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.

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