# column mass mixing ratio derivations

1. column mass mixing ratio from column mass density

symbol

description

unit

variable name

$$\sigma$$

column mass density of total air

$$\frac{kg}{m^3}$$

column_density {:}

$$\sigma_{x}$$

column mass density of air component x (e.g. $$\sigma{O_{3}}$$)

$$\frac{kg}{m^3}$$

<species>_column_density {:}

$$q_{x}$$

column mass mixing ratio of quantity x with regard to total air

$$\frac{kg}{kg}$$

<species>_column_mass_mixing_ratio {:}

The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

$q_{x} = \frac{\sigma_{x}}{\sigma}$
2. column mass mixing ratio dry air from column mass density

symbol

description

unit

variable name

$$\sigma_{dry\_air}$$

column mass density of dry air

$$\frac{kg}{m^3}$$

dry_air_column_density {:}

$$\sigma_{x}$$

column mass density of air component x (e.g. $$\sigma{O_{3}}$$)

$$\frac{kg}{m^3}$$

<species>_column_density {:}

$$\bar{q}_{x}$$

column mass mixing ratio of quantity x with regard to dry air

$$\frac{kg}{kg}$$

<species>_column_mass_mixing_ratio_dry_air {:}

The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

$\bar{q}_{x} = \frac{\sigma_{x}}{\sigma_{dry\_air}}$
3. column mass mixing ratio from column 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

$$\frac{g}{mol}$$

$$q_{x}$$

column mass mixing ratio of quantity x with regard to total air

$$\frac{kg}{kg}$$

<species>_column_mass_mixing_ratio {:}

$$\nu_{x}$$

column volume mixing ratio of quantity x with regard to total air

$$ppv$$

<species>_column_volume_mixing_ratio {:}

The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

$q_{x} = \nu_{x}\frac{M_{x}}{M_{air}}$
4. column mass mixing ratio dry air from column 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

$$\frac{g}{mol}$$

$$\bar{q}_{x}$$

column mass mixing ratio of quantity x with regard to dry air

$$\frac{kg}{kg}$$

<species>_column_mass_mixing_ratio_dry_air {:}

$$\bar{\nu}_{x}$$

column volume mixing ratio of quantity x with regard to dry air

$$ppv$$

<species>_column_volume_mixing_ratio_dry_air {:}

The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

$\bar{q}_{x} = \bar{\nu}_{x}\frac{M_{x}}{M_{dry\_air}}$
5. stratospheric column mass mixing ratio dry air from stratospheric column 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

$$\frac{g}{mol}$$

$$\bar{q}_{x}$$

stratospheric column mass mixing ratio of quantity x with regard to dry air

$$\frac{kg}{kg}$$

stratospheric_<species>_column_mass_mixing_ratio_dry_air {:}

$$\bar{\nu}_{x}$$

stratospheric column volume mixing ratio of quantity x with regard to dry air

$$ppv$$

stratospheric_<species>_column_volume_mixing_ratio_dry_air {:}

The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

$\bar{q}_{x} = \bar{\nu}_{x}\frac{M_{x}}{M_{dry\_air}}$
6. tropospheric column mass mixing ratio dry air from tropospheric column 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

$$\frac{g}{mol}$$

$$\bar{q}_{x}$$

tropospheric column mass mixing ratio of quantity x with regard to dry air

$$\frac{kg}{kg}$$

tropospheric_<species>_column_mass_mixing_ratio_dry_air {:}

$$\bar{\nu}_{x}$$

tropospheric column volume mixing ratio of quantity x with regard to dry air

$$ppv$$

tropospheric_<species>_column_volume_mixing_ratio_dry_air {:}

The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

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