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I remember someone asking about elevations in this tutorial, and at the time I wasn't sure where they would be, but now that we're covering ellipsoids, this is the part to see for elevations.
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In engineering traditionally a datum line is used for a construction project for elevations. When building a dam or a bridge or a high rise building, some depth level is selected which will be a convenient level from which to reference all elevations in the project. Quite often it's a plane about 100 feet below the earth's surface. This is a theoretical plane and nobody ever has to go digging down to "find it" because that would accomplish nothing. They wouldn't be able to "see" anything there anyway. It's just a number on a piece of paper like a plan map.
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In this tutorial, the ellipsoids described are theoretical spheroid constructions that closely imitate the "smoothed out" shape of the earth, and as such they are located in some places above the surface of the earth, and in some places cutting through hills or mountains or even through flat plains or lakes.
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For geodetic surveying then, ellipsoids are closely related to datum lines since vertical measurements to describe elevations are measured as being above or below the ellipsoid by a particular number of meters.
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That last section, above, that came out in italics was not supposed to. Here is a copy of it without the italics:
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For example, along much of the coastline of the continental United States, the ellipsoid is above the land surface...so low-lying coastal land may have a negative ellipsoid height! In the mountains, the ellipsoid is typically below the surface. One problem with ellipsoid-based heights is that they do not accurately predict the direction of water flow. To do this, we need to convert to orthometric heights which are more closely related to gravity.
The surface of Earth is most closely described as an ellipsoid, a sphere somewhat flattened at the poles. We can convert the geometric coordinates derived from GPS satellites to points on this ellipsoid surface. This lets us express positions in terms of defined geodetic latitude, longitude, and height.
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These two paragraphs are important for this thread, and we'll probably be referring back to them later.
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