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In trying to understand Geoid vs Ellipsoid height, I ran across this page.

One of the claims is:

Zero elevation as defined by Spain is not the same zero elevation defined by Canada

Basically, they are indicating that MSL is not constant and that makes comparing things harder.

So my question is: why not measure elevation as a radius from the center of the earth?

I guess I'm proposing {lat, lon, radius} to define a point on or near the earth. This could eliminate many problems in my thinking. (Let's use inertial center of the earth as our reference point...)

Who cares that the topography of the earth is not constant? It wasn't constant in the first place, and to get height above ground, you just need some terrain data and a simple subtraction. I guess I'm proposing using one common reference point that doesn't change.

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  • How much have you read about datums? And more specifically ECI and ECEF? Where is the center of the earth that is a fixed point that doesn't change?
    – Chris W
    Commented May 22, 2014 at 20:23
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    If you don't use some sort of gravity-related origin, water can flow uphill!
    – mkennedy
    Commented May 22, 2014 at 20:40
  • @ChrisW Nothing. I'll read your links. When I said "doesn't change" I meant with respect to the surface of the earth. Obviously, that is not entirely true, as earthquakes or tectonic plate movement and the like can change things, but I was thinking it would be FAR more constant than the average level of the ocean for the last 19 years. I am anticipating something similar to ECEF, but using lat/lon to allow folks to intuitively know the location in question. ECEF is hard to know without converting.
    – kmort
    Commented May 22, 2014 at 20:41
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    Since we can't physically observe the center of the earth, we have to use other kinds of observations, mathematics, and models (collectively known as geodesy) to approximate the shape of the earth, with varying degrees of accuracy (and no one model is perfect for every place on earth, that's why there are so many).
    – blah238
    Commented May 22, 2014 at 20:43

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One thing to keep in mind is that lat/long is geodetic and not geocentric:

latitude

If we were to calculate elevation as a radius from the center of the ellipse, our elevation lat/long would be different than our horizontal lat/long!

This is why there are two different datums. The horizontal datum is just a smooth ellipse, because it's easier to do trig functions on. Most (all?) vertical datums use a geoid, which takes local gravity into account. Establishing horizontal locations has always been a separate process than establishing an elevation.

If you really want to combine horizontal and vertical datums, then...

Welcome to the ITRF fan club! This is the datum and projection for you! One difference is that ITRF doesn't use lat/long at all, it goes all-out Cartesian X/Y/Z to point to any place on or near Earth. This is handy, since the GNSS (GPS, GLONASS, etc) satellites rotate around the Earth's center of mass, it makes a nice, native coordinate system for getting locations from satellites.

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  • Wait, wait, wait... "horizontal datum is just a smooth ellipse". I think this means that lat/lon as I know them are not based on a perfect sphere, which means, well, it blows my mind! I thought wrong. I think that means my scheme as it stands won't work well. ITRF looks nice, and I am a fan, but is still suffers from same "problem" as ECEF in that it's hard to mentally associate coordinates with locations on the earth without converting to some other system.
    – kmort
    Commented May 23, 2014 at 12:53
  • But it's not uncommon to use the GRS80 ellipsoid to convert the Cartesian coordinates to lat/lon/heights.
    – Weston
    Commented Jun 26, 2014 at 14:01

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