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With constant atmospheric scale height $H$, a molecular band at height $\Delta z$ above the measured continuum satisfies $P_{\mathrm{band}}=P_{\mathrm{cont}}{e}^{-\Delta z/H}$. If an opaque exoplanet cloud deck sets that continuum, then $P_c\simeq P_{\mathrm{cont}}$; 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 $mH$, thenWithout 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.

Cloud particles can scatter or absorb, so not every atmospheric haze makes a high-albedo planet. Weak molecular bands alone also admit low abundance or high mean molecular weight; a consistent spectral combination is stronger evidence than a single signature.

Three observable signatures are a blue optical transmission slope, muted molecular transmission features, and enhanced reflected optical light.

Small-particle atmospheric haze can increase the apparent transit radius toward short wavelengths, roughly $0.3$--$1\mu \mathrm{m}$. For Rayleigh scattering-like extinction, $\sigma \propto {\lambda }^{-4}$ and an isothermal atmospheric scale height model gives $d{R}_p/d\ln \lambda \simeq -4H$. Larger particles instead produce a flatter, approximately grey continuum.

An optically thick exoplanet cloud deck can truncate the slant path through gas and flatten molecular bands in a exoplanet transmission spectrum, for example over $0.4$--$2.5\mu \mathrm{m}$ and the water band around $1.4\mu \mathrm{m}$. The observed quantity is reduced band-to-continuum radius contrast, not necessarily a low molecular abundance.

exoplanet cloud scattering can produce a high geometric albedo and distinctive optical secondary eclipses/phase curves around $0.4$--$0.9\mu \mathrm{m}$. Longitudinal exoplanet cloud variation can shift a reflected-light phase maximum. A spectral slope or flat spectrum alone is not a unique exoplanet cloud identification: particle size, gas scattering, metallicity and stellar contamination must be considered together.

The two measurements sample different atmospheric regions and different radiative transfer geometries. An exoplanet emission spectrum probes the dayside; an exoplanet transmission spectrum probes the morning and evening limbs of the day-night terminator. Several alternatives to an exoplanet cloud deck can therefore suppress the transmission feature.

Temperature, mean molecular weight, limb chemistry, continuum opacity and the dayside temperature gradient are alternatives or degeneracies to test. In particular, the three-scale-height amplitude alone cannot establish different CO abundances between the hemispheres.

Assume an isothermal terminator, constant gravity and mean molecular weight, and use the stated nightside atmospheric scale height as the terminator value. Hydrostatic equilibrium gives $P(z)=P_{\mathrm{ref}}{e}^{-(z-z_{\mathrm{ref}})/H}$. A band radius three atmospheric scale heights above a measured continuum at $0.1\mathrm{bar}$ therefore corresponds toThis is the band's characteristic pressure, not automatically the top of an exoplanet cloud deck. The distinction matters because an opaque cloud generally raises the continuum and removes the lower part of a molecular feature; it does not cap the height of a strong molecular line above the cloud.

If the quoted $0.1\mathrm{bar}$ is the actual observed continuum and the cloud dominates its opacity, the consistent estimate is insteadIf $0.1\mathrm{bar}$ refers to a clear-atmosphere reference continuum, an additional clear band height is necessary. Let that height be $NH$. A cloud at height $z_c$ leaves a residual feature of $3H$ when $NH-z_c=3H$. Thus the cloud pressure degeneracy of a transmission feature givesFor example, a $5\mathrm{mbar}$ cloud estimate requires the extra assumption that the clear band spans six scale heights, so the cloud raises the continuum by three. Identifying the cloud with the level three scale heights above the original continuum gives the same numerical value, but is not justified by the observed band height alone. Without a clear-band opacity or equivalent reference radius, there is no unique cloud-top pressure. A strong dayside emission feature also does not supply that missing terminator information.

One approach uses exoplanet transmission spectra. Three aerosol signatures are:

A second approach uses the dayside spectrum and brightness obtained with exoplanet secondary eclipses, optionally supported by orbital phase variations. Its three useful aerosol signatures are:

Transmission measures aerosol extinction along the limb; eclipse/reflection measurements test dayside scattering and emission. No single flattened feature proves clouds: small atmospheric scale height, low molecular abundances, stellar heterogeneity and thermal-gradient degeneracies must be considered. Joint wavelength coverage and geometries make the inference stronger.

For the two-zone cloudy annulus transmission model, assume a uniform stellar disc, an opaque planet below $R_p$, $0\le H_c\le H$, and constant total slant optical depth within each radial zone. Neglect scattered light entering the beam and the planet's own emission. A ray transmits the fraction $e^{-\tau }$, so each zone blocks its projected area multiplied by $1-e^{-\tau }$.

The opaque disc, cloudy annulus and clear annulus have areas $\pi R_p^2$, $\pi [(R_p+H_c{)}^2-R_p^2]$ and $\pi [(R_p+H{)}^2-(R_p+H_c{)}^2]$, respectively. Thus the exoplanet transmission spectrum, expressed as total transit depth, isHere ${\tau }_{\lambda ,c}$ means the total optical depth on rays assigned to the cloudy zone. If it denotes cloud extinction alone, its exponent must instead contain the sum of cloud and gas optical depths. For a geometrically thin exoplanet atmosphere, the two atmospheric prefactors become $2R_p{H}_c/R_s^2$ and $2R_p(H-H_c)/R_s^2$.

An opaque exoplanet cloud deck gives the simpler expressionThe exoplanet cloud deck raises the wavelength-independent occulting radius and suppresses the clear atmospheric contribution. If $H_c=H$, the spectrum is flat at $(R_p+H{)}^2/R_s^2$; if $H_c=0$, the ordinary annulus model for transmission spectroscopy is recovered. Stellar limb darkening and varying tangent-ray optical depth would require an intensity-weighted radial integral rather than this constant-depth model.

Assume an isothermal atmosphere in hydrostatic equilibrium, with constant gravity $g$, mean molecular weight $\mu$, and an ideal gas equation of state. Use $h$ for the atmospheric scale height, to distinguish it from the total observable height $H$. Thenso the cloud-top pressure in an isothermal atmosphere isAn opaque, approximately grey exoplanet cloud deck can flatten the exoplanet transmission spectrum if the remaining gas above it has little wavelength-dependent extinction. If its top nearly reaches the observable atmospheric extent, $H_c\simeq H$, this gives $P_c\simeq P_s{e}^{-H/h}$. More generally, a top at $N$ atmospheric scale heights has $P_c/P_s=e^{-N}$; illustrative values $N=5$ and $10$ give $6.7\times 10^{-3}$ and $4.5\times 10^{-5}$.

A flat exoplanet transmission spectrum and $P_s$ alone do not determine a unique cloud-top pressure. The temperature, gravity, mean molecular weight and cloud altitude, or equivalent opacity information, are also needed. A large mean molecular weight can itself suppress spectral features, so the exoplanet cloud deck interpretation is conditional.

In the annulus model for transmission spectroscopy, an added aerosol optical depth changes the signal to $A[1-e^{-({\tau }_{\mathrm{gas}}+{\tau }_{\mathrm{aerosol}})}]$. Large particles can supply nearly wavelength-independent extinction. An opaque high exoplanet cloud deck then masks deeper gas, flattens the optical exoplanet transmission spectrum, and weakens atomic or molecular features.

Small particles can instead produce a rising transit radius toward short wavelengths. In an isothermal atmosphere, the slant optical depth of an isothermal atmosphere isTaking the effective radius near ${\tau }_{\lambda }\sim 1$ gives $z(\lambda )=H\log {\sigma }_{\lambda }+\mathrm{constant}$. For Rayleigh scattering, ${\sigma }_{\lambda }\propto {\lambda }^{-4}$, so the scattering slope of a transmission spectrum isA steeper-than-expected optical slope or suppressed gas features can therefore indicate atmospheric haze or exoplanet clouds. These signatures are not unique: high mean molecular mass reduces $H$, gas itself can produce Rayleigh scattering, and stellar surface heterogeneity can mimic slopes. Consistent optical and infrared features help distinguish these explanations.

In an isothermal hydrostatic atmosphere, pressure falls as $P(z)=P_0{e}^{-z/H}$. If a water-band line core becomes optically thick at pressure $P_{\mathrm{line}}$ and an opaque cloud fixes the nearby continuum at $P_{\mathrm{cl}}$, the exoplanet transmission spectrum feature spansA two-scale-height feature therefore requiresTaking a representative near-infrared water-band pressure $P_{\mathrm{line}}\sim 1\mathrm{mbar}$ gives $P_{\mathrm{cl}}\sim 7\mathrm{mbar}$, so the appropriate estimate is an exoplanet cloud deck top near $10\mathrm{mbar}$. The numerical value scales directly with the assumed line-core pressure.

Other explanations include a high mean molecular weight, subsolar water abundance, a colder terminator, atmospheric haze, patchy two-limb clouds, stellar contamination, or instrumental systematics. Optical scattering slopes, broader James Webb Space Telescope molecular coverage, repeated transits, secondary-eclipse spectra, phase curves, and precise mass and radius measurements can distinguish these possibilities.

An exoplanet cloud deck divides the projected atmospheric annulus into cloudy and clear radial zones. Their contributions to the exoplanet transmission spectrum add as projected areas multiplied by $1-e^{-{\tau }_{\lambda }}$ for each zone's slant optical depth.