The distance measured perpendicular to the ellipsoid surface from a point on the Earth's surface to the ellipsoid.

Ellipsoidal Height

Definition

Ellipsoidal height, also known as geodetic height or geometric height, is the perpendicular distance from a point on or above the Earth's surface to the reference ellipsoid along the normal direction. This measurement is fundamental in modern surveying and geodetic positioning systems.

Relationship to Reference Ellipsoids

The ellipsoidal height is measured perpendicular to the selected reference ellipsoid, which serves as the mathematical model for the Earth's shape. Different reference systems use different ellipsoids, such as the WGS84 ellipsoid used in GPS and GNSS positioning. The choice of reference ellipsoid affects the calculated ellipsoidal heights.

Distinction from Orthometric Height

It is crucial to distinguish ellipsoidal height from orthometric height (also called elevation or altitude). Orthometric height is measured perpendicular to equipotential surfaces (level surfaces) following the direction of gravity. The difference between ellipsoidal height (h) and orthometric height (H) is the geoid undulation (N), expressed as: h = H + N.

The geoid undulation represents the separation between the ellipsoid and the geoid, which is an equipotential surface approximating mean sea level. This undulation varies across the Earth's surface and can reach values of ±100 meters in extreme cases.

Applications in Modern Surveying

Ellipsoidal height has become increasingly important with the widespread adoption of GNSS technology. Global Navigation Satellite Systems such as GPS provide direct measurements of ellipsoidal height with high accuracy. Modern surveying professionals must understand the relationship between ellipsoidal and orthometric heights for proper data interpretation.

Measurement Methods

Ellipsoidal heights are primarily determined through:

GNSS Positioning: Direct measurement using satellites with centimeter-level accuracy

Geometric Leveling Combined with Gravity Data: Converting orthometric heights to ellipsoidal heights using geoid models

Reference Station Networks: Utilizing established control networks with known ellipsoidal heights

Geoid Models

Accurate conversion between ellipsoidal and orthometric heights requires precise geoid models. Modern geoid models, such as EGM2008 (Earth Gravitational Model 2008) or regional variants, provide refined estimates of geoid undulation. These models are continuously improved through satellite gravity data and local gravity measurements.

Practical Considerations

In surveying projects, understanding ellipsoidal heights is essential for:

Establishing accurate vertical control networks

Integrating GNSS measurements with traditional surveying methods

Conducting precise engineering surveys

Developing digital elevation models

Water resource and drainage planning

Surveyors must consistently apply appropriate geoid models and document which reference system is used in their measurements.

Future Developments

As GNSS technology advances and becomes more accessible, ellipsoidal heights will continue to play a central role in surveying. Improved geoid models and higher-precision positioning contribute to more accurate vertical control in surveying operations worldwide.

Understanding ellipsoidal height is essential for modern surveyors working with contemporary positioning technologies and integrating multiple data sources in their professional practice.