volume mixing ratio averaging kernel derivations

  1. 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.

    \[\begin{split}A^{\nu}_{x}(i,j) = \begin{cases} n(i) \neq 0, & A^{n}_{x}(i,j) \frac{n(j)}{n(i)} \\ n(i) = 0, & 0 \end{cases}\end{split}\]

  2. 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.

    \[\begin{split}A^{\bar{\nu}}_{x}(i,j) = \begin{cases} n_{dry_air}(i) \neq 0, & A^{n}_{x}(i,j) \frac{n_{dry_air}(j)}{n_{dry_air}(i)} \\ n_{dry_air}(i) = 0, & 0 \end{cases}\end{split}\]