The GPS Observer
NAVD 88 GPS-derived orthometric heights, part 4.Thus far, this series of articles has discussed basic concepts of GPS-derived heights (part 1, March 2001), NGS’ guidelines for establishing GPS-derived heights (part 2, May 2001) and basic procedures for detecting GPS-derived height data outliers (part 3, July 2001). This article, the fourth and final part of this series, will briefly discuss basic procedures that need to be followed for establishing accurate North American Vertical Datum of 1988 (NAVD 88) GPS-derived orthometric heights.
With the computation of the latest national geoid model, GEOID 99, and the development of NGS guidelines for establishing GPS-derived ellipsoid heights [becoming known as the NGS-58 document (http://www.ngs.noaa.-
gov/PUBS_LIB/NGS-58.html)], estimating accurate NAVD 88 GPS-derived orthometric heights is relatively easy when all things are normal. It is impossible to describe all situations in a short article, so I will address the basic procedures with a few caveats. 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.
The three basic rules are fairly simple.
Three Basic 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, GEOID99, when computing GPS-derived orthometric heights, and
Rule 3: Use the latest National Vertical Datum, NAVD 88, height values to control the project’s adjusted heights.
The four basic control requirements are also simple, but may be difficult to implement locally.
Four Basic Control Requirements for Estimating GPS-Derived Orthometric Heights:Requirement 1: GPS-occupy stations with valid NAVD 88 orthometric heights; stations 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 the base and summit of mountains, even if the distance is less than 20 km.
The problem here for some users may be locating enough valid NAVD 88 heights. First, let’s define a valid NAVD 88 height. Valid NAVD 88 height values include, but are not limited to, the following: control points that have not moved since their heights were last determined, were not misidentified and are consistent with NAVD 88. This appears to be fairly simple, but it may be difficult for some users to determine if a bench mark has moved since the height was last determined. In addition, in some areas of the country the user may not find valid NAVD 88 bench marks every 20 km due to crustal movement. The user then may have to perform some classical precise leveling observations (see POB article titled Standards and Specifications for Vertical Control Networks, Part 4, November 2000) to evaluate the existing NAVD 88 heights and determine the relative accuracy of the geoid model in the area extent of the project.
This doesn’t mean that the user must perform a leveling survey such that all GPS stations are leveled to or even perform a large leveling network survey. The purpose of the leveling is to evaluate the geoid model and properly connect to the NAVD 88. Since each case is different, i.e., NAVD 88 height problems and geoid accuracy will vary in each region of the country, as well as each individual project accuracy requirement will be different, it is impossible to describe exactly what the user will have to do. NGS will, however, assist users when they are planning their surveys. (For more information on planning surveys, please contact Steve Frakes, Spatial Reference System Division, NGS at 301/713-3191 or by E-mail: Steve.Frakes@noaa.gov.
The five basic procedures for estimating GPS-derived orthometric heights probably appear to users to be the most difficult to understand. However, as users perform more GPS surveys and discuss their results with others, they seem to quickly understand why these procedures are needed.
Five Basic 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, detect and remove all data outliers. [NOTE: If the user follows NGS’ guidelines for establishing GPS-derived ellipsoid heights, the user will already know which vectors may need to be rejected, and following the GPS-derived ellipsoid height guidelines should have already re-observed those base lines.]
The user should repeat procedures 1 and 2 until all data outliers are removed.
Procedure 3: Compute the differences between the set of GPS-derived orthometric heights from the minimum constraint adjustment (using GEOID99) from procedure 2 and the corresponding published NAVD 88 bench marks.
Procedure 4: Using the results from procedure 3, 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, perform a constrained adjustment holding one latitude value, one longitude value and all valid NAVD 88 height values fixed.
So what do these procedures really mean? The last article in this series mentioned that during the analysis of the GPS-derived ellipsoid heights, the user needed to perform a minimum-constraint least squares adjustment and look for outliers. This ensures that the GPS-derived ellipsoid heights meet the user’s desired standards. Now, the user must ensure that the NAVD 88 heights to be used to control the final set of GPS observations and geoid heights are valid. This is not a complex procedure if the user knows how to perform a least squares adjustment of GPS data. Explaining least squares adjustments is beyond the scope of this article. Today, most GPS manufacturers provide support software that includes performing least squares adjustments.
The techniques described below are meant to be fairly simple for users to implement. They are not rigorous and are not the only way to detect outliers. They will, however, assist the user in determining which NAVD 88 bench marks are valid. The user simply computes the GPS-derived orthometric heights and compares the results with the published NAVD 88 heights. (See Figure 2.) All relative height differences between adjacent station pairs need to agree within 2 cm for 2-cm surveys and 5 cm for 5-cm surveys to be considered valid NAVD 88 bench marks.
The reader should note that most relative differences in Figure 2 are less than 2 cm, but there is a difference in the upper central part of the project, i.e., 3.6 cm, that appears to be large relative to its neighbors. This station should be investigated as a potential outlier. The user should also note that there appears to be a systematic trend between the two sets of heights. That is, the differences tend to increase in value going from the south to the north-northeast.
Best fitting a tilted plane to the height differences is a good method of detecting and removing any systematic trend between the height differences. (See Figure 3.) Most GPS adjustment software available today has an option for solving for a tilted plane or rotations and scale parameters to remove the systematic trend from data if one exists. After a trend has been removed, all differences should be less than ± 2 cm. The user should note that in this example, all differences are less than ± 2 cm except the one in the northwest corner of the project. This bench mark needs to be investigated and probably should not be used to control the results. Although, it should be noted that the difference is only 2.4 cm (not bad for government work, huh?). The potential outlier near the upper central part of the project still indicates large relative differences between its neighbors and should be investigated.
These four articles were meant to provide the reader with basic concepts and procedures for estimating GPS-derived orthometric heights. NGS has developed seminars to 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, NGS at 301/713-3191 or by E-mail: Ed.McKay@noaa.gov.