Next: 4 Nota Bene
Up: 3 Geoid Height, Step
Previous: 3.7 Fully normalized associated
Contents
Now you are have all the quantities you need to compute the geoid
undulation
as a function of geographical longitude
and
latitude
by the well-known formula (Heiskanen and Moritz, 1967)
![\begin{displaymath}\begin{split}N(\lambda,\varphi) = \frac{GM_{\mathrm{g}}}{\gam...
...n(m\lambda)\right] \bar{P}_{nm}(\sin\bar{\varphi}). \end{split}\end{displaymath}](img117.png) |
(30) |
Here,
and
are the spherical harmonic
coefficients of degree
and order
. Note that in this formula,
you need to use the mass gravity constant
and the
scale factor
of the geopotential model.
are the fully normalized harmonics,
or fully normalized associated Legendre functions. They are described
in the previous section (Section 3.7). Note that the
harmonics
are evaluated at the geocentric latitude
, and not at the geographical latitude
.
mlosch@awi-bremerhaven.de