temperature derivations

  1. 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.

    \[T = \frac{p}{kn}\]

  2. 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.

    \[T = \frac{M_{air}}{M_{dry\_air}}T_{v}\]

  3. 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.

    \[T_{surf} = \frac{p_{surf}}{kn_{surf}}\]