number density derivations

  1. number density of air component from mass density

    symbol

    description

    unit

    variable name

    \(M_{x}\)

    molar mass of air component x

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

    \(n_{x}\)

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

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

    <species>_number_density {:}

    \(N_A\)

    Avogadro constant

    \(\frac{1}{mol}\)

    \(\rho_{x}\)

    mass density of air component x (e.g. \(\rho_{O_{3}}\))

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

    <species>_density {:}

    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.

    \[n_{x} = \frac{\rho_{x}N_{A}}{10^{-3}M_{x}}\]
  2. number density of total air from mass density

    symbol

    description

    unit

    variable name

    \(M_{air}\)

    molar mass of total air

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

    molar_mass {:}

    \(n\)

    number density of total air

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

    number_density {:}

    \(N_A\)

    Avogadro constant

    \(\frac{1}{mol}\)

    \(\rho\)

    mass density of total air

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

    density {:}

    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.

    \[n = \frac{\rho N_{A}}{10^{-3}M_{air}}\]
  3. number density of total air from pressure and temperature

    symbol

    description

    unit

    variable name

    \(k\)

    Boltzmann constant

    \(\frac{kg m^2}{K s^2}\)

    \(n\)

    number density

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

    number_density {:}

    \(p\)

    pressure

    \(Pa\)

    pressure {:}

    \(T\)

    temperature

    \(K\)

    temperature {:}

    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.

    \[n = \frac{p}{kT}\]
  4. number density from volume mixing ratio

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

    \(ppv\)

    <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.

    \[n_{x} = \nu_{x}n\]
  5. number density from volume mixing ratio dry air

    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 (e.g. \(n_{O_{3}}\))

    \(ppv\)

    <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.

    \[n_{x} = \bar{\nu}_{x}n_{dry\_air}\]
  6. number density of air component from column number density

    symbol

    description

    unit

    variable name

    \(c_{x}\)

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

    \(\frac{molec}{m^2}\)

    <species>_column_number_density {:}

    \(n_{x}\)

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

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

    <species>_number_density {:}

    \(z^{B}(l)\)

    altitude boundaries (\(l \in \{1,2\}\))

    \(m\)

    altitude_bounds {:,2}

    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.

    \[n_{x} = \frac{c_{x}}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]
  7. number density of total air from dry air number density and H2O number density

    symbol

    description

    unit

    variable name

    \(n\)

    number density

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

    number_density {:}

    \(n_{dry\_air}\)

    number density of dry air

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

    dry_air_number_density {:}

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

    number density of H2O

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

    H2O_number_density {:}

    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.

    \[n = n_{dry\_air} + n_{H_{2}O}\]
  8. number density of dry air from total air number density and H2O number density

    symbol

    description

    unit

    variable name

    \(n\)

    number density

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

    number_density {:}

    \(n_{dry\_air}\)

    number density of dry air

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

    dry_air_number_density {:}

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

    number density of H2O

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

    H2O_number_density {:}

    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.

    \[n_{dry\_air} = n - n_{H_{2}O}\]
  9. number density of H2O from total air number density and dry air number density

    symbol

    description

    unit

    variable name

    \(n\)

    number density

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

    number_density {:}

    \(n_{dry\_air}\)

    number density of dry air

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

    dry_air_number_density {:}

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

    number density of H2O

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

    H2O_number_density {:}

    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.

    \[n_{H_{2}O} = n - n_{dry\_air}\]
  10. number density of total air from column number density

    symbol

    description

    unit

    variable name

    \(c\)

    column number density

    \(\frac{molec}{m^2}\)

    column_number_density {:}

    \(n\)

    number density

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

    number_density {:}

    \(z^{B}(l)\)

    altitude boundaries (\(l \in \{1,2\}\))

    \(m\)

    altitude_bounds {:,2}

    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.

    \[n = \frac{c}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]
  11. number density of air component from partial pressure and temperature

    symbol

    description

    unit

    variable name

    \(k\)

    Boltzmann constant

    \(\frac{kg m^2}{K s^2}\)

    \(n_{x}\)

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

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

    <species>_number_density {:}

    \(p_{x}\)

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

    \(Pa\)

    <species>_partial_pressure {:}

    \(T\)

    temperature

    \(K\)

    temperature {:}

    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.

    \[n_{x} = \frac{p_{x}}{kT}\]
  12. surface number density of total air from surface pressure and surface temperature

    symbol

    description

    unit

    variable name

    \(k\)

    Boltzmann constant

    \(\frac{kg m^2}{K s^2}\)

    \(n_{surf}\)

    surface number density

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

    surface_number_density {:}

    \(p_{surf}\)

    surface pressure

    \(Pa\)

    surface_pressure {:}

    \(T_{surf}\)

    surface temperature

    \(K\)

    surface_temperature {:}

    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.

    \[n_{surf} = \frac{p_{surf}}{kT_{surf}}\]