# Establishing Orthometric Heights Using GNSS — Part 1

June 3, 2015  -

Editor’s Note: This month, we introduce a column by David B. Zilkoski, one of our two new Survey Scene editors. Zilkoski has worked in the fields of geodesy and surveying for more than 40 years, including serving as director of the National Geodetic Survey. See his full bio at the end of this article. He is joined by coeditor David Doyle, who contributed the May column.

## The Three Types of Heights Involved in Computing GNSS-Derived Orthometric Heights

By David B. Zilkoski

David B. Zilkoski

This column is the first in a series of newsletters discussing issues associated with establishing orthometric heights using GNSS. The purpose of my columns is not to promote a particular procedure or process, but to provide the reader with information and analysis tools to consider when using GNSS to estimate orthometric heights.

This information is not new. During the past two decades, I have written several articles and papers on estimating GNSS-derived orthometric heights and presented numerous seminars describing guidelines on how to estimate GNSS-derived heights. However, due to the automation of technology and “blackbox” processes, many users are accepting results without performing the proper analysis to ensure that their results are reasonable and correct. These processes and procedures are not difficult to perform, but they can be very beneficial to obtaining an understanding of the accuracy of your results and ensuring your results are correct.

To understand how to estimate GNSS-derived orthometric heights at centimeter-level accuracy, you must have a basic understanding of the types of heights involved, how these heights are defined and related and how accurately these heights can be determined. In other words, you need to obtain a basic understanding of ellipsoid, geoid and orthometric heights and how they are related and their estimated accuracies.

To adequately address these topics, a series of Survey Scene newsletters will be separated into several sections. Some of this material will be a review (and probably boring) for those of you that have been performing GNSS-derived orthometric height surveys but, hopefully, you will gain a little benefit from the review. For those of you just starting out, I hope this will whet your appetite to obtain a better understanding of heights.

The following is a brief outline of what the columns will address:

• Description of the three types of heights involved in computing GNSS-derived orthometric heights. That is, the definition of ellipsoid, geoid and orthometric heights, and how they are related. The user should understand what potential issues can arise due to how each height was defined, modeled and published. For example, in the United States, what errors exist in the published NAVD88 heights due to the leveling network design and remaining systematic errors in the leveling data? Constraining a North American Vertical Datum of 1988 (NAVD 88) published height that’s less accurate than your GNSS-derived orthometric height may allow your results to be consistent with the surrounding published heights, but could be distorting the rest of your results. In the end, you may need to do that, but you should know how your decision has influenced the rest of your results. I was the NAVD 88 project manager, so I know where all the problems are hidden. I am just kidding about knowing where all the problems are hidden, but there are issues associated with performing a nationwide network adjustment. NGS’ latest scientific geoid models can be useful in identifying potential issues in NAVD88.
• Basic procedures for detecting published NAD 83 (2011) ellipsoid height outliers and how repeatability does not mean accuracy. Why you can’t assume that the published ellipsoid heights between two closely spaced stations is accurate to the published formal errors.
• A description of the differences between a scientific gravimetric geoid model and a hybrid geoid model, and why it is important to use both geoid models in your analysis. The latest NGS hybrid geoid model, Geoid12B, is made consistent with the published NAVD 88 heights. This means you will be consistent with NAVD 88 when using GEOID12B to estimate GNSS-derived orthometric heights. However, this doesn’t guarantee that your GNSS-derived orthometric heights are accurate. NGS’s new beta experimental geoid height model xGEOID14B is not distorted to fit the published NAVD 88 heights, so it is useful for identifying valid NAVD 88 benchmarks.
• Basic procedures for validating NAVD 88 height constraints used to estimate GNSS-derived orthometric heights. How to ensure your monuments haven’t moved since their last survey, and how good are your leveling-derived orthometric height constraints? Based on all available information and data, basic procedures to determine how good the final set of GNSS-derived orthometric heights really are. NGS 59 guidelines outline basic rules and procedures that need to be adhered to for computing accurate NAVD 88 GNSS-derived orthometric heights.
• A description of NGS’ proposed 2022 Vertical Reference Frame and why it will be a good replacement for NAVD 88.

#### Background

Since 1983, NOAA’s National Geodetic Survey (NGS) has performed control survey projects in the United States using GPS satellites. NGS used these early GPS surveys projects to develop guidelines and procedures to estimate GPS-derived orthometric heights. These publications are known as NGS 58 and NGS 59.

Over the past three decades, GNSS 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 vertical control networks at the 2-cm level. Understandably, interest has been growing in using GNSS techniques to replace all leveling requirements. During the next decade, scientists will continue to develop better models and tools to facilitate GNSS-derived orthometric heights replacing classical line-of-sight surveying for many applications. In the meantime, it is important to have a clear understanding of the basic concepts of establishing GNSS-derived orthometric heights, otherwise water (or something worse) may not flow “down hill.”

Let’s start with a review of the three types of heights used when estimating GNSS-derived orthometric heights and how they are related.

#### Types of Heights and Their Relationship

Orthometric 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. Years ago, the term ellipsoid height may have been a new concept to many traditional surveyors, but prevalent today because ellipsoid heights are readily derived from GNSS 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). It should be noted that h=H+N is an approximate equation because H is measured along the plumb line normal to the geoid, where h is measured along a line normal to the ellipsoid (see Figure 1). For all practical survey projects, this small difference can be ignored.

Figure 1. Relationship of ellipsoid, geoid and orthometric heights.(Figure from POB article by David Zilkoski, The GPS Observer column, Feb. 28, 2001)

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 GNSS.

Orthometric height differences (dH) can then be obtained from ellipsoid height differences (dh) by subtracting the geoid height differences (dN):

dH = dh – dN

Each of these heights and height differences have systematic errors that are accounted for by following appropriate procedures during data acquisition, by applying corrections based on environmental conditions and models, and/or estimating parameters using adjustment techniques. There will always be remaining errors that are not accounted for, and you must perform the appropriate procedures to detect, reduce or eliminate these errors in the final set of GNSS-derived orthometric heights.

#### Relative Accuracy Estimates

Adhering to NGS guidelines (NGS 58), ellipsoid height differences (dh) over short baselines (less than 10 km) can now be determined with 2 sigma uncertainties that are typically better than +/ 2 cm. The requirement that each baseline must be repeated and agree to within 2 cm of each other, and they must be repeated on two separate days, during different times of the day, should provide a final GNSS-derived ellipsoid height better than 2 cm at the 2-sigma level. The requirement that spacing between local network stations cannot exceed 10 km helps to keep the relative error in geoid height small.

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 GNSS-derived orthometric height with 2-sigma uncertainties that are typically +/- 2 cm. Therefore, it is possible to establish GNSS-derived orthometric heights to meet certain standards, not millimeter standards, but 2-cm (95%) standards are routinely met now using GNSS.

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 kilometer distance. Less accurate results are achieved when third-order leveling methods are employed. Depending on the accuracy requirements, GNSS 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 more accurate National high-resolution geoid models, e.g., GEOID12A, the limiting factor is ensuring that the NAVD 88 orthometric height values used to control the project are valid. Strategically occupying benchmarks with GNSS that have valid NAVD 88 height values is critical to detecting, reducing 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: benchmarks that have not moved since their heights were last determined, were not misidentified, and are consistent with NAVD 88.)

#### Conclusion

This newsletter addressed the basic concepts of GPS-derived heights. To reiterate, it is important that you understand there are three types of heights involved with estimating GNSS-derived heights: ellipsoid, geoid and orthometric. Each of these heights has its own error sources that need to be detected, reduced or eliminated by following specific procedures or applying special models. This series of newsletter columns will address these potential errors sources and provide procedures to assist you in identifying these errors.

My next column in this series, coming in the August Survey Scene, will review guidelines for detecting, reducing or eliminating error sources in ellipsoid heights, and provide a brief discussion on using published NAD 83 (2011) ellipsoid heights in your analysis.

#### References

NOAA Technical Memorandum NOS NGS-58, Guidelines for Establishing GPS-derived Ellipsoidal Heights (Standards: 2 cm and 5 cm), Version 4.3.

NOAA Technical Memorandum NOS NGS-59, Guidelines for Establishing GPS-derived Orthometric Heights (Standards: 2 cm and 5 cm), are available. These guidelines address the establishment and densification of vertical control networks through the use of GPS surveys and valid NAVD 88 orthometric control.

David B. Zilkoski has worked in the fields of geodesy and surveying for more than 40 years. He was employed by National Geodetic Survey (NGS) from 1974 to 2009. He served as NGS director from October 2005 to January 2009. During his career with NGS, he conducted applied GPS research to evaluate and develop guidelines for using new technology to generate geospatial products. Based on instrument testing, he developed and verified new specifications and procedures to estimate classically derived, as well as GPS-derived, orthometric heights.

Now retired from government service, as a consultant he provides technical guidance on GNSS surveys; computes crustal movement rates using GPS and leveling data; and leads training sessions on guidelines for estimating GPS-derived heights, procedures for performing leveling network adjustments, the use of ArcGIS for analyses of adjustment data and results, and the proper procedures to follow when estimating crustal movement rates using geodetic leveling data.

### About the Author: David B. Zilkoski

David B. Zilkoski has worked in the fields of geodesy and surveying for more than 40 years. He was employed by National Geodetic Survey (NGS) from 1974 to 2009. He served as NGS director from October 2005 to January 2009. During his career with NGS, he conducted applied GPS research to evaluate and develop guidelines for using new technology to generate geospatial products. Based on instrument testing, he developed and verified new specifications and procedures to estimate classically derived, as well as GPS-derived, orthometric heights. Now retired from government service, as a consultant he provides technical guidance on GNSS surveys; computes crustal movement rates using GPS and leveling data; and leads training sessions on guidelines for estimating GPS-derived heights, procedures for performing leveling network adjustments, the use of ArcGIS for analyses of adjustment data and results, and the proper procedures to follow when estimating crustal movement rates using geodetic leveling data. Contact him at dzilkoski@gpsworld.com.

### 1 Comment on "Establishing Orthometric Heights Using GNSS — Part 1"

1. ArabHussain Shah says:

I like this article,because Computing GNSS-Derived Orthometric Heights are major issue of GPS survey.There is answer to “precision of GNNS-Derived Orthometric Hights”

I appreciate,