Spheroid / Ellipsoid
While we are familiar with perfectly spherical representations of the Earth, it may prove surprising to learn that the Earth is more of an oblate spheroid, in simple terms a squashed sphere bulging at the equator, due to the centripetal force of rotating on its axis:
More accurately still, Earth can also be depicted as a rather lumpy rock:
Earth's geoid is a calculated surface of equal gravitational potential energy, representing the shape the sea surface would be if the ocean were not in motion. The geoid is the shape that the ocean surface would take under the influence of the gravity (not a consistent 9.81 m/s²) and rotation of Earth alone, if other influences such as winds and tides (gravitational effects of the Moon and Sun) were absent.
Undulation or geoidal separation is the distance in between the Spheroid and Geoid as illustrated below (undulation is the value - Ngeoid). Undulation is the result of several phenomena but is primarily caused by variations in earth's gravitational field. Denser areas of the earth have stronger gravitational pull and vice-versa.
In the example NMEA GGA string below, 39.65 Metres is the height of the GPS antenna above the Ellipsoid and 8.54 Metres is the Geoid - Ellipsoid separation (undulation).
Figure 3 - Undulation
In the example NMEA GGA string below 39.65 Metres is the height of the GPS antenna above the Ellipsoid & 8.54 Metres is the Geoid - Ellipsoid separation (undulation):
It is not practical to represent undulation as a mathematical formulae (unlike spheroids), undulation is measured and and tabulated as a model. Geoidal models of the earth are often created represented at equally spaced intervals. Current Veripos products and services use either EGM96 or EGM08 models. EGM96 has a spatial resolution of 15 minutes ( approx. 37 million values) and EGM08 2.5 minutes (approx 1.5 million values). The table below details which EGM model is used for each Veripos product: