PS Exam Preparation

Comprehensive preparation for the NCEES Principles and Practice of Surveying (PS) exam. 5 modules covering all 5 exam domains with 50 in-depth topics.

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Lesson 3

Datums, Reference Frames & Equipment

Learning Objectives

After completing this topic, you should be able to:

Define and distinguish between horizontal and vertical geodetic datums
Explain the development and characteristics of NAD 27 and NAD 83
Describe the differences between NGVD 29 and NAVD 88
Identify the role of WGS 84, ITRF, and GRS 80 in modern surveying
Explain why datum transformations are necessary and how they are performed
Describe the equipment used for geodetic control surveys
Understand the relationship between ellipsoid heights, geoid heights, and orthometric heights

Overview

A geodetic datum defines the reference framework used to express positions on or near the Earth's surface. Horizontal datums establish the basis for latitude/longitude and plane coordinates; vertical datums establish the basis for elevations. Every survey measurement is referenced to a datum, and mixing datums or applying the wrong datum transformation is a common source of significant error.

The PS exam tests your understanding of the major datums used in the United States, their historical development, their relationships to each other, and the practical implications of datum selection and transformation.

Key Concepts

Figure PS.5.3 — Datum Relationships: Ellipsoid, Geoid, and Earth Surface

What Is a Datum?

A datum consists of:

A reference surface -- An ellipsoid (for horizontal datums) or a geoid/tidal surface (for vertical datums)
An origin -- A defined starting point or set of constraints
A realization -- The physical network of control stations whose published coordinates define the datum in practice

Changing the datum changes the coordinates of every point, even though nothing has physically moved on the ground.

Horizontal Datums

NAD 27 (North American Datum of 1927)

Characteristic	Value
Reference ellipsoid	Clarke 1866
Origin	Meades Ranch, Kansas (fixed point)
Adjustment	Piecemeal, over many decades
Coordinate system	Latitude/longitude; State Plane (US feet)
Limitations	Distortions accumulate away from origin; inconsistent adjustments

NAD 27 was the standard horizontal datum for the U.S. for over 50 years. Its key limitations include:

Fixed origin at Meades Ranch created systematic distortions across the continent
The Clarke 1866 ellipsoid does not fit the Earth as well as modern ellipsoids
Piecemeal adjustments over decades introduced internal inconsistencies
No direct compatibility with satellite positioning systems

Many older survey records, deeds, and plats reference NAD 27 coordinates. Surveyors must recognize when working with NAD 27 data and apply appropriate transformations.

NAD 83 (North American Datum of 1983)

Characteristic	Value
Reference ellipsoid	GRS 80 (Geodetic Reference System 1980)
Origin	Earth's center of mass (geocentric)
Adjustment	Simultaneous continental adjustment
Coordinate system	Latitude/longitude; State Plane (meters or US feet)
Realizations	NAD 83 (1986), HARN, CORS96, 2007, 2011, etc.

NAD 83 replaced NAD 27 to provide a geocentric, satellite-compatible datum. Important characteristics:

Geocentric origin eliminates the distortions caused by NAD 27's single fixed origin
GRS 80 ellipsoid provides a better global fit than Clarke 1866
Multiple realizations reflect improvements in the control network over time
NAD 83 (2011) is the current realization, based on the most recent CORS positions

NAD 83 realizations differ from each other. NAD 83 (1986) coordinates can differ from NAD 83 (2011) coordinates by up to 1 meter at the same physical point. Always specify which realization you are using.

Relationship Between NAD 27 and NAD 83

The shift from NAD 27 to NAD 83 at any given point varies geographically but is typically:

Approximately 10 to 100 meters in the continental U.S.
Not a simple uniform shift -- the magnitude and direction vary by location
NGS provides the NADCON tool for transforming between NAD 27 and NAD 83

Vertical Datums

NGVD 29 (National Geodetic Vertical Datum of 1929)

Characteristic	Value
Reference surface	Mean sea level at 26 tidal gauging stations
Adjustment	Simultaneous adjustment of leveling networks in 1929
Also known as	Sea Level Datum of 1929 (original name)
Limitations	Held sea level fixed at 26 stations; sea level is not level

NGVD 29 was established by holding mean sea level fixed at 26 tide gauge stations along the Atlantic, Pacific, and Gulf coasts. This creates a fundamental problem: mean sea level is not at the same elevation at all locations due to ocean currents, temperature, salinity, and other factors. By forcing mean sea level to the same zero value at all 26 stations, systematic distortions were introduced into the leveling network.

NAVD 88 (North American Vertical Datum of 1988)

Characteristic	Value
Reference surface	Helmert orthometric heights, single tidal benchmark
Origin	Father Point/Rimouski, Quebec (single primary tidal benchmark)
Adjustment	Simultaneous adjustment of 625,000 km of leveling
Improvement	Eliminates multi-station sea level forcing of NGVD 29

NAVD 88 improved upon NGVD 29 by:

Using a single tidal benchmark (Father Point, Quebec) instead of 26 stations
Incorporating 625,000 km of leveling data in a simultaneous adjustment
Including Canadian and Mexican leveling data for continental consistency
Eliminating the systematic distortions caused by forcing sea level at multiple stations

Differences between NGVD 29 and NAVD 88:

Vary by location from approximately -40 cm to +150 cm across the U.S.
Are NOT a constant offset -- they change geographically
NGS provides the VERTCON tool for transforming between NGVD 29 and NAVD 88
Many older benchmark datasheets show both NGVD 29 and NAVD 88 elevations

Global Reference Frames and Ellipsoids

WGS 84 (World Geodetic System 1984)

Developed by the U.S. Department of Defense for the GPS system
Geocentric datum, regularly updated to align with ITRF
For most practical surveying purposes, WGS 84 and NAD 83 are nearly identical (within 1-2 meters)
GPS receivers natively report positions in WGS 84

Common wrong path — "WGS 84 = NAD 83" for survey work. It is true that WGS 84 and NAD 83 coincide within 1-2 meters, which makes them effectively interchangeable for navigation, GIS, and many recreational applications. But for survey-grade work, the 1-2 meter difference matters enormously. A modern RTK survey achieving centimeter precision on WGS 84 coordinates, if labeled as "NAD 83" without proper transformation, would be positioning points that are actually 1-2 meters from the correct NAD 83 location — orders of magnitude worse than the positioning precision. Students who answer "they're the same" on the exam are wrong for surveying contexts. They are close enough for navigation; they are NOT interchangeable for control, boundary, or ALTA-grade work. Always check the reported datum and apply the correct transformation when moving between them for precise applications.

Quick retrieval check — try before reading on.

▶A surveyor collects RTK observations that produce coordinates in WGS 84 with a stated precision of 2 cm. The project requires NAD 83 (2011) coordinates. How does the surveyor handle the datum difference, and why is "they're the same" an unacceptable answer?

Apply an explicit transformation from WGS 84 to NAD 83 (2011) — don't rely on "they're the same."

At the 1-2 meter scale, WGS 84 and NAD 83 look identical. At the 2-cm scale the surveyor is achieving, they are not. The correct procedure depends on the GNSS system and processing approach:

If using a CORS/RTN network that publishes its base station coordinates in NAD 83 (2011), the rover's "WGS 84" output is actually computed relative to those NAD 83 bases and is already effectively NAD 83 (2011) — no further transformation needed. Confirm with the network provider.
If using a true global WGS 84 or ITRF base (e.g., IGS station, satellite-based correction service like Trimble CenterPoint or Hexagon HxGN), the output is in the ITRF/WGS 84 frame and must be transformed to NAD 83 (2011) — typically using NGS's HTDP (Horizontal Time-Dependent Positioning) tool, which accounts for tectonic plate motion between the ITRF observation epoch and the NAD 83 reference epoch.
If the surveyor simply labels WGS 84 coordinates as "NAD 83" without transformation, every point is about 1-2 meters off in the horizontal position — unacceptable for any survey-grade application.

The "they're the same" answer might be correct for a GPS navigation question but is wrong for any surveying scenario that specifies "NAD 83 (2011)" as the required deliverable datum. Always transform, or confirm that the RTN/CORS provider has already performed the transformation.

ITRF (International Terrestrial Reference Frame)

Maintained by the International Earth Rotation and Reference Systems Service (IERS)
The most accurate global reference frame available
Regularly updated (ITRF2014, ITRF2020, etc.)
Accounts for plate tectonics, so coordinates change over time (epoch-dependent)
NAD 83 is fixed to the North American plate; ITRF is not

GRS 80 (Geodetic Reference System 1980)

The reference ellipsoid for NAD 83
Defined by four parameters: semi-major axis, flattening, angular velocity, gravitational constant

Parameter	GRS 80 Value
Semi-major axis (a)	6,378,137.0 m
Flattening (1/f)	298.257222101

GRS 80 and WGS 84 ellipsoids are nearly identical -- the difference in flattening produces a maximum difference of approximately 0.1 mm at the poles

Ellipsoid Height, Geoid Height, and Orthometric Height

This relationship is fundamental to understanding how GNSS-derived heights relate to traditional leveling:

h = H + N

Where:

h = Ellipsoid height (geometric height above the ellipsoid, measured by GNSS)
H = Orthometric height (height above the geoid, the "elevation" used in practice)
N = Geoid height (separation between the ellipsoid and the geoid at that location)

Practical implications:

GNSS measures ellipsoid heights directly
Orthometric heights (elevations) require a geoid model to convert from ellipsoid heights
NGS publishes geoid models (GEOID18, etc.) for this conversion
In the continental U.S., the geoid is approximately 10 to 53 meters below the GRS 80/NAD 83 ellipsoid (N is negative)
Ignoring the geoid undulation when using GNSS heights can introduce errors of tens of meters

Equipment for Geodetic Control Surveys

Classical methods:

Theodolites and total stations for angle measurement (triangulation, traversing)
Electronic distance measurement (EDM) instruments for trilateration
Precise levels and invar rods for differential leveling
Barometers and thermometers for atmospheric corrections

Modern methods:

Dual-frequency GNSS receivers for satellite positioning
GNSS antennas with known phase center offsets
Real-time kinematic (RTK) base stations and rovers
Networked CORS for post-processing and real-time corrections
Digital levels with bar-code rods for precise leveling

Datum Transformations

When combining data from different datums, transformations are required:

Transformation	Tool	Application
NAD 27 to NAD 83	NADCON	Horizontal datum conversion
NGVD 29 to NAVD 88	VERTCON	Vertical datum conversion
NAD 83 to ITRF	HTDP (Horizontal Time Dependent Positioning)	Epoch-dependent conversion
WGS 84 to NAD 83	Direct (nearly identical for most practical work)	GPS to NAD 83
Ellipsoid to orthometric	Geoid model (GEOID18)	GNSS height conversion

Key warning: Never assume datums are interchangeable. Even small datum differences can produce significant coordinate shifts.

Exam Tips

Memorize the key facts: NAD 27 uses Clarke 1866 ellipsoid, origin at Meades Ranch; NAD 83 uses GRS 80 ellipsoid, geocentric origin
NGVD 29 used 26 tidal gauging stations; NAVD 88 uses a single primary tidal benchmark (Father Point, Quebec)
The relationship h = H + N is critical: ellipsoid height = orthometric height + geoid height
NAD 83 has multiple realizations -- coordinates at the same point differ between realizations by up to 1 meter
GRS 80 and WGS 84 ellipsoids are nearly identical for practical purposes
NADCON transforms between NAD 27 and NAD 83; VERTCON transforms between NGVD 29 and NAVD 88
ITRF is epoch-dependent (accounts for plate tectonics); NAD 83 is plate-fixed (does not)
In the U.S., the geoid undulation (N) is negative, meaning the geoid is below the ellipsoid