column number density derivations
- total column number density of air component from partial column number density profile: - symbol - description - unit - variable name - \(c_{x}\) - total column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:} - \(c_{x}(i)\) - column number density profile of air component x (e.g. \(c_{O_{3}}(i)\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:,vertical} - The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[c_{x} = \sum_{i}{c_{x}(i)}\]
- total column number density of total air from partial column number density profile: - symbol - description - unit - variable name - \(c\) - total column number density of total air - \(\frac{molec}{m^2}\) - column_number_density {:} - \(c(i)\) - column number density profile of total air - \(\frac{molec}{m^2}\) - column_number_density {:,vertical} - The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[c_{x} = \sum_{i}{c_{x}(i)}\]
- tropospheric column number density of air component from partial column number density profile and altitude: - symbol - description - unit - variable name - \(c_{x}\) - tropospheric column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - tropospheric_<species>_column_number_density {:} - \(c_{x}(i)\) - column number density profile of air component x (e.g. \(c_{O_{3}}(i)\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:,vertical} - \(z_{TP}\) - tropopause altitude - \(m\) - tropopause_altitude {:} - \(z^{B}(l)\) - altitude boundaries (\(l \in \{1,2\}\)) - \(m\) - altitude_bounds {:,2} - The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[\begin{split}c_{x} = \sum_{i}{\begin{cases} z^{B}(2) \leq z_{TP}, & c_{x}(i) \\ z^{B}(1) < z_{TP} < z^{B}(2), & c_{x}(i) \frac{z_{TP} - z^{B}(1)}{z^{B}(2) - z^{B}(1)} \\ z_{TP} \leq z^{B}(1), & 0 \end{cases}}\end{split}\]
- stratospheric column number density of air component from partial column number density profile and altitude: - symbol - description - unit - variable name - \(c_{x}\) - stratospheric column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - stratospheric_<species>_column_number_density {:} - \(c_{x}(i)\) - column number density profile of air component x (e.g. \(c_{O_{3}}(i)\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:,vertical} - \(z_{TP}\) - tropopause altitude - \(m\) - tropopause_altitude {:} - \(z^{B}(l)\) - altitude boundaries (\(l \in \{1,2\}\)) - \(m\) - altitude_bounds {:,2} - The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[\begin{split}c_{x} = \sum_{i}{\begin{cases} z^{B}(2) \leq z_{TP}, & 0 \\ z^{B}(1) < z_{TP} < z^{B}(2), & c_{x}(i) \frac{z^{B}(2) - z_{TP}}{z^{B}(2) - z^{B}(1)} \\ z_{TP} \leq z^{B}(1), & c_{x}(i) \end{cases}}\end{split}\]
- tropospheric column number density of air component from partial column number density profile and pressure: - symbol - description - unit - variable name - \(c_{x}\) - tropospheric column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - tropospheric_<species>_column_number_density {:} - \(c_{x}(i)\) - column number density profile of air component x (e.g. \(c_{O_{3}}(i)\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:,vertical} - \(p_{TP}\) - tropopause pressure - \(Pa\) - tropopause_pressure {:} - \(p^{B}(l)\) - pressure boundaries (\(l \in \{1,2\}\)) - \(Pa\) - pressure_bounds {:,2} - The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[\begin{split}c_{x} = \sum_{i}{\begin{cases} p^{B}(2) \geq p_{TP}, & c_{x}(i) \\ p^{B}(1) > p_{TP} > p^{B}(2), & c_{x}(i) \frac{\ln(p^{B}(1)) - \ln(p_{TP})}{\ln(p^{B}(1)) - \ln(p^{B}(2))} \\ p_{TP} \geq p^{B}(1), & 0 \end{cases}}\end{split}\]
- stratospheric column number density of air component from partial column number density profile and pressure: - symbol - description - unit - variable name - \(c_{x}\) - stratospheric column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - stratospheric_<species>_column_number_density {:} - \(c_{x}(i)\) - column number density profile of air component x (e.g. \(c_{O_{3}}(i)\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:,vertical} - \(p_{TP}\) - tropopause pressure - \(Pa\) - tropopause_pressure {:} - \(p^{B}(l)\) - pressure boundaries (\(l \in \{1,2\}\)) - \(Pa\) - pressure_bounds {:,2} - The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[\begin{split}c_{x} = \sum_{i}{\begin{cases} p^{B}(2) \geq p_{TP}, & 0 \\ p^{B}(1) > p_{TP} > p^{B}(2), & c_{x}(i) \frac{\ln(p_{TP}) - \ln(p^{B}(2))}{\ln(p^{B}(1)) - \ln(p^{B}(2))} \\ p_{TP} \geq p^{B}(1), & c_{x}(i) \end{cases}}\end{split}\]
- column number density of total air from dry air column number density and H2O column number density - symbol - description - unit - variable name - \(c\) - column number density - \(\frac{molec}{m^2}\) - column_number_density {:} - \(c_{dry\_air}\) - column number density of dry air - \(\frac{molec}{m^2}\) - dry_air_column_number_density {:} - \(c_{H_{2}O}\) - column number density of H2O - \(\frac{molec}{m^2}\) - H2O_column_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. \[c = c_{dry\_air} + c_{H_{2}O}\]
- column number density of dry air from total air column number density and H2O column number density - symbol - description - unit - variable name - \(c\) - column number density - \(\frac{molec}{m^2}\) - column_number_density {:} - \(c_{dry\_air}\) - column number density of dry air - \(\frac{molec}{m^2}\) - dry_air_column_number_density {:} - \(c_{H_{2}O}\) - column number density of H2O - \(\frac{molec}{m^2}\) - H2O_column_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. \[c_{dry\_air} = c - c_{H_{2}O}\]
- column number density of H2O from total air column number density and dry air column number density - symbol - description - unit - variable name - \(c\) - column number density - \(\frac{molec}{m^2}\) - column_number_density {:} - \(c_{dry\_air}\) - column number density of dry air - \(\frac{molec}{m^2}\) - dry_air_column_number_density {:} - \(c_{H_{2}O}\) - column number density of H2O - \(\frac{molec}{m^2}\) - H2O_column_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. \[c_{H_{2}O} = c - c_{dry\_air}\]
- column number density of air component from 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. \[c_{x} = n_{x} \lvert z^{B}(2) - z^{B}(1) \rvert\]
- column number density of total air from number density: - symbol - description - unit - variable name - \(c\) - column number density of total air - \(\frac{molec}{m^2}\) - column_number_density {:} - \(n\) - number density of total air - \(\frac{molec}{m^3}\) - 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. \[c = n \lvert z^{B}(2) - z^{B}(1) \rvert\]
- column number density of air component from column mass density: - This conversion applies to both total columns as well as partial column profiles. - symbol - description - unit - variable name - \(c_{x}\) - column number density of air component x (e.g. \(n_{O_{3}}\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:} - \(M_{x}\) - molar mass of air component x - \(\frac{g}{mol}\) - \(N_A\) - Avogadro constant - \(\frac{1}{mol}\) - \(\sigma_{x}\) - column mass density of air component x (e.g. \(\sigma_{O_{3}}\)) - \(\frac{kg}{m^2}\) - <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. \[c_{x} = \frac{\sigma_{x}N_{A}}{10^{-3}M_{x}}\]
- column number density of total air from column mass density: - This conversion applies to both total columns as well as partial column profiles. - symbol - description - unit - variable name - \(c\) - column number density of total air - \(\frac{molec}{m^2}\) - column_number_density {:} - \(M_{air}\) - molar mass of total air - \(\frac{g}{mol}\) - molar_mass {:} - \(N_A\) - Avogadro constant - \(\frac{1}{mol}\) - \(\sigma\) - 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. \[c = \frac{\sigma N_{A}}{10^{-3}M_{air}}\]
- column number density from column volume mixing ratio - symbol - description - unit - variable name - \(c\) - total column number density of total air - \(\frac{molec}{m^2}\) - column_number_density {:} - \(c_{x}\) - total column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:} - \(\nu_{x}\) - column volume mixing ratio of quantity x with regard to total air - \(ppv\) - <species>_column_volume_mixing_ratio {:} - The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[c_{x} = \nu_{x}c\]
- column number density from column volume mixing ratio dry air - symbol - description - unit - variable name - \(c_{dry\_air}\) - total column number density of dry air - \(\frac{molec}{m^2}\) - dry_air_column_number_density {:} - \(c_{x}\) - total column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:} - \(\bar{\nu}_{x}\) - column volume mixing ratio of quantity x with regard to dry air - \(ppv\) - <species>_column_volume_mixing_ratio_dry_air {:} - The pattern : for the dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all. \[c_{x} = \bar{\nu}_{x}c_{dry\_air}\]
- column number density of air component from volume mixing ratio: - symbol - description - unit - variable name - \(a\) - WGS84 semi-major axis - \(m\) - \(b\) - WGS84 semi-minor axis - \(m\) - \(c_{x}\) - column number density of air component x (e.g. \(c_{O_{3}}\)) - \(\frac{molec}{m^2}\) - <species>_column_number_density {:} - \(f\) - WGS84 flattening - \(m\) - \(g\) - normal gravity at sea level - \(\frac{m}{s^2}\) - \(g_{0}\) - mean earth gravity - \(\frac{m}{s^2}\) - \(g_{h}\) - gravity at specific height - \(\frac{m}{s^2}\) - \(GM\) - WGS84 earth’s gravitational constant - \(\frac{m^3}{s^2}\) - \(M_{air}\) - molar mass of total air - \(\frac{g}{mol}\) - molar_mass {:} - \(N_A\) - Avogadro constant - \(\frac{1}{mol}\) - \(p\) - pressure - \(Pa\) - \(p_{0}\) - standard pressure - \(Pa\) - \(p^{B}(l)\) - pressure boundaries (\(l \in \{1,2\}\)) - \(Pa\) - pressure_bounds {:,2} - \(R\) - universal gas constant - \(\frac{kg m^2}{K mol s^2}\) - \(T_{0}\) - standard temperature - \(K\) - \(z\) - altitude - \(m\) - \(\nu_{x}\) - volume mixing ratio of quantity x with regard to total air - \(ppv\) - <species>_volume_mixing_ratio {:} - \(\phi\) - latitude - \(degN\) - latitude {:} - \(\omega\) - WGS84 earth angular velocity - \(rad/s\) - 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. \begin{eqnarray} g & = & 9.7803253359 \frac{1 + 0.00193185265241{\sin}^2(\frac{\pi}{180}\phi)} {\sqrt{1 - 0.00669437999013 {\sin}^2(\frac{\pi}{180}\phi)}} \\ m & = & \frac{\omega^2a^2b}{GM} \\ p & = & e^{\frac{\ln(p^{B}(2)) + \ln(p^{B}(1))}{2}} \\ z & = & -\frac{RT_{0}}{10^{-3}M_{air}g_{0}}\ln(\frac{p}{p_{0}}) \\ g_{h} & = & g \left(1 - \frac{2}{a}\left(1+f+m-2f{\sin}^2(\frac{\pi}{180}\phi)\right)z + \frac{3}{a^2}z^2\right) \\ c_{x} & = & -\nu_{x}\frac{N_A}{10^{-3}M_{air}g_{h}}(p^{B}(2)-p^{B}(1)) \end{eqnarray}