number density derivations
- 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. \[n_{x} = \frac{\rho_{x}N_{A}}{10^{-3}M_{x}}\]
- 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. \[n = \frac{\rho N_{A}}{10^{-3}M_{air}}\]
- 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. \[n = \frac{p}{kT}\]
- 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. \[n_{x} = \nu_{x}n\]
- 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. \[n_{x} = \bar{\nu}_{x}n_{dry\_air}\]
- 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. \[n_{x} = \frac{c_{x}}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]
- 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. \[n = n_{dry\_air} + n_{H_{2}O}\]
- 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. \[n_{dry\_air} = n - n_{H_{2}O}\]
- 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. \[n_{H_{2}O} = n - n_{dry\_air}\]
- 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. \[n = \frac{c}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]
- 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. \[n_{x} = \frac{p_{x}}{kT}\]
- 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. \[n_{surf} = \frac{p_{surf}}{kT_{surf}}\]