mass density derivations
mass density of air component from number 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.
\[\rho_{x} = \frac{10^{-3}n_{x}M_{x}}{N_{A}}\]mass density of total air from number 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.
\[\rho = \frac{10^{-3}n M_{air}}{N_{A}}\]mass density of air component from column mass density
symbol
description
unit
variable name
\(z^{B}(l)\)
altitude boundaries (\(l \in \{1,2\}\))
\(m\)
altitude_bounds {:,2}
\(\rho_{x}\)
mass density of air component x (e.g. \(\rho_{O_{3}}\))
\(\frac{kg}{m^3}\)
<species>_density {:}
\(\sigma_{x}\)
column mass density of air component x (e.g. \(c_{O_{3}}\))
\(\frac{kg}{m^2}\)
<species>_column_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.
\[\rho_{x} = \frac{\sigma_{x}}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]mass density of total air from dry air mass density and H2O mass density
symbol
description
unit
variable name
\(\rho\)
mass density
\(\frac{kg}{m^3}\)
density {:}
\(\rho_{dry\_air}\)
mass density of dry air
\(\frac{kg}{m^3}\)
dry_air_density {:}
\(\rho_{H_{2}O}\)
mass density of H2O
\(\frac{kg}{m^3}\)
H2O_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.
\[\rho = \rho_{dry\_air} + \rho_{H_{2}O}\]mass density of dry air from total air mass density and H2O mass density
symbol
description
unit
variable name
\(\rho\)
mass density
\(\frac{kg}{m^3}\)
density {:}
\(\rho_{dry\_air}\)
mass density of dry air
\(\frac{kg}{m^3}\)
dry_air_density {:}
\(\rho_{H_{2}O}\)
mass density of H2O
\(\frac{kg}{m^3}\)
H2O_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.
\[\rho_{dry\_air} = \rho - \rho_{H_{2}O}\]mass density of H2O from total air mass density and dry air mass density
symbol
description
unit
variable name
\(\rho\)
mass density
\(\frac{kg}{m^3}\)
density {:}
\(\rho_{dry\_air}\)
mass density of dry air
\(\frac{kg}{m^3}\)
dry_air_density {:}
\(\rho_{H_{2}O}\)
mass density of H2O
\(\frac{kg}{m^3}\)
H2O_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.
\[\rho_{H_{2}O} = \rho - \rho_{dry\_air}\]mass density of total air from column mass density
symbol
description
unit
variable name
\(z^{B}(l)\)
altitude boundaries (\(l \in \{1,2\}\))
\(m\)
altitude_bounds {:,2}
\(\rho\)
mass density of total air
\(\frac{kg}{m^3}\)
density {:}
\(\sigma\)
column mass density of total air
\(\frac{kg}{m^2}\)
column_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.
\[\rho = \frac{\sigma}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]