Geographic Coordinate System

One of the most common coordinate systems in use is the geographic coordinate system, which uses degrees of latitude and longitude to describe a location on the earth’s surface.  Lines of latitude run parallel to the equator and divide the earth into 180 equal portions from north to south (or south to north).  The reference latitude is the equator and each hemisphere is divided into ninety equal portions, each representing one degree of latitude.  In the northern hemisphere degrees of latitude are measured from zero at the equator to ninety at the north pole.  In the southern hemisphere degrees of latitude are measured from zero at the equator to ninety degrees at the south pole.  To simplify the digitization of maps, degrees of latitude in the southern hemisphere are often assigned negative values (0 to -90°).  Wherever you are on the earth’s surface, the distance between lines of latitude is the same (60 nautical miles,), so they conform to the uniform grid criterion assigned to a useful grid system. 

Lines of longitude, on the other hand, do not stand up so well to the standard of uniformity.  Lines of longitude run perpendicular to the equator and converge at the poles.  The reference line of longitude (the prime meridian) runs from the north pole to the south pole through Greewich, England.  Subsequent lines of longitude are measured from zero to 180 degrees east or west (values west of the prime meridian are assigned negative values for use in digital mapping applications) of the prime meridian.  At the equator, and only at the equator the distance represented by one line of longitude is equal to the distance represented by one degree of latitude.  As you move towards the poles, the distance between lines of longitude becomes progressively less until, at the exact location of the pole, all 360° of longitude are represented by a single point you could put your finger on (you probably would want to wear gloves, though).

 So, using the geographic coordinate system, we have a grid of lines dividing the earth into squares that cover approximately 4,773.5 square miles at the equator…a good start, but not very useful for determining the location of anything within that square.  To be truly useful, a map grid must divided into small enough sections that they can be used to describe with an acceptable level of accuracy the location of a point on the map.  To accomplish this, degrees are divided into minutes (') and seconds ("). There are sixty minutes in a degree, and sixty seconds in a minute (3600 seconds in a degree).  So, at the equator, one second of latitude or longitude = 101.3 feet.  

An alternative method of notation in the geographic coordinate system, often used for many GIS applications (Geographic Information Systems, or GIS, is discussed in detail in another exercise), is the decimal degree system.  In the decimal degree system the major (degree) units are the same, but rather than using minutes and seconds, smaller increments are represented as a percentage (decimal) of a degree.  The decimals can be carried out to four places, resulting in a notation of DD.XXXX, DDD.XXX.  When using four decimal places, the decimal degree system is accurate to within ± 36.5 feet (11.12 m).  However, because the accuracy of the fourth decimal place is often uncertain, decimal degree coordinates are often rounded to three decimal places.  This results in an accuracy of ± 364.8 feet (111.2 m).  To give you an example of how the two systems of measurement compare, the location of Red Hill on the ISU campus expressed using minutes and seconds is 42°51’36" W, 112°25’45"N.  Using decimal degree notation this same location is written as -42.8600°, 112.4292° N.  Perhaps you have noticed that, despite its common usage, the geographic coordinate system is not very easy to use.  To demonstrate this, find a topographic map (or any other map that uses the geographic coordinate system), pick a point on that map, and describe it in terms of degrees, minutes and seconds.  When you’re done with that, try it using decimal degrees.
Besides the fact that the grid on a map using the geographic referencing system is not constant from north to south, it is also just not very easy to use.  Fortunately, both problems are solved to some extent by using the Universal Transverse Mercator coordinate system, which will be covered next.