BackgroundSince 1983, NGS has performed control survey projects in the United States using GPS satellites. Analysis of GPS survey data has shown that GPS can be used to establish precise relative positions in a three-dimensional Earth-centered coordinate system. GPS carrier phase measurements are used to determine vector baselines in space, where the components of the baseline are expressed in terms of Cartesian coordinate differences. These vector baselines can be converted to distance, azimuth and ellipsoidal height differences (dh) relative to a defined reference ellipsoid.
Over the past decade, GPS surveying techniques have proven to be so efficient and accurate that they are now routinely used in place of classical line-of-sight surveying methods for establishing horizontal control. Understandably, interest has been growing in using GPS techniques to establish accurate vertical control. Progress, however, had been hampered due to difficulties in obtaining sufficiently accurate geoid height differences to convert GPS-derived ellipsoid height differences to accurate orthometric height differences.
These factors have recently coalesced, making GPS-derived orthometric heights a viable alternative to classical line-of-sight leveling techniques for many applications:
- completion of the general adjustment of NAVD 88 (http://www.ngs.noaa.gov/
- development of NGS guidelines for establishing GPS-derived ellipsoid heights to meet 2- and 5-cm standards (http://www.ngs.noaa.-
- computation of an accurate, nationwide, high-resolution geoid model, GEOID99 (http://www.ngs.noaa.gov/GEOID/).
Basic ConceptsOrthometric heights (H) are referenced to an equipotential reference surface, e.g., the geoid. The orthometric height of a point on the Earth’s surface is the distance from the geoidal reference surface to the point, measured along the plumb line normal to the geoid. These are the heights most surveyors have worked with in the past and are often called “mean sea-level” heights. Ellipsoid heights (h) are referenced to a reference ellipsoid. The ellipsoid height of a point is the distance from the reference ellipsoid to the point, measured along the line that is normal to the ellipsoid. The term ellipsoid height may be a new concept to many traditional surveyors and has become prevalent because ellipsoid heights are readily derived from GPS measurements. At the same point on the surface of the Earth, the difference between an ellipsoid height and an orthometric height is defined as the geoid height (N).
Several error sources that affect the accuracy of orthometric, ellipsoid and geoid height values are generally common to nearby points. Because these error sources are in common, the uncertainty of height differences between nearby points is significantly smaller than the uncertainty of the absolute heights of each point. This is the key to establishing accurate orthometric heights using GPS.
Orthometric height differences (dH) can then be obtained from ellipsoid height differences (dh) by subtracting the geoid height differences (dN):
dH = dh dN
Adhering to NGS’ guidelines, ellipsoid height differences (dh) over short baselines, i.e., less than 10 km, can now be determined from GPS carrier-phase measurements with 2-sigma uncertainties that are typically better than ±2 cm. This is now possible because of the availability of a greater number of satellites, more accurate satellite orbits, full-wavelength dual-frequency carrier-phase data, improved antenna designs and improved data processing techniques. The requirement that each baseline must be repeated and agree to within 2 cm of each other, and must be repeated on two separate days during different times of the day, should provide a final GPS-derived ellipsoid height better than 2 cm at the 2-sigma level. It should also be noted that the GPS-derived ellipsoid height guidelines documented by NGS were intentionally designed to produce ellipsoid heights slightly better than 2 cm, i.e., about 1.4 cm, so they could also be used when generating 2 cm GPS-derived orthometric heights. The requirement that spacing between local network stations cannot exceed 10 km helps to keep the relative error in geoid height small, i.e., typically less than 0.5 cm. Adding in the small error for the uncertainty of the geoid height difference and controlling the remaining systematic differences between the three height systems will produce a GPS-derived orthometric height with 2-sigma uncertainties that are typically ±2 cm. Therefore, it is possible to establish GPS-derived orthometric heights to meet certain standards (not millimeter standards) but 2-cm (95 percent) standards are routinely met now using GPS.
In many areas of the United States, geoid height differences can be determined with uncertainties that are typically better than 1 cm for distances of as much as 20 km and less than 2-3 cm for distances from 20 to 50 km. The small values for the differential geoid height uncertainties have been demonstrated in tests in several regions of the United States. Larger uncertainties can be expected in other areas, depending on the density of the observed gravity network and uncertainties in the determination of observed and interpolated gravity anomalies.
When high-accuracy field procedures are used, orthometric height differences can be computed from measurements of precise geodetic leveling with an uncertainty of less than 1 cm over a 50 km distance. Less accurate results are achieved when third-order leveling methods are employed. Depending on the accuracy requirements, GPS surveys and present high-resolution geoid models can be employed as an alternative to classical leveling methods. In the past, the primary limiting factor was the accuracy of estimating geoid height differences. With the computation of the latest national high-resolution geoid model, GEOID99, and the development of the 2- and 5-cm guidelines for estimating GPS-derived ellipsoid heights, the limiting factor is ensuring that the NAVD 88 orthometric height values used to control the project are valid. Strategically occupying bench marks with GPS that have valid NAVD 88 height values is critical to detecting, reducing, and/or eliminating blunders and systematic errors between the three height systems. [Note: Valid NAVD 88 height values include, but are not limited to, the following: bench marks that have not moved since their heights were last determined, were not misidentified and are consistent with NAVD 88.]
There are three basic rules, four control requirements and five procedures that need to be adhered to for computing accurate NAVD 88 GPS-derived orthometric heights. This will be the subject of the last of the articles in this series. This article addressed the basic concepts of GPS-derived heights. To reiterate, it is important the user understands there are three types of heights involved with estimating GPS-derived heights: ellipsoid, geoid and orthometric. Each of these heights has its own error sources that need to be detected, reduced and/or eliminated by following specific procedures or applying special models. The next article will discuss guidelines for detecting, reducing and/or eliminating error sources in ellipsoid heights.
NGS has developed seminars on NAVD 88 and GPS-derived heights. The seminars provide detailed information about the results of NAVD 88 and conversion processes, and how to determine accurate GPS-derived orthometric heights.
For more information on NGS training workshops and guidelines, please contact Edward McKay, Spatial Reference System Division at 301/713-3191 or by E-mail at Ed.McKay@noaa.gov.