a three dimensional object, the earth, onto a two dimensional plane, the map paper (DiBiase 2005).  This map is drawn such that each "box" on the map is represented by 7.5º of both longitude and latitude.  As can be seen, the distance between the latitude lines is greater than between the longitude lines.  This map tends to preserve the longitudinal (horizontal) reference while the latitudinal (vertical) reference is slightly distorted.

Additionally, because longitude lines converge at the poles, the more northern (or upper) portions of this map should be slightly closer together.  However, this projection has the longitudinal lines running parallel, resulting in a further slight distortion.

The geographic coordinate system is a measurement system that defines positions on the Earth's surface.  The geographic coordinate system is comprised of two curved measurement scales, longitude and latitude.  The origin of the measurement scale for longitude is the Prime Meridian, defined by international treaty as zero degrees, and ranging 180 degrees east and 180 degrees west to a common point called the International Date Line.  The Prime Meridian runs from the North Pole through the town of Greenwich, England, to the South Pole.  All coordinates to the west of the Prime Meridian are expressed as negative values, and coordinates to the east of the Prime Meridian are expressed as positive values until meeting on the opposite side of the world from Greenwich, England, 180 degrees from the Prime Meridian.  Lines of Longitude are approximately 111 kilometers apart at the equator and all Lines of Longitude converge at both the North and South pole.  The origin for the measurement scale for latitude is the equator and ranges from 0 degrees to plus or minus 90 degrees at the north and south pole respectively.  Lines of latitude are parallel (DiBiase, 2005).  Also, it should be noted that the accuracy of measurements using the coordinate system can increase infinitely as one subdivides the longitude and latitude values into greater levels of precision (Murray, 2005)

The Universal Transverse Mercator (UTM) Coordinate system provides a means of identifying a unique geographic location by using a flat grid system.  The UTM system divides the world in to 60 longitudinal zones each 6 degrees wide starting with the International Date Line and proceeding eastward around the globe.  Each UTM zone extend from approximately 80 degrees south latitude to 84 degrees north latitude (National Geodetic Survey (2005) UTM Utilities).

The UTM coordinate grid relates to the area of coverage for each UTM zone.  Each UTM zone is divided into a Northern Zone and Southern Zone, with each having its own coordinate system point of origin.  By definition, the origins of both zones are located 500,000 meters west of the UTM zone's central meridian, or the meridian running directly through the middle of the zone.  For the Northern Zone, the point of origin for the coordinate system is on the equator and 500,000 meters west of the UTM's central meridian.  For the Southern Zone, the point of origin for the coordinate system is an imaginary point 500,000 meters west of the South Pole.

UTM coordinates are then specified by "Eastings" or the number of meters to the east of the point of origin, and by "Northings" or the number of meters to the north of the point of origin.  Also, since each UTM is 6 degrees at the equator (or approximately 666,000 meters) and the point of origin is 500,000 meters to the west, then "Easting" coordinates in the zone are greater than 166,000 and less than 666,000 meters.  "Northings" are based on a scale of 0 to 10,000,000 meters.

NAD 27 to NAD83

Both NAD27 and NAD83 are horizontal datums.  A horizontal datum defines the geographic relationship between two abstract concepts, a coordinate system grid and an approximation of the Earth's surface called an ellipsoid.

The North American Datum of 1927 (NAD27) was the horizontal datum in use for North America prior to the advent of the Global Positioning System (GPS).  NAD27 was based on the Clarke 1866 ellipsoid whose point of origin is Meades Ranch, Kansas.  With the advent of the GPS, a new geocentric ellipsoid was required and the Clarke 1866 ellipsoid was replace with the GRS-80 ellipsoid.  The change of this reference system along with other changes due to known local distortions resulted in a shift in the coordinate system referencing fixed geodetic reference points.  These changes are reflected in a newer horizontal datum, the North American Datum of 1983 (NAD83). (DiBiase, 2005)

The State Plane Coordinate (SPC) system divides the United States into 125 unique zones covering all 50 states in an effort to minimize the distortion of the map projection to 1 part in 10,000 or better.  SPC zones are either a Transverse Mercator projection for 'horizontal' zones or a Lambert Conical Conformational projection for 'vertical' zones. SPC coordinates are frequently used for surveying and mapping because they are easier to use than geographic coordinates for computing distances and areas.  (DiBiase, 2005)

The SPC limits each map projection to the political boundary of a state or a subdivision of a state.  The subdivisions of a state are groupings of counties, although the states of North and South Carolina, and Tennessee are not subdivided, but are each their own zone (Stem 1990).  The system uses a coordinate system of Eastings and Northings for ease of use in calculating distances and area.  Each coordinate is a positive value, and the error rate is 1 part in 10,000.  The point of origin for each projection are to the south of each zone and the Eastings for each zone vary from 200,000 to 800,000 meters (DiBiase, 2005).

State Plane Coordinates are used for large scale surveying and mapping projects because plane coordinates are much easier to use than longitude and latitude in calculations of distances and area and preserve the property of conformality, meaning that the angles plotted on the coordinate system are equal to the angles measured on the surface of the earth.

Coordinate System Comparison

Perhaps the best way to compare and contrast the coordinate systems would be to provide a little practical exercise.  I actually live several miles outside of Dillsburg.  Using a hand-held GPS device, I calculated the location of my house to be N 40º 4.152' latitude and W 076º 56.770' longitude.  Converting these coordinates to their full decimal equivalents allowed me to provide the input data to have the location of my house plotted on the map above, shown some distance from the town of Dillsburg.  In addition, converting the partial decimal equivalent minute data from the GPS to minutes and seconds, I then used the National Geodetic Survey UTM and SPC Utilities to convert the geographic coordinates for my house into UTM and SPC coordinate measurements as follows:

Home and Dillsburg UTM Comparison:

Home and Dillsburg State Plane Coordinate Comparison:

Conclusion

From the above, it was great to use the geographic coordinates of longitude and latitude to place points on a map, and it is necessary to use longitude and latitude with working with geographic data that crosses  UTM Zones or SPC Zones or Area.  However, it you are working within the same zone or area, the use of UTM or SPC coordinates makes the calculation of distances and areas significantly easier.  Also, due to its larger scale, the maximum SPC error rate is smaller than the UTM error rate ( 1 in 10,000 vs 1 in 2,500 respectively).

Some Final Thoughts

Since all data was obtained from the National Geodetic Survey web site using the NAD83 datum, no conversions from the NAD27 datum were required.  Further, all GPS data is referenced to the NAD83 datum.  Using the NAD83 datum, all UTM and SPC data is referenced in meters.

Both the UTM and the SPC data indicated that my house is both south and east of the Dillsburg geodetic marker, and this is also reflected in the geographic data shown in the map above.  What I find interesting is that the distances both south and east for the UTM and the SPC data are different, while the calculated straight line distance from my house to the geodetic marker differed by only two tenths of a meter.

Weinelt, Martin (2005) Online Map Creation. http://www.aquarius.geomar.de/omc/. Accessed 30 January 2005.

James E. Stem (1990) The State Plane Coordinate System of 1983, National Geodetic Survey Manual, NOAA Manual NOS NGS  5, Reprinted March 1990.  Accessed 19 January 2005.

http://www.e-education.psu.edu/courses/geog482/graphics/ManualNOSNGS5.pdf