.]]
The is that Equipotential Surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were to be extended through the continents (such as with very narrow canals). According to C.F. Gauss , who first described it, it is the "mathematical figure of the Earth," a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive Gravitational measurements and calculations. Despite being an important concept for almost two hundred years in the history of geodesy, it has only been defined to high precision in recent decades. It is often described as the true physical Figure Of The Earth , in contrast to the idealized figure of a Reference Ellipsoid .
|
\overline{P}_{nm}(\sin\phi)\left
m\lambda+\overline{S}_{nm}\sin m\lambda
ight
ight),
where
and
are ''geocentric'' (spherical) latitude and longitude respectively,
are the fully normalized surface, and is somewhat involved to compute. The gradient of this potential also provides a model of the gravitational acceleration. EGM96 contains a full set of coefficients to degree and order 360, describing details in the global geoid as small as 55 km (or 110 km, depending on your definition of resolution). One can show there are
:
different coefficients (counting both
and
, and using the EGM96 value of
). For many applications the complete series is unnecessarily complex and is truncated after a few (perhaps several dozen) terms.
New even higher resolution models are currently under development. For example, many of the authors of EGM96 are working on an updated modelPavlis, N.K., S.A. Holmes. S. Kenyon, D. Schmit, R. Trimmer, "Gravitational potential expansion to degree 2160", ''IAG International Symposium, gravity, geoid and Space Mission GGSM2004'', Porto, Portugal, 2004. that will incorporate much of the new satellite gravity data (see, e.g.,
GRACE ), and will support up to degree and order 2160 (1/6 of a degree, requiring over 4 million coefficients).
