# column volume mixing ratio derivations

1. column volume mixing ratio from column number density

symbol

description

unit

variable name

$$c$$

total column number density of total air

$$\frac{molec}{m^2}$$

column_number_density {:}

$$c_{x}$$

total column number density of air component x (e.g. $$c_{O_{3}}$$)

$$\frac{molec}{m^2}$$

<species>_column_number_density {:}

$$\nu_{x}$$

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.

$\nu_{x} = \frac{c_{x}}{c}$
2. column volume mixing ratio dry air from column number density

symbol

description

unit

variable name

$$c_{dry\_air}$$

total column number density of dry air

$$\frac{molec}{m^2}$$

dry_air_column_number_density {:}

$$c_{x}$$

total column number density of air component x (e.g. $$c_{O_{3}}$$)

$$\frac{molec}{m^2}$$

<species>_column_number_density {:}

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

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.

$\bar{\nu}_{x} = \frac{c_{x}}{c_{dry\_air}}$
3. column volume mixing ratio from column 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

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

$$q_{x}$$

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.

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

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

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

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.

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

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

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

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.

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

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

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

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.

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