Now, what’s tomorrow’s challenge?
APN-006 Rev 1 June 30, 1997
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Technical Bulletin
GEOID ISSUE
What is a Geoid?
The equipotential surface which best represents mean sea-level. (An equipotential surface is any
surface where gravity is constant.) This surface not only covers the water but is projected
throughout the continents. Most heights throughout North America use this surface as its zero
value, i.e., all heights are referenced to this surface.
When heights were being determined through conventional surveys using levels at the turn of the
century, surveyors used tidal gauges on the east or west coast as their zero value. Subsequent
surveys then went inland using this reference system.
What is an Ellispsoid?
An ellipsoid is a mathematical surface which is sometimes used to represent the earth. Whenever
you see latitudes and longitudes describing the location, this coordinate is being referred to a
specific ellipsoid. GPS positions are referred to an ellipsoid known as WGS84 (World Geodetic
System of 1984).
What is the relationship between a Geoid and an Ellipsoid?
The relationship between the geoid and ellispoid is shown in the diagram Figure 1.
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Figure 5 Geoidal Relationships
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+ PHDQVHDOHYHOKHLJKWRUJHRLGKHLJKWRURUWKRPHWULFKHLJKW
KHLJKWDERYHWKHJHRLG
K HOOLSVRLGDOKHLJKWKHLJKWDERYHHOOLSVRLG
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From the above diagram and formula, to convert heights between the ellipsoid and geoid, we
require the geoid-ellipsoid separation value. This value is not easy to determine. Therefore, a
world-wide model is generally used to provide these values. NovAtel (www.novatel.ca) GPS receivers
store this value internally. This model can also be augmented with local height and gravity information.
A more precise geoid model is available from governement survey agencies, e.g., U.S National
Geodetic Survey (www.ngs.noaa.gov
) or Geodetic Survey of Canada (www.geod.emr.ca).
Why is this important for GPS users?
The above formula is critical for GPS users as they typically obtain ellipsoidal heights and need
to convert these into mean sea-level heights. Once this conversion is complete, users can relate
their GPS derived heights to more “usable” mean sea-level heights.
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