column mass mixing ratio derivations
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 for 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.
\[q_{x} = \frac{\sigma_{x}}{\sigma}\]column mass mixing ratio 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 for 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.
\[\bar{q}_{x} = \frac{\sigma_{x}}{\sigma_{dry\_air}}\]column mass mixing ratio from column volume mixing ratio
symbol description unit variable name \(M_{air}\) molar mass for total air \(\frac{g}{mol}\) molar_mass {:} \(M_{x}\) molar mass for 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.
\[q_{x} = \nu_{x}\frac{M_{x}}{M_{air}}\]column mass mixing ratio dry air from column volume mixing ratio dry air
symbol description unit variable name \(M_{dry\_air}\) molar mass for dry air \(\frac{g}{mol}\) \(M_{x}\) molar mass for 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.
\[\bar{q}_{x} = \bar{\nu}_{x}\frac{M_{x}}{M_{dry\_air}}\]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 for dry air \(\frac{g}{mol}\) \(M_{x}\) molar mass for 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.
\[\bar{q}_{x} = \bar{\nu}_{x}\frac{M_{x}}{M_{dry\_air}}\]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 for dry air \(\frac{g}{mol}\) \(M_{x}\) molar mass for 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.
\[\bar{q}_{x} = \bar{\nu}_{x}\frac{M_{x}}{M_{dry\_air}}\]