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\begin{document}

\title{True Geopotential in Meteorology}



\author[1]{Peter C Chu}%
\affil[1]{Naval Postgraduate School}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
Geopotential in meteorology is the same as gravity potential in geodesy
but with the opposite sign. Meteorologists don't use the true
geopotential (\selectlanguage{greek}Φ\selectlanguage{english}) associated with the true gravity g =
i\selectlanguage{greek}\emph{g\textsubscript{λ}}\selectlanguage{english}+j\selectlanguage{greek}\emph{g\textsubscript{φ}}\selectlanguage{english}+k\emph{g\textsubscript{z}},
but use the normal geopotential (\selectlanguage{greek}Φ\selectlanguage{english}\emph{\textsubscript{N}}) with the
normal gravity {[}-\emph{g}(\selectlanguage{greek}\emph{φ},\selectlanguage{english}\emph{z})K{]}, or the standard
geopotential (\selectlanguage{greek}Φ\selectlanguage{english}\textsubscript{0}) with the standard gravity
(-\emph{g}\textsubscript{0}k, \emph{g}\textsubscript{0} = 9.81
\textsuperscript{} m/s\textsuperscript{2}). Here, (\selectlanguage{greek}\emph{λ}, \selectlanguage{english}\selectlanguage{greek}\emph{φ},
\selectlanguage{english}\emph{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
\selectlanguage{greek}Φ\selectlanguage{english}\textsubscript{0} and \selectlanguage{greek}Φ\selectlanguage{english}\emph{\textsubscript{N}} is considered minor but
between \selectlanguage{greek}Φ\selectlanguage{english}\textsubscript{0} and \selectlanguage{greek}Φ \selectlanguage{english}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 \selectlanguage{greek}Φ
\selectlanguage{english}and standard geopotential \selectlanguage{greek}Φ\selectlanguage{english}\textsubscript{0} for the troposphere (1000 -
100 hPa) and in turn to compute the nondimensional \emph{B} and \emph{C}
numbers, representing the importance of the latitudinal-longitudinal
gradient of disturbing geopotential (\selectlanguage{greek}Φ-Φ\selectlanguage{english}\textsubscript{0}) versus the
pressure gradient force and the Coriolis force. The \emph{B} number
varies from 0.4176 (maximum) at 850 hPa to 0.1630 (minimum) at 200 hPa.
The \emph{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 \selectlanguage{greek}Φ \selectlanguage{english}in meteorology. A new equation for the geostrophic wind
is also presented.%
\end{abstract}%



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\textbf{Hosted file}

\verb`essoar.10508710.1.docx`  available at \url{https://authorea.com/users/510118/articles/598585-true-geopotential-in-meteorology}

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