Calculating Geoid Height
A geoid height is the ellipsoidal height from an ellipsoidal datum to a geoid. • Hence, geoid height models are directly tied to the geoid and ellipsoid that define them (i.e., geoid height models are not interchangeable).
Understanding the geoid and "height"
The geoid is one approximation of Earth's shape due to gravity, roughly coinciding with mean sea level. Because the inside of our planet is non-uniform, gravity is not constant at the surface. If Earth were completely covered in an ocean, the water would swell over gravity highs (where there is more mass below the surface) and depress in areas of gravity lows (where there is less mass below the surface). The geoid approximates this hypothetical ocean surface, representing a geopotential surface. To think of it another way, if we were able to walk on the geoid, we would experience a constant value of gravity.
The height of the geoid is often reported relative to the internationally recognized WGS84 reference ellipsoid. The GPS in our phones, for example, records elevations relative to this ellispoid. Sometimes, it is useful to know elevations relative to mean sea level—this is where the geoid height calculation comes in: to convert ellipsoidal heights to heights above the geoid (aka orthometric heights). The NGA (National Geospatial-Intelligence Agency) publishes models that describe the earth's gravitational field (see the Earth Gravitational Models here), and updates them as we learn more through satellite geodesy. It is becoming standard to use EGM2008 over its predecessors, but a 2020 model is soon to become standard.
Example
Understanding Geoid Height Calculation
Calculating geoid height is essential for determining the deviation of the Earth's surface from the reference ellipsoid. The geoid height represents the Earth's gravity field and is used in geodesy and navigation.
The key concepts of geoid height calculation include:
- Geoid Height: The difference between the reference ellipsoid and the Earth's geoid surface, indicating the elevation above or below the ellipsoid.
- Ellipsoid Height: The height above the reference ellipsoid at a specific location.
- Geoid height is crucial for precise measurements in surveying, mapping, and navigation.
Steps to Calculate Geoid Height
To calculate geoid height, follow these steps:
- Obtain the ellipsoid height at the location using GPS or other surveying methods.
- Obtain the geoid model data for the same location (usually through geodetic databases).
- Subtract the ellipsoid height from the geoid model height to find the geoid height.
Example: If the ellipsoid height from GPS data is 150 meters and the geoid model height is 145 meters, the geoid height is -5 meters, meaning the location is below the reference ellipsoid.
Methods for Calculating Geoid Height
Some common methods for calculating geoid height include:
- GPS and Ellipsoid Heights: Using GPS data to measure the ellipsoid height and subtracting it from geoid model data.
- Geoid Models: Using established geoid models like EGM2008 or WGS84 to estimate geoid heights based on geographical coordinates.
- Gravity Measurements: Using gravity data to compute geoid height in specific regions based on gravitational anomalies.
Factors Affecting Geoid Height Calculation
Several factors can influence the accuracy of geoid height calculations:
- Model Resolution: Higher resolution geoid models provide more accurate estimates of geoid height.
- GPS Accuracy: GPS measurements can have errors due to signal interference or incorrect settings.
- Regional Variations: Geoid height varies significantly across the Earth's surface, depending on local gravitational anomalies.
Example: Using a regional geoid model with better resolution may provide more accurate geoid height measurements in mountainous regions.
Applications of Geoid Height Calculation
Geoid height calculation is useful in various scenarios, such as:
- Improving accuracy in surveying and mapping applications.
- Enhancing the precision of GPS navigation systems.
- Assessing sea level rise and global warming effects based on geoid changes.
Example: Comparing geoid height measurements over time to assess the impact of glacier melting on local sea levels.
Common Operations in Geoid Height Calculation
When calculating geoid height, the following operations are common:
- Subtracting ellipsoid height from geoid model height to find the geoid height.
- Using specialized software or geodetic tools to compute and visualize geoid heights.
- Incorporating geoid height data into geophysical studies or engineering projects.
| Calculation Type | Description | Steps to Calculate | Example |
|---|---|---|---|
| Using GPS and Ellipsoid Heights | Calculating geoid height by comparing GPS-derived ellipsoid height with the local geoid model. |
|
If the GPS-derived ellipsoid height is 300 meters and the geoid model height is 290 meters, the geoid height is 10 meters. |
| Geoid Undulation Calculation | Calculating geoid height by determining the undulation of the geoid relative to the ellipsoid. |
|
A geoid undulation of -0.5 meters for a specific point results in a geoid height 0.5 meters below the ellipsoid at that location. |
| Satellite Altimetry | Using satellite altimetry data to calculate geoid height by measuring the distance between the satellite and the Earth's surface. |
|
Satellite data provides a sea surface height of 350 meters and an ellipsoid height of 345 meters, giving a geoid height of 5 meters. |
| Gravitational Potential Method | Using the Earth's gravitational potential to compute geoid height. |
|
A gravimetric study reveals that the gravitational potential at a specific point leads to a geoid height of 12 meters. |
