number density averaging kernel derivations
number density AVK of air component from column number density AVK
symbol
description
unit
variable name
\(A^{c}_{x}(i,j)\)
AVK of column number density profile of air component x (e.g. \(A^{c}_{O_{3}}(i,j)\))
\(\frac{molec/m^2}{molec/m^2}\)
<species>_column_number_density_avk {:,vertical,vertical}
\(A^{n}_{x}(i,j)\)
AVK of number density profile of air component x (e.g. \(A^{n}_{O_{3}}(i,j)\))
\(\frac{molec/m^3}{molec/m^3}\)
<species>_number_density_avk {:,vertical,vertical}
\(z^{B}(i,l)\)
altitude boundaries (\(l \in \{1,2\}\))
\(m\)
altitude_bounds {:,vertical,2}
The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.
\[\begin{split}A^{n}_{x}(i,j) = \begin{cases} z^{B}(i,1) \neq z^{B}(i,2), & A^{c}_{x}(i,j) \frac{\lvert z^{B}(j,2) - z^{B}(j,1) \rvert}{\lvert z^{B}(i,2) - z^{B}(i,1) \rvert} \\ z^{B}(i,1) = z^{B}(i,2), & 0 \end{cases}\end{split}\]number density AVK from volume mixing ratio AVK
symbol
description
unit
variable name
\(A^{n}_{x}(i,j)\)
AVK of number density profile of air component x (e.g. \(A^{n}_{O_{3}}(i,j)\))
\(\frac{molec/m^3}{molec/m^3}\)
<species>_number_density_avk {:,vertical,vertical}
\(A^{\nu}_{x}(i,j)\)
AVK of volume mixing ratio profile of air component x (e.g. \(A^{\nu}_{O_{3}}(i,j)\))
\(\frac{ppv}{ppv}\)
<species>_volume_mixing_ratio_avk {:,vertical,vertical}
\(n(i)\)
number density profile of total air
\(\frac{molec}{m^3}\)
number_density {:,vertical}
The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.
\[\begin{split}A^{n}_{x}(i,j) = \begin{cases} n(j) \neq 0, & A^{\nu}_{x}(i,j) \frac{n(i)}{n(j)} \\ n(j) = 0, & 0 \end{cases}\end{split}\]number density AVK from volume mixing ratio dry air AVK
symbol
description
unit
variable name
\(A^{n}_{x}(i,j)\)
AVK of number density profile of air component x (e.g. \(A^{n}_{O_{3}}(i,j)\))
\(\frac{molec/m^3}{molec/m^3}\)
<species>_number_density_avk {:,vertical,vertical}
\(A^{\bar{\nu}}_{x}(i,j)\)
AVK of volume mixing ratio profile of air component x (e.g. \(A^{\bar{\nu}}_{O_{3}}(i,j)\))
\(\frac{ppv}{ppv}\)
<species>_volume_mixing_ratio_dry_air_avk {:,vertical,vertical}
\(n_{dry_air}(i)\)
number density profile of dry air
\(\frac{molec}{m^3}\)
dry_air_number_density {:,vertical}
The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.
\[\begin{split}A^{n}_{x}(i,j) = \begin{cases} n_{dry_air}(j) \neq 0, & A^{\bar{\nu}}_{x}(i,j) \frac{n_{dry_air}(i)}{n_{dry_air}(j)} \\ n_{dry_air}(j) = 0, & 0 \end{cases}\end{split}\]