Project 1:
Plotting Coordinates and Projections

Kathryn Chaney



Eastern_US_TM
                       Eastern continental United States in the Transverse Mercator projection.  (Penn State Online GIS                                         Education Interactive Album of Map Projections, 2005)

The map above portrays the eastern half of the continental United States in the Transverse Mercator projection with distortion ellipses to better illustrate scale distortion.  The map projection, Transverse Mercator, is the mathematical process that converts a geographic coordinates (on a globe) to plane coordinates (on a map).   For the map above, the coordinate boundaries are as follows: North = 48.00 dd, South = 28.00 dd, East = -69.00dd and West = -90.00dd.  I also, chose a central meridian equal to the longitude of the Huntingtown, MD point, -76.616 dd.  Huntingtown, MD, my home town, is the only cultural feature labeled on the map.

Transverse Mercator serves as the foundation for the Universal Transverse Mercator coordinate grid as well as a portion of the State Plane coordinate system, both are discussed later in this report. (Penn State Online GIS Education Interactive Album of Map Projections, 2005)  As the name suggests, Transverse Mercator is a variation of the Mercator projection; the variation is the "cylinder" is in constant contact with meridian in Transverse Mercator opposed to a parallel, usually the equator, as is the case in Mercator. (DiBiase, 2005)   Like many people interested in geographic data, I often prefer graphic explanations over verbal.  For other "a pictures worth a thousand words" types, see below for illustrations of  Transverse Mercator and Mercator projections.

TM graphic.
    Explanation of Transverse Mercator Projection.  (United States Geological Survey  Map Projections Poster, 2000)

mercator
Explanation of Mercator Projection.  
(United States Geological Survey  Map Projections Poster, 2000)

Transverse Mercator falls under the category of conformal projections, as do several other projections.  These conformal projections accurately depict the shape but that characteristic is preserved at the expense of correctly representing size. (DiBiase, 2005)  The map below (resembling a football because of the the concave meridians and parallels that result from this projection) better illustrates the distortion, by distortion ellipses.  Distortion increases as you move away from the central meridian, where the scale is accurate.  Distances, while true on the central meridian, become distorted in addition to size distortion once you are beyond  15° of the central meridian.( United States Geological Survey Map Projections Poster, 2000) 

western hemi in TM

                               Majority of Western Hemisphere in the Transverse Mercator projection.  
                                       ( Penn State Online GIS 
Education  Interactive Album of Map Projections, 2005)

                             
 The maps were created using Ryan Baxter's Interactive Album of Map Projections (http://projections.mgis.psu.edu), the site is based on John Snyder's and Phil Voxland's Album of Map Projections (1994) and is one of the more interesting uses of ArcIMS I have seen.  


Geographic Coordinates
As I have stated, the place name shown on the map above represents the location of my home town. The geographic coordinates of Huntingtown, MD are:
Latitude: 38° 37' 15" N, Longitude: 76° 36' 58" W

The geographic coordinate system is an unprojected three dimensional global system rather than a flat but very convenient plane. (DiBiase, 2005)  A geographic location is described as the point along a longitude, east-west measurement, crossed by a latitude, north- south measurement.  Longitudes and latitudes are measured in angles as degrees, minutes and seconds or decimal degrees.  

The general population seems to be most familiar with geographic coordinates expressed in degrees, minutes and seconds and had little to no exposure to decimal degrees.  Case in point, here is a story a colleague shared, a manager had made promises to his superiors that he could produce a high quality geographic data product (imagery) of a specified area of interest (AOI) in record time and the project appeared to be progressing on schedule.  However, when the production process was complete the manager had a high resolution and very accurate finished product of a location nowhere near the specified AOI!  The manager apparently was not familiar with decimal degrees, which were required to specify the AOI, and dropped all the negative symbols off the coordinates.


UTM Coordinates
The UTM coordinates (NAD83 or NAD27) of my home town are:
Easting: 359310.126 meters, Northing: 4275940.058 meters, Zone: 18

The UTM (Universal Transverse Mercator) coordinate system has almost global coverage because it extends from 84°30' North to 80°30' South, so the extreme polar regions are absent.(DiBiase, 2005)   To lessen distortion, this system is divided into 60 zones (divided at the equator) where each zone is projected with two stand lines. See below for an illustration of the UTM zones.

UTM zones
Illustration of the 60 UTM zones.  (DiBiase, David, Scales and Transformation, Lesson 2, 2005)

A pair of standard lines, in a given zone, will be 180,00 meters east and west of the central meridian. (DiBiase, 2005)  This fact and the characteristics of  map projection ensures  an error no greater than 1 part in 2,500 (for every 2,500 meters it will not be off by more than a meter).   Coordinates in UTM are positive Eastings and Northings because for each half of each zone an origin is set to the southwest of that specific zone. 

UTM is a projected coordinate system therefore, a horizontal datum to required to mesh UTM to an ellipsoid (represents the shape of Earth).  When working with map projections it is necessary to define what datum was used.  I commonly work with data in NAD83 or NAD27 and every so often get to explain the differences that stem from the two datums.  The root cause being the defined center for the associated ellipsoids. NAD27 is expressed feet and connected to the ellipsoid Clarke 1886 that is centered on the Earth's surface in Kansas but NAD83, expressed in meters, with the ellipsoid GRS 80 that utilizes a gravitational center. (DiBiase, 2005) The end result (besides t-shirts printed with, "NAD83 we're not in Kansas anymore"), a point in one coordinate system can be expressed in two different ways based on datum.  For example, the magnitude of total shift in the coordinates is 30.729 meters between NAD83 and NAD27 for the town center of Huntingtown, MD. (National Geodetic Survey, NADCON - North American Datum Conversion Utility, 2002)


National or Regional Coordinates
The State Plane coordinates (NAD83 ) of Huntingtown, MD are:
Easting: 433430.223 meters, Northing: 105986.507 meters, Zone: Maryland (1900)

The State Plane coordinate system (SPC) is similar to UTM in that both are projected coordinate systems, divided into multiple zones utilizing standard lines to improve accuracy. (DiBiase, 2005) SPC system is comprised of 124 to 125 zones that cover only the United States; the SPC zones are smaller that the UTM zones and smaller coverage area (large scale) usually means less distortion.  With SPC we can expect distortion to be no greater that 1 part in 10,000.  Most states have multiple zones.  Zones that have more height than width utilize Transverse Mercator projections, similar to all UTM zones, but SPC zones that have more width than height (ex: Maryland and Virginia) use Lambert Conic Conformal and the two standard lines run east to west.  Like UTM the coordinates are positive Eastings and Northings but the origin of a SPC zone lines up that zone's central meridian with a Northing of 0.

Comparison was used to explain Geographic, UTM and State Plane Coordinate systems  but there are a few comparisons that are most useful to me.   The only coordinate system that is free of distortion and covers the world is Geographic.  Great, it's perfect, why use anything else?  It isn't practical for people to carry globes - imagine the size globe that would be need to serve the function of a USGS quad.  Since the pocket globe isn't an option, let's look at UTM and SPC.

Unlike the Geographic system, UTM and SPC are projected and exhibit distortion as a result of flattening the globe.  Transverse Mercator is the projection used for the 60 UTM zones spanning most of the globe but this projection is only used for a portion of the SPC zones and the remainder use Lambert Conformal Conic.  Regardless of projection UTM and SPC utilize standard lines to increase accuracy.  Both UTM and SPC have added complications if you need to across zones in your work but the unique projections per zone lessen distortion.

"Use the right tool for the job",  we have all heard this saying and it applies to maps and other geographic data as well as "fixing" things with a large hammer.  If a user has an understanding of the characteristics of coordinate systems, datums, map projections and their relationships they will select the correct "tool".  Also, with accurate and complete metedata converting geographic data is an option.   


Sources 

DiBiase, David (2005) Scales and Transformation, Lesson 2. The Pennsylvania State University World Campus Certificate Program in GIS. Accessed 10 October 2005.

National Geodetic Survey (2002) NADCON - North American Datum Conversion Utility. http://www.ngs.noaa.gov/TOOLS/Nadcon/Nadcon.html Accessed 25 October 2005.
National Geodetic Survey (2002) SPC Utilities. http://www.ngs.noaa.gov/TOOLS/spc.html Accessed 6 November 2005.
National Geodetic Survey (2002) UTM Utilities. http://www.ngs.noaa.gov/TOOLS/utm.html Accessed 6 November 2005.
United States Geological Survey (2002) Geographic Names Information System. http://geonames.usgs.gov/ Accessed 31 October 2005. 
United States Geological Survey (2000) Map Projections Poster. http://erg.usgs.gov/isb/pubs/MapProjections/projections.html Accessed 8 November 2005. 
Penn State Online GIS Education (2005) Interactive Album of Map Projections http://projections.mgis.psu.edu/ Accessed 6 November 2005.

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.