Friday, September 16, 2005

Geocaching, datum and geoids

Looking for a good definition of "datum" I ended up going after benchmarks placed by the National Geodetic Survey in bridges, railroad tracks and other undisturbed locations around U.S.

I was trying to convince myself that this would help verify how accurate my GPS card is but at the end it is quite fun just to go after these "treasure hunts". GeoCaching keeps a database and a photo gallery of benchmarks and their locations. You can search for benchmarks by ZIP or their Point/Permanent ID (PID) and log your findings.

You can also look up the NGS database thru several ways including a dynamic map that displays the locations of these marks. Look for entries with Adjusted in their description and make sure the marker is a benchmark disk (and not a rivet, for example).

For each of them you can check the corresponding datasheet describing its PID, NAD 83 coordinates, type of marker and how to find it. Give yourself a good quiet time to read these directions, they can be quite overwhelming. Obviously, a compass will help you figure out which way is what.

World Geodetic System 1984 (WGS 84)

Going after a good and clear definition might take you for a pretty good spin. And that's exactly what I ended up doing while trying to figure out what exactly WGS 84, NAD 83 and datum meant.

A good descripition for WGS 84 and a great explanation of geodetic datum can be found at the WGS website in the "WGS 84 Implementation Manual", a training document for navigational systems available there.

"There are many geodetic reference datums in use throughout the world providing references for the charting of particular areas. Each datum has been produced by fitting a particular mathematical Earth model (ellipsoid) to the true shape of the Earth (geoid) in such a way as to minimize the differences between the ellipsoid and the geoid over the area of interest. [...] These different datums and ellipsoids produce different latitude and longitude grids and hence, different sets of geographical coordinates."

And later in the same chapter:

"Ground-derived coordinates (Latitude and longitude) are determined with measurements and calculations on mathematical reference models. These models represent the shape of the Earth in a particular geographic region and are called geodetic datums."

"Ellipsoidal Datum = Cartesian Datum + Shape of Earth Ellipsoid"

A position is defined by its coordinates in three axes (x, y and z). Each of these reference points uses "Earth’s centre of mass" as its geocentric origins. Those benchmarks (some provide horizontal references, other vertical) and their corresponding measurements tells us how much above (or below) the geoid they are.

Source: WGS 84 Implementation Manual
Source: WGS 84 Implementation Manual.

"The Z-axis coincides with the mean rotational axis of the earth. The mean equatorial plane perpendicular to this axis forms the (X-Y) plane. The (X-Z) plane is generated by the mean meridian plane of Greenwich. The latter is defined by the mean rotational axis and the zero meridian of the BIH (Bureau International de l´Heure) adopted longitudes ("mean" observatory of Greenwich)."

North American Datum 1983 (NAD 83)

You might also be wondering if there is difference between WGS 84 and NAD 83. Both are based on ellipsoid models but according to this document, you might find differences among references made with both systems. But not greater than one meter according to it.

The idea is that everyone in the world makes use of the same reference model. US had a previous datum (NAD 27) that is now considered outdated and unfit for use with GPS. According to the NGS FAQ, NAD 83 is the "horizontal control datum for the US, Canada, Mexico and Central America". (If you are wondering NAVD 88 is the vertical control datum or water and tidal levels for US.)

There is also discussion about in the future to make use of the International Terrestrial Reference Frame coordinated by the International Earth Rotation Service.

But after all this, nothing like looking for caches with a good GPS receiver...