mass mixing ratio derivations
mass mixing ratio from mass density
symbol
description
unit
variable name
\(\rho\)
mass density of total air
\(\frac{kg}{m^3}\)
density {:}
\(\rho_{x}\)
mass density of air component x (e.g. \(\rho_{O_{3}}\))
\(\frac{kg}{m^3}\)
<species>_density {:}
\(q_{x}\)
mass mixing ratio of air component x with regard to total air
\(\frac{kg}{kg}\)
<species>_mass_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.
\[q_{x} = \frac{\rho_{x}}{\rho}\]mass mixing ratio from volume mixing ratio
symbol
description
unit
variable name
\(M_{air}\)
molar mass of total air
\(\frac{g}{mol}\)
molar_mass {:}
\(M_{x}\)
molar mass of air component x
\(\frac{g}{mol}\)
\(q_{x}\)
mass mixing ratio of quantity x with regard to total air
\(\frac{kg}{kg}\)
<species>_mass_mixing_ratio {:}
\(\nu_{x}\)
volume mixing ratio of quantity x with regard to total air
\(ppv\)
<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.
\[q_{x} = \nu_{x}\frac{M_{x}}{M_{air}}\]mass mixing ratio from mass mixing ratio dry air
symbol
description
unit
variable name
\(q_{x}\)
mass mixing ratio of air component x with regard to total air
\(\frac{kg}{kg}\)
<species>_mass_mixing_ratio {:}
\(q_{dry\_air}\)
mass mixing ratio of dry air with regard to total air
\(\frac{kg}{kg}\)
dry_air_mass_mixing_ratio {:}
\(\bar{q}_{x}\)
mass mixing ratio of air component x with regard to dry air
\(\frac{kg}{kg}\)
<species>_mass_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.
\[q_{x} = \bar{q}_{x}q_{dry\_air}\]mass mixing ratio dry air from mass density
symbol
description
unit
variable name
\(\rho_{dry\_air}\)
mass density of dry air
\(\frac{kg}{m^3}\)
dry_air_density {:}
\(\rho_{x}\)
mass density of air component x (e.g. \(\rho_{O_{3}}\))
\(\frac{kg}{m^3}\)
<species>_density {:}
\(\bar{q}_{x}\)
mass mixing ratio if air component x with regard to dry air
\(\frac{kg}{kg}\)
<species>_mass_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.
\[q_{x} = \frac{\rho_{x}}{\rho_{dry\_air}}\]mass mixing ratio dry air from volume mixing ratio dry air
symbol
description
unit
variable name
\(M_{dry\_air}\)
molar mass of dry air
\(\frac{g}{mol}\)
\(M_{x}\)
molar mass of air component x
\(\frac{g}{mol}\)
\(\bar{q}_{x}\)
mass mixing ratio of quantity x with regard to dry air
\(\frac{kg}{kg}\)
<species>_mass_mixing_ratio_dry_air {:}
\(\bar{\nu}_{x}\)
volume mixing ratio of quantity x with regard to dry air
\(ppv\)
<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.
\[\bar{q}_{x} = \bar{\nu}_{x}\frac{M_{x}}{M_{dry\_air}}\]mass mixing ratio dry air from mass mixing ratio
symbol
description
unit
variable name
\(q_{x}\)
mass mixing ratio of air component x with regard to total air
\(\frac{kg}{kg}\)
<species>_mass_mixing_ratio {:}
\(q_{dry\_air}\)
mass mixing ratio of dry air with regard to total air
\(\frac{kg}{kg}\)
dry_air_mass_mixing_ratio {:}
\(\bar{q}_{x}\)
mass mixing ratio of air component x with regard to dry air
\(\frac{kg}{kg}\)
<species>_mass_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.
\[\bar{q}_{x} = \frac{q_{x}}{q_{dry\_air}}\]dry air mass mixing ratio from H2O mass mixing ratio
symbol
description
unit
variable name
\(q_{H_{2}O}\)
mass mixing ratio of H2O with regard to total air
\(\frac{kg}{kg}\)
H2O_mass_mixing_ratio {:}
\(q_{dry\_air}\)
mass mixing ratio of dry air with regard to total air
\(\frac{kg}{kg}\)
dry_air_mass_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.
\[q_{dry\_air} = 1 - q_{H_{2}O}\]dry air mass mixing ratio from H2O mass mixing ratio
symbol
description
unit
variable name
\(\bar{q}_{H_{2}O}\)
mass mixing ratio of H2O with regard to dry air
\(\frac{kg}{kg}\)
H2O_mass_mixing_ratio_dry_air {:}
\(q_{dry\_air}\)
mass mixing ratio of dry air with regard to total air
\(\frac{kg}{kg}\)
dry_air_mass_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.
\[q_{dry\_air} = \frac{1}{1 + \bar{q}_{H_{2}O}}\]
H2O mass mixing ratio from dry air mass mixing ratio
symbol
description
unit
variable name
\(q_{H_{2}O}\)
mass mixing ratio of H2O with regard to total air
\(\frac{kg}{kg}\)
H2O_mass_mixing_ratio {:}
\(q_{dry\_air}\)
mass mixing ratio of dry air with regard to total air
\(\frac{kg}{kg}\)
dry_air_mass_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.
\[q_{H_{2}O} = 1 - q_{dry\_air}\]