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# Compute Geoid Height

### Earth Gravitational Model

The gravitational equipotential surface approximately coinciding with meas sea level is called the geoid. The tool named “EGM” uses to compute the height of the geoid above the WGS84 ellipsoid using interpolation in a grid of values for the geopotential (earth gravity) models: EGM96 and EGM2008. They are supplied by the U.S. National Geospatial-Intelligence Agency (NGA) EGM Development Team. This geopotential models’s detailed description are as the followings:

• EGM96 stands for Earth Gravitioanl Model 1996. This model uses a 15-minute grid of point values in the tide-free system.  This tool is designed for the calculation of a geoid undulation at a point whose latitude and longitude is specified. The tool  use the potential coefficient model EGM96 and a set of spherical harmonic coefficients of a correction term (“CORRCOEF“).
• EGM2008 stands for Earth Gravitational Model 2008. The EGM2008 model has a cell size of 2.5 x 2.5 minute, resulting in a grid of 4321 rows x 8640 columns containing 4 byte IEEE float values defining the difference between the WGS84 ellipsoid height and Mean Sea Level (MSL).

The height of the geoid above the ellipsoid, N, is sometimes called the geoid undulation or geoid separation. It can be used to convert a height above the ellipsoid, h, to the corresponding height above the geoid (the orthometric height, roughly the height above mean sea level), H, using the relations

h = N + H; H = −N + h.

### Compute Geoid Height

When you start the Surveyor Pocket Tools, on the main window you will see the tool named “EGM“. Double click the tool to run and the small handy window is displayed as the screenshot below. On the top there is a selection of “EGM Model” that there are only two models: EGM96 and EGM2008, default is EGM2008. Below the “EGM Model“, there are text boxes use to input the coordinate value to be computed the geoid height. The geodetic coordinates must be based on WGS84. The angle display format can be defined to degree decimal, DDºMM’SS.SSSS” or DDºMM.MMMM’. On the right side is a result of geoid height from computation. On the middle of the window there is a button is denoted to”Compute” the geoid height from given geodetic coordinates.

#### Define Angle Display Formats and Input Geodetic Coordinates

There are many possible display formats for geographic or geodetic coordinates (latitude/longitude). Follow the link below for tutorial how to define the settings.

How to define angle display formats and input geodetic coordinates?

If you need to save a input or output point into database called Geo Database. Please follow the tutorial link:

How to use Geo Database?

#### Example

Given:

Point name “GC-503”, latitude = 14°36’47.6521″N, longitude = 98°1’34.78727″E, this geodetic coordinates are based on WGS84. Find the geoid height on “EGM2008” and “EGM96” model.

Enter the coordinate values as the screenshot below. Click the button to calculate. The geoid height will be displayed on the text box on the right side. The geoid height of the given point is -38.944 m. On the same geodetic coordinates change the “EGM Model” to “EGM96” then click to compute the geoid height. The result is -38.563 m. The difference results between two models is ±0.381 m. You can pin the marker to the Google Maps or Google Earth if you want to know its location by click and respectively. if you want to store the coordinates into the Geo Database just click the icon or click when you want to display and restore coordinate from Geo Database.

#### Conclusion

The EGM tool is a small and handy tool uses to calculate the geoid heigh on the EGM96 & EGM2008 model.