Cloud pressure degeneracy of a transmission feature (source code)

= Cloud pressure degeneracy of a transmission feature

With constant <atmospheric scale height> $H$, a molecular band at height $\Delta z$ above the measured continuum satisfies $P_{\rm band}=P_{\rm cont}e^{-\Delta z/H}$. If an opaque <exoplanet cloud deck> sets that continuum, then $P_c\simeq P_{\rm cont}$; the band <pressure> is not the cloud <pressure>. If the clear band height would be $NH$ above a clear continuum at $P_0$ and the cloud reduces the visible feature to $mH$, then
$$
P_c=P_0e^{-(N-m)}.
$$
Without the clear-atmosphere band opacity or $N$, the measured feature amplitude alone cannot locate the cloud top. This follows directly by subtracting the two hydrostatic height relations.