# Undulation of the geoid

(Redirected from Geoid undulation)

Undulation of the geoid is the height of the geoid relative to a given ellipsoid of reference. In maps and common use the height over the mean sea level (such as orthometric height) is used to indicate the height of elevations while the ellipsoidal height results from the GPS system.

The process of the undulation is not standardised, as different countries use different mean sea levels as reference but most commonly refers to the EGM96 geoid. Calculating the undulation factor is mathematically challenging. This is why many handheld GPS receivers have built-in undulation lookup tables[1] to determine the height above sea level.

The deviation ${\displaystyle N}$ between the ellipsoidal height ${\displaystyle h}$ and the orthometric height ${\displaystyle H}$ can be calculated by

${\displaystyle N=h-H}$

Likewise, the deviation ${\displaystyle \zeta }$ between the ellipsoidal height ${\displaystyle h}$ and the normal height ${\displaystyle H_{N}}$ can be calculated by

${\displaystyle \zeta =h-H_{N}}$

Geoid undulations display uncertainties which can be estimated by using several methods, i.e. least-squares collocation (LSC), fuzzy logic, artificial neutral networks, radial basis functions (RBF), and geostatistical techniques. Geostatistical approach has been defined as the most improved technique in prediction of geoid undulation.[2]

## References

1. ^ Wormley, Sam. "GPS Orthometric Height". www.edu-observatory.org. Archived from the original on 20 June 2016. Retrieved 15 June 2016.
2. ^ Chicaiza, E.G.; Leiva, C.A.; Arranz, J.J.; Buenańo, X.E. (2017-06-14). "Spatial uncertainty of a geoid undulation model in Guayaquil, Ecuador". Open Geosciences. 9 (1): 255–265. doi:10.1515/geo-2017-0021. ISSN 2391-5447.