temperature derivations
temperature from pressure and number density
symbol
description
unit
variable name
\(k\)
Boltzmann constant
\(\frac{kg m^2}{K s^2}\)
\(n\)
number density
\(\frac{molec}{m^3}\)
number_density {:}
\(p\)
pressure
\(Pa\)
pressure {:}
\(T\)
temperature
\(K\)
temperature {:}
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.
\[T = \frac{p}{kn}\]temperature from virtual temperature
symbol
description
unit
variable name
\(M_{air}\)
molar mass of total air
\(\frac{g}{mol}\)
molar_mass {:}
\(M_{dry\_air}\)
molar mass of dry air
\(\frac{g}{mol}\)
\(T\)
temperature
\(K\)
temperature {:}
\(T_{v}\)
virtual temperature
\(K\)
virtual_temperature {:}
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.
\[T = \frac{M_{air}}{M_{dry\_air}}T_{v}\]surface temperature from surface pressure and surface number density
symbol
description
unit
variable name
\(k\)
Boltzmann constant
\(\frac{kg m^2}{K s^2}\)
\(n_{surf}\)
surface number density
\(\frac{molec}{m^3}\)
surface_number_density {:}
\(p_{surf}\)
surface pressure
\(Pa\)
surface_pressure {:}
\(T_{surf}\)
surface temperature
\(K\)
surface_temperature {:}
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.
\[T_{surf} = \frac{p_{surf}}{kn_{surf}}\]