are two important factors that influence the quality and usefulness of a spectrum. It is thus imperative to consider them when designing a spectrometer. In this section we use our synthetic dataset to explore how the degrees of freedom, both total and per atmospheric parameter, and the information content evolve with increasing S/N and R.

We would intuitively expect $d_s$ and $H$ both to increase with increasing R and S/N. Figure 4 shows a contour plot of $d_s$ and $H$ calculated for the synthetic spectrum generated in Figure 1 for a variety of S/N’s and R’s. The maximum increase in both occurs with a simultaneous increase in S/N and R.

We point out that the contour plots in Figure 4 can only be taken in the context of the spectral window within which we are applying the retrieval, and the number of parameters we are trying to retrieve. In other words, for the 8 parameters we are retrieving here, there is no benefit to increasing R or S/N beyond a few hundred and $\sim$100, respectively. If we do happen to have a higher R and S/N, it is likely that we would be able to retrieve more forward model parameters 