Polarization averaging

  • $y_{7,i}$: record $i$ from Waspam7
  • $y_{3,i}$: record $i$ from Waspam3
  • $s_{3}$: noise for Waspam 3
  • $s_{7}$: noise for Waspam 7

Averaged: $y=\dfrac{1}{N}\sum_{i=1}^N \left(\dfrac{1}{s_3^2} + \dfrac{1}{s_7^2}\right)^{-1}\left(\dfrac{y_{3,i}}{s_3^2}+\dfrac{y_{7,i}}{s_7^2}\right)$

Remove artifacts

  1. Clip beginning and end of spectra since outermost channels often contain systematic artifacts caused by switching between the two branches in the CTS
  2. Find channels in right wing containing spike and replace these with the average between the closest unaffected channels

Shift spectra to $\nu_0$ from HITRAN

  1. Locate linecentra in spectra
  2. Calculate offset ($\Delta \nu$) between linecentra and $\nu_0$ from HITRAN
  3. Shift frequency from measurement using $\Delta \nu$ to align linecentra from measurement with linecentra ($\nu_0$) from HITRAN

Tropospheric correction

  1. Assumed two layer atmosphere with contribution from troposphere and above troposphere:

    $T_b(\nu)=\mathcal{T}T_{b0}(\nu) + (1-\mathcal{T})T_{trop}$

    With $\mathcal{T}(T_{b0}(\nu)+ T_{cb})$ being the contribution above the tropopause and $(1-\mathcal{T})T_{trop}$ being the contribution from the troposphere
  2. Tropospheric temperature $T_{trop}$ is calculated from ERA5 data the average from ground to tropopause (red): $T_{trop}=245.57$ K.
  3. The transmission ($\mathcal{T}$) through the troposphere is calculated with:

    $\mathcal{T}=1-\dfrac{T_{bg}}{T_{trop}}$,

    where $T_{bg}$ is the background temperature, and is taken from the line-wing (red)

Tropospheric correction

Finally the unattenuated signal $T_{b0}$, without tropospheric contribution can be calculated as:

$T_{b0}(\nu) = \dfrac{T_{b}(\nu) - \left(1-\mathcal{T}\right)T_{trop}}{\mathcal{T}}$