# mass mixing ratio derivations

1. 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.

$q_{x} = \frac{\rho_{x}}{\rho}$
2. 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.

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

$q_{x} = \bar{q}_{x}q_{dry\_air}$
4. 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.

$q_{x} = \frac{\rho_{x}}{\rho_{dry\_air}}$
5. 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.

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

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

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

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