volume mixing ratio averaging kernel derivations
- volume mixing ratio AVK from number density 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. \[\begin{split}A^{\nu}_{x}(i,j) = \begin{cases} n(i) \neq 0, & A^{n}_{x}(i,j) \frac{n(j)}{n(i)} \\ n(i) = 0, & 0 \end{cases}\end{split}\]
- volume mixing ratio dry air AVK from number density 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 with regard to dry air (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. \[\begin{split}A^{\bar{\nu}}_{x}(i,j) = \begin{cases} n_{dry_air}(i) \neq 0, & A^{n}_{x}(i,j) \frac{n_{dry_air}(j)}{n_{dry_air}(i)} \\ n_{dry_air}(i) = 0, & 0 \end{cases}\end{split}\]