In summary, both $d_s$ and $H$ are quantitative measures of the quality and usefulness of the observations in determining the atmospheric state, within the context of a given forward model. From their definitions we would expect that a spectrum with a higher S/N, or a higher R, would result in higher values. We will show this in section $\S$3.

Forward Model
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A relatively simple forward model, ${\bf F(x)}$, which nonetheless captures the basic physics and the measurement process, is at the core of our retrieval. We assume a simplified understanding of the physical and chemical state of the exoplanet atmosphere, i.e., a parameterized temperature structure, the major volatile constituents, the important radiative processes, and the instrument line profiles etc. Our forward model, as most such models, is an approximation because the data are of limited quality, the underlying physics is relatively ill-understood, and simplifying approximations are necessary. Examples of physics missing in our ${\bf F(x)}$ include absent species, inaccurate line lists, clouds, aerosols, 3D effects etc., or possibly insufficient parameterization of the atmosphere. Therefore, our retrievals must be taken in context of our chosen forward model. Herein, we only consider the dayside spectra of hot-Jupiters with near solar metallicity, 