partial pressure derivations
partial pressure from number density and temperature
symbol description unit variable name \(k\) Boltzmann constant \(\frac{kg m^2}{K s^2}\) \(n_{x}\) number density for air component x (e.g. \(n_{O_{3}}\)) \(\frac{molec}{m^3}\) <species>_number_density {:} \(p_{x}\) partial pressure for air component x (e.g. \(p_{O_{3}}\)) \(Pa\) <species>_partial_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.
\[p_{x} = n_{x}kT\]partial pressure from volume mixing ratio
symbol description unit variable name \(p\) pressure \(Pa\) pressure {:} \(p_{x}\) partial pressure for air component x (e.g. \(p_{O_{3}}\)) \(Pa\) <species>_partial_pressure {:} \(\nu_{x}\) volume mixing ratio for air component x (e.g. \(\nu_{O_{3}}\)) \(ppv\) <species>_volume_mixing_ratio {:} 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.
\[p_{x} = \nu_{x}p\]partial pressure from volume mixing ratio dry air
symbol description unit variable name \(p_{x}\) partial pressure for air component x (e.g. \(p_{O_{3}}\)) \(Pa\) <species>_partial_pressure {:} \(\bar{\nu}_{x}\) volume mixing ratio for air component x (e.g. \(\nu_{O_{3}}\)) \(ppv\) <species>_volume_mixing_ratio_dry_air {:} 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.
\[p_{x} = \bar{\nu}_{x}p_{dry\_air}\]