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    Re: GPS jamming concerns
    From: Frank Reed
    Date: 2016 Aug 10, 15:41 -0700

    Bob Goethe, you quoted Calder:

    Therefore, for a considerable period of time, it is going to be essential for navigators to check the datum of every chart used...and, when using a GPS, to ensure that it is operating on the chart datum. Remember that if the datum is not WGS 84 based, the GPS software may introduce an unknown degree of error in the datum-conversion process.  Even if the chart is based on WGS 84, the GPS mucst be checked to ensure that it is also on WGS 84.  It is only a matter of time before someone playing with the buttons on a GPS accidentally sets it to some obscure datum with a considerable offset, resulting in the boat running aground.  (pp. 21-23)

    That "considerable period of time" came to a close perhaps sooner than anyone expected. Calder wrote those words at least 15 years ago, maybe 20 in the original version. This is no longer a significant issue unless you are using old charts. As far as I have been able to determine, all modern charts are published referencing the WGS84 ellipsoid or an ellipsoid which differs from it only on a scale of a meter or smaller. If you drop in GPS-derived coordinates in a modern mapping application, for example the workhorse Google Maps, you will rarely find discrepancies in the satellite imagery (which is actually high-altitude aerial photography in most of the western world) larger than a few meters. Once everything was digitized, it was a simple matter to convert all legacy mapping products to WGS84. The mathematical process is trivial. At this point in time, you can basically forget about map datums.

    The offset of the prime meridian by a hundred meters at Greenwich is different. This results from the "deflection of the vertical" and it is due to the fundamental distinction between astronomically-determined latitude and longitude and "true" latitude and longitude, which is what we get with careful ground measurement and also from GPS. True or geodetic latitude and longitude are pure mathematical coordinates projected out from the center of the Earth, very similar to, though slightly modified from the pure spherical coordinates that we all studied at some point in a math class. You project the coordinates out from the Earth's center, and then by measurement of relative positions, you determine where each rock and boulder falls on that coordinate grid. That is our map of the Earth.

    Astronomical latitude and longitude are a bit different from "true" geodetic latitude and longitude. Astronomical latitude and longitude are developed by projecting spherical coordinates out onto the stars. We get pure coordinates on the celestial sphere which we can then observe from anywhere on Earth. That was the primary goal of the Greenwich Observatory in the early 18th century: map the stars on the celestial sphere so that those markers would be available to any observer on the ground anywhere on Earth. Those coordinates are then pulled back down to ground level using the local vertical: the celestial coordinates at the zenith are equivalent to the geographic coordinates on the ground. The local vertical is a very close surrogate for a direct line from the celestial sphere back to the center of the Earth. But not quite. First, there is a relatively large difference due to the rotation of the Earth. Rather than accept  a large divergence between astronomically-derived latitudes and longitudes in favor of pure spherical coordinates, geographers, astronomers, geodesists, and the rest "decided" to use ellipsoidal coordinates with a modified latitude as standard coordinates on the globe. This hasn't changed. That's why the WGS84 mapping datum is an ellipsoid. It's a "hack" that maintains the validity of most latitudes and longitudes at a scale greater than a mile or so.

    At a smaller scale on the globe there are all sorts of bumps and valleys in the Earth's gravitational field, and these tilt or deflect the local vertical from the "correct" direction. If you travel five nautical miles across the globe the local vertical should ideally rotate by exactly five minutes of arc, preserving the one-to-one mapping from the celestial sphere to the terrestrial globe. Instead, after travelling exactly five nautical miles, the local vertical may have rotated 5.1 minutes of arc or 4.95 minutes. Any astronomically-derived set of latitude and longitude coordinates must be corrected for this if it's going to be used with charts using "true" latitudes and longitudes as derived by traditional surveying methods or by satellite fixes or any other self-consistent method that determines the correct geometric relationships among points. Fortunately, this has all been mapped now. It's a known correction that can be applied at each and every point on the globe (within some margin of error). At roughly 98% of points on the globe this deflection is 0.2 minutes of arc or less. Near significant tectonic features like ocean trenches, other subduction zones, uplifting mountain ranges, mid-ocean volcanic islands, etc. (but not much at mid-ocean ridges and other spreading zones) the deflection can be as large as one minute of arc implying that astronomical coordinates will necessarily differ from GPS coordinates by one nautical mile or more. This is "like" a difference in datum, but it's a physical effect, a real phenomenon, rather than an arbitrary selection for the convenience of mapping.

    Frank Reed

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