mass mixing ratio derivations

  1. mass mixing ratio from mass density

    symbol description unit variable name
    \(\rho\) mass density of total air \(\frac{kg}{m^3}\) density {:}
    \(\rho_{x}\) mass density of air component x (e.g. \(\rho_{O_{3}}\)) \(\frac{kg}{m^3}\) <species>_density {:}
    \(q_{x}\) mass mixing ratio of air component x with regard to total air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio {:}

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

    \[q_{x} = \frac{\rho_{x}}{\rho}\]

  2. mass mixing ratio from 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 \(\frac{g}{mol}\)  
    \(q_{x}\) mass mixing ratio of quantity x with regard to total air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio {:}
    \(\nu_{x}\) volume mixing ratio of quantity x with regard to total air \(ppv\) <species>_volume_mixing_ratio {:}

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

    \[q_{x} = \nu_{x}\frac{M_{x}}{M_{air}}\]

  3. mass mixing ratio from mass mixing ratio dry air

    symbol description unit variable name
    \(q_{x}\) mass mixing ratio of air component x with regard to total air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio {:}
    \(q_{dry\_air}\) mass mixing ratio of dry air with regard to total air \(\frac{kg}{kg}\) dry_air_mass_mixing_ratio {:}
    \(\bar{q}_{x}\) mass mixing ratio of air component x with regard to dry air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio_dry_air {:}

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

    \[q_{x} = \bar{q}_{x}q_{dry\_air}\]

  4. mass mixing ratio dry air from mass density

    symbol description unit variable name
    \(\rho_{dry\_air}\) mass density of dry air \(\frac{kg}{m^3}\) dry_air_density {:}
    \(\rho_{x}\) mass density of air component x (e.g. \(\rho_{O_{3}}\)) \(\frac{kg}{m^3}\) <species>_density {:}
    \(\bar{q}_{x}\) mass mixing ratio if air component x with regard to dry air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio_dry_air {:}

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

    \[q_{x} = \frac{\rho_{x}}{\rho_{dry\_air}}\]

  5. mass mixing ratio dry air from 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 \(\frac{g}{mol}\)  
    \(\bar{q}_{x}\) mass mixing ratio of quantity x with regard to dry air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio_dry_air {:}
    \(\bar{\nu}_{x}\) volume mixing ratio of quantity x with regard to dry air \(ppv\) <species>_volume_mixing_ratio_dry_air {:}

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

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

  6. mass mixing ratio dry air from mass mixing ratio

    symbol description unit variable name
    \(q_{x}\) mass mixing ratio of air component x with regard to total air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio {:}
    \(q_{dry\_air}\) mass mixing ratio of dry air with regard to total air \(\frac{kg}{kg}\) dry_air_mass_mixing_ratio {:}
    \(\bar{q}_{x}\) mass mixing ratio of air component x with regard to dry air \(\frac{kg}{kg}\) <species>_mass_mixing_ratio_dry_air {:}

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

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

  7. dry air mass mixing ratio from H2O mass mixing ratio

    symbol description unit variable name
    \(q_{H_{2}O}\) mass mixing ratio of H2O with regard to total air \(\frac{kg}{kg}\) H2O_mass_mixing_ratio {:}
    \(q_{dry\_air}\) mass mixing ratio of dry air with regard to total air \(\frac{kg}{kg}\) dry_air_mass_mixing_ratio {:}

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

    \[q_{dry\_air} = 1 - q_{H_{2}O}\]

  8. H2O mass mixing ratio from dry air mass mixing ratio

    symbol description unit variable name
    \(q_{H_{2}O}\) mass mixing ratio of H2O with regard to total air \(\frac{kg}{kg}\) H2O_mass_mixing_ratio {:}
    \(q_{dry\_air}\) mass mixing ratio of dry air with regard to total air \(\frac{kg}{kg}\) dry_air_mass_mixing_ratio {:}

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

    \[q_{H_{2}O} = 1 - q_{dry\_air}\]