volume mixing ratio derivations

  1. volume mixing ratio from number density

    symbol

    description

    unit

    variable name

    \(n\)

    number density of total air

    \(\frac{molec}{m^3}\)

    number_density {:}

    \(n_{x}\)

    number density of air component x (e.g. \(n_{O_{3}}\))

    \(\frac{molec}{m^3}\)

    <species>_number_density {:}

    \(\nu_{x}\)

    volume mixing ratio if air component 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.

    \[\nu_{x} = \frac{n_{x}}{n}\]
  2. volume mixing ratio from 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

    \(\frac{g}{mol}\)

    \(q_{x}\)

    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.

    \[\nu_{x} = q_{x}\frac{M_{air}}{M_{x}}\]
  3. volume mixing ratio from partial pressure

    symbol

    description

    unit

    variable name

    \(p\)

    pressure

    \(Pa\)

    pressure {:}

    \(p_{x}\)

    partial pressure of air component x (e.g. \(p_{O_{3}}\))

    \(Pa\)

    <species>_partial_pressure {:}

    \(\nu_{x}\)

    volume mixing ratio of air component 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.

    \[\nu_{x} = \frac{p_{x}}{p}\]
  4. volume mixing ratio from volume mixing ratio dry air

    symbol

    description

    unit

    variable name

    \(\nu_{x}\)

    volume mixing ratio of air component x with regard to total air

    \(ppv\)

    <species>_volume_mixing_ratio {:}

    \(\nu_{dry\_air}\)

    volume mixing ratio of dry air with regard to total air

    \(ppv\)

    dry_air_volume_mixing_ratio {:}

    \(\bar{\nu}_{x}\)

    volume mixing ratio of air component 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.

    \[\nu_{x} = \bar{\nu}_{x}\nu_{dry\_air}\]
  5. volume mixing ratio dry air from number density

    symbol

    description

    unit

    variable name

    \(n_{dry\_air}\)

    number density of dry air

    \(\frac{molec}{m^3}\)

    dry_air_number_density {:}

    \(n_{x}\)

    number density of air component x (e.g. \(n_{O_{3}}\))

    \(\frac{molec}{m^3}\)

    <species>_number_density {:}

    \(\bar{\nu}_{x}\)

    volume mixing ratio of air component 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.

    \[\bar{\nu}_{x} = \frac{n_{x}}{n_{dry\_air}}\]
  6. volume mixing ratio dry air from 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

    \(\frac{g}{mol}\)

    \(\bar{q}_{x}\)

    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.

    \[\bar{\nu}_{x} = \bar{q}_{x}\frac{M_{dry\_air}}{M_{x}}\]
  7. volume mixing ratio dry air from partial pressure

    symbol

    description

    unit

    variable name

    \(p_{dry\_air}\)

    partial pressure of dry air

    \(Pa\)

    dry_air_partial_pressure {:}

    \(p_{x}\)

    partial pressure of air component x (e.g. \(p_{O_{3}}\))

    \(Pa\)

    <species>_partial_pressure {:}

    \(\bar{\nu}_{x}\)

    volume mixing ratio of air component 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.

    \[\bar{\nu}_{x} = \frac{p_{x}}{p_{dry\_air}}\]
  8. volume mixing ratio dry air from volume mixing ratio

    symbol

    description

    unit

    variable name

    \(\nu_{x}\)

    volume mixing ratio of air component x with regard to total air

    \(ppv\)

    <species>_volume_mixing_ratio {:}

    \(\nu_{dry\_air}\)

    volume mixing ratio of dry air with regard to total air

    \(ppv\)

    dry_air_volume_mixing_ratio {:}

    \(\bar{\nu}_{x}\)

    volume mixing ratio of air component 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.

    \[\bar{\nu}_{x} = \frac{\nu_{x}}{\nu_{dry\_air}}\]
  9. dry air volume mixing ratio from H2O volume mixing ratio

    symbol

    description

    unit

    variable name

    \(\nu_{H_{2}O}\)

    volume mixing ratio of H2O with regard to total air

    \(ppv\)

    H2O_volume_mixing_ratio {:}

    \(\nu_{dry\_air}\)

    volume mixing ratio of dry air with regard to total air

    \(ppv\)

    dry_air_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.

    \[\nu_{dry\_air} = 1 - \nu_{H_{2}O}\]
  10. dry air volume mixing ratio from H2O volume mixing ratio dry air

    symbol

    description

    unit

    variable name

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

    volume mixing ratio of H2O with regard to dry air

    \(ppv\)

    H2O_volume_mixing_ratio_dry_air {:}

    \(\nu_{dry\_air}\)

    volume mixing ratio of dry air with regard to total air

    \(ppv\)

    dry_air_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.

    \[\nu_{dry\_air} = \frac{1}{1 + \bar{\nu}_{H_{2}O}}\]
  11. H2O volume mixing ratio from dry air volume mixing ratio

    symbol

    description

    unit

    variable name

    \(\nu_{H_{2}O}\)

    volume mixing ratio of H2O with regard to total air

    \(ppv\)

    H2O_volume_mixing_ratio {:}

    \(\nu_{dry\_air}\)

    volume mixing ratio of dry air with regard to total air

    \(ppv\)

    dry_air_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.

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