GPS Altitude

 

            Barometric altitude is determined by an outside pressure reading, a standard model of the atmosphere, and the barometric correction to the standard sea level pressure (29.92 inches of mercury, or 1013 millibars).  Altitude calculated by this standard model  becomes more and more inaccurate as you rise above the location where the baro-correction is reported because the atmosphere is never "standard".  If we all agree nonetheless to use that standard then we will be separated from other traffic by flying an assigned baro-altitude on IFR flights.  But this does not guarantee separation from rocks in the sky, so we have generous margins in the minimum safe altitudes (MSA) published in our area.

            But with the advent of WAAS corrections to our GPS position, our 3D location is accurate to a few meters.  From the altitude portion of the solution we can determine our MSL altitude.  Add a terrain database of MSL altitude on a world wide grid of small dimensions, and GPS altitude can be used for Terrain maps on a GPS.  Areas 100 ft below you and higher are colored red to warn you of these sky rocks, and yellow areas are 100 - 1000' below you.

            It is fascinating to learn how your GPS can figure out your MSL altitude to this 2 meter accuracy, independent of where you are (lat/lon) and of your altitude. To do so requires some understanding of MSL, of the shape of the earth, and of its Geoid.  For starters, GPS vertical position is first referenced to the WGS 84 reference ellipsoid as a height above the ellipsoid (HAE altitude). 

            Since the earth spins, centrifugal force makes it bulge at the equator; it bulges less at higher latitudes and not at all at the poles (centrifugal force is zero there).  So it's no surprise its basic shape (if it were all water) is an ellipse of revolution.  The major radius  of this ellipsoid is 6,378.137 kilometers (note the typo in the drawing), and the minor radius is 6,356.752 kilometers, a difference of 21.4 kilometers. It turns out that this surface is very roughly the same as the mean sea level surface.  Rough means the errors can be as much as 100 meters – not good enough to miss the rocks.

            So, enter the earth's Geoid, which is taken to be the same as the zero MSL surface (it's very close, but strictly not the same). It's a surface on which the gravitational potential is constant, and lies on the mean levels of all the earth's seas. They are all at different levels, but are all at their local value of zero MSL.  The geoid has been very accurately mapped, most recently with the satellite called GOCE (Gravity Field and Steady-State Ocean Circulation Explorer).

            From that data the Geoid surface can be referenced to the ellipsoid, the difference being the Geoid height.  There is a worldwide database of Geoid height (Google it) that can be stored in GPS receivers and added or subtracted from HAE to get MSL at your position. The Geoid height ranges from 100 meters below the ellipsoid in the oceans off the southern tip of India, to 80 meters above in the ocean between Scotland and Iceland and in the oceans around Indonesia and the Philippines, north of Australia.  These variations in MSL from the ellipsoid surface are the result of variations in density of the earth's crust and mantle, which locally affect gravity. Plumb bobs don't always point straight "down"; instead they are perpendicular to the Geoid surface, and the Geoid surface is irregular.

            In the USA, the geoid varies from 25-30 m above HAE in California and the Northeast, and to as low as 7 – 15 m above it in the Colorado area. It is truly remarkable that the mathematical shape (ellipsoid) of the HAE surface is that close to MSL.