### •  GEOGRAPHIC COORDINATE SYSTEMS  •

For convenience, we sometimes treat the earth as though it was 2 dimensional. Think paper maps and computer screens. But there's no getting around the fact that the "real" earth is a 3-dimensional solid and defining locations on it's surface starts with choosing one or another of the mathematical models that the science of geodesy (earth measurement) has come up with over the years. These earth models, more properly called "datums", address the physical properties of the earth such as size, shape and axis of rotation. They also capture arbitrary properties such as the location of the prime meridian. Geographic coordinate systems express locations as angles of latitude (north-south) and longitude (east-west). The Latitude and Longitude article on the National Atlas website explains it very well.

GCS Coordinates Come In Three Flavors
GCS coordinates are expressed using any one of three mathematical models - Degrees Minutes Seconds (DMS), Degrees Minutes (DM) and Decimal Degrees (DD). The table on the right shows how each of the models might be used to give the location of the WisDOT-5L06 survey marker on the UWGB campus.

WGS 84 Latitude & Longitude
DMS   44° 31' 40.2" N    87° 54' 58.9" W
DM   44° 31.669' N    87° 54.982' W
DD   44.52782  -87.91636
All three of the mathematical models accomplish the job of defining the location of a point on the earth's surface. However the DD model is the only one that is suitable for plugging GCS coordinates into computer analyses. In our work, the first thing we do when we encounter DM or DMS data is convert it to DD. There are a gazillion ways to do the conversion. Setting it up as a set of formulas in Excel is nice because you can really see what's going on.

Northern Hemisphere Latitudes
Eastern Hemisphere Longitudes
Southern Hemisphere Latitudes
Western Hemisphere Longitudes

GCS Coordinates Are Numbers
Numbers used to define location are scientific measurements in the same sense as any measured variable. The rules governing the accuracy and precision of numeric information apply. Regardless of the mathematical model used (DMS vs DM vs DD), the number of decimal places (precision) in a GCS coordinate pair should reflect the accuracy of the method used to determine the values.

Accuracy DMS DM DD Acceptable Accuracy and Precision For
+ .0001 meters ddd mm ss.ssssss   ddd.dddddddddd Some survey control
+ .001 meters ddd mm ss.sssss   ddd.ddddddddd Some survey control
+ .01 meters ddd mm ss.ssss   ddd.dddddddd Cadastral mapping
+ .1 meters ddd mm ss.sss   ddd.ddddddd Cadastral mapping
+ 1 meter ddd mm ss.ss   ddd.dddddd Some natural resources mapping
+ 10 meters ddd mm ss.s ddd mm.mmm ddd.ddddd Most natural resources mapping
+ 100 meters ddd mm ss ddd mm.mm ddd.dddd Some natural resources mapping
+ 1000 meters   ddd mm.m ddd.ddd Rougher mapping
+ 10,000 meters   ddd mm ddd.dd Really rough mapping

See our Lambeau Field example for another way to look at coordinate pair precision

GCS Coordinates Are Not Just Numbers
A GCS coordinate pair used in written or spoken communication should correspond to one, and only one, point on the earth's surface. That means there's more to it than getting the numbers right:

• The name of the Geographic Coordinate System (and the associated datum) must be stated - there is no standard
• The pair order must be stated - there is no standard for which comes first, latitude or longitude
• DMS and DM coordinate pairs must include units so that degree, minute and second values can be distinguished from one-another
• Latitude values must specify northern vs southern hemisphere to make sure points wind up on the correct side of the equator
• Longitude values must specify eastern vs western hemisphere to make sure points wind up on the correct side of the prime meridian
• DD coordinate pairs should be structured for recognition by computer software (no non-numeric characters)

A simple table is an efficient way to insert GCS coordinates in to written work:

Point WGS 84 Latitude WGS 84 Longitude
WisDOT-5L06
44° 31.669' N
87° 54.982' W

An algebraic expression is another way to do the same job:

 WGS 84 lon/lat = 87° 54' 58.9" W / 44° 31' 40.2" N

GCS - OMG !!
Sometimes folks use geographic coordinates in their work without fully understanding the mathematics and symantics. Work products can get released into the wild containing undefinitive coordinate pairs (don't correspond to any real place) and ambiguous coordinate pairs (correspond to more than one real place). The usual result of these miscues is minor embarrassment, but sometimes the consequences are more serious. Official records of important land features or events can wind up incorrect or incomplete. We've collected some "howto" and "how-not-to" examples.

GCS Coordinates and Distance Measurements
Geographic coordinates are great for expressing location, but they are lousy for expressing distances. Here are some rules of thumb that can help when you have to jump back and forth between linear and angular distances.

• Earth circumference (360°) ~ 40,000 kilometers
• 1 degree of latitude ~ 111 kilometers (69 mi)
• 7½ minutes of latitude ~ 14 kilometers (8.6 mi) - this number is significant because the map tiling scheme for USGS topo maps is based on 7½ minute quadrangles.
• 1 minute of latitude ~ 1850 meters (1.15 mi)
• 1 second of latitude ~ 31 meters (102 ft)
• .00001 degrees of latitude ~ 1.11 meters (3ft 8in) - this number is significant because most natural resources work uses coordinates computed to five decimal places.