number density derivations
number density of air component from mass density
symbol
description
unit
variable name
\(M_{x}\)
molar mass of air component x
\(\frac{g}{mol}\)
\(n_{x}\)
number density of air component x (e.g. \(n_{O_{3}}\))
\(\frac{molec}{m^3}\)
<species>_number_density {:}
\(N_A\)
Avogadro constant
\(\frac{1}{mol}\)
\(\rho_{x}\)
mass density of air component x (e.g. \(\rho_{O_{3}}\))
\(\frac{kg}{m^3}\)
<species>_density {:}
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.
\[n_{x} = \frac{\rho_{x}N_{A}}{10^{-3}M_{x}}\]number density of total air from mass density
symbol
description
unit
variable name
\(M_{air}\)
molar mass of total air
\(\frac{g}{mol}\)
molar_mass {:}
\(n\)
number density of total air
\(\frac{molec}{m^3}\)
number_density {:}
\(N_A\)
Avogadro constant
\(\frac{1}{mol}\)
\(\rho\)
mass density of total air
\(\frac{kg}{m^3}\)
density {:}
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.
\[n = \frac{\rho N_{A}}{10^{-3}M_{air}}\]number density of total air from pressure and temperature
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.
\[n = \frac{p}{kT}\]number density from volume mixing ratio
symbol
description
unit
variable name
\(n\)
number density of total air
\(\frac{molec}{m^3}\)
number_density {:}
\(n_{x}\)
number density of air component x (e.g. \(n_{O_{3}}\))
\(\frac{molec}{m^3}\)
<species>_number_density {:}
\(\nu_{x}\)
volume mixing ratio of air component x (e.g. \(n_{O_{3}}\))
\(ppv\)
<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.
\[n_{x} = \nu_{x}n\]number density from volume mixing ratio dry air
symbol
description
unit
variable name
\(n_{dry\_air}\)
number density of dry air
\(\frac{molec}{m^3}\)
dry_air_number_density {:}
\(n_{x}\)
number density of air component x (e.g. \(n_{O_{3}}\))
\(\frac{molec}{m^3}\)
<species>_number_density {:}
\(\bar{\nu}_{x}\)
volume mixing ratio of air component x (e.g. \(n_{O_{3}}\))
\(ppv\)
<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.
\[n_{x} = \bar{\nu}_{x}n_{dry\_air}\]number density of air component from column number density
symbol
description
unit
variable name
\(c_{x}\)
column number density of air component x (e.g. \(c_{O_{3}}\))
\(\frac{molec}{m^2}\)
<species>_column_number_density {:}
\(n_{x}\)
number density of air component x (e.g. \(n_{O_{3}}\))
\(\frac{molec}{m^3}\)
<species>_number_density {:}
\(z^{B}(l)\)
altitude boundaries (\(l \in \{1,2\}\))
\(m\)
altitude_bounds {:,2}
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.
\[n_{x} = \frac{c_{x}}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]number density of total air from dry air number density and H2O number density
symbol
description
unit
variable name
\(n\)
number density
\(\frac{molec}{m^3}\)
number_density {:}
\(n_{dry\_air}\)
number density of dry air
\(\frac{molec}{m^3}\)
dry_air_number_density {:}
\(n_{H_{2}O}\)
number density of H2O
\(\frac{molec}{m^3}\)
H2O_number_density {:}
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.
\[n = n_{dry\_air} + n_{H_{2}O}\]number density of dry air from total air number density and H2O number density
symbol
description
unit
variable name
\(n\)
number density
\(\frac{molec}{m^3}\)
number_density {:}
\(n_{dry\_air}\)
number density of dry air
\(\frac{molec}{m^3}\)
dry_air_number_density {:}
\(n_{H_{2}O}\)
number density of H2O
\(\frac{molec}{m^3}\)
H2O_number_density {:}
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.
\[n_{dry\_air} = n - n_{H_{2}O}\]number density of H2O from total air number density and dry air number density
symbol
description
unit
variable name
\(n\)
number density
\(\frac{molec}{m^3}\)
number_density {:}
\(n_{dry\_air}\)
number density of dry air
\(\frac{molec}{m^3}\)
dry_air_number_density {:}
\(n_{H_{2}O}\)
number density of H2O
\(\frac{molec}{m^3}\)
H2O_number_density {:}
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.
\[n_{H_{2}O} = n - n_{dry\_air}\]number density of total air from column number density
symbol
description
unit
variable name
\(c\)
column number density
\(\frac{molec}{m^2}\)
column_number_density {:}
\(n\)
number density
\(\frac{molec}{m^3}\)
number_density {:}
\(z^{B}(l)\)
altitude boundaries (\(l \in \{1,2\}\))
\(m\)
altitude_bounds {:,2}
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.
\[n = \frac{c}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]number density of air component from partial pressure and temperature
symbol
description
unit
variable name
\(k\)
Boltzmann constant
\(\frac{kg m^2}{K s^2}\)
\(n_{x}\)
number density of air component x (e.g. \(n_{O_{3}}\))
\(\frac{molec}{m^3}\)
<species>_number_density {:}
\(p_{x}\)
partial pressure of 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.
\[n_{x} = \frac{p_{x}}{kT}\]surface number density of total air from surface pressure and surface temperature
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.
\[n_{surf} = \frac{p_{surf}}{kT_{surf}}\]