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. dry air mass mixing ratio from H2O mass mixing ratio

    symbol

    description

    unit

    variable name

    \(\bar{q}_{H_{2}O}\)

    mass mixing ratio of H2O with regard to dry air

    \(\frac{kg}{kg}\)

    H2O_mass_mixing_ratio_dry_air {:}

    \(q_{dry\_air}\)

    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.

    \[q_{dry\_air} = \frac{1}{1 + \bar{q}_{H_{2}O}}\]
  1. 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.

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