Abstract
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 =
igλ+jgφ+kgz,
but use the normal geopotential (ΦN) with the
normal gravity [-g(φ,z)K], or the standard
geopotential (Φ0) with the standard gravity
(-g0k, g0 = 9.81
m/s2). 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
Φ0 and ΦN is considered minor but
between Φ0 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 Φ0 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-Φ0) 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.