abundances remain fairly constant.

Since many of these parameters may vary over many orders of magnitude we find it convenient with the above formalism to solve for the logarithm of the atmospheric state. With that, the state vector of parameters that we would like to retrieve can be given by $${\bf x} = \left[ \begin{array}{ccc}
\log (\kappa_{v_{1}}) \\
\log (\kappa_{v_{1}}) \\
\log (\kappa_{IR}) \\
 \alpha \\
\log ( f_{H2O})\\
\log ( f_{CH4})\\
\log ( f_{CO})\\
\log ( f_{CO2})\\
  \end{array} \right]$$ where $f_{i}$ is the mixing ratio of species $i$ in parts per million (ppm) and the opacities are in cm$^2$g$^{-1}$.

We also include H$_2$-H$_2$ and H$_2$-He collision induced opacity. The mixing ratios of H$_2$ and He vary little with the atmospheric levels that produce the bulk of the dayside thermal emission (500-2000 K, 10-10$^{-4}$ bar). We fix $f_{H_2}$ and $f_{He}$ to thermochemical abundances (assuming solar elemental abundances) of 0.86 and 0.14, respectively. These values may change on the tens of percent level in enriched atmospheres, however, this variation has negligible effect on the resultant infrared spectra. Also, we do not include NH$_3$ as an opacity source as it has little influence in the spectral region we consider.

We use the 