1.2 Datum and reference frames

Geodetic Datums

A geodetic datum is a reference framework that defines how positions are described on Earth's surface. Without a shared datum, coordinates from different surveys, GPS receivers, or map sources won't line up correctly. Every time you overlay two datasets in a GIS, the software needs to know what datum each one uses so it can place features in the right spot.

This section covers the core components of datums: ellipsoids, geoids, horizontal and vertical references, coordinate reference systems, transformations between datums, and how datums change over time.

Horizontal vs. Vertical Datums

Horizontal datums define the reference surface for latitude and longitude. They tell you where something is on the Earth's surface in two dimensions. WGS84 and NAD83 are the most common horizontal datums you'll encounter.

Vertical datums define the reference surface for elevation. They tell you how high something is. NAVD88 (used in North America) and EGM96 (a global geoid model) are widely used vertical datums.

In practice, horizontal and vertical datums work together to give you a full 3D position. A GPS receiver, for example, outputs coordinates in WGS84 (horizontal) and gives you an ellipsoidal height that you then convert to an orthometric height using a geoid model (vertical).

Importance of Datums in Geospatial Data

Datums make it possible to combine data from different sources. If one survey used NAD27 and another used NAD83, the same physical location will have slightly different coordinates in each dataset. Ignoring this difference can introduce positional errors of tens of meters or more.

Choosing the right datum matters for every application: cadastral surveying, topographic mapping, navigation, and infrastructure design all depend on coordinates that are consistent and accurate relative to a known reference.

Evolution of Datums Over Time

Early datums like NAD27 were built from ground-based triangulation surveys tied to a single origin point (Meades Ranch, Kansas). These worked well locally but accumulated errors over large distances.

Modern datums like WGS84 and the ITRF (International Terrestrial Reference Frame) are based on global satellite observations from GNSS, satellite laser ranging, and VLBI. They provide centimeter-level consistency worldwide. Datums are periodically updated as measurement techniques improve and as Earth's surface shifts due to tectonic motion.

Ellipsoids and Geoids

These are two different models of Earth's shape, and understanding the distinction between them is fundamental to working with datums and heights.

Ellipsoid Models of Earth's Shape

An ellipsoid (also called a reference ellipsoid) is a mathematically smooth surface that approximates Earth's overall shape as an oblate spheroid, slightly flattened at the poles and bulging at the equator.

An ellipsoid is defined by a few key parameters:

• Semi-major axis (a): the equatorial radius
• Semi-minor axis (b): the polar radius
• Flattening (f): describes how much the ellipsoid deviates from a perfect sphere, calculated as $f = \frac{a - b}{a}$

Common ellipsoids include WGS84 (used with GPS), GRS80 (nearly identical to WGS84, used with NAD83), and Clarke 1866 (the older ellipsoid behind NAD27).

Geoid Models of Earth's Gravity Field

The geoid is the equipotential surface of Earth's gravity field that most closely corresponds to mean sea level. Unlike the smooth ellipsoid, the geoid is lumpy and irregular because Earth's mass is unevenly distributed.

Geoid models are built from a combination of satellite gravity missions (like GRACE and GOCE), surface gravity measurements, and topographic data. EGM2008 and EIGEN-6C4 are examples of high-resolution global geoid models.

Relationship Between Ellipsoids and Geoids

The ellipsoid gives you a clean mathematical surface for calculations. The geoid captures the physical reality of gravity. The vertical distance between them at any point is called the geoid undulation (or geoid height), symbolized as $N$.

Geoid undulations vary across the globe and can range from roughly $-100$ m to $+100$ m depending on location and the ellipsoid used. This separation is what connects the two types of height measurement (ellipsoidal and orthometric), as described in the vertical datums section below.

Types of Geodetic Datums

Datums can be classified by their geographic scope and how they're realized.

Global vs. Regional Datums

Global datums like WGS84 and ITRF provide a single consistent reference frame for the entire planet. They're essential for satellite-based positioning, remote sensing, and any application that crosses national boundaries.

Regional datums like NAD83 (North America), ETRS89 (Europe), and GDA2020 (Australia) are optimized for a specific area. They often provide a better local fit to the geoid and maintain compatibility with existing national survey networks. The tradeoff is that they may not align perfectly with global datums at the centimeter level.

Examples of Commonly Used Datums

• WGS84: The World Geodetic System 1984, the native datum of GPS. Used globally for navigation and mapping.
• NAD83: The North American Datum 1983. The standard horizontal datum across the U.S., Canada, and Mexico.
• ETRS89: The European Terrestrial Reference System 1989. Fixed to the stable part of the Eurasian plate, so coordinates don't drift with plate motion.
• GDA2020: The Geocentric Datum of Australia 2020. Replaced GDA94 to correct for the ~1.8 m of northward plate motion Australia experienced since 1994.

Datum Transformations and Conversions

When you need to combine datasets referenced to different datums, you perform a datum transformation. Several methods exist:

• Simple shifts: Apply constant offsets in X, Y, Z (3-parameter).
• Similarity (Helmert) transformations: Apply translations, rotations, and a scale factor (7-parameter).
• Grid-based methods: Use a grid of known offsets to interpolate corrections at any point. NADCON (U.S.) and NTv2 (Canada, Australia, and others) are common grid-based approaches.

The right method depends on which datums are involved, the accuracy you need, and what transformation parameters are available.

Coordinate Reference Systems

A coordinate reference system (CRS) defines how numerical coordinates map to actual locations on Earth. It combines a datum with a coordinate system (either angular or projected).

Geographic Coordinate Systems

Geographic coordinate systems express positions as latitude and longitude, which are angular measurements relative to the equator and the prime meridian. The coordinates are in degrees (or decimal degrees) and are tied to a specific ellipsoid and datum.

WGS84, NAD83, and ETRS89 each define their own geographic CRS. Two points with the same lat/lon values but different geographic CRS will not be in the same physical location.

Projected Coordinate Systems

Projected coordinate systems take the curved Earth and flatten it onto a 2D plane so you can work in linear units like meters or feet. This involves a map projection, which always introduces some distortion.

Common projected CRS include:

• UTM (Universal Transverse Mercator): Divides the world into 60 zones, each 6° wide. Conformal (preserves angles).
• State Plane Coordinate System: Used in the U.S., with zones designed to minimize distortion within each state.
• Albers Equal Area: Preserves area, commonly used for thematic maps of large regions.

Your choice of projection depends on what property matters most (shape, area, distance, or direction) and the geographic extent of your project.

Importance of Choosing the Appropriate CRS

Using the wrong CRS can cause visible misalignment between layers, incorrect area or distance calculations, and confusion when sharing data. Always check the CRS of every dataset you bring into a project, and reproject as needed so everything is in a common system.

Documenting the CRS in your metadata is just as important as choosing the right one. If someone else can't tell what CRS your data uses, they can't use it reliably.

Datum Shifts and Transformations

Reasons for Datum Shifts

Datum shifts happen for several reasons:

• Better measurements: As satellite technology improves, the mathematical definition of a datum gets refined.
• Tectonic plate motion: Earth's plates move a few centimeters per year, gradually shifting the coordinates of fixed points.
• Updated reference frame realizations: The ITRF is updated periodically (e.g., ITRF2014, ITRF2020), and each update slightly changes the coordinates of reference stations.

Methods of Datum Transformations

1. Similarity (Helmert) transformations model the relationship between two datums using translations, rotations, and scale:

   • 3-parameter: Translation only ($\Delta X, \Delta Y, \Delta Z$).
   • 7-parameter: Adds three rotations and a scale factor.
   • 14-parameter: Adds time derivatives of all seven parameters, accounting for how the relationship changes over time.

2. Grid-based transformations interpolate corrections from a grid of known control points. NADCON handles NAD27-to-NAD83 conversions in the U.S., while NTv2 is used in Canada, Australia, and parts of Europe.

3. Geoid modeling is used alongside horizontal transformations when you also need to convert between vertical datums.

Accuracy Considerations in Transformations

Transformations between closely related datums (e.g., WGS84 and the latest realization of NAD83) can achieve sub-centimeter accuracy with good parameters. Transformations involving older datums like NAD27 are typically accurate to about 0.1–0.5 m because the original survey networks had lower precision and fewer control points.

Always report the expected accuracy of your transformation so downstream users know the limitations of the data.

Vertical Datums and Height Systems

Orthometric vs. Ellipsoidal Heights

Ellipsoidal height ($h$) is the distance from the ellipsoid surface to a point, measured along the ellipsoid normal. GPS receivers output this directly. It's a purely geometric quantity with no physical meaning tied to gravity or water flow.

Orthometric height ($H$) is the distance from the geoid to a point, measured along the plumb line. This is what most people mean by "elevation." Water flows from higher orthometric height to lower orthometric height, which is why engineering and hydrological applications require orthometric heights.

The relationship between them is:

$H = h - N$

where $N$ is the geoid undulation at that location.

Geoid Undulations and Deflections of the Vertical

Geoid undulations ($N$) are the height difference between the ellipsoid and the geoid at a given point. They're positive where the geoid sits above the ellipsoid and negative where it sits below. You need an accurate geoid model (like EGM2008 or GEOID18 in the U.S.) to convert GPS-derived ellipsoidal heights to usable orthometric heights.

Deflections of the vertical describe the angular difference between the direction of gravity (plumb line) and the ellipsoid normal. They have two components: $\xi$ (north-south) and $\eta$ (east-west). These matter in precise surveying and astronomical observations but are less commonly encountered in routine GIS work.

Vertical Datum Realizations and Benchmarks

Vertical datums are physically realized through networks of benchmarks, which are stable monuments with precisely determined elevations established through spirit leveling.

• NAVD88 (North American Vertical Datum of 1988) is the standard vertical datum in the U.S. and Canada.
• EVRF2007 (European Vertical Reference Frame 2007) covers Europe.
• AHD (Australian Height Datum) is used in Australia.

These realizations are periodically updated to correct for land subsidence, post-glacial rebound, and improved measurements.

Temporal Variations in Datums

Datums are not fixed forever. Earth's surface moves, and the reference frames that define datums must account for that motion.

Plate Tectonics and Crustal Deformation

Tectonic plates move at rates of a few centimeters per year. Australia, for instance, moves roughly 7 cm/year northward, which is why GDA94 coordinates drifted noticeably from reality over two decades, prompting the switch to GDA2020.

Beyond steady plate motion, sudden events like earthquakes can shift coordinates by meters in seconds. Volcanic activity and glacial isostatic adjustment (the slow rebound of land after ice sheets melt) also cause measurable vertical and horizontal changes.

Monitoring and Modeling Temporal Changes

• Continuously Operating Reference Stations (CORS): Networks of permanent GNSS receivers track position changes over time, producing velocity estimates for each station.
• InSAR (Interferometric Synthetic Aperture Radar): Compares radar images taken at different times to detect millimeter-level surface deformation over large areas.
• Geophysical models: Plate motion models (like NNR-MORVEL56) and deformation models predict how coordinates will change, allowing corrections to be applied.

Datum Stability and Maintenance

A datum is only useful if it stays accurate. Datum maintenance involves regularly updating station coordinates, refining transformation parameters, and sometimes adopting entirely new reference frame realizations.

For example, the ITRF is updated every few years (ITRF2008, ITRF2014, ITRF2020), with each version incorporating more data and better models. Regional datums tied to the ITRF inherit these improvements through updated transformations.

Datum Selection and Best Practices

Factors Influencing Datum Choice

When selecting a datum, consider:

• Geographic extent: A local project might use a regional datum; a multinational project needs a global one.
• Compatibility: What datum do your existing datasets and collaborators use?
• Accuracy requirements: High-precision geodetic work may require the latest ITRF realization, while a general web map can use WGS84.
• Legal or regulatory requirements: Many countries mandate a specific datum for cadastral or government mapping.
• Tooling: Make sure transformation parameters and software support are available for your chosen datum.

Datum Documentation and Metadata

Always record the datum in your project metadata. At minimum, document:

• Datum name and version (e.g., NAD83(2011), ITRF2014)
• Realization epoch (the date the coordinates are valid for)
• Ellipsoid parameters
• Any transformations applied to the data

Standardized metadata formats like ISO 19115 and FGDC provide structured ways to record this information so others can correctly interpret and reuse your data.

Future Trends and Developments in Datums

Satellite positioning is getting more precise with multi-GNSS constellations (GPS, GLONASS, Galileo, BeiDou) all contributing observations. This drives more frequent and more accurate reference frame updates.

Time-dependent reference frames are becoming the norm. Rather than treating coordinates as static, future datums will explicitly model how positions change over time, reducing the need for periodic "epoch updates."

International coordination through organizations like the International Association of Geodesy (IAG) and the UN Committee of Experts on Global Geospatial Information Management (UN-GGIM) is pushing toward globally harmonized datums, which will simplify cross-border data integration.