The Earth is commonly visualized as a sphere, but this simple geometric model is not accurate enough for precise scientific measurements. Earth’s true physical shape is defined by the geoid, a concept that accounts for the planet’s uneven mass distribution and gravitational pull. This irregular, gravity-based surface is the actual reference for determining elevations. Understanding the geoid is fundamental for geodesy, the science of measuring Earth’s shape, orientation, and gravity field, and explains why high-accuracy positioning systems require more than just a geometric model.
Defining the Earth’s Geoid
The geoid is formally defined as the equipotential surface of the Earth’s gravity field that best fits the mean sea level across the globe. This means the combined effect of gravity and the centrifugal force from Earth’s rotation is exactly the same at every point on this surface. If the oceans were completely at rest, free from tides, currents, and winds, the surface of that hypothetical global ocean would trace the geoid.
Because the density of the Earth’s interior is not uniform, gravity varies across the surface, causing the geoid to be an irregular shape. Areas with higher mass density, such as mountain roots, exert a stronger gravitational pull, causing the geoid surface to bulge outward. Conversely, regions with a mass deficit, like deep ocean trenches, have weaker gravity, causing the geoid to dip inward. This uneven surface is often visualized as a “lumpy potato,” though deviations from a smooth shape are only up to about 100 meters globally.
The geoid extends seamlessly under the continents, following the path dictated by the gravitational potential beneath the landmasses. The direction of gravity, or the local “down,” is always perpendicular to the geoid surface. This physical property makes the geoid the natural reference for all gravity-based height measurements.
Geoid Compared to the Ellipsoid
Distinguishing the geoid from the ellipsoid is central to understanding modern positioning. The ellipsoid is a smooth, mathematically defined, flattened sphere that serves as a simple, geometric model of the Earth. It is defined by a few parameters, making it easy to use for calculating horizontal coordinates like latitude and longitude. Systems like the Global Positioning System (GPS) use an ellipsoid (e.g., WGS 84) as their reference surface for calculating position and geometric height.
In contrast, the geoid is a physical surface based on gravity, which is irregular and cannot be represented by a simple mathematical formula. The height measured by GPS is the ellipsoidal height, which is the geometric distance above the smooth ellipsoid. This height is not intuitive for real-world applications because it does not follow the direction of gravity. Therefore, both the smooth ellipsoid and the irregular geoid are needed for accurate mapping.
The key link between these two surfaces is the geoid height, also known as geoidal separation or undulation. This value is the vertical distance between the geoid and the ellipsoid at any given location. Geoid heights can range from approximately -100 meters to +100 meters worldwide. This separation value allows scientists to convert a purely geometric GPS height into a useful, gravity-based elevation.
Methods Used to Determine the Geoid
Scientists map and model the geoid by collecting highly accurate measurements of the Earth’s gravitational field. One traditional method involves ground-based gravity surveys, or gravimetry, where instruments measure the local acceleration due to gravity at many points on the Earth’s surface. These terrestrial measurements provide high-resolution data for local areas but are time-consuming and expensive to conduct globally.
For a global and uniform model, satellite missions have become indispensable for measuring gravitational variations. Missions like the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady-state Ocean Circulation Explorer (GOCE) have provided unprecedented data. GRACE mapped the long-wavelength features of the geoid by measuring subtle changes in the distance between two satellites caused by gravitational variations below them. GOCE provided a high-resolution map of the static geoid using a sensitive satellite gravity gradiometer.
The data from these sources are combined and processed to create global geopotential models, such as EGM2008, which are mathematical representations of the Earth’s gravity field. These models express the field as a series of spherical harmonic coefficients, allowing for the precise calculation of the geoid height at any point on the globe. The accuracy of these models is constantly being refined as new data from satellite and ground-based sources become available.
Practical Uses of the Geoid in Measurement
The most significant practical application of the geoid is its role as the foundation for vertical datums, or height systems. Engineering, construction, and public works require elevation measurements that relate to the flow of water, which follows gravity. The geoid, being a surface of equal gravitational potential, inherently provides this necessary reference.
While GPS provides a height above the smooth ellipsoid (ellipsoidal height), this is not the elevation most people use. The elevation above the geoid is known as the orthometric height, which is the modern, precise equivalent of “height above mean sea level.” The geoid model acts as the conversion factor that translates the geometric GPS height into the usable orthometric height.
The relationship is expressed simply as: Orthometric Height = Ellipsoidal Height – Geoid Height. By subtracting the modeled geoid height from the GPS-derived ellipsoidal height, surveyors can quickly and accurately determine the elevation relative to the gravity-based vertical datum. This process makes the geoid model an indispensable tool for modern infrastructure projects and accurate geospatial data collection.