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.

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