The GPS Observer
This is the fourth article in a short series of articles on vertical control. Professor Reilly has done an excellent job of presenting the standards and specifications for geodetic leveling in the previous three articles. I will briefly address two topics in this article—vertical datums, NGVD 29 and NAVD 88, and GPS vertical control. Yes, that’s right; GPS can be used to establish vertical control.
First, a vertical datum is a reference surface, e.g., a representation of the geoid, to which heights are referred. The basic difference between vertical datums used in the United States is how they were realized. Other differences occur because of distortions due to local adjustments, different corrections applied to leveling data, , e.g., refraction correction, and type of height (either Helmert or normal).
History of U.S. Geodetic Vertical DatumsThe first leveling route in the United States considered to be of geodetic quality was established in 1856-57 under the direction of G.B. Vose of the U.S. Coast Survey. The leveling survey was required to support current and tide studies in the New York Bay and Hudson River areas. The first leveling line officially designated as "geodesic leveling" by the Coast and Geodetic Survey followed an arc of triangulation along the 39th parallel. This 1887 survey began at bench mark A in Hagerstown, Md.
By 1900, the vertical control network had grown to 21,095 km of geodetic leveling. A reference surface was determined in 1900 by holding elevations referenced to local mean sea level (LMSL) fixed at five tide stations. Data from two other tide stations indirectly influenced the determination of the reference surface. Subsequent readjustments of the leveling network were performed by the Coast and Geodetic Survey in 1903, 1907 and 1912.
The next general adjustment of the vertical control network was accomplished in 1929. By then, the international nature of geodetic networks was well understood, and Canada provided data for its first-order vertical network to combine with the U.S. network. The two networks were connected at 24 locations through vertical control points (bench marks) from Maine/New Brunswick to Washington/British Columbia. Although Canada did not adopt the "Sea Level Datum of 1929" [name changed to National Geodetic Vertical Datum of 1929 (NGVD 29) in 1973] determined by the United States, Canadian-U.S. cooperation in the general adjustment greatly strengthened the 1929 network. Table 1 lists the kilometers of leveling involved in the readjustments and the number of tide stations used to establish the datums.
North American Vertical Datum of 1988Approximately 625,000 km of leveling were added to the National Spatial Reference System (NSRS) since NGVD 1929 was created. In the intervening years, discussions were held periodically to determine the proper time for the inevitable new general adjustment. In the early 1970s, the National Geodetic Survey (NGS) conducted an extensive inventory of the vertical control network. The search identified thousands of bench marks that had been destroyed, due primarily to post-World War II highway construction, as well as other causes. Many existing bench marks were affected by crustal motion associated with earthquake activity, post-glacial rebound (uplift) and subsidence resulting from the withdrawal of underground liquids. As indicated earlier, other problems (distortions in the network) were caused by forcing the 625,000 km of leveling to fit previously determined NGVD 29 height values.
For the general adjustment of the North American Vertical Datum of 1988 (NAVD 88) and the International Great Lakes Datum of 1985 (IGLD 85), a minimum-constraint adjustment of Canadian-Mexican-U.S. leveling observations was performed. The height of the primary tidal bench mark at Father Point/Rimouski, Quebec, Canada, was held fixed as the constraint. Father Point/Rimouski is an IGLD water-level station located at the mouth of the St. Lawrence River and is the reference station used for IGLD 85. Therefore, IGLD 85 and NAVD 88 are one and the same. This constraint also satisfies the requirements of shifting the datum vertically to minimize the impact of NAVD 88 on U.S. Geological Survey (USGS) mapping products and provides the datum point desired by the IGLD Coordinating Committee for IGLD 85. The only difference between IGLD 85 and NAVD 88 is that IGLD 85 bench mark values are given in dynamic height units, and NAVD 88 values are given in Helmert orthometric height units. Geopotential numbers for individual bench marks are the same in both systems.
The general adjustment of NAVD 88 was completed in June 1991. All heights from the general adjustment were loaded into the NGS geodetic data base in September 1991. It should be noted that there are more than 500,000 USGS and U.S. Army Corps of Engineers (COE) third-order bench marks for which NGS does not yet have any data. NGS will publish the NAVD 88 heights, but the USGS and COE must prepare the data in computer-readable form and submit them to NGS.
NGS recognized that the use of GPS data and high-resolution geoid models to estimate accurate GPS-derived orthometric heights would be an important part of the implementation of NAVD 88 and developed a strategy for implementing GPS-derived orthometric heights in 1993.
Establishing NAVD 88 Heights Using GPSProfessor Reilly ended his first article by stating "The elevations established with GPS using the geoid model are acceptable for topography and other engineering requirements, especially when ties to existing bench marks are made." His second article showed that vertical control standards are stated in millimeters. It is true that using GPS and highresolution geoid models to establish GPS-derived orthometric heights to 1 mm is difficult at best, even at a 1-km spacing. Professor Reilly also mentioned in his second article that "This is a history article, ... the U.S. National Geodetic Survey (NGS) has only one leveling crew for the entire United States. In the future, much of the vertical control will have to be established by other means." Well, the future is now. 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.
Guidelines have been written for establishing GPS-derived ellipsoid heights to meet 2- and 5-cm standards and a guide describing how to use GPS, GEOID99 and NAVD 88 published heights for establishing GPS-derived orthometric heights to meet 2- and 5-cm standards has been drafted.
The key here is meeting a "2-cm standard"—not a "a few mm standard," and that NAVD 88 published control values have been established using precise geodetic leveling techniques. It should also be noted that most surveyors tie into NGS control and usually perform third-order, or lower, leveling procedures. As described in Professor Reilly’s third article, when a user performs third-order leveling, the maximum allowable misclosure is 1.2 cm per square root of the leveling distance in kilometers. This means that for third-order leveling, the allowable misclosure between two control stations spaced 4 km apart is 2.4 cm. Therefore, if a surveyor’s leveling difference agreed with the published difference to within 2.4 cm, the results would meet the requirements of the project. Of course, the actual standard deviation of the final height difference may be much better than 2.4 cm if the user followed all the specifications and procedures for third-order leveling, i.e., using calibrated one-piece rods, double-running all new sections, balancing sight lengths and computing corrections for systematic errors, such as for refraction error. The ties to NAVD 88 published heights help control any remaining systematic effects and detect blunders. In this case a blunder less than 2.4 cm may go undetected.
There are three basic rules, four control requirements, and five procedures which need to be adhered to for estimating GPS-derived orthometric heights.
Three Rules for Estimating GPS-Derived Orthometric Heights:
- Rule 1: Follow NGS’ guidelines for establishing GPS-derived ellipsoid heights when performing GPS surveys.
- Rule 2: Use NGS’ latest National Geoid Model, e.g., GEOID99, when computing GPS-derived orthometric heights.
- Rule 3: Use the latest National Vertical Datum, NAVD 88, height values to control the project’s adjusted heights.
Four Control Requirements for Estimating GPS-Derived Orthometric Heights:
- Requirement 1: GPS-occupy stations with valid NAVD 88 orthometric heights should be evenly distributed throughout project.
- Requirement 2: For project areas less than 20 km on a side, surround project with valid NAVD 88 bench marks, i.e., minimum number of stations is four; one in each corner of project. [NOTE: The user may have to enlarge the project area to occupy enough bench marks even if the project area extends beyond the original area of interest.]
- Requirement 3: For project areas greater than 20 km on a side, keep distances between valid GPS-occupied NAVD 88 bench marks to less than 20 km.
- Requirement 4: For projects located in mountainous regions, occupy valid bench marks at base and summit of mountains, even if distance is less than 20 km.
Five Procedures for Estimating GPS-Derived Orthometric Heights:
- Procedure 1: Perform a 3-D minimum-constraint least squares adjustment of the GPS survey project, i.e., constrain one latitude, one longitude, and one orthometric height value.
- Procedure 2: Using the results from the adjustment in procedure 1 above, detect and remove all data outliers. [NOTE: If the user follows NGS’ guidelines for establishing GPS-derived ellipsoid heights, then the user will already know which vectors may need to be rejected and following the GPS-derived ellipsoid height guidelines should have already reobserved those base lines.] The user should repeat procedures 1 and 2 until all data outliers are removed.
- Procedure 3: Compute differences between the set of GPS-derived orthometric heights from the minimum constraint adjustment (using the latest National geoid model, e.g., GEOID99) from procedure 2 above and published NAVD 88 bench marks.
- Procedure 4: Using the results from procedure 3 above, determine which bench marks have valid NAVD 88 height values. This is the most important step of the process. Determining which bench marks have valid heights is critical to computing accurate GPS- derived orthometric heights. [NOTE: The user should include a few extra NAVD 88 bench marks in case some are inconsistent, i.e., are not valid NAVD 88 height values.]
- Procedure 5: Using the results from procedure 4 above, perform a constrained adjustment holding one latitude value, one longitude value, and all valid NAVD 88 height values fixed.
[Note: Valid NAVD 88 height values include, but are not limited to, the following: bench marks which have not moved since their heights were last determined, were not misidentified and are consistent with NAVD 88.]
The use of GPS data and a high-resolution geoid model to estimate accurate GPS-derived orthomeric heights will be a continuing part of the implementation of NAVD 88. It is important that users initiate a project to convert their products to NAVD 88. The conversion process is not a difficult task but will require time and resources. 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, telephone: 301/713-3191 or E-mail: Ed.McKay@noaa.gov