GPS Q&A
By John Bohlke

Q. How can I compute GPS-derived elevations by applying geoid heights? J.S. Rapid City, S.D.

A. Computing elevations with GPS requires an understanding of the ellipsoid and the geoid. Generally, we are interested in the elevation that represents the height above mean sea-level (orthometric height). Unfortunately, GPS can only provide the user with an ellipsoid height that is computed based on a smooth model of the Earth, the GRS80 ellipsoid. The ellipsoid does not accurately represent mean sea-level due to undulations in the Earth's gravitational pull. Therefore a local geoid surface must be developed in order to determine the difference between mean sea-level and the ellipsoidal surface. A local geoid model can be constructed by making gravity measurements at each GPS point. As you can see from Figure 1, the height above mean sea-level is equal to the ellipsoid height minus the geoid height (H=h-N). In the conterminous United States the elevation is always larger than the ellipsoid height because the geoid heights range from -53 meters to -5 meters.
      Since most people do not perform gravity measurements, they consult a geoid model program from the NGS titled GEOID93. (The NGS recently released an updated and more accurate version titled GEOID96 that can be found on their web page at http://www.ngs.noaa.gov or on their ftp site at ftp.ngs.noaa.gov.) Based on gravity measurements taken throughout the U.S., the geoid program allows the user to determine the geoid separation from the latitude and longitude of any point. The accuracy of using a geoid model depends on the quality and amount of gravity measurements in the model and on the amount of geoidal undulation in the region. In many areas within the U.S. GEOID93 will produce an accuracy on the order of 3 centimeters.

Q. What are some other ways to compute accurate GPS-derived elevations?
F.P. Bloomington, Minn.

A. An accurate GPS elevation may be possible using a variety of methods. First of all, it is important to remember that the vertical accuracy of GPS is typically twice that of the horizontal accuracy. The most accurate elevations can be obtained by collecting GPS data on various vertical control points on a project. The user can hold the control in an adjustment program in order to achieve accurate elevations on the other GPS points. The results will be more reliable and much easier to analyze if the geoid heights are applied to the points before performing the adjustment. It is important to use GPS on three or more vertical control points spread throughout the project in order to obtain the best vertical accuracy.
      Another method of calculating elevations with GPS requires knowledge about the local geoid model. The user can enter various latitudes and longitudes into the GEOID96 program to determine the geoidal undulation in a particular area. In place of using the ellipsoid height, users may achieve mean sea-level elevations by processing the data based on a mean sea-level elevation or by using the mean sea-level elevation at their real-time base station in areas where the geoid remains constant. This technique is not recommended on projects with baselines over several miles or in areas where the geoid height is large. In all cases it is important to check the results on known control.

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