Some Concepts That Underpin GIS - Introducing Geographic Information Systems with ArcGIS - page 14

the one mathematicians use in more abstract systems. 7 The origin is considered to be the center of the
Earth. The equator serves as intersection of the x-y plane and the hypothetical sphere of the Earth. To
determine the coordinates of a point, one angle (latitude) is measured from the x-y plane. The other
angle (longitude) is contained in the x-y plane and is measured from the meridian that passes through
Greenwich, England. The third number in a mathematical spherical coordinate system is the distance
along the ray from the origin to the point. When added to the latitude-longitude system, altitude is
usually defined instead to be the distance to the point along the ray from mean (average) sea level (MSL)
or from a gravity-defined pseudo-ellipsoid used with the NAVSTAR Global Positioning System to be
discussed shortly.
By using three numbers, you can determine and communicate the position of any point on Earth. Of
course, an externally defined set of parameters must qualify these numbers. Any given point on the
surface has probably been addressed by dozens of different sets of numbers, based on the parameters
(e.g., units) of the coordinate system chosen. These parameters must match when you combine GIS data.
Determining Where Something Is: Latitude and Longitude
A fundamental principle underlies all geography and GIS: Most things on Earth don't move (or
move very slowly) with respect to each other. Therefore, we can talk about the position of something
embedded in or attached to the ground and know that its position won't change (much). It seems like a
straightforward idea, but position confuses a lot of people when it is described as a set of numbers. 8
Let's suppose that in 1955 somewhere in the United States you (or your parents, or their parents) drove a
substantial metal stake or pin vertically into solid ground. Now consider that the object, unless disturbed
by human beings or natural forces such as erosion or an earthquake, would not have moved with respect
to the planet since then. 9 In other words, it is where it was, and it will stay there. Three numbers—
latitude, longitude, and altitude—could identify the location of the object in1955. However, over the last
half century, teams of mathematicians and scientists (skilled in geodesy) developed other sets of numbers
to describe exactly the same spot where your object now resides. The actual position of the object didn't
change, but additional descriptions of the where of the object have been created.
Ignoring the matter of altitude for the moment, suppose that the object was driven into the ground at
latitude 38.0000000° (North) and longitude 84.5000000° (West), according to calculations done before 1955
that indicated the location of the center of the Earth, its shape, and the location if its poles. Most people
and organizations in the United States in 1955 used the North American Datum of NAD27 (NAD27) to
estimate the latitude-longitude graticules, based on parameters of the earth-approximating ellipsoid
determined by Clarke in 1866. 10
7 For example, in the two dimensional Cartesian plane, a mathematician will measure angles starting from the positive
x-axis (east) as zero and increasing counterclockwise, to 360 degrees (which is, again, zero). The navigator (think: compass)
or cartographer will also use 360 degrees to represent a full circle, but measures clockwise from the positive y-axis (north).
8 Descriptions of points aren't always just numbers. A possibly apocryphal “metes and bounds” description of a point
in Kentucky a couple of centuries ago was “Two tomahawk throws from the double-oak in a northerly direction.”
9 Well, hasn't moved much. If it was on the island of Hawaii, it has moved northwest at about 4 inches per year. Also,
if you are unfortunate enough to be in a place where there was an earthquake, it might well have moved and not
returned to its original position.
10 Based on a monument on Meades Ranch, in Kansas; the Clarke 1866 ellipsoid was meant to minimize the error
between itself and the geoid in the United States.