volume mixing ratio derivations
volume mixing ratio from number density
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 if air component 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.
\[\nu_{x} = \frac{n_{x}}{n}\]volume mixing ratio from mass 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.
\[\nu_{x} = q_{x}\frac{M_{air}}{M_{x}}\]volume mixing ratio from partial pressure
symbol
description
unit
variable name
\(p\)
pressure
\(Pa\)
pressure {:}
\(p_{x}\)
partial pressure of air component x (e.g. \(p_{O_{3}}\))
\(Pa\)
<species>_partial_pressure {:}
\(\nu_{x}\)
volume mixing ratio of air component 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.
\[\nu_{x} = \frac{p_{x}}{p}\]volume mixing ratio from volume mixing ratio dry air
symbol
description
unit
variable name
\(\nu_{x}\)
volume mixing ratio of air component x with regard to total air
\(ppv\)
<species>_volume_mixing_ratio {:}
\(\nu_{dry\_air}\)
volume mixing ratio of dry air with regard to total air
\(ppv\)
dry_air_volume_mixing_ratio {:}
\(\bar{\nu}_{x}\)
volume mixing ratio of air component 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.
\[\nu_{x} = \bar{\nu}_{x}\nu_{dry\_air}\]volume mixing ratio dry air from number density
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 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.
\[\bar{\nu}_{x} = \frac{n_{x}}{n_{dry\_air}}\]volume mixing ratio dry air from mass 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.
\[\bar{\nu}_{x} = \bar{q}_{x}\frac{M_{dry\_air}}{M_{x}}\]volume mixing ratio dry air from partial pressure
symbol
description
unit
variable name
\(p_{dry\_air}\)
partial pressure of dry air
\(Pa\)
dry_air_partial_pressure {:}
\(p_{x}\)
partial pressure of air component x (e.g. \(p_{O_{3}}\))
\(Pa\)
<species>_partial_pressure {:}
\(\bar{\nu}_{x}\)
volume mixing ratio of air component 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.
\[\bar{\nu}_{x} = \frac{p_{x}}{p_{dry\_air}}\]volume mixing ratio dry air from volume mixing ratio
symbol
description
unit
variable name
\(\nu_{x}\)
volume mixing ratio of air component x with regard to total air
\(ppv\)
<species>_volume_mixing_ratio {:}
\(\nu_{dry\_air}\)
volume mixing ratio of dry air with regard to total air
\(ppv\)
dry_air_volume_mixing_ratio {:}
\(\bar{\nu}_{x}\)
volume mixing ratio of air component 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.
\[\bar{\nu}_{x} = \frac{\nu_{x}}{\nu_{dry\_air}}\]dry air volume mixing ratio from H2O volume mixing ratio
symbol
description
unit
variable name
\(\nu_{H_{2}O}\)
volume mixing ratio of H2O with regard to total air
\(ppv\)
H2O_volume_mixing_ratio {:}
\(\nu_{dry\_air}\)
volume mixing ratio of dry air with regard to total air
\(ppv\)
dry_air_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.
\[\nu_{dry\_air} = 1 - \nu_{H_{2}O}\]dry air volume mixing ratio from H2O volume mixing ratio dry air
symbol
description
unit
variable name
\(\bar{\nu}_{H_{2}O}\)
volume mixing ratio of H2O with regard to dry air
\(ppv\)
H2O_volume_mixing_ratio_dry_air {:}
\(\nu_{dry\_air}\)
volume mixing ratio of dry air with regard to total air
\(ppv\)
dry_air_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.
\[\nu_{dry\_air} = \frac{1}{1 + \bar{\nu}_{H_{2}O}}\]H2O volume mixing ratio from dry air volume mixing ratio
symbol
description
unit
variable name
\(\nu_{H_{2}O}\)
volume mixing ratio of H2O with regard to total air
\(ppv\)
H2O_volume_mixing_ratio {:}
\(\nu_{dry\_air}\)
volume mixing ratio of dry air with regard to total air
\(ppv\)
dry_air_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.
\[\nu_{H_{2}O} = 1 - \nu_{dry\_air}\]