Vertical Datums

Overview#

A vertical datum is a reference surface from which elevations or heights are measured. While horizontal datums define positions on the Earth's surface, vertical datums define the "zero" from which we measure how high or low a point is. Without a clearly defined vertical datum, the simple question "What is the elevation of this benchmark?" has no meaningful answer.

The need for a vertical reference arises because the Earth's gravity field is irregular. Water does not flow "downhill" relative to a geometric shape -- it flows in response to gravity. An elevation system must therefore be tied to a physical surface that reflects gravity, not just geometry. This surface is the geoid: the equipotential surface of the Earth's gravity field that best fits mean sea level in a global sense.

"The geoid is an equipotential surface of the Earth's gravity field that best fits, in a least-squares sense, global mean sea level." -- Ghilani & Wolf, Elementary Surveying, 13th Ed., Ch. 19

Vertical datums fall into two broad categories:

• Tidal datums are based on observations of sea level at tide gauge stations. They connect the leveling network to a physical manifestation of the geoid -- the ocean surface averaged over time. Mean Sea Level (MSL), Mean Lower Low Water (MLLW), and Mean Higher High Water (MHHW) are all tidal datums.
• Geodetic vertical datums are realized through vast networks of spirit leveling, tied to one or more tidal benchmarks. They provide a consistent, nationwide (or continental) elevation framework.

Every elevation reported on a survey plat, topographic map, or construction plan is referenced -- explicitly or implicitly -- to a vertical datum.

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NGVD 29 (National Geodetic Vertical Datum of 1929)#

The first nationwide vertical datum in North America was originally called the Sea Level Datum of 1929. It was renamed to the National Geodetic Vertical Datum of 1929 (NGVD 29) in 1973 to eliminate the misleading implication that its zero surface coincided everywhere with mean sea level.

How It Was Established

NGVD 29 was the product of a general adjustment of the first-order leveling networks of both the United States and Canada. The adjustment incorporated:

• 26 tide gauge stations along the Atlantic, Pacific, and Gulf coasts of the US, plus stations in Canada
• Approximately 75,000 km (46,000 miles) of leveling lines
• A fixed constraint that mean sea level at each tide gauge was held as the zero elevation

By constraining the adjustment to all 26 tide stations simultaneously, the network was effectively warped to force agreement with observed sea level at those locations. This was a practical compromise, but it introduced systematic distortions.

Limitations

The fundamental problem with NGVD 29 is that mean sea level is not the same surface everywhere. Due to ocean currents, temperature variations, salinity, atmospheric pressure, and wind (collectively called sea surface topography), the mean sea level at one tide gauge may differ from the mean sea level at another by more than a meter relative to the geoid. Forcing these different water surfaces to be the same "zero" distorted the leveling network.

Additionally, over the decades following 1929, ongoing leveling revealed internal inconsistencies. Crustal motion, post-glacial rebound, subsidence, and simple accumulation of observational errors degraded the datum's accuracy. By the 1980s, discrepancies of several centimeters to tens of centimeters were common.

Despite these limitations, NGVD 29 appears on many older surveys, USGS topographic maps, FEMA flood maps (some still reference NGVD 29), and legal descriptions. Surveyors must be able to recognize it and convert between it and modern datums.

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NAVD 88 (North American Vertical Datum of 1988)#

NAVD 88 replaced NGVD 29 as the official vertical datum of the United States following a massive readjustment completed in June 1991. It was designed to correct the fundamental flaws of NGVD 29.

How It Was Established

Rather than constraining the adjustment to multiple tide gauges, NAVD 88 used a minimum-constrained adjustment -- only a single tidal benchmark was held fixed:

• Primary Tidal Benchmark: Father Point (Pointe-au-Pere) at Rimouski, Quebec, Canada

This single-point constraint eliminated the distortions inherent in NGVD 29's multi-gauge approach. The adjustment incorporated:

• Approximately 1,001,500 km (625,000 miles) of leveling -- more than 13 times the network used for NGVD 29
• Leveling data from the US, Canada, and Mexico
• Helmert orthometric heights, which apply an approximate gravity correction to leveled height differences, making them more physically meaningful than the uncorrected "normal" heights of NGVD 29

"The minimum-constraint adjustment of NAVD 88 held only a single point fixed, thus removing the distortions that resulted from constraining NGVD 29 to 26 tide gauges." -- Ghilani & Wolf, Elementary Surveying, 13th Ed., Ch. 19

Differences from NGVD 29

The shift from NGVD 29 to NAVD 88 is not a constant offset. Across the conterminous United States (CONUS), the differences range from approximately -40 cm to +150 cm (about -1.3 ft to +4.9 ft), depending on location. Along the Gulf Coast and in parts of the Rocky Mountain West, the differences can be particularly large. NGS provides VERTCON, a tool for computing the approximate shift between NGVD 29 and NAVD 88 at any location.

Comparison: NGVD 29 vs. NAVD 88

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Types of Height#

One of the most important concepts in modern surveying is understanding that "height" has several distinct meanings, each tied to a different reference surface.

Ellipsoidal Height ($h$)

The ellipsoidal height is the distance measured along the normal to the reference ellipsoid (e.g., GRS 80 or WGS 84) from the ellipsoid surface to the point. This is what a GNSS receiver computes directly. It is a purely geometric quantity -- it has no relationship to gravity or the direction water flows. Two points with the same ellipsoidal height are generally not at the same elevation in any physically meaningful sense.

Orthometric Height ($H$)

The orthometric height is the distance measured along the plumb line from the geoid to the point. This is the height obtained from spirit leveling (with appropriate gravity corrections). It is the quantity surveyors call "elevation." Points on the same equipotential surface of gravity have equal orthometric heights, and water will not flow between them.

"The orthometric height of a point is the distance, measured along the plumb line, from the geoid to the point." -- Ghilani & Wolf, Elementary Surveying, 13th Ed., Ch. 19

Geoid Undulation ($N$)

The geoid undulation (also called geoid height or geoidal separation) is the distance between the ellipsoid and the geoid at a given location, measured along the ellipsoid normal. In CONUS, geoid undulations for the GRS 80 / NAD 83 ellipsoid range from approximately $-8\text{ m}$ to $-53\text{ m}$, meaning the geoid is everywhere below the ellipsoid in North America.

The Fundamental Relationship

These three quantities are related by the equation:

$h = H + N$

Or equivalently, to find orthometric height from GNSS observations:

$H = h - N$

Where:

• $h$ = ellipsoidal height (from GNSS)
• $H$ = orthometric height (elevation)
• $N$ = geoid undulation (from a geoid model)

This relationship is fundamental to converting GNSS-derived heights into usable elevations.

Dynamic Heights

Dynamic heights are obtained by dividing the geopotential number at a point by a constant reference gravity value (typically normal gravity at latitude 45 degrees):

$H^{dyn} = \frac{C}{\gamma_{45}}$

Dynamic heights have the property that two points with equal dynamic heights are on the same equipotential surface -- water absolutely will not flow between them. This makes dynamic heights essential for hydraulic engineering and the management of the Great Lakes system, where water level consistency is critical. However, dynamic heights do not correspond to physical distances and are rarely used in routine surveying.

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Geoid Models#

Because GNSS provides ellipsoidal heights and surveyors need orthometric heights, accurate geoid models are essential. The National Geodetic Survey (NGS) has developed a series of hybrid geoid models for use in the United States:

These are called hybrid geoid models because they are not pure gravimetric geoid models. Instead, they combine a gravimetric geoid with GPS observations on leveled benchmarks to produce a model that, when applied with $H = h - N$, yields orthometric heights consistent with the NAVD 88 leveling network.

"Hybrid geoid models are developed by fitting a gravimetric geoid to GPS/leveling data to obtain a model consistent with the published NAVD 88 orthometric heights." -- Ghilani & Wolf, Elementary Surveying, 13th Ed., Ch. 19

Accuracy and Resolution

GEOID18 has a spatial resolution of $1' \times 1'$ (approximately 1.8 km) and achieves an accuracy on the order of 1.0 cm RMS in regions with dense GPS-on-benchmarks data. In areas with sparse control, accuracy degrades. Mountain regions and areas of rapid geoid change present the greatest challenges.

How to Use Geoid Models

NGS provides several tools for applying geoid models:

• NGS Coordinate Conversion and Transformation Tool (NCAT) -- online tool for point-by-point conversions
• NOAA's GEOID tool -- provides $N$ values at specified coordinates
• Most professional GNSS processing software (Trimble Business Center, Leica Infinity, Carlson) integrates geoid models directly, applying the $H = h - N$ conversion automatically during post-processing

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GPS-Derived Orthometric Heights#

The ability to determine accurate elevations from GNSS without running level lines is one of the most significant advances in modern surveying. The basic procedure is straightforward:

1. Observe the ellipsoidal height $h$ with GNSS
2. Obtain the geoid undulation $N$ from a geoid model
3. Compute $H = h - N$

However, achieving accurate orthometric heights from GNSS is far more demanding than achieving accurate horizontal positions.

Sources of Error

Several factors degrade the accuracy of GPS-derived orthometric heights:

• GNSS vertical precision is inherently weaker than horizontal precision by a factor of roughly 1.5 to 3 due to satellite geometry (VDOP > HDOP)
• Geoid model errors propagate directly into the derived orthometric height
• Antenna height measurement errors -- a blunder of even a few millimeters in the antenna height measurement maps directly into the vertical
• Multipath -- reflected signals are more problematic for the vertical component
• Tropospheric modeling errors -- residual atmospheric delays primarily affect the vertical

NGS Guidelines (Technical Memoranda 58 and 59)

NGS has published detailed guidelines for determining accurate GPS-derived orthometric heights:

• NOS NGS 58 -- Guidelines for Establishing GPS-Derived Ellipsoidal Heights
• NOS NGS 59 -- Guidelines for Establishing GPS-Derived Orthometric Heights

Key recommendations include:

• Occupy known benchmarks with published NAVD 88 heights to calibrate the GNSS-geoid model combination
• Use multiple sessions with redundant baselines
• Perform network adjustments that constrain to benchmarks
• Ensure consistent antenna height measurements with calibrated equipment
• A minimum of three benchmarks in the project area for quality control (four or more preferred)
• Apply the latest geoid model available from NGS

Without following these guidelines, raw GPS heights can easily be wrong by 5--15 cm or more, which is unacceptable for most surveying applications.

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NSRS Modernization and NAPGD2022#

The National Geodetic Survey has been working on a comprehensive modernization of the National Spatial Reference System (NSRS) that will retire both NAD 83 and NAVD 88.

The New Geopotential Datum: NAPGD2022

The new vertical datum, originally targeted for release in 2022 and now expected to be delivered in phases beginning in 2025, is designated NAPGD2022 (North American-Pacific Geopotential Datum of 2022). Key features include:

• Geoid-based datum: Instead of a leveling network, NAPGD2022 will define the vertical datum through a high-accuracy gravimetric geoid model derived from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project
• Time-dependent geoid: The datum will account for changes in the geoid over time due to glacial isostatic adjustment, subsidence, and other geodynamic processes
• Epoch-based coordinates: Heights will be associated with a reference epoch, and tools will be provided to transform between epochs
• No leveling network required: The new datum eliminates the need for a physical leveling network as the definition of the datum, though leveling will still be used for local accuracy

Impact on Surveyors

The transition from NAVD 88 to NAPGD2022 will affect practicing surveyors in several ways:

• Published elevations on benchmarks will change (shifts on the order of a meter or more in some locations)
• GPS-derived heights will become more straightforward, as the geoid model is the datum rather than a bridge between GPS and a leveling network
• Legacy surveys referenced to NGVD 29 or NAVD 88 will require transformation
• FEMA floodplain maps, construction documents, municipal benchmarks, and utility records will all need updating over time
• Software updates will be required to incorporate the new datum and transformation tools

NGS will provide transformation tools (similar to VERTCON and NCAT) to convert between NAVD 88 and NAPGD2022.

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Key Takeaways#

• A vertical datum defines the zero surface for measuring elevations. Without specifying the datum, an elevation value is incomplete.
• NGVD 29 was constrained to 26 tide gauges and suffered from distortions caused by sea surface topography. It is superseded but still appears on legacy documents.
• NAVD 88 uses a single-point constraint at Father Point, Rimouski, and is based on over 1,000,000 km of leveling. It is the current official vertical datum.
• Ellipsoidal height ($h$) from GNSS, orthometric height ($H$) from leveling, and geoid undulation ($N$) are related by $h = H + N$.
• Accurate geoid models (currently GEOID18) are essential for converting GNSS heights to orthometric heights.
• GPS-derived orthometric heights require careful procedures (NGS 58/59 guidelines) and control on known benchmarks to achieve acceptable accuracy.
• NAPGD2022 will replace NAVD 88 with a geoid-based datum, fundamentally changing how surveyors work with vertical control.
• Always identify the vertical datum on every survey. A height without a datum reference is an incomplete measurement.

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References#

• Ghilani, C. D., & Wolf, P. R. (2012). Elementary Surveying: An Introduction to Geomatics (13th ed.). Pearson.
• National Geodetic Survey. (2021). Blueprint for the Modernized NSRS. NOAA/NGS.
• Zilkoski, D. B., Richards, J. H., & Young, G. M. (1992). Results of the General Adjustment of the North American Vertical Datum of 1988. ACSM Surveying and Land Information Systems, 52(3), 133--149.
• National Geodetic Survey. (1997). NOS NGS 58: Guidelines for Establishing GPS-Derived Ellipsoidal Heights. NOAA/NGS.
• National Geodetic Survey. (2008). NOS NGS 59: Guidelines for Establishing GPS-Derived Orthometric Heights. NOAA/NGS.
• Smith, D. A., & Roman, D. R. (2001). GEOID99 and G99SSS: 1-Arc-Minute Geoid Models for the United States. Journal of Geodesy, 75, 469--490.