column number density averaging kernel derivations
column number density column AVK of air component from column number density AVK
symbol
description
unit
variable name
\(A^{c}_{x}(i)\)
column AVK of column number density profile of air component x (e.g. \(A^{c}_{O_{3}}(i)\))
\(\frac{molec/m^2}{molec/m^2}\)
<species>_column_number_density_avk {:,vertical}
\(A^{c}_{x}(i,j)\)
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}
The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.
\[A^{c}_{x}(i) = \sum_{j}{A^{c}_{x}(j,i)}\]tropospheric column number density column AVK of air component from total column number density column AVK
symbol
description
unit
variable name
\(\tilde{A}^{c}_{x}(i)\)
column AVK of tropospheric part of column number density profile of air component x
\(\frac{molec/m^2}{molec/m^2}\)
tropospheric_<species>_column_number_density_avk {:,vertical}
\(A^{c}_{x}(i)\)
column AVK of column number density profile of air component x (e.g. \(A^{c}_{O_{3}}(i)\))
\(\frac{molec/m^2}{molec/m^2}\)
<species>_column_number_density_avk {:,vertical}
\(z_{TP}\)
tropopause altitude
\(m\)
tropopause_altitude {:}
\(z^{B}(i,l)\)
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.
\[\begin{split}\tilde{A}^{c}_{x}(i) = \begin{cases} z^{B}(i,1) < z_{TP}, & A^{c}_{x}(i) \\ z^{B}(j,1) \geq z_{TP}, & 0 \end{cases}\end{split}\]stratospheric column number density column AVK of air component from total column number density column AVK
symbol
description
unit
variable name
\(\tilde{A}^{c}_{x}(i)\)
column AVK of stratospheric part of column number density profile of air component x
\(\frac{molec/m^2}{molec/m^2}\)
tropospheric_<species>_column_number_density_avk {:,vertical}
\(A^{c}_{x}(i)\)
column AVK of column number density profile of air component x (e.g. \(A^{c}_{O_{3}}(i)\))
\(\frac{molec/m^2}{molec/m^2}\)
<species>_column_number_density_avk {:,vertical}
\(z_{TP}\)
tropopause altitude
\(m\)
tropopause_altitude {:}
\(z^{B}(i,l)\)
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.
\[\begin{split}\tilde{A}^{c}_{x}(i) = \begin{cases} z^{B}(i,2) \leq z_{TP}, & 0 \\ z^{B}(j,2) > z_{TP}, & A^{c}_{x}(i) \end{cases}\end{split}\]column number density AVK of air component from 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.
\[\begin{split}A^{c}_{x}(i,j) = \begin{cases} z^{B}(j,1) \neq z^{B}(j,2), & A^{n}_{x}(i,j) \frac{\lvert z^{B}(i,2) - z^{B}(i,1) \rvert}{\lvert z^{B}(j,2) - z^{B}(j,1) \rvert} \\ z^{B}(j,1) = z^{B}(j,2), & 0 \end{cases}\end{split}\]