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Round to Flat: Part one, Datums

 

The Three Pieces of the Puzzle

What we typically think of as a projection is actually a combination of three separate elements: Datum, Projection, and Coordinate System.  Think of Datum and Projection as two steps in an equation and Coordinate System as the description of the solution.

What is a Datum?

Not 42.  The hypercomputer Deep Thought took millions of years but finally calculated the Ultimate Answer to Life, the Universe, and Everything.  Though without first knowing the Ultimate Question, the answer is meaningless and without context.  Likewise, a datum is the first question towards the ultimate answer of flattening the earth.  Without a datum, Projections and Coordinate Systems are without reference.


(Deep Thought, from concept art for the motion picture adaptation of The Hitchhiker’s Guide to the Galaxy)

Before you can flatten out something that is round, you first have to know how round it is to start with.  A Datum is the mathematical model that describes the general shape of the earth, specifically, ‘how squished is it?’.  The Earth is not a perfect sphere; it has varying bumps and lumps here and there depending on gravitational fields, oceans, mountain ranges, etc. 

Overall, though, the Earth tends to bulge at the equator and be squished at the poles because it is spinning around (yes…once every day).  Folks near the equator are actually screaming west to east at just over 1,000 miles per hour.  In effect, the datum represents the shape of the earth, or the surface of the earth at "zero elevation."

In any case, there are several datums from which to choose, depending on where on earth it is that you are interested in mapping.  Some specialized datums are designed to describe with high accuracy a specific region, such the North American Datum of 1983 (NAD 83), however they fair poorly the farther one travels from the region of interest.  Others do a good job of averaging out the squish factor for the whole earth, such as the World Geodetic System of 1984 (WGS 84); it’s not super precise anywhere, but it does a relatively good job everywhere.  The Global Positioning System (GPS) uses WGS 84 because it’s potential geographic scope is world-wide.

Depending on the reference datum, the same exact lat/long coordinates can refer to slightly different places on the earth.  For example, NAD 27 and WGS 84 datums could plot the same lat/long coordinates hundreds of meters away from each other (that’s a big deal to an engineer or the Military, or a sailor plotting a course through a reef).

Popular Confusions

There is a big misnomer in the GIS community (and the enterprise in general) regarding the WGS 84 datum.  WGS 84 is not a Projection; it is not a Coordinate System.  The oddly-categorized geo-reference options and poorly-identified defaults provided in the bewildering interface of desktop GIS software has led to the misconception that WGS 84 is something other than just a datum.  Often it is used synonymously with undefined or unprojected.  For the record, if you are looking at a flat map, it most definitely has been projected.

Datum vs. Elevation:  A datum can only describe a single squish factor.  Areas that have a lot of tall mountain ranges don’t get a special bulge on the datum.  If the mountain range is extensive enough, it most likely has its own specialized datum.  The kicker is that while that local datum is super-accurate for that mountainous region, it is awful for the rest of the world.  Give and take.

Summary

A datum is the assumed baseline reference for the 3D shape of the earth.  It is a mathematical variable that describes the earth’s squish factor.  Once established, the wonderful world of Projections and Coordinate Systems await…

John Nelson / IDV Solutions / john.nelson@idvsolutions.com

 

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