geopotential derivations

1. geopotential from geopotential height

   symbol	description	unit	variable name
   \(g_{0}\)	mean earth gravity	\(\frac{m}{s^2}\)
   \(z_{g}\)	geopotential height	\(m\)	geopotential_height {:}
   \(\Phi\)	geopotential	\(\frac{m^2}{s^2}\)	geopotential {:}

   The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

   \[\Phi = g_{0}z_{g}\]

2. surface geopotential from surface geopotential height

   symbol	description	unit	variable name
   \(g_{0}\)	mean earth gravity	\(\frac{m}{s^2}\)
   \(z_{g,surf}\)	surface geopotential height	\(m\)	surface_geopotential_height {:}
   \(\Phi_{surf}\)	surface geopotential	\(\frac{m^2}{s^2}\)	surface_geopotential {:}

   The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

   \[\Phi_{surf} = g_{0}z_{g,surf}\]