The vertical distance from a point on the Earth's surface perpendicular to the reference ellipsoid measured along the normal line.

Ellipsoidal Height

Definition and Concept

Ellipsoidal height, also known as geodetic height or geometric height, is a fundamental measurement in modern surveying and geodesy. It represents the perpendicular distance from a point on or above the Earth's surface to the reference ellipsoid along the ellipsoid normal—an imaginary line perpendicular to the ellipsoid's surface at a given location.

Relationship to Other Height Systems

Ellipsoidal height differs from orthometric height (elevation), which measures distance vertically upward according to the direction of gravity. The difference between these two measurements is the geoid undulation, or N value. The mathematical relationship is expressed as:

h = H + N

Where:

h = ellipsoidal height

H = orthometric height (elevation above sea level)

N = geoid undulation

This distinction is critical for surveyors and engineers working with GPS/GNSS technology, which inherently measures ellipsoidal heights.

Modern Applications

With the widespread adoption of satellite positioning systems like GPS, GLONASS, and Galileo, ellipsoidal heights have become increasingly important in surveying practice. GNSS receivers directly provide coordinates in three dimensions, including ellipsoidal height relative to a reference ellipsoid (typically WGS84).

Reference Ellipsoids

Different reference ellipsoids are used globally depending on regional and national surveying standards. Common examples include:

WGS84 (World Geodetic System 1984): Used internationally and by GPS

GRS80 (Geodetic Reference System 1980): Basis for many national systems

NAD83: Used in North America

ETRS89: Used in Europe

Each ellipsoid has specific parameters defining its shape, size, and orientation relative to Earth's center.

Practical Surveying Considerations

Surveyors must carefully convert between ellipsoidal heights and orthometric heights for many applications. This requires accurate geoid models, which are continuously refined through satellite gravity measurements and ground surveys. Modern geoid models like EGM2008, EGM2020, and regional variations provide undulation values at specific locations.

Vertical Datum Transformations

In jurisdictions with established vertical datums based on mean sea level, surveyors must apply appropriate transformations to convert GNSS-derived ellipsoidal heights to project-required orthometric heights. This process involves:

1. Obtaining accurate geoid undulation values for the project area 2. Applying corrections for local vertical datums 3. Validating results through spirit leveling connections where necessary

Technical Advantages

Ellipsoidal heights offer several advantages in modern surveying:

Direct GNSS measurement: Satellite positioning systems directly provide ellipsoidal heights

Three-dimensional positioning: Enables complete 3D coordinate determination

Global consistency: Same reference system worldwide

Automation compatibility: Easily integrated into surveying software and GIS systems

Challenges and Limitations

While powerful, ellipsoidal heights present challenges including the need for accurate geoid models, sensitivity to reference ellipsoid selection, and the requirement for transformation to traditional orthometric heights in many applications.

Conclusion

Ellipsoidal height represents a crucial bridge between traditional surveying practices and modern satellite-based positioning technology. Understanding its relationship to orthometric height and proper application of geoid models ensures accurate and reliable three-dimensional surveying in contemporary practice.