volume mixing ratio derivations

1. 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.

$\nu_{x} = \frac{n_{x}}{n}$
2. 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.

$\nu_{x} = q_{x}\frac{M_{air}}{M_{x}}$
3. 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.

$\nu_{x} = \frac{p_{x}}{p}$
4. 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.

$\nu_{x} = \bar{\nu}_{x}\nu_{dry\_air}$
5. 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.

$\bar{\nu}_{x} = \frac{n_{x}}{n_{dry\_air}}$
6. 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.

$\bar{\nu}_{x} = \bar{q}_{x}\frac{M_{dry\_air}}{M_{x}}$
7. 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.

$\bar{\nu}_{x} = \frac{p_{x}}{p_{dry\_air}}$
8. 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.

$\bar{\nu}_{x} = \frac{\nu_{x}}{\nu_{dry\_air}}$
9. 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.

$\nu_{dry\_air} = 1 - \nu_{H_{2}O}$
10. 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.

$\nu_{H_{2}O} = 1 - \nu_{dry\_air}$