sensitive to higher altitudes because of the large absorption, thus an increase in in $\kappa_{v1}$ will result in an increase in temperature which in turn results in a flux increase. Also, in this particular case $\alpha=0.5$ meaning both $\kappa_{v1}$ and $\kappa_{v2}$ have identically the same results. Additionally, $\kappa_{v1}$=$\kappa_{v2}$ which causes the spectrum to have no sensitivity to changes in $\alpha$.

The spectral response is most sensitive to the water abundance more than any other gas across all wavelengths in this example (Figure 2). This makes the retrieval of water more precise than the other species. The greatest sensitivity to changes in the CO$_2$ abundance occur at 2.1 and 2.8 $\mu$m, which both happen to be located near the sensitivity minima of CO and CH$_4$, though it still has to contend with water. Both CO and CH$_4$ have greatest sensitivity in the 2.3 $\mu$m band making it difficult to simultaneously retrieve both.

![Columns of the Jacobian for the synthetic spectrum evaluated at the true state. This is the response of the flux as a function of wavelength due to a small positive perturbation in one of the parameters in [**x**]{}. The top panel is the flux response for the parameters that 