Have you ever considered what it means to say that Mt. Elbert, the highest peak in Colorado, has a height of 14,433 feet? Where is this measured from -- the center of the Earth, the surface of the Earth, or somewhere else? How do we define zero height or zero elevation?

The *zero surface to which elevations or heights are referred *is called
a **vertical datum**. Traditionally, surveyors and mapmakers have tried to
simplify the task by using the average (or mean) sea level as the definition of
zero elevation, because the sea surface is available worldwide. The mean sea
level (MSL) is determined by continuously measuring the rise and fall of the
ocean at "tide gauge stations" on seacoasts for a period of about 19 years. This
averages out the highs and lows of the tides caused by the changing effects of
the gravitational forces from the sun and moon which produce the tides. The
**mean sea level (MSL)** then is defined as *the zero elevation for a local
or regional area.* But what do you do for Mt. Elbert? Where is the MSL in
Colorado? There is no tangible surface of the ocean from which to measure
height.

It turns out that MSL is a close approximation to another surface, defined by
gravity, called the **geoid**, which is the *true zero surface for
measuring elevations*. Because we cannot directly see the geoid surface, we
cannot actually measure the heights above or below the geoid surface. We must
infer where this surface is by making gravity measurements and by modeling it
mathematically. For practical purposes, we assume that at the coastline the
geoid and the MSL surfaces are essentially the same. Nevertheless, as we move
inland we measure heights relative to the zero height at the coast, which in
effect means relative to MSL.

What's the problem here -- is the receiver broken? Probably not. Standard GPS receivers and software have built-in flexibility to meet a variety of applications. Different applications need heights or elevations with respect to different zero surfaces. Most GPS receivers have built-in software to do these transformations. The user needs to specify the correct vertical reference system. If the user makes wrong assumptions, the results can be very confusing at best. For the pilot trying to make an instrument landing (precision approach), having the wrong height information can have dire consequences!A sailor aboard an anchored destroyer turns on his Navstar Global Positioning System (GPS) receiver and reads that his present height is minus 25 meters. Knowing the ship hasn't sunk, he questions the accuracy of his equipment. The manual says his receiver has a vertical accuracy of plus or minus 9 meters, so he decides to record the measurements for several hours to see if the elevation will ever be positive. Later, when he compares the readings, he finds that all are negative with a mean value of minus 20 meters.

The ** topographic surface** is the actual visible surface
of the Earth. To represent horizontal positions on maps and charts, we need a
mathematical model of the Earth which includes a set of numbers for the size and
shape of the Earth. Because the Earth is slightly flattened at the poles, a
sphere won't work. A flattened sphere, which is called an

- MSL elevation is roughly equivalent to orthometric height (H), the technical name for height above the geoid.
- Geoid height (N) is the separation between the geoid and the ellipsoid. It can be plus or minus.
- Ellipsoid height (h) is the distance above or below the ellipsoid (plus or minus). Ellipsoid height is also called geodetic height.

*For example, to get MSL elevation from ellipsoid height, you simply
have to subtract the geoid height (H equals h minus N).*

By definition, the geoid describes this irregular gravity shape. Because there is no way to accurately measure the geoid, it has been roughly approximated in the past by MSL. Technically, the geoid differs from MSL by several meters due to other ocean effects beyond the scope of this pamphlet.

The MSL elevation from the geoid model is not very accurate in some areas, because until recently, we just didn't know exactly how the geoid was shaped. Now we have the technology to improve the geoid model to about one-meter level of accuracy. NIMA has an ongoing project to develop an improved geoid by mid-1996, which in turn will be used as a zero surface to establish consistent and accurate elevations worldwide. In the meantime, realize that if you ignore vertical datum issues errors of up to 100 meters could result!

Each Unified Command has an MC&G officer and a NIMA Liaison. Call the headquarters of your MAJCOM to get in touch with them.

National Imagery and Mapping Agency

8613 Lee Highway

Fairfax, VA 22031-2137