govern the temperature profile, $\kappa_{v_{1}}$, $\kappa_{v_{2}}$, $\kappa_{IR}$. The bottom panel is the flux response to a small perturbation in the gas mixing ratios, $f_{H2O}$, $f_{CH4}$, $f_{CO}$, and $f_{CO2}$. The Jacboian is calculated as a change in the planet-to-star flux ratio, $\Delta (F_p/F_{*})$ to a positive logarithmic perturbation in a given parameter, $\Delta \log(x_j)$. Note that in the bottom panel an increase in the gas mixing ratios always results in a decrease in $F_p/F_{*}$. In this particular case, the spectrum is equally sensitive to $\kappa_{v_{2}}$ and $\kappa_{v_{1}}$ because $\alpha$ is 0.5. If $\alpha=0$ than the spectrum will have no sensitivity to $\kappa_{v_{2}}$ and if $\alpha=1$ the spectrum will have no sensitivity to $\kappa_{v_{1}}$. Also, for this synthetic dataset $\kappa_{v_{2}}$=$\kappa_{v_{1}}$ which results in no sensitivity to $\alpha$ ](Figure2.pdf){width="50.00000%"}

Figure 3 shows the retrieval process for this initial synthetic test case. We determine the quality of the retrieval using the standard reduced chi-squared given by $$\chi^2=\frac{1}{N}\sum_{i=1}^N \frac{(y_i-F_i)^2}{\sigma_i^2}$$ where $N$ is the total number of data points, $y_i$, $F_i$, and $\sigma_i$, are defined in $\S$2.1. If $\chi^2$ is less than one, then the difference between the model fit and data is typically better than 1 $\sigma$. We should stress however, that a perfect fit 