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. \[A^{c}_{x}(i) = \sum_{j}{A^{c}_{x}(j,i)}\]
- 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. \[\begin{split}A^{c}_{x}(i,j) = \begin{cases} z^{B}(j,1) \neq z^{B}(j,2), & A^{n}_{x}(i,j) \frac{\lvert z^{B}(i,2) - z^{B}(i,1) \rvert}{\lvert z^{B}(j,2) - z^{B}(j,1) \rvert} \\ z^{B}(j,1) \neq z^{B}(j,2), & 0 \end{cases}\end{split}\]