Heights

One of the simplest sounding things is to find the height or altitude of something. The problem is "With respect to what?" .

Historically we use Mean Sea Level (msl) as a height reference, even in Kansas. This means two things. First the height of the sea, on average, must be measured. An second the height must be carefully surveyed from point to point from the sea coast inland. This is in fact what was / is done. In fact 19 year averages of tide gauges are usually taken. This is a complete cycle of moon motions.

With modern satellite systems you would think that altitudes would be as easy to measure as horizontal position. This is essentially correct, but there is the problem of the reference. What you get from satellites in not what has historically been measured.

Satellites basically measure the coordinates of the receiver as x-y-z coordinates with the origin at he center of the earth. In order to get a height, they have to use a reference surface. Typically this is the ellipsoid. But those heights, call ellipsoidal heights, are not what you see on maps.

The map heights, which we try to match with satellite systems, are measured with respect to a bumpy surface called the Geoid. In essence this is the surface of the sea, that is continued onto land. It is the surface water would follow if the land did not get in the way.

We have:

• Map - historical heights
  • Measured from the Geoid
  • Reflect the bumpy nature of gravity field
  • Often called Mean Sea Level heights
  • Officially called orthometric heights
  • Basic values from tide gauges
  • Found from careful surveys from coast inland
• Satellite based heights
  • Measured from Ellipsoid
  • Called ellipsoidal heights.
  • Not affected by bumpy gravitational field

The geoid, is easy to define in words, but very hard to find. One head of NGS once said "It's funny, we know height very precisely, but with respect to a surface we know only poorly."

 

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