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May 12 2011

This isn’t a Bowling Ball

Planet Earth Bowling Ball

even the most mathematically sophisticated geoid can only approximate the real shape of the earth.                          – Witold Fraczek

The earth is hardly a nice sphere like a bowling ball or even a nice simple spheroid. All of our models of the earth are exactly that: approximate models that we are continually fine tuning. GPS has significantly sped up this process. The “Geoid” is an approximation of Mean Sea Level (MSL), the most refined model we have. If we could see or measure MSL, we could use this as the basis of elevation everywhere and have it be a universal datum. This could actually happen in the future! When you see “geoid99” or now “geoid09,” you are seeing the version of this geoid model of the earth.  GPS has shown us the MSL is not as smooth as we think. The “Ellipsoid” is a spheroid best-fitted to the shape of the earth. Clark 1866 (basis of NAD27), GRS80 (basis of NAD83 & WGS84), and ITRF00 are examples of ellipsoids. GPS receivers reference to a specified ellipsoid relative to your benchmark in conjunction to a geoid model to give you an actual elevation. This is why this is important to understand: your elevation data is all relative to a model. As long as you know what the model is, you’re usually fine but you have to be very careful with how you move between vertical elevation datums & systems.

It might be easier just to break it down in terms of level of approximation (most accurate to least):

  1. Global Mean Sea Level geoid (exact representation of MSL of the earth)
  2. Refined model of MSL/the geoid (Geoid99, Geoid03, Geoid09 and so forth)
  3. Reference ellipsoids (referred to by datums) that are mathematical models the actual geoid (Clark 1866, GRS80)

Because the surface of the Earth is irregular and complex, geodesists use simplified mathematical models of the Earth for many applications. The simplest model of the Earth is a sphere. A much more complex model of the Earth is the geoid, used to approximate mean sea level. Even the geoid is a simplified model, however, when compared to actual topographic relief, as shown in this image of four figures of the Earth (Grand Canyon).

Four figures of the Earth (Grand Canyon)

I know this can feel very complex and difficult to understand but hopefully the figures are helpful! Why do we still use both an ellipsoid model and a geoid model? Because we still don’t have an exact geoid and what we have is constantly being refined. GPS receivers always build off a reference ellipsoid model and then can use a specified current geoid to give you an actual elevation.  Typically though, when you look on a Garmin (or even a Trimble Geoexplorer) at your elevation, you are seeing the ellipsoid height, not the orthometric elevation you would see on a quad map.  Most of the time the geoid doesn’t matter for data you receive, you just assume the elevation is correct and that the surveyor moved correctly from elevation to ellipsoid and back when collecting the data.

Ellipsoid, Geoid, Topological Elevation - Earth Models

The geoid height is the difference between the reference ellipsoid and the geoid. A datum is chosen for a certain area because the reference ellipsoid built into it is simply a much better approximation of the geoid for that area. The ellipsoid height is the difference between the ground and the reference ellipsoid. Knowing all this helps you understand the root of your elevation data. What is the reference ellipsoid used (datum?)? What geoid were the geoid heights based on when doing the survey?

Do you have other resources that have helped you understand this better? Have you ever run into data errors because of a mix up between geoid versions or reference ellipsoids?

Sources:

“Mean Sea Level, GPS, and the Geoid” By Witold Fraczek, Esri Applications Prototype Lab

“The Elements of Geodesy: The Figure of the Earth” from NOAA

“3D Geospatial Data” by Eric Gakstatter

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