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True Geopotential in Meteorology
  • Peter C Chu
Peter C Chu
Naval Postgraduate School

Corresponding Author:pcchu@nps.edu

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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.