mass density derivations
- mass density of air component from number 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. \[\rho_{x} = \frac{10^{-3}n_{x}M_{x}}{N_{A}}\]
- mass density of total air from number 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. \[\rho = \frac{10^{-3}n M_{air}}{N_{A}}\]
- mass density of air component from column mass density - symbol - description - unit - variable name - \(z^{B}(l)\) - altitude boundaries (\(l \in \{1,2\}\)) - \(m\) - altitude_bounds {:,2} - \(\rho_{x}\) - mass density of air component x (e.g. \(\rho_{O_{3}}\)) - \(\frac{kg}{m^3}\) - <species>_density {:} - \(\sigma_{x}\) - column mass density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{kg}{m^2}\) - <species>_column_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. \[\rho_{x} = \frac{\sigma_{x}}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]
- mass density of total air from dry air mass density and H2O mass density - symbol - description - unit - variable name - \(\rho\) - mass density - \(\frac{kg}{m^3}\) - density {:} - \(\rho_{dry\_air}\) - mass density of dry air - \(\frac{kg}{m^3}\) - dry_air_density {:} - \(\rho_{H_{2}O}\) - mass density of H2O - \(\frac{kg}{m^3}\) - H2O_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. \[\rho = \rho_{dry\_air} + \rho_{H_{2}O}\]
- mass density of dry air from total air mass density and H2O mass density - symbol - description - unit - variable name - \(\rho\) - mass density - \(\frac{kg}{m^3}\) - density {:} - \(\rho_{dry\_air}\) - mass density of dry air - \(\frac{kg}{m^3}\) - dry_air_density {:} - \(\rho_{H_{2}O}\) - mass density of H2O - \(\frac{kg}{m^3}\) - H2O_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. \[\rho_{dry\_air} = \rho - \rho_{H_{2}O}\]
- mass density of H2O from total air mass density and dry air mass density - symbol - description - unit - variable name - \(\rho\) - mass density - \(\frac{kg}{m^3}\) - density {:} - \(\rho_{dry\_air}\) - mass density of dry air - \(\frac{kg}{m^3}\) - dry_air_density {:} - \(\rho_{H_{2}O}\) - mass density of H2O - \(\frac{kg}{m^3}\) - H2O_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. \[\rho_{H_{2}O} = \rho - \rho_{dry\_air}\]
- mass density of total air from column mass density - symbol - description - unit - variable name - \(z^{B}(l)\) - altitude boundaries (\(l \in \{1,2\}\)) - \(m\) - altitude_bounds {:,2} - \(\rho\) - mass density of total air - \(\frac{kg}{m^3}\) - density {:} - \(\sigma\) - column mass density of total air - \(\frac{kg}{m^2}\) - column_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. \[\rho = \frac{\sigma}{\lvert z^{B}(2) - z^{B}(1) \rvert}\]