True Geopotential in Meteorology

Geopotential in meteorology is the same as gravity potential in geodesy
but with the opposite sign. Meteorologists don’t use the true
geopotential (Φ) associated with the true gravity g =
i*g*_{λ}+j*g*_{φ}+k*g*_{z},
but use the normal geopotential (Φ_{N}) with the
normal gravity [-*g*(*φ*,*z*)K], or the standard
geopotential (Φ_{0}) with the standard gravity
(-*g*_{0}k, *g*_{0} = 9.81
^{} m/s^{2}). Here, (*λ*, *φ*,
*z*) are the (longitude, latitude, altitude) with (i, j, k/K) the
corresponding unit vectors with k/K normal to the Earth
spherical/ellipsoidal surface. In meteorology, difference between
Φ_{0} and Φ_{N} is considered minor but
between Φ_{0} and Φ has not been identified. This study
uses two publicly available datasets: (a) ICGEM EIGEN-6C4 and (b)
NCEP/NCAR Reanalysis long term mean data to obtain true geopotential Φ
and standard geopotential Φ_{0} for the troposphere (1000 -
100 hPa) and in turn to compute the nondimensional *B* and *C*
numbers, representing the importance of the latitudinal-longitudinal
gradient of disturbing geopotential (Φ-Φ_{0}) versus the
pressure gradient force and the Coriolis force. The *B* number
varies from 0.4176 (maximum) at 850 hPa to 0.1630 (minimum) at 200 hPa.
The *C* number varies from 0.6168 (maximum) at 1,000 hPa to 0.1573
(minimum) at 200 hPa. These values show the importance to use the true
geopotential Φ in meteorology. A new equation for the geostrophic wind
is also presented.