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}